ANALYSIS OF HIGH FIELD Q-SLOPE (HFQS) CAUSES AND DEVELOPMENT OF NEW

CHEMICAL POLISHING ACID FOR NIOBIUM SRF CAVITIES

By

Didi Luo

A DISSERTATION

Michigan State University

in partial fulfillment of the requirements

Submitted to

for the degree of

Physics – Doctor of Philosophy

2020

ABSTRACT

ANALYSIS OF HIGH FIELD Q-SLOPE (HFQS) CAUSES AND DEVELOPMENT OF NEW

CHEMICAL POLISHING ACID FOR NIOBIUM SRF CAVITIES

By

Didi Luo

Buffered Chemical Polishing (BCP) was the most conventional polishing method for supercon-
ducting radiofrequency (SRF) Niobium (Nb) cavity surface preparation before the discovery of
Electropolishing (EP), which is superior to BCP in high gradient performance. The High Field
Q-slope (HFQS) is entirely eliminated by taking the low-temperature bake (LTB) post EP, which
guarantees high gradient performance in EP’ed cavities. The mechanism of the HFQS is well
understood for EP’ed cavities. On the other hand, there is no common consensus on the HFQS with
BCP, since even BCP with LTB does not always resolve the HFQS. BCP is much easier to apply
and still a vital preparation technology for very complicated SRF structures like low beta cavities.
Therefore, overcoming the issue of HFQS with BCP is highly beneficial to the SRF community.
This thesis mines a large number of available data sets on BCP’ed cavity performance with fine
grain, large grain, and even single-crystal niobium materials under different experimental settings.
We found that all existing explanations for HFQS with BCP are inconsistent with some experi-
mental results, and propounded nitrogen contamination as a new model to explain the result. Our
conclusion is made based on previously unresolved phenomena which include (1) applying multiple
BCP post EP; the maximum gradient does not always agree with roughness; (2) cavity treated with
EP acid adding a drop of HNO3 started to have non-resolvable HFQS; (3) maximum field of BCP
single-crystal cavities are lower than EP large grain cavities; (4) temperature map shows no high
roughness area heating for a large-grain BCP cavity. We then checked that nitrogen contamination
agrees with all existing data and nicely explains unresolved phenomena.

According to this result, we have started developing a new nitrogen-free chemical polishing
acid. H2O2 with HF mixture was reported able to react with Nb, and there is no extra element
contamination in it, so we replace the conventional BCP with this mixture to start our study.

We discovered that this new acid could not provide sufficient smooth finishing surface, even
after we adjusted all the parameters. However, adding a copper catalyst allows this acid to provide
a smooth surface similar to or even better than conventional BCP. The copper remnant can be
neglected according to an EDS study on the Nb surface. We studied the reaction mechanism and
deduced that several other metals that can be promising as catalysts. One of those is iron, which
was later shown to have the catalyst effect; this proved the mechanism we found is right.

Further study can focus on other potential catalysts (such as Pb and Sn) and testing cavities
treated by these acids. Pb is superconducting under operation temperature, may reduce potential
harm to cavity performance, and Sn may react with Nb and generate Nb3Sn on its surface, which
is another promising material for SRF cavities. These studies will offer more possibilities for SRF
material.

To my family

iv

ACKNOWLEDGEMENTS

First of all, I would like to express my sincere gratitude to my advisor Prof. Kenji Saito for the
continuous support of my Ph.D study and related research, for his enthusiasm, motivation, and
immense knowledge. His guidance helped me in all the time of research and writing of this thesis.
Besides my advisor, I would like to thank the rest of my thesis committee: Prof. Steven Lund,
Prof.
Jie Wei, and Prof. Yoshishige Yamazaki, for their insightful
comments and encouragement, but also for the questions which incented me to widen my research
from various perspectives.

Johannes Pollanen, Prof.

My sincere thanks also goes to Ting Xu, Laura Popielarski, John Popielarski, Chris Compton in
FRIB and Reza Loloee in Department of Physics and Astronomy for who provided me opportunities
to take related training, and who gave access to the laboratory and research facilities. Without their
precious support it would not be possible to conduct this research.

I would also like to thank Ethan Metzgar and George Simpson in FRIB for the help during my
Nb chemical etching experiments; Walter Hartung, Sang-hoon Kim, Mengxin Xu, Cong Zhang,
Zhihong (Winter) Zheng in FRIB for the training and help during cavity vertical tests and solenoid
tests; Tasha Summers for the tutorial and help of CS-studio scan-file developing; Baokang Bi in
Keck Microfabrication Facility of the MSU Department of Physics and Astronomy for the training
of facilities; Xudong Fan in MSU Center For Advanced Microscopy for the Transmission Electron
Microscopy (TEM) training and services.
I also thank US Particle Accelerator School for the
invaluable learning opportunities and social interactions that have been immensely beneficial to my
thesis research and my growth in the field of accelerator science.

I thank Daniel Alt, Michael Balcewicz, Crispin Contreras, Robert Hipple, Bryan Isherwood,
Andrew LaJoie, Kellen McGee, Derek Neben, Christopher Richard, Safwan Shanab, and Chun
Yan Jonathan Wong for their questions and feedback during the discussion of our regular meeting
consists of MSU graduate students in accelerator physics. I am also grateful to Jian Gao, Yue Hao,
Alfonse Pham, Haitao Ren and Qiang Zhao who provided their astute comments and career advice.

v

I appreciate the assistance from Kim Crosslan at the Department of Physics and Astronomy that
allowed me to meander through all kinds of paperwork unscathed.

Last but not the least, I would like to thank my family and all my friends for supporting me

spiritually throughout writing this thesis and my life in general.

vi

TABLE OF CONTENTS

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CHAPTER 1

x
. xiii

1.2 RF Acceleration .

1.1 Particle Accelerators

Facility for Rare Isotope Beams (FRIB)

LIST OF TABLES .
LIST OF FIGURES .

.
.
INTRODUCTION .
.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.1 History and Application of Accelerators . . . . . . . . . . . . . . . . . . .
8
1.1.2 History of SRF Accelerators . . . . . . . . . . . . . . . . . . . . . . . . .
9
1.1.2.1 History of SRF and Several SRF Machines . . . . . . . . . . . .
1.1.2.2
TRISTAN and KEKB . . . . . . . . . . . . . . . . . . . . . . . 11
1.1.2.3 HERA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.1.2.4 CEBAF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
TESLA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.1.2.5
1.1.2.6
LCLS-II
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.1.2.7 ATLAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.1.3 Current Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.1.4
. . . . . . . . . . . . . . . . . . . 18
1.1.5 Accelerator Facility Components . . . . . . . . . . . . . . . . . . . . . . . 21
1.1.6 Acceleration Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.2.1 RF Resonant and Frequency . . . . . . . . . . . . . . . . . . . . . . . . . 25
Power loss and the Quality Factor
1.2.2
. . . . . . . . . . . . . . . . . . . . . . 27
Field in a Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.2.3
1.2.4
Skin Depth . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.2.5 Accelerating Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Shunt Impedance, R/Q, E
/E


 and B
/E


 . . . . . . . . . . . . . . . . 32
1.2.6
. 33
1.3.1
Phenomena: T
, Meissner effect and H
 . . . . . . . . . . . . . . . . . . . 34
1.3.2 Explanation and Two Fluid Model
. 35
1.3.3 Thermodynamic Study of Superconductor . . . . . . . . . . . . . . . . . . 37
1.3.4 Type II Superconductor & GL Theory . . . . . . . . . . . . . . . . . . . . 38
1.3.5 BCS Theory: Formation of Superconductivity . . . . . . . . . . . . . . . . 42
1.4 The Reason of Choosing Nb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
1.5 Superconducting RF .
1.6 Frequency Selection for SRF Cavities
. . . . . . . . . . . . . . . . . . . . . . . . 47
1.7 Cavity Performance Limitation and Solution . . . . . . . . . . . . . . . . . . . . . 48
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
1.8 EP & BCP . .
CHAPTER 2 HIGH FIELD Q SLOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.1 Discovery of HFQS .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.2 Low T Baking and the Role of Oxygen . . . . . . . . . . . . . . . . . . . . . . . . 56

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . .

1.3 Superconductivity .

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3.2 Experiments .

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2.5 Conclusion . .

3.1 Acid Component

2.3 Others’ Study .
2.4 Our Analysis .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
.
2.4.1 Reanalysis of Multiple BCP Post EP with Fine-grain Cavity . . . . . . . . . 59
2.4.2 HFQS of BCP’ed Large-grain Cavity . . . . . . . . . . . . . . . . . . . . . 61
2.4.3 BCP after EP with Large-grain Cavity . . . . . . . . . . . . . . . . . . . . 62
2.4.4 Multiple BCP with Large-grain Cavity . . . . . . . . . . . . . . . . . . . . 63
2.4.5 BCP with Single-crystal Cavity . . . . . . . . . . . . . . . . . . . . . . .
. 64
2.4.6 EP & BCP Difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
2.4.7 Nitrogen Diffusion Calculation for the Same Condition with LTB . . . . . . 69
2.4.8 Nitrogen Contamination . . . . . . . . . . . . . . . . . . . . . . . . . .
. 70
2.4.9 Generation of Nitrogen Contamination and observation . . . . . . . . . . . 72
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
CHAPTER 3 NEW ACID: ACID DEVELOPMENT . . . . . . . . . . . . . . . . . . . . 76
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.1.1 Oxide Layer Remover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.1.2 Oxidizer Choosing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.1.3 Record on This Acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.2.1 General Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.2.2
Preliminary Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.2.3 Degreaser Influence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.2.3.1
Experiment and Result . . . . . . . . . . . . . . . . . . . . . . . 83
3.2.3.2 One Accident of Copper Nut Contamination #
 . . . . . . . . . . 84
. 85
Experiment of Acid Ratio Variance . . . . . . . . . . . . . . . . 87
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
. 90
3.3.1.1
Temperature Difference Experiment . . . . . . . . . . . . . . . . 90
3.3.1.2 Cu Influence #
 . . . . . . . . . . . . . . . . . . . . . . . . . . 90
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
.
. 92
3.3.3.1
Experiment for Viscosity Influence . . . . . . . . . . . . . . . . 94
3.3.3.2 Using H2SO4 to Increase Viscosity . . . . . . . . . . . . . . . . 95
3.3.3.3 Copper Case with Higher Viscosity #
 . . . . . . . . . . . . . . 96
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.4.1 Orientation of Large-grain Nb Crystalline . . . . . . . . . . . . . . . . . . 97
3.4.2 Roughness between Grain-boundaries and Internal Grain . . . . . . . . . . 98
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.4.3 Discussion .
CHAPTER 4 COPPER CATALYST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
. 101
4.1.1 A Quick Check of Copper amount and H2O2 Concentration Influence . . . 101
4.1.2 Copper Amount Variation for 45: 10 Recipe Using Cu Powder . . . . . . . 103
4.1.3 HF Amount Variation for 3 × 10−4 mole Copper Powder
. . . . . . . . . . 103

3.2.4 Another Guess: Ratio Based on Reaction Equation . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3.2 Acid Ratio .
.
3.3.3 Viscosity Impact

.

3.4 High Roughness Study .

3.3.1 Temperature Influence

4.1 Setup optimization .

3.3 Control Parameters

3.2.4.1

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viii

4.2 Summary of Experiments .
4.3 Mechanism . .

4.1.4 Copper Amount Variation for 29: 15: 11 Recipe Using Thin Cu Wire . . . 105
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
. 108
. . . . . . . . 112

4.3.1 Chemical Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 General Chemical Polishing Principle and the Bubble Effect
4.3.3 Micro EP Effect: Electrodes Forming on Nb Surface During Single

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4.5 Discussion . .

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4.4.1 Experiment and EDS Analysis Result

Displacement Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 115
4.4 Copper Remnant Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
. 115
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
CHAPTER 5 CONCLUSION AND FURTHER WORK . . . . . . . . . . . . . . . . . . . 118
APPENDICES .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
APPENDIX A E & M FIELD IN A RF CAVITY . . . . . . . . . . . . . . . . . . . . 122
APPENDIX B CRYOMODULE SOLENOID TEST IN FRIB . . . . . . . . . . . . . 130
APPENDIX C STUDY FOR LOW FIELD Q SLOPE ISSUE IN FRIB . . . . . . . . 141
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

BIBLIOGRAPHY .

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ix

LIST OF TABLES

Table 1.1: FRIB driver accelerator primary parameters [36].

. . . . . . . . . . . . . . . . . 20

Table 1.2: FRIB Cavities Performance 2 K [39]

. . . . . . . . . . . . . . . . . . . . . . . 21

Table 1.3: Example of Cavity shape VS. 
 for different particles. Ɖ is the geometry factor

that only relates to cavity shape [40]. . . . . . . . . . . . . . . . . . . . . . . . . 26

Table 1.4: A comparison of superconductor (SC) cavity (Nb at 4.2 K) and normal con-

ducting (NC) cavity [40]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Table 1.5: 2Ɗ(0)/
 


 value of some superconductors measured by tunnelling method

[48].

.

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. .

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Table 1.6: H
, H
1, H
2 and Ginzburg–Landau factor 
 value for some superconductors.
2 is type II superconductor. The values also depend on material purity.


 > 1/√

This table is adopting pure bulk Nb value [48, 69].

. . . . . . . . . . . . . . . . 45

Table 2.1: Estimation of roughness during KEK multiple EP and BCP process.

. . . . . . . 60

Table 2.2: Main differences between EP & BCP . . . . . . . . . . . . . . . . . . . . . . . 68

Table 2.3: Diffusion parameters for the interstitial elements N and O in Nb [105]. . . . . . . 70

Table 3.1: Oxidization power comparison for some normal oxidizer . . . . . . . . . . . . . 77

Table 3.2: Preliminary Recipe .

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Table 3.3: Study of degreaser influence on roughness for new Acid. Reaction time is 30
minutes for all cases. R
 is the average value of 10 measured points on each
sample, 


 is the standard deviations of the measured values.

. . . . . . . . .

. 84

Table 3.4: Double the H2O2 amount for new Acid recipe. The 50 %HF amount for all
cases are 10 mL, the R
 of Nb samples before reaction is 4.94 
m ± 2.92 
m.
Trial 1 reaction starts from room temperature and all others start from 35 ◦C.

. . 86

x

Table 3.5: Systematical ratio dependence study. H2O2 and HF are both using 50%.
Starting temperature is 20 ◦C, roughness before reaction is 4.31 
m ± 1.237

m. Sample 1, 5’, 6’ and 7’ should have higher finishing roughness because
some measure values exceed the measurement range 25.2 
m and can only
read 25.2 
m. *Sample 7’ has too high reaction speed and too dangerous
to control temperature, about 50 mL water was added when the temperature
increased too high and very dangerous.

. . . . . . . . . . . . . . . . . . . . .
Table 3.6: Viscosity dependence for H2O2 and HF ratio equals to ∼ 3: 1, same as
Table 3.5 sample # 1. The reaction time for all cases are 120 minutes instead
of 60 minutes for sample # 1 in Table 3.5. H2O2 and HF are both using 50%,
H3PO4 is 90%. Starting temperature is 20 ◦C, roughness before reaction is
3.582 
m ± 1.683 
m.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

. 91

Table 3.7: Viscosity dependence for H2O2 and HF ratio equals to ∼ 1: 1, same as
Table 3.5 sample # 6’. The reaction time for all cases are 120 minutes instead
of 40 minutes for sample # 6’ in Table 3.5. Starting temperature is 20 ◦C,
roughness before reaction is 3.582 
m ± 1.683 
m. . . . . . . . . . . . . . . . . 94

Table 3.8: Comparison of copper cases with or without H3PO4. #
 is the Cu case in
section 3.3.1, Table 3.9. H2O2 is in 35% and HF is using 50%, and the ratio
is 45: 10, Cu amount is ∼ 3.10−4 mol and Starting temperature is 20 ◦C for
both cases. The roughness before reaction for 
 is 9.067 
m ± 2.953 
m and
for 
 is 4.000
m ± 2.783 
m.

. . . . . . . . . . . . . . . . . . . . . . . . . . . 96

Table 4.1: H2O2 concentration and Cu amount variation results, HF concentration is 50

% for all cases.

.

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Table 4.2: Cu powder amount variation results . . . . . . . . . . . . . . . . . . . . . . . . 103
Table 4.3: HF amount variation results for 3 × 10−4 mole Copper Powder. 6’ has same

condition with 2’, but with stirring. . . . . . . . . . . . . . . . . . . . . . . . . . 104

Table 4.4: Additional reaction for case 3’, 4’ and 5’. The same Nb samples are without

 in

extra mechanical polishing, so the roughness before reaction are from R(cid:48)
Table 4.3. The Nb were put into the original acid saved from last reaction. . . . . 104

Table 4.5: Copper variation for H2O2 (50%): HF (50%): H2O = 29: 15: 11 Recipe using

thin copper wire.

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.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Table 4.6: Copper remnant removal experiment setup . . . . . . . . . . . . . . . . . . . . . 116

Table B.1: FRIB 50 cm solenoid package design requirements. The fringe field require-

ment applies at the magnetic shield.

. . . . . . . . . . . . . . . . . . . . . . . . 131

xi

Table B.2: FRIB magnetic shield parameters.

. . . . . . . . . . . . . . . . . . . . . . . . . 132

Table B.3: Dynamic heat load of CM-1 cavities at 2 K. Measurements were done at the
nominal accelerating gradient of 5.6 MV/m (except for C#1, which was at 7
MV/m, having an initially miscalibrated field level). . . . . . . . . . . . . . . . . 138

Table C.1: BCS fitting average result for 10 QWRs before Re-Toque and 10 QWRs after
Re-Toque in FRIB. The R


,


 and R

,

- R

,


 are from fitting, while
R

,2
 is directly from averaging the test data.

. . . . . . . . . . . . . . . . . . 145

xii

LIST OF FIGURES

Figure 1.1: Phase stability schematic: point S is the ideal case. point E arrives early,
experiences a smaller field; point L arrives later, experiences a larger field
than S; point U is too far from point S and is in the unstable phase.[10] . . . . .

Figure 1.2: Example of LHC design, here k = 2808, N1 = N2 = N = 1.15 ×1011, f = 11.25

, 
∗

 
∗

,
 = 16.7 

, and peak luminosity per IP is 1 ×1034
.
.
.
.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

kHz, A = 

∗
cm−2s−1.[18]

Figure 1.3: Livingston Plot shows the history of particle beam energy increasing [19].

. . .

Figure 1.4:

Improvement of the luminosity (particle/particle colliding performance), for
past, present and possible future colliders [21].

. . . . . . . . . . . . . . . . .

3

7

8

9

Figure 1.5: High intensity ion accelerators (Image courtesy of Prof. Jie Wei at FRIB) [36] . 18

Figure 1.6: Chart of nuclides showing projected fast rare-isotope beam rates provided
by FRIB in particles per second (pps). For reference, stable nuclides (black
squares), the traditional closed nuclear shells (dashed lines), estimates of the
astrophysical r and rp-process paths (solid black lines), and possible nucleon
drip lines (solid grey lines) are depicted [38].

. . . . . . . . . . . . . . . . . . 19

Figure 1.7: Layout of FRIB driver accelerator [36].

. . . . . . . . . . . . . . . . . . . . . 19

Figure 1.8:

: Dewar test results for 

 = 0.043 QWRs: (a) Q0 at 4.3 K; (b) Q0 at 2 K; (c)
X-rays at 2 K. [39].

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

.

Figure 1.9: Dewar test results for 

 = 0.086 QWRs: (a) Q0 at 4.3 K; (b) Q0 at 2 K; (c)

X-rays at 2 K. [39].

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 22

. 23

Figure 1.10: LC circuit model of an accelerating cavity[40].

. . . . . . . . . . . . . . . . . 24

Figure 1.11: LC circuit evolving to a resonant cavity[40].

. . . . . . . . . . . . . . . . . . . 25

Figure 1.12: Cavity shape examples for different frequency and 
 [41].

. . . . . . . . . . . . 26

Figure 1.13: Skin Depth

.

.

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 30

Figure 1.14: Specific heat Vs. T for Sn in superconducting state and normal conducting

state [52].

.

.

.

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

xiii

Figure 1.15: The dots curve shows the experiment result of the thermal conductivity ratio
change with temperature for Nb, the solid line curve and the dashed line
curve shows two theoretical predictions, where 

 is the thermal conductivity
in Superconducting state and 

 is the thermal conductivity in the normal
conducting state [56].

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Figure 1.16: Type I and Type II superconductor H
 and T relation. There is a new vortex

state for type II superconductor.

. . . . . . . . . . . . . . . . . . . . . . . . . 40

Figure 1.17: Periodic arrangement of vortices in a type-II superconductor in an external
applied magnetic field. Each vortex has a normal core, where the supercon-
ducting order parameter |
|2 (blue line) drops to zero on the scale of 
 while
the magnetic field profile (red line) exponentially decays on the scale of 
 [63].

41

Figure 1.18: Cavity size comparison for different frequencies [70].

. . . . . . . . . . . . . . 48

Figure 1.19: EP mechanism: current concentrates on the peaks and lead to more reaction
on the peak area; this reduces the height difference between peak and valley,
thus reduces the roughness of Nb surface [72].

. . . . . . . . . . . . . . . . . 50

Figure 1.20: EP equipment Single-cell cavity setup at KEK [72].

. . . . . . . . . . . . . .

. 50

Figure 1.21: An example of a BCP system for a large cavity: acid is filled in and pumped
out of the cavity by the pipe, then ultra-pure water is filled in to wash away
the acid. Cooling water is spilled on the outside of the cavity [71].

. . . . . . . 51

Figure 2.1: An example of High Field Q (HFQS) on EP Nb cavities, before and after

baking. HFQS started at 28 MV/m for this cavity. [73] . . . . . . . . . . . . . . 54

Figure 2.2: HFQS on BCP Nb cavities, before and after baking.

(Courtesy of CEA-

Saclay) [74]

.

. .

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Figure 2.3: Variation of the surface roughness by EP for fine-grain Nb. [75] . . . . . . . .

. 55

Figure 2.4: Variation of the surface roughness by BCP for fine-grain Nb. [75] . . . . . . .

. 55

Figure 2.5: FRIB cavity performance at 2 K in Vertical Test, 
 = 0.041 QWRs, B
/E




= 10.71 mT/(MV/m) .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 56

Figure 2.6: Q vs E results for 6 different polishing treatments, all cavities are tested after

HPR and baking in KEK. [71] . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

xiv

Figure 2.7: Roughness vs E


,


 results for 6 steps of the polishing treatment (each
with HPR and baking) in KEK multiple EP and BCP experiment. Each result
is marked with the respective number in Fig. 2.6. The roughness information
is from Table 2.1. [71] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Figure 2.8: Comparison of quality factor behaviors at high gradients between the Large-

grain (LG) and Fine-grain (FG) cavities by BCP with baking. [96]

. . . . . . . 62

Figure 2.9: Q vs E of DESY large-grain TESLA (ILC shape, B
/E


 = 4.26 mT/[MV/m])
cavity treated with EP and an additional 50 
m of BCP. Both results are after
baking. (Courtesy of DESY & JLab) [97]

. . . . . . . . . . . . . . . . . . . . 63

Figure 2.10: KEK 



 vs Increasing BCP amount results, first round and second round.

All results were taken after LTB.

. . . . . . . . . . . . . . . . . . . . . . . . . 65

Figure 2.11: Temperature map for a cavity before LTB at 110 mT (left) and after 100 ◦C
baking at 130 mT. No. 10 correspons to the thermometer located around
equator. [99] . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. .

. 65

Figure 2.12: Q Vs 



 for the cavity that shown temperature map in Fig. 2.11. [99] . . . . . 66

Figure 2.13: Q vs E of the 1.5 GHz High Gradient (HG, blue curve, B
/E


 is 4.47
mT/(MV/m)) shape and 2.2 GHz Low Loss-ILC (LL-ILC, red curve, B
/E



is 3.56 mT/(MV/m)) shape single-crystal (SC) Cavities treated by BCP. Both
results are after baking. (Courtesy of JLab) [100, 101] . . . . . . . . . . . . . . 67

Figure 2.14: Q vs E DESY single-crystal TESLA (ILC shape, B
/E


 = 4.26 mT/[MV/m])
cavities treated with BCP: before post-purification [102] in blue curve; after
post-purification in red curve. Both results are after baking. (Courtesy of
DESY & JLab) [103]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Figure 2.15: A comparison of diffusion concentration for nitrogen (left) and oxygen (right)
on niobium surface ( with different x-axis scale), calculated from Eq. 2.6 with
t = 40 hrs and T = 150 ◦C.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Figure 2.16: KEK cavity performance degradation with nitrogen exposure [106] . . . . . . . 73

Figure 2.17: Q vs E for KEK fine-grain Type A cavity, blue cross curve is an example for
normal EP cavity performance [77], red circle curve is the cavity dealer with
EP plus one drop of nitric acid [111]. Both cavities was applied baking after EP. 73

Figure 2.18: Reaction speed vs 1/T for different BCP ratio. [113] . . . . . . . . . . . . . . . 74

xv

Figure 3.1: R
1, R
2, R
3, R
4 and R
5 are the distances from the mean line (m) to
highest 5 peaks in the range of sampled reference length, R
1, R
2, R
3, R
4
and R
5 are the distances from the mean line (m) to lowest 5 valleys in the
range of sampled reference length.

. . . . . . . . . . . . . . . . . . . . . . . . 79

Figure 3.2: Preliminary results in Nomura Plating. Ltd. Conventional BCP recipe, 5 min

reaction, ∼ 100 
m removal.

. . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Figure 3.3: Preliminary results in Nomura Plating. Ltd. Original Recipe, 60 min reaction,

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

∼ 80 
m removal.

∼ 40 
m removal.

. 81

. 82

Figure 3.4: Preliminary results in Nomura Plating. Ltd. Original Recipe, 30 min reaction,

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.5: Preliminary results in Nomura Plating. Ltd, original recipe With stirring, 30

min reaction.

.

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

Figure 3.6: Experiment set up.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Figure 3.7: R
 Vs Removal and H2O2 Amount, the green bars show previously used 35%

concentration, and the red bar is H2O2 using 50% result.

. . . . . . . . . . . . 86

Figure 3.8: R
 Vs Removal for different H2O2 Amount, the green bars show previously

used 35% concentration, and the red bar is H2O2 using 50% result.

. . . . . . 87

Figure 3.9: Temperature dependence, removal and roughness. The blue bars shows 4
different temperature cases with the same acid recipe. The red bar is one trial
with Cu added in acid before Nb reaction. Standard deviation is about 25%
for roughness.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

. .

.

Figure 3.10: R
 Vs T .

.

.

. .

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 89

Figure 3.11: R
 Vs Removal

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Figure 3.12: R
 Vs Removal and HF. The reaction condition is shown in Table 3.5.

. . . . . 92

Figure 3.13: R
 Vs HF .

.

.

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Figure 3.14: R
 Vs Removal

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Figure 3.15: R
 Vs H3PO4/Acid Ratio and Removal

. . . . . . . . . . . . . . . . . . . . . 95

Figure 3.16: Microscope images for fine-grain sample reacted with new acid (A) and with

new acid plus H2SO4 (B).

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

xvi

Figure 3.17: Orientation Imaging Microscopy (OIM) image of a joint point of three grains
on a large-grain Nb sample after ∼ 10 
m removal by new acid. Different
color indicate different crystalline orientation.

. . . . . . . . . . . . . . . . . . 98

Figure 3.18: Reaction difference is observed in one large-grain sample. This sample was

reacted with new acid and the removal is ∼ 20 
m.

. . . . . . . . . . . . . . . 99

Figure 3.19: SEM images and roughness map for large-grain sample reacted with new acid.

99

Figure 3.20: SEM images and roughness map for large-grain sample reacted with conven-

tional BCP.

.

.

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Figure 4.1: A comparison between new acid sample without and with Cu catalyst.

. . . . . 101

Figure 4.2: R
 Vs Cu amount and Removal. Green squares are roughness after reaction,
and red squares are roughness before reaction. 1 ppm equals to 1 mg/L
(defined in analytical chemistry).

. . . . . . . . . . . . . . . . . . . . . . . . . 106

Figure 4.3: R
 Vs Cu amount. Green squares are roughness after reaction, and red squares
are roughness before reaction. 1 ppm equals to 1 mg/L (defined in analytical
chemistry).

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

. .

. .

.

Figure 4.4: A summary of the whole optimization process with conventional BCP result.
Grey marks are new acid without catalyst, red triangles are BCP (1: 1: 2)
cases, blue dots are HF variation results, green crosses are Cu variation results
that using the previous best 15 mL recipe from the HF variation results. The
Cu variation influence is already shown in Fig. 4.2 and 4.3.

. . . . . . . . . . . 107

Figure 4.5: A comparison between new acid with Cu catalyst sample and BCP sample.

. . 108

Figure 4.6: SEM Image of Nb samples after new acid polishing (a) and after BCP (b), 75

times magnification. .

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Figure 4.7: SEM Image of Nb samples after new acid polishing (a) and after BCP (b),

350 times magnification.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Figure 4.8: SEM Image of Nb samples after new acid polishing (a) and after BCP (b),

350 times magnification.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Figure 4.9: SEM Image of another Nb sample after new acid polishing (a) 75 times (b)

350 times and (c) 3000 times magnification.

. . . . . . . . . . . . . . . . . . . 110

Figure 4.10: Acid component is 45 mL 35% H2O2, 10 mL HF with (a) Fe amount 2 ×
10−4 mole, 35 
m removal, R
 = 13.52 ± 5 
m and (b) Fe amount 1 × 10−4
mole, 38 
m removal, R
 = 16.08 ± 3 
m.

. . . . . . . . . . . . . . . . . . . . 112

xvii

Figure 4.11: Bubble generating (a) and growing (b) on metal peak and valley during

chemical polishing.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Figure 4.12: Force on bubbles

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Figure 4.13: Three selected areas to do the EDS analysis on non-rinsed Nb sample treated

with new acid plus Cu catalyst.

. . . . . . . . . . . . . . . . . . . . . . . . . . 116

Figure 4.14: EDS Result of Nb sample after new acid on Selected Area 1 in Fig. 4.13.

. . . . 117

Figure A.1: Cutoff frequency .

Figure A.2: TM010 mode .

Figure A.3: 

 Vs d .

Figure A.4: 

 Vs 


Figure A.5: 

 Vs 


.

.

.

.

.

.

.

.

Figure A.6: TM020 mode

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Figure B.1: Layout of FRIB-1 Cryomodule (CM-1). C: cavity (green); S: solenoid pack-
age (blue). Cavities 1 - 4 are shielded by mu-metal (black) and Cavities 4 - 8
are shielded by A4K (red).

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

Figure B.2: CST Studio model of the 50 cm solenoid package.

Inner cylinder: main
solenoid; intermediate rectangles: dipoles; outer rings: bucking coils. The
diameter is 39 cm.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

.

.

.

Figure B.3: Diagram of the cooling system for cryomodule testing. . . . . . . . . . . . . . . 133

Figure B.4: Coil currents as a function of time for part of the solenoid tests in CM-1.

. . . . 136

Figure B.5: Coil currents as a function of time for part of the solenoid tests in CM-2. The

two adjacent cavities were turned on between 15:08 and 16:06.

. . . . . . . . . 137

Figure B.6: Example of PID control while ramping the solenoid current at 0.3 A/s. The

set point is a voltage drop of 30 mV.

. . . . . . . . . . . . . . . . . . . . . . . 137

Figure B.7: Example of CS-Studio scan system operation window . . . . . . . . . . . . . . 138

xviii

Figure B.8: Integral test scan file, REA_CMTF:PSOL_N0001:I_CSET is the solenoid
current setting, REA_CMTF:PSC1_N0001:I_CSET is the corrector 1 (dipole
y) current setting, and the other is the REA_CMTF:PSC1_N0001:I_CSET is
the corrector 2 (dipole x) current setting.

. . . . . . . . . . . . . . . . . . . . . 139

Figure C.1: Q Vs. E


 for an example of FRIB 
 = 0.085 QWR. Q has sharply dropping

in E


 < 2 Mv/m region for the 2 K test case.

. . . . . . . . . . . . . . . . . . 141

Figure C.2: 

 Vs. 1/T for for the same 
 = 0.085 QWR in Fig. C.1. There is a transit
point of this result on 1/T = 0.31 (K−1) region, which is around indium
superconducting transit temperature T = 3.4 K.

. . . . . . . . . . . . . . . . . 142

Figure C.3: FRIB 
 = 0.041 quarter wave resonators (QWRs), 
 = 0.085 QWRs, 
 = 0.29
half wave resonators HWRs and 
 = 0.53 HWRs. Both QWRs have bottom
flanges that sealed with indium wire.

. . . . . . . . . . . . . . . . . . . . . . . 143

Figure C.4: 

 Vs. 1/T for an example 
 = 0.085 QWR. Separate BCS fitting was done
for T > 3.4 K (left figure) and T < 3.4 K (right figure) and the fitting result
parameters are shown in the boxes on the figures.

. . . . . . . . . . . . . . . . 145

xix

CHAPTER 1

INTRODUCTION

This chapter overviews particle accelerators’ history and applications, introduces superconducting
RF (SRF) accelerator facilities, and then the Facility for Rare Isotope Beams (FRIB) at Michigan
State University. There is no difference in the principle of beam acceleration between supercon-
ducting RF accelerators and normal conducting ones. However, it will be essential to show the
electrodynamics to understand the beam acceleration principle. At first, electromagnetics related
to RF cavity design will be described, then superconductivity theory and its application to the
accelerator will be reviewed. At the end of this chapter, design strategy, fabrication and processing
will be introduced.

1.1 Particle Accelerators

1.1.1 History and Application of Accelerators

It has been 100 years since E. Rutherford first succeeded to collide alpha particles with a 0.0004
cm metal foil target [1]. At that time particle accelerator was not yet developed, he used a natural
radiating source for this a breakthrough in nuclear science in 1919. He discovered the atom nucleus
structure (Rutherford model) by analyzing the diffraction pattern made on a Zinc sulfide fluorescent
screen placed behind the target. This inspired nuclear scientists to achieve particles with higher
energy to work as “bullet”.

In 1932, J. D. Cockcroft and E. T. Walton invented the first DC accelerator to more precisely
probe the nuclear: the Cockcroft-Walton Accelerator [2]. The high DC voltage to accelerate charged
particles is generated from low voltage AC or a pulsing DC input. The generator is made out of
a voltage multiplier ladder network from capacitors and diodes. They succeeded in creating the
first artificial nuclear disintegration in history using their accelerator. In 1951, they were awarded
the Nobel Prize in Physics for “Transmutation of atomic nuclei by artificially accelerated atomic

1

particles”.

In the year of 1933, R. J. Van de Graaff invented a DC accelerator powered by another kind
of high voltage generator: Van de Graaff generator [3]. This generator is using the triboelectric
effect and accumulates charges by using an insulated belt to transfer electrons onto one metal comb
connected with a metal sphere and another metal comb grounded.

The breakdown voltage limits both DC accelerators (the Cockcroft-Walton Accelerator and the

Van de Graff DC accelerator), and particles’ final energy is at most ∼ 10 MeV [4].

By applying a high-frequency voltage to drift tubes, G. Ising in 1924 [5], and E. Wideroe in
1928 [6] independently invented another linear accelerator. This RF approach allows bypass of
breakdown voltage limits. Due to the limitations of high-frequency technology at that time, such
accelerators could only accelerate potassium ions to 50 keV energy, which was of little practical
significance. However, inspired by this principle, E. O. Lawrence invented the cyclotron in 1932
[7] and used it for artificial radioisotope productions. For this achievement, he won the Nobel Prize
in physics in 1939.

Due to the restriction of the mass and energy of the accelerated particles, a conventional cy-
clotron can only accelerate the protons to about 25 MeV. However, if the intensity of the accelerator’s
magnetic field is designed to increase synchronously along the radius with the particle energy, it
can accelerate the protons to hundreds of MeV. Such a machine is called isochronous cyclotron.

The angular frequency the particle 
 = 

/
 in a cyclotron depends on the particle mass,

which has relativistic effect that 



 = 




/(cid:112)1 − 
2/
2. When the velocity of the particle

approaching the speed of light, the mass increases and seriously changes the angular frequency,
to deviate from the original cyclotron frequency. This causes the particle to get progressively
more out of step with the accelerating voltage as its speed increases. This problem is solved in
the synchrocyclotron by varying the frequency of the accelerating voltage to track the relativistic
effects (increase in effective mass with energy).

In order to further explore the structure of the nucleus and generate new elementary particles,
In 1945,

it is necessary to study the principle of building higher energy particle accelerators.

2

Figure 1.1: Phase stability schematic: point S is the ideal case. point E arrives early, experiences a
smaller field; point L arrives later, experiences a larger field than S; point U is too far from point S
and is in the unstable phase.[10]

scientists V. I. Veksler of the former Soviet Union [8] and E. M. Mcmillan of the United States [9]
independently discovered the principle of automatic phase stabilization.

The principle of automatic phase stabilization, or Phase Stability, refers to in some resonance
accelerators, the motion of ideal particles (stable phase, point S in Fig. 1.1) accelerated in a specific
equilibrium phase can be completely synchronized with the high-frequency RF electric field, and
the energy will continuously increase.
In contrast, the non-ideal particles which deviate from
the ideal particles in a specific range of phase and energy (stable phase, point E and point L in
Fig. 1.1) will have stable phase oscillation around the ideal particles. Then a spread of particles
are accelerated together tracking the ideal energy case to their final energy on target. Point U is
in the unstable phase, the distance between it and the point S will increase during the acceleration
process, and it eventually get lost.

The discovery of phase stability detection is a significant revolution in the history of the

development of accelerator; it led a series of breakthrough to the new high energy accelerators:

• Synchrocyclotron which decreases the RF frequency of the electric field according to the
increased particle energy, and keeps the synchronization between RF frequency and particle
energy.

• Synchrotron which is a kind of circular accelerator; by controlling the frequency of the

3

magnetic field and the accelerating electric field in accordance with the acceleration of
the particles, acceleration is performed while keeping the orbital radius of the accelerating
particles constant.

• Modern proton LINAC and other accelerators.

These strategies also give more efficient focus strength per field onset.

Since then, accelerators have been built to address the theoretical limitations, but increasing
the electric power and the bending and focusing strength has been economically limited. With
the increase in accelerating energy, the weight and cost of the magnets used in cyclotrons and
synchrotrons rose sharply, and the accelerating energy was limited to less than 1 GeV. For example,
the size of the vacuum aperture in the Synchrotron ring must be large due to the poor transverse
focusing force. As a result, the magnetic pole gap of the magnet is large, which still requires
a very heavy and large magnet. It would be impossible to use such huge magnets to accelerate
protons above 10 GeV (the magnet used in the 10-GeV proton synchrotron of the USSR Academy
of Sciences has a mass of 36,000 t [11, 12]).

In particle accelerators, when charged particles pass through a uniform magnetic field, due to
the Lorentz force, weak focusing will appear in the particle accelerator. Due to circular motion,
the orbits of two particles with slightly different positions may approximate or even cross each
other. Due to divergence, a beam of particles with a position change will focus in a magnetic field.
Each rotating beam is focused on one spot rather than one point, and it only intersects once per
revolution. This oscillations in accelerators were theoretically studied by D. W. Kerst and R. Serber
for the first time in electronic induction accelerator (also called betatron) in 1940 [13].

In 1952, E. D. Courant, M. S. Livingston and H. S. Schneider published a paper on the principle
of strong focusing (or alternating gradient focusing)[14], according to which the construction of a
strong focusing accelerator can significantly reduce the size of the vacuum aperture and the cost
of the magnets, making it possible for the accelerator to achieve higher energy. This is another
revolution in the history of accelerators. Since then, the principle of strong focusing has been

4

widely used in a ring and linear accelerators.

In contrast with weak focusing’s uniform magnetic field, strong focusing refers to the principle
that when the net effect of alternating electric field gradient acting on a bundle of charged particles,
both the vertical and horizontal focusing of protons could be made strong at the same time, by
correlation of orbit with kicks provided. This allows tight control of proton paths in the machine
and increases beam intensity while reducing the overall construction cost of a more powerful
accelerator. For comparison, a 6.2 GeV weakly focused proton synchrotron with a total magnet
weight of 10,000 tons was built at Lawrence national laboratory in 1954. While, Brookhaven
national laboratory’s 33 GeV strong-focused proton synchrotron has a total weight of just 4,000
tons. This illustrates the tremendous practical significance of the principle of strong focusing [12].
For relativistic particles accelerating in a straight orbit, radiation of particles is not a severe
effect since their speed increase is minimal as they gain further energy and approach c. However,
particles in a circular orbit experience an acceleration that increases as they acquire high kinetic
energies. In a circular accelerator that keeps the particle at constant radius, the energy lost of a
relativistic electron to synchrotron radiation per turn is


0 =

4




3(
0
2)3 · 
4




=


2
3
0

· 
4




,

(1.1)

where 
 = 
/(
0
2), 
 is the radius of the circular accelerator, 
0 is the permittivity of free space
and

1
4

0


2



2

,



 =

(1.2)
in Eq. 1.1 is the classical electron radius [15]. Note that since 
 = 
/(
0
2), electrons lose energy
about 1013 times faster than protons. This is one main reason of the strategy that LHC protons
are travelling not electrons, and most electron accelerators are LINACs. Practically, synchrotron
radiation is emitted in a well-defined narrow radiation cone with an aperture angle inversely
proportional to 
.

Furthermore, under certain conditions, synchrotron radiation can be produced coherent. Such
devices are known as free-electron lasers (FEL) that until recently have existed as the only useful

5

sources of coherent far-infrared and THz radiation. FELs are becoming increasingly appealing as
sources for coherent x-ray radiation, two examples are the x-ray FEL at DESY [16] and the Linac
Coherent Light Source (LCLS) at SLAC [17].

The ultra-high energy also dramatically increases the magnetic field strength demand of the
bending magnet, which promotes the research and application of superconducting magnets. They
can generate magnetic fields that are up to ten times stronger than those generated by ordinary
ferromagnetic-core electromagnets, which are limited to fields of around 2 T to avoid saturation.
The field of an SC magnet is generally more stable, and can be smaller, since they do not need a
large yoke. Most importantly, for large magnets, they can consume much less power. One of the
most challenging uses of SC magnets is in the LHC particle accelerator. The niobium-titanium
(Nb-Ti) magnets safely operate at 1.9 K at 8.3 T [12].

Electron synchrotrons use electromagnetic fields to provide the acceleration energy, allowing for
even more significant radiation losses, with a limit of about 10 GeV. Electron linear accelerators,
use electromagnetic fields to accelerate electrons to higher energies with limits being largely
economically driven.

Increasing the acceleration energy to such a level exposes new problems from an experimental
point of view. In nuclear and early high energy physics experiments, accelerators are generally used
to bombard the nuclei in the stationary target with accelerated particles, and then the momentum,
direction, charge and quantity of the secondary particles generated are studied. The actual useful
energy of the accelerated particles to participate in high energy reactions is limited. If two charged
particles with the identical mass collide each other, the accelerated particle energy can be fully
used for high-energy reactions or the generation of new particles. The principle was first proposed
by an Italian scientist, B. Taouschek in 1960, and the ADA collider with a diameter of about 1
meter was built at Italy’s Frascati national laboratory to verify the principle. Their success has
opened a new era in accelerator development. Modern high-energy accelerators are basically in
the form of colliders. The collider has been able to increase the equivalent energy of high-energy
reactions from 1 TeV to 10-1000 TeV, which is another fundamental leap in the development history

6

Figure 1.2: Example of LHC design, here k = 2808, N1 = N2 = N = 1.15 ×1011, f = 11.25 kHz, A
= 

∗


,
 = 16.7 

, and peak luminosity per IP is 1 ×1034 cm−2s−1.[18]


 
∗


, 
∗

of accelerator energy [12].

The important figure of merit of the accelerator parameter of the collider is the Luminosity (L),

which is defined as follows:


 = 

.

(1.3)

Here, Y is the event rate, 
 is a cross-section of a physical l process, and L is the Luminosity of
the collider. Higher L can produce a higher yield of phycics events. The Luminosity is given by


 =


 
2 

4

∗

 
∗




=


 
2 
 

4

∗


.

(1.4)

Here k is the number of bunches, N is the number of protons per bunch, f is the revolution frequency,
and 
∗

 are the rms beam sizes at the collision point. An example of LHC design value is
shown in Fig. 1.2.


 and 
∗

In the 90 years since the world’s first accelerators were built, their energy has increased by
roughly nine orders of magnitude as shown in the Livingston Plot [19] (see Fig. 1.3, plot stops
2010), while the cost per unit of energy has fallen by about four orders of magnitude. Another
breakthrough of the accelerator technology is the application of the SRF technology [20], first
succeeded in the TRISTAN accelerator in 1989. Thus, accelerator performance, especially the
luminosity, is much improved since the 1970s. Fig. 1.4 shows the Luminosity improved in high-
intensity ion accelerators.

7

Figure 1.3: Livingston Plot shows the history of particle beam energy increasing [19].

1.1.2 History of SRF Accelerators

With the continuous development of high-energy physics, the requirements of accelerated particle
energy are higher and higher. By the 1970s, many accelerator laboratories planned to use super-
conducting technology to build accelerators in order to increase the energy and reduce the size of
accelerators. Detailed introductions and summaries can be found in Ref. [22, 23].

Some examples of SRF accelerators include:

• Proton machine: SNS, ESS, CADS, MYRRHA, Project-X;

8

Figure 1.4:
present and possible future colliders [21].

Improvement of the luminosity (particle/particle colliding performance), for past,

• heavy-ion machine: FRIB, IFMIF, EURISOL, ATLAS;

• electron machine: E-XFEL, KEKB, LCLS-II, ILC.

1.1.2.1 History of SRF and Several SRF Machines

The first successful application of SRF for particle acceleration was achieved in 1965 when electrons
were accelerated in an SC lead-plated cavity at SLAC. This was a result of a series of developments
in the early 1960’s. In 1961, A. P. Banford and G. H. Stafford proposed and calculated the possibility
of building a superconducting proton linear accelerator [24]. In 1962, Fairbank, Schwettman and
Wilson Turneaure conducted pioneering studies on small scale TE011 and TM010 cavities and
obtained a Q of 1 ×1010 at 1.7 K [25]. The accelerating fields in the cavities were close to the
theoretical limit of 30 MV/m. At the 1963 International Conference on High Energy Accelerators

9

in Dubna, the Stanford group published a very preliminary design of a 20 GeV, 10% duty cycle
superconducting accelerator. This was at a time when no real cavity had ever been built. Robert
Hofstadter made plans to build a 2 GeV superconducting accelerator in a tunnel on the HEPL site
with a gradient of about 13 MeV/m. They obtained a gradient of only 2-3 MeV/m in full-scale
accelerator structures at 1.3 GHz due to parasitic electron multipactor effects [22].

In the 1970’s, R&D on niobium superconducting cavities started earnestly at many institutes
including Stanford, Karlsruhe, CERN, Argonne, Cornell, KEK, U. Illinois, DESY [25]. The
Superconducting Acceleration program at Stanford coincided with the invention of free electron
laser. In 1968, Pantell from Stanford University added mirrors at both ends of the wiggler magnet
through which the beam of electron LINAC passed, which improved the performance of millimeter
wave spontaneous emission [26]. In 1975, J. Madey used the beam of a 24 MeV superconducting
LINAC to obtain the free-electron laser (FEL) in the infrared band for the first time, which opened
up a new scientific and technological field [27, 28].

Large-scale construction of SRF machines began in the mid-1980s. In those days, the interest of
the high energy physics community was to discover the top quark, the last member of the six flavors
of quarks, and the weak bosons (Z0 and W±). For this experiment, colliding electrons and positrons
continuously at the same energy was the best way to increase luminosity. SRF cavities was the
best choice for such a continuous wave (CW) machine due to their higher operating gradient (∼ 5
MV/m) which brought economic benefits. Electron/positron ring colliders were designed for this
purpose and R&D on large-scale application of SRF began in earnest. Four major developments
took place in the 1980s: 1) elliptical cavities were invented to address the multipacting issues at
DESY; 2) high-quality niobium material became commercially available from vendor production;
3) very reliable and reproducible surface treatment was developed, especially electropolishing (EP)
at KEK; and 4) niobium film coated copper cavity at CERN. These advancements in R&D enabled
the construction of large-scale SRF machines, which started in energy upgrade programs for ring
colliders at TRISTAN at KEK, HERA at DESY, LEP-II at CREN, and CEBAF at JLab (this is not
a collider but for a machine for quark nuclear physics) [25]. These projects are described in more

10

detail below to demonstrate the use of SRF technology in accelerators.

The use of superconducting magnets in accelerators also occurred at the same time as the
development of SRF technology. In 1983, Fermilab created a superconducting proton synchrotron
[12]. After using superconducting magnets, the energy of the 400 GeV proton synchrotron with
a diameter of 2 km was increased to 1 TeV. In 1991, the electron proton collider HERA was
successfully built by DESY of Germany[29]. Its proton energy is 820 GeV, and its orbit length
is only 6.3 km. These developments show that superconducting technology has been successfully
applied to accelerators, which brings a good prospect for the construction of the accelerators.
Accelerator experts from all over the world are encouraged to choose superconducting magnet
technology to design accelerators with higher energy. In the LEP orbit of the existing large-scale
Positron Collider (LEP), CERN has designed and built a 7 TEV proton collider LHC using a
superconducting magnet with a high magnetic field (working temperature 1.9 K, magnetic field
strength 8.33 T), and plans to accelerate the LHC to 1150 TEV (2.76 TEV/U) after stripping all the
outer electrons of lead [22].

1.1.2.2 TRISTAN and KEKB

Since 1973, a storage ring complex, TRISTAN (Transposable Ring Intersecting Storage Acceler-
ators in Nippon) planned a colliding beam scheme with electrons (or positrons) at 17 GeV and
protons at 180 GeV. However, the design was finally changed to an electron/positron ring collider
with beam energy of 28 GeV using normal conducting cavities (colliding energy of 56 GeV at center
of mass), to explore the top quark. This is a circular collider, but it also consists of an octagonal
tunnel connected with a straight accelerator to perform electron-positron impact experiments. The
positron production accelerator and electron-positron linear accelerator have a length of 400 meters,
an incident storage ring of about 370 meters, the main ring length of 3 kilometers and a depth of 11
meters underground. In the course of a linear accelerator, there is a facility for storing experimental
equipment. The electron beam rotates clockwise, and the positron beam rotates counterclockwise
to collide at interaction points. The octagonal ring shape is to reduce the curvature of the bent

11

portion in which electrons and positrons lose energy by synchrotron radiation [22].

TRISTAN was energy upgraded by installing superconducting cryomodules. This project was
the world’s first application of SRF cavities on a large scale. By this upgrade project, TRISTAN
colliding energy was boosted from 56 GeV to 64 (beam energy from 28 GeV to 32 GeV); 32
508MHz 5-cell bulk niobium cavities assembled into 16 cryomodules were installed and operated
at 4.3 K. They used spherical shape for the structure to mitigate multipacting. This construction
started in 1986, the first 8 cryomodules were completed in 1989, followed by the completion of
the last 8 cryomodules in 1990. The specifications for the spherical shape cavities were: gradient




 > 5 MV/m and Q-value 
0 > 1 × 109 at 5 MV/m. TRISTAN SRF cavity performance was
better than the spec by a factor two in many cavities; they achieved 
0 = 2.5 × 109 at 5 MV/m,
and maximum gradient 10 MV/m [30]. Unfortunately, TRISTAN did not succeed in discovering
the top quark (TEVATRON at FNAL discovered this quark at 173 GeV in 1995), but succeeded
in demonstrating large-scale SRF application to the world. TRISTAN’s other main contributions
to the SRF community are: 1) made high purity niobium sheet with RRR 200 commercially
available from niobium production companies (for example Tokyo Denkai); and 2) developed very
reliable electropolishing (EP) method.

TRISTAN was closed in 1994. KEK switched to constriction of KEKB. This is an asymmetric
electron (8.0 GeV) positron (3.5 GeV) colliding ring machine to discover CP violation. This is an
intensity frontier machine, which needs to accelerate a beam current > 1A. They used single cell
cavities and built 8 cryomodules which installed one 508 MHz cavity per cryomodule. The cavity
performance was similar to TRISTAN (∼ 5 MV/m at 
0 = 2 × 109, at 4.3K). The main R&D
issues were high power input coupler (∼ 1 MW at CW) and higher order absorber. KEKB applied
TRISTAN SRF coaxial coupler, adding bias functionality on the inner conductor. KEK developed
HIP bonded Ferrite ring inside copper cylindrical beam pipe. Higher-order mode (HOM) damper
successfully worked and could damp HOM powers up to 16 kW (KEKB). KEKB upgraded the
luminosity installing SRF carb cavities. Finally KEKB reached the Luminosity > 2.1 × 1034. The
major contributions to SRF community were: 1) development of extremely high beam load SRF

12

system; and 2) development of crab cavity. KEKB has contributed to the establishment of the CP
violation theory by Kobayashi and Masukawa. They received the Nobel Prize in Physics 2011.

1.1.2.3 HERA

HERA (Hadron-Electron Ring Accelerator) was a particle accelerator at DESY in Hamburg that
began energy up operation in 1992 [29, 31]. At HERA, the only lepton-proton collider in the world
during its operation, 27.5 GeV electrons or positrons collided with 820 GeV protons to provide a
unique window on high energy physics. Protons and leptons were stored in two independent rings
that were overlaid upon each other. The rings had four straight sections that constituted interaction
regions. As a first in Europe, HERA used superconducting magnets for the entire proton ring [22].
After 15 years of data taking, HERA switched off in 2007.

HERA successfully demonstrated large-scale application of SRF cavities in 1991. Sixteen 500
MHz 4-cell cavities were fabricated using high RRR (300) niobium sheet materials. They also
applied the spherical shaped cavities. HERA SRF cavity specification was: 



 = 5 MV/m and

0 = 1 × 109 at 5 MV/m at 4.3K. They used the buffered chemical polishing for their cavity
processing. Their cavity performance was also better than their specifications, they achieved

0 ∼ 2 × 109, maximum gradient ∼ 8 MV/m in the vertical test (certification).

1.1.2.4 CEBAF

The Continuous Electron Beam Accelerator Facility (CEBAF), founded in 1984, is a machine for
nuclear physics. It is located in JLab in Newport News, Virginia, in USA. The machine appears
like a racetrack with four distinct arcs on each end. Each of the two straight sections of the track
consists of a superdoncuting linacs, whereas each arc section contains steering magnets matched
with a different beam energy. In this novel design, the electron beam is recirculated through the
linacs five times with increasing energy, and the beam bends in a different arc in each passing [32,
33]. CEBAF produced 4 GeV electrons in 1995, and has since undergone energy upgrades to reach
12 GeV.

13

To oeprate the SRF linacs in CEBAF, JLab houses the largest liquid helium refrigerator in the
world [25]. CEBAF SRF system consists of 42 cryomodules and one quarter cryomodule, in which
338 1.5 GHz 5-cell niobium cavities were installed. All cavities were fabricated from high RRR
niobium sheets. One cryomodule consists of four helium tanks, where each tank installs a pair of
5-cell cavities. The cavity adopted an elliptical shape to provide better mechanical stiffness and
stability compared to the spherical cross section. The cavities were individually treated by BCP
and rinsed with ultra-pure water. No hydrogen degassing was done. Two cavities were assembled
in class 100 clean room into hermetically sealed pairs using indium gaskets. The performance of
each cavity pair was measured prior to installation into the cryomodule. The specification of the
CEBAF cavities are: 



 > 5 MV/m and 
0 > 2.4 × 109 at 5 MV/m at 2 K. CEBAF cavity
performance satisfied their specifications with a good margin.

1.1.2.5 TESLA

Since 1990, the great successes mentioned above directed the SRF community to an energy frontier
machine to discover the Higgs particle (in those days, Higgs was not yet discovered but CERN
discovered it in 2012 at the energy 125 GeV, since then, the goal changed to a Higgs factory
to investigate the precise properties of Higgs in more detail) or other new elementary particles.
The proposed machine is a linear collider with a colliding energy of 500 GeV (250 GeV + 250
GeV) at center of mass. TESLA (TeV Energy Superconducting Linear Accelerator) international
collaboration started in 1990 aiming to develop a superconducting linear collider as the central lab
of development at DESY. Electrons/positrons are accelerated only once in a long linac ( 15 km
each) in this scheme. To reach such a high colliding energy, high gradient operation (originally
23.5 MV/m for TESLA but increased to 31.5 MeV for ILC) was required. In such a high gradient
operation, the RF dynamic load is too heavy for cryogenics in CW operation, so the RF duty was
reduced to several % instead. However, the pulse operation brings some difficulty in the SRF cavity
operation (microphonics issue). The mechanical or PIEZO tuner development is another important
R&D item. TESLA chose 1.3 GHz 9-cell niobium bulk cavities. TESLA R&D was focused on high

14

gradient cavity performance, cost-effective cavity fabrication, cure for pulse operation, and cost-
effective cryomodule production. In the high gradient cavity R&D, the high field Q-slope (HFQS),
which is the main theme in this PhD program, limited the gradient below 20 MV/m. However, it
was discovered that KEK recipe developed in TRISTAN R&D, i.e. EP + low temperature bake
(LTB), could mitigate the HFQS perfectly. The gradient was pushed up to > 30 MV/m by this
technology. However, in BCP’ed cavity case, LTB can not mitigate the HFQS. Many studies took
place to understand this issue but it is still no conclusive result after more than two decades.

Superconducting and normal conducting linear collider developments were being completed in
parallel until the early 2000s. International Committee for Future Accelerator (ICFA) selected SRF
for the future linear collider in 2004. After 2004, TESLA changed its name to ILC (International
Linear Collider) and the R&D was continued in many institutes including KEK, DESY, FNAL,
Jlab, Cornell and Saclay. The aim was to start construction in mid-2020s. These research programs
have improved SRF cavities and cryomodule system in reliability and cost-effective production.
Now many institutes apply these result for the X-FEL machines in DESY, ICLS-II, Shanghai XFEL,
etc. One example is shown below.

1.1.2.6 LCLS-II

The wide application of synchrotron radiation and the requirements from users to improve light
source performance generates urgent demand for high brightness and ultra-short pulse light source.
Hence the fourth generation of synchrotron radiation light source has been put on the agenda, and
light source based on the free-electron laser is the primary way to realize the fourth generation
light source. At the end of the 20th century, the Stanford Linear Accelerator Center (SLAC) started
preliminary research on the linac coherent light source (LCLS), an X-ray free-electron laser based
on electron LINAC. LCLS, which started lasing in 2009, uses the last third of SLAC’s original 3
km normal-conducting LINAC. The success of LCLS motivated the LCLS-II project which will
add a superconducting accelerator that occupies another one-third of SLAC’s original 3 km linear
accelerator tunnel. LCLS-II will generate an almost CW short pulse X-ray laser beam whose high

15

repetition-rate greatly enhances the capabilities of the light source [12, 17].

LCLS-II employs 300 TESLA-type 1.3 GHz 9-cell cavities. The cryomodule is based on
TESLA design but the return gas pipe is made much bigger for CW operation. The feature of
LCLS-II cavity is in the high Q performance. LCLS-II cavity specification is 
0 > 2.7 × 1010
at operation gradient 16 MV/m at 2 K. FNAL developed Nitrogen diffusion method to push up
the 
0 from 1-2 × 1010 in TESLA cavity to > 3 × 1010. LCLS-II applied this method. They
already completed the production and are now installing cryomodules in the SLAC tunnel. They
successfully achieved such a high Q cavity in industrial production. The maximum gradient is
limited below 20-25 MV/m by this method due to HFQS. They are developing more high Q and
high gradient cavity for LCSL-II HE.

With the continuous improvement of accelerator energy, scientific understanding of the micro-
scopic material world is gradually deepened, and great achievements have been made in particle
physics research. Nowadays, accelerators are used far beyond basic research. Accelerators are
employed for materials science, solid-state physics, molecular biology, chemistry, geology and
archaeology. There are also industrial applications in isotope production for the diagnosis and
treatment of tumor, radiation sterilization, radiation breeding, food preservation, ion implantation,
the radiation modification of materials, plum trace analysis, simulation of space radiation, nuclear
radiation simulation and other applications. These applied accelerators have low energy but often
require high intensity. They usually employ individual process devices that are convenient for
specific applications. Therefore, there are also particular research and optimization directions.

1.1.2.7 ATLAS

The use of SRF in heavy ion accelerators is also undergoing intense development. One of the
pioneers is ATLAS at Argonne National Laboratory. In 1998, the Argonne cascade LINAC system
ATLAS used a 9 MV tandem electrostatic accelerator as the injection system, followed by a post
accelerator composed of 46 and 97.0 MHz superconducting separation ring cavities. The RF
power of the ATLAS is 6 kW. Four of the cavities are used for beam recombination and both.

16

Subsequently, a 48.5 MHz and 72.7 MHz 18 section superconducting quarter-wavelength cavity
injector was built to improve the performance. The superconducting cavities are made of niobium
and operate at 4.2 K low temperature. The phase of each superconducting cavity can be adjusted
independently to operate under CW, so it can accelerate all kinds of ions from Li to U, with the
energy of 5 - 17 MeV/u and beam intensity of 50 - 500 nA [34, 35].

1.1.3 Current Facilities

Accelerators in high energy physics or nuclear physics have two trends: High Energy Frontier
(discovery machines) and intensity frontier machines. The typical example of a high energy
frontier machine is the LHC mentioned above. An example of an intensity frontier machine is
KEKB, which accelerates high current electron/positron beams with larger than 1 A current. In
nuclear physics, the intensity frontier machine is key since very high energies are not necessary for
relevant processes [22].

A summary of high-intensity ion accelerators operating or being planned around the globe is

shown in Fig. 1.5. They serve a variety of purposes, including:

1. Nuclear physics (e.g. FRIB, USA; RIKEN, Japan; RISP, Korea; FAIR, Germany; HIAF,

China).

2. The intensity frontier of high energy physics (e.g. PIP-II, USA; J-PARC, Japan).

3. Spallation neutron production (e.g. SNS, USA; ISIS, UK; ESS, Sweden).

4. ADS for nuclear waste transmutation and subcritical power generation (e.g. CADS, China;

MYRRHA, Belgium).

5. Plasma physics with a beam-driven warm dense matter or high-energy-density physics (e.g.

FAIR, Germany; HIAF, China).

A comprehensive overview as of 2014 can be found in Ref. [36]. A standard metric of high-
intensity ion accelerators is the average beam power on target defined by (maximum beam energy

17

Figure 1.5: High intensity ion accelerators (Image courtesy of Prof. Jie Wei at FRIB) [36]

× average beam current). Proton accelerators have already achieved beam power above 1 MW, and
multiple MW to >10 MW facilities are presently under construction. For heavy-ion accelerators,
FRIB is set to advance the continuous-wave (CW) power frontier by two orders of magnitude when
it reaches full operating specifications at 400 kW [37].

1.1.4 Facility for Rare Isotope Beams (FRIB)

The Facility for Rare Isotope Beams (FRIB) is under construction on the campus of Michigan
State University. Fig. 1.6 shows the projected rare isotope fast-beam rates available at FRIB. The
designed rates are several orders of magnitude higher than currently available rates and include
thousands of undiscovered isotopes.

FRIB driver accelerator is designed to accelerate all stable ions (from proton to uranium)
to energies above 200 MeV/u with beam power on the target up to 400 kW (Table 1.1). After

18

Figure 1.6: Chart of nuclides showing projected fast rare-isotope beam rates provided by FRIB
in particles per second (pps). For reference, stable nuclides (black squares), the traditional closed
nuclear shells (dashed lines), estimates of the astrophysical r and rp-process paths (solid black
lines), and possible nucleon drip lines (solid grey lines) are depicted [38].

Figure 1.7: Layout of FRIB driver accelerator [36].

19

Table 1.1: FRIB driver accelerator primary parameters [36].

Parameter
Primary beam ion species
Beam kinetic energy on target
Maximum beam power on target
Macropulse duty factor
Beam current on target (238U)
Beam radius on target (90%)
Driver LINAC beam-path length
Average uncontrolled beam loss

Value

H to 238U

> 200
400
100
0.7
0.5
517
< 1

Unit

MeV/u

kW
%
emA
mm
m
W/m

production and fragment separation, the rare isotope beams can also be stopped, or stopped and
then reaccelerated. The fast, stopped, and reaccelerated rare isotope beams serve a vast range of
scientific users in the fields of nuclear physics and applications.

As shown in Fig. 1.7, the driver accelerator is folded into three segments to optimize the use of

space. It consists of:

• Electron Cyclotron Resonance (ECR) ion sources;

• a low energy beam transport containing a pre-buncher and electrostatic deflectors for machine

protection;

• a Radiofrequency Quadrupole (RFQ) LINAC: LINAC segment 1 (with Quarter-wave Res-
onators (QWR) of 
 = 0.041 and 0.085) accelerating the beam up to 20 MeV/u where the
beam is stripped to higher charge states, LINAC segments 2 and 3 (with Half-wave Resonators
(HWR) of 
 = 0.29 and 0.53) accelerating the beam above 200 MeV/u;

• folding segments to confine the footprint and facilitate beam collimation;

• a beam delivery system to transport to the target a tightly focused beam.

The reaccelerator (ReA) consists of similar 
 = 0.041 and 0.085 accelerating structures. More
cavities performances information can be found in Ref. [39].

FRIB produce more than 350 cavities: 16 
 = 0.041 QWRs, 104 0.085 QWRs, 72 0.29 HWRs,
148 0.53 HWRs. One 0.041 cryomodule includes four QWRs, 0.085 cryomodule includes eight

20

Table 1.2: FRIB Cavities Performance 2 K [39]

Q0

Gradient

Cavity
0.041 QWR > 5.1 MV/m 1 × 109
0.085 QWR > 5.6 MV/m 1 × 109
> 7.6 MV/m 5.6 × 109
0.29 HWR
> 8.1 MV/m 7.6 × 109
0.53 HWR

QWRs, 0.29 cryomodule includes 6 HWRs, 0.053 cryomodule includes 8 HWRs. There are totally
44 accelerating cryomodules, and two beam maching modules. All cryomodules were completed
and installed in the FRIB tunnel. Now phased beam commissioning is underway, in order segment
1, 2, and 3. The cavity performance in vertical Dewar is shown in Fig.1.8 and Fig. 1.9.

The specifications are shown in Table 1.2.
All the cavities met the FRIB specification. FRIB cavities were treated by BCP, High pressure
water rinsing, and assembled in class 10 clean room. Low Temperature Baking was not taken.
Many of the cavities were limited by field emission. About 30% of cavities gradient were limited
by High Field Q slope, which we will discuss in next chapter. If we succeed to resolve the HFQS
issue with BCP’ed cavities, FRIB cryomodules operation will be pushed up to > 10 MV/m. This
is one motivation of this project.

1.1.5 Accelerator Facility Components

Particle Accelerators are sophisticated devices, and generally consists of four essential parts and
associated auxiliary systems.

1. Particle sources are used to provide the particles needed to accelerate, including electrons,

positrons, protons, antiprotons, heavy ions...

2. The vacuum acceleration system has some form of accelerating electric field, and the whole
system is placed in a vacuum chamber with high vacuum in order to accelerate the particles
from being affected by the scattering of molecules in the air.

21

Figure 1.8: : Dewar test results for 

 = 0.043 QWRs: (a) Q0 at 4.3 K; (b) Q0 at 2 K; (c) X-rays
at 2 K. [39].

22

Figure 1.9: Dewar test results for 

 = 0.086 QWRs: (a) Q0 at 4.3 K; (b) Q0 at 2 K; (c) X-rays at
2 K. [39].

23

3. The guiding and focusing system uses a particular form of an electromagnetic field to
guide and constrain the accelerated particle beam so that it receives the acceleration of the
electric field along a predetermined orbit. All of these require the integration of precise and
sophisticated technologies.

4. Beam transport and analysis system is composed of electromagnetic field lenses, bending
magnets and electromagnetic field analyzer.
It is used to transport and analyze charged
particle beam between particle source and accelerator or between accelerator and target
chamber.

1.1.6 Acceleration Field

To generate the accelerating electric field, one can choose DC or AC field. For accelerator using
DC field, it needs a high voltage generator, for example, Van de Graaff generator (10 MV voltage).
The advantage of DC acceleration is that it can accelerate any charged particles and can smoothly
adjust the final energy. However, the voltage of DC acceleration is limited to 35 MV, by voltage
breakdown, or vacuum breakdown (one possible explanation is field emission, see Ref.[12].). The
examples of DC accelerator was discussed in Section 1.1.1.

Figure 1.10: LC circuit model of an accelerating cavity[40].

For acceleration using AC field, it can reach much higher accelerating gradient (several MV/m)
and increase the space accelerating efficiency. A straightforward instrument that generates AC is an
LC circuit (Fig. 1.10) with one capacitor (C) and one inductor (L), where the resonant frequency of

24

0 = 1/

. By controlling the entering time and considering the charged particle’s
the system is 
2
initial velocity, the particles can be accelerated or decelerated by the field between the capacitor’s
plates. The most applied AC field frequency falls into the radio frequency (RF) region (several 10
MHz to 3 GHz) because the resonant size at that region is more applicable.

1.2 RF Acceleration

An RF cavity is the essential acceleration element in an accelerator; it adopts RF resonant
travelling wave or standing wave to generate a resonantly oscillating electric field to accelerate
charged particles. (Travelling wave is applied normal conducting LINAC, while SRF cavity applies
the standing wave.)

1.2.1 RF Resonant and Frequency

A simple LC circuit can evolve to an accelerating cavity resonator (Fig. 1.11), which encloses
electromagnetic waves and prevents them from being radiated and associated power loss. Specific
sizes are chosen to get a stably resonant standing wave and get acceleration field. Therefore the
requirements of the size are related to the particle velocity, and some examples are shown in
Table 1.3.

Figure 1.11: LC circuit evolving to a resonant cavity[40].

In order to accelerate the particle efficiently, the particle transit time should be less or equal to

half period of RF wave:










 









≤ 1
2 
0

,

25

(1.5)

Table 1.3: Example of Cavity shape VS. 
 for different particles. Ɖ is the geometry factor that only
relates to cavity shape [40].


 ≈ 1

Electron Accelerators
350 MHz ≤ f ≤ 3 GHz
d ≈ 35 cm (f = 350 MHz)

Ɖ ≈ 270 

Proton Accelerators


 ≈ 0.5
Ɖ ≈ 170 

500 MHz ≤ f ≤ 1.5 GHz
d ≈ 20 cm (f = 350 MHz)

Ion Accelerators
0.05≤ 
 ≤ 0.2

50 MHz ≤ f ≤ 150 MHz
d ≈ 15 cm (f = 100 MHz)

Ɖ ≈ 20 

where d





 is the length of the cavity and 
0 = 
0/(2
) is the RF frequency. This equation is
equivalent to:

2






 
0 ≤ 

,

(1.6)

where 
 = 
 







/
 and 
 is the speed of light.

The final speeds highly depend on the particle mass due to relativity; thus the size and shape of
the cavity depending on 
 also. Table 1.3 shows some examples of the sizes for different particles.
Fig. 1.12 also shows some cavity examples of different frequency and 
.

Figure 1.12: Cavity shape examples for different frequency and 
 [41].

There are a lot of considerations in size and shape for optical cavity design, including the beam
aperture, the frequency-based performance, the cavity surface processing difficulty, the material
cost and the construction difficulty. These will be overviewed in the following sections.

26

1.2.2 Power loss and the Quality Factor

The power loss of a cavity is an essential index of cavity performance, it is not only the sign of
electricity consumption but also influence the limit (for example thermal breakdown of a cavity)
for the cavity. For an accelerator cavity, its power loss can be defined by current and resistance.
According to Ohm’s Law, there exist a current density J near the surface of the conductor:

J = 
E
 =

(1 − 
)n × H
.

1



(1.7)

Where 
 is the electric conductivity and E is the electric field. The average Power Loss 




 per
surface area S relates with J by:













=

1
2


|
|2 =

1
2



|
|2 =



|
|2.

1
2

(1.8)

Here 

 = 1/(

) is the surface resistance. Eq.1.8 can then be integrated over the cavity surface:

Þ






 =

1
2





|
|2

,

(1.9)

To show that the power loss is related to the cavity surface resistance R
 and the applied field H over
the surface. On the other hand, considering the energy U stored in the conductor, Stored Energy U:






 = − 






.

(1.10)

The Quality Factor Q of the cavity, which indicates the measure of the sharpness of the response
of the cavity is defined as 2 ×  times the ratio of the time-averaged energy stored in the cavity to
the energy loss per cycle:


 = 
0











.

(1.11)

By conservation of energy, so the power dissipated in Ohmic losses is the negative of the time rate
of change of stored energy U. We can write U as the function of time:

with solution (U(t=0) = U0):








= −
0




,


(
) = 
0
−

0
/
.

27

(1.12)

(1.13)

Compare to Eq.1.9 and Eq.1.10, we can get

Combine with 
 = 1

2 
0|
|2 = 1






 =
2 
0|
|2, so that


0




.


 =


0








=















=

Ɖ




.

(1.14)

(1.15)

Here the Ɖ is the Geometrical Factor that mentioned in Table 1.3 and can be calculated by:

Þ

Þ
Þ


 |
|2



 |
|2



Ɖ = 

 · 
0 = 

 ·

1
2 




0


 |
|2



= 
0
 ·

.

(1.16)

In Eq. 1.15, Ɖ is only related to the cavity geometry designed and R
 is only related to the material
properties.

1.2.3 Field in a Cavity

In Section 1.2.2, we mentioned the 




 is determined by the surface resistance and applied field
H. For the field in an RF accelerator cavity, the electric field is used to accelerate the charged
particles, and the magnetic field generates heat and power loss.

The RF cavity can be treated as a waveguide. The electric field and magnetic field inside the
waveguide can be derived from Maxwell’s equations. Derivation details are shown in Appendix A.
A detailed explanation can be found in Ref. [42–45].

The expressions for TM010 mode fields in a cylinder pillbox cavity that are commonly used for

RF acceleration is:



 = 
0
0( 2.045


)
−


,




(cid:114) 




 = −



0
1( 2.045





)
−


,





(1.17)

(1.18)

where 
 is the r direction position, R is the radius of the cavity, 
 is the azimuthal angle, E0 is the
electric field in the center, J
(
) is the ordinary Bessel Function of the first kind of order 
. This
groups of the function show the electric field and magnetic field value in every position with time
variance.

28

1.2.4 Skin Depth

In a conductor, Ohm’s law relates the electric field to the current density and so to the magnetic
field via Ampere equation, the relevant equations are





J = 
E.

∇ × H = J, ∇ · B = 0, ∇ × E + 
B

= 0,

(1.19)
With B = ∇×A, Faraday’s law shows that the curl of E+ 
A/

 vanishes. As a result, we can write
E = −
A/

 − ∇
. With the assumption of negligible free charge and the time-varying B as the
sole source of the electric field, we may set the scalar potential 
 = 0 and have E = −
A/

. Note
that we have the subsidiary conditions, ∇· E = 0 and ∇· A = 0. For a media of uniform, frequency-
independent permerability 
, Ampere’s law can be written ∇ × B = 
J = 

E. Elimination of B
and E in favor of A and use of the vector identity, ∇×∇× A = ∇(∇ · A) −∇2A, yields the diffusion
equation for the vector potential,

∇2A = 




A




.

(1.20)

If we look at Eq.1.20, we may find out that this also holds for E. If the conductivity is constant in
space, it follows that the B and J also satisfy the same diffusion equation.

We can estimate the time 
 for decay of an initial configuration of fields with typical spatial

variation defined by the length L. We put ∇2A = 
(A/
2)and 
A/

 = 
(A/
). Then


 = 
(


2).

(1.21)

We can also estimate the distance L over which fields exist in a conductor subjected externally to
fields with harmonic variation at frequency 
 = 1/
,
1√





 = 
(

(1.22)

).

For a field described by Eq.1.20, an example is showed in Fig. 1.13: A semi-infinite conductor
of uniform conductivity 
 and permeability 
 occupies the space z > 0. The surface at z = 0−
is subjected to a spatially constant, but time-varying, magnetic field in the x direction, 

(
) =

0cos(

). At z = 0+ and the half space z > 0, the magnetic field still has only x component

29

Figure 1.13: Skin Depth

that 

(
) = 
0cos(

) because of the continuity of the tangential component of H, the normal
component of B across z = 0 and the linearity of Eq.1.20.

The steady-state solution for 

(
, 
) can be written as 

(
, 
) = Ò(
)
−


, where from

Eq.1.20, Ò(
) satisfies

( 
2


2 + 



)Ò(
) = 0.
A trial solution of the form, Ò(
) = 


 
 leads to the condition

or


 = ±(1 + 
)


2 = 



,

(cid:114) 




.

2

(1.23)

(1.24)

(1.25)

(1.26)

(1.27)

Comparing with this result Eq.1.22, the square root has the dimensions of an inverse length
characteristic of the medium and the frequency. The length is defined as the Skin Depth 
:

(cid:115)


 =

2






.

So that Ò(
) = 

±(1−
) 



 , the solution for H
 is the real part of



(
, 
) = 

−
/


(
/
−

) + 


/


(−
/
+

).

30

B must equals to zero, for the whole value not go to infinity as 
 → ∞. Compare the solution to
the boundary value, 

(0+, 
) = 
0
−


, shows that 
 = 
0, so that the solution is



(
, 
) = 
0
−
/



/
−


 .

(1.28)

From Ampere’s and Ohm’s laws, and knowing the fact that only H
(
, 
) exist for H
 (

 = 

) in
this case, we know that there is only a tangential component of E
, given by



 = |

| = | 1











| =

1 − 






0


/
−


 .

Define Surface Impedance 
, and

So that the real part of 
,


 ≡ 






= 

 + 


 =



(
) = 

 =

1 − 





(cid:114) 



2


= (1 − 
)

1




,

=

(cid:114) 



2


.

(1.29)

(1.30)

(1.31)

R
 is Surface Resistance. This case can be easily applied to other directions of H. A detailed
explanation can be found in Ref. [42–44].

1.2.5 Accelerating Voltage

We all know 
 = 
 
 for a uniform E field across a gap d. By analogy, we take the Accelerator
Voltage is:





 ≡











(
 = 0, 
)

(
 
+
) 





(
 = 0, 
)


 




0
We used 
 = 
/
 here. For TM010, E
(
 = 0, 
) = 
0, therefore:

(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) .

(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) =

(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)Þ 

(cid:12)(cid:12)(cid:12)(cid:12) = 
0


(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) 


 



2




2


(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) .

(1.32)

(1.33)

(1.34)

(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)Þ 


0

(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) =

0

(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)Þ 

(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)Þ 


0

(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) = 
0

(cid:12)(cid:12)(cid:12)(cid:12)










 = 
0




 





 )
(1 − 

 



For half-pillbox, 

/2
 = 
/2, therefore





 =


0


/2

.

31

Another important property is the Transit Time Factor T, which takes into account the time-variation
of the field during particle transit through the accelerating gap, for TM010:


 =





0


2



=

= 0.637.

|Þ 

0 
0

| =





A detailed explanation can be found in Ref. [42, 45].

1.2.6 Shunt Impedance, R/Q, E
/E


 and B
/E




The Shunt Impedance R

 is defined as:




 =


2







.

(1.35)

(1.36)

It is a measure of the strength with which an eigenmode of a resonant radio frequency structure
interacts with charged particles on a given straight line, typically along the axis of rotational
symmetry. It indicates how efficiently energy is consumed for beam acceleration.

R/Q is a critical cavity parameter that is defined as follow:






=








=


2

0


.

(1.37)

R

 depends on the surface resistance, so it depends on the materials. R/Q does not depend on the
materials. R/Q means how strongly the acceleration energy is concentrated on the beam axis of the
cavity, i.e. a measure of the goodness of the cavity shape.

A pillbox cavity has no beam pipe. The real cavity needs the beam aperture to let beam transit
the cavity. This is out of the Pillbox cavity design. Computer codes are needed to design the cavity
having an aperture. Here, the detail is not shown, but only the result is discussed. The RF surface
electric field is strongest at the cavity bore aperture (iris). If the surface electric field is too strong,
electrons will be field emitted from cavity surface (field emission, FE) by tunneling effect. If the
work function of the metal surface is the smaller, the field emission becomes the more serious, i.e.
exponentially increases due to tunneling effect. The contamination decreases the work function
value and makes field emission easier. Speaking technical, one has to make clean this area to
suppress the field emission.

32

Table 1.4: A comparison of superconductor (SC) cavity (Nb at 4.2 K) and normal conducting (NC)
cavity [40].

Q0

R
/Q0

Dissipated power [kW/m]
(for E


 = 1 MV/m)
Total AC power [kW/m]
(for E


 = 1 MV/m)

SC Cavity NC Cavity
2×109
2×104

330

0.0015

0.36

900

56

112

On the other hand, the smaller E
/E


 is better against FE. Therefore, in cavity design,
E
/E


 is made smaller as much as possible. However, another parameter optimization interferes,
for instance, the diameter of the bore. As a result, the realistic cavity design E
/E


 is about 2 for
SRF cavities. This optimization is especially crucial for SRF cavities because their performance is
susceptible to FE.

B
/E


 is not an issue with the normal conducting cavity (for example copper cavity), however,
it is very important for Superconducting RF cavity design. Superconductivity collapses at a critical
magnetic field (H
 for type-I, H
1, H
2 for type-II). The candidate of the RF critical field is H
1,
H
2, or H
 for the type-II superconductors. However, for SRF cavities, the real critical field is
considered as the superheating field, which is about 180 - 200mT for niobium material. The
magnetic quench happens at the high surface magnetic field area where locates around the equator
of the cavity. In the SRF cavity design, B
/E


 is as small as possible. However, other factors,
like beam bore radius interferes. The real SRF cavity optimization B
/E


 typically gives 3.5 -
4.5 mT/(MV/m). A detailed explanation can be found in Ref. [45].

1.3 Superconductivity

Superconducting RF cavities have some merits over normal conducting RF cavities because
their small surface resistance below T
 and R
 of the superconductor is ∼ 105 magnitudes smaller
than the normal conductor, so that:

33

• Nearly all RF power goes to the beam, save the RF power budget, even considering the

cooling cost.

• The continue-wave (CW) operation becomes applicable, in normal conductor copper case,

the power dissipation of CW could melt the metal and break the cavity.

• The low electrical loss in an SRF cavity allows their geometry to have large beam pipe

apertures while still maintaining a high accelerating field along the beam axis.

A comparison of a typical superconductor cavity and normal conductor cavity is shown in Table 1.4.
The theory of superconductivity is not fully understood, much is still under investigation. Several
models have strong supporting evidence — the two-fluid model and BCS theory — that will be
introduced in this chapter.

1.3.1 Phenomena: T
, Meissner effect and H


In 1908, Onnes succeeded in liquefying helium and then began to study the metal resistivity in this
temperature region, finding that at 4.2 K, Hg’s resistance mutated to a zero DC resistance state.
For a long time after that, people regarded the superconducting state as the “ideal conductor” with
zero DC resistance [46].

But that assumption has run into difficulties. In an ideal conductor, 
 = 0, so 
 → ∞, by


 = 

, has E= 0 in the conductor. We can get from Faraday’s law, that in a conductor

∇ × 
 = − 






,

and if we assume 
 = 1 as most metal is, we can get


 = 
0
 = 
0

,

(1.38)

(1.39)

where H
 is the applying magnetic field before the resistance drop to zero. Therefore, when there
is no resistance in the conductor, the magnetic field in the conductor remains the same no matter
how the external magnetic field changes.

34

Thence, the ideal conductor first cooled to T
 and then added the external magnetic field,
and then added the external magnetic field and then cooled to T
, and then removed the external
magnetic field, the two order of the conductor internal magnetic field is not the same: the first is
equal to zero, the second is equal to the external magnetic field.

However, in 1933, Meissner and Ochsenfeld found that the magnetic field inside a supercon-
ductor was always zero, regardless of the order applied. Even if a superconductor is cooled to a
superconducting state with an external magnetic field, it will never have an internal magnetic field.
This effect is called the Meissner effect [46, 47].

When Onnes discovered the superconductor, he immediately thought of making a non-dissipated
magnet. However, when he added the magnetic field to the superconductor, the superconductor
recovered its resistance and returned to the normal state when the magnetic field reached a certain
value [48]. This field is called the critical magnetic field H
. It is observed from experiments that
most superconductor follows the relation:



 = 

(0)[1 − ( 





)2],

(1.40)

where T
 is the critical temperature, T is the real temperature, and H
(0) is the critical field at 0 K.

1.3.2 Explanation and Two Fluid Model

The physics of superconductors is exciting and encouraging. Even before the discovery of the
Meissner effect in 1924, Keesom had been trying to apply thermodynamics to superconducting
phase transitions [48, 49]. Even though he regards as that superconductors were still considered ideal
conductors and superconducting transitions were considered non-equilibrium processes, which
contradicted thermodynamics, which was based on reversible phase transitions. However, a series
of thermodynamics formulas for the superconducting phase transition established by Keesom based
on thermodynamic premise is consistent with a large number of experiments. Gorter proposed in
1933 that the success of Keesom’s thermodynamic treatment means that superconducting phase
transition should be reversible [50].

35

Another logical thought is about electrons. If all the electrons become superconducting electrons
below T
, then H
 should be temperature independent. In real, H
 has temperature dependence.
Therefore the superconducting electrons are a part of the total number of electrons, and the other
part is normal electrons. The ratio of the two must be temperature-dependent.

In 1934, Gorter and Casimir proposed a two-fluid model [48, 51]:

• When the conductor is in the superconducting state, the free electrons are divided into two
parts: one is the superconducting electrons 

, accounting for 
 = 

/
 of the total; the other
is the normal electrons 

, accounting for 1 − 
 = 

/
 of the total. 
 = 

 + 

. Two parts
of electrons occupy the same volume, penetrate each other in space and move independently
of each other. The relative number 
 and 1 − 
 of two kinds of electrons are functions of
temperature.

• 

 superconducting electrons condense in a low energy state.

• The 

 normal electrons are scattered by the conductor lattice and move randomly, which

contributes to the entropy.

• The superconducting phase transition is a second-order phase transition, and the supercon-

ducting state is an ordered state.

This model can explain the superconducting state with zero resistance: when the temperature
is lower than T
, the motion of the superfluid electrons is unimpeded. If there is current in the
conductor, it is all caused by the motion of the superfluid electrons. After the superfluid electrons
appear, there is no electric field in the conductor, so the normal electrons do not load current, so
there is zero resistance effect. Later we will calculate the SRF surface resistance based on this
two-fluid model. One can see that this model can derive a very close formula to the BCS Surface
resistance.

36

Figure 1.14: Specific heat Vs. T for Sn in superconducting state and normal conducting state [52].

1.3.3 Thermodynamic Study of Superconductor

There are some inferences about the properties of superconductivity, which we will briefly introduce
here but will not derive. The stable state of any system is the state with the lowest free energy.
When the sample is cooled below T
, it becomes a superconducting state. Therefore, when T <
T
, the free energy of the superconducting state must be less than the normal state. Besides, the
superconducting state has a higher degree of order than the normal state, and the entropy of the
superconducting state is also lower than the normal state. Moreover, since the phase transition
process of superconducting state and the normal state does not change the latent heat, the phase
transition at T = T
 is a second-order phase transition in the case of zero magnetic field [48].

As with normal metals, the specific heat capacity of a superconductor consists of contributions


 from the lattice and 

 from electrons. An experiment measured the specific heat of both
superconducting and normal conducting Sn is shown in Fig. 1.14. The normal state below T
 is
achieved by applying different values of a magnetic field to Sn. Overall the superconducting specific
heat is higher than the normal conducting state. There exists a leap around the T
 for different
values of applying field; the leap shifts to lower temperature when the applying field increases.

This extra specific heat capacity is mainly contributed by the superconducting electrons, which

37

is also the conclusion of the experiment. Keesom [53] made X-ray diffraction images to study the
lattice change of Pb before and after the superconducting phase transition in 1924; and Wilkinson
made neutron scattering of Pb and Nb [54], before and after the superconducting phase transition in
1955. Both of which found no change in the lattice, indicating that the normal to superconducting
phase transition only involved changes in the electronic turntable, independent of the lattice.

The two-fluid model can explain the change of specific heat capacity of superconductor near T
:
if the temperature of a superconductor is increased by Ɗ
, the first step is to destroy 

 (

 < 

)
ordered superconductor electrons with 

 heat, and make them 

 (

 = 

) normal electrons, and
then 

+ 

 normal electrons get heat to do irregular thermal movement to increase the temperature
of the system.

The thermal conductance of pure metals at low temperatures comes mainly from the thermal
conductance of electrons. For superconductors, superconducting electrons carry no heat, so the
thermal conductance in the superconducting state is still decided by the number of normal electrons.
In the superconducting state, the number of normal electrons is decreased exponentially with
distressing temperature. Therefore the thermal conductivity in the superconducting state is inferior
compared to that in the normal conducting state (Fig. 1.15). It is an issue in SRF application if
the thermal conductivity is too low. When RF is loaded into the SRF cavity, the imperfections on
the SRF surface is RF heated, the temperature increases easily over the Tc, as the result quench
happens (thermal instability) [55].

1.3.4 Type II Superconductor & GL Theory

When applying a low magnetic field, Type-II superconductors do not show complete Meissner effect
(like Type I superconductor) but have a mixed state of superconductivity and normal conductivity
(called as vortices state).

It occurs above a certain critical field H
1 (lower critical magnetic field). The vortex density
increases with increasing field strength until superconductivity is destroyed at a higher critical field
H
2. The relation is shown in Fig. 1.16.

38

Figure 1.15: The dots curve shows the experiment result of the thermal conductivity ratio change
with temperature for Nb, the solid line curve and the dashed line curve shows two theoretical
predictions, where 

 is the thermal conductivity in Superconducting state and 

 is the thermal
conductivity in the normal conducting state [56].

There was long confusing in these two types of superconductors until Abrikosov theory (1957)
[57, 58] has been established. People regarded that the type-II was due to the low purity of the
superconductor material.

In addition to experimental observations, the two superconductors can also be theoretically
distinguished by the positive and negative interfacial energies. The Ginzburg-Landau theory [59–
61] and Abrikosov gave the method of judging the interface energy by introducing a Ginzburg-
Landau parameter 
:

When 
 < 1/√

2, the interface energy is positive, and it is type I superconductor; when 
 > 1/√

2,

the interface energy is negative, and it is type II superconductor. In the 
 definition equation:

(1.41)


 =





0

.

(cid:114) 



0
2





 =

,

(1.42)

is the London penetration depth. When a superconductor is placed in a magnetic field 

, its

39

Figure 1.16: Type I and Type II superconductor H
 and T relation. There is a new vortex state for
type II superconductor.

internal magnetic field near the surface decays exponentially with depth x.

The London penetration depth 

 =


. It is derived from London equations:

√


(
) = 

(− 
√



).

(1.43)


 is the depth at which the magnetic field decays to 1/
 of

for superconductor zero resistance and









 =




2




,


 = − 





2∇ × 

,

for superconductor Meissner Effect.

Another parameter in 1.41 is the coherence length in the superconducting phase


0 =





 




,

(1.44)

(1.45)

(1.46)

and it is the spatial extent of a Cooper pair introduced in Bardeen–Cooper–Schrieffer theory (BCS
Theory) [48, 62].

40

Figure 1.17: Periodic arrangement of vortices in a type-II superconductor in an external applied
magnetic field. Each vortex has a normal core, where the superconducting order parameter |
|2
(blue line) drops to zero on the scale of 
 while the magnetic field profile (red line) exponentially
decays on the scale of 
 [63].


 =

so that


0(
)

(
) =


 =


0

√
2
2

√

2
0



(cid:12)(cid:12)(cid:12)(cid:12) 








(cid:12)(cid:12)(cid:12)(cid:12)
=



0(
)

(
),

2

0(0)

,

2

(1.47)

(1.48)

is the Ginzburg–Landau parameter, it is a constant for each superconductor and will not change
with temperature.

In the Abrikosov theory, one can find two impotent formulas which relate to the easily measured

parameters H
, H
2 [48] and 
0:



 =




2


√
2
∗ =
√

2








2 =




2

Ò
/2

√
2

2

0
√
2



=

2


=


0
√
2



,

2



0
2

2

,


0 =

Ò

2


= 2.0678 × 10−15 
 · 
2.

Fig. 1.17 shows the vortex state diagram and the model for a type II superconductor.

41

(1.49)

(1.50)

(1.51)

1.3.5 BCS Theory: Formation of Superconductivity

After expounding the experimental proof that superconductivity is caused by electrons and has
nothing to do with the lattice, Corak made more accurate measurements of the specific heat
capacity of superconductors with the change of temperature in 1956, and found that the specific
heat capacity of superconductors and temperature is exponential [64]. The relationship between
the number of electrons crossing the energy gap and the temperature is similar in a single electron
system with an energy gap. In 1960, P. l. Richards and M. Tinkham experimentally measured the
energy gaps of some superconductors [65].

The proof of the existence of an energy gap leads to the thermodynamic study of superconduc-
tivity in which electrons condense below an energy gap to form a stable state. Besides, to reduce
the energy of the system, the electrons must have an attraction other than the Coulomb repulsion,
which is due to the electron-phonon interaction.

E. Maxwell discovered in 1950 that the critical temperature of the Hg isotope’s T
 had a
relationship with its mass of 

 

 = Constant, revealing the effect of the lattice on electron
behavior in the superconducting state [66]. In 1950 Fr(cid:165)
hlich proposed a physical model: electron-
phonon interactions could couple electrons together as if they were interacting with each other [67].
The presence of a lattice can help shield electrons from Coulomb repulsion, from 
0
2/
2 to


−
/

 ,

1



(1.52)

and from Coulomb forces over long distances to short-range forces of 

 ∼ 10 ˚
, which is the
Debye shielding length.

The model of superconductivity produced by electron-phonon interaction can explain why
superconductors are all bad conductors: for example, the critical temperature of Pb is very high,
so the electron-phonon interaction is very strong, so they are bad conductors at room temperature;
and good conductors such as Cu, Au and Ag at room temperature have very weak electron-phonon
interaction, and there is no superconductivity at very low temperature.

It is assumed that the energy transition of an electron causes the fluctuation of charge density in

42

the conductor to 


, which affects the simple harmonic vibration of the lattice and causes a forced
oscillation. We know that in the process of undamped forced oscillation, only when the frequency
of the forced force is less than the natural frequency, the motion and the forced force can be in
phase, and only in phase can bring attraction. This requires
1)| < 

,

1
|
( 
1) − 
( 
(cid:48)

(1.53)
where 

 is the Debye frequency and is the average frequency of the crystal lattice; 
( 
1) and

( 
(cid:48)

1) are the energy of the electron before and after the transition.
According to Pauli’s incompatibility principle, there are only two electrons with an opposite spin
in each energy state at absolute zero degrees. The distribution of electron state is Fermi distribution,
and Fermi energy E
 is the maximum value of energy. Because the maximum frequency or average
frequency of lattice vibration is far less than E
, only the electronic transition near Fermi surface
can make the formula hold, and the energy difference of electronic transition deep in Fermi surface
is acceptable must be higher than 

.

1 + 
(cid:48)

For the two electrons in this state, if their momentum is 
1 and 
2, the total momentum
before and after the transition should be conserved as 
 = 
1 + 
2 = 
(cid:48)
2, and the respective
momentum after the transition should be about equal to 

, then the two electrons before and
after the transition are limited to the shadow of the intersection of the two spherical shells. When

 = 0, the momentum direction of the two electrons is opposite, and the magnitude is the same, the
volume of the intersecting part of the sphere shell reaches a sharp maximum, then the probability of
the electron transition through the attraction reaches the maximum. Therefore, two electrons with
opposite momentum near the Fermi surface have the strongest attraction. The bound state of the
two electrons is called the Cooper pair. Also, because the Pauli principle forbids the electron with
the same spin being close to each other, Cooper pair requires the opposite spin beside the opposite
momentum near Fermi surface (E
 ± 

 range).

The above is the explanation at 0
. At 
 ࣔ 0
, some states near Fermi surface are occupied
by thermally excited electrons, which affect the formation of Cooper pair, reduce the transition
of electron pair, and gradually weaken the effective attraction. At a specific limit temperature,

43

Table 1.5: 2Ɗ(0)/
 


 value of some superconductors measured by tunnelling method [48].

Superconductor
In
Nb
Pb
Sn

2Ɗ(0)/
 



T

3.41 K 3.63 ± 0.1
9.22 K 3.84 ± 0.06
7.20 K 4.29 ± 0.04
3.72 K 3.46 ± 0.1

the attraction will be reduced to a level that is not enough to shield the Coulomb force, or the
states that a pair of electrons may transition are all occupied by thermally excited electrons, and
the superconducting state disappears. This temperature is the critical temperature, and its size is
related to the attraction strength of electrons at absolute zero. More information can be found in
Ref. [48].

This theory can also explain the isotopic phenomenon: when the lattice ion mass becomes
larger, the frequency of phonon 

 decreases, the number of states of a pair of electrons forming
Cooper pair decreases, the attraction decreases, and the T
 also decreases.


 


 = 1.14

 
−1/
(0)
 ,

(1.54)

is the famous BCS T
 equation [48, 68]. Another essential parameter for superconductor is the
energy gap:

Ɗ =




1

Ò

(0)


≈ 2

 


− 1

(0) 


,

(1.55)

(1.56)

and it has a relation with the critical temperature:

2Ɗ(0) = 3.53
 


.

Both the energy gap and the critical temperature can be measured in experiments, and they agree
with Eq. 1.56.

1.4 The Reason of Choosing Nb

There is much consideration for choosing the material to fabricate superconducting RF cavity.
Among those superconductor materials, Nb is selected for most facilities based on the below
reasons:

44

Table 1.6: H
, H
1, H
2 and Ginzburg–Landau factor 
 value for some superconductors. 
 > 1/√

2
is type II superconductor. The values also depend on material purity. This table is adopting pure
bulk Nb value [48, 69].

Superconductor H
(10−1
) H
1(10−1
) H
2(10−1
)
Nb
Nb3Sn
Sn
In
Pb

1.95
5.4
0.309
0.29
0.80

1.70

2.4
245



0.9
45
0.2

0.3

• Most high-temperature superconductors are ceramic (in the class of copper oxides) that are
hard to do machining. Nb is a single element metal; it is soft to do shaping and easy to
weld. Nb3Sn (18.3 K) with higher T
 is another material well used to fabricate SRF cavity
or magnets. It is extremely brittle, so the manufacturing of the Nb3Sn SRF cavity is adding
a vapor diffusion process to a formed Nb cavity.

• Metal superconductors also have better thermal conductivity than ceramic ones, which is

important for keeping cavity surface on the superconducting state.

• The transition temperature of Nb is relatively high (9.22 K, as shown in Table 1.5) compare
to other superconducting metal. This makes the superconducting state of Nb easy to reach
and keep, which makes the system more reliable and saves cryogenic power.

• Nb has no serious pollution to the environment. Pb with T
 = 7.2 K was also used to product
SRF cavities but was discontinued because it is harmful to human health and environment.

• Nb is Type II superconductor with H
2 = 240 mT (Table 1.6), is relatively high compared to
other conductors, which makes its superconducting state easier to keep. Several additional
surface treatments are necessary to avoid overwhelming heat in the vortex state.

1.5 Superconducting RF

We have discussed some of the analyses about normal conductors in an alternating electro-
magnetic field (Subsec: 1.2.4). In a superconductor, some relations are going to change since the

45

resistance of the conductor becomes zero.

For normal conductors, the Skin Depth 
 is defined as AC fields penetrate thickness where

the current density falls to 1/
 of the surface that 
 = (cid:112)2/
0

. The Surface Impedance


 = (1 − 
)(cid:112)

/2
, and the real part of 

 is the Surface Resistance 

 =(cid:112)

/2
 = 1/

.

For superconductors, the two-fluid model defines the London Penetration Depth 

 as the H

field penetrate to the superconductor and falls to 1/
 of the surface.


2

 =







2
0

,

(1.57)

where 
 and 
 are the mass and the charge of the electron, 

 is the number of superconducting
state electrons (in the two-fluid model), 
0 is the permeability of a vacuum. And the impedance

(cid:114) 


0



 − 




= 

 + 


.



 =

So the surface resistance becomes



 =

1
2




2
2

0
3

,

where 
 is the frequency of the field, and



 =




2





,

(1.58)

(1.59)

(1.60)

is the conductance, 

 is the number of unpaired electrons, 
 is the mean free time.

For BCS theory, we already know that the number of unpaired electrons is proportional to exp(-
Ɗ(0)/k
T) when T < T
, they form the normal current which flows parallel with the supercurrent
that forms from the cooper pairs. This supercurrent carries the whole current due to its zero
resistance. Cooper pairs only get scattered when the energy gain from the lattice vibration or the
electric field exceeds the energy gap 2Ɗ(0). These two conditions lead to the existence of a critical
temperature T
 (thermal lattice vibration limit) as shown in Eq. 1.56 and critical current density J

(electric field limit).

For RF currents, the cooper pairs do not screen the applied field perfectly due to (mass and
momentum) inertia; a time-varying electric field is induced from the time-varying magnetic surface

46

field in the skin layer. The electric field E


 is proportional to dH/dt, which is proportional to 
H,
so that the internal current j


 is proportional to n






H, and we know the P



 ∝ 



 · 



,
so that






 ∝ 







2
2 ∝ exp(−Ɗ(0)


 



Compare with

we can get






 =




2,

1
2



 = 


2exp(−Ɗ(0)


 



).

)
2
2.

(1.61)

(1.62)

(1.63)



 in Eq. 1.63 depends on the material parameters, such as the Fermi velocity v
, the London
Penetration depth 

, the coherence length 
0, the mean free path 
, and the temperature T [45].
Separate the surface resistance by two parts by temperature dependence, we have R
 = 
0 + 




with R0 is the residue resistance, and R


 is the BCS resistance. A simplified expression that fit
experiment well (for T < T
/2, f in GHz, and f« 2Ɗ/h ≈ 1012 Hz) is:
)2exp(−17.67

(1.64)
For superconducting Nb (T
 = 9.2 K), at T = 4.2 K, f = 100 MHz, R


 = 2.5 ×10−9 , R0 = 1
×10−9 , H
(0) = 1.59 ×105 (A/m); while for normal conducting Copper, R
 is ∼ 10−4  [45].





() = 2 × 10−4 1

( 

1.5




).




1.6 Frequency Selection for SRF Cavities

As we shown in Appen. A, the frequency is related to the size of a cavity. For example, for
TM010 mode, a pillbox cavity radius R = 2.405
/(2
 
) (as in Eq. A.47) and length d = 
/(2 
) (as
in Eg. A.48), both equations indicate lower frequency cavities have a larger size, and this makes
the cavities have some properties:

• High diameter aperture is needed for high beam density, and it is only possible when the

cavity size is big enough.

• Large cavities are hard to fabricate or do surface processing; it need more material and more

cooling liquid, which increase the expense.

47

Figure 1.18: Cavity size comparison for different frequencies [70].

• Large cavities have more possibility of defects; the Nb type II superconductor may more

normal conducting core, makes its performance not reliable enough.

2 · (


2
2
0
3

Fig. 1.18 shows a comparison of cavities with different sizes. In the meantime, surface resistance

) (as in Eq. 1.59). This indicates that lower frequency cavities
of SRF cavity is 

 = 1
have lower surface resistance, and this sharply lowers the power usage of the facility and makes the
system more stable. Some study shows that single-crystal Nb cavity has much better performance.
However, the size of a piece of single-crystal is extremely hard to increase, so it can only fabricate
high-frequency cavities. All these parameters need to be considered when selecting the cavity
frequency.

1.7 Cavity Performance Limitation and Solution

Nb is Type II superconductor as introduced in section 1.3.4 and it has normal cores in vortex state
when the magnetic field is between H
1 and H
2. Surface defects, impurities and contamination
could trap the magnetic field and cause extra heating in the normal cores, increase the size of them,
and increase the risk of cavity quench. There are several potential cavity degradation parameters,

48

the corresponding processing and some method that can improve the performance [71]:

• Centrifugal barrel polishing can effectively remove the surface layer that rich in large me-

chanical defects and contamination.

• Chemical Treatment, Electric Polishing (EP) and Buffered Chemical Polishing (BCP), can
give the surface a clean and smooth surface with extra polishing with ∼ 100 
m removals.

• High-Pressure Water Rinsing (HPR) can wash away the acid residue and remove contamina-

tion particles, effectively reduce multipacting and field emission.

• Ultrasonic rinsing in H2O2 can remove sulfur surface contamination from EP acid.

• Post-purification and increase RRR and the thermal conductivity by using Ti gas getter to

absorb oxygen, nitrogen carbon and other contamination elements.
• Low-Temperature Baking (LTB, at 120 ◦C) can diffuse the oxygen to deeper crystal structure
and recover (totally for EP, partially for BCP) High Field Q slope (details in Chap. 2).

1.8 EP & BCP

As we mentioned earlier, surface processing is necessary to obtain a good RF surface. About 100
microns thick chemically etching (polishing) is a common step. This can remove the mechanically
damaged layer or contamination [71].

Two kinds of chemical polishing are frequently used: Electric Polishing (EP) and Buffered
Chemical Polishing (BCP). EP applies positive electrode to Nb metal cavity (anode) and adding
a cathode made of aluminum, filled cavity half full with a mixed solution of sulfuric acid and
hydrofluoric acid with a volume ratio of 1: 10, with a chemical equation

2 Nb + 10 HF + 5 H2SO4

e−−−−→ 2 NbF5 + 10 H2O + 5 SO2 ↑ .

(1.65)

EP originally performed vertically, and it encountered difficulties that the roughness of Nb
surface is high. After a while, Saito invented horizontal EP with an optimized current density

49

Figure 1.19: EP mechanism: current concentrates on the peaks and lead to more reaction on the
peak area; this reduces the height difference between peak and valley, thus reduces the roughness
of Nb surface [72].

Figure 1.20: EP equipment Single-cell cavity setup at KEK [72].

50

Figure 1.21: An example of a BCP system for a large cavity: acid is filled in and pumped out of the
cavity by the pipe, then ultra-pure water is filled in to wash away the acid. Cooling water is spilled
on the outside of the cavity [71].

50 mA/cm2 at 25 V, 30 ◦C with a rotation speed of 0.4 to 1 rpm. This EP generates a smooth
mirror-like finishing surface because the current concentrate more at peaks than bottoms lead to
more reaction of the peak area, and reduce the height difference and thus reduce high roughness.
The schematic diagram is shown in Fig. 1.19, and one example is shown in Fig. 1.20.

While BCP is directly etching with nitric acid, hydrofluoric acid and phosphoric acid solution
with a volume ratio of, 1: 1: X (where X is the number between 1 and 4 that regulates the rate of
reaction), and the chemical equation for BCP is:

2 Nb + 10 HF + 2 HNO3 −−−→ 2 NbF5 + 2 NO2 ↑ + 6 H2O.

(1.66)

There are two ways of etching Nb parts with BCP: one is directly immersing them completely in
the acid bath, this is very easy to apply and will etch the outside a bit which could consume some
Nb and lead to less than requirement thickness. The other way is filling the acid to the large Nb

51

structures (cavities) and cool the acid by cooling the outside of the cavity using cold water. The
acid is pumped into the cavity and then drain out, then the system switches to ultra-pure water to
rinse the cavity inside. In this case, the system is more complicated but safer, consuming less acid,
and waste less Nb. Fig. 1.21 shows a system for Nb cavity etching.

EP is popular for simple shape cavities with high 
; while BCP is cheap and easy to apply, and

is popular for complicated shape cavities with low 
.

52

CHAPTER 2

HIGH FIELD Q SLOPE

This chapter shows overviews of High Fields Q-Slope (HFQS) issue for buffered chemical polished
(BCP) SRF niobium cavities, which is remained unresolved for 20 years. The main goal of this
thesis is to discover the cause of the HFQS and develop the cure. Here, we will discover the cause
of HFQS by mining past many efforts.

2.1 Discovery of HFQS

High Field Q slope (HFQS) is a phenomenon where Q0 (unloaded Q) performance of the SRF
cavity begins to exponentially drop with increasing gradient around 15 - 25 MV/m (ILC cavities)
due to heating at RF high magnetic field region (equator area) on the SRF surface [73, 74], and
it finally limits the acceleration gradient to around 30 MV/m. It happens to all cavities that adopt
EP or BCP as a surface processing method. HFQS severely degrades the SRF cavity high gradient
performance, thus limiting the final energy of the accelerated particles.

This problem was later neglected after the international linear collider (ILC) chose EP as the
baseline surface preparation technology, which was developed in 1985 for KEK TRISTAN 508
MHz 5-cell SRF cavities [72], because EP’ed cavities can completely recover from HFQS via 120
◦C bake for 48 hours [73]. Fig. 2.1 shows the Q0 vs E


 (accelerating gradient) of an EP’ed cavity
before and after the Low-Temperature Baking (LTB). However, BCP’ed cavities still suffer from
HFQS even after the LTB (see Fig. 2.2).

FRIB is an example of a heavy-ion accelerator project whose cavities suffer from HFQS. All
FRIB cavities are treated with BCP. Statistically, the performance of ∼ 35% of the cavities at FRIB
is limited by pure HFQS (HFQS without X-rays) [76]. An example is shown in Fig. 2.5, the FRIB
cavities experience Q0 drop starting from B
 ∼ 85 mT in 
 = 0.041 Quarter Wave Resonators
(QWRs).

53

Figure 2.1: An example of High Field Q (HFQS) on EP Nb cavities, before and after baking. HFQS
started at 28 MV/m for this cavity. [73]

Figure 2.2: HFQS on BCP Nb cavities, before and after baking. (Courtesy of CEA-Saclay) [74]

54

Figure 2.3: Variation of the surface roughness by EP for fine-grain Nb. [75]

Figure 2.4: Variation of the surface roughness by BCP for fine-grain Nb. [75]

55

Figure 2.5: FRIB cavity performance at 2 K in Vertical Test, 
 = 0.041 QWRs, B
/E


 = 10.71
mT/(MV/m)

2.2 Low T Baking and the Role of Oxygen

There is an interesting history behind the LTB for EP’ed cavities. The superiority of EP over
BCP with high gradient performance was discovered in 1996 at KEK [77]. They called the high
field limitation with BCP’ed cavities as “European headache” (nowadays called HFQS) because
European and US SRF institutes were mainly using BCP and having this problem.

KEK’s preparation recipe included the LTB post EP. Its purpose was to improve high vacuum
quality to evaporate absorbed water on the SRF surface. They did not yet recognize the critical role
of LTB for the high gradient cavity performance at that time. KEK transferred their EP method to
DESY in 1998, but the first EP’ed cavity at DESY suffered from HFQS. They revisited the KEK
recipe and noticed they were missing the baking process. They applied the baking process and
finally got high gradient cavity performance [78]. Since then, a very intensive study started to
understand the HFQS in many SRF institutes in the world.

Among those studies, researches on niobium samples indicate that baking at progressively
higher temperatures causes a conversion of the external Nb2O5 layer to metallic sub-oxides NbO,

56

NbO2 and an overall reduction of the oxide layer thickness. This oxygen diffusion theory shows
strong evidence because the diffusion effect matches the cavity performance [74, 79–81]:

1. At the effective baking temperature 80 - 120 ◦C, only oxygen and hydrogen sufficiently diffuse

dipper to London Penetration Depth (
 ∼ 40 nm) [79].

2. The LTB benefit increases and saturates at a certain limit at less than 200 ◦C, while hydrogen

diffuse enough on a much lower temperature (less than 100 ◦C).

3. The saturation of cavity improvement matches the oxygen diffusion reaching the maximum,

where the diffusion distance x reaches more than the London Penetration Depth.

4. According to oxygen diffusion simulation, 145 ◦C for 3 hours has similar diffusion depth to
110 ◦C for 60 hours, while the baking effect for these two conditions is also similar [80, 82].

Halbritter proposed a Taylor series of the surface resistance that obtained from the Ginzburg-

Landau theory [83]:



 = 

0[1 + 
(




/

)2 + 
(
4





)]
Where 

0 (equals to 



 + 



) and 
 are fitting parameters, and
0 )(
/
 + 

),


 = 



(
0)
2


Ɗ/(2

2

(2.1)

(2.2)

where 
 is the thermal conductivity, R
 is the Kapitza resistance, d is the wall thickness, T0 is the
helium bath temperature, and B
 is the critical field B
(0) ∼ 200 mT. He explains the medium filed
Q slope using this equation: the helium bath influences the heating of the inner surface of the cavity
due to low thermal conductivity and Kapitza resistance of niobium. 

 
 ∼ 6 - 20 W/(m·K) for
different purity niobium samples [84], the Kapitza resistance between Nb and helium is 1.25×10−4
(m2K)/W. For Nb2O5, the thermal conductivity is 1 - 2 W/(m·K) [85], only 10% of the Nb metal
and the Kapitza resistance is 0.05 (m2K)/W [86].

57

2.3 Others’ Study

There exists a lot of other models for the HFQS: thermal feedback [87], Oxygen contamination
[74, 79–81], field enhancement at grain-boundary steps (or macro surface roughness, in this thesis
we are mostly talking about this roughness) [88], field enhancement induced by surface roughness in
the grain (or micro surface roughness) [89], interface tunneling exchange [90], Hydrogen trapping
[91], and flux trapping [92]. A good summary is shown in the reference [93]. Among these models,
the Oxygen contamination model can sufficiently explain HFQS in the LTB effect with EP’ed
cavities [74]; however, it cannot explain why LTB fails to remove the HFQS for BCP’ed cavities.
An entirely consistent model of HFQS with BCP’ed cavities does not exist even now. Recently,
a new model based on Josephson Effect that weak superconducting cores increase exponentially
with the field that generates the exponential power loss thus induces HFQS is built by K. Saito [94]
which will not be discussed in this thesis.

As mentioned above, in the early 2000s HFQS studies with BCP’ed cavities were mostly for
fine-grain niobium cavities. Discussion of the results focuses around the topography of niobium
surface treated by BCP, as a natural consequence of the effects of surface roughness (Rtm, the
height difference between the third-highest peak to the third-lowest minimum), grain-boundaries,
defect and dislocation were the main concerns. Fig. 2.3 and 2.4 show the polishing characteristics
of EP and BCP respectively [75]. EP makes the surface smoother exponentially with increased
material removal.
In contrast, BCP makes the surface smooth in the early stage but gradually
rougher with increased material removal due to the preferential etching at grain-boundary areas,
and the roughness saturates around 3 - 5 
m depending on the grain size of the niobium material.
The experiments in the early 2000s established the following facts:

1. The LTB does not sufficiently improve BCP’ed cavity HFQS, the Q-drop is somehow miti-

gated, but the gradient limit sees little improvement (Fig. 2.2).

2. Sometimes the Q-drop is eliminated by the LTB, but the field limitation still does not change,

unlike EP, especially in large-grain or single-crystal cavities.

58

Figure 2.6: Q vs E results for 6 different polishing treatments, all cavities are tested after HPR and
baking in KEK. [71]

3. BCP after EP lowers the onset field of the HFQS. Successive BCP makes the HFQS (Fig. 2.6)

worse.

4. The degraded HFQS is entirely recovered by EP plus LTB with a rather heavy material
removal (150 
m, see Fig. 2.6). The RF field enhancement might explain the degradation of
BCP HFQS on the rougher surface.

These experimental facts seem to support the field enhanced model on the rough surface [89]
or grain-boundary steps [88]. However, more detailed analysis does not support these models for
BCP HFQS as shown below.

2.4 Our Analysis

2.4.1 Reanalysis of Multiple BCP Post EP with Fine-grain Cavity

The cavity inner surface roughness in the experiments of Fig. 2.6 can be estimated from the surface
polishing characteristics in Fig. 2.3 and 2.4. Table 2.1 shows the results. The calculation assumed

59

Figure 2.7: Roughness vs E


,


 results for 6 steps of the polishing treatment (each with HPR
and baking) in KEK multiple EP and BCP experiment. Each result is marked with the respective
number in Fig. 2.6. The roughness information is from Table 2.1. [71]

Table 2.1: Estimation of roughness during KEK multiple EP and BCP process.

Rtm (
m) Uncertainty (
m)

Process
Baseline
+ EP 50 
m + baking
+ EP 70 
m + baking
+ BCP 60 
m + baking
+ BCP 70 
m + baking
+ EP 100 
m + baking
+ EP 50 
m + baking

3.50
0.82
0.57
3.49
4.43
0.70
0.65

0.50
0.06
0.04
0.31
0.46
0.07
0.05

60

initial surface roughness is 3.5 
m. Fig. 2.7 also shows the surface roughness vs. the limiting field
in the experiment. It has a hysteresis: the EP 100 
m at step 5 should improve the roughness to less
than 1 
m for most assumptions of the initial roughness, which is enough to reach a high gradient
> 30 MV/m but in reality, the gradient is still limited < 30 MV/m. It is apparent that from step 4 to
5, the roughness improves a lot by EP, while the maximum field does not improve so much; from
step 5 to 6, the roughness does not change much while the maximum gradient increases from 26
MV/m to about 36 MV/m. This fact suggests there is something in addition to surface roughness
that is causing BCP’ed cavity HQFS.

When getting a little ahead, the improvement from step 5 to step 6 can be explained if the cause
of HFQS is nitrogen contamination by the nitric acid in the BCP acid, as will be shown later in
detail. The contamination was accumulating (primarily through grain-boundaries) during multiple
BCP, and 100 
m EP in step 5 is not enough to remove them all.

2.4.2 HFQS of BCP’ed Large-grain Cavity

BCP has preferential etching on grain-boundary steps. During the BCP process, surface inside
the grain is getting smoother while the gain boundary step difference is getting larger. The grain
size of fine-grain cavities is ∼ 50 
m [95]. Surface roughness is usually measured by a needle
scanning a 0.8 mm width, so the measured surface roughness with fine-grain Nb materials combines
topography in the grain and on grain-boundary step.

To date, large-grain niobium sheets are available by directly slicing large-grain Nb ingot. The
grain size is on several cm scales. The measured BCP finishing surface roughness is ∼ 0.1 
m, it is
very smooth (lower than EP ∼ 0.5 
m) and even mirror-like. Measurements of large-grain surface
roughness count the roughness in the grain only, because the grain size is beyond measurement
range.

Considering the BCP polishing property, the smoothness of large-grain niobium is because

there are much fewer grain-boundaries, while the roughness in the grain doesn’t change much.

Fig. 2.8 shows a comparison of the cavity performance between BCP fine-grain and large-grain

61

Figure 2.8: Comparison of quality factor behaviors at high gradients between the Large-grain (LG)
and Fine-grain (FG) cavities by BCP with baking. [96]

cavities [96]. The onset of BCP HFQS is pushed up to > 40 MV/m, higher than that of fine-grain
cavities. This is a rare case with BCP’ed large-grain cavity, even large-grain cavities mostly the
gradient is limited lower than 40 MV/m with flat Q0 (see Fig. 2.9). The gradient is limited by flat
Q is different from fine-grain cavities. The fine-grain cavity is limited Q-drop, as seen in Fig. 2.8.
This experiment shows less grain-boundary steps give much better performance, or more grain-
boundary steps give a worse performance, thus indicating the grain-boundary is firstly responsible
for the BCP HQFS. The surface roughness in the grain (micro-roughness) is ruled out as a cause
of BCP HFQS by this experimental result.

2.4.3 BCP after EP with Large-grain Cavity

DESY investigated the BCP impact post EP for large-grain cavity [97]. Fig. 2.9 shows the result.
BCP (50 
m removal) degrades the high gradient performance remarkably and is similar to the
BCP fine-grain cavities. In the Fig. 2.8, the LBT post-BCP could perfectly eliminate the HFQS.
So we emphasized the first responsibility of the HFQS with BCP’ed cavities could be in grain-

62

Figure 2.9: Q vs E of DESY large-grain TESLA (ILC shape, B
/E


 = 4.26 mT/[MV/m]) cavity
treated with EP and an additional 50 
m of BCP. Both results are after baking. (Courtesy of DESY
& JLab) [97]

boundaries. One will notice in Fig. 2.9 that the behavior of the field limitation is changed from a
remarkable exponential Q-drop (HFQS) to the rather shape quench. The result in Fig. 2.9 suggests
that the problem is still on the grain-boundaries but has less impact on the exponential Q-drop in
the large-grain niobium material, or other issues within the crystalline in the large-grain material
such as dislocation.

2.4.4 Multiple BCP with Large-grain Cavity

KEK investigated the impact of successive BCP on large-grain cavity [98]. A 1.3 GHz Ichiro shape
cavity was mechanically polished inside (∼ 80
m by the centrifugal barrel polishing (CBP) to
smooth the grain-boundary steps). Note that Ichiro cavity shape has a smaller B
/E


 ratio (3.56
mT/[MV/m]) compared to the ILC shape (B
/E


 = 4.26 mT/[MV/m]). After 750 



C hydrogen
degas annealing for 3 hrs, a bulk etching of 160 
m took place using vertical BCP (V-BCP, BCP
in the vertical position with a cavity, conventional BCP in most institutes). The tight loop test took

63

place in total five times removing 30 
m each time by V-BCP (first cycle). In these tests, the LTB
is applied post-V-BCP for all measurements. The result is shown in Fig. 2.10. The decreasing
of E


 onset of HFQS is observed with increased V-BCP material removal. This result clearly
shows that the cause of HFQS is getting more serious with increased material removal by BCP. Two
potential causes are considered: 1) the grain-boundaries are still a problem, even for the large-grain
material; 2) accumulation of contamination. For potential cause 1), resetting the surface roughness
by mechanical grinding might be a useful way.

In the second cycle, the surface topography was reset by CBP, then the tight loop test was
repeated by H-BCP. The original experimental goal was to validate that the H-BCP (BCP in the
horizontal position with cavity) performance is better than normal V-BCP due to more uniform
material removal. Again the degradation of onset HFQS happened for each extra 30 
m BCP, the
average of the E


 onset of HFQS (red line) increased compared to the 1st cycle (pink line), but
E


,


 average (dark blue line) is lower than the 1st cycle (blue line). The conclusion from these
results is that resetting surface roughness does not work to improve the HFQS for E


,


, which
suggests lowering the (macro) surface roughness does not sufficiently increase the BCP maximum
gradient.

Temperature map result for a large-grain cavity also shows that there is no preferential heating
on the grain-boundary area [99], where the high roughness region is mainly located. The before
and after baking temperature map shows the reducing of the heating area is not located in the
grain-boundary area, either (Fig. 2.11). The Q Vs 



 result for before and after-LTB is shown in
Fig. 2.12, where the Q improvement is from the LTB.

2.4.5 BCP with Single-crystal Cavity

single-crystal cavity can completely rule out concern of the topographic issue with BCP HFQS,
which has no grain-boundaries and can attain 0.1 
m scale very smooth surface even by BCP. To
date, single-crystal niobium sheets are available via directly slicing the ingot with very large-grain
at 15 - 30 cm scale. Cavities half cups are assembled by electron beam welding (EBW); however, it

64

Figure 2.10: KEK 



 vs Increasing BCP amount results, first round and second round. All
results were taken after LTB.

Figure 2.11: Temperature map for a cavity before LTB at 110 mT (left) and after 100 ◦C baking at
130 mT. No. 10 correspons to the thermometer located around equator. [99]

65

Figure 2.12: Q Vs 



 for the cavity that shown temperature map in Fig. 2.11. [99]

does not produce any grains if the crystal orientation is arranged with the two half cups [94]. So we
can fabricate the entire interior cavity surface with a single-crystal. P. Kneisel fabricated a 2.2 GHz
single-crystal Low Loss-ILC shape cavity cutting out single-crystal sheets from the large gain ingot
(CBMM material), treated it with BCP plus baking and investigated the performance [100]. The
result is shown in Fig. 2.13 red curve. We found that combining BCP and LTB for single-crystal
cavity, the HFQS disappeared like standard EP cavities, while the maximum gradient is still below
the fundamental limit. The LTB eliminates the HFQS, but field gradient still limited ∼ 45 MV/m
(160 mT) and did not reach the fundamental field limit (∼ 180 mT), unlike EP’ed cavities. The
limitation behavior is changed from the exponential Q-drop to a sharp quench. Originally HFQS
was defined by exponential Q-drop behavior. However, here we regard as that the sharp quench also
produced by the same cause as the HFQS. Above the result with 2.2 GHz single-crystalline cavity.
This fact provides direct evidence to rule out the topography as a major cause of BCP HFQS.

A nearly single-crystal 1.5 GHz High Gradient shape cavity shows a similar conclusion. This
cavity was fabricated with an Nb ingot that has a ∼ 20 cm diameter grain in the center and several

66

Figure 2.13: Q vs E of the 1.5 GHz High Gradient (HG, blue curve, B
/E


 is 4.47 mT/(MV/m))
shape and 2.2 GHz Low Loss-ILC (LL-ILC, red curve, B
/E


 is 3.56 mT/(MV/m)) shape single-
crystal (SC) Cavities treated by BCP. Both results are after baking.
(Courtesy of JLab) [100,
101]

small grains ∼ 1 cm. It is treated with BCP plus LTB , with a very smooth surface on most of the
cavity. The field limit is 143 mT, as shown in Fig. 2.13 blue curve.

This evidence shows that even the limitation behavior changed, BCP cannot reach the fun-
damental field limit like EP and suggests there is still something else limiting the gradient in
BCP.

The same experiment took place for 1.3 GHz ILC type single-cell cavity fabricated at DESY
[102]. Heraeus produced the single-crystal sheets. Fig. 2.14 blue curve shows the result of BCP
(112 
m and 120 ◦C bake for 6 hours). Q curve is very flat up to the gradient limit. The gradient
is limited by 37.5 MV/m (∼ 160 mT) which is close but still below the fundamental limit 180 mT.
One crucial fact is that this performance is worse than the DESY large-grain TESLA (ILC
shape) cavity treated with EP in Fig. 2.9, which has a maximum gradient of 40.5 MV/m (∼ 173
mT). This goes against the common understanding: single-crystal cavity, even treated with BCP,
has a very smooth surface and better thermal conductivity, so it should have better performance than

67

Figure 2.14: Q vs E DESY single-crystal TESLA (ILC shape, B
/E


 = 4.26 mT/[MV/m]) cavities
treated with BCP: before post-purification [102] in blue curve; after post-purification in red curve.
Both results are after baking. (Courtesy of DESY & JLab) [103]

Table 2.2: Main differences between EP & BCP

R
 (
m)

Grain-boundary
Prefer Etching
Contamination H, F, O, C, S H, F, O, C, N, P

Yes

BCP

2

EP
0.5

No

large-grain cavity. This indicates the surface roughness itself cannot explain all the performance
degradation.

Post-purification was also tested for this cavity. The result is shown in Fig. 2.14 red curve.
After the post-purification, the cavity was BCP’ed and took 120 ◦C bake for 12 hrs. This process
does not improve the field limit. The performance failed to improve even with reduced stress or
improved dislocation on the SRF surface by post-purification. This also suggests that BCP still
contains other issues.

68

2.4.6 EP & BCP Difference

By the above data mining, we can conclude that the topographic character of the SRF surface
produced by the BCP polishing feature is not the only cause of the HFQS with BCP’ed cavities.
Therefore, we need to look for other causes.

This chapter focuses on finding why BCP cannot get enough improvement as EP from LTB, so
we may only focus on the differences between those two methods. As shown in Table 2.2, EP and
BCP difference: roughness (discussed before and ruled out) and potential contamination (H, O, C,
and S for EP; H, O, C, N and P for BCP). F from HF is proved not harmful for cavity performance,
and P in phosphoric acid has never been reported to react with Nb. Then the only contamination
difference is N and S. S problems in EP were discussed in several papers and solved; therefore, N
becomes the only potential contamination that causes worse performance in BCP. It is well known
that nitrogen reacts with Niobium and generates niobium nitride.

2.4.7 Nitrogen Diffusion Calculation for the Same Condition with LTB

Fick’s second law predicts how diffusion causes the concentration to change with time.
partial differential equation which is one dimension reads:

It is a









2



2

,

= 


(2.3)
c is the concentration in dimensions (example: in 


/
3), 
 = 
(
, 
) is a function that depends
on location x and time t [104]. A simple case of diffusion with time t in one dimension (taken as
the x-axis) from a boundary located at position x = 0, where the concentration is maintained at a
value 
0 is


(
, 
) = 
0erfc( 


),




(2.4)

where erfc is the complementary error function, r is the Diffusion Distance and defined as r =
√
2



, D is the diffusion coefficient (or Diffusivity) in dimensions ( example 
2/
) define as:


 = 
0exp(− 



 



),

69

(2.5)

Table 2.3: Diffusion parameters for the interstitial elements N and O in Nb [105].

Interstitial Temperature Frequency Factor Atomic Activation
Element
Energy E
 (eV)
Oxygen

Range (◦C)
40 - 150

150

150 - 300

Nitrogen

Carbon

130 - 280

300

150

D0 (cm2/s)
2.0 × 10−2
1.5 × 10−2
8.6 × 10−3
9.8 × 10−2
4.0 × 10−3
1.5 × 10−2

3.0 × 10−21 - 2.3 × 10−16
8.9 × 10−21 - 4.5 × 10−16
5.3 × 10−21 - 3.7 × 10−16

Diffusivity
D (cm2/s)
7.7 × 10−17
3.0 × 10−16
3.0 × 10−16

1.17
1.20
1.51
1.65
1.43
1.15

where 
 
 = 8.6173324× 10−5

/
 is the Boltzmann’s constant, T is the absolute temperature, 


is the atomic activation energy, 
0 is the frequency factor, these parameters are shown in Table 2.3,
the Diffusivity are calculated from Eq. 2.5 with the corresponding temperature shown in the same
table.

At 150 ◦C, D
 is 7.7 × 10−17 and D
 is 8.9 × 10−21, so if the diffusion time t is 40 hours,
the Diffusion Distance for oxygen is 66 nm, while for nitrogen the Diffusion Distance is only 0.71
nm. This means during the LTB process oxygen diffuse to the distance similar/longer than the
London Penetration Depth while nitrogen still stays on the surface. This agrees with our nitrogen
contamination induce HFQS assumption that low-temperature baking can fully recover the EP
cavities, but only partially improve BCP cavity performance because nitrogen contamination still
exists on the RF surface.

Our diffusion case is more close to a“thin-film” problem that the thin film is initially located at

x = 0:


(
, 
) =


√





−
2/
2

,

(2.6)

where N is the number of “source” atoms per unit area initially placed at x = 0, r is the Diffusion
Distance, same as in Eq.2.4.

2.4.8 Nitrogen Contamination

Our first attention to the nitrogen contamination was the gas exposure test on the fresh SRF surface
just after the vertical test, without vacuum break before the gas exposure [106]. We found that Argon

70

Figure 2.15: A comparison of diffusion concentration for nitrogen (left) and oxygen (right) on
niobium surface ( with different x-axis scale), calculated from Eq. 2.6 with t = 40 hrs and T = 150
◦C.

gas usually exposure has no performance degradation, but pure nitrogen gas exposure produces a
remarkable Q degradation, as shown in Fig. 2.16. In this case, the low temperature (70 ◦C) bake
even lower than 120 ◦C seems an effective cure. We also notice that a similar experiment shows
the opposite result: exposing Nb cavity to Nitrogen gas for three days has no degradation observed
in their case [107].

Our hypothesis that nitrogen contamination produces the HFQS is first corroborated by the
experimental results summarized in Fig. 2.17. This experiment was originally done for the de-
velopment of hydrogen-free EP [108]. Adding nitric acid (HNO3) of (61% w/w) 1500 ppm into
the EP acid (48% HF: 93% H2SO4 = 1: 10 V/V) was very effective to prevent hydrogen doping
during EP. However, unlike the normal EP case, the HFQS still exists even after baking. The only
difference between these two processes (normal EP and new EP used EP acid added HNO3) is the
small amount of the nitric acid so that we think the N contamination gives this degrading of the
cavity field limit.

The second decisive evidence is in the recent nitrogen doping study. FNAL has successfully
developed the nitrogen doping method to increase Q of SRF Nb cavities [109]. They put nitrogen

71

0.00.51.01.52.0x (nm)0.00.20.40.60.81.0ConcentrationDiffusion of N050100150200x (nm)0.00.20.40.60.81.0Diffusion of Ogas into the vacuum furnace at 800 - 900 ◦C vacuum annealing to contaminate the surface. They
proved that only the interstitial nitrogen in the niobium contributes to enhancing the Q because it
shortens the mean free path. During the doping process, niobium-nitride metal phase (Nb
N
) is
also generated on the top surface. This has to be removed by several microns of electropolishing;
otherwise remarkable field limit happens. Later, low temperature (∼ 120◦C) nitrogen infusion was
developed [110]. The cavities treated with this method have a much higher maximum gradient;
in the meantime, niobium nitride does not exist. This further indicates nitrogen contamination
(especially niobium nitride) lowers the gradient.

Thirdly, KEK experiment with stepwise BCP and reset (Fig. 2.10) indicates that, if the HFQS is
attributed to N contamination, the CBP before second experiment cycle only resets the roughness but
does not remove all the contamination, or BCP after CBP already produced deeper N contamination,
and this explains the degradation of the reachable gradient.

Finally, the KEK experiment with multiple EP followed by BCP and then more EP (Fig. 2.6)
also agree with this assumption. After the step 5, 100 
m EP removal for Nb is sufficient for recover
the roughness to less than 1 
m; however, it is not enough to remove the contamination in the deep
site, so the maximum gradient is limited to only ∼ 26 MV/m.

While after step 6, even though the roughness does not change much, it removes 50 
m more
Nb, which contains most N contamination. Therefore, the E


,


 increased a lot and is close to
the original result, ∼ 37 MV/m.

2.4.9 Generation of Nitrogen Contamination and observation
During nitrogen doping, Nb
N
 starts to generate at temperature ∼ 400 ◦C ([112], is 673 K,
corresponds to 0.058 eV). Nb
N
, which has a very low thermal conductivity (1/10 of Nb at low
temperature), is harmful to cavity performance and could be the reason for low E


 and HFQS.
While the low temperature (120 ◦C) infusion does not form Nb
N
 so this can produce high
gradient and high Q cavity performance [109].

We can then assume that if Nb
N
 can be generated on Nb surface on BCP, it can cause HFQS.

72

Figure 2.16: KEK cavity performance degradation with nitrogen exposure [106]

Figure 2.17: Q vs E for KEK fine-grain Type A cavity, blue cross curve is an example for normal
EP cavity performance [77], red circle curve is the cavity dealer with EP plus one drop of nitric
acid [111]. Both cavities was applied baking after EP.

73

Figure 2.18: Reaction speed vs 1/T for different BCP ratio. [113]

The reaction energy of BCP is estimated by measuring the temperature dependence of the polishing
rate [113]. The result is shown in Fig. 2.18. The results are well fit by the Arrhenius equation:


(
) = 
0exp(− 


 



)

(2.7)

The constant value of 2695.2 for the BCP acid composition HF: HNO3: H3PO4 = 1: 1: 1 (V/V)
corresponds to 0.232 eV (∼ 2419 ◦C). Nb
N
 can form (but with very low probability reaction)
by the nitric acid reacting with niobium in such energy. JLAB has observed nitrogen by SIMS
on BCP’ed niobium sample [114]. Nitrogen element mostly stays on the surface 0.05 
m. On
the other hand, FNAL showed that interstitial nitrogen and Nb
N
 phase lie at different depths on
niobium top surface. Nb
N
 mostly resides on the surface within 2 
m [115]. These indicate the
niobium contamination on Nb top surface by BCP is in Nb
N
 phase.

We discussed in Eq. 2.1 and Eq. 2.2 that the low thermal conductivity could cause 

 increasing,
where the 
Nb2O5 ∼ 1 W/(m·K) and the Kapitza resistance between Nb and Nb2O5 is 0.05 (m2K)/W.
For niobium nitride, 
NbxNy ∼ 1 W/(m·K) and the Kapitza resistance between Nb and NbxNy is

74

0.9 ×10−5 (m2K)/W [116].

2.5 Conclusion

HFQS with BCP’ed cavities is not perfectly removed by the LTB, unlike EP’ed cavities. There
is no common consensus on the mechanism of the HFQS in BCP’ed cavities to date. We mined
past data on fine-grain, large-grain and single-crystal cavities to show inconsistencies in previous
explanations, and developed a new model for the root cause of the BCP HFQS. This model says
that the nitrogen contamination, especially niobium–nitride phase (Nb
N
) is the remain cause
of the HFQS BCP’ed cavities. The niobium-nitride phase is generated by the reaction between
niobium and the nitrogen from the decomposed nitric acid in the BCP reaction. Nitrogen in
niobium-nitride phase does not move by the LTB; thus, the HFQS is not recovered by the LTB.
Not only does the nitrogen contamination model agree with all experimental data sets, it also
offers coherent explanations for previously unresolved phenomena in circumstances including: (1)
applying multiple BCP post EP (Fig. 2.6 and Fig. 2.7); (2) adding HNO3 to EP (Fig. 2.17); and (3)
maximum field of BCP single-crystal cavities ( Fig. 2.13 and Fig. 2.14) lower than EP large-grain
cavity ( Fig. 2.9 ). These results provide evidence for our model and inspire us to develop a new
acid that can solve this HFQS problem.

75

CHAPTER 3

NEW ACID: ACID DEVELOPMENT

In our previous data analysis in the last chapter, we concluded that the potential root cause could
be nitrogen contamination on the surface. The nitric contamination could be created by nitric acid
during BCP which uses the mixture of hydrofluoric acid (HF), nitric acid (HNO3), and phosphoric
acid (H3PO4). Based on this thought, we started to develop a new chemical polishing acid that
replaces the nitric acid by another N-free oxidizer, such as hydrogen peroxide.

3.1 Acid Component

As we introduced in chapter 1, general idea and mechanism of chemistry polishing (non-
electrical and electrical) is to continuously oxidize the metal and remove the oxide layer by HF, to
refresh the metal surface. So we need to choose a strong enough oxidizer, and oxide layer remover.
We then try to find a replacement acid, which should be consist of both of these functions.

3.1.1 Oxide Layer Remover

HF is a weak acid but can dissolve niobium oxide very effectively, and there are only two component
elements. The acid strength refers to the tendency of an acid, symbolized by the chemical formula
HA, to dissociate into a proton, H+, and an anion, A−. The dissociation of a strong acid in solution
is effectively complete, except in its most concentrated solutions. There is no motive to replace the
HF, so we only change the oxidizer HNO3 in the conventional acid.

The reaction of HF with Niobium oxide is

Nb2O5 + 10 HF −−−→ 2 NbF5 + 5 H2O.

(3.1)

76

Table 3.1: Oxidization power comparison for some normal oxidizer

Standard electrode potential (V)

Diluted HNO3

0.9, 1.1 when heated

0.17
0.341
0.52
0.77
0.8

0.96
0.983
1.1
1.23
1.358
1.47
1.5
1.691
1.692
1.776
1.98
2.076
2.694
2.866

Potential Range

E < 0.77V

0.77 V < E < 1.23 V

1.23 V < E < 1.83 V

E > 1.83 V

Diluted H2SO4

Oxidizer
Cu2+
Cu+
Fe3+
Ag+
H2SO4

HNO2
HNO3
O2
Cl2
HClO3
Au3+
Pb4+
Au+
H2O2
Ag2+
O3
O
F2

3.1.2 Oxidizer Choosing

Table 3.1 shows some normal oxidizer and their standard electrode potential, which indicate their
oxidization power. H2SO4 is used in EP acid, which needs to add electrodes to make the reaction
happen; thus, we need an oxidizer stronger than that (0.9 V). Table 3.1 shows the HNO3 has a
standard electrode potential of 1.1 V, so the new acid should have similar or higher value than that.
Based on our previous analysis conclusion Chap. 2, the new acid should have no nitrogen
element, and it better be no introducing other potential contamination elements, so H2O2 with the
standard electrode potential equals to 1.776 V, should be the best choice. It is a strong oxidizer
that consists of simple elements, with low price and no pollution to the environment after waste
acid treatment. We decide to choose H2O2 mixing with HF as the promising new etching acid for
niobium cavity. This kind of acid mixture is already utilized for the treatment of engine parts made
of iron in the automotive industries.

77

3.1.3 Record on This Acid

We found two studies with this acid mixture. One was in the early 1980s to resolve the issue in
wastewater treatment in the conventional BCP acid [117] because HNO3 has an issue with the
wastewater treatment. This mixture of HF and H2O2 was unstable, and the resultant polished
surface was not smooth. They concluded it was due to the higher water content. This acid was not
applied.

The second one was to improve the BCP’ed cavity performance [118] at the end of the 1990s
at Saclay, France. They attempted to find an alternative chemical treatment of the conventional
BCP, precisely similar to our study, but they had no conscious about the nitrogen contamination
with niobium in their study. A various mixture of HF (5 - 15 mol/L) and H2O2 (2.5 - 5 mol/L) was
applied to niobium samples. However, the surface was always degraded by severe grain-boundary
etching and resulted in significant roughness (mean peak-to-valleys > 50 
m). They did not give
an explanation of the mechanism for this rough finishing surface. They gave up to persuade the
optimization of this acid. We did not know their experimental results until we started new acid
development. This was a fortune for us. If we know earlier, we would not have tried this kind
of acid. Later, one will see the difficulty that we also meet, but finally, we have discovered the
resolution with this new acid as seen in the Chap. 4.

3.2 Experiments

3.2.1 General Experimental Setup
Before the experiments, niobium samples were cut to 50 mm × 15 mm × 4 mm and were mechan-
ically polished by emery paper to adjust the initial surface roughness. The surface roughness after
etching was measured at no fewer than 5 points near the initial measurement points, and the results
were averaged. The standard deviation was used to construct the error bar.

To maintain consistency with previous published data sets of superconducting Nb surface, we

78

Figure 3.1: R
1, R
2, R
3, R
4 and R
5 are the distances from the mean line (m) to highest 5
peaks in the range of sampled reference length, R
1, R
2, R
3, R
4 and R
5 are the distances from
the mean line (m) to lowest 5 valleys in the range of sampled reference length.

Table 3.2: Preliminary Recipe

RRR of Nb

300

45 ◦C

Initial Temperature H2O2% H2O2 (mL) HF % HF (mL)

35

45

50

10

take 
z as a measure of surface roughness defined by:

5



=1



 =

1
5

(

,
 − 

,
),

(3.2)

where 

,
 and 

,
 denote the 

Ò highest peak and 

Ò lowest valley (Fig. 3.1) within the evaluation
length respectively [119]. 
z is directly measured by the stylus (roughness tester, the measurement
range is several micrometers).

3.2.2 Preliminary Results

Because of the tight FRIB cavity production schedule and waiting for Job Safety Analysis (JSA)
approval for FRIB chemical room use, originally this experiment started in Nomura Plating Ltd,
Japan and got a promising preliminary result. The original recipe is shown in Table 3.2. This is
based on a study of the automobile industry from Toyota [120, 121]. The result is luckily good, the
R
 is ∼ 2.5 
m with about 80 
m removal.

I tried several times to reproduce the preliminary result with the same recipe in the Physics
department’s chemistry room but failed to reproduce the result. All trials have very rough finishing
surface, R
 = 8 ∼ 9 
 m with only about 20 
m removals.

79

Figure 3.2: Preliminary results in Nomura Plating. Ltd. Conventional BCP recipe, 5 min reaction,
∼ 100 
m removal.

I went to visit Nomura. Ltd Plating to check their recipe step by step, and reproduced their first
good results, R
 ∼ 2.5 
m, similar to BCP (Fig. 3.2), only have some small structures looks like
dirt (Fig. 3.3), which need to be solved.

A half-reaction-time experiment was done (the etching time reduced from 60 min to 30 min),
to study the formation process of the roughness structure on Nb surface, as shown in Fig. 3.4.
However, no visible roughness building process was observed.

We then tried to eliminate those small structures by stirring the acid during the reaction, unlike
the original recipe that just put the Nb sample in the acid and watch. Another motive to do the
stirring is to reproduce my experiment in the MSU physics department chemistry room, where I
always do the stirring during the reaction. The result is shown in Fig. 3.5.

80

Figure 3.3: Preliminary results in Nomura Plating. Ltd. Original Recipe, 60 min reaction, ∼ 80

m removal.

In the stirring case, the structures and dirt somewhat disappear (as shown in Fig. 3.5), but the
roughness got very high, 7 ∼ 9 
m with the same reaction time (1 hr, removal= 40 
m ), similar
to my experiment result in MSU physics department’s chemical room. We then confirmed that
stirring could make the Nb surface rough.

After visiting Nomura plating, I started to try to reproduce their good result without stirring,

but to our surprise, we still fail to get their R
 = 2.5 
m results.

We then summarized several other possibilities from comparing the experiment process in two

places:

• Acid vibration during temperature control makes finishing surface rough. At first, I was
trying to maintain the temperature bath, while the self-made thermostat is not very stable. I

81

Figure 3.4: Preliminary results in Nomura Plating. Ltd. Original Recipe, 30 min reaction, ∼ 40

m removal.

remove the acid beaker (made of polyethylene) out of the bath when the water bath too hot.
This moving process may generate vibration during the reaction.

• Reaction speed highly depends on acid temperature.

• Acid temperature may influence the finishing surface. The finishing surface depends on
oxide layer formation and removal, which depends on the oxidation and removal reaction
speed. The two reactions may have different temperature dependence, and affect the surface
roughness.

• Different pre-etching degreaser may influence the finishing surface. The degreasing process
in Nomura Plating is another difference from my MSU experiments. There may exist some

82

Figure 3.5: Preliminary results in Nomura Plating. Ltd, original recipe With stirring, 30 min
reaction.

surface process we do not know.

The acid vibration while putting in or removing the beaker from the water bath was ruled out
after I did the experiment which I did not move the beaker and tried to make the beaker stay stably.

3.2.3 Degreaser Influence

3.2.3.1 Experiment and Result

To study the degreasing influence, I tried three degreasers: Alconox (MSU physics department
sample/container cleanser), Acetone, Micro-90 (FRIB routine cleanser for cavity assembling ),
and Micro-90 with HF rinsing. Nb samples were immersed in these degreasing solutions with

83

Table 3.3: Study of degreaser influence on roughness for new Acid. Reaction time is 30 minutes
for all cases. R
 is the average value of 10 measured points on each sample, 


 is the standard
deviations of the measured values.

Method
Alconox
Acetone
Micro-90

Micro-90 + HF Rinse

Micro-90 with Cu accident

d (
m) R
 (
m) 


 (
m) R(cid:48)
20.5
12.0
14.0
23.5
93

6.77
6.32
6.59
5.58
8.05

2.58
3.11
2.10
2.21
2.21


 (
m) 

(cid:48)
12.08
10.32
13.42
11.87
13.85


 (
m)
2.96
2.48
2.61
4.46
2.49

Figure 3.6: Experiment set up.

30 minutes ultrasonic, then rinsed with ultrapure water and wipe dry. The same acid recipe was
applied to these samples for 30 minutes, and the reaction temperature is 43.7 ± 1.47 ◦C. The result
is shown in Table 3.3.

It is apparent that all finishing roughness R(cid:48)


 are higher than before reaction, and there is no
obvious roughness difference with different degreasing methods. All of the results are far higher
than Nomura Plating’s R(cid:48)


 = 2.5 
m results.

After trying these possibilities, we still fail to reproduce result in Nomura Plating; then we

started to look for the optimization route by controlling parameters systematically.

3.2.3.2 One Accident of Copper Nut Contamination #


In an experiment to see the Micro-90 degreasing effect on etching result, I accidentally dropped
a copper nut (tied to the Nb sample to make it easy to take out of the acid, see Fig. 3.6) into the

84

acid before I put the Nb sample (result in Table 3.3, last term). Massive amount of bubbles were
generated. I took the nut out with tweezers after about 30 seconds, the bubbling stopped, and the
acid solution became slightly blue, which is the color of copper ion.

The Nb sample (pre-cleaned with Micro-90) was put into this acid mixture and found that
colossal bubbling happened again, on the Nb surface. This phenomenon is very different from
previous experiments. In all of them, Nb quietly stays in the acid.

The temperature also increased quickly, unlike the other experiments maintain the temperature
(43.7 ± 1.47 ◦C), this case started with ∼ 18 ◦C, reached 27.2 ◦C in 5 minutes, 33 ◦C in 10 minutes,
50 ◦C in 20 minutes and increased to above 90 ◦C in less than 30 minutes.

The reaction speed is also much higher than the other four cases, maybe partially due to high
temperature. This new phenomenon was also studied later, parallel with the main series. This case
is named #
 for future convenience.

3.2.4 Another Guess: Ratio Based on Reaction Equation

The original acid ratio is the chemical polishing recipe for steel, the reaction is:

2 Fe + 3 H2O2 −−−→ Fe2O3 + 3 H2O,

Fe2O3 + 12 HF −−−→ 2 Fe(HF2)3 + 3 H2O.

The overall reaction is:

2 Fe + 3 H2O2 + 12 HF −−−→ 2 Fe(HF2)3 + 6 H2O,

the H2O2 and HF ratio is 1: 4, while for Nb, the reaction is:

2 Nb + 5 H2O2 + 10 HF −−−→ 2 H2NbOF5 + 8 H2O,

or written as

2 Nb + 5 H2O2 + 10 HF −−−→ 2 NbF5 · H2O + 8 H2O,

and the H2O2 and HF ratio is 1: 2.

85

(3.3)

(3.4)

(3.5)

(3.6)

(3.7)

Figure 3.7: R
 Vs Removal and H2O2 Amount, the green bars show previously used 35% concen-
tration, and the red bar is H2O2 using 50% result.

Table 3.4: Double the H2O2 amount for new Acid recipe. The 50 %HF amount for all cases are 10
mL, the R
 of Nb samples before reaction is 4.94 
m ± 2.92 
m. Trial 1 reaction starts from room
temperature and all others start from 35 ◦C.

Trial H2O2 (mL) H2O2% Time (min)
1
2
4
5

40
60
60
60

35
35
35
50

90
90
45
45

d (
m) T (◦C) R(cid:48)
8.0
12.5
12.0
59.0

19.90
35.89
34.83
42.83


 (
m) 

(cid:48)
4.42
7.89
11.24
18.97


 (
m)
1.45
2.94
3.56
4.90

So we decided to try doubling the H2O2 amount based on the reaction difference, to see if there

is an improvement.

86

H2O2 Amount (mL)5060708090Removal (m)102030405060μz (m)0.02.55.07.510.012.515.017.5Figure 3.8: R
 Vs Removal for different H2O2 Amount, the green bars show previously used 35%
concentration, and the red bar is H2O2 using 50% result.

3.2.4.1 Experiment of Acid Ratio Variance
The result is shown in Table 3.4. For trial # 1, the starting temperature was 19.2 ◦C (room
temperature), the reaction speed was too low, only 8 
m in 40 minutes.

All other trials started with a temperature of 35 ◦C and reacted 60 minutes. The average
temperatures for each case during the experiment was shown in Table 3.4. We can get some
information from this group of experiments:

• Trial # 2 with doubled H2O2 amount has similar removal amount but has lower finishing

roughness comparing with trial # 4.

• It has the finishing surface of 7.89 ± 2.94 
m with only 12.5 
m removal but is not enough
for our goal (3 
m).

• All 35% cases have very low reaction speed, ∼ 0.2 
m/min, much slower than the BCP case.

87

H2O2 Amount (mL)5060708090Removal (m)102030405060μz (m)0.02.55.07.510.012.515.017.5Figure 3.9: Temperature dependence, removal and roughness. The blue bars shows 4 different
temperature cases with the same acid recipe. The red bar is one trial with Cu added in acid before
Nb reaction. Standard deviation is about 25% for roughness.

• The 50% case for trial # 5 has much higher (5 times) reaction speed. We may consider
using this concentration for the latter experiments to shorten the reaction time and get a more
obvious reaction result.

Even we have no firm conclusion in this group of experiments because of low removal, the
oxidization Vs removal ratio is an important process parameter. A systematical optimization for
acid ratio will be shown later.

88

Temperature C°303234363840Removal (µm)10152025303540Rz (µm)02468101214Figure 3.10: R
 Vs T

Figure 3.11: R
 Vs Removal

89

Temperature C°303234363840Removal (µm)10152025303540Rz (µm)02468101214Temperature C°303234363840Removal (µm)10152025303540Rz (µm)024681012143.3 Control Parameters

3.3.1 Temperature Influence

Temperature controlling is the most complicated and dangerous procedure in the experiment:

• The thermostat water bath is not accurate and varies based on the location.

• The thermometer is hard to be fixed.

• The flotation force on the acid beaker makes it easy to fall.

• The water tank block the view makes it hard to view or control the equipment.

These factors make it more dangerous, especially when working with HF acid.

3.3.1.1 Temperature Difference Experiment

We decided to study the temperature influence first, to see if the complicated step of temperature
worth the effort. The result is shown in Fig. 3.9.

If we only check the R
 Vs T, it seems like higher temperature leads to higher roughness, as
shown in Fig. 3.10. However, the roughness difference is not very obvious, especially considering
the 25% measure error. If the R
 Vs d (see Fig. 3.11) get checked, one may also think the roughness
is growing with reaction. Since the temperature does not influence roughness too much, we decided
to experiment with room temperature to make the process safer and easier to control, and potential
hydrogen absorption in niobium during etching.

3.3.1.2 Cu Influence #


The etching used the new acid resolved Cu in an accident as reported in the section 3.2.3.2 still
stays in my mind for a long time. So, I did The experiment of the acid resolved copper using the
previous recipe. The reaction beaker was put in a room temperature water bath to slow the sharp

90

Table 3.5: Systematical ratio dependence study. H2O2 and HF are both using 50%. Starting
temperature is 20 ◦C, roughness before reaction is 4.31 
m ± 1.237 
m. Sample 1, 5’, 6’ and
7’ should have higher finishing roughness because some measure values exceed the measurement
range 25.2 
m and can only read 25.2 
m. *Sample 7’ has too high reaction speed and too
dangerous to control temperature, about 50 mL water was added when the temperature increased
too high and very dangerous.

Trial H2O2 (mL) HF (mL) Time (min)
6
4
2
1
5’
6’
7’

60
60
60
60
60
40
40

4
7
10
13
19
28
37

51
48
45
42
36
27
18

d (
m) T (◦C) R(cid:48)
4.5
10.0
20.5
31.0
45.0
251.5
107.0

20.14
20.91
21.60
24.29
33.08
53.07
49.60*


 (
m) 

(cid:48)
5.02
10.63
19.53
19.09
23.48
22.82
22.94


 (
m)
1.162
2.688
2.707
5.019
2.288
3.074
2.596

increase of reaction temperature. The average temperature was 32.3 ◦C (22.1 ◦C increased to 44.8
◦C), removal is 35.5 
m in 30 minutes reaction time.

As shown in Fig. 3.9 and Fig. 3.11, the result is very encouraging, not only the finishing
roughness is 7.2 ± 1.6 
m, far less than the other cases ( above 10 
m), and the reaction speed is
also much higher. This was more studied later, and we finally discovered the copper catalyst effect,
which will be described in the next chapter. Here, we continued the optimization test of the new
acid mixture for a while.

3.3.2 Acid Ratio

One group of systematic acid-ratio variance-dependence experiments were done, the condition and
result are shown in Table 3.5. All Nb samples were mechanically polished to 4.31 
m ± 1.237 
m
and ultrasonic cleaned with Alconox, then rinsed with ultra-pure water. Reaction beakers were put
in room-temperature water bath to slow the temperature increasing.

The Roughness Vs. HF amount and Vs. removal graph is shown in Fig. 3.12. If only check
the roughness VS HF amount (Fig. 3.13), one may think the finishing surface depends on the acid
ratio, that the lower the HF amount is, the smoother the finishing surface is. However, the reaction
speed also highly depends on the ratio. The roughness difference for each ratio may be only due to

91

Figure 3.12: R
 Vs Removal and HF. The reaction condition is shown in Table 3.5.

the removal difference.

It is evident that: less HF, reaction very slow, because the removal of the oxide layer is too slow;
more HF reaction get much faster (this makes the experiment very dangerous), the temperature
increase very fast, too.

There is no visible optimization result, all cases have very high finishing roughness, and the R


seems proportional to the removal. Some other essential parameters need to be checked.

3.3.3 Viscosity Impact

We also tried to change the viscosity because much study shows that viscosity has an essential
impact on the finishing surface.

92

HF (mL)4681012141618Removal (μm)51015202530354045Rz (μm)5.07.510.012.515.017.520.022.5Figure 3.13: R
 Vs HF

Figure 3.14: R
 Vs Removal

93

HF (mL)4681012141618Removal (μm)51015202530354045Rz (μm)5.07.510.012.515.017.520.022.5HF (mL)4681012141618Removal (μm)51015202530354045Rz (μm)5.07.510.012.515.017.520.022.5Table 3.6: Viscosity dependence for H2O2 and HF ratio equals to ∼ 3: 1, same as Table 3.5
sample # 1. The reaction time for all cases are 120 minutes instead of 60 minutes for sample # 1
in Table 3.5. H2O2 and HF are both using 50%, H3PO4 is 90%. Starting temperature is 20 ◦C,
roughness before reaction is 3.582 
m ± 1.683 
m.

Trial H2O2 + HF (mL) H3PO4 (mL)
1
A
B
C

55
37
28
18

0
18
27
37

d (
m) T (◦C) R(cid:48)
31.0
22.0
10.5
3.0

24.29
25.47
23.54
21.70


 (
m) 

(cid:48)
19.09
17.09
10.85
5.17


 (
m)
5.019
3.963
4.702
1.930

Table 3.7: Viscosity dependence for H2O2 and HF ratio equals to ∼ 1: 1, same as Table 3.5 sample
# 6’. The reaction time for all cases are 120 minutes instead of 40 minutes for sample # 6’ in
Table 3.5. Starting temperature is 20 ◦C, roughness before reaction is 3.582 
m ± 1.683 
m.

Trial H2O2 + HF (mL) H3PO4 (mL)
6’
D
E

55
28
18

0
27
37

d (
m) T (◦C) R(cid:48)
251.5
23.0
10.0

53.07
23.77
22.97


 (
m) 

(cid:48)
22.82
21.46
13.61


 (
m)
3.074
3.218
3.491

The viscosity of etching acid can influence the performance of BCP as follows. It is practical to
slow the diffusion electrolyte reaction products by the chemical reaction, making the morphology:
peak area has higher acid concentration, and more reaction happens, and vice versa for the valley
area. Also, it prevents preferential etching. This polishing effect is enhanced when the viscosity is
high [122–124].

3.3.3.1 Experiment for Viscosity Influence
In order to study the viscosity effect, we then tried HF+H2O2+H3PO4 mixture because phosphoric
acid has a high viscosity and is commonly used in BCP.

Two groups of experiments were done. One based on section 3.3.2, trial # 1 (42 mL H2O2: 13
mL HF), increase H3PO4 over acid ratio from 0 to 1: 2, 1: 1 and 2: 1. Another one is based on
section 3.3.2, trial # 6’ (51 mL H2O2: 4 mL HF), increase H3PO4 over acid ratio from 0 to 1: 1
and 2: 1.

No improvement was observed for both groups of experiments. As seen in Fig. 3.15, the
increased viscosity slower the reaction speed; however, the results for both groups showed that

94

Figure 3.15: R
 Vs H3PO4/Acid Ratio and Removal

only material removal speed was reduced, some case such has minimal reaction while the surface
remained very rough.

3.3.3.2 Using H2SO4 to Increase Viscosity
HF+H2O2+H2SO4 mixture was also used in another trial. This group of experiments were done in
Nomura Plating. Ltd because the mixture is possibly explosive. The reason for the material speed
reduction in the above H3PO4 mixture is probably due to the poor oxidation capability. Sulfuric
acid will add oxidation power as well as high viscosity to the new acid.

The results showed surface roughness R
 = 10.4 ± 6.2 
m after ∼ 8.4 
m etched. The mixture

95

H3PO4/Acid Ratio0.00.51.01.52.02.53.0Removal(m)0510152025303540μz (m)0510152025Figure 3.16: Microscope images for fine-grain sample reacted with new acid (A) and with new acid
plus H2SO4 (B).

Table 3.8: Comparison of copper cases with or without H3PO4. #
 is the Cu case in section 3.3.1,
Table 3.9. H2O2 is in 35% and HF is using 50%, and the ratio is 45: 10, Cu amount is ∼ 3.10−4
mol and Starting temperature is 20 ◦C for both cases. The roughness before reaction for 
 is 9.067

m ± 2.953 
m and for 
 is 4.000
m ± 2.783 
m.

Trial H2O2 + HF (mL) H3PO4 (mL)





0
27

55
28

d (
m) T (◦C) R(cid:48)
35.5
16.5

32.3
19.92


 (
m) 

(cid:48)
7.19
9.01


 (
m)
1.640
3.511

consisted of 10 mL 50% HF, 45 mL 35% H2O2, and 60 mL 98% H2SO4. We also tried other
composition ratios, but the results had no significant differences. Fig. 3.16 shows the SEM image
of the adding H2SO4 cases (B) and original new acid (A) results. There is no obvious difference
between these two cases.

3.3.3.3 Copper Case with Higher Viscosity #


Copper case with H3PO4 was also studied. We use the acid ratio same as the previous sample #

in section 3.3.1 case 28 mL, and add 27 mL of H3PO4, then add copper. One Nb sample was put
into the acid mixture after copper finished reaction. The increased viscosity does not help the Nb
get a better surface and even worsen it. We think maybe the high viscosity blocked the bubbles
from getting away.

Overall we found none of these trials can reduce the roughness. Same as in section 3.3.1 and in

96

section 3.3.2, there is also a trend for the R
 Vs Removal in this case. We think some fundamental
parameters should exist, but we have not found. Without meeting those criteria, all trials can only
have small scale impact, but the roughness will still stay at quite a high level.

3.4 High Roughness Study

We got high roughness for all cases (except for the copper cases) of our new acid experiments.
Before getting the mechanism of it, we can study the location of the high roughness first. There are
two possibilities:

• High roughness due to grain-boundaries.

• High roughness in the grain gets erosion from the new acid.

Considering that we are using fine-grain (∼ 
m) Nb samples for all experiments, one straight-
forward guess is that the grain-boundary preferential etching leads to the high roughness just like
the BCP cases.

Different reaction speed for grain crystalline direction is another possibility relate to grain-
boundaries. This is because different orientation has different atom density, which may cause
different reactions speed.

Large-grain (1 - 2 cm scale) niobium samples has much fewer grain-boundaries than fine-grain
(∼ 50 
m scale) ones and these boundaries are visible after the reaction. Experiments with these
large-grain (∼ cm size) Nb samples were done to study the possible grain-boundary influence. If
the large-grain Nb sample gets lower roughness than before, we can confirm grain-boundary –
either preferential etching or orientation reaction speed difference – lead to the high roughness.
Otherwise the high value most from in grain roughness.

3.4.1 Orientation of Large-grain Nb Crystalline
One large-grain Nb sample composed of three large crystallines with sizes ∼ 1.5 cm × 0.5 cm were
studied after new acid reaction (10 
m removal). A joint point image was captured by Orientation

97

Figure 3.17: Orientation Imaging Microscopy (OIM) image of a joint point of three grains on
a large-grain Nb sample after ∼ 10 
m removal by new acid. Different color indicate different
crystalline orientation.

Imaging Microscopy (OIM) to get the orientation information, as shown in Fig. 3.17.

According to the OIM result, it is obvious that different grain has a different orientation.
However, some noise points exist on the image due to high roughness which means this method
results can be influenced by roughness. If we apply OIM on the fine-grain sample, the resulting
image will have more roughness noise than the large-grain one that we cannot distinguish the
orientation from the roughness. One fine-grain Nb sample which was also removed ∼ 10 
m by
new acid was observed, while no signal of OIM image can get.

3.4.2 Roughness between Grain-boundaries and Internal Grain

Among the large-grain samples, one sample shows different reaction speed on different grains.
For example, Fig. 3.18 shows step structure on grain-boundaries while no visible grain-boundary
preferential etching observed on this figure. The roughness crosses the grain-boundary is ∼ 7

m, while the internal grain is ∼ 2 
m. This indicates the reaction speed difference on different
grains in the fine-grain Nb sample (grain size ∼ 50 
m) can cause the high roughness, because
the measurement route of the roughness tester is several millimeters long, and would cross ∼ 100
grains.

However, we noticed the internal grain roughness∼ 2 
m is still high compare with conventional
BCP large-grain roughness, which is only ∼ 250 nm. Fig. 3.19 and Fig. 3.20 shows SEM images

98

Figure 3.18: Reaction difference is observed in one large-grain sample. This sample was reacted
with new acid and the removal is ∼ 20 
m.

Figure 3.19: SEM images and roughness map for large-grain sample reacted with new acid.

and roughness map of large-grain Nb sample treated with new acid and with conventional BCP.

We conclude that both grain difference and in-grain erosion caused the high roughness of new

acid with Nb sample.

99

Figure 3.20: SEM images and roughness map for large-grain sample reacted with conventional
BCP.

3.4.3 Discussion

For the new acid, we got the confirmation that the grain-boundary influence is as severe as BCP
cases because of the reaction speed difference on density difference from different crystalline
orientation. Additionally, some erosion effects always exist on the internal grain surface reaction,
and we have no information on why this happens.

As seen above, we made many efforts for the new acid optimization: acid agitation, acid mixture
ratio, pre-preparation choice, temperature control, viscosity, and other trials. Unfortunately, we
could not find the critical condition in any of these parameters to get the smooth finished surface ∼
3 
m.

Our conclusion for the rough finishing surface with the new acid is due to mainly the preferential
etching performance of this new acid, which will be the behind the reason why Saclay gave up this
mixture. We remain a question why Nomura plating succeeded to the smooth finishing surface
using this mixture; even they need to improve the finishing microstructure as seen in Fig. 3.2 and
Fig. 3.3. However, if the preferential etching is the leading cause of the rough finishing surface,
we have to give up this new acid, as Saclay did it. However, we still have hope for the new acid
resolved copper, as shown in section 3.3.1.2. So I decided to continue more study for this acid.

100

CHAPTER 4

COPPER CATALYST

We described several experiments related to a copper contamination accident that happened during
the new acid experiment process in section 3.2.3.2, section 3.3.1.2, and section 3.3.3.3. We found
this copper additive somewhat helped to solve the high roughness problems, so we decided to
optimize this copper case and meanwhile try to find the mechanism of the high roughness reason
for our new recipe. Two example pictures are shown in Fig. 4.1.

4.1 Setup optimization

4.1.1 A Quick Check of Copper amount and H2O2 Concentration Influence

We are curious about the H2O2 concentration and the copper amount influence, and we did one
group of experiment.

For the copper used in the experiment; initially, the accident was caused by a copper nut drop

Figure 4.1: A comparison between new acid sample without and with Cu catalyst.

101

Table 4.1: H2O2 concentration and Cu amount variation results, HF concentration is 50 % for all
cases.

Trial H2O2 % Cu (mol)
3.10× 10−4
H
6.20× 10−4
I
2.09× 10−4
J

35
35
50

d (
m) T (◦C) R(cid:48)
41
40
53

26
28
28


 (
m) 

(cid:48)
5.95
6.68
5.49


 (
m)
1.52
1.52
1.16

into the acid, there was no reaction amount of cooper information. For the second and third
experiment, we used a sealing copper gasket (Commercial product with the purity of > 99.0 %
copper) which was discarded from cavity assembly. We cut it in half. The half ring is pure enough
and easy to handle. The Cu mole amount is calculated from its mole mass 63.546 g/mol, where the
Cu mass is measured before and after the half gasket reaction.

A controlling of the Cu amount is based on the reaction time, 30 seconds and 60 seconds are
the two options which we used in this group of experiments. Acid mixture for a sample # H and
J both has the 30 seconds reaction on the same Cu, the Cu amount resolved in the acid for two
reactions are 0.3945 g; and I has a 60 seconds reaction, for which the amount of Cu dissolved in
acid is 0.2657g, correspondence to 2.09×10−4 mole, which is lower than the Cu amount resolved
in acid for sample H, this may be due to the H2O2 higher concentration.

For all three cases, Nb sample roughness was 3.51 ± 1.45 
m before reaction; the reaction
time was 40 minutes, the starting temperature was 20 ◦C. For the volume of acid mixture, 50 %HF
amount is 10 mL, H2O2 amounts is 45 mL and the concentrations are list in Table 4.1.

For trial # J, we used 50% H2O2 and compare with # H which used 35% H2O2, the Cu amount
is slightly different even both cases has 30-second copper reaction before Nb was put in, this should
be due to acid concentration difference. The result of # J is not too different, while the Nb reaction
was too fast and dangerous, so for the following cases, we continue our experiment with 35% H2O2.
For trial # H and I, it seems like # H has slightly smoother result. To study the copper effect more,
we purchased Copper powder for more accurate controlling of the copper amount and continued
the experiment.

102

Trial
R
S
T
U

Cu (mol)
1.24× 10−4
3.02× 10−4
6.45× 10−4
1.15× 10−3


 (
m) 

(cid:48)
6.74
6.05
8.32
8.22


 (
m)
1.62
1.64
1.99
1.34

Table 4.2: Cu powder amount variation results
d (
m) T (◦C) R
 (
m) 


 (
m) R(cid:48)
40.0
46.0
57.0
56.5

0.915
1.722
2.817
3.606

25.9
27.3
27.3
26.3

4.68
5.41
7.74
6.76

4.1.2 Copper Amount Variation for 45: 10 Recipe Using Cu Powder

In the following experiments, we want to control the copper amount in the mixture to see the
influence, so we need more accurate value. We used copper powder (99.9 % pure) in this group of
experiments. The copper powder is tough to transfer, so we use small centrifuge tube as a container
when measuring the copper powder, and put the whole opened tube into the acid and wait until the
reaction between copper and acid finished, and take the tube out before putting Nb in.

We also try to get similar Nb removal, so we watch the color of the acid instead of setting a
specific reaction time because the similar shade of green color indicates similar Nb dissolved in
acid. Case R and S have 50 minutes, T had 60 minutes, and U had 70 minutes reaction time.

The acid recipe follows # H and I, 45 mL 35% H2O2 plus 10 mL 50% HF and starting
temperature also 20 ◦C. The Nb roughness before reaction for each case is very different because
of bad controlling of mechanical polishing; the data is listed in Table 4.2.

We got the best result from sample S (3 × 10−4 mole Copper), slightly better than all other
cases. However, even though the measured value more accurate, the copper powder is tough to
handle. The powder is very easy to spit out even we put the whole centrifuge tube in acid. (Trial #
S split a bit copper) The copper powder is also easy to adhere to the beaker’s wall or gloves due to
electrostatic attraction. This again makes the amount of copper very uncertain.

4.1.3 HF Amount Variation for 3 × 10−4 mole Copper Powder

In this case, we want to keep the H2O2 concentration, and copper amount stay the same and only
study the HF concentration influence. We improved the experiment method by using 29 mL 50%

103

Table 4.3: HF amount variation results for 3 × 10−4 mole Copper Powder. 6’ has same condition
with 2’, but with stirring.

Trial HF (mL) H2O (mL) d (
m) R
 (
m) 


 (
m) R(cid:48)
2’
3’
4’
5’
6’

66.5
83.5
76.0
90.5
78.0

1.27
2.38
1.30
2.02
1.63

4.18
4.86
4.64
4.61
5.05

10
15
20
25
10

16
11
6
1
16


 (
m) 

(cid:48)
7.32
6.27
6.59
10.10
8.14


 (
m)
1.35
1.55
1.62
2.86
1.62

Table 4.4: Additional reaction for case 3’, 4’ and 5’. The same Nb samples are without extra
mechanical polishing, so the roughness before reaction are from R(cid:48)

 in Table 4.3. The Nb were put
into the original acid saved from last reaction.

Trial HF (mL) H2O (mL)
3”
4”
5”

15
20
25

11
6
1

d (
m) R(cid:48)
11.5
34.0
30.5


 (
m) 

(cid:48)
6.27
6.59
10.10


 (
m) 
(cid:48)(cid:48)
1.55
1.62
2.86


 (
m) 

(cid:48)(cid:48)
6.04
9.36
13.03


 (
m)
1.30
2.24
3.20

H2O2 for all cases, add different amount of HF, and adjust the concentration of H2O2 by adding
water to reach a total volume of acid 55 mL. The Copper amount for each case is 2.72 ± 0.45 ×
10−4 mol. The starting temperature is 18 ◦C and the ending temperature is about 32◦C for all cases.
50% HF amount and water amount are shown in Table 4.3. 2’ and 6’ has 70 minutes of reaction
time, and other cases have about 10 minutes reaction time because higher HF amount leads to very
high reaction speed.

Additional reactions for three cases are done for case 3’, 4’ and 5’, shown in Table 4.4, to

compensate the possible different reaction amount of Nb.

In the two groups of experiments, trail 3’ and 3” show an optimum roughness compare with
other cases listed in Table 4.3 and Table 4.4, so we decided to choose this recipe to continue the
optimization.

This time we tried to directly put the copper powder in the beaker before any reaction to avoid
copper spit during opening the small tube used in section 4.1.2. However, we are still not sure
about the amount of copper since some may still spit out or adhere to the beaker wall and does not
react with acid.

104

Table 4.5: Copper variation for H2O2 (50%): HF (50%): H2O = 29: 15: 11 Recipe using thin
copper wire.

Trial Cu mg/L d (
m) R
 (
m) 


 (
m) R(cid:48)
a
b
c
d
e
h
i
j
k
l

2.83
2.24
2.61
2.23
1.93
1.81
1.42
1.45
1.85
1.70

33.5
36.0
34.5
35.5
29.0
62.0
71.5
64.5
51.0
51.5

230
282
329
381
425
403
403
464
522
573


 (
m) 

(cid:48)
3.67
3.36
3.23
4.06
2.90
4.07
3.82
3.97
4.66
4.90


 (
m)
0.71
0.76
0.90
0.78
0.48
0.79
0.89
0.84
0.94
1.12

0.99
0.81
0.91
0.73
0.67
1.23
0.46
0.44
0.70
0.55

4.1.4 Copper Amount Variation for 29: 15: 11 Recipe Using Thin Cu Wire
We then switched to a very thin copper wire (99.999 % pure) and the diameter is ∼ 0.127 mm, the
length density is ∼ 0.11 g/m. We first cut a wanted estimated length of the copper, then measure
the mass for a more accurate value. This is our optimized way of controlling the copper amount
because it is accurate and easy to handle. The roughness before the reaction was also improved to
a lower and stable value. We are using recipe of sample 3’ for this round of experiment, which is
29 mL 50% H2O2, 15 mL 50% HF and 11 mL H2O.

The amount of copper for each cases are shown in Table 4.5. For example, case #j has 464

mg/L Cu, correspondence to 4 × 10−4 mol Cu in 55 mL mix acid, which is 7.27 × 10−3 mol/L.

We tested the copper concentration from 230 mg/L to 573 mg/L, of which results are summarized

in Table 4.5.

Case # e has 2.90 ± 0.48 
m roughness with 425 mg/L copper (best result), while other cases,
such as case # c has 3.23 ± 0.90 
m, is not much worse than this best result, especially when we
consider the roughness before reaction, see Fig. 4.3. The finishing roughness still has a worsening
trend, but it is much mitigated by using copper resolved acid. The role of the copper is considered
a catalyst effect, which will discuss later. Till now, we think Cu amount 329 to 425 mg/L has the
best effect to help our new acid to smooth the Nb finishing surface, while it does not need to be
very accurate.

105

Figure 4.2: R
 Vs Cu amount and Removal. Green squares are roughness after reaction, and red
squares are roughness before reaction. 1 ppm equals to 1 mg/L (defined in analytical chemistry).

4.2 Summary of Experiments

A summary of our experiment is shown in Fig. 4.4. The grey ones are all reactions without
Cu catalyst; the red triangles are BCP results with Acid ratio 1: 1: 2 (Volume ratio HNO3: HF:
H3PO4); the blue dots are HF variation test and the green crosses are Cu amount variation.

The finishing roughness trend with no copper catalyst cases is much higher than those with
catalyst cases. The copper catalyst cases after optimization are similar to the BCP cases. (red solid
triangle mark in Fig. 4.4). One can see in Fig. 4.4 that the best-optimized mixture recipe with
the copper catalyst can suppress the grain-boundary preferential etching on the new mixture (no
copper), reached R
 = 3 
m after 75 
m material removal, which satisfies our goal.

For the morphology, a large scale photo is shown two samples together reacted with new acid
with catalyst and reacted with BCP in Fig. 4.5. The roughness on millimetre-scale is similar for
both cases, while the BCP sample has some typical “orange skin” structure.

106

Cu Amount (ppm)250300350400450500550Removal (m)3040506070μz (m)23456Figure 4.3: R
 Vs Cu amount. Green squares are roughness after reaction, and red squares are
roughness before reaction. 1 ppm equals to 1 mg/L (defined in analytical chemistry).

Figure 4.4: A summary of the whole optimization process with conventional BCP result. Grey
marks are new acid without catalyst, red triangles are BCP (1: 1: 2) cases, blue dots are HF
variation results, green crosses are Cu variation results that using the previous best 15 mL recipe
from the HF variation results. The Cu variation influence is already shown in Fig. 4.2 and 4.3.

107

Cu Amount (ppm)250300350400450500550Removal (m)3040506070μz (m)23456020406080100120140Removal (μm)051015202530Roughness Rz (μm)4 mL7 mL10 mL13 mL19 mL10 mL15 mL20 mL25 mLBCP 112New CP, HF ratio variableCu catalyst, HF variableNew CP, H3PO4 variableNew CP, T variableNew CP, H2O2 variableCu catalyst, Cu variableFigure 4.5: A comparison between new acid with Cu catalyst sample and BCP sample.

Three magnification of SEM images are shown in Fig. 4.6, Fig. 4.7 and Fig. 4.8. It is more
clear that for 500 
m scale (Fig. 4.6), the new acid sample is more smooth, while in the 20 
m
scale (Fig. 4.8), the BCP sample has less structures.

4.3 Mechanism

4.3.1 Chemical Reactions

This section explains the chemical reactions that occur when Cu is added into the polishing acid
mixture and discusses their implications.

A series of reactions happen during the experiment:

Cu + H2O2 −−−→ CuO + H2O,

CuO + H2O2 −−−→ CuO2 + H2O,
2 CuO2 −−−→ 2 CuO + O2 ↑ .

108

(4.1)

(4.2)

(4.3)

Figure 4.6: SEM Image of Nb samples after new acid polishing (a) and after BCP (b), 75 times
magnification.

(a)

(b)

Figure 4.7: SEM Image of Nb samples after new acid polishing (a) and after BCP (b), 350 times
magnification.

(a)

(b)

109

Figure 4.8: SEM Image of Nb samples after new acid polishing (a) and after BCP (b), 350 times
magnification.

(a)

(b)

Figure 4.9: SEM Image of another Nb sample after new acid polishing (a) 75 times (b) 350 times
and (c) 3000 times magnification.

(a)

(b)

(c)

110

These reactions constitute a H2O2 decomposing process with Cu as the catalyst, and can be written
as:

Then the CuO reacts with HF:

2 H2O2

Cu−−−→ 2 H2O + O2 ↑ .

CuO + 2 HF −−−→ CuF2 + H2O,

or

CuO + 4 HF −−−→ Cu(HF2)2 + H2O.

The Cu2+ dissolves in the acid, and when Nb is put into the acid, reaction

5 Cu2+ + 2 Nb −−−→ 5 Cu + 2 Nb5+,

(4.4)

(4.5)

(4.6)

(4.7)

happens due to single-displacement reaction, and Nb5+ dissolves into the acid to generate a Cu layer
outside the Nb, and reaction Eqs. 4.1 to Eqs. 4.7 continuously happen, until any of the component
is consumed. During this process, Cu accelerates the reaction and is not consumed, thus acting as
a catalyst.

The combination of the whole process can be written as:

20 H2O2 + 20 HF + 4 Nb Cu−−−→ 4 NbF5 + 5 O2 ↑ + 30 H2O.

(4.8)

The critical components of the whole reaction series are reaction Eqs. 4.4 and reaction Eqs. 4.7:
there will be no gas product without reaction Eqs. 4.4, which is essential to finishing surface
roughness (will be explained later); if there is no reaction Eqs. 4.7, the metal ions will be excluded
from the reaction series and stay in the acid. Therefore, any metals that meet these two processes
should be able to work as a catalyst for this acid. Reaction Eqs. 4.7 needs the metal to be less
reactive (in the reactivity series) than Nb, and reaction Eqs. 4.2 needs the metal to be at least
oxidizable by H2O2 (can be found from Standard electrode potential), so the series of potential
catalysts are: (Nb), Zn, Cr, Ga, Fe, Cd, In, Tl, Co, Ni, Mo, Sn, Pb, W, Ge, Cu, Tc, Ru, Po, Hg, Ag.

111

Figure 4.10: Acid component is 45 mL 35% H2O2, 10 mL HF with (a) Fe amount 2 × 10−4 mole,
35 
m removal, R
 = 13.52 ± 5 
m and (b) Fe amount 1 × 10−4 mole, 38 
m removal, R
 = 16.08
± 3 
m.

(a)

(b)

In this series, the more reactive (closer to Nb) the metal is, the slower reaction Eqs. 4.7 will be,
which is closer to the scenario without a catalyst. Conversely, the less reactive (closer to Ag) the
metal is, the stronger the metal ion’s oxidization power, so it is more catalyst effective.

We also tried Fe, which is closer to Nb than Cu, and the reaction happened as we predicted
and the finishing surface roughness was 
z = 10 ∼ 16 
m depending on the amount of Fe. The
result agrees with our analysis of catalyst effectiveness. As shown in Fig. 4.10, the roughness is
very sensitive with the Fe amount, when the amount is 2 × 10−4 mole, some bubble-sign like large
scale holes exist, we think this is over amount; however, when the Fe amount is 1 × 10−4 mole, the
roughness and morphology is very similar to no catalyst case, we think this is under amount.

4.3.2 General Chemical Polishing Principle and the Bubble Effect

The underlying principle of general chemical polishing is a higher reaction rate at the peaks than at
the valleys. This produces a soothing effect on the surface; some fundamental studies can be found
in Ref. [122]. Several parameters are essential for the finishing surface, such as viscosity [123,

112

Figure 4.11: Bubble generating (a) and growing (b) on metal peak and valley during chemical
polishing.

(a)

(b)

124], oxidation layer formation [125], temperature.

For a chemical polishing process, the reaction rate difference arises because the peak has higher
acid amount to react with than the valley for a similar reaction area [122, 126]. This difference can
be enhanced by bubbles generated on the metal surface which block the reaction more around the
valley area than at the peak [127] because bubble grow slower and stay longer on the valley area.
Bubbles that grow during the reaction will start departing the surface once they reach a critical
condition when the floating force becomes more significant than the surface tension, and the value
of it is related to the tangent plane area (Fig. 4.11). For the peak, the surface tangent area is only a
dot while for the valley, the surface tangent area is more close to a ring, which makes the surface
tension much higher than on the peak area, this makes the bubbles stay longer on the valley area
(Fig. 4.12). Some study of bubbles in liquid can be found in Ref. [128, 129].

Hence, bubbles take a longer time to depart from valleys and block the reaction at valleys for a
longer time than they do at peaks. This effect enlarges the reaction rate difference and facilitates
the generation of a smoother surface.

113

Figure 4.12: Force on bubbles

The reaction on Nb of the H2O2 plus HF without Cu is:

5 H2O2 + 2 Nb + 10 HF −−−→ 2 NbF5 · H2O + 8 H2O.

(4.9)

One noticeable difference between this reaction (Eqs. 4.9) and the Cu case (Eqs. 4.8) is the O2
gas generated on Nb surface, and these oxygen gas bubbles may help generate the smooth surface.
Another evidence for that bubbles play a role for the smoothing effect is the Fe catalyst ex-
periment, when there is more Fe, too many bubbles will be generated, and worsen the surface
with bubble marks (Fig. 4.10a); when there is less Fe, the result is more close to no catalyst case
(Fig. 4.10b).

Unfortunately, we are not able to get an optimized Fe amount to get a smooth Nb surface. We
think this is due to Fe ion has less oxidation power, it reacts less than Cu ion in Nb oxidation
equation (Eq. 4.7) but react more than Cu ion in the H2O2 decomposing equation (Eq. 4.4). Thus if

114

less Fe is added, not enough Fe ion involved in oxidation, while if more Fe added, too many bubbles
are generated, and it can hardly get a balance. This also supports our bubble effect explanation.

4.3.3 Micro EP Effect: Electrodes Forming on Nb Surface During Single Displacement

Reaction

There is an extra benefit from adding Cu: the Cu generated on Nb surface from Eqs. 4.7 forms
cathode, increases the total reaction rate (especially on the peaks because the peaks already react
faster [126]) and intensifies the reaction rate difference. This is due to Galvanic corrosion, which
is similar to the aluminum case in Ref. [125].

We cannot distinguish which dominate the smoothing process, the bubble effect or the micro
EP effect. The Fe ion less oxidation power can also explain the microcurrent effect: less oxidation
power induces less micro-current and less peak filed enhancement reactions.

4.4 Copper Remnant Study

Although copper can be found as a catalyst to chemically polish new acids, potential copper
contamination is concerned. Instead of analyzing the copper’s impact on the Niobium Cavity, we
first try to find the possibility of removing the copper from the surface of the Niobium Cavity.

We have mentioned that the Cu only reacts on the Nb surface and in the acid (Eqs. 4.4 to
Eqs. 4.7). Energy-dispersive X-ray spectroscopy (EDS) analysis is a method that can detect the
elements on the 1000 nm surface of a conductor, and it should be able to analyze the contamination
on Nb surface, so we decided to adopt this method to study the Cu remnant.

4.4.1 Experiment and EDS Analysis Result

Five samples were treated with the same optimized acid (copper amount 347 mg/L), and then four
of them were rinsed by different acid listed in Table 4.6. We then do the EDS analysis on the
samples to check the element on the Nb surface. However, we did not get any Cu signal even on
the non-rinsed Nb sample, one example signal spectrum is shown in Fig. 4.14 for Selected Area 1

115

Table 4.6: Copper remnant removal experiment setup

Sample # Reaction Amount

1
2
3
4
5

72.5 
m
77 
m
76 
m
85.5 
m
86 
m

Treatment

None

15 mL HF + 40 mL H2O rinse
15 mL HF + 40 mL H2O rinse
Mix Acid Without Cu rinse
Mix Acid Without Cu rinse

Time
None
5 min
10 min
5 min
10 min

Figure 4.13: Three selected areas to do the EDS analysis on non-rinsed Nb sample treated with
new acid plus Cu catalyst.

in Fig. 4.13. Other areas have similar signal and shown no Cu. This indicates that the Cu amount
is very low and cannot be detected by EDS.

4.5 Discussion

In this chapter, we investigated the new mixture with copper resolved in detail. We have
discovered the best optimization between 329 mg/L and 464 mg/L of the resolved copper into the
mixture consisted of H2O2 (50%, 29 mL, HF (50%, 15 mL), and water (11 mL), total mixture

116

Figure 4.14: EDS Result of Nb sample after new acid on Selected Area 1 in Fig. 4.13.

volume 55 mL. This optimized mixed acid can provide almost no preferential etching for enough
material removal (70 
m, maybe more), which thanks to the copper catalyst effect. The material-
removing speed is ∼ 5 
m/min and the finished surface roughness is ∼ 3 
m if the initial roughness
is adjusted around 2 
m. This etching performance is compatible with that of the current BCP acid
(1: 1: 2).

Then we investigated the chemical reactions, found out that the difference between the reactions
for with and without Cu catalyst then concluded bubbles during reactions and micro-EP effect
enhanced the smoothing effect which improved the roughness to roughness similar to conventional
BCP. In the end, we did EDS analysis and found there is no sufficient Cu contamination to get Cu
signal on the Nb surface; this indicates the Cu contamination amount is very low and maybe will
not influence the future Nb cavity performance.

117

CHAPTER 5

CONCLUSION AND FURTHER WORK

This dissertation describes the original motive of solving High Field Q Slope (HFQS) problem,
which is a phenomenon that the Nb superconducting cavity Quality Factor started drop exponentially
when the accelerating gradient reaches a specific value (

 = 80 ∼ 100 mT). This HFQS problem
is one of the primary limits of Nb cavity performance, especially for those treated with Buffered
Chemical Polishing (BCP) method. The process of 120 ◦C Low-Temperature Baking (LTB) can
relief the dropping slope at high electric field especially for the EP processed Nb cavities, which
is associated with the oxygen diffusion. However, this LTB method could not provide a solution to
the BCP HFQS problem, can only partially improve the slope.

There are several proposed models for this BCP particular degradation; however, none of them
can explain the BCp’ed HFQS behavior for cavities made of fine grain, large grain, and single-
crystalline niobium material consistently. Instead of their models, we concluded by massive past
data mining that nitrogen contamination during BCP should be the root cause of the BCP HFQS,
which is caused by the nitric acid in the current BCP acid.

The above conclusion motivated us to develop a nitrogen-free chemical polishing acid for Nb.
After the basic chemical polishing method investigation, we decided to use hydrogen peroxide as
our oxidizer and continue to use HF as our oxide layer remover in the mixed acid. The hydrogen
peroxide has no extra element introduced in the acid, and it has enough oxidization power to react
with Nb, this made us adopt it in our new acid development. Our goal for this acid is: getting the
reaction to happen with a moderate speed; and with a finishing surface similar to conventional BCP
(R
 ∼ 3 
m).

This dissertation covers the process of acid developing. We firstly tried several experiments
outside MSU before we get job safety analysis (JSA) approved with an acid composed of 45 mL
35% H2O2 and 10 mL 50% HF with a starting temperature 45 ◦C. We then try to reproduce the
result in MSU after the JSA approval, but we got very high roughness on all result surface.

118

We started over the process by doing controlling parameters experiments, and tried temperature,
stirring or not, temperature maintaining methods, viscosity, component concentration and acid ratio.
Most of these influence the reaction ratio but have no improvement on surface roughness. All trials
have very high roughness after enough reaction.

We found the high roughness located both in the grain and on grain-boundaries, by comparing
results of single-crystal Nb and fine-grain Nb that processed by conventional BCP and our new
acid. This means both erosion effect and reaction speed different on different crystal orientation
(preferential etching) both exist in the new acid reaction.

We found Cu can be a catalyst in our reaction, which can improve the smoothness, and the
operation is merely adding a small amount of Cu in the acid before putting Nb in. We applied the
controlling parameter process again, include acid ratio, viscosity and Cu amount, and we eventually
found a relatively best recipe, and finally achieve a smooth Nb surface that similar to conventional
BCP result.

We studied the mechanism and deducted the chemical reaction formulas. By comparing the
reaction with and without Cu, we found the most obvious difference is that the one with Cu has
oxygen bubbles generated on the Nb surface. The Cu ions consistently oxidize Nb by metal single
displacement reaction and become Cu metal and then dissolve in acid become Cu ion again. There
is no Cu consumption in the process, and that is why we think the catalyst is the role of Cu. The Cu
is a catalyst of H2O2 decomposing. The oxygen bubbles generated on the Nb surface stay in valley
longer than on the peak, which generates a reaction speed difference and enhances the polishing
process. The single displacement reaction on the Nb surface also generate microcurrent on the Nb
surface, which may form Micro-EP effect, and also help improve the surface smoothness.

Thus any metal that: its ion can react with Nb metal by single displacement reaction, and can
help with H2O2 decomposing, should be able to be our new acid catalyst. We tried Fe, and the
results agree with our mechanism analysis.

In the end, we studied the Cu remnant amount. There is no signal of Cu when we do EDS
analysis; this means the copper amount is very low and not detectable by EDS. In the future,

119

if some potential degradation still happened on Nb cavities by Cu contamination, it should be
easy to remove by reacting a small amount on the surface with the original new acid, because
Cu reacts much faster than Nb in the acid. Another possible solution is trying a new catalyst: a
superconductor under cavity operation temperatures, such as indium or lead; or use Sn to react
with Nb and generate Nb3Sn on its surface, which is another promising material for SRF cavities.
These studies will offer more possibilities for SRF material.

120

APPENDICES

121

APPENDIX A

E & M FIELD IN A RF CAVITY

A.1 Field in wave guide

Because of the cylindrical geometry, we can single out the spatial variation of the fields in the

z direction, and assume

 =

 E(
, 
)
±

 
−




B(
, 
)
±

 
−




E(
, 
, 
, 
)
B(
, 
, 
, 
)

Maxwell equations take the coming form:

For our case, both E and B satisfy(cid:104)∇2

∇ × E = 

B
∇ · B = 0
∇ × B = −



E
∇ · E = 0


 + (


2 − 
2)(cid:105) E

B

 = 0,

where


 = ∇2 − 
2
∇2


2

.

Separate the fields into components parallel to and transverse to the z axis,

E = E
 + E
,

E
 = ˆ


,

E
 = ( ˆ
 × E) × ˆ
.

122

(A.1)

(A.2)

(A.3)

(A.4)

(A.5)

(A.6)

(A.7)

And the same setting for B. Do some calculation, we can get









(cid:124)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:123)(cid:122)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:125)− ( 




+ 







(cid:124)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:123)(cid:122)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:125)
(cid:124)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:123)(cid:122)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:125) = 

(

 − 

)

+ 











)



ˆ
 × B


∇
E


− 
E






And ˆ
 · (∇
 × E
) = 

B
. Do the same thing to ∇ × B = −



E and sum up, we can get

.


B






E

+ 

ˆ
 × B
 = ∇
 

,



− 



ˆ
 × E
 = ∇
 

,
∇
 · E
 = − 







ˆ
 · (∇
 × E
) = 



,
ˆ
 · (∇
 × B
) = −





,

, ∇
 · B
 = − 







.

Considering eq.A.1, we can get

⇒ 
E






= ∇
 

 − 

ˆ
 × B
,

and

⇒ E
 =





2

 − 
2 (
∇
 

 − 
ˆ
 × ∇
 

).

Use the same method, we can get

B
 =





2

 − 
2 (
∇
 

 + 


ˆ
 × ∇
 

).

(A.8)

(A.9)

(A.10)

(A.11)

(A.12)

(A.13)

(A.14)

Only consider the Transverse Electro-magnetic (TEM) wave, let 

 = 

 = 0, 

 = 

 
 
, satisfies

∇
 × E
 
 
 = 0, ∇
 · E
 
 
 = 0.

This means the 

 
 
 is irrotational and no charge, and therefore

√



,


 = 
0 = 


B
 
 
 = ±√



 ˆ
 × E
 
 
 .

(A.15)

(A.16)

(A.17)

In hollow cylinders and on transmission lines at high frequencies, there occur two types of field
configuration because of considering eq.1.22, 

, 

 and the boundary conditions be satisfied. The

123

presence of surface charges and currents at the interface allows the existence of a normal component
of 
(
 = 
 
) at the boundary, and also a tangential component of 
(
 = 

), but the tangential
component of E and the normal component of B must be continuous across the boundary. The
boundary conditions are

n × E = 0,

n · B = 0,

where n is a unit normal at the surface S. And also



|
 = 0,









|
 = 0.

A.2 TM mode and TE mode

(A.18)

(A.19)

Since the boundary conditions on 

 and 

 are different, the eigenvalues will in general be

different. So the fields are divided into two categories:

Transverse Magnetic(TM) waves 

 = 0 everywhere, boundary condition 

|
 = 0.


 |
 = 0 .
Transverse Electric(TE) waves 

 = 0 everywhere, boundary condition 



For the propagation of waves inside a hollow waveguide of uniform cross section, the transverse

magnetic and electric fields for both TM and TE waves are related by




 =

where

and for TM waves

for TE waves

H
 =
where 

±

 
 is 

(

) for TM (TE) waves, and



 =

±1

 ˆ
 × 

,
(cid:114) 

(cid:114) 





, (TM mode)
, (TE mode)












=

=




0

0






E
 =

±



2 ∇

,

±



2 ∇

,

(∇2


 + 
2)
 = 0,

124

(A.20)

(A.21)

(A.22)

(A.23)

(A.24)

the boundary conditions are

for TM(TE) modes.


2 = 


2 − 
2,


|
 = 0,












|
 = 0,

(A.25)

(A.26)

Due to these equations and boundary conditions, there will be a spectrum of eigenvalues that

and we can define a cutoff frequency,

2 = 


2 − 



2,







 =



√



.

Figure A.1: Cutoff frequency

Then the wave number can be written as
√



 =





(cid:113)


2 − 
2

.

(A.27)

(A.28)

(A.29)

For a cylindrical waveguide, because of reflections at the end surfaces, the z dependence of the
fields is that appropriate to standing waves:


sin(
 
) + 
cos(
 
).

125

(A.30)

If the plane boundary surfaces are at z=0 and z=d, the boundary conditions can be satisfied at each
surface only if


 = 







( 
 = 0, 1, 2, ...).

For TM fields the vanishing of 

 at 
 = 0 and 
 = 
 requires



 = 
(
, 
)cos( 






)( 
 = 0, 1, 2, ...).

Similar for TE fields, the vanishing of 

 at z=0 and z=d requires



 = 
(
, 
)sin( 






)( 
 = 0, 1, 2, ...).

Then we can get for TM fields

TE fields

,

and consequently

and

E
 = − 





2 sin( 




2 cos( 












)∇

,



) ˆ
 × ∇

.

H
 =

E
 = −





2 sin( 







) ˆ
 × ∇



H
 =







2 cos( 







)∇

,


2 = 


2 − ( 





)2,


2



 =

1








2 + ( 





(cid:20)

)2(cid:21)

.

(A.31)

(A.32)

(A.33)

(A.34)

(A.35)

(A.36)

(A.37)

(A.38)

(A.39)

The cylinder waveguide, with radius R and length d, for a TM mode the transverse wave equation
for  = 

 , subject to the boundary condition 

 = 0 at 
 = 
 has the solution

where


(
, 
) = 
0

(


 
)
±


,




 =








,

126

(A.40)

(A.41)




 is the n th root of the equation,

(
) = 0. The integers m and n take on the values m=0,1,2,...,
n=1,2,3,... The resonance frequencies are given by





 =

1√



For TE modes, the boundary condition on

gives

so that

(cid:118)(cid:117)(cid:116)(cid:34) 
2




2 + ( 






)2(cid:35)

.



[ 



 


|
] = 0,


(cid:48)






,




 =

(cid:115)(cid:20) 
(cid:48)



2

2 + ( 






)2(cid:21)

.





 =

1√


(cid:118)(cid:117)(cid:116)(cid:34) 
2

(A.42)

(A.43)

(A.44)

(A.45)

(A.46)

(A.47)

Almost every RF cavity operates using the TM010 accelerating mode. This mode has a longitudinal
electric field 

 in the center of the cavity and is the lowest mode, which can accelerate the beam.

So that

2.405√

 

we can see the frequency is independent of d in this mode, and we can get

1√




010 =


=0,
=1


2

=

.

+ ( 0 × 





)2(cid:35)


 =

=

=

2.405
2.405
√

×
010
√

×2
 

2.405 × 3 × 108
/

2 × 3.14 × 1.3 × 109



2.405 × 


2
 


=

= 0.0884 m,

for f = 1.3 GHz, we can choose d half of the wavelength, so that


 =



2 =



2 


=

3 × 108
/


2 × 1.3 × 109



= 0.1153 m.

(A.48)

In reality, when calculate the geometrical factor on the Pill Box cavity, the value is 263 . The real
cavity shape is optimized using computer codes like Superfish (2D), CST Studio (3D). The real
cavity shape case for ILC cavity, the geometrical factor is 270 .

The expressions for TM010 mode fields are



 = 
0
0( 2.045





)
−


,

127

(A.49)

(cid:114) 








 = −



0
1( 2.045





)
−


 .

(A.50)

In Fig.A.2, Fig.A.3, Fig.A.4, Fig.A.5,we can see the field distribution in TM010 mode.

Figure A.2: TM010 mode

Figure A.3: 

 Vs d

And for TM020 mode, in Fig. A.6, we can see the E direction change when off the center.
For TE moodes, the lowest one is TE111, the resonance frequency is:

(cid:115)(cid:20)

)2(cid:21)


111 =

1.841√

 


1 + 2.912( 




.

(A.51)

For large d, (d > 2.03 R), the resonance frequency 
111 is smaller than that for the lowest TM
mode. And because the frequency depends on the ratio d/R, it’s possible to provide easy tuning by
making the separation of the end faces adjustable. Detailed deduction can be found in Ref. [42].

128

Figure A.4: 

 Vs 


Figure A.5: 

 Vs 


Figure A.6: TM020 mode

129

APPENDIX B

CRYOMODULE SOLENOID TEST IN FRIB

B.1 Cryomodules

In the FRIB cryomodules, superconducting solenoid packages for transverse focusing and
steering are interspersed with the cavities. An example is shown schematically in Fig. B.1: the

 = 0.085 QWR cryomodule (CM) contains 8 cavities and 3 superconducting solenoid packages.
This cryomodule is similar to the cryomodules fabricated for the MSU re-accelerator, ReA3 [130].
An important feature of the cryomodule design is the local magnetic shielding around the SRF
cavities [131]. The shields operate at cryogenic temperature ((cid:39) 25 K). Some parameters of the
solenoid packages in FRIB are listed in Tab. B.1.

The cavities and solenoid packages are certified individually via Dewar tests prior to assembly
onto the cold mass. After assembly of the cold mass into the cryomodule, the cavities and solenoids
are tested again in situ. For the solenoid packages, the goal is to make sure that all of the coils
can reach the FRIB design requirements (Table B.1), can operate stably and robustly, and do not
adversely impact the SRF cavity performance. There are several considerations for the test:

• Energizing test of superconducting solenoid in the cryomodule bunker test handles high
current ∼ 90 A and have to be concerned safety.
It potentially causes magnet quenches,
which will make a damage on the solenoid magnet.

Figure B.1: Layout of FRIB-1 Cryomodule (CM-1). C: cavity (green); S: solenoid package (blue).
Cavities 1 - 4 are shielded by mu-metal (black) and Cavities 4 - 8 are shielded by A4K (red).

130

Table B.1: FRIB 50 cm solenoid package design requirements. The fringe field requirement applies
at the magnetic shield.

Operating temperature
Solenoid nominal current

Þ 
2



Peak solenoid field on beam axis
Fringe field

4.5 + 0.5/−0.0 K
≤ 90.9 A
≥ 13.6 T2·m
≥ 8.0 T
≤ 270 gauss

• Magnet quench will be a problem with safety by the highly vaporized helium gas pressure in

the worst case.

• Because of the close proximity, the influence of the solenoid fringe field on cavity performance

is a major concern.

This document describes the solenoid test procedures, mu-metal replacement of original shield-
ing material effectiveness, an example of solenoid test result and the solenoid package CS-Studio
automatic scan files.

B.2 FRIB Solenoid Package

The solenoid package is designed for focusing and steering the beam with fringe field com-
pensation [132]. Figure B.2 shows a model of the coils, including the 8 T main solenoid, the two
bucking coils for fringe field cancellation, and the two steering dipole coils. The model was made
using CST Studio1. All of the coils are made of NbTi superconducting wire. The bucking coils
are designed to reduce the fringe field to ∼ 270 gauss at the magnetic shield. The bucking coils
produce a field of 0.06 T, and are wired in series with the main solenoid, with a nominal current of
90 A [132].

B.3 Local Magnetic Shield

As discussed above and illustrated in Figure B.1, the SRF cavities are enclosed by local magnetic
shields. This approach has two benefits: lower material cost for the shields, and better shielding of

1Computer Simulation Technology AG, Darmstadt, Germany

131

Figure B.2: CST Studio model of the 50 cm solenoid package. Inner cylinder: main solenoid;
intermediate rectangles: dipoles; outer rings: bucking coils. The diameter is 39 cm.

Table B.2: FRIB magnetic shield parameters.
Magnetic permeability 
 ≥ 10 000 at 25 K
Thickness
1 mm for QWR

the cavities from the remnant magnetic field in the cryomodule.

The need to mitigate the fringe field’s effect on the SRF cavity performance sets the shield
requirements. For the FRIB QWRs, the magnetic field at the cavity must be ≤ 15 milligauss.
Fringe fields higher than (cid:39) 300 gauss cannot be screened by the shield, hence they will produce
a drop in the cavity quality factor after a cavity quench. The magnetic shield requirements are
summarized in Table B.2.

For the ReA3 cryomodules, the local shields were made of A4K material, with 
 > 10 000
even at cryogenic temperature ((cid:39) 25 K). However, a recent analysis [131] showed that mu-metal of
thickness 1 mm with 
 > 9000 at (cid:39) 25 K can meet the shielding requirements for the FRIB QWRs.
Since cryogenic magnetic shields such as Cryoperm and A4K are very expensive compared to
mu-metal, switching to mu-metal is economically advantageous, if mu-metal can provide adequate
shielding. To evaluate the shielding performance of mu-metal relative to A4K, CM-1 includes
shields of both types, as shown in Fig. B.1.

132

Figure B.3: Diagram of the cooling system for cryomodule testing.

B.3.1 Cryomodule Test System

Figure B.3 shows a diagram of the cryogenic circuit for cryomodule testing. The cavities and
solenoid packages are cooled via independent supply lines. The cavities are cooled to 2 K and the
solenoid packages are cooled to 4.5 K. The current leads for the solenoid and dipoles are made of
high-temperature superconductor (HTS) wires, cooled by helium gas from the solenoid header. The
helium gas flow rate is controlled with a Proportional-Integral-Derivative (PID) loop based on the
measured current lead voltage. As only one set of power supplies is available for the cryomodule
test, one solenoid package is energized at a time.

133

B.4 Cryomodule Test Procedures

1. Energizing readiness check for the superconducting package: 1, Current calibration for
magnet sources; 2, Magnet cable connection; 3, Resistance measurement for the connection;
4, Control system checking at a low current (2 A) prior to the solenoid test .

2. Magnet exciting system check: 1, protection cover on the Top can; 2, Open the water valve
to cool the current sources behind the rack and Connect the gas cooling control cable in the
bunker; 3, Set file names for data tracking and save the file to “srftest” folder; 4, Set the
helium gas flow rate and switch the system to“Auto”.

3. Main solenoid excitation: gradually increase the current to 60 A with a 10 A step at the
ramping rate 0.2 A/s and watch the voltage drop below 3 mV and insulation vacuum carefully.
When stable, continually increasing the current to maximum (90 A or 91 A) with a 5 A step.

4. Main solenoid operation: 1, Hold the solenoid current at the max for at least 10 min; 2,
change the current setting to negtive maximum with the same ramping rate and hold for 10
min; 3, set to 0 A with 0.3 A/s ramping rate.

5. Bending corrector (dipole X for vertical bending and dipole Y for horizontal bending)
operation test, this is similar to the main solenoid excitation and operation: set the ramping
rate to 0.3 A/s, increase the current to 15 A with a 5 A step and then increase to 19 A with
1 A step; hold for 5 min, switch to -19 A and hold for another 5 min, then set to 0 A; then
repeat this for the other dipole.

6. Polarization Check by measuring the fringe field direction outside cryomodule. Sometimes

the cable for dipole x and y are switched, and need to be verified.

7. Solenoid and dipoles integrated operation test, this is the demonstration of full magnet
operation under the mutual fields and to make sure the mechanical robustness on the magnet
frame. The running pattern is same as CM-1 example that shown in Fig. B.4.

134

8. All magnets and two cavities (acceleration gradient at about 5 MV/m) integrated operation
test, this process simulates the cryomodule operation in the tunnel. The running pattern is
same as CM-2 example that shown in Fig. B.5.

9. Turn off cavities and degauss the magnets: repeatly set negative 75% of the maximum for all

the magnets until less than 0.1 A and then set to 0 A.

10. Turn off system, disconnect cables and close valve.

B.5 Example: CM-1 Solenoid Package Test

In the CM-1 test, we were able to energize all of the coils in all of the solenoid packages to their
operating currents (Table B.1). The gas cooling of the HTS leads was adequate, with lead voltage
drops below 40 mV.

Figure B.4 shows the magnet currents as a function of time for one of the solenoid packages
during the test. The main solenoid and dipoles were operated individually and collectively. The
magnets were ramped to their nominal currents with both polarities (±90 A for the solenoid, ±20 A
for the dipoles). Different ramp rates were used, up to 0.5 A/s, to check the PID capability. We
observed no magnet quenches during the tests, which indicates that the solenoid packages operate
robustly.

The solenoid package and the nearest two cavities were turned on for one hour to test the
influence of the solenoid package operation on the cavity performance. This test was repeated for
each solenoid package. In all cases, no degradation in cavity performance was observed. This
indicates that both mu-metal and A4K provide adequate shielding of the fringe field. A cavity
quench test was not done due to administrative limits on the cavity fields. After the coils were
energized, the solenoid package was demagnetized (see the last hour in Figure B.4 for an example).
The dynamic heat loads of the cavities at 2 K were measured to evaluate their shielding. The
results are summarized in Table B.3. No systematic differences were seen between the A4K shields
and the mu-metal shields. Thus, the mu-metal shielding of QWRs was successfully validated.

135

Figure B.4: Coil currents as a function of time for part of the solenoid tests in CM-1.

B.6 CM-2 Solenoid Package Test

CM-2 contains the first lot of 50 cm solenoid packages produced from a vendor; all of the
cavities are shielded with A4K. The testing procedure for CM-2 was the same as that of CM-1.
Figure B.5 shows some results from the CM-2 test. All 3 solenoid packages were tested without
quenches. The stable and robust operation indicates that the vendor-produced solenoid packages
do not affect the cavity performance.

Figure B.6 shows an example of the PID control for the He gas flow to cool the current leads as

the solenoid is ramped up at 0.3 A/s. The PID control works very well.

B.7 Automatic Test Using CS-Studio Scan Files

CS-studio Scan System supports several commands and can easily automated operations in
beam controlling. This inspires us to develop several scan files for solenoid package test, which

136

09:0709:3610:0410:3311:0211:3112:0012:2812:5713:26Time of Day-100-80-60-40-20020406080100Current (A)Main SolenoidDipole XDipole YFigure B.5: Coil currents as a function of time for part of the solenoid tests in CM-2. The two
adjacent cavities were turned on between 15:08 and 16:06.

Figure B.6: Example of PID control while ramping the solenoid current at 0.3 A/s. The set point
is a voltage drop of 30 mV.

137

12:4212:5613:1113:2513:4013:5414:0914:2314:3814:5215:0715:2115:3615:5016:05Time of Day-1000100Current (A)024681012141618E Field (MV/m)Cavity 1Cavity 214:3814:5215:0715:2115:3615:5016:05Time of Day-1000100Current (A)0255075100PV (mV)Table B.3: Dynamic heat load of CM-1 cavities at 2 K. Measurements were done at the nominal
accelerating gradient of 5.6 MV/m (except for C#1, which was at 7 MV/m, having an initially
miscalibrated field level).

Cavity
C#1
C#2
C#3
C#4
C#5
C#6
C#7
C#8

load (W)

Dynamic heat Shielding
Material
Mu-metal
Mu-metal
Mu-metal
Mu-metal
A4K
A4K
A4K
A4K

6.2
2.4
2.5
1.0
2.4
2.5
2.4
2.6

Figure B.7: Example of CS-Studio scan system operation window

will save the testing time and avoid input errors. The easily aborting and editing properties also
made it safe to use (Fig. B.7). We simply reproduce the procedures in the scan files we made. A
example of integral test scan file is shown in Fig. B.8.

This process is the automatic version for the test steps talked before, PV values are preset in the

scan files so that we can save time for input values every single time during the test.

138

Figure B.8: Integral test scan file, REA_CMTF:PSOL_N0001:I_CSET is the solenoid current
setting, REA_CMTF:PSC1_N0001:I_CSET is the corrector 1 (dipole y) current setting, and the
other is the REA_CMTF:PSC1_N0001:I_CSET is the corrector 2 (dipole x) current setting.

139

B.8 Conclusion

We introduced FRIB cryomodule, include solenoid packages design and test procedures, and
showed examples in the first two FRIB cryomdules.
In the first cryomodule test, we verified
that our in-house designed and fabricated solenoid packages meet FRIB specifications for field
performance and stable operation. We found that mu-metal is a viable alternative to A4K for local
magnetic shielding in FRIB cryomodules. Since the A4K magnetic shields for the FRIB 
 = 0.085
cryomodules have already been ordered, we will use mu-metal for other FRIB cryomodules (
 =
0.041, 0.290, and 0.53), which will result in a substantial cost reduction. In the second cryomodule
test, we successfully validated the performance and stable operation of vendor-produced solenoid
packages.

140

APPENDIX C

STUDY FOR LOW FIELD Q SLOPE ISSUE IN FRIB

FRIB requires a 200 MeV per nucleon driver linac with a total of 332 superconducting radio-
frequency (SRF) cavities of 4 different types: 
 = 0.041 quarter wave resonators (QWRs, 12
cavities), 
 = 0.085 QWRs (100 cavities), 
 = 0.29 half wave resonators (HWRs, 72 cavities) and

 = 0.53 HWRs (148 cavities). The 2 K test of superconducting quater-wave resonator (QWR) of
FRIB, especially the resonator with 
 = 0.085, was found to have a significant Q-factor decrease in
the low field region (E


 < 2 Mv/m), as shown in Fig. C.1. This appendix discussed the reason of
this degradation and the method to study it.

Figure C.1: Q Vs. E


 for an example of FRIB 
 = 0.085 QWR. Q has sharply dropping in E



< 2 Mv/m region for the 2 K test case.

141

Figure C.2: 

 Vs. 1/T for for the same 
 = 0.085 QWR in Fig. C.1. There is a transit point of this
result on 1/T = 0.31 (K−1) region, which is around indium superconducting transit temperature T
= 3.4 K.

C.1 Transit Point

We noticed for some test results of the QWRs, the 

 Vs 1/T curve during decreasing temperature
from 4 K test to 2 K test at E


 ∼ 2 MV/m has a turning point located at ∼ T = 3.4 K region
(Fig. C.2), this matches the indium metal superconducting transit point.

Indium wire is used as sealing between the cavity body and the bottom flange on the FRIB
QWRs. This structure was designed to be performed High Pressure water rinsing, which could
increase the quality factor of the QWRs significantly.

The indium sealing made the cavity has two superconductor exposed to RF field, with transit
temperature at 3.4 K for indium and 9.26 K for niobium. The T = 3.4 K located in the range
of operation temperature 4 K and 2K, so the transit point of normal conducting In transit to
superconductor In was monitored during the temperature decreasing process.

We noticed the T
 for indium is not exact 3.4 K, this may due to indium exposed in small value

142

Figure C.3: FRIB 
 = 0.041 quarter wave resonators (QWRs), 
 = 0.085 QWRs, 
 = 0.29 half
wave resonators HWRs and 
 = 0.53 HWRs. Both QWRs have bottom flanges that sealed with
indium wire.

of magnetic field. Based on T
 = 3.4 K, H
(0) = 0.03 T, transit point at 1/T = 0.31 K−1 and T

relation with H
(0):

we can get 

(
) (cid:27) 0.1 

(0) (cid:27) 3 ×10−3 T.



(
) (cid:27) 

(0) · [1 − ( 





)2],

(C.1)

On the meantime, the Nb is always superconductor during the whole test. This indicate that we
can have two BCS superconductor equations for the cavity: for T > 3.4 K, In is normal conductor,
and the resistance does not change with temperature, so the equation is:



 = 
0 + 

 



2





 
(−Ɗ(0)
 



 



).

(C.2)

The R0 includes the residue resistance of superconducting Nb and In normalconducting resistance.
while for T ≤ 3.4, both In and Nb are superconductors, so the equation becomes:



 = 
(cid:48)

0 + 

 



2





 
(−Ɗ(0)
 



 



) + 





2





 
(−Ɗ(0)




 



),

(C.3)

143

where Ɗ(0)
 
/
 
 = 19.28 K, and Ɗ(0)

/
 
 = 6.19 K, and this R0’ includes both residue resistance
for superconducting Nb and In. We can adopt these two equations, applying BCS fitting for the
result data, and get some information that related to the low field Q drop problem.

C.2 BCS Fitting

We first separate the result data by the transit point,plot two graphs and do BCS fitting for the
T > 3.4 K part (Fig. C.4, left), with the equation: m1+m2*exp(-19.28*x)*x (Eq.C.2, 1/T as x), and
get m1 = 5.835, which is the R0 in n and m2 = 1237.7 is the 

 

2 in Eq.C.2. In this case,


0 = 


,

 + 

 
,


,

where 


,

 is the normal conducting resistance and 

 
,


 is the Nb residue resistance, both
resistances do not change with temperature.

Then we do Niobium and Indium BCS fitting for T < 3.4 K (Fig. C.4, right). Use the value
we got for 

 

2 = 1237.7 from the first fitting, we use the equation: m1’+1237.7 *exp(-
19.28*x)*x+m2’*exp(-6.19*x)*x (Eq.C.3, 1/T as x) we get m1’ = 3.776, which is the the R0 in 

and m2’ = 43.18 is 



2 in Eq.C.3. In this case,


(cid:48)
0 = 


,


 + 

 
,


 = 



,


,

is the sum of f both Nb and In’s superconducting residue resistance. Compare with Eq. C.2 and
Eq. C.2, we can get


0 − 
(cid:48)

0 = 


,

 − 


,


,

this agrees with the fact that the two part of graph is separated with indium T
.

C.3 Statistic Result

During studying this low field Q drop issue of 
 = 0.085 QWRs, Dr. Zheng in cryomodule
department found that some simple re-toque of the bottom flange can solve this problem. Thus
we compare the before and after re-toque data of some QWRs, and get the average value shown in
Tab. C.1.

144

Figure C.4: 

 Vs. 1/T for an example 
 = 0.085 QWR. Separate BCS fitting was done for T > 3.4
K (left figure) and T < 3.4 K (right figure) and the fitting result parameters are shown in the boxes
on the figures.

Table C.1: BCS fitting average result for 10 QWRs before Re-Toque and 10 QWRs after Re-Toque
in FRIB. The R


,


 and R

,

- R

,


 are from fitting, while R

,2
 is directly from averaging
the test data.

Cavity Status

Before Re-Toque
After Re-Toque

Decrease

R


,


 R

,

- R

,


 R

,2

4.75 

0.95 

0.84 

2.83 

40.52%
11.38%

2.13 

1.98 

7.20%

The residue resistance of the cavity is dropped by 40.52% after the re-toque, which is much
higher improvement than the other two parameters. Here “residue” means it does not change with
temperature. The residual resistance is temperature independent and is related to many causes:
surface imperfections and inclusions, residual dc magnetic field, condensed gases, etc...

C.4 Conclusion

Through statistical analysis of all the data of QWR vertical test, data fitting with BCS principle,
it is found that the main reason for this phenomenon is that the residual resistance of indium wire
used for sealing is too high in 2K superconductive state. The extra resistance may due to the oxide
layer, re-toque process pressed the indium wire more, and breaks the oxide layer. This assumption

145

agree with the fact that 
 = 0.085 QWRs have more serious Q drop, this is because the bottom
flange of them are heavier than the 
 = 0.085 QWRs, so the gap between the cavity and bottom
flange is larger, and indium wire has more un-broken oxide layer.

146

BIBLIOGRAPHY

147

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