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31293 0102 291

This is to certify that the

dissertation entitled

An Eight Tesla Superconducting Magnet
for Cyclotron Studies

presented by

Jong-Won Kim

has been accepted towards fulfillment
of the requirements for

Doctor degree in Science

Department of Physics

7

44/1? X27491

 

 

 

Major professor L

Date af% #7?
/ /

MSU is an Affirmative Action/Equal Opportunity Institution O< 12771

‘

LIBRARY
Michigan State
University

 

PLACE IN FIET URN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.

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13A,!“ 3 El

 

 

 

 

 

 

 

 

 

AN EIGHT TESLA SUPERCONDUCTIN G
MAGNET FOR CYCLOTRON STUDIES

By

J ong—Won Kim

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1994

ABSTRACT

8 TESLA SUPERCONDUCTING MAGNET FOR CYCLOTRON
STUDIES

By

J ong—Won Kim

Superconducting magnets have become broadly used for cyclotrons due to advan-
tages of compactness and lower operation costs compared to conventional magnets.
To gain benefits of higher magnetic fields beyond the 5 tesla cyclotron magnets which
are under operation in several laboratories including the MSU / N SCL, a test magnet
which can produce fields higher than 8 tesla was constructed. Our goal was to develop
the coil construction technique, to use the magnet as a test stand, and to pursue a

conversion to a cyclotron in the future.

The basic magnet design has the characteristics of a superconducting isochronous
cyclotron. Because of the large magnetic forces in high field coils, the coil design has
been intensively studied with computations and experiments. When construction was
completed, the magnet proved to produce fields higher than 8 tesla at 4.4 K. Mag-
net properties such as spring constants of link assemblies and magnetic off-centering
forces, magnet inductances, and heat leak to 4 K were measured and compared with
computations. Magnetic fields were also measured along a radial line at a fixed angle,

and compared to 3-d field calculations made with the TOSCA program.

Using the 8 tesla magnet to generate a broad range of radially flat fields from 2

to 8 tesla, emittance measurements of an internal ion source would be possible in the

 

magnet’s center region. Computations were made to yield a possible experimental

scheme for the measurement.

An eventual use of the 8 tesla magnet could be a conversion to a cyclotron. In the
design study presented in the appendix, the 8 tesla magnet is assumed to accelerate
deuterons in a central field of 7.2 tesla. This would yield a deuteron energy of 35
MeV, i.e. a cyclotron K value of 70 MeV. To utilize the maximum field produced by
the 8 T magnet (~8 tesla), an ion with a lower Q / A such as He+ has been suggested

as a design particle, yielding a K value of approximately 90 MeV.

ACKNOWLEDGMENTS

The 8 tesla magnet was completed by the collective effort of the N SCL accelerator
group. Credit for the successful completion is due to each person who has been
involved in the project. Most of all, Guenter Stork deserves a great deal of my
appreciation for his skillful magnet design and assembly. The machine shop personnel

have also been a great help throughout the project.

Prof. Henry Blosser, who initiated this project and has supervised all the way
with his great enthusiasm, has influenced my life as well as this project. His advice
and encouragement during my thesis project are very much appreciated. It is also a
pleasure to acknowledge my gratitude to Dr. Albert Zeller who joined this project at

the beginning, and has given much valuable advice.

I want to thank Dr. Felix Marti, Mr. Dave Johnson and Prof. Mort Gordon
for many invaluable discussions during the cyclotron group meetings. In addition, I
am indebted to Prof. Jerry Nolen, Prof. Aaron Galonsky, Prof. Michael Dubson,
and Prof. Julius Kovacs for their comments and help on my thesis as guidance
committee members. Fellow graduate students, Leung-Sheng Lee and Jeff Schubert,
have been greatly helpful in the construction of the 8 tesla coils. Special thanks go to
colleagues in the accelerator group, Jim Bailey, Dong-o Jeon, Bo Zhang for fruitful
conversations and discussions about accelerator physics and our future. Finally, my

family and relatives deserve my greatest thanks for their constant love and support.

iv

 

Contents

LIST OF TABLES

LIST or FIGURES

1 Introduction

2 Design of the 8 tesla magnet and its components

I

11

Initial Design Considerations .......................

A

EQ'TJEUUOE

[~qu

Design

>

FJUOUJ

Design parameters of the 8 T magnet ..............
Magnetic fields ..........................
’Tightly banded coils’ vs ’Free coils’ ...............
Stress estimates for the 8 T coil .................
Relaxation of preloads ......................
Selection of banding material ..................
Test of stainless steel cable as a banding material .......

Effect of transverse Young’s modulus of banding on frictional
coil motion ............................

Magnet quench simulations ...................
Effect of an aluminum bobbin in a quench ...........
Selection of design operating current ..............
Stray magnetic fields .......................
of magnet components ......................
Support links ...........................
Spring constants of the link system ...............
Test of sample links ........................
Median plane structure of the 8 T coil .............

Current leads ...........................

vi

vii

00030365

13
19
21
23
24

38
43
43
45
49
52

3 Construction of the 8 T magnet system
I Materials in the coil ............................
II Coil winding ................................
111 Test of coils in the liquid helium dewar .................
IV Vacuum system ..............................

V Cryogenic system and radiation shields .................

4 Measurements of 8 T magnet properties
I Coil centering ...............................
II Accident during initial magnet operations ...............
III Strain gages for coil stress measurements ................
IV Coil stress measurements of the 8 T magnet ..............
V Magnet quench study ...........................
VI Inductances of the magnet ........................
VII Heat leak in the magnet .........................

5 Field mapping and analysis

6 Conclusion
A Plan for the ion source emittance measurement
I Source emittance measurement under rf extraction ...........
A Central region designed for emittance measurement ......
B Conclusion .............................

II RF resonator for ion extraction .....................

B Conversion of the 8 T magnet to a cyclotron
I Magnetic fields ..............................
11 Central Region ..............................

III Conclusion .................................

vi

60
60
63
66
70
71

74
74
77
79
80
82
85
89

93

100

103
103
104
109
110

List of Tables

2.1
2.2
2.3

2.4

2.5

2.6

2.7
2.8

3.1

3.2

4.1

4.2

4.3

5.1

A.1

Cost comparisons of the 7 T, 8 T, and 9 T magnets ..........
Design parameters of the 8 T magnet ..................

Transverse Young’s modulus of the coil wound with aircraft cable as a
function of the applied loads. ......................

Critical current data of the 8 T conductor from Supercon Inc. for T:

4.22 K. The measurement was made on a strand used for the small coil.

Self inductances of the coils and aluminum bobbin, and mutual induc-
tances computed with POISSON. The row labeled ’Present’ displays
the inductances for the Figure 2.9 coil configuration. In the ’Assumed’
line, the mutual inductances of the coils to the bobbin are assumed to
be larger, such as might be achieved with thin coils as described in the
text. ....................................

Cost comparison of yoke and active shielding of stray fields considering
only additional steel and superconductors. Unit prices of steel and
superconductor come from the 8 T magnet cost .............

Comparison of G-lO, and Scotchply ...................

Spring constants of a vertical off-centering force calculated by POIS-
SON at 8 tesla. ..............................

Properties of the 8 T conductor .....................

Work days per coil set spent on actual winding .............

Comparisons of link spring constants calculated or measured using dif-
ferent methods ..............................

Comparisons of measured magnet inductances to calculations with
POISSON after iron saturation. .....................

Heat leak at 4.4K .............................
Calibration of the Hall probe by the N MR probe ............
The initial conditions used for orbit calculations in Figure A.2 & 3:
initial energy (E,), source opening size, and normalized emittance, en

(cofl7)(mm-mrad). The a is the maximum incident angle of ions with
respect to the normal to the source opening. ..............

vii

29

37

42
45

47

62
64

77

88
91

94

106

A.2 Parameter variations for the new orbit distributions in Figure A.3. One
parameter is varied for each case. .................... 109

A.3 Ac analysis of the circuit shown in Figure A.5 with RESON. A mea-
surement of the actual test resonator with elongated 8 turns to simulate
the 14 turn coil resonator in Figure A5, is displayed in the last row. 113

A.4 Resonance frequency depending on the coil dimensions ......... 116

viii

 

List of Figures

1.1

2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9

2.10

2.11
2.12
2.13
2.14
2.15
2.16
2.17

3.1
3.2
3.3
3.4

4.1
4.2

A schematic view of the 8 tesla magnet .................

Field forms of two coil system for three different splits in a coil . . . .
Magnetic field profiles for three different excitations .........
2-d finite element analysis of tightly banded coil case .........
2-d finite element analysis of free coil case ...............
A removable winding form used for the 8 tesla coil construction

Total axial and radial forces on the coils at 8 tesla excitation .....
Stress distributions in the 8 T coil calculated with STAN SOL

QUEN CH code calculation for a 8 T magnet quench ..........

The effect of aluminum bobbin on a quench of the 8 T magnet calcu-

lated with QUENCH ...........................

Effect of aluminum bobbin on a quench with larger mutual inductance
assumed ..................................

Active shielding case ...........................
Yoke shielding case ............................
Horizontal and vertical support link assemblies .............
Combination joint and pin joint .....................
View of the midplane structure .....................
Cross-sectional view of the current leads ................

Heat leak measurement on current leads ................

Mylar forming die .............................
Paper cutting apparatus used for coil winding .............
A coil set under winding .........................

Coil test in a large open dewar ......................

Idealized link systems and measured spring constants .........

Strain gage test and a test stand ....................

3

10
12
15
17
18
20
22
33

35

36
40
41
44
50

61
65
67
69

75
81

4.3

4.4
4.5
4.6

5.1
5.2

5.3

5.4

A.1

A.2

A.3

A.4
A.5
A.6

B.1
B.2
B.3

Comparison of current decay measurements at magnet quenches with

QUEN CH calculations ..........................
Quench history of the 8 T magnet ....................
Magnet inductances measured as a function of currents ........

Heat leak measured as a function of LHe level .............

Model used for TOSCA calculations ...................

Measured magnetic fields compared with TOSCA calculations for three
different excitations ............................

Error fields between measurement and calculations for two different
iron saturation points ...........................

Fourier analysis of TOSCA fields ....................

Central region designed for ion source emittance measurement under
rf extraction ................................

Projections of rectangular initial phase spaces into the slit coordinate
space ....................................

Projections of phase space into slit coordinate space with a physical
parameter varied. .............................

Plan view for the ion source emittance measurement ..........
Configuration of the coil resonator and its equivalent circuit .....

Circuit diagram for testing the resonator ................

Configuration of the 8 T magnet for D+ cyclotron and magnetic fields
Contour map of median plane field and focusing frequencies .....

Central region of the 8 T magnet with orbit trajectories for D+

84
86
87
9O

95

96

97
98

105

107

108
111
112
115

Chapter 1

Introduction

With the advent of superconducting magnet technology, cyclotrons have become more
compact and more cost effective by using much higher magnetic fields than previous
room temperature cyclotrons. Present superconducting cyclotron magnets use an
’average’ field1 of about 5 tesla [Tri90] compared with 1-2 tesla fields for room tem-
perature cyclotrons. Construction costs as well as operating costs have been reduced
approximately 50% by this doubling or tripling of the average field strength along
with the resulting 10 to 20 fold reduction in magnet weight. A further field increase
from 5 to 8 tesla is likely to yield a similar benefit. This will, however, entail tighter
tolerances resulting from smaller space, and will thereby bring more challenges in de-
sign and construction of cyclotron subsystems. The use of 8 tesla in a future cyclotron

will be a significant step in the development of smaller, and less costly cyclotrons.

The major goal of this project is to construct a magnet which would operate re-
liably at 8 tesla with a general structure appropriate for an isochronous cyclotron.
The Harper hospital cyclotron, using a current density of 13,000 amp / cm2 at approx-
imately 5 tesla, is a present landmark in this direction [B1089]. The selection of 8
tesla rather than some higher fields is due to the critical current limit of the N bTi

superconductor at 4.2 K. To achieve even higher fields (as in the 10 tesla magnets

 

1’average’ field is the azimuthal average of the magnetic field at a given radius

1

of the LHC at CERN [Kat90]), one would need to move to a different basic magnet
concept involving either: 1) a complicated cryogenic system to reduce the operating
temperature to 1.8 K, or 2) N b3Sn superconductor at 4.2 K. Both of these alternatives
would likely cost substantially more than the well established N bTi technique at 4.2

K. Therefore, 8 tesla has been selected as the goal of the present project.

The 8 tesla magnet, shown schematically in Figure 1.1, has been designed to
serve both as a cyclotron and as a multipurpose test stand to study cyclotron related
phenomena. This thesis presents details of the design and construction of a super-
conducting magnet, and the measurements of its properties and fields. Future uses
of this magnet as a cyclotron and as an emittance measuring apparatus are described

in the appendix.

The design process for this magnet involved many numerical studies of possible
alternative configurations of coil and magnet as described in chapter 2. Calculations
of magnetic fields and forces in the coil were used to compare the advantages of

different options, and the design parameters were finalized.

High field superconducting coils demand a careful evaluation of coil stresses. Max-
imum stresses have been calculated and reduced to an acceptable level using preloads
on the superconductor and on the banding. In particular, tensile and shear stresses

were reduced so that quenches induced by large stresses were avoided.

The coil shape was fully determined after magnetic fields and stress calculations
were completed, and then dimensions and maximum operating current of the su-
perconductor were selected. Quench simulations and hardware considerations were

undertaken simultaneously to ensure that the design parameters are acceptable.

As the computational study progressed, the mechanical magnet design was begun

based on previous experience in construction of superconducting cyclotrons. Some

Rupture disc/

 
  
   

Cryogen
Distribution box

Current leads—\

7?—

Horizontol link

 

104cm

 

Vertical link——>

Figure 1.1: A schematic view of the 8 tesla magnet. Some details of the mechanical
design as a superconducting magnet are shown.

prototype components such as support links were experimentally tested to obtain the

optimal design configurations.

Coil winding was one of major works in this project. Coil failures due to mistakes
in the winding process have not been unusual in the history of superconducting mag-
nets [Gre81][Des79]. After a few months of preparations, it took about two months to
complete the winding of all four coils. The coils were then tested in a large commer-
cial liquid helium (LHe) dewar to find possible faults in the winding process. Both
small and large coil pairs worked properly. The test was an important step in moving
the project forward. In chapter 3, details of the construction of the 8 T magnet, its

test, and features of magnet system are presented.

After completing the magnet assembly, properties such as spring constants of
support links and magnet inductances were measured, as described in chapter 4. The
magnetic field was mapped for different excitations. The measurements were made
at a fixed angle, and were compared with 3—D calculations by TOSCA [Tos]. Field

measurements and their analyses are provided in chapter 5.

A possible first use of the magnet may be to measure ion source emittance using
the radiofrequency (rf) extraction in a broad field range of 2—8 tesla. Preparing for
that, some computations have been made, and also a rf resonator to extract ions from
the source has been tested. These results are presented in the appendix. The central
region of the emittance test assembly is designed to spread the beam for differing rf
starting times. A three slit system could then roughly distinguish three parameters:
rf starting time (T), and radial phase space (r,pr). Complications, however, related
to initial ion energy and plasma meniscus require some experimental data before the
present slit system described in the appendix is further optimized. Calculations in the
appendix could serve as a guide for future computational and experimental studies

of ion source emittance measurements.

A preliminary study of possible conversion of the 8 tesla magnet to a cyclotron is
also presented in the appendix. A single particle and fixed energy machine is assumed
in computations. A deuteron was used as a projectile, and the central region of the 8
tesla magnet was designed to operate at the third harmonic of the cyclotron frequency

in a central field of 7.2 tesla with 50 kV dee voltage.

Chapter 2

Design of the 8 tesla magnet and
its components

The design studies of the 8 tesla (T) magnet are presented in this chapter. Several
magnet design options are compared to show their pros and cons. In parallel with
the computations, experimental tests have been performed on magnet components to

obtain realistic design parameters.

I Initial Design Considerations

A Design parameters of the 8 T magnet

The 8 tesla field was adopted due to the fact that the current density in a N bTi coil at
higher fields is severely limited (assuming the N bTi superconductor is used at 4.2 K;
the peak field in the conductor is 7.9 tesla when the peak field in the magnet gap is 8
tesla). The critical current of typical N bTi superconductors drops nearly 50% when
the field increases from 8 to 9 tesla (for instance the critical current of the 8 T magnet
conductor at 4.2 K is 650 A at 8 tesla, and 360 A at 9 tesla). To show economical
reasons of choosing an 8 T magnet, cost comparisons for 7 T, 8 T, and 9 T magnets
are made in Table 2.1, including the costs of the yoke and of the superconductor.

The following is assumed in calculations: ( 1) the magnetic rigidity is fixed to be 1.5

6

 

Table 2.1: Cost comparisons of the 7 T, 8 T, and 9 T magnets

 

LMagnet I J (average in coil) 1 Yoke I Superconductor I Total cost I

7 T 17,000 A/cm2 8.7 ton, 3 35 k 39,000 ft 3 32 k 3 67 k
8 T 12,400 A/cm2 3.0 ton, 3 32 k 46,000 ft 3 37 k 3 69 k
9 T 7,300 A/cm2 10.7 ton, $ 43 k 63,000 ft 3 50 k 3 93 k

 

 

 

 

 

 

 

 

 

 

 

tesla-m, (2) the yoke thickness is determined by the requirement of the same fringe
field at the yoke edge. (3) the maximum current is 400 A for all three magnets. The
material costs to build a 9 T magnet are sharply increased from the cost of an 8 T

magnet, and a 7 T magnet is less compact than an 8 T magnet.

The pole radius is about 20 cm which is convenient to accommodate the diagnos-
tic devices for beam studies. This radius will also allow the magnet to become an
interesting nuclear physics cyclotron in the future. The cyclotron Kb at 20 cm and 8
tesla is approximately 100 MeV so that E/ A for Q / A=0.25 is 6 MeV/n. A cyclotron
of this energy range would be a useful tool for studying high angular momentum

states in nuclei using heavy ion reactions [N uc].

The basic coil structure is a layer type winding without connection joints inside
the coil. There are in total four coils: two small and two large. A small coil pair
is serially connected, and so is the large coil pair, in order to produce the median
plane symmetry. The resulting two current system allows the small and large coils to
be independently energized as in other cyclotrons (K1200, K500, Agor, Chalk River,
etc.) to obtain different field shapes from different coil excitations. This field shaping
by using different current ratio on the two coils is a unique feature of superconducting
cyclotrons; which allows them larger dynamic range than conventional room temper-
ature cyclotrons for different ions and their energies. The superconducting coils are

potted with epoxy which results in compactness and high current density. The sta—

 

Table 2.2: Design parameters of the 8 T magnet

 

Coil total four coils: two small and two large coils
potted with Stycast 2850 FT, 48 layers for each coil
large coil : 2904 turns, small coil : 1363 turns
Cu/NbTi= 1.9, bare wire : 1.0 x 2.1 mm

Banding 304 stainless steel wire, 1.1x2.0 mm
2.35 cm thick overall
Clam shell on the outside of the banding:
3 segments of solid 304 stainless steel, 0.58 cm thick

 

 

 

Current 400 A for both coils at 8.2 tesla
Jame: 13,028 amp/cmz, J,mau=12,434 amp/cm2
Pole radius: 21.2 cm, pole gap: 8.1 cm

 

 

 

 

Yoke 1020 SAE steel, 8 tons, radius=63.8 cm, height=104 cm

 

bility of potted coils at 8 tesla is a main concern of this project. Because of the high
stresses, stainless steel is used on the outside of the coils to reinforce the coils. The
magnet has a pillbox type yoke as in many superconducting cyclotrons. The overall

design parameters of the 8 T magnet are displayed in Table 2.2.

The maximum current density of superconducting wire depends on manufacturing
technology as well as on inherent critical currents of superconductors. The critical
current density of some round N bTi wires is larger than 40,000 amp/cm2 (average in
conductor, Cu/Sc ratio=1.6) at 8 tesla, 4.2 K [Als]. However, a maximum operating
current of about 20,000 amp/cm2 (average in conductor) at 8 tesla, 4.4 K was chosen
after considering the design current density of other working magnets. The maximum
current of 400 A at 8 tesla was decided according to considerations such as heat leakage

and magnet inductances as described in section 2.I.K.

B Magnetic fields

The field profiles need to be defined to determine the specific coil configuration. The

ion source emittance measurement, which is planned to be one of the first uses of the

 

magnet, works optimally with a radially flat magnetic field in the required range of 2-8
tesla. In addition, the isochronous fields for heavy ions are nearly flat (a final energy
of 6 MeV/n needs only a 500 gauss increase at a full radius of ~20 cm when the center
field is 8 tesla). The magnetic fields can also be further shaped by manipulating pole
tip configurations in conjunction with the two coil currents as in other isochronous

cyclotron magnets.

Compact superconducting cyclotrons basically have split solenoid coils with me-
dian plane symmetry, and two image coils are serially connected (room temperature
penetrations for the beam and for diagnostic elements must pass through the coil at
the solenoid split). A single current system is suitable for fixed (or slightly variable)
energy cyclotrons accelerating a few different ions with use of trim coils to shape
the magnetic fields. However, in order for a cyclotron to widely vary its projectiles
and their energies, subdivisions in the main superconducting coil are commonly used
to enhance control of the magnetic field shape, reducing the power needed for room
temperature trim coils. The coils could be multiply divided in principle, but their
field forms tend to become redundant. One split with two controllable currents is a
natural choice in terms of cost, and provides adequate variation of field forms with
coil excitations. The split location is then the parameter which needs to be optimized.
In this study, three locations were investigated: one third from the top or the bottom,
and at the middle of the coil. Figure 2.1 shows the field forms from each coil when a
current density of 13000 amp / cm2 is used. These are calculated by a program which
integrates the Biot-Savart formula for each turn assuming median plane symmetry.
The lower the split location is, the steeper the field slope is at the edge of the pole.
The location of the split is basically determined according to the uses intended for
the particular magnet. The coils of K500, K1200, for instance, have bottom and top

splits, respectively. The AGOR cyclotron magnet on the other hand has the split

 

10

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

24.4CM
J2 J2
J2
J1
J1
J1
3.13CM —|l—-—
24:11:14 0 f 0"
30.5CM
(A) (B) (C)
50 l l l l l l l I J l 1
(C) /x
CD 40... _
:3 (B) m
a —————————
L£30— (A) //<_\‘
LJ. \ \
o ~~~~~~~~~ m (A) \
E 20“ \ \ \ \—
ES \ \
Z ———————————— (B) \ \
o 104 x \ \ \ _
E (C)
O l I l l l

 

 

l l l l l l
O 2 4 6 8 10 12 14- 15 18 2O 22 24
RADIUS (cm)

Figure 2.1: A quarter of coil cross—sections and magnetic field forms are shown for
three different splits in the coils (median plane symmetry is assumed). A current
density of 13,000 (amp/cmz) is used. The solid lines are the field forms of the inner
coil (J1), and the dashed lines are those of the outer coil (J2). The split in the 8 T
coil is (c).

 

11

coils separated further to accelerate protons as well as heavy ions [Com88]. For the 8
T magnet, we chose the top split since calculations indicate that the magnetic fields

fit better to the radially flat profiles at low excitations with the top split.

The capability of field shaping could be enhanced by using a reverse current in one
of the two coils. The K1200 magnet, for instance, uses reverse current in the outer
small coils when light ions are accelerated. The field form by this reverse current
is helpful in generating isochronous fields for light ions, which can be inferred from
Figure 2.1. This scheme, however, was not accepted for the 8 T magnet because of the
desire to keep the coil design simple. In order to realize the reverse current scheme,
there needs to be a complex mechanical support structure to clamp the outer coils

against electromagnetic forces which are directed away from the median plane.

Since we have taken into consideration the eventual conversion of the 8 T magnet
into a cyclotron, the magnet has the characteristics of an isochronous cyclotron in
its magnetic field calculations; the pole tips have separate sectors. This is simulated
by a stacking factor of 0.5 on the pole tips using the program POISSON [Men87],
which means that the sector structure occupies 50% of the total volume. (The pro-
gram POISSON solves electrostatic or magnetostatic problems in a 2-d Cartesian or
3-d cylindrical geometry by ‘successive point over-relaxation method’.) The magnetic
fields are fitted to flat profiles for three different excitations, and displayed in Fig-
ure 2.2. The pole tip is contoured in the valley region as in other superconducting
cyclotrons to shape the fields. Even with a two coil system, it is difficult to make
the magnetic field fit the flat profile in a broad field range with a single pole tip
configuration. Trim coils usually employed for minute adjustments of field shapes are
not considered because of the complexity of the system; sets of pole tips will be used

instead to trim the profiles of the specific fields covering the range of 2-8 tesla.

 

12

50.3 cm

Weight: ~8 tons

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

J2
_‘__r‘-l_ J1
S.F.=0.5
0 24.4 cm 62.0 cm
80.5 . . 1 1 .
80.01//

7905/ J: 13640 omp/cm2
790' J2— — 13950 (imp/cm2

78.5
V505

50.0

f .
49-5 J— — 8130 amp/cm2 /\ '

 

 

 

49-0 J;- —- 4185 omp/cm2

48.5
17.5

l7.0* '
16'5“ J1: 1395 omp/cm2 i

16.0 _ 2

1551 J2— 0 omp/cm

'02‘468101121'41‘61'820
Radius (CM)

 

 

Mognetic Field( (kG)

 

 

 

Figure 2.2: The magnetic fields are profiled to have a flat radial dependence covering
the required range of 2-8 tesla. The flat profiles radially are chosen for ion source
emittance experiments. The pole tips are contoured in the valley region as in other
isochronous cyclotrons.

 

13

C ’Tightly banded coils’ vs ’Free coils’

The most probable quench origin of superconducting solenoid coils is in the innermost
layer where magnetic fields and stresses are maximum. If the coil is left on the winding
form, a large shear stress occurs at the innermost layer due to the counter-force of
friction on the coil form versus the axial magnetic force. The shear stress on that

layer is then a likely cause of quenches (shear stresses in the coil originate from field

variations, OBr/ar and BBz/Bz).

Besides the shear stress, differential thermal contractions produce tensile stress
on the interfaces of different materials. When the coils cool down to 4 K, the es-
timated tensile stress on the Formvar insulator amounts to 4000 psi. This thermal
stress in combination with the shear stress generates stress concentration sites on the

interfaces, which could be potential quench origins.

Two different coil winding methods were considered in order to minimize stress
problems in the coil. They are: the ’free coil’ method, and the ’tightly banded coil’
method. The difference between these two types depends on whether the innermost
layer is free from the winding form or tightly clamped to the winding form by winding
and banding preloads. (The free coils are also often banded; however, the innermost

layer is clear from the bobbin.)

Tightly banded coils have some advantages over free coils, and are widely used.
One main advantage is that the coil construction is much easier because the coil does
not have to be removed from the winding form. In these coils, however, the shear
stress can easily exceed the shear strength of the epoxy bonds in the potted coils.
Cracks and de—bonds of epoxy joints induced by large shear stress can cause magnet

quenches at lower than design current, which can result in severe coil training.

In addition, frictional coil motions on the bobbin can easily cause repetitive

 

14

quenches in tightly banded coils; the axial magnetic force compresses the coil, and
frictional motion occurs at the interface between the coil and bobbin, with the inverse
motion occurring when the coil de-excites. Two different approaches have been used
to circumvent this problem. The first is to satisfy the equation below so that the

frictional force prevents any axial coil motion on the interface.
11F, > Fa, (2.1)

where p is the frictional constant, F, is the residual radial force on the coil/bobbin
interface, and Fa is the axial magnetic force in the coil at the highest excitation.
However, this approach has difficulties at very high fields in that the preloads required
to produce a sufficiently large F, can be excessive. For instance, over 15,000 psi of
winding preloads and 30,000 psi of banding (2.54 cm thick aluminum) preloads on
a 1.3 cm thick stainless steel bobbin are needed to meet this condition for the 8 T
magnet. These high pretensions are not easy to apply in the actual winding, and also

they are limited by the yield strengths of each material.

A partial free coil method uses lower preloads, but ones which are high enough to
always keep the residual radial stress on the boundary compressive [Ant89]. In this
approach, the innermost layer will slide on the bobbin, and a smooth slip plane is
necessary to avoid sudden motions which can generate more heat than can be diffused
away. This approach may not work as expected, because it is difficult to ensure
smooth sliding. For the 8 T magnet, a design based on this method has a winding
tension of 10,000 psi on a 1.3 cm thick stainless steel bobbin, and a banding tension of
25,000 psi by aluminum wire with an overall thickness of 2.54 cm. Stress distributions
with these preloads were calculated with a finite element analysis program developed
in this lab [Dek], and are shown in Fig.2.3. The calculated shear stresses are larger
than the shear strength of the epoxy or the Formvar insulator bonds. However,

these stresses are overestimated in the calculation due to the constrained boundary

 

 

 

15

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

24 l 24 l l 1 l
1
A205 - 20- 0000 —
E A
o E
"16— - £316- —
§ 8
o 12- - .3 12- 12000 ~
13 .2
'5 o
is 8" " I§ E3" I
'§ x
<
< 4- - 4- a *-
0 I 2I6 2'8 I O I 2'6
22 24- 30 22 24 28
Radius (cm)2 6Radiazl 8Stress (psi)2 Radius (cm), 6Hoop Stresso (psi):52
24 l l l l

,520— -

E

U

v16- ~

0

8

o 12- -

+1

.9

o

_ 8.1 \m I

.9.

X

< 4_ 3 _

O

 

 

 

22 22 28 28 ab 32
Radius (cm), Plane Shear (psi)

Figure 2.3: Two dimensional stress distributions are calculated by the finite element
program for a tightly banded coil. The winding tension applied on the wire is 10, 000
psi with a stainless steel bobbin of 1. 3 cm thick, and the banding preload IS 25, 000
psi by aluminum wires with a total thickness of 2. 54 cm. The sign convension is that
tensile stresses are positive, and compressive stresses negative.

 

 

 

16

these stresses are overestimated in the calculation due to the constrained boundary
condition at the interface (slip motions are not allowed on the boundary; the program
at present is not able to handle the boundary condition realistically). The radial
and hoop stress distributions are similar to those calculated by STAN SOL [Joh76]
in regions away from the boundary. (The program STAN SOL computes forces in
an infinitely long azimuthally symmetric, cylindrical structure in which the radial
dependence of the magnetic field is inserted numerically using data from the z slice

of the real coil at which the field is the highest.)

Free coils are basically accomplished by removing the contact of the innermost
layer with the bobbin. There are two different methods to fulfill this idea; 1) the
coil is wound like the tightly banded coil, but with lower pretensions so that the
coil lifts off the bobbin at low excitation to become a free coil at high excitation,
or 2) the coil is wound on the winding form, and then the form is removed after
completing the winding. The shear stress and frictional motions due to contact with
the bobbin are then eliminated; the coil deforms freely, and finds its natural shape.
There are however other constraints to coil deformation, such as the banding and the
median plane support. The banding constrains mostly outer layers of the coil where
magnetic fields are low so that some frictional motions can be tolerable. The median

plane support usually has smooth slip surfaces to reduce the frictional heat.

For a free coil which has the same dimensions as the 8 T coil with a winding
preload of 5000 psi, and a bandng preload of 10,000 psi by aluminum wires with a total
thickness of 2.54 cm, shear stress was calculated assuming that the coil is bonded (i.e.
no sliding) to a solid stainless steel midplane structure (a usual boundary condition
in the finite element program); results are shown in Figure 2.4. The maximum plane
shear stress of 4000 psi at the inner corner is unsafe compared to the shear strength

of the epoxy band so that the band may break, generating heat to initiate a quench

 

Axial Distance (cm)

17

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

24 l l l I 24 l l l l
20~ - 20- ’ —
A
E
16- - éi16- ’ —
Q)
o
C
12" " 3 12" < r
.9 5000
o
8‘ " —O 8"l \____\ ..
4“ N ' 4‘ @2590!) (000 ‘
O r I I I 0 I I I I
22 24 26 28 30 32 22 24 26 28 3O . 32
Radius (cm), Radial Stress (psi) Radius (cm), Hoop Stress (p81)
24 l l l n l
,220- -
E
U
VIS- *-
Q)
8
0 12—1 .—
4.4
.9
o
_ 8—l ..
U
3?
< 4- M _
M
0

 

 

 

22 23 28 2

26 30 3
Radius (cm), Plane Shear (psi)

Figure 2.4: The stress distributions in a free coil at 8 tesla excitation calculated by
the finite element program. The coil is assumed to be bonded to the solid stainless
steel midplane structure. The winding preload is 5000 psi, and the banding preload
is 10,000 psi by aluminium wires with a total thickness of 2.54 cm.

 

 

 

18

Spacer
for large coil winding

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Eflock
to unflate amassenufly
A<'-l
P w
I
l i i
L‘ "' :1» cm: I
O l- .1 O [I Ed
l CL
0 i 5%
I <30 _—‘_ T T
:1 _—- r- l— — Z
------ '—"—""'—"l'- —- -€-@-G— -- —- fi--—-—-—-—-* -;'---‘—----7- — I—
? :
o o _ _. p 2
o i" ‘
l _ D a
l—
i ll“
:I — ..
/\<‘ Secuon A-A

Figure 2.5: A removable winding form used for the 8 tesla coil construction to ensure
removal of the coils from the bore tube.

 

19

motions at the coil/midplane interface but strong in the axial direction to support
the coil to coil force was then conceived, (and was the structure actually used for the

8 T magnet as described in section 2.II.D).

After reviewing the difficulties of tightly banded coils in avoiding the shear stress
and frictional motions, the free coil approach was chosen for the 8 T magnet. A
removable winding form shown in Figure 2.5 was employed since this method ensures

that the coil is completely free from the bore tube.

D Stress estimates for the 8 T coil

The total forces on each coil are calculated by the FORCE subroutine in the POISSON
code group which integrates the Maxwell stress tensor [Jac75] around the boundary
of the specified region. Calculated forces at the maximum design currents (I: 400 A
for both coils) are shown in Figure 2.6. The average axial stress is 3000 psi on the

median plane support, and 3600 psi on the plane between small and large coils.

By using a free coil instead of a tightly banded coil, shear stress on the innermost
layer is avoided. However, the stress estimation becomes more complicated because
the program has to simulate the process of the winding form removal. Some preloads
are partially relaxed by this process since the zero radial stress boundary shifts from
the inner surface of the winding form to the innermost layer of the coil. To estimate
the stresses on the free coils, the program STAN SOL is primarily used. (Since the
highest hoop stress is the major concern, a z dependent stress analysis capable of
calculating the axial and shear stresses was omitted.) The procedure to calculate the
stress distributions in the coil including the effect of the winding form removal is as

follows:

1) Compute the stress distributions with the winding form included when the winding

 

 

 

20

 

 

F = 2.:5E+6 N

L

F = —2.7E+6 l\

 

h

 

 

 

F = 4.0E+5 N

A
W

F: 6.8E+6 N

 

 

 

 

 

 

J,=J2= 13950 A/cm2

 

 

 

Figure 2.6: Total axial and radial forces on the inner and outer coils are calculated
with the program POISSON at 8 tesla excitation with 1:400 A. The axial stress on

the midplane is 3000 psi.

21

and handing preloads are considered, and obtain the pressure exerted by the winding
form on the innermost layer of the coil.

2) Modify the stress distributions to account for the radial force which is removed by
removing the winding form. This can be simulated in STANSOL by computing the
incremental effect of an inward radial pressure applied at the interface between coil
and winding form with magnitude set to give zero net radial stress at this interface.
3) Subtract the stress distributions of 2) from 1), to obtain the stress distribution in
the ’free coil’, but before the coil cools down to 4 K.

4) Calculate the thermal and magnetic stresses

5) Add 3) and 4) to obtain the final stress distributions at 8 tesla.

Resulting stress distributions at each step are depicted in Figure 2.7. The maxi-

mum hoop stress in the conductor is near 16,000 psi, which is a comfortable value.

E Relaxation of preloads

In the actual coil, some relaxation of the preloads on the winding and banding was
implied by measurements of the coil diameter before and after curing the epoxy. A
change of 0.18 mm in the outside diameter of the banding was measured, and it
was quite uniform for all four coils, regardless of location. Both a simple calculation
and STAN SOL indicated that the reduced diameter of the banding corresponded to

release of the entire banding preload.

The simple estimate of the preload loss was made using a standard formula [C0085]
for the case of an infinite, homogeneous, linearly elastic cylinder; in this circumstance

the hoop stress is

Y u du

= :3(;+VE)’ (2.2)

00

where 1/ is Poisson’s ratio, u is the displacement, and Y is Young’s modulus. Since the

banding is relatively thin and homogeneous, its radial displacement is approximately

 

22

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 10000 I 1 (IO) 1 1
Q A
w -200- - '8 6000- / r
0- a.
V V
3’, —400- p g; 2000- -
8 93
"" +4
if) —600- — m -2000- -
B a.
'6 o
o —800- — o —eooo~ —
a: I
-1000 i i i i 1 -10000 i . i i i
22 24 26 28 3o 32 34 22 24 26 28 3o 32 34
Radius (cm) Radius (cm)
0 l 1 (lb) I I 30000 I l (lb> l l
”\J M”
if -500- " : - (:24ooo- —
I X m
D. I I” O.
V I I v
m -1000- x ”x - 18000~ ~
(1) xx : if), M
8 4500‘ ‘2. .2‘ - 8 12000- ~
+4 g l 44
(D a : (n
‘6 -2000- 3.: .1‘ - a 6000- —
Lg “at,I a? 8
0: —2500- U - I o-
—3000 -6000 i i
22 2'4 2'6 28 3'0 3'2 34 22 214 26 . 28 3o 32 34
Radius (cm) Radius (cm)

Figure 2.7: After the coils are wound and banded on the winding form, the stress
distributions are depicted in (a) by circle. At this point, the interface between the coil
and winding form at the radius of about 24 cm, is under compression by 620 psi. This
stress is reset to the no winding form condition by applying an inward radial pressure
of 620 psi at 24 cm, and then the distributions are as shown in (a) by cross. The

stress distributions after cool down (circle) and full excitation (cross) are displayed
in (b).

 

 

23

independent of radius so that the second term in parenthesis vanishes. With r=32.8
cm and u=0.09 mm, 09 is about 8300 psi; this figure corresponds closely to loss of

the entire pretension on the banding.

Some of the winding preload in the coil, especially of the outer layers probably
also relaxed in the curing cycle. However, this does not greatly affect the maximum
hoop stress in the coil which occurs at the innermost layer. The maximum hoop stress

without the banding preload reaches 20,000 psi vs 16,000 psi with the design preload.

In principle, if the hoop stress on the conductor is higher than the yield strength
of the copper matrix (~15,000 psi), the copper may deform plastically while the
filaments remain elastic because of their higher yield strength, which would mean that
the filament would carry nearly all of the additional applied stress. The difficulty in
accurately clarifying the situation is that the superconductors are twisted, giving an
admixture of the characteristics of a spring rather than pure solid wires. As a result,
the effective characteristic of stress versus strain is difficult to describe. (To avoid this
poorly defined region, the stress level is normally kept below the yield strength of the
matrix material.) Monolithic conductors like the one used for 8 T coils with low Cu
to Sc ratio may be more tolerable to the high stress than the cable type conductor or
a conductor with a large amount of stabilizer, since the superconductor (NbTi) itself
can sustain much higher stresses without degrading the critical current [Ree83]. (The
successful operation of the coil at fields in excess of design values as described in a
later section implies a sharing of stress between NbTi and Cu in a way which leaves

the critical current essentially at the level indicated by the manufacturer’s tests.)

F Selection of handing material

To reduce the circumferential (hoop) stress on the conductor, induced by the strong

radial magnetic force, circular superconducting coils are often ’banded’ with highly

24

pre-tensioned wires. Two alternative banding materials are widely used 1) stainless
steel to use its large elastic modulus, and 2) aluminum to utilize its high thermal
shrinkage. Material properties of aluminum and stainless steel relative to those of the
coil (which is dominantly copper) are: Young’s modulus: Y,ta;n1m steel 2 30 Mpsi,
Yazumgnum c: 11 Mpsi, Yam," 2 16 Mpsi, where 1 Mpsi= 6.9 GPa and 1 MPa= 145
psi ; (L293-L4)/L293 (‘76): 0.306 for 304 stainless steel, 0.415 for aluminum, and 0.324

for copper [Bub].

The stainless steel banding suppresses the coil displacement by the magnetic force
more effectively than aluminum due to the higher modulus, thus reducing the coil
stress. This advantage of stainless steel is weakened by its smaller thermal shrinkage
than copper so that a portion of any preload is relieved when the coil cools down to
4 K. Whether the stainless steel or aluminum banding is used for the 8 T magnet
with the same preload and overall thickness, the maximum hoop stress on conductor
is similar; 16,000 psi, 17,000 psi with the stainless steel and aluminum banding,
respectively at 8 tesla. In the 8 T magnet, ’clam shells’ of solid stainless steel (see
section 2.II.D) surround the banding to support the coil from the outer surface, and
for these, stainless steel banding may be advantageous because of matching in the
thermal shrinkage at 4 K, and also because of ease in welding. The rectangular
stainless steel wire was therefore chosen for the 8 T coil banding, whereas both large
cyclotrons in this lab (K1200, K500) employ rectangular aluminum wires for banding.
(Advantage in weight of aluminum banding could be an important factor for some

applications.)
G Test of stainless steel cable as a banding material

Rectangular solid wires are usually chosen for the banding because they make the

winding orderly. Stainless steel cable (largely used for aircraft) was also considered

25

Table 2.3: Transverse Young’s modulus of the coil wound with aircraft cable as a
function of the applied loads.

 

 

 

 

 

Load applied Incremental Stress Incremental Strain Young’s modulus(Yb)
3060 Kg 630 psi 0.002 0.31 Mpsi
5080 Kg 680 psi 0.002 0.34 Mpsi
8640 Kg 680 psi 0.002 0.34 Mpsi
11,380 Kg 650 psi 0.002 0.32 Mpsi

 

 

 

 

 

 

and tested, since a commercial company (Cryomagnetics Inc.) was using it for their
high field magnets. The elastic modulus of the cable itself was measured first. Because
of the structural stretch, the effective modulus was small at the beginning of loading

(2 10 Mpsi). As the cable was stretched out, the modulus reached 18 Mpsi.

A small test cylinder was wound with this cable to develop an orderly-layered
winding technique and to measure the actual elastic modulus of multiple layers of
such cable. The same tensioning equipment later employed for the 8 T coil winding
was used to wind the coil on an aluminum form. After the winding was completed,
the coil package was dipped into liquid nitrogen to shrink the aluminum form away

for removal.

The elastic modulus of the coil was measured with the help of the MSU Dept. of
Forestry. Only the axial modulus was measured since the measurement of the radial
modulus requires a complicated loading system inside the coil. Table 2.3 shows the
differential elastic modulus for the applied loads. The axial stiffness is similar to that
of hard wood and smaller by two orders of magnitude than the modulus of the parent

material.

If the radial stiffness of the banding can be kept the same as that of the solid
stainless steel banding, an axially soft banding would be beneficial for the supercon-

ducting coil since the shear stress due to the banding can be reduced. When the

 

26

SC-coils are energized, the axially soft banding would compress or expand together
with the coil, rather than risking the SC-coils sliding on the interface and generat-
ing heat. In practice, the outer layer of the SC-coil contacting the banding is not
likely to be the quench origin because of lower magnetic fields than in the inner layer.
The axial softness advantage, therefore, was not considered as a dominant factor in

selecting banding material, and rectangular 304 stainless steel wire was chosen.

H Effect of transverse Young’s modulus of banding on fric-
tional coil motion

Although the shear stress due to banding may not cause coil performance degradation
because of lower magnetic fields than in the inner layer, it would be a good feature to
reduce overall shear stress in the coil by employing an axially soft banding. The larger
transverse Young’s modulus of handing (Yb) is, the higher shear stress is generated
if the banding is perfectly bonded to the coil. In reality, however, coil sliding occurs
when the banding is not soft enough to follow the axial coil displacement, reducing
the residual shear stress. Based on a simple model, Yb is quantitatively related to the

coil sliding motion against the banding for the 8 T coil case.

It is assumed that both the coil and banding are bonded on the 220 plane, and
that the radial magnetic pressure (P,) from the coil uniformly pushes the banding;
i.e. P, is a constant (see the illustration below). The static frictional pressure is then
,uP,, and the resulting axial frictional force on dz in the banding is uPr27rrdz, where
p is a frictional coefficient, and r is the radius at the interface. Another assumption
is that this axial frictional force acts as a body force, which could be justified by
a thin banding. The axial stress in the banding (0'2) with a cross-sectional area of

27r(r+t/2)t, is then given as a linear function of z, where t is the banding thickness

 

27

 

 

 

(r>>t);
,uPr27rr pP, ,uP,
d z = 2 —_d a z = — 3 -
a 21r(r+t/2)t Z t z a t (I Z) (2 3)
Banding
Zii l zii
1- Coil p,

 

 

 

 

 

 

The axial banding displacement (u) is obtained from the relationship of stress and

strain, 02: deu/dz, and from Eq.2.3;

22 #13,. 1
= l — — : .—
u(z)band A( z 2 ), where A t Yb,

 

(2.4)

By the similar procedure, the axial coil displacement is related to the axial magnetic
force as written below;

1 1 22 22 00

“(2)821 = 3777000 — 3) = 30“ — 3), where B = [Y ,1,

 

(2.5)

where 00 is the axial stress on the median plane (~3000 psi at 8 tesla), l is the coil
height, and Yam-1 is the transverse Young’s modulus of the coil. In deriving Eq.2.5, a
uniform axial body force in the coil is assumed. As a result, the axial coil displacement
is underestimated since the axial magnetic force is generally larger for larger 2 rather

than a constant in a split solenoid.

 

28

Eq.2.4, 2.5 are applied to the large coil of the 8 T magnet at 8 tesla, which has a
2.54 cm thick banding. When the transverse Yb is 0.3 Mpsi, A is about 7x10‘4cm'1
(t=2.54 cm, I: 14 cm, Pr: 2000 psi, and p=0.3, where a universal p, value is used since
the frictional coefficient usually depends on many uncontrollable variations such as
surface conditions, see reference [Ken80]), and B is 2X10‘5cm‘1, which means that the
banding displacements by the frictional force would match with the coil displacements
by the axial magnetic force. The cable banding described in the previous section which
has Yb: 0.3 Mpsi would therefore move together with the coil, and solid stainless steel
banding which has Yb: 30 Mpsi would not. When the transverse Young’s modulus
is between 0.3 and 30 Mpsi so that A is close to B, it would be difficult to predict the

coil/banding behavior because of uncertainties in p and in the model.

I Magnet quench simulations

Quench phenomena have been extensively studied by many researchers [Dre82] [Kad85]
[Kur88]. Using these techniques, the design parameters of the 8 T coil and conductor
were evaluated in the circumstance of coil quenching. Quench scenarios were simu-
lated using the program QUEN CH [Wil68] to evaluate the coil behavior. (QUEN CH
solves the heat diffusion and the coupled circuit equations to obtain physical param-

eters as a function of time.)

Quenches in superconducting coils can be subdivided into two classifications: 1)
short sample limited, and 2) energy deposited. A ’short sample limited’ quench occurs
when the coil current reaches the critical current of the conductor whereas an ’energy

deposited’ quench occurs when a mechanical disturbance in the coil generates heat

larger than the critical energy.

The maximum operating current of the coil is determined relative to the short

sample critical current, and defined as the current margin, In; in Eq.2.6, which comes

29

Table 2.4: Critical current data of the 8 T conductor from Supercon Inc. for T: 4.22
K. The measurement was made on a strand used for the small coil.

 

B (Tesla) IC (A)
5.0 1500
6.0 1219
7.0 939

 

 

 

 

 

from reference [Dev90] .

_ [C(TO) — Iop

m,- -— 10(T0) , (26)

where Ic is the critical current, and 10,, is the operating current. Since 16(4.4K) of the
8 T magnet conductor is 580 A and Iop(4.4K) is about 400 A at 8 tesla, m, is 31%.
(In this estimation, the critical current at 8 tesla is obtained by linear extrapolation
since the measured data provided by Supercon Inc. ends at 7.0 tesla as shown in
Table 2.4.) For comparison this margin is considerably higher than the 10% of the
SSC dipole’s m,- and somewhat above the 25% of the HERA dipole’s m,- [Dev90].
Current margin is, of course, an expensive parameter when many magnets have to
be built because of the higher cost of the conductor and the larger magnet size. In
both the SSC and HERA magnets, the winding technique was carefully perfected in
many prototypes so that the smaller margin could be used without jeopardizing the
overall design safety factor. (The design m,- of the 8 T magnet reaches 0% at a main
field of 8.7 tesla at 4.4 K, where I: 450 A, and the maximum magnetic field in the

coil is 8.5 tesla.)

The second type of quench, due to energy-deposit, is initiated by disturbances such
as wire motion or epoxy cracks, which cause the temperature at the quench origin

to increase, resulting in reduced critical current, resistive dissipation, and consequent

30

thermal runaway. An important question is the amount of energy needed to initiate a
quench. The analyses below of the critical energy and critical normal volume closely
follow the method described in reference [Dev90]; underlying concepts are detailed in

chapter 5 of M. Wilson’s book [Wil83].

A minimum energy deposit can be obtained from the critical energy density and
minimal normal volume at the operating current and temperature. The critical energy
density is an integral of the specific heat between operating and critical temperature
as defined in (2.7).

Tc
EC: T dTC(T), (2.7)

where C(T) is the volumetric specific heat. A minimal normal volume (Vmin) is needed
to continue to propagate the normal region [Wil83]. If the normal region is smaller
than Vmgn, it diffuses away, and a superconducting state is restored. The minimum

energy deposit can be then defined as below from reference [Dev90]);

3/2 2
WC : Echin = 2Dth EC A (2.8)
p I ’

where the Dth=k/ C is thermal diffusivity of conductor, k is thermal conductivity, p

 

is resistivity, A is cross section area of conductor, and I is the current at quench. At
8 tesla and 400 amps, Tc is approximately 4.9 K, and using the specific heat data
from reference [Wil83], E6 = 1200 J /m3, and WC: 14pJ; i.e. a tiny fraction of the
total magnetic field energy density of 70 MJ/m3 at 8 tesla (EC = 477 J / m3, and We:

2.5pJ for the SSC prototype dipole [Dev90]).

Some electromagnetic energy of the coil is stored as strain energy (although most
of the energy is in the magnetic field). If the epoxy (or insulator) cracks, this stored

strain energy is released as heat. The elastic energy stored in volume V under stress

ofa'is

a
= —— 2.9
U YV ( )

31

When the elastic energy release equals the minimum energy deposit, the coil quenches.

Then, Vmgn to propagate the normal region is

YWc
02

 

Vm... = 2 (2.10)

Assuming that the insulation on the wide face of the conductor cracks, the minimum

crack length in order to initiate a coil quench can be written as follows;

Vmin
1m... _ —w—t, (2.11)

where t is the thickness of the Formvar insulator (2 0.05 mm for the 8 T magnet
conductor), and w is the conductor width (2 2.0 mm). With 0:: 4000 psi and Y:
300,000 psi for Formvar insulator, it is calculated that Vmgn= 0.07 mm3, 1min: 0.7

mm. These small values imply that tiny cracks can easily trigger a quench.

Once a quench has started, the QUEN CH program calculates the ensuing spread of
the quench region. Two different cases may be assumed: 1) both large and small coil
pairs quench at the same time, 2) one coil quenches first, followed by the other coils.
The second case is more frequent, and worse than the first because the current transfer
from the quenched coil pair to the other coil pair due to the inductive coupling at
first increases the current in that coil above its normal value. It is, however, unlikely
that only one coil will quench and the other will stay in a superconducting state for
a long period of time, considering that the liquid helium would run out quickly. The
delay time was difficult to estimate without experimental information. The QUENCH
results presented in Figure 2.8 assume, for example, a 2 second delay between the
large coil and the small coil quenches; either coil becomes fully normal in less than
a second after the start of the quench (as shown in the normal volume verse time
plot in Figure 2.8). The small coil energy dissipation of 0.3 MJ in a 2 second period

is sufficient to increase the average small coil temperature to 60 K. The assumed 2

32

second delay thus should he certainly long enough to initiate the large coil quench
by disturbing liquid helium, and if the actual delay is less, the current build up is
reduced. (The hot spot temperature and IR drop increases for a longer delay, but not

significantly: for instance, Vmazz 4.7 kV, and Tm“: 380 K with a 6 second delay.)

In these simulations, the quench is assumed to be initiated at the inner corner of
the coil, and the transverse propagation velocity is assumed to be 5% of the longitu—
dinal velocity (along the conductor), which is in the range of 01-10% usually used for
potted coils. (The definition of the velocity ratio can be found in reference [Wil83].)
Another assumption in the present calculation is that the stored energy is dissipated
in only one of the serially connected image coils while the other coil remains in a
superconducting state. In actual operation, the image coil may or may not quench
before a significant amount of stored energy is dissipated in the quenched coil, which
is difficult to predict. If the other coil quench follows immediately, the PR dissipa-
tion will be shared, leading to lower hot spot temperature as well as lower voltage to
ground at the center tap — the single coil quench considered here is therefore a worst

case situation.

The hot spot temperature of 350 K shown in Figure 2.8 would not be expected to
degrade any coil material, but thermal differentials could conceivably cause damage
such as cracks. Measurements of hot spot temperature for potted coils in other labora-
tories however indicate that these coils comfortably survive much higher temperatures
[Dev89]; experiments at BN L for instance showed that the hot spot temperature of

800 K caused no damage [MeB].

The left center plot in Figure 2.8 shows that the maximum IR drop reaches 4.5
kV, and the consequent voltage drop between layers is about 100 V, which can be
easily sustained due to the wire insulation and epoxy paper. If the quench is entirely

in one coil of a pair as assumed, a real voltage to ground of one half of the IR drop

33

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

600 l l l l l J 400 l L J 1 l
350 -‘ X X I x I '-
500 ~ " g “a!“
/a V300 " x' ”
- - ° - o.
2400 >< . Large Cail gzso- L
:300- O I smOIl COII _ I'20oq _
5 x "5
a 150 - ~
g 200_ xx ,_ U) W o o o o o
O .... 100- -
100 - ’2. — :3
‘24: 50 " '-
2
0 i g in - l J i 0 i ‘T I i i
0 4 6 8 10 12 14 0 2 4 . 6 8 10 12 14
Time (sec) Time (sec)
5000 J L l 1 A1 1 100 a l K J l :: 1: : l = 1
o I
3: ° ‘
4000 - I x - {3 so ~ x -
x v 0
‘ ‘
A : x Q)
g 3000 -‘ s x — g 50 .. o x P
g i: '5 .
v 5 " > o
g 2000 " x x r T) 40 '* x '-
i *_ E . ..
x 8
1000 rmao'. xxx - Z 20 ‘9 x l-
: 0°. In x o :
0 g l l o i U I = i 0 *f i I i
0 2 4 . 5 8 10 12 14 0 2 6 8 10 12 14
Time (sec) Time (sec)
2500000 I J l 1 l l
‘3‘!” x I II I I
2000000 .. x ..
C? x
V 1500000” -
8 f
L
2 1000000 "i P
w 0”...“ o o o o 0
500000 4 °°° ~
0 I I 1 I
0 4 . 6 8 10 12 14
Time (sec)

Figure 2.8: When the large coil is assumed to quench two seconds after the small
coil, the physical parameters are calculated as a function of time by QUEN CH. The

hot spot temperature and IR drop across the coil seem to be in the acceptable range.
The energy in the bottom graph is the 12R dissipation.

 

34

(i.e. 2.3 kV) will appear at the median plane interconnection between the two coils,

and the insulation on this interconnection was designed to handle this voltage.

J Effect of an aluminum bobbin in a quench

In high field solenoids for high energy physics experiments, high-conductivity alu—
minum is often used as the bobbin material in order to spread quench energy broadly
through the coil [Gre84]. Another important attribute of aluminum comes from its
higher thermal contraction relative to copper; an aluminum bobbin thus shrinks away
from the coil when cooling down to 4 K, or the coil lifts off the bobbin at low excita-
tions. (Instead of plain aluminum, a bimetal which has the aluminum side toward the
coil, and the stainless steel side as part of the helium tank, was an option considered
for the 8 T magnet since aluminum is rather difficult to weld as an ultravacuum tight
structure.) A schematic View of a coil of this type and a circuit diagram are shown in
the upper part of Figure 2.9. The two coils and the bobbin constitute three coupled
circuits as shown at the upper right of Figure 2.9, and with this model the system
was studied analytically. For these studies, inductances of the circuits were obtained

from stored energies calculated by POISSON; results are given in Table 2.5.

The effect of the aluminum bobbin during a magnet quench as analyzed by the
program QUEN CH is shown in the lower part of Figure 2.9. The stored energy, unfor-
tunately, shifts to the aluminum bobbin rather slowly because of the poor magnetic
coupling between the bobbin and the coil. The bobbin temperature does not even
reach 10 K before the normal zone has propagated through the coil (due to the large
Ar of the 8 T coil compared to typical high energy solenoids). Even at this level,
the bobbin heating may trigger a quench in the series connected median plane image
coil of the quenched coil, but the triggering is not fast enough to greatly improve the

quench behavior.

 

Current (Amp)

IR drop (V)

Figure 2.9: Top: a schematic view of the aluminum bobbin and coils is shown with
a circuit diagram. Lower: QUENCH code results when both coils are assumed to
quench simultaneously. The inductances are tabulated in the row of Table 2.5 labeled
’present’. Because of the poor magnetic coupling, the aluminum bobbin is not an

35

 

 

-> ‘- .953 cm
Aluminum bobbin
7F__ _.
23.370 cm

 

 

 

 

 

 

.lL__..
R 23.1 cm ——.l

 

 

 

 

 

 

  

 

 

 

 

Small coil
% I:

I:

g 11

ZLarge cofl

 

 

 

 

 

 

 

 

 

 

 

 

 

n. ' l 41
t a b
”I 0° 0 O x _
10‘ o 2 Large Coil - .
’ x : Small Coil .
’0 o : Aluminum bobbin? -
0 O
0‘ ~ ~
' ..
”I C I ..
a P
n. I I I I I I I I
o 4 8 8 10 12 i4 8 12 14
Time (sec) Time (sec)
m 1 m4 J 1 Ana _
N
25m _ v b
80- ~
a) :9
2000 ~ E a
2 oo-lia -
1500 - O y?
> 40-8 .
000 l- g g
20-0 ~
500 on " 5 B
X
o I: g I2 '78 I z a! I f I I I
0 4 6 8 9 0 4 6 U 12 14
Time (sec) Time (sec)
2500000 1 41 l l I 1
AZOOOOOOd on D o .-
j
V
15000004 .
>4
0
3 1000000- r
C x x x x
LIJ
500000« -
0 °° ° 0
0 4 5 ii
Time (sec)

important gain in protecting the coils during a quench.

36

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10 i I 1 1 L 4 180 2 o
5 M 160‘ P
10 4 ° °°
a ‘ ° ° ° 0 140‘ 0 h
E 1020 a : Large Coil ~§ 120-1 x _
3 3 x : Small Coil V 100-: b
45 10 .. o : Aluminum bobbin : E‘ 80- f
(D
t 102~ ”'2 60‘ P
3 . '5 8 '
O 10129 a 6 " 40‘ r-
1 . 20.‘ F
10° r T i i '1 l 0 I
0 2 4 5 8 10 12 14 0 12 14
Time (sec)
3000 . i . I 1 1 100‘56 ‘ I =
D
2500— '"f? x
§> 80-a '
S?20004 " m
: § 60-121 _
.. — 3
183 1500 > 40
— - o ’-
9; 1000a ' E x
500‘ a o a _ 5 20—0 _
WX x D a Z
x x g 3
0% r I 1: r : cl 3 I: C O 1 I I
0 2 4 ,6 8 K) 12 14 0 4 10 12 14
Time (sec) Time (sec)
2500000 1 ‘ ‘ ' ' ’
2000000~ "
A
'3
\«'1500000- "
>‘ D U U
8‘
g 1000000~ ° 0 0'
LU
500000« x x x”
0 -i . ’-‘-"' I
0 12 14

 

Time (sec)

Figure 2.10: With the larger k13(=7-I’L’j-fi—3) and 1023 assumed in the last row of Table

2.5, (which can be achieved by radially thinner coils than the 8 T coils) a large portion
of the stored energy is transferred to the aluminum bobbin. A reduction of hot spot
temperature and IR drop is noticeable, when compared with those in Figure 2.8 &

2.9

37

Table 2.5: Self inductances of the coils and aluminum bobbin, and mutual inductances
computed with POISSON. The row labeled ’Present’ displays the inductances for the
Figure 2.9 coil configuration. In the ’Assumed’ line, the mutual inductances of the
coils to the bobbin are assumed to be larger, such as might be achieved with thin
coils as described in the text.

 

I I L1(large coil) IL2(small coil) I L3(Al bobbin) LM12 I M23 I M13 I
Present 21.6 6.47 1.2 x 10‘5 4.91 0.0017 0.0043
Assumed 21.6 6.47 1.2 X 10‘5 4.91 0.0068 0.011

 

 

 

 

 

 

 

 

 

 

 

 

For the aluminum bobbin to function effectively as a quench protection, the mag-
netic coupling coefficient (k=%) should be close to 1, which can be realized by a
thin coil (Ar<< r, where Ar is the coil thickness, and r the mean radius of the coil),
but not in radially thick coils such as in the 8 T magnet. To quantitatively show the
effect of magnetic coupling on energy transfer, a second calculation was made with
the 8 T coils assumed to be closely coupled to the bobbin by larger mutual induc-
tances as given in the row labeled ’Assumed’ of Table 2.5; quench analysis results in
this situation are shown in Figure 2.10. The energy shift is faster so that the hot spot
temperature and the voltage drop are noticeably reduced. The bobbin heating speeds
up the quench propagation by inducing a quench in regions remote from the quench
origin before the quench propagates through the coil, which reduces the danger of
overheating in the region of the quench origin. This is a quench protection strategy
known as ’quench back’ [Gre84] which is frequently used in large high energy physics
detector solenoids. (Heaters can serve a similar purpose in an active fashion, and are

employed for long, series connected magnets such as the SSC and HERA [MeBS7].)

Reviewing the above results, it was concluded that the shorted circuit element
given by high-conductivity aluminum does not appreciably improve the quench be-
havior of the 8 T magnet. Additionally, the use of the large differential thermal

contraction of aluminum to free the coil is unnecessary if a removable winding form

38

is used. A stainless steel (304) helium vessel and a removable winding form were
therefore chosen for the 8 T magnet because of ductility at low temperature, ease of

welding, and low cost compared to a bimetal bore tube.

K Selection of design operating current

The 400 A design operating current of the 8 T magnet was decided after considering
the coil behavior during a quench, which is acceptable at 400 A and the trade-off
between heat leak and coil quench response. Larger operating currents (and smaller
inductances) allow faster coil response to voltage changes at the expense of larger heat
leaks through the current leads. For these magnets, current leads usually dominate
the total 4 K heat leak since the heat leak of an optimized, 4 K to 300 K, gas cooled
current lead is approximately 1 mW / A [Lec86]. Experience from other magnets was
also a factor in the operating current decision, including taking into account the effect
of the wire size on the conductor preload and on the winding time. The 400 A of the
8 T coil is in fact between the 200 A of the Harper cyclotron and the 700 A of the

K500, and similar to the 500 A current of the S800 spectrograph.

L Stray magnetic fields

Stray fields from high field magnets can be hazardous to human beings, and also
to electronic devices, vacuum pumps, etc. in the vicinity. A design goal for the 8
T magnet was then to reduce the stray field strength to less than 30 gauss beyond
the radius of two meters. (This choice was arbitrary since the requirements of stray
field reduction rely on the particular application and location of the magnet; N SCL

research cyclotron magnets as an example have much higher fringe fields.)

Two different methods for controlling the fringe field were considered. The first

method uses sets of reverse current coils located on the outside of the yoke to reduce

 

39

the stray fields, which is known as active shielding [Haw90]; the upper part of Figure
2.11 shows a typical active shielding configuration. The second method simply makes
the return yoke of the magnet sufficiently thick to reduce flux leakage to specified

tolerance levels.

A disadvantage of the active shielding method is that the main coils need addi-
tional amp-turns to compensate for the reverse magneto-motive—force from the shield
coils. More importantly, a complicated magnet structure could be costly for either
room temperature or superconducting reverse current coils. Most magnets then use
yoke shielding due to its effectiveness and simplicity, even though a significant mass
increase is unavoidably entailed. For the 8 T magnet, yoke sizes were adjusted to
satisfy our stray field requirement using a simple cylindrical yoke and calculating the
field with the code POISSON. To further minimize mass, the yoke could be contoured
(corners rounded, etc) to give a more uniform flux density [Ish87]; the result would
however be a much more complicated shape than the simple pillbox shape, and this

makes such a flux optimization design not economically attractive.

A simple cylindrical yoke with thickness to give stray fields meeting the design
specification at 8 tesla is shown in Figure 2.12, and compared with the active shielding
results of Figure 2.11. The thicker yoke does not greatly increase the absolute mass

due to the small magnet size.

Costs of the two options are compared considering only additional steel and su-
perconductors, and tabulated in Table 2.6 for the magnet configurations of Figures
2.11 & 12. For the 8 T magnet, the active shielding scheme costs significantly more,

and the yoke shielding option was therefore chosen.

Another important external field design characteristic is the magnetic force exerted

by the external field on nearby magnetic objects. To assess this problem the radius

40

41.9 cm

 

 

34.4 cm—‘

 

 

 

 

 

 

 

 

 

 

 

 

0 45.7 53.5 cm

1 l l l l
400 \

 

 

 

 

 

 

 

 

70 120 170 . 220 270 320 370
Distance (cm)

Figure 2.11: A cross section of a quarter of the magnet is shown with reverse current
coils on the outside of the yoke, which is known as active shielding. The stray fields
are reduced in both radial and axial directions. The current densities of each coil are:
J1: 13,950 amp/cmz, J2: —13,950 amp/cmz, and .13: -7750 amp/cm". The dashed
line is the field without reverse current coils, and the solid line with these coils in use.
The yoke is thinner than the yoke shielding case.

41

50.8. cm

 

 

27.4 Cm"

 

 

 

 

 

 

 

 

 

 

 

 

D 36.5 cm 62.0 cm

 

 

 

 

 

—— : thick yoke

—— : active shielding _

 

 

 

 

70 120 17'0 22'0 27'0 320 370
Distance (cm)

Figure 2.12: The yoke is thickened to confine the flux. The current density is 13,950
amp/cmz. The solid line is the field with a thick yoke, and the dashed line with the
active shielding of Figure 2.11. Both stray fields roughly meet our criterion, with the
active shielding significantly less effective close to the magnet.

 

42

Table 2.6: Cost comparison of yoke and active shielding of stray fields considering
only additional steel and superconductors. Unit prices of steel and superconductor
come from the 8 T magnet cost.

 

 

 

thick yoke shielding active shielding
Unit price $2 /lb $0.002/ A ft
Addition 3.6 tons 400 A, 51,000ft
Cost $16,000 $41,000

 

 

 

 

at which the magnetic force equals the gravitational force (the ’lifting’ condition) was
roughly estimated; for ’long’ objects like a steel wrench, the lifting criterion on the

field is given by Moon [M0084].

32—8 _>_ 5.4 X 10'3tesla2/m (2.12)
as

An experimental test of this effect was performed in the median plane, with the
internal main field at 7 tesla; in this run, condition (2.12) was satisfied at a radius of
81 cm for an object with width/length2 0.2, whereas the measured lifting condition

radius was approximately 90 cm.

43
II Design of magnet components

A Support links

The support link of a superconducting magnet should be strong enough to sustain
possible off-centering forces, and it should be a poor heat conductor in order to reduce
the heat influx into the liquid helium. The usual choices of materials satisfying both
conditions are composites, whose fibers are available in various forms [Ree83]. Among
them, S- and E—glasses are the most commonly used. The commercial products
containing these fiberglasses are G—10 (E—glass), and Scotchply (S-glass, product of
3M). The properties of the two products are compared in Table 2.7. The S-glass / epoxy
is usually preferred, as the ratio of strength to thermal conductivity of S-glass is
about twice as high as that of E-glass [Ban91]. The K1200 and Harper hospital
superconducting (SC-) cyclotrons and the SC-ECR ion source built in this lab have

employed this product for their links.

Mechanical details of the support link system of the 8 T magnet are shown in
Figure 2.13. The vertical links support both the helium tank and 80 K radiation

shields. The weight supported by the top three links is about 800 kg.

The vertical links of other MSU SC-cyclotron magnets are usually attached to
the top and bottom plates of the helium vessel. Unlike these, both horizontal and
vertical links of the 8 T magnet are attached to the midplane ring since the coils are
free from the inner bore tube, and welded onto the ring at the outer coil edge (see
section 2.II.D). As a result, the narrow radial gap between the helium vessel and the
heat shield restricts Scotchply links from being used for the vertical support since
they are rather bulky as being wound into a belt shape. G-10 bars, which are radially

thin and azimuthally wide when installed in the magnet, were chosen for the vertical

links.

 

44

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    

3?
>

@

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

”I
Verticol Link > El; Stm'n BO”
ill;
A ml A
f-"Fl
80 K Shield $33,180:?“ eCgfijubled
Cryostat
300 K We“
[‘41:— Helium Vessel
B Outer Woll
" ‘ in"
(D
@ ril G-lO Link
B_B B at cold end
TOp View
Til ~ .
A0 ann< lvlldplone Ring
"7‘1" lll

Aoin Bolt

 

Horizontal Link

 

 

 

Scotchply (S-gloss) Link

Figure 2.13: Horizontal and vertical link assemblies in the 8 T magnet. Both links
are doubled at the warm end to match with the strength at the cold end. Strain bolts
are employed to read the forces on the links.

45

Table 2.7: Comparison of G-10, and Scotchply

 

I Properties I Temperature l Scotchply I G-10 I

Young’s modulus 300 K 48.0 GPa 28.0 GPa
4 K N / A 35.9 GPa
Tensile strength 300 K 1790 MPa 415 MPa

 

 

 

 

 

 

 

 

 

In link assembly, the link pin at the warm end can be the weakest part. which
takes ’double shear’ stress (two shear planes in the pin, refer [Ger90]). Especially,
the horizontal link pin is weaker than the vertical link pin because of the smaller pin
diameter; 1.27 cm, 0.95 cm for the vertical and horizontal link pins, respectively. The
shear stress at a tension of 3.8)(104 N (the ultimate tensile strength (UTS) of the
horizontal link unit, see section 2.11.0), is

r = T3—An-_- 39,000 psi,
where A is the cross-sectional area of the pin. The shear stress is greater than the
ultimate shear strength of the standard 304 stainless steel (material strengths in
shear are usually half as large as those in tension, and the UTS of 304 stainless steel

is ~30,000 psi at 300 K). Titanium alloy pins were used, whose UTS is rated higher
than 100,000 psi.

B Spring constants of the link system

For the stable coil support, the spring constant of the link assembly should be larger
than that of the magnetic off-centering force. If this condition is not satisfied, the coil
continues to de-center in response to an initial perturbation, and link breakage/ coil
damage would usually result. The spring constants of the link assembly and of mag-
netic off-centering forces due to the misalignment of the coil relative to the magnet

center were estimated for both vertical and horizontal directions. The spring con-

46

stants were also measured as a function of current in the 8 T magnet system with all

links connected, and are described in section 4.1.

For a rough first approximation, the vertical off-centering force can be estimated
using the image current method. When an infinitely long current filament (current:
I) is placed midway between two ferromagnetic walls with infinite permeability, the
off-centering force per unit length (F) was worked out by Hague [M0084] as shown in

the illustration below.

 

 

Izw mt
411' D an D ( lm)
(m4@

#9

Because of the two walls, the image filaments due to one wall create image filaments
behind the other wall, which results in an infinite array of filaments. The analytic
formula was applied to the 8 T magnet case for a small displacement; F /ux 27rRz
,uon'lcoulgmagc/4D2X27rRz 4.2x107 N /m, where R is the average radius of the coil, D
(57.4 cm) is the yoke gap in the coil region, Ice“: 3x106 A at 8 tesla, and Iimagez
lam-1. The approximation neglects effects of the cylindrical geometry, the partially
saturated state of the iron, and the marked deviation from flatness of the coil cavity.
The result never-the-less provides an initial order-of-magnitude sense for the spring

constant needed in the support system design.

For a more accurate result, the program POISSON was used to calculate the ver-
tical off-centering force by directly introducing an axial coil displacement. Table 2.8
shows the forces and spring constants from this study for two different coil displace-
ments at the maximum design current. The off-centering forces are almost linear for

different but small displacements, which agrees with analytic reasoning.

47

Table 2.8: Spring constants of a vertical off-centering force calculated by POISSON
at 8 tesla.

 

Displacement 1.2 mm 2.5 mm
Off-centering force 1.4x 104 N 3.1x104 N
Spring constant 1.1x107 N/m 1.3x 107 N/m

 

 

 

 

 

 

To test the codes for the accuracy of force calculations, forces in the centered coils
in the magnet were calculated with POISSON, and then compared to the TOSCA
[Tos] calculations. Computations by the two different codes relatively agreed well
in this case, but for the off-centered coils, significant difierences in both calculated
axial and radial off-centering forces were observed. Usually, accurate estimates of
off-centering forces are difficult to achieve because: 1) off-centering forces are much
smaller than the coil forces, and 2) grid sizes in the finite element analysis are often

larger than the coil displacements so that the fields are not accurately described.

An analytic approximation was made for the radial off-centering force, which
considers the yoke and poles to be a set of dipole moments. The interactions between

the coil and yoke and between the coil and pole tip are independently considered.

The dipole moment of the yoke was subdivided into four effective dipole moments
which interacts with the coil dipole (Myokeez i-Jmtmau-onAh, where A is the total yoke
cross-sectional area, h is the yoke height, and Jsaturatz'on: 1.7x106 A/m). The force
between two anti-parallel dipoles is given in text books (13": (Ml-V)§, where m1 is
the dipole moment, and B is the dipole field from m2, see p.182 in [J ac75]). Then the
off-centering force due to two yoke dipoles, which are located across the coil in the

direction of coil displacement interacting with the coil dipole is given below to first

order;

48

_ Ho 12 .
6F}; — MCOilMyOkc4—7rr—5673 (2.13)

where M6051 is the dipole moment of the coil at 8 tesla, and (ST is the coil displacement
relative to the magnet’s center. The spring constant (6Fh/6r) by this approximation
is about 0.9x107 N/m.

The spring constant due to the interaction between the pole and coil is also cal-
culated using the equation, 171: (fit-VH3: However, in this case, the gradient of the
coil field was numerically obtained with POISSON, and the dipole moment, m, comes
from the off—centered portion of the pole tips with respect to the coil center. Assuming
saturated pole tips at 8 tesla, the spring constant estimate is about 0.6 x107 N /m.
Therefore, the spring constant of the radial magnetic off-centering force including

both the coil/yoke and coil/pole tip interactions is 1.5 x107 N/m.

The spring constants of the link assembly were calculated or measured for the
vertical and horizontal links, respectively, to compare to the spring constants from the
magnetic off-centering forces. The spring constant of an entire vertical link assembly
(composed of a single link unit at the cold end and a doubled link unit at the warm

end) is related to the spring constant of a single link by the following equation;

1/kcold + 1/2kwarm : l/klink assembly, (2.14)

where kcold is the spring constant of the cold end, and kwarm is of the warm end.
The kvertgcaz of a link assembly is about 1.5 x107 N /m, and for six link assemblies
together (three upper, three lower), keff=9 x107 N / m, which is comfortably higher
than the spring constants in Table 2.8 for either displacement. The spring constant
of a horizontal link unit was measured using a strain bolt and two dial indicators in a
test stand, The spring constant of an entire link assembly which was computed using

Eq.2.1 was 2.0x107 N /m. The overall spring constant for the three link assemblies

49

together at 120° spacing is then keff=3.0 x107 N / m, which is larger than the dipole

approximation.

C Test of sample links

Irrespective of the spring constant, a maximum on the allowed coil displacement is set
by the breaking strength of the links. Usually this is limited by the strength at the
link attachment point where the stress concentration resulting from the discontinuity
on the joint is the key factor requiring optimization. To confirm this detail of the
design, the G-10 vertical link was studied by testing two kinds of joints [Kim90]
shown in Figure 2.14: 1) bolted and bonded (combination) joint, and 2) pin joint.
The measured tensile strength of the combination joint was no higher than that of
a pin joint. Arrangements of bolts and bolt sizes in the combination joint were not
throughly optimized since the pin joint was generally preferred for the 8 T magnet

due to its pivot action.

To reduce the stress concentration around the joint area, the link attachment
region is shaped as seen from the test link configuration in Figure 2.14. The pin-hole
size ((1), the width of the link attachment region (w), and the shortest distance (h)
from the hole to the end of the link are the parameters which are related to stress
concentration factor. Considering the 2.5 cm wide link body, which was roughly
decided from the strength requirement, the pin-hole size (d) was first set at 1.27 cm,
and then w was optimized; the breaking strength of each vertical link assembly was
decided to be 4x104 N, which would allow more than 5 mm off-centering without link
breakage. Several different widths were tried, and it was concluded that there was no
significant tensile strength increase beyond the width of 3.8 cm with h of 2 cm (h was
roughly determined as a minimum distance not to greatly reduce the link strength

for d/w20.4). This optimization was rather approximate, and could be improved by

 

50

 

 

 

 

 

 

 

 

 

 

 

[Applied load I Pin joint I
1400 kg N 0 samples are damaged. Linear and reversible up to this point.
1530 kg Pin hole becomes elongated.

Prefracture stress concentration lines are dimly shown.

1670 kg High stress region appears clearly.

All samples seem to be damaged
1760 kg Several samples are broken
1800 kg All samples are broken

Combination joint
1400 kg Broken, no observation is made
since the breaking location is behind the fixture

 

 

 

 

Side view with fixture

 

2.54cm stainless st.

 

 

 

  
 
 

fixture

’ ”l
$0.480m
o - break
10 32 ULF/ location

 

 

 

 

 

 

 

 

 

M L
0. 320m ->l i<—
bonded surfaces Thickness =O.64cm
Combination Joint Pin Joint

 

Figure 2.14: Configurations of tentative G-10 links with a combination joint and a pin
joint. Tensile strengths of the links for both joints were tested, and are summarized
in the table. Only one sample was tested for the combination joint, and six samples

for the pin joint.

51

adjusting the d, in addition to the w and h.

Six G-10 link samples with a pin joint shown in Figure 2.14 were tested, and
general characteristics are summarized in the table in Figure 2.14. The stress con-
centration factor [Coo85]) of the link joint is about 3; K: amaz/ 0mm, where am“,
is the ultimate tensile strength of G-lO (2 49 kpsi), and 0mm is the average tensile

stress at the link breakage (2 16 kpsi).

Since stress concentration data on the pin joint were not available for composites
such as G-10, the link design was performed by experimental tests rather than by
computations. However, a simple design evaluation of the test link was made using
the homogeneous material data before finalizing the actual link design for the 8 T
magnet. The stress concentration curve in reference [Fr040] was fitted by polynomials
of d/w for h/w20.7: K=30(d/w)2—33(d/w)+11, and the joint strength is given as
follows;

11) — (1

Strength of joint 0< ——K— (2.15)

When using the above equations, the optimum w is 2.8 cm for a d of 1.27 cm, which
means that the width of the tentative link (w=3.8 cm) is wider than the optimized

one, which is usually useful for the strength.

To ease the design and fabrication, however, the actual 8 T magnet vertical links
differ from the tested sample links; the link width (w) was reduced to a uniform
2.85 cm without enlarged pin joint area, the thickness was increased to 0.79 cm, and
G-lOCR instead of G-lO was used to keep the breaking strength near 2x10‘t N at
300 K (the tensile strengths are 49 kpsi, 56 kpsi for G-10 and G-10CR, respectively
[Spa]). The tensile strength of the actual G-10 link was not measured because of
the consistent test results for different sample links, which allowed confident use of

inferred tensile strength of 2x104 N without further testing.

 

52

The horizontal links were designed to be the same links used for the SC-ECR
[Ecr]. Therefore, a particular study to find the optimum shape was not made. The
tensile strengths of two samples which had different number of layers (7 and 12) were
measured and compared to results from the ECR group. A tensile breaking stress of
130,000 psi was obtained with the 7 layer link, which was the same number of layer
with the ECR link and similar in breaking stress. (The 12 layer link broke at 50,000
psi at which the outer layers initiate the breakage; the link might not be properly
fabricated.) All of the horizontal links actually used for the 8 T magnet were checked
by a 70,000 psi stress, and no damage was observed. Each link can support up to
3.8X104 N (at room temperature — it would presumably be higher at 80 K), but the
maximum load is preferably limited to below 2.6 X104 N because some fibers seem
to break at higher loads, which may cause the tensile strength reduction after many

loading cycles.

D Median plane structure of the 8 T coil

The design of the midplane structure in a superconducting cyclotron magnet needs
to meet a contradictory requirement; it must support large axial clamping forces, and
yet allow space for room temperature penetrations into the main field region and for
thermal insulation of these penetrations. The midplane structure of the 8 T magnet
follows the design concept utilized for other MSU cyclotron magnets: strong sup-
port of the axial force and minimal allowance of room temperature penetrations (see
[Ag086] for different design). A technical difficulty involved in the usual MSU design
is that the space for thermal insulation is quite restricted, which might introduce a

large heat leak.

Another design feature of the midplane structure is related to the coil motion. A

low friction slip plane is frequently employed to allow coil sliding against the midplane

 

53

support when coils are energized. The method needs a thermal barrier between
superconductor and slip plane since the heat generated by frictional motion must
diffuse away; a low friction, smooth slip plane is also essential. In reality, it is however
quite difficult to insure smooth low friction sliding. Rather than resorting to this
uncertain design scheme, the midplane structure of the 8 T magnet is designed to be
weak for radial expansion so that it moves together with the coil. Stacks of the 1.6 mm
thick aluminum plates fill the space in the midplane as shown in Figure 2.15, and they
are sandwiched between two thin G-10 plates (1.2 mm thick). The resulting radial
stiffness of the median plane structure is determined by two G-lO plates rather than

by aluminum stacks (since the stacks can freely stretch azimuthally and radially).

Though it is clearly probable that the G-lO plate will expand with the coil by
frictional force without coil sliding, numerical calculations are made to analytically
demonstrate this. The body force in the plate (F 1,), which radially expands the plate,
originates from the frictional force due to the axial magnetic pressure, Pa; dF,=
pPa21rrdr on the area of 21rrdr, where p is the frictional coefficient. The differential
equation of force equilibrium (see p.90 of [00085]) is established by the radial, hoop
stresses in the plate (a,(r), 09(r)), and by the radial body force, with Pa assumed to

be independent of r;
do, + or, — 09 pPa

d, r + T = 0, (2.16)

 

where t is the plate thickness.

G-iO plate CITdFr

Po2flrdrT>_

  

L

 

 

['[l

 

54

     
 

8O i< Stfiem

Connecfion Bar(X5)

 
 

Ckmn She”
(

  
    

Welded
onto

 
 
    
    

Bandhg
(soild stainless steel)

Secfion A-A Penevafion Tube

 

 

Top View

Figure 2.15: Top view of a section of the midplane structure, and a side view to show
its attachment to the coil. There are twelve penetration holes.

55

From Hooke’s law, the relationships between stress and strain are written below

[C0085] ;

 

 

0‘, = (E,- + V69) 09 = (69 + V6,), (2.17)

1—V2 1—V2

where V is the Poisson’s ratio. The strains are determined by displacements, u(r);

du

u
:17, 69 — ; (2.18)

6,:

Substitution of Eq.2.17 and Eq.2.18 into Eq.2.16 yields

 

d 1 d 1 —— V2 ”Pa
The solution is then
_ C2 (1 " V2)I‘Pa 2
u — C17" + r — 3Et r (2.20)

From the boundary conditions, ar(a) = 0,.(b) = 0, the coefficients Cl, and Cg are

obtained;

(1+ V)(2 + V) pPa a3 — b3 (1+ V)(2 + V) #3; a2!)2
01 = C2 :

E 3t a2—122 E 3t a+b

 

 

(2.21)

The displacements of the G-10 plate can be obtained from Eq.2.20 for a given axial
pressure, Pa (~3000 psi, at 8 tesla). Calculations approximately predict that the plate
displacements by the stationary frictional force are larger than the coil displacements
at any excitation, which means that the plate will certainly expand together with the
coil without sliding against each other. The frictional force with p=0.3 for instance
can expand the plate roughly by 0.8 mm at 8 tesla, while the coil expands only 0.25
mm by radial magnetic force due to its high stiffness, which was calculated by the

program STANSOL.

E Current leads

Current leads are available as commercial products. However, the one used in the

8 T magnet was designed and built in house because commercial leads are bulky,

56

requiring larger holes in the yoke of the 8 T magnet (a standard commercial lead pair
rated at 500 A is in two separate tubes of 1.27 cm O.D.— American Magnetics Inc.,

while an 8 T magnet current lead pair is in a tube of 1.59 cm O.D.).

Mechanical details of the 8 T magnet current leads are shown in Figure 2.16. The
leads are made of superconductors like leads of many other magnets in this lab [Pur]
(Cu:SC=2:1, 3 bundles of twisted 0.25 mm thick conductors, each bundle containing
147 individual wires cabled first into 3 wire clusters and then into two successive seven
cluster groups (one surrounded by six)), rather than plain copper, which is in more
frequent use in other institutions. Since the temperature at the cold end of current
leads would be lower than the critical temperature, that section of the leads is in the
superconducting state, reducing the ohmic heat. This feature would reduce the heat

leak rather insignificantly, but it is still worthwhile to use.

An optimized shape of the leads which transfers minimum heat into LHe can
be obtained for a given lead material when the thermal equilibrium equations are
solved, as detailed in reference [Wil83]. For the copper which is the matrix material
for superconductor, the optimum length to area ratio is given by M. Wilson;

11%“: 2.6x107 A/m,
where 10 is the maximum current, X0 is the lead length, and A is the cross-sectional
area. The configuration of the 8 T magnet current leads approximately corresponds to
an optimized shape at 400 A if the twisting effect of the conductors is not considered
(X0: 100 cm, A: 14.9 mmz, where A is only for the copper component of the
superconducting strands). To calculate the optimal shape factor, a complete heat
exchange between lead wires and boil-off helium gas is assumed, which is applicable
when a sufficient cooling surface area is allowed. Using many stranded wires in
the lead, a minimum cooling area is easily met, however, a longer and larger lead

configuration is preferred to extend burnout time in the case of an accident which

 

 

 

Instrument
leads port

 

 

 

 

 

Lead connector
(copper) ///’

 

 

 

Lead wke
(superconductor)//'fi

 

 

 

 

Epoxy Feed Tube

 

 

SECTION B-B

 

 

 

 

1

 

 

 

 

SECTION A-A

Figure 2.16: Cross-sectional views of the current leads of the 8 T magnet. Mechanical
details are shown and noted.

 

 

58

cuts off helium flow. The length of 1 meter used for the 8 T magnet leads provides a

robust lead as known from with other superconducting magnets.

A current leads with the same design as the 8 T magnet leads was built and tested
in a 50 liter liquid helium vessel. The heat leak was measured as a function of current,
and is plotted in Figure 2.17. The measurement includes the heat leak into the vessel
itself, but it is not subtracted in the figure because of uncertain magnitude; the heat
leak into the vessel sensitively depends on the pressure fluctuations in the return line
of boil-off helium gas (a measured heat leak without pressure fluctuation effects is less
than 0.1 W) [Kim92b]. The heat leak on a typical commercial 500 A current leads

from American Magnetics Inc. [Ame] is also shown in Figure 2.17.

As an effort to reduce the heat leak through the current leads, high temperature
superconductors (HTS) have been tried and reported as having promising results
by other researchers [Nie93][Ued93]; the heat leak in HTS current leads with an
intermediate heat sink was reduced 40 ‘70 compared to that in conventional optimized
leads designed to carry 1 kA [Wu91]. Accessing the advanced technology involved
in such leads would however have delayed the 8 T magnet project by a considerable
amount, and so use of conventional leads was selected as the best system for the 8 T

magnet situation.

 

 

59

 

 

 

 

 

14 l l l l

1.2- ”'
‘5' 1.0- .0‘
E
_O 0.83 ‘
o ._——— ’0/

__ _9 —— --' 6"

3 0.6 1*- -
4.;
8 0-4‘ x : measurement 7
I

0.2- 0 : commercial leads ‘

0.0 i i l l

O 100 200 300 400 500

Current (Amp)

Figure 2.17: Heat leak as a function of current was measured in a 50 liter liquid helium
vessel (cross). The heat leak of the vessel itself is included since its contribution was
difficult to accurately estimate (roughly 0.1 W). The solid line is a fitted curve. The
dashed line with circles is the heat leak of a typical commercial 500 A current leads

[Ame].

Chapter 3

Construction of the 8 T magnet
system

I Materials in the coil

The main constituents of the 8 T potted coils are the layer-to—layer insulation, the
epoxy adhesive, the conductor insulation, and the metallic composite NbTi in Cu

superconductor. In this section, properties of these materials are reviewed.

The coil to bobbin insulation is composed of five layers of 0.13 mm thick Mylar.
Multiple layers are employed to utilize the superior dielectric strength per unit thick-
ness compared to a thick insulator of a single layer (pin holes are unlikely to line
up in successive layers). To cover the corners of the coil effectively, ’angled’ layers
of Mylar were formed by a heated forming die (Figure 3.1), which shapes the Mylar
into a circular ’bracket’ (cylinder plus plane). Before the pressing process began, the
aluminum forming tool was heated to 200°C which is close to the melting tempera-
ture of Mylar. This method was originally suggested by Dupont Corp. which noted
that the stability of formed mylar is established only when heated close to its melting
temperature. Some layers of Mylar were glued together with EPON 828 epoxy to
increase their rigidity.

Between each layer of the coil, a sheet of epoxy impregnated paper was inserted

60

 

61

Steel shaft
2.54 cm 0.0.

 

Drill bushing

 

Aluminum disc

 

2 layers of Mylar

 

Aluminum ring

 

 

 

\.

//////// W
s\\\\\\

III/IIIII]7IIIIIILIIIIIIIIIIIIIIIZ

:l

 

 

 

 

 

 

/////////////////// cums

‘\\\\\\\\L\\\\\\\\\‘\ Y \

 

 

 

 

 

 

 

 

 

 

U W

 

 

 

 

 

 

_._-_-_-_-_-_-_-_-_-_I.-

Figure 3.1: Mylar forming die. To cover the corners of the coil effectively, layers of
Mylar were thermally formed.

 

 

62

Table 3.1: Properties of the 8 T conductor

 

 

 

 

 

 

 

 

 

 

Superconducting Alloy Composition N b—46.5 w/o Ti
Matrix material OF HC Copper
Volume ratio Cu/SC 1.90 : 1
Twist length 2.54 cm
Bare Wire Size 1.05 mm X 2.03 mm
Insulated Wire Size 1.14 mm x 2.13 mm
Filament size and number 139 pm, 54
Critical current at 8 tesla, 4.2 K 650 A

 

 

to reinforce the conductor insulation. To control the amount of epoxy added on the
paper, the paper was passed through a 0.25 mm wide slit after being soaked with

Stycast 2850F T [Sty] epoxy in a pot.

Another function of the paper is to inhibit the propagation of epoxy cracks pro-
duced by thermal and electromagnetic stresses. In large scale magnets, fiberglass cloth
pre—impregnated with epoxy has been used to achieve similar goals. That option was
considered, but the crossply cloth commercially available was thicker (0.3 mm) than

paper so that the overall current density decreases. (It was also more expensive.)

At each end of each layer, tapered G-10 pieces were used as layer transition spacers.
They were cut from a sheet of G-10 stock with a saw blade installed in a horizontal
milling machine, and hot formed so they would conform to the cylindrical curvature
of the bobbin without significant added force. Reference [Kim92a] describes more
details involving these spacers. With these spacers, the resulting coil winding is a

true helix on every turn.

The major portion of the coil is filled with superconducting wire, the total vol-
ume of conductor in the coil (the packing factor) being about 75%. Table 3.1 lists

properties of the conductor.

 

63

II Coil winding

The coil is the most delicate component of a superconducting magnet, and for the 8
T magnet significant effort was invested in carefully controlling each step of the coil
winding process. Winding devices were carefully prepared and checked before the
actual winding; a small test coil was first fabricated and many coil tests were made

as winding progressed.

The central element of the winding system was a large lathe (82 cm diameter
x 3.0 m bed length), which rotates the winding form and moves the tool carriage
carrying the winding arm at the same speed as the winding layer advances; the
lathe tool carriage supported both the conductor tensioner and a ’pusher’ arm which
compressed each turn against the previous turn. Other winding devices include the

epoxy pot, a paper cutting device, the turn counting system, etc.

The tensioner is a device arranged to provide a constant winding tension which
matches that of a reference spring. The operating principle is that a hydraulic motor
feeds conductor onto the rotating coil form at a rate which holds the position of
the tensioner carriage constant with respect to the constant force spring using the
feedback signal from a linear potentiometer. As a result the wire, held by two V belts
on the carriage, is always pulled on by the springs and therefore tensioned by the

spring load in just the same way as it would be if the springs were solidly attached

to the wire.

The pushing arm powered by pneumatic cylinders pushes the wire against the layer
beneath it, and also laterally against the previous turn to wind tightly. The pressures
in both directions are controlled by regulators. A downward (radial) pressure of about
1015 psi was used, and 15-20 psi was for the side pressure (regulators are connected

with air cylinders of 3.2 cm diameter and 3.8 cm diameter for downward and lateral

 

64

Table 3.2: Work days per coil set spent on actual winding

 

 

 

 

 

 

 

 

 

 

 

 

I Work I Work progress rate LDays taken I
Superconductor winding 6 layers / day 16
Lead outlet and insulation 2
Banding 9 layers/ day 5
Preparations between two coils 2

r Winding one coil set I I 25 I

 

pressures, respectively). The large lateral pressure is rather unusual compared to

other MSU coils, but was thought to help tightly packing the wires.

The epoxy pot was borrowed from the coil winding tools used for the Harper
Hospital cyclotron, but modified to accommodate the rollers to soak the paper with
epoxy more thoroughly. The paper cutting device was newly built and employed
a slide with a lead screw to control the cutting length as shown in Figure 3.2 The
conveniences added to the new system improved overall efficiency in the lengthy

winding process.

The number of turns was counted with a counter whose shaft spins together with
the lathe spindle (located at the end of the spindle), which allowed an exact turn
counting. A step type counter triggered by a cam on the lathe spindle was also

employed for mutual checking.

The Stycast epoxy was mixed with 4.5 % of Catalyst 11 by weight and poured
into the epoxy pot. During the winding process, the pot was cleaned and refilled with
fresh epoxy every 5-6 hours. While impregnating paper in the epoxy pot, the pot was

warmed to 35 °C using a heater in order to reduce the epoxy viscosity.

A test coil was wound before the actual winding, to test the winding devices and

to develop the winding technique. After practicing winding and unwinding, a test

65

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7%? [i
. [.1. j I
\ Al plate
2 2 Toggle clamp
Slide with
2’3 m Lead screw
at /
iii /
ii pig, 5 I Epoxy pot
ll l ‘ /
I] L [Slit for paper
it] T'_’J< Heater
j

 

 

 

Figure 3.2: The paper cutting apparatus employing a slide with a lead screw. Two
aluminum plates set the paper length, and a razor blaze was used to cut the paper.

The heater and epoxy pot are also sketched.

66

coil 28 cm in diameter and 4 layers was finally wet wound and cured. The thickness
of epoxy paper between each layer was measured, and the overall thickness of the 8

T coil with 48 layers was accurately estimated.

The progress of the actual winding strongly depends on the preparations made and
unexpected problems. For instance, a day was spent to replace the tensioner V belts
after they were contaminated with oil from the banding wires. As the coils are potted,
it is important to keep the winding period as short as possible, to avoid changes in
epoxy characteristics prior to the hardening cycle. The first coil set, involving the
small and large coils in the same side of the median plane, is shown in Figure 3.3.

The small coil already has its banding in place, and the large coil is being wound.

The coil was cured in a large bakery oven. It took about 20 hours to completely
cure the whole coil body due to its mass (peak temperature: 140 °C). The coil

temperature was monitored with a thermometer attached on the banding.

The winding took about a month for each coil set with two graduate students
working for an average of 10 hours with support from the machine shop. Detailed

analysis of workdays for the 8 T coil winding is given in Table 3.2.

III Test of coils in the liquid helium dewar

The coils were tested before being installed in their permanent cryostat in order to
ensure basic coil performance before undertaking the many procedures involved in
assembly of the cryostat. For this test, the coils with their banding and their welded
banding (calm shell structure), were welded onto the midplane structure described in
section 2.II.D. The leads were connected, and level gages installed. The coil package
was then mounted in a small cylindrical LHe container to reduce the quantity of

LHe required for a test, and the whole assembly installed in a large commercial

67

 

Figure 3.3: The first coil set under winding. The small coil already has its banding
in place, and the large coil is being wound.

68

dewar (Figure 3.4). A relatively long current lead (4 meters) was needed to make a
connection from the coil to the existing 500 A commercial current leads at the dewar
top. The connection leads were made of four parallel conductors, obtained from spare

superconductors for the K500 cyclotron.

In the first test run, the large coils quenched at 250 A. The quench occurred at a
LHe level of 75% of the entire coil height. At this level the current leads going to the
upper coil were not directly cooled by the liquid helium. One probable explanation
of this quench is that the normal zone at the joint propagated into the coil. The heat
generated on the joint is roughly estimated as 10’4 W at 200 A, which is usually
negligible under good cooling conditions. However, this normal region can propagate
into the coil when the liquid helium level is below the joint and the leads into the coil.
The next test was done with the helium container completely filled. The large coil
was operated at 350 A without a quench. A higher current was not tried to avoid the
strong magnetic forces induced on adjacent iron structures in the test area. The hoop
stress on the large coil at 350 A corresponds to the stress level at a 6 tesla excitation
of the magnet with the iron yoke in place. The current was increased at the same rate
as in the first test to see if the eddy current heating was the cause of the quenching

in the first run, but this turned out not to be the cause.

The small coils were operated at a. current of 430 A. To reach a higher current
than in the big coil test without jeopardizing the current leads, the dewar pressure
was raised to 3 psig from 1 psig for a short time allowing more gas flow through the

current leads so as to maintain 150 mV voltage drop in the leads.

This test showed coil performance of at least 70 ‘70 of the design expectation, and
since the adjacent iron structures made higher current testing hazardous, the testing

was terminated and magnet assembly work was begun.

69

Current Leads

8T Coil

LHe container

 

Figure 3.4: The schematic view of open dewar with 8 T coil package inside. The long
current leads connecting the commercial 500 amp current leads to the 8 T COIlS, and

the LHe feed line are shown.

70

IV Vacuum system

Superconducting cyclotron magnets usually have two separate vacuum chambers: a
cryostat vacuum chamber for the thermal insulation of the liquid helium vessel, and a
beam vacuum chamber for experiments. Vacuum requirements are somewhat different
for the two chambers. Air leaks should be eliminated for the beam chamber, especially
for the acceleration of heavy ions, but they are more tolerable for the cryostat vacuum
because of strong cryopumping by the 4 K vessel. For the cryostat vacuum, however,
a helium leak from the helium vessel can cause serious problems. After the magnet
is fully assembled, it is very difficult to repair a helium leak, and even with a small
leak, the heat load to 4 K increases dramatically; for the beam transport magnets
in the MSU/NSCL with a helium leak, the heat load was doubled at 2X10'5 torr
[Lau]. It was, however, not easy to check for leaks on the helium vessel because of
difficulties in achieving a good vacuum due to the large impedance from the small
diameter tube; 120 cm long tube with 1.5 cm O.D. designed for the helium gas return
was the only pumping line available. Due to the limited conductance of the line, the
pumping speed was not enough to make a good vacuum (< 10‘5) to operate the leak
checker at a high sensitivity. The vacuum achieved and calculated considering the
reduced pumping speed was at best about 2 x 10‘3 torr with a 140 l / sec turbo pump.
The RGA (Residual Gas Analyzer) in a bad vacuum mode and methanol were mainly
used for leak detection. The coil tank was then cold shocked by filling with liquid
nitrogen to reveal latent cracks in the welded regions due to the thermal shrinkage.
The leak checking was resumed after the cold shock, and the vacuum reached the

same level, which indicated that no leaks were developed by thermal shock.

The beam chamber is a vacuum space surrounded by the yoke and pole tips. The

limited conductance is again the dominating factor in determining the vacuum level.

71

With a 7.6 cm wide and 50 cm long pumping line (rf hole in the magnet), the vacuum
will be in the range of 10"5 torr with 300 l/s pumping speed for air at STP, which is
obtained from the conservation law, S1P1= Sng, where S is the pumping speed, and
P is the vacuum pressure; P at the pump side is assumed to be in the 10'7 range, and
a constant virtual leak is assumed. But when the ion source is in operation at the
rate of 1 atm cc/sec, the vacuum will deteriorate to a 10‘4 torr range. To improve

the vacuum, there needs to be more pumps added.

V Cryogenic system and radiation shields

To operate the 8 T superconducting magnet at 4.4 K, liquid helium is continuously
supplied from the 500 liter dewar connected to the CTI 1400 refrigerator. The helium
vessel usually operates at 1.1—1.4 atmosphere, which is determined by the helium gas
return line pressure. The warm helium gas effusing from the current leads returns to
the compressor operating at 1—2 psi inlet pressure, and the cold gas ( 310 K) coming
directly from the vessel returns to the heat exchanger of the refrigerator at 3—6 psi
to increase the liquid production efficiency. Liquid nitrogen is also provided to the
magnet to keep the radiation shields at 80 K. For the supply and return of these
cryogens, a distribution box with the bayonet connections is located at the top of the
magnet so that a U tube or flexible lines can transfer cryogens between the magnet

and the refrigerator or the dewar.

The radiation shields which surround the helium vessel have to endure the forces
induced during fast magnetic flux changes such as a quench. The resulting force may
be strong enough to collapse the shields. This accident has actually happened to
the K500 [Mar81] arousing caution in shield designing. While the induced force on

the inner shield is directed radially outward, the outer shield takes an inward radial

72

pressure because of the B2 reversal across the coil. From experience of the K500
shield collapsing, the outer shield seems to be more easily subjected to the rupture,

although the magnetic pressure is much higher on the inner shield.

The radial pressure on the outer shield of the 8 T magnet during a quench at 400

A is estimated with the equation below;
PL = Jng't = O'Eoth, (3.1)

where a is the conductivity of the copper at 80 K ((7'_V1/(2x10"7 Qcm)), t is the shield
thickness, and E9 is the electric field on the shield induced at a quench (E9: AAg,
where A is from I(t)= I(0)e"\t, and A9 is the magnetic vector potential; A: 0.3 sec"1
calculated with QUENCH, A991 0.6 T.m calculated with POISSON for a quench at
8 tesla). The pressure is a function of time, and the highest pressure appears shortly
after the quench initiation as the flux changes speed up. The maximum pressure on
the outer shield is calculated to be about 3 psi. Much higher pressure is induced on
the inner shield due to the high 82; Bz~6 tesla on the inner shield compared to ~02

tesla on the outer shield. The calculated pressure on the inner shield is as high as

110 psi.

The collapsing pressure of the perfectly cylindrical shell is estimated by the formula

in reference [Ava87];

W. = KY (33, (3.2)

where Y is the elastic modulus of the material, D is the shield diameter, and K is the
numerical coefficient related to the shell dimensions, which is graphed in [Ava87]. The
estimated collapsing pressure of the outer shield using Eq.3.2 is about 10 psi (K~90,
D: 75.2 cm), and 20 psi for the inner shield. These estimations do not include the
effects of the edge support and of stronger material properties at 80 K. Although the

calculated magnetic pressure on the inner shield is higher than the collapsing pressure

73

during a quench at 8 tesla, there is no evidence of the shield damage after a series of
quenches for the 8 T magnet; the measured heat leak was not affected by the quench
events, although it is not an absolute indication of no shield damage. (If strain gages

were installed on the shields, magnetic pressure could be measured during a quench.)

Chapter 4

Measurements of 8 T magnet
properties

I Coil centering

The superconducting coils need to be centered with respect to the pole tips and
the yoke to avoid large magnetic off-centering forces and unwanted field harmonics.
While assembling the magnet, the coils were roughly centered. Fine adjustment of coil
centering was then performed in the process of energizing the coils after the magnet
was fully assembled. As the coils are energized, force imbalances measured on the

strain bolts installed on all nine links were corrected by shifting the coils.

In section 2.II.B, the spring constants of links and of magnetic off-centering forces
were independently estimated. In a magnet system with all links attached, if assuming
that there is no interaction between horizontal and vertical links and that interactions
with other attachments to the coils such as current leads are insignificant, the spring
constants of both link assembly and off-centering force can be measured at the same
time using force equilibrium equations in a disturbed link system; i.e. by displacing
the links, and by measuring the incremental loads on all the links. A diagram of link

systems in this analysis is illustrated in Figure 4.1.

74

   
  

1.00

O

75

Displacement of
COll center

Ax :D i sp I acemeni' of
Strain bolt

 

0.75 a
0.50 -
0.25 a
0.00 -

I
-0.25 -

Vertical (N/m) (x107)

-0.50

 

 

0

l
50

 

10rO 150 260 2§o 360 350 400
Currents (Amp)

Radial (N/m) (x107)

F2

rm]

0 Axucnange of link length

1.00

0.75 -

0.50 a

0.25 d

0.00 -

-0.25 -

-0.50

 

 

Coil _ .sz

 

 

 

 

 

 

 

 

0

i
50

 

160 150 260 250 360 350 400
Currents (Amp)

Figure 4.1: Link systems are idealized to obtain analytic expressions for measurements
of spring constants. The spring constants of the magnetic off-centering forces were
measured as a function of current, and are shown in the bottom graphs.

76

The equilibrium equations for the vertical links are given below;
AX] + AXz = AX, Fmag + F] = F2, (4.1)

where AX is the displacement made equally on the three top or bottom links, AXI is
the length change of the links, and AX2 is the displacement of the coil median plane.

The forces, F1, F2, and Fmag can be expressed by Hooke’s law;
F1 = I‘5‘iJe'r'tz'calA){1, F2 : kverticalAXZ, Fmag = kmagAX2a (4-2)

where kvmgcaj is the spring constant of the vertical links, and humag is the spring
constant of the vertical magnetic off-centering force. After doing some algebra, the

spring constants of the link and the off-centering force are written in terms of measured

quantities:
F2 F1
kver ica = _ 1 _ .
F2 — F1 F1

 

kvma = 1 — 4.

For the horizontal links, the spring constants are given by similar equations as

shown below. The displacement in this case is made on only one link:

2F F
khorizontal : E'Xlu- + 5.211;) (4-5)
F2 —F1 .51

Ichmag = ”XX—(1 217.2) (4.6)

In this analysis, the deformation effect of the bobbin and midplane ring is not in-

cluded, which would result in smaller spring constants.

The spring constants of the link assembly obtained in section 2.II.B are compared
to measurements made in the magnet system using Eq.4.3 85 5, and shown in Table

4.1. Another measurement was also performed by making equal displacements for all

77

Table 4.1: Comparisons of link spring constants calculated or measured using different
methods

 

I Measurements I Vertical (N /m) I Horizontal (N /m) I

 

 

 

 

From section 2.II.B 1.6x 107 1.4x107
Eq.4.3 & 5 1.0x107 1.1x107
Equal displacements 0.9 x 107 1.3 x107

 

 

 

 

 

horizontal or vertical links as described in reference [Mil78] to eliminate the effects of
other attachments to the coils such as cryogen lines or current leads, and the results

are given in the last row of Table 4.1.

The spring constants of the magnetic off-centering forces were extracted using
Eq.4.4 & 6, and displayed as a function of current in the lower part of Figure 4.1.
(The restoring force at 0 A presumably implies the reaction of the entire system to the
displacements because of the attachments to the coil which are ignored in deriving
Eqs.4.3—6.) The spring constant of the vertical off-centering force calculated with
POISSON (1.1x107 N/m, at 400 A, section 2.II.B) is larger than the measurements.
For the radial off-centering, the spring constant of 1.5x 107 N / m estimated by a dipole

model at 400 A in section 2.II.B is also larger than the measurements.

II Accident during initial magnet operations

After the 8 T magnet was cooled down to 4 K during the initial operations, the
magnet test was performed without a complete analysis of the test scheme. The
large and small coils were in a series connection, utilizing only one of the two power
supplies (Dynapower Corp. 20V / 500 A). This scheme originated from the idea that by
ramping both coils at the same rate, the coils could be tested without being affected

by heat generated from relative sliding motion between small and large coils.

ll

 

78

However, this connection led to a problem due to not considering the quench
voltage. When only one of the small and large coil pairs quenches and the other stays
in the superconducting state, for instance a large voltage is induced at the connection
joint between the two coil pairs, where two terminals from each current leads for the
two coil pairs make the joint (and the other two terminals are connected to the power
supply). Normally, the maximum voltage on the current leads is limited by the power
supply (20 V max.) when the two coil pairs are individually excited; i.e. the current
leads are not designed against high voltages. The program QUEN CH estimates that
the voltage at the joint is about 500 V after a second (as 100 kW at 200 A). (During
a quench, a high voltage, which is estimated to be as high as 2.5 kV, can appear at
the median plane connections between the image coil pairs. However, the insulation

is designed for that voltage, using Teflon sleeves of 0.15 mm thick and Kapton tapes

(3M) of 0.07 mm thick.)

Due to this large energy discharge, many instrument wires sharing the outgoing
tube with the current leads (see Figure 2.16) were damaged, including all strain gage
leads, and the large coil showed a short to ground. The short location, roughly
verified by TDR (time domain reflectometry) was near the cold end of current leads
where the current lead wires are bare and the insulation for the instrument leads
is 0.03 mm thick Formvar only. Fortunately, however, two instruments important in
basic magnet operation, a helium level sensor and a temperature sensor survived, and
the short in the large coil appeared to be weak, the short resistance increasing after

another magnet operation.

At present, the magnet itself is operational without much influence from the ac-
cident, but the loss of major instrumentation such as lead voltage taps, strain gages,

spare temperature and helium level sensors, was substantial.

79

4.3 Strain gages for coil stress measurements

To compare actual stress with design expectations, coil stress measurements using
strain gages bonded on the coils were tried. Since stress is a tensor quantity, it can
not be measured directly except for special cases. With Hooke’s equation, stress can
be determined from strain measurements and material properties. A single gage con-
figuration was mainly used to measure the principal coil strain, because its direction
is clearly along the circumference of the coil. Strain gages with a rosette geometry
(a group of three gages arranged in a 0°, 45°, 90° pattern) were also attached on
the upper large coil, which can determine the complete stress distributions on the

measurement plane [Ger90].

The strain gages can be subject to parasitic effects coming from installation, mag-
netic fields, and lead wires among other things [Han92]. A connection known as the
three wire method (top part of Figure 4.2) was employed to avoid some of the lead
problems by cancelling the false signal. The magnetic field effect was also taken into
account by using a strain gage attached to a floating plate. The output due to the

magnetic field can be measured by this gage.

To ensure the operation of strain gages at least at 80 K, an actual test was per-
formed with the same apparatus used for tensile strength measurements of support
links schematically shown in the middle of Figure 4.2. Two different types of strain
gages purchased from Measurements Group Inc. were tested: CEA-06-125UR-120(fl),
and SK-06—125RA-350(Q), where the operating temperature of the ’SK’ type extends
to 80 K, and possibly to 4 K, while the CEA type is mainly for room temperature
use. The test results comparing the outputs of the strain bolt and gage are shown
in the lower part of Figure 4.2. The strain bolt at room temperature is believed to

give more reliable measurement. The comparison in the figure shows that the strain

 

80

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 
  

 

 

 

l
I
i ll
I “DUMMV'
ARM
A l
EXCITATION
3 I VOLTAGE
| ourpur
STRMN VOLTAGE
GAGE l
- c l,‘ _ ll
LEADWIRES I READOUT
I msmuuem
_ STRNN BOLT
z HYDRAULIC CYLINDER
l j
Fl
1
LN: CONTNNER
V/
[Ii-7 STRAIN GAGE
l 1
32500 1 I 1 L
x /
v a : CEA—1200 /
+5 2000‘ x : SK-3500 / ‘
.9 o : SK—3500, 77K
3 _ _
O 1500
S
O iooo~ —
3
U)
.E 500* -
O
L
('7) 0 f r T i
O 500 1000 1500 2000 2500

Strain bolt (Kg)

Figure 4.2: Top: a three wire method of strain gage connection to cancel out the false
output induced in leads. Middle: experimental set-up to compare the readouts from
strain bolt and gage at 300 K and 80 K. Bottom: the output comparisons of strain
bolt and gage. The reading from the gage is higher than that of strain bolt, but the
reason is uncertain.

 

81

gage outputs seem to be consistently higher than the strain bolt output. At 80 K,
the output of the CEA type was very unstable compared to that of the SK type as

expected.

When the strain gage is subjected to temperature variations, its resistance changes
appear as ’apparent strain’. The resulting thermal output depends on the material
to which the gage is attached. The stainless steel used in this test shrinks more
than the 1018 steel for which Measurement Group Inc. provides the thermal output
data ( (L293-L4)/L293 (%) is 0.19 for steel, and 0.31 for 304 stainless steel). After
the correction of thermal shrinkage was made, the measurement agreed with the
company’s data within 5%, which showed the possibility of measuring the thermal

stress in the coil.

The strain gages were attached to the clam shell structure of the 8 T coils, which
surrounds the banding, because other places inside the coil are not easily accessible
for gage installation. The stress on the shell structure can be used to deduce the coil
stress distributions using STAN SOL calculations; by matching the measurements and

calculations on the shell, the coil stress distributions can be then inferred.

4.4 Coil stress measurements of the 8 T magnet

When the coil was cooled down and energized, the strain gages were used to measure
the coil stress. Thermal outputs from different strain gages were not consistent, and
they were drifting. The average strain (of three gages) was approximately 2000 ac
(i200), which is approximately the strain caused by the thermal shrinkage in a free
body made of stainless steel (1800 Inc). Since the coil shrinks away from the banding

and clam shell structure, it is understandable.

The strain caused by electromagnetic forces was then measured. The first mea-

 

82

surement was made on the clam shell of the large coil. The strain reading was almost
a constant until the current was ramped to 200 A. When the current was increased
to 300 A, the hoop stress on the clam shell increased roughly by 1200 psi. This
stress increase is much lower than 5100 psi from the STAN SOL calculation in which
a complete contact with the banding is assumed. If the contact is loose, the clam
shell would be subjected to much lower pressure, as the measurement implies. The
lower hoop stress could be due to the loose fit, but the possibility of the false output

on the strain gage could not be excluded.

Since the lead wires of all strain gages were damaged during the accident described
in section 4.11, coil stress data beyond that described here could not be obtained. In

general, measurement of coil stresses at 4 K is not an easy task.

4.5 Magnet quench study

Quenches of the 8 T magnet were studied to understand the quench causes. Variations
of physical parameters during a quench, such as the coil current decay and the coil

temperature increase, were measured and compared with computations.

When the magnet quenches, it is difficult to actually measure the physical param-
eters such as the hot spot temperature and the IR drop in the coil because of the
high voltage induced on the instrument lead wires and on the voltage taps, so that
strong insulation is required for those wires to carry out measurements. The current
is the only physical quantity, which can be easily measured. The decays of the coil
currents were recorded with current transformers (HOLEC, 500 A), and compared
with the QUENCH calculations for the large coil in Figure 4.3. A quench at low

currents (2200 A for both small and large coils) was induced by the depletion of

 

 

83

 

 

 

 

 

450 l l I l
400- : Measurement ”
'6 350‘ __ : QUENCH Simulation ”
U 300 — r
a)
@250— —
L
o _ _.
_, 200
A 150n _
C; 100 a —
50 —< _
O l t I f r
O 5 1O 15 20 25
Time(sec)
250 l J l l

 

I(A), Large coil

 

 

 

0 i

 

l 7
o 5 10 15 20 25
Tlme(sec)

Figure 4.3: Current decays of magnet quenches were measured and compared with
the QUENCH calculations (transverse velocity = 0.075 longitudinal velocity). Mea-
surements were made for a large coil pair only in this case.

 

84

the liquid helium, and a quench around 400 A (small coil current: 300 A) occurred
during the current ramping. The comparison shows that the actual current decay is
faster during the first few seconds after a quench than the QUEN CH simulation, and
slower at low currents. This trend has also been observed in other magnet quench
studies [Wil83]. The discrepancy between the simulation and calculation may come
from the assumptions made in the calculation such as the quench origin (corner of
the innermost layer), and the transverse velocity of quench propagation, as well as

from uncertain material properties.

The coil temperature increase after a quench was measured with Allen-Bradley
carbon resistors (500 Q at 300 K) attached to the clam shell structure, from which
the stored energy was estimated. This measurement method is however inaccurate
because: 1) the resistor was not well calibrated, and 2) the equilibrium coil tem-
perature differs from the resistor reading because the resistor is being continuously
cooled by cold helium gas whose enthalpy is much higher than the enthalpy of the
coil materials at low temperature. For instance, when the coils quench at Ismail: 330
A and Large: 400 A, the stored energy obtained with this method was only 60% of

the energy calculated from magnet inductances (see the following section).

In the initial magnet operations, the magnet quenched at relatively low currents,
and the currents at quenches varied (see Figure 4.4), which is typical for a quench
induced by wire motion. However, it soon became apparent that the currents could
be increased by following the particular current ramping paths; the large coil should
be energized first up to 420 A before the small coil is energized over 300 A, which can

be noticed from the current ramping procedures described in the table in Figure 4.4.

To reveal the cause of these quenches, the LHe bath temperature was lowered
from 4.4 K to 4.2 K by venting the boiled-off helium gas to the air. If the quench

occurs due to the wire motion, the current at a quench should be independent of

85

 

 

 

 

500 l l l l |
'5 450 - _
o
E 400 - _
E 12
(f) 350 — lo _
a“ 5 1 1? 13
300 - 7 —
E 3 9
o 2 4
V250 — 5 —
200

 

l l
200 250 300 350 400 4éo 500
l (amp), Large Coil

same rate
rate

 

Figure 4.4: The quench history of the 8 T magnet is displayed as a time sequence. To
reach higher currents, it was necessary to follow a particular current ramping path as
shown in the figure by an arrow. The magnet operating temperature was 4.4—4.5 K,
depending on the LHe supply pressure which was difficult to regulate.

 

86

small temperature changes. On the other hand, when a critical current limit causes a
quench, the current at a quench should react sensitively to temperature changes. By
reducing the LHe bath temperature, the small coil current before a quench increased
by 23 A compared to the previous quench points (see quench # 10 and 12 in the table
in Figure 4.4). This could be explained as either I) evidence that the present quench
may be caused by the critical current limit, or 2) training that the currents at a quench
continue to increase. (This test was performed only once because of the excessive LHe
loss for each experiment; over 100 liters.) Another unexpected phenomenon is that
the current ramping path influences the quench point, and that the small coil current

has never reached 400 A while the large coil can be easily operated over 400 A.

The maximum currents at quench were Ismail: 370 A, Large: 420 A, and the
highest field achieved in the magnet gap was 8.2 T. The current margin (mg) defined

in section 2.1.1 is about 26%, since Io, is 560 A at 8.1 tesla on the conductor at 4.4 K.

4.6 Inductances of the magnet

Inductances of a magnet employing steel are a function of iron saturation. As the
iron progressively saturates, the magnet inductances approach the coil inductances.
While the coil inductance is one of the design considerations, the inductance due to
the magnet steel is not a main concern for DC magnets such as cyclotron magnets.
High inductances slow down current ramping rates at low magnetic fields (3 2.5 tesla),
and contribute to the stored energy, which are usually considered to be unfavorable

in magnet operation.

Since the 8 T magnet has the small and large coils, they are inductively coupled

as below.

0111 d]2 _ d12 d11 _
LIE-+Mdt —Vi L-zdt +Md, —V2, (4-7)

 

87

Table 4.2: Comparisons of measured magnet inductances to calculations with POIS-
SON after iron saturation.

 

I I L1 I L2 I M [Stored Energy]

POISSON 22.0 6.68 5.03 3.1MJ
Measurement 20. 4.4 5.9

 

 

 

 

 

 

 

 

 

 

where, L1 and L2 are the inductances of each coil, M is the mutual inductance, and
V1, V2 are the driving voltages. The L1 and L2 of each coil were measured by
removing the mutual inductance term using two different methods: 1) ramping each
coil individually with the other coil circuit opened, and 2) ramping only one coil
with the other coil current regulated by power supply (results obtained from the two
methods agreed within 20 % before iron saturation, and within 5 % after saturation).
Unequal currents in the two coils were then converted to an equivalent current using
qu 2(I,mau+2lla,ge) / 3, which was obtained from the relative contributions of each coil
to the total field [Hum89]. The mutual inductance was then measured by ramping

both coils at similar speeds.

If the polarity of the power supply system were reversible, the inductances could be
measured by using different combinations of the polarity in each coil, as demonstrated
in inductance measurements of the K1200 magnet [Hum89]. The inductances of the
8 T magnet measured as a function of current are shown in Figure 4.5. When the
pole tips are saturated at high fields, the measured inductances are compared to
calculations with POISSON in Table 4.2. The measured mutual inductance is larger

than the calculated one (M2SL1L2 is the only condition to be satisfied).

 

88

 

   
   
      

 

 

 

 

120 1 1 1
100- _
A X : L (Large call)
I .
v 80- A : L (Small call) _-
8 O : M
c 50— _
B
S
U 40— _
E
20— ,_
>
o , I j
0 50 100 150 200

l (Small coll)=l (Large coil), (Amp)

Figure 4.5: The magnet inductances measured as a function of currents. The currents
of the two coils are converted to an equivalent current as described in the text. The
inductances reach the saturated values around 2.5 tesla.

 

89

VII Heat leak in the magnet

The heat leak into the LHe was measured when the magnet was cooled down for the
first time, and is displayed as a function of LHe level in Figure 4.6. Calculations,
including the contributions of conduction, radiation, and the current leads were also
made, and are compared to the measured heat leak in Table 4.3. The conduction
contributes only a small portion of the total heat leak. The radiation heat leak was
calculated using the experimental heat leak data between 4 K and 80 K surfaces
covered with 3M aluminum tapes [Leu85] since superinsulation is not employed in

that space.

The measured heat leak is much higher than the calculations in Table 4.3, and
average heat leaks differ across the median plane. Two different heat sources may
be added when the liquid helium level is over 50 %: 1) LHe loss due to the helium
pressure change right after finishing the LHe transfer, and 2) large heat leak through
the median plane structure due to the poor thermal insulation, which contributes less

when LHe does not make direct contact with the structure.

When the liquid helium transfer is completed with the valve closed, the helium
pressure usually decreases depending on the LHe transfer pressure. To reduce the
boiling temperature according to the pressure drop, some LHe has to evaporate,
carrying the heat away. However, the helium pressure effect was difficult to identify;
variations of the LHe transfer pressure were not well correlated with the heat leak
near the top of LHe level. (The possibility of thermal short between the helium vessel
and the 80 K shield at the vessel top was also considered as a large heat leak source,
although it is unlikely from the fact that the heat leak decreases rapidly with a small
LHe level drop.)

In room temperature penetration holes, the gap between 300 K and 4.4 K is 0.6 cm

 

90

 

 

 

 

 

20 IllIllllllllllllllllll’lllllllllllllllllllllllll
-l ..
/'\ d "
L "‘ X
£15— _
\ a .
q l-
(I) q .
+4
52 10‘ -
¥ - p
q.—
0 ' p
7: 5— x _
Y Y
O - TX M P
x x
m d x x x l-
O IIUIII'IIIIUUI TIIIIIUIIIIUII 'I'rTl'l'lIrT'l'l'I

 

100 90 80 7'0 60 50 4'0 30 20 lo a
LHe level (70)

Figure 4.6: The heat leak to 4 K as a function of LHe level. The large heat leak
near the vessel top may come from the helium pressure drop after stopping the liquid

helium transfer

91

Table 43: Heat leak at 4.4K

 

 

 

 

 

 

 

 

 

 

 

 

 

Items Heat Load at 4.4 K
Estimation Two current leads 1.4 W
Radiation 0.04 W
Conduction on links 0.15 W
Total 1.6 W

Measurements LHe level Average Heat load
Without He leak <50 % 3.0 W
>50 % 4.8 W
With He leak <50 % 4.8 W
>50 % 11 W

 

 

 

 

so that only 15 layers of superinsulation were employed. In addition, those penetration
holes could not be perfectly insulated because of the difficulties in connecting to the
superinsulation in other regions, which could cause a large heat leak. It is believed
that a larger overall heat leak than the calculation is due to this large heat load in
the median plane structure even when the LHe level is below 50%. A similar heat

leak problem has been observed for the K1200 magnet [Lau83].

After operating the magnet for about a week, a helium leak into the insulation
vacuum was detected. It was noticed because of an enormous increase in heat leak;
LHe loss became more than 100 1/ hr after 2-3 hours without pumping the cryostat
chamber. With continuous pumping, the helium loss was reduced to 18 l/hr, which
barely allowed continuous operation of the magnet with the supply of LHe from the
500 liter dewar with a LHe production rate at 20 l / hr by CTI 1400 refrigerator. When
the magnet was warmed to room temperature after the initial tests, suspicious joints

of Cajon fittings were re-tightened, and the helium leak has disappeared.

The heat load on the 80 K radiation shields is usually not seriously considered
because of the low cost of LN 2. The calculated heat load on the 8 T magnet shields

is 3.5 W from radiation (1 W/m2 with 18 layers of superinsulation [Shu86]), and 1.5

‘-

 

92

W from conduction. The total heat load of 5.0 W can be easily removed with liquid

nitrogen, employing a 0.63 cm O.D. transfer line.

 

Chapter 5

Field mapping and analysis

Magnetic fields were measured using a Hall probe (F .W.BELL). The probe was in—
stalled in a copper tube, and the tube was inserted into a penetration hole at a fixed
angle. The Hall probe was later calibrated by a N MR probe (SEN TEC D20 probe
#7, range: 30—68 kgauss(kG)) which was located at the center of the magnet’s axial
hole, where the field is uniform enough to generate sharp resonance signals. Table
5.1 shows the magnetic fields measured by the two probes at the same location. The
fields by the Hall probe were fitted to the fields by the NMR probe using second
degree polynomial: B: 0.0713 + 0.9932BHaU + 0.5760X10‘3B12gau, where the B and
B Ha" are in units of kG. All measured fields by the Hall probe displayed in this section
were corrected according to this equation. In the range of 35—64 kG where the N MR
calibration was carried out, the error due to the fitting and significant figures in the
Hall probe readout is estimated to be 0.05 %. (The N MR probe which can calibrate
near 8 tesla was highly required to avoid extrapolation, but was not available during

the measurements.)

Because of the symmetry of the twelve penetration tubes and of threefold sym-
metry of the yoke, there are two angles at which the magnetic fields are different if
perfect symmetric fields are assumed. Measurements were made only at one angle

since mapping at this stage was intended for a comparison with the calculation rather

93

94

Table 5.1: Calibration of the Hall probe by the N MR probe

 

Hall Probe (kG) 35.27 39.74 43.94 52.83 56.78 60.96 63.29
NMR(kG) 35.820 40.442 44.816 54.138 58.300 62.775 65.235

 

 

 

 

 

 

 

 

 

 

 

than for particular uses of magnetic field data.

The 3-d magnetic fields were calculated with the finite element program, TOSCA.
The magnet model includes a twelfth of the yoke and all four coils as displayed
in Figure 5.1. For three different excitations, magnetic fields were measured and
compared to the TOSCA calculations in Figure 5.2. Measured fields in the flat region
seem to be lower than the calculated fields by nearly a constant, insensitive to the
radius and excitations. To explain this, it was thought that the saturation point
of the steel used in the magnet may be lower than the saturation point in the BH
table (But: 2.14 T) for TOSCA. This is probable since the pole tip and the yoke are
made of the 1020 steel while the BH table used in TOSCA may be more adequate
for steel with lower carbon content. When the measured fields are subtracted from
the calculated fields using B,atu,.at.-on=2.14 T, a difference of about 500 gauss is visible
as shown in the lower graph of Figure 5.3. When the saturation point of the BH
table in the code was reduced by 500 gauss, the agreement appears better for high
fields (upper graph in Figure 5.3), but it still seems unsatisfactory for lower fields,
especially in the center region. The mesh size effects on TOSCA calculations were not
thoroughly examined, but should be smaller than the present differences in the fields.
Large differences near the center hole between measurements and TOSCA calculation

were not thoroughly understood.

TOSCA fields are Fourier analyzed, and shown in Figure 5.4. The third harmonic

component, 3;; which is important as a flutter for sector focusing in isochronous

95

 

 

. 'U l

"r?- can:

><_L IN-i

<8:

cam]

LLJSI

0.2!,

Ci.”

..J

53

D.

m “r.
' ‘T”
-4-

 

 

(\J
-:r-
m
(\l
.72."
60") l
um
gm
_._>CI'J 0C: i
'\ c:
.42...)
o: u >«:__,
ID I
l:n\.
dz—
5m

 

 

Figure 5.1: A magnet model used for TOSCA. One twelfth of the yoke and four coils
are involved in the model. Some details of the magnet such as the rf holes and room
temperature penetration holes are also included.

ll

 

Magnetic Field (T)

Figure 5.2: For three different excitations, measured magnetic fields are compared to

96

 

8.0
7.5 —-
7.0 -—
6.5 —
6.0 -
5.5 -
5.0 —-
4.5 -
4.0 —
3.5 --*
3.0 —

2.0 --
1.5 -
1.0 —~
0.5 --

l1=4OO A, l2=300 A

 

  
 
  
    
   
 

: Measurement
:TOSCA

 

 

 

 

 

0.0

calculations by TOSCA.

 

l l l l
10 15 20 25 30

Radius (cm)

 

97

 

 

 

 

 

 

 

 

- B
10 O O l I measurement] TOSCILK l 1
ft}? saturation: 209 ISSIO
U)
:3 500- T
O
8
:9 O-
.0.)
L
L
O -500-
L
L
LL]
-1000 O i I é l 11 ? 1]] 1]..
1000 1 l ' I 9 f ‘ D
1]? saturation= 214 IGSIO
U) —- - — - I |1=400 A, 12:300 A
8. SOD-l T
0 — — — I 15200 A, |2=200 A
E o— — ; |1=50 A, l2=50 A ._
.9.)
L
L.
O —500"
L_
L
L1_l
~1000 l l l l l l l
0 2 4 6 8 10 12 14 15
Radius (cm)

Figure 5.3: Differences between the measurements and calculations are plotted when
the iron saturation point is 2.14 T in the lower graph, and 2.09 T in the upper graph.

 

98

 

OoooOOOOOOOOOQOO
O

 

 

 

 

 

O
O
G)
0
0
O

- 0
<5
4:)
a
« o
o

 

8100‘ 0 o
co

m 0 O

n n (1 (Ln 0 0

6“8’ '10T1‘21'41‘6 18 20
Radius (cm)

 

 

0

«Po

0

 

00
<5
No

Figure 5.4: A field at Izargc=400 A, Imau=300 A is Fourier analyzed to see the com-
ponents of higher harmonics in the present magnet configuration.

 

 

99

cyclotrons, is weak. Higher harmonic fields in the present magnet configuration are
mainly caused by rf holes and penetration holes included in the model. The pole tips

do not have sector structures yet.

" ‘-

 

 

 

Chapter 6

Conclusion

The 8 tesla superconducting magnet was built and tested, mainly to study cyclotron
related phenomena. Because of limited experience in constructing superconducting
magnets using N bTi superconductor at 4.4 K to produce over 8 tesla on a large scale
(with a bore diameterZ 0.5 m), it was uncertain that this 8 T magnet could be
built to operate reliably. Long term operational results are not available yet, but the
magnet has proven to be able to produce fields over 8 tesla. In retrospect, among the
design options we have studied, the selection of the free coil could be the reason for
the successful generation of an 8 tesla field. The free coil has been also studied by
other groups [Bob85] [Ant89] for superconducting NMR magnets, which drew similar

conclusions.

With the 8 T magnet completed, some utilization was planned. Ion source emit-
tance measurements and a conversion to a cyclotron would be the probable uses of
the magnet. These were studied by computations, as described in the appendix, to
produce experimental schemes for the source emittance measurement and to explore
cyclotron design parameters for a future cyclotron project. In one plan, the conver-
sion project may proceed prior to source emittance experiments since the cyclotron
project seems to be more interesting, with the 8 T magnet designed appropriate for

an isochronous cyclotron.

100

 

101

The acceleration of heavy ions is less severely restricted by focusing difficulties in
a high field isochronous cyclotron. Hence, it would be beneficial to build heavy ion
cyclotrons using magnetic fields still higher than 8 tesla. A 10 tesla magnet could
be built by employing the present 8 T magnet construction technique, with the ad-
dition of a cryogenic system which can reduce the LHe bath temperature to 1.8 K
(for instance by reducing the helium pressure to 0.016 atmosphere). However, the
coil stress due to the higher magnetic field and current density is much larger for a 10
tesla magnet; a thicker banding with higher preloads and special copper matrix whose
yield strength is higher than 20,000 psi at the cost of resistivity would be required to
withstand higher coil stress without degrading the critical current. (Also the refrig—
eration required to go from 4.5 K to 1.8 K is about twice as much). Superconducting
magnets for over 10 tesla could be made using Nb3Sn superconductors, but this would

involve a much more difficult coil winding technique.

Compactness in a cyclotron is usually a more appealing feature in commercial ap-
plications than in academic research. Conventional commercial cyclotrons designed
to produce isotopes, for instance mostly use room temperature magnets in a 1-2 tesla
field range [Cy092]. Uses of high field superconducting magnets for these commercial
cyclotrons are often limited because: the overall system is more complex, and the
coil construction is more difficult. However, commercial company such as the Ox-
ford Instruments has already constructed a commercial superconducting cyclotron,
and maybe more broadly used in the future. Hopefully, experience gained from the
construction and the operation of the 8 T magnet and a future cyclotron conver-
sion project will add significant reliability record to future high field superconducting

cyclotrons.

The uses of superconducting magnets have been expanding for more than a decade,

but rather more slowly than expected because of the complexity in supporting equip-

 

102

ments such as cryogenic systems. High Tc superconductor led to much optimism
about eliminating the need for liquid helium systems. However, to date progress to-
ward large scale several tesla magnet operating at liquid nitrogen temperature has

been minimal.

 

Appendix A

Plan for the ion source emittance
measurement

I Source emittance measurement under rf extrac-
tion

A plan was made to measure the radial emittance (r,p,) of the internal ion source as
a function of rf starting time in the center region of the 8 T magnet. The magnet
will provide magnetic fields with a flat radial profile in a range of 2—8 tesla. The
radial phase space information is important in designing a cyclotron because of the

relationship with the orbit centering and extraction efficiency.

Initial conditions for tracking orbits in a cyclotron system are usually provided
from measuring the ion source phase space. If ions are extracted from the source
by dc electric fields (such as in an ECR source), source emittance can be measured
using the two slit system [Tom72]. A cyclotron with an internal source, on the other
hand, employs rf electric fields to extract ions. Source emittances for such a cyclotron,
however, have not been measured to the author’s knowledge using rf extractions, and
initial conditions for the orbit codes have been inferred from dc extraction measure-
ments. If the voltage at the moment of ion extraction can be indicated in a narrow

range, the measured dc emittance can be used as initial conditions at corresponding

103

 

ll

104

voltages.

A Central region designed for emittance measurement

The design goal of the 8 T magnet’s center region for emittance measurement was to
spread the beam for differing rf starting times so that the emittance could be compared
for different rf ranges selected by slits. As suggested in reference [Kim92c], three slits

can roughly separate three coordinates: 1) rf phase, and 2),3) radial emittance (r,p,).

In a real system, however, one more physical parameter, initial energy, needs to be
considered in designing the central region. The initial ion energy was first assumed to
be fixed at 250 eV, and then different initial energy effects in orbit trajectories were
considered. The initial energy of 250 eV was inferred from dc emittance measurement
with a 30 kV extraction voltage [Tom72] using the phase space conservation law. If
the momentum transfer from electron to ion is the only mechanism in determining
the ion energy, however, the initial energy may be a few eV, which is acquired by
collisions with electrons of a few keV emitted from a cold or hot cathode. Actually,
ion energy of a few to a few tens of eV has been more frequently assumed in designing

the central region of other MSU cyclotrons using an internal source [B1063] [Bai89].

In orbit tracking, ions are generally assumed to start at the source opening, where
the plasma is at ground potential. In reality, however, rf electric fields penetrate into
the plasma, and the plasma meniscus changes as a function of the rf phase [Ben72].
Fixing the initial location and energy for ions starting from widely different rf phases

is thus difficult to be justified.

The central region shown in Figure A.1 provides a two gap acceleration with a
flight path of about 90° between two gaps so that the orbits are spread in an orderly

fashion in the ground region where the slits are located. Several such orbits are shown

‘-

 

105

 

 

 

 

  

. '._\

WW

P—O 5 I T=280° “I Collecfo'v

T =250°

      

 

 

 

Figure A.1: A central region designed to measure the source emittance under the rf
extraction. The orbits of D+ are started with four different rf phases with 250 eV
initial energy in an 8 tesla flat field. The three slits are shown in the ground region,

which are approximately evenly spaced.

106

Table A.1: The initial conditions used for orbit calculations in Figure A.2 & 3: initial
energy (E;), source opening size, and normalized emittance, 6,, (60,67)(mm-mrad).
The a is the maximum incident angle of ions with respect to the normal to the source
opening.

 

I E;(eV) I oz I Opening I 6,, I Fig.A.2 I
250 :l:22° 0.38 mm 0.15 solid
250 i22° 0.76 mm 0.30 dash
250 21:44° 0.76 mm 0.60 dot

| 35 H90°I076 mm]0.30] ]

 

 

 

 

 

 

 

 

 

 

 

 

 

in Figure A.1 for different rf starting times, using deuterons in an 8 tesla flat field.
Part I of the CYCLONE program [Mar81] was modified to handle many particles and

to include slit actions.

The relationship between slit coordinates and phase space in each defined rf time is
needed to construct the source emittance from measuring the ion currents in slit space.
For different emittances and initial conditions described in Table A.1, boundaries of
rectangular source phase space are projected into the slit coordinate space as shown in
Figure A.2 for starting times differing by 10°. The spread caused by larger emittance
appears to include smaller ones in an orderly manner, and the ions having rf starting

times differing by 10° go into fully separated regions in the slit space.

An initial ion energy (E,) of 35 eV was then used to see the orbit distribution
changes in the slit coordinate space from the 250 eV case; 35 eV, 01 = :l:90° was
chosen to keep the radial phase space area same with 250 eV, oz = :l:22° case as
shown in Table A.1, where p, and a are related by pr = Wsina. For two different
initial energies, phase space projections on the slit coordinate space are shown in (a)
of Figure A.3. The orbit distributions with E5=35 eV (dashed line) are shifted to
larger radii at the slit S3 than the distributions with E;=250 eV (solid line), and

more strongly focused at the slit S2. If the initial energy varies as a function of rf

 

 

    

 

 

 

 

 

 

 

 

 

77 l I I L l l
.73“ ‘2‘. -
.69 a :7 , —
E .65T.W " .° __
3 .61- _
8 .57~ -
O
E .534 . ,. -
E ':""'"‘:';"""":-... ”1,.
U .45” ,, .’,r.’--"“...'. l-
a .41-4 7:240“ ”f‘fj‘:,...---;-;.,....-----:__;;.;..;...-.~~--~‘__
-33 T 7:230:77-“ -
.29 l A I l I l r
.43 .48 .53 .58 .63 .68 .73 .78
67 I l l I l L
.65— —
.63“ ,7
”<5 .61- ~
3 .59- -
B .57- l—
0 ,.
.E .55" —
E
8 .53“ __
o .51- -
g .49‘ —
.47 r _ -
.45 ‘ l—
.43 I l l T l l

 

 

 

.43 .48 .53 .58 .63 .68 .73 .78
SI Coordinate (cm)

Figure A.2: Projections of rectangular initial phase spaces displayed in Table A.1 into
the slit coordinate space. The emittances are separated in the slit coordinate space
for rf starting times differing by 10°

 

 

108

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_L L J L l I 1 l .77 4 I l l l I J I

" ’72 (o) ’5‘ .701 f7" -r=270' (0) .
g '66- r 5’ " 8 63" T 4777’ 1":260. ,_
o .60'I ”% ” ' 3 .55., < —‘ T)=250i ..
‘4 ’ ’ o — W’

5:; .54. a . .g .49. ._. ”.2..- -
t. l— .42.. d 7 . _
° .4 . ’ ° ”i=4”

8 8 8 .351 . -
a .42" B .3. .-
93 L i L L i I r 1 i L L L 1 1 L I
A . A b) _-
. (b) __ E .70'- P (

5 ‘66 3 634?:27‘ l

J)
2 ~50‘ .« i 3 .561 V -
g gag-51'5"” x” _ g 49. ‘zfl” _
:6 .54. l/ 6 . " —a—”
8 8 .35 -
.4 « . . _
a 2 g .28
.;S A 0% l l [‘17’21 l
E 66 E .701 4 fl_/.‘ (0) -
3 ° 1 8 .631 <’_ ’ ~ _ I; _
.2 50‘ 3 .56- ,z’ , ~
0 0 ~ ~_':)
”SS4“ -% .4’9"I ” ,’ "
E ‘ 42‘ (fl:-
8 .484 8 ' ’. Iz-v“
O 0 '35] W
.421 " n '-
8 m :3]
E 55.. (d) _ ’§ .70“ (d) -
3 ' .9. .63~ ,/ ‘ 4’ .
Q.) .60“ '3...» ”‘- w "' Q) .4 V I x ’ (— ..
‘5 a’li” I” I ‘6 .56 1 g
..g .54« .: ,-; ~ .g .49- <, ~74 -
5 48" (-"' ’ _ g .42 " flj—v, *-
8 / ° 55‘ 1&7”. "
.42 - - , , - ~.-«_o _
a ' 8 '281 as?”

 

 

 

 

 

 

I I I I I I I I .21 f I I I l I I I
36.40 .45 .50 .55 .60 .65 .70 .75 .80 .85 .40 .45 .50 .55 .60. .65 .70 .75 .80 .85
SI Coordinate (cm) SI Coordinate (cm)

Figure A.3: Projections of rectangular phase spaces for different If starting times into
slit coordinate space with each of the three different parameters varied as described
in Table A.2; a) is the case with no parameters changed, and parameter changes in
b),c),d) are described in Table A.2. Two different initial energies (a solid line: 250
eV, and a dashed line: 35 eV) come from Table A.1 with the same €n(=0.30).

109

Table A.2: Parameter variations for the new orbit distributions in Figure A.3. One
parameter is varied for each case.

 

[ Parameter I Old value I New value I Figure A.3 I

 

 

 

 

 

 

 

 

voltage 50 kV 45 kV (b)
magnetic field 8 tesla 7.5 tesla (c)
rf frequency 61 MHz 55 MHz (d)

 

 

starting time, the different initial energy would be difficult to separate from the orbit

distributions due to the other three parameters (7', r, p,).

There are three parameters one can vary during measurements in a fixed central
region and slit system: extraction voltage, magnetic field, and rf frequency, as dis-
played in Table A.2. With each of the three parameters varied, the orbit distributions
are displayed in Figure A.3 for two different initial energies with the same 6,, (=03
mm-mrad) in Table.A.1. When the rf frequency is moved away from the resonance
frequency by varying the magnetic field or the rf frequency itself (case (c) and (d) in
Figure A.3, respectively), the orbit distributions seem to be more widely spread, espe-
cially at the slit 82, which allows a narrower slice of If starting times. The frequency
swing could be used to enhance resolution in a fixed central region configuration, but
the swing range is limited by the acceptance of the puller electrodes since the puller

is optimized at f0 (61 MHz at 8 tesla).

B Conclusion

Since there is no good experimental information available on ion source phase space
which includes rf electric field effects, it seems to be difficult to fully optimize this
measurement system. A way to tackle this problem would be to measure the source
emittance with the three slit system in the present design, and then better resolution

could be achieved by further optimizing the slit system after the experiments.

110

A.2 RF resonator for ion extraction

As part of the ion source emittance measurement system, an rf resonator was built
and tested. The resonator was designed to be actually used as an ion extractor with
minor modifications after finishing the test. A plan View which includes the resonator,

transmission line, vacuum feedthru, etc. is shown in Figure A.4.

For source emittance experiments in high magnetic fields, a high voltage on the
extractor is preferred in order to increase the initial orbit radius, which allows more
space for measurement devices. A peak voltage of 50 kV seemed to be acceptable with
the initial orbit radius of approximately 0.5 cm for D+ at 8 tesla (higher voltage entails
larger power loss and larger distance to the ground to sustain the voltage). Peak
electric fields are greater than 150 kV / cm under the magnetic fields perpendicular to
the electric fields. A pulsed rf technique [B1092] could be utilized to test the electric

field limits.

To use for the ion source emittance measurement, a simple coil-type resonator
was chosen, rather than a more complicated system such as dees with dee stems.
The ac circuit analysis program, RESON, developed in this lab [Vin91] was used to
determine the coil dimensions with a resonance frequency (f0) near 60 MHz. For the
14 turn coil shown in the lower part of Figure A.5, inductance and resistance were
roughly calculated to be 0.7 ,uH, 0.29 fl, and capacitance of each turn was assumed
to be 1 pF (as a check capacitance per unit length as calculated assuming two infinite

parallel wires giving 2 pF / turn [P0290]).

With these inputs, RESON computed the f0 and power loss of the distributed
circuit displayed in the upper part of Figure A.5, and the results are tabulated in
Table A.3. The last row of Table A.3 shows the measured f0 and Q value of the actual

resonator, comparing with RESON calculations. The test resonator has only 8 turns

111

One of three

/———s|it system

  
       

Adjustable shorted end

<

5.080m

  
   
   
   

Teflon
or Mocor

A

Alumina insulator

 

 

 

Coil resonator, cooper tube Teflon
(08cm O..,D 08mm w> (if—49m)
rf shielding Q"\@
SECTION. A-A

 

Figure A.4: A plan view for the ion source emittance measurement showing the
resonator, transmission line, vacuum feedthru, one of three slits, etc. in the median
plane of the 8 T magnet.

112

Distributed Circuit

R1 L4 R2 L2 Rn [_n
lltW—WW— - - W

 

 

C9 C1 C2 8C3 C0

 

 

 

 

 

n=0.7 turn/cm, 14 turns r=1.6 cm

’\l\l\l\l\l\l\l\l\l\l\l\l\l\r

r=3.l7 mm

L=0.7 microH, Rs=0.29 Ohm at 60 MHZ
(>4 pF for each turn

Figure A.5: The configuration of the coil resonator in the lower part of the figure,
and an equivalent circuit for RESON calculations. The calculation results are given

in Table A.3.

 

113

Table A.3: Ac analysis of the circuit shown in Figure A.5 with RESON. A measure-
ment of the actual test resonator with elongated 8 turns to simulate the 14 turn coil
resonator in Figure A.5., is displayed in the last row.

 

 

 

 

I Circuit I Capacitance I fo(MHz) I Power loss (kW) I Q I
Distributed Cn=1 pF, n=1~14 67.9 4.3 1020
Measurement 63.6 1200

 

 

 

 

 

 

 

so as to be accommodated inside the 8 T magnet (radius: 21 cm, gap height=8.1
cm), but the turns are elongated to match the total conductor (copper tube) length

of the 14 turn coil in Figure A.5 as explained later in this section.

Along with computations, test resonators with different coil shapes were made,
and the f0 and Q value were measured with a vector impedance meter (HP 4815A).
Since the impedance meter range was limited to 100 k9, Q value and resistance (R) at
f0 were obtained with Eq.A.1 [P0290] written below, using the measured impedances

(Z) and their phases (qS) at f near f0.

t
R = z./——1+tan2¢, Q = 1’ ”:3. (AI)

where 7 is f/fo.

 

Three issues were mainly considered in designing the resonator: 1) mechanical

rigidity, 2) resonance frequency (~60 MHz, at 8 tesla), and 3) coupling.

The rigidity of the coil resonator as a function of the tube diameter was investi-
gated. The resonator was supported only at the grounded end by being soldered onto
the rf shielding box wall (soldering is also for a good electrical connection). With
this scheme, a tube as large as 1.27 cm O.D. could not be rigidly supported, and
larger tubes are limited by the space available inside the 8 T magnet; supporting the
resonator only at one end could not prevent mechanical vibrations of the free end.

Since the resonator has to stay horizontal in the present plan, a supporting insulator

 

114

was added, although insulator contact to the high voltage region of a resonator in a
vacuum is usually avoided because of the probable voltage breakdown through the
insulator. Two Teflon rods (2.54 cm O.D.) were inserted inside the coil, and screwed
to the wall as shown in Figure A.4; Teflon will be replaced by Macor to utilize the
higher stiffness. In this arrangement, electric fields in the insulators are lower than

when they support the coil from the outside.

To study the dimensional effects of the coil resonator on the resonance frequency,
different tube sizes and lengths were tested and the results are displayed in Table
A.4. In the test, the coil was installed into a copper box which is similar to the rf
shielding box in Figure A.4. It was observed that a quarter wavelength of the fa
is about 5—10% shorter than the actual tube length, which occurs due to capacitive
loading. Because of the space problem again, the maximum coil turn number was
limited to approximately eight with use of a 0.8 cm O.D. tube. The turns had to be

elongated to acquire the length needed to maintain the f0.

The resonator assembly in the final design was installed into a rectangular vacuum
box (61x30x38 cm). The vacuum was kept better than 1X10‘5. The resonance fre-
quency and Q value were then measured using a 100 W solid state rf amplifier (EN I
3100L), and later using the K500 rf system. (The K500’s rf system was temporar-
ily used for the test. This system however could not be used for future emittance
experiments as the rf system will be needed for the coupling project between K500
and K1200 cyclotrons.) The block circuit diagram is displayed in Figure A.6. The f0
was around 65 MHz in the initial test, which is close to the upper limit of the K500
rf system; the frequency limit of the rf system with a 3/4). mode in the If cavity
is about 65 MHz unless some modifications are made to the capacitor or inductor
[Ma187]. The f0 was reduced to 63 MHz by increasing capacitance at the high voltage

end, in fact simulating the ion source.

 

115

Resonator
Vacuum

T—line Feeatnru

E : Z=61fl 2:? II”
V

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Directional
COUDIer l

 

 

 

 

Scope)

 

 

W

 

 

 

Signal Power

 

 

 

 

 

Generator

 

 

 

 

Figure A.6: A circuit diagram for testing the resonator. The power amplifier was an
100 W solid state model in the initial test, and later the K500 rf system was used.

 

116

Table A.4: Resonance frequency depending on the coil dimensions.

 

ITube O.D. (cm) I Tube length(cm) I fo(MHz) I A /4(cm) I

 

 

 

 

0.64 170 46.8 160
0.78 223 35.9 209
1.3 134 60.9 123

 

 

 

 

 

 

An inductive coupling between the resonator and the transmission line was consid-
ered, which could be realized by loops often employed for cavity excitations. However,
the mechanical mechanism needed to adjust the loop location was too complicated
to be implemented for the test resonator. A direct contact coupling was then chosen.
Since the characteristic impedance of the transmission line (Z0) was 61 Q (coaxial
tubes with the inner tube of 0.95 cm OD, and the outer tube of 2.61 cm O.D.),
it was necessary to find the same impedance point on the resonator at f0. The res-
onator impedance at the coupling point (ZL) was calculated by measuring Z,” at the
end of the transmission line with the resonator coupled, using the transmission line

impedance equation below (see p.79 of [Poz90]),

Zin — jZotanfll
Z0 — jthanfll’

 

ZL = Z0 (A.2)

where 5:271, and l is the length of the transmission line. By adjusting the location

of the shorted end of the resonator (see Figure A.4), the coupling impedance was

matched to 61 Q (i1 0) at 63 MHZ.

Some impedance mismatches on the transmission line occur in the vacuum feedthru
and in the cooling water outlet sections. This effect was however neglected since that
section length was short (25 cm) compared to a quarter wavelength of the fa (120
cm). For fine tuning, an adjustable matching element, a variable capacitor, is seri-
ally connected between the transmission line and the 50 Q coaxial line from the rf

amplifier as shown in Figure A.6.

 

117

The resonator was tested first with low power. With a 1.6 W forward power,
1 mW was reflected, and the reflected wave was spectrum analyzed. The second
harmonic component was the largest when the impedance was well matched. The
resonator was tested up to 80 W at which the peak voltage is estimated to be 6 kV.
(The K500 rf amplifier was used a few times with low power, but the power higher
than 100 W was not successfully tested.) Higher power tests would continue if the

project to measure the ion source emittance is resumed (~5 kW for 50 kV).

 

Appendix B

Conversion of the 8 T magnet to a
cyclotron

A conversion of the 8 T magnet to a cyclotron was planned after the magnet was
successfully tested, and a design study was performed. The 8 T magnet was assumed

to become a single ion and fixed energy cyclotron.

The deuteron (D‘l’) which is often employed to produce neutrons for cancer ther-
apy by (d,Be) reaction [B1089], was used as a projectile in the present calculations.
However, computations revealed difficulties in achieving good axial focusing when
such a light ion is accelerated in an 8 tesla average field. The central magnetic field
was reduced to 7.2 tesla to enhance the axial focusing and to increase the initial orbit

radius.

The central region of the 8 T magnet with a PIG (Penning Ion Gauges) source was
designed to accelerate D+ at h=3. Because of the desire to utilize the full magnetic
field produced from the 8 T magnet and to ease the cyclotron design and construction,

He+ has lately been considered as a design ion.

118

 

119

51.9 cm

 

0.813
0.81

 

 

 

S.F.=1.0

 

 

 

 

 

 

 

 

 

 

0198
r ,3
S.F.=O.76 63.8 cm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

75 ' '
E74 - _
E
.973- —
LL.
.2
‘53 72' : Calculated actual field ”
c:
g 71_ — —' t: lsochronous field _
70 u l I l
0 4 8 12 16 20
Radius (cm)

Figure B.1: The configuration of the 8 T magnet as a cyclotron to accelerate deuterons
at a central field of 7.29 T. Stacking factors of each iron region used for POISSON
calculations are shown in the figure. The computed magnetic field is compared to a
prefect isochronous field.

120

B .1 Magnetic fields

The 8 T magnet configuration with Bp= 1.2 T-m for accelerating D+ is shown in
Figure B.1. The sector structure in the pole tips is formed by contouring hills and
valleys as in other isochronous cyclotrons. The lower part of Figure B.1 displays
computed and perfect isochronous magnetic fields; a finer field profiling is usually
accompanied by full field mapping. As the yoke already has three rf holes, three-
sector structure was assumed without considering different sector number effects on
focusing characteristics (see [Blo74]). The magnetic fields were calculated using the
same method that has been used for designing other MSU cyclotrons; the program
POISSON calculates the average field, and the current sheet program calculates the

azimuthal field profile assuming saturated pole tips [Gor80].

Figure B.2 shows the contour map of the total field in the median plane. The spiral
structure of hills and valleys is clearly visible. Focusing frequencies of the isochronous
field, 14,112, were calculated with the E0 code [Gor84], and are plotted in the lower

part of Figure B.2 as a function of energy.

B .2 Central Region

The central region of the 8 T magnet was designed to accelerate D+ in the third
harmonic of the cyclotron frequency (turf = 3wcy, fey: 55.56 MHz at 7.29 tesla). For
the orbit code, electric fields in the central region were calculated with the program
RELAX3D [K03], and the isochronous magnetic field obtained in the previous section
was used. The ion source chimney has a diameter of 3.2 mm, which is only a half
as large as that of the Harper hospital cyclotron. (the Harper cyclotron design sig—
nificantly influenced this design study because of the similarities in operation mode;

h=3, 30 kV at 4.5 tesla). The reduction of the source chimney size was necessary to

 

 

 

 

 

 

KIN - 0.00034-00 “I? I- 0.2003601 m - 0.0008002

 

L l

 

1.04

1.024

L.

S.
1.00“

 

 

 

 

 

0

5 0 18 2

E (iMeV)

0

Figure B.2: (Top) Contour map of the field in the median plane. The maximum field
at the hill is about 8.1 tesla. (Bottom) The focusing frequencies of the isochronized

field.

122

clear the orbits and to accommodate the acceleration voltage of 50 kV at 7.2 tesla

without increasing the maximum electric field beyond 150 kV / cm.

The orbits in the central region were calculated using the CYCLONE program.
The starting time (T0) of the roughly centered ray is 220° (the peak rf voltage is
at 270°, and the initial energy is assumed to be 100 eV). The orbits starting at 7'0
together with Toi10° are shown in Figure B8. The energy gain in the first few turns

is efficient so that the ions pass through the central region as quickly as possible.

III Conclusion

Design studies of the 8 T magnet conversion to a cyclotron are presented. At a central
field of 7.29 tesla, axial focusing for D+ is provided with large spirals in the sector
structure, and the central region is designed to operate at h=3. Since the 8 T magnet
was not designed to extract beam out of the magnet, extraction mechanisms were
not studied. When the design ion is fully decided, further field shaping and orbit

calculations will follow.

123

US LOANC: JKIM.8T CENT C3 18TLFL.DAT'1

..‘ —~

 

~A
.......
‘I
a

.........
............
......
.-

'-
o
u
‘o
'I
o

I
a
n
u
o
e
I
o
a
'o
'-

o
a
I
.....
O.

.....

Figure B.3: Central region of the 8 T magnet designed to accelerate D+ at h=3 in
the central magnetic field of 7.29 tesla. The starting rf phase is 220° along with 210°
and 230°, represented by solid, dashed and dotted lines, respectively

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