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Characteristics of the Superconducting
Magnets for the 8800 Spectrometer

By

Bo Zhang
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

1997

ABSTRACT

CHARACTERISTICS OF THE SUPERCONDUCTING
MAGNETS FOR THE S800 SPECTROMETER

BY

Bo Zhang

The National Superconducting Cyclotron Laboratory’s K1200 cyclotron is capable
of providing high quality heavy-ion beams with rigidities of 1.6 GeV/c. However, the
highest velocity beams are 200 MeV/nucleon, or 1.28 GeV/c. In order to study
the properties of single particle states populated in reactions at these energies, a
magnetic spectrometer with an energy resolution E/AE of 104 is necessary. To achieve
the physics goals, a large acceptance, high resolution spectrometer (S800) has been
designed and constructed. The spectrometer system chosen for the 5800 is a QQDD
configuration. A strongly focussing y—quad immediately after the target allows a large
solid angle and x-focussing quad before the dipoles makes efficient use of the dipoles.

This thesis describes the magnets that are the heart of the 3800.

In the first part of this thesis the beam optics calculations of the 3800 spectrometer
are presented. Part two is dedicated to the design and construction of two dipoles
for the S800 spectrometer. The third part addresses the design and construction
of high gradient, large aperture quadrupoles for the 8800. The S800 is a software
corrected spectrometer; that is, the energy loss and scattering angle are inferred from
measurements of the particle’s position and angle at the focal plane. In order for the

calculations to work, precise and accurate magnetic field maps of the 8800 magnets are

important for achieving high resolution using ray reconstruction. The last part of this
thesis also includes the field mapping and harmonic analysis of the S800 quadrupole
doublet and S800 beamline quadrupole triplets, essential to the ray reconstruction

process.

To my wife Wei and my daughter Amy.

iv

ACKNOWLEDGEMENTS

I wish to thank the staff, students and faculty of the National Superconducting
Cyclotron Laboratory for their support of my education and the completion of this
dissertation. I recognize that without their contributions this thesis would be all

blank pages.

First, I owe my deepest gratitude to my advisor, Prof. Brad Sherrill for his guid-
ance, supervision and encouragement during my graduate career. His patience, sense
of humor and understanding have been greatly appreciated and are acknowledged.
Second, I would like to specially thank Dr. Al Zeller for his continuous advice and
comments on my research work. His guidance and deep knowledge of this field have
made the completion of this work possible. It is also a pleasure to acknowledge my
former advisor, Prof. Jerry Nolen for his guidance in my early graduate career and

freedom he gave me to work on accelerator physics to pursue my academic interests.

I would like to thank Prof. Maris Abolins, Prof. Thomas Kaplan and Prof.
Gary Westfall, for kindly serving on my advisory committee and for many helpful
comments and suggestions about my dissertation. My thanks go to Prof. Martin
Berz, Jon DeKamp, Dr. Helmut Laumer, Dr. Felix Marti, Prof. David Morrissey,
Dr. John Vincent and Dr. Xiaoyu Wu for their help and various discussions. Special
thanks goes to Steve Bricker, Richard Burleigh, Jac Caggiano, Barry Davids, Phil
Johnson, Len Morris Dr. Dave Sanderson, Rick Swanson, Jim Wagner and Roger
Zink for the design and construction of the S800 dipoles, quadrupoles and the quad

mapper.

I am fortunate to count among my friends many fellow graduate students and staff
at Michigan State University. I am indebted to the friendship of Michael F iasky, Dr.

Nengjin Ju, Dr. Jong-won Kim, Bin Lian, Bing Ren, Jeff Schubert, Jun Sheng, Dr.

V

Weishi Wan, Dr. Hong Wang, Jing Wang, Dr. Qing Yang. From them with them, I

learned a lot.

I want to thank my parents Yinglian Sun, Guangai Zhang and my brother Hong
Zhang for helping me reach this point, my grandmother Dingjing Liu for special role

she has played in my life.

Finally, I want to thank the person who taught me the most important lessons of

my graduate years, and gave me the love and affection to make it through: my wife

Wei Liu.

I am also very grateful to Michigan State University and National Science Foun-

dation for the financial support during my graduate study.

vi

Contents

LIST OF TABLES ix
LIST OF FIGURES xi
1 Introduction 1
2 Optical Properties of the NSCL Superconducting Spectrometer 6

3 Design and Construction of Large Superconducting Spectrometer
Dipoles 17

3.1 Why use superconducting coils in conventional spectrometer magnets 17

3.2 Design parameters of S800 dipoles .................... 19
3.3 S800 Dipole Construction ........................ 31
3.4 Commissioning of the S800 Dipole Magnets .............. 35
4 Design and Construction of High Gradient, Large Aperture Quadrupoles
for the S800 41
4.1 Magnetostatics of quadrupoles ...................... 41
4.2 Quadrupole types ............................. 44
4.2.1 Cos(20) quads ........................... 45
4.2.2 Panofsky quads .......................... 45
4.2.3 Iron dominated quads ...................... 46
4.3 Physical parameters of Q1, Q2 and a sextupole as related to the 3800 47
4.4 Magnetostatic calculations ........................ 48
4.4.1 Magnetic field calculation of Q1 ................. 48
4.4.2 Magnetic field calculation of Q2 and the sextupole ...... 58
4.5 Quench simulations ............................ 71
4.6 Heat load calculations .......................... 75
4.6.1 Support link heat loads ...................... 75
4.6.2 Radiation heat loads ....................... 77

4.7

4.6.3 Vent pipe heat loads .......................
4.6.4 Feed and return line heat loads .................
4.6.5 Total heat loads for the Q1/Q2 doublet .............
Construction of Q1, Q2 and the sextupole ...............
4.7.1 Coil winding ............................
4.7.2 The Q1, and Q2 coils testing ...................
4.7.3 The Q1, Q2 and sextupole magnet assembly ..........

5 Magnetic Field Mapping and Analysis

5.1
5.2
5.3
5.4
5.5
5.6

Introduction and need for quality maps .................
Quadrupole mapper ............................
S800 beamline quadrupole triplet mapping ...............
Magnetic field analysis of the S800 beamline quadrupoles .......
Q1, Q2 and sextupole magnet field mapping ..............
Magnetic field analysis of Q1, Q2 and the sextupole ..........

6 Conclusion

LIST OF REFERENCES

viii

78
78
79
80
80
81
84

86
86
87
90
91
94
96

111

115

List of Tables

2.1
2.2

2.3

3.1

4.1
4.2
4.3

4.4
4.5
4.6

4.7
4.8
4.9
4.10

5.1

5.2
5.3

5.4
5.5

5.6

Parameters of the S800 superconducting spectrometer. ........

Sensitivity analysis of misalignment and multipole errors. The energy
resolution is parts in 10,000. .......................

Sensitivity analysis of misalignment and multipole errors. The energy
resolution is parts in 10,000. .......................

S800 dipole conductor and coil specifications ...............

The physical parameters of Q1 and Q2 magnets .............
Longitudinal granularity for Q1 used in the TOSCA calculations.

Q1 multipole analysis results for half of the magnet at a radius of 8.8
cm. ....................................

The calculated parameters of the Q1 magnet. .............
Longitudinal granularity for Q2 used in the TOSCA calculations.

Q2 multipole analysis results for half of the magnet at a radius of 8.8
cm ......................................

The calculated parameters of the Q2 magnet. .............
The calculated parameters of the sextupole magnet ...........
Calculation heat loads for the Q1/ Q2 doublet ..............
Inductances of the Q1 and Q2 magnets ..................

The fourth order polynomial fitting coefficients for the field differences
between NMR and Gaussmeter measurements ..............

Mapping Time and File Size for S800 Beamline Quadrupole Triplet. .

The Hall generator voltages and gradients of a S800 beamline quadrupole

as function of current. ..........................

Mapping Time and File Size for the Q1/Q2 Doublet. .........

The measurements of Q1 shunt current, cryogenic Hall generator volt-
age and field gradient. ..........................

The measurements of Q2 shunt current, cryogenic Hall generator volt-
age and field gradient. ..........................

ix

15

16

31

48
53

54
54
60

65
67
67
79
82

89
91

93
96

97

5.7 The measurements of the sextupole shunt current, cryogenic Hall gen-
erator voltages and field gradient. .................... 99

5.8 Q1 and Q2 multipole analysis results at a radius of 8.8 cm ....... 104

5.9 Harmonic components of the field at the center and end of Q1 at a
radius of 8.8 cm for several currents. The numbers are defined by

B../B2 in % ................................. 109

5.10 Harmonic components of the field at the center and end of Q2 at a
radius of 8.8 cm for several currents. The numbers are defined by

B,,/B2 in % ................................. 109

List of Figures

1.1

1.2

2.1
2.2

2.3

3.1
3.2
3.3

3.4

3.5

3.6

3.7

3.8

3.9

3.10

3.11

Floor plan of the NSCL showing the beam distribution system to allow
experiments with the K1200 and K500 cyclotrons ............ 3
Figure of merit versus year of construction for forty years of spectrom-
eter development. ............................ 5
The view of the S800 beam analysis system and the spectrometer. . . 9
The x- and y-envelopes calculated by TRANSPORT for the S800 beam-
line and spectrometer. .......................... 12
Side view of S800 showing position of magnetic elements ........ 13
S800 H-frame dipole POISSON calculation ................ 22
S800 dipole showing dimensions in cm. ................. 24
Deviations of the field from the central field at low field as a function
of charge in trim coil currents ....................... 25
Deviations of the gradients from the central field at low field as a
function of charge in trim coil currents. ................ 26
Deviations of the fields at 14.8 kG for several cases showing the effects
of trim coils and filters ........................... 27
Deviations of the gradients at 14.8 kG for several cases showing the
effects of trim coils and filters ....................... 28
Deviations of the fields over the dynamic range needed for spectrometer
operation. ................................. 29
Deviations of the gradients over the dynamic range needed for spec-
trometer operation, scaled to the 1.5 T field ............... 30
Central magnetic field as measured by a Hall Gaussmeter as function
of current .................................. 38
Measured and POISSON calculation deviations of the field gradient

with trim coil on and off. The data were measured at the center of D1
as a function of radius. .......................... 39

The heat load of the first dipole magnet as a function of insulation
vacuum pressure. ............................. 40

xi

4.1

4.2
4.3
4.4
4.5

4.6

4.7
4.8

4.9
4.10
4.11

4.12

4.13

4.14
4.15

4.16

4.17

4.18
4.19
4.20
4.21
4.22

5.1

Octant of the NSCL beamline quadrupole with magnetic field lines

using the POISSON code. ........................ 47
Octant of Q1 with magnetic field lines calculated by POISSON. . . . 50
Q1 coils and iron geometry used for TOSCA calculations ........ 51

Details of the Q1 mesh used in the r0 plane for the TOSCA calculation. 52

Multipole components of the Q1 radial field for the quadrupole (n=2)
term and the first three allowed terms (n=6,10 and 14) are plotted as
functions of z, the distance along the beamline axis from the center of

the Q1 magnet at r = 8.8 cm. ...................... 55
Integrated multipole component of the Q1 radial field I; bmdz for n=2,

6, 10 and 14 at r = 8.8 cm ......................... 56
TOSCA calculations of the Q1 gradient as a function of current. . . . 57

The x- and y-components of force per unit length on the straight section
of the Q1 coil are calculated with the program TOSCA at I = 86A. 59

Octant of Q2 and the sextupole with field lines calculated by POISSON. 61
Computer simulation for Q2 and the sextupole magnets using TOSCA. 62

Details of Q2 and the sextupole mesh used in the r0 plane for the
TOSCA calculation. ........................... 63

Multipole components of the Q2 radial field for the quadrupole (n=2)
term and the first three allowed terms (n=6,10 and 14) are plotted as
functions of z, the distance along the beamline axis from the center of

Q2 magnet at r = 8.8 cm. ........................ 65
Integrated multipole component of the Q2 radial field [6’ bmdz for n=2,
6, 10, and 14 at r = 8.8 cm. ....................... 66
TOSCA calculation for Q2 gradient as a function of current. ..... 68
The x- and y-components of force per unit length on the straight section

of the Q2 coil are calculated with the program TOSCA at IQ2 = 90A
and Lamp“. = 0A. ............................ 69

The radial and azimuthal components of force per unit length on the

straight section of the sextupole coils are calculated with the program

TOSCA at luxtupoze = 3A and qu = 90A. ............... 70
The comparison of the internal voltages in Q1, NSCL standard beam-

line quads and S800 beamline quads after quenching. ......... 72
Decay of currents in Q2 and the sextupole after quenching ....... 73
Internal voltages in Q2 and the sextupole after quenching. ...... 74
View of a longitudinal section of Q1, Q2 and sextupole. ....... 76
Q1 and Q2 coils assembly. ........................ 83
Sextupole coils assembly .......................... 85

The magnetic field difference between the NMR and gaussmeter mea-
surements for one channel. The solid lines through the data are fourth
order polynomial fits ............................ 88

xii

5.2

5.3
5.4

5.5

5.6
5.7

5.8

5.9

5.10

5.11

5.12

5.13

5.14

5.15

5.16

5.17

5.18

5.19

The radial component of the magnetic field for the triplet when the
currents for the three quadrupoles are 5, 15 and 10 A respectively.

The gradient produced in a quadrupole as a function of current. . . .

The effective length of the S800 beamline quadrupole as a function of
current. ..................................

The radial component of magnetic field at the center at a radius of
7.43 cm. .................................

Fourier analysis of the radial component of the field in Figure 5.5. . .

The radial component of the magnetic field for the Q1 / Q2 doublet
when the currents for Q1 and Q2 are 84 and 70 A respectively.

The radial component of the magnetic field for the sextupole when the
sextupole current is 3 A, Q1 and Q2 are off. ..............

The Q1 gradient differences between the measurements and TOSCA
calculations versus current .........................

The Q2 gradient differences between the measurements and TOSCA
calculations versus current .........................

The Q1 effective length differences between the field measurements and
TOSCA calculations versus gradient. ..................

The Q2 effective length differences between the field measurements and
TOSCA calculations versus gradient. ..................

Fourier analysis of the radial component of the field in Q1 magnet at
I = 45 A. .................................

Fourier analysis of the radial component of the field at the center and
end of Q2 at I = 45 A. ..........................

Multipole components of the Q1 radial field for the quadrupole (n=2)
term and the first three allowed terms (n=6,10 and 14) are plotted as
functions of z, the distance along the beamline axis at r = 8.8 cm and

I=80A. .................................

Integrated multipole component of the Q1 radial field I; bmdz for n=2,
6, 10 and 14 at r = 8.8 cm and I: 80 A. ................

Multipole components of the Q2 radial field for the quadrupole (n=2)
term and the first three allowed terms (n=6,10 and 14) are plotted as
functions of z, the distance along the beamline axis at r = 8.8 cm and

I=90A. .................................

Integrated multipole component of the Q2 radial field [0’ bmdz for n=2,
6,10and14atr=8.8cmandl=90A .................

The Q2 and sextupole magnet multipole components at center of the
magnets at 102 = 70A and Iuflupozc = 3A. ...............

xiii

92
92

94

95
95

97

98

100

100

101

101

104

105

106

107

108

Chapter 1

Introduction

Magnetic spectrometers have played an important role in nuclear physics research
and have many advantages over other types of particle detectors. First of all, they
have the ability to separate products of interest from unwanted products, in some
cases to the level of one part in 1012 [Mu88]. This allows the detection of products
with low production cross sections relative to more probable reactions. Secondly, they
also have the ability to make very precise determinations of momentum and energy.
For example, with the Split-pole spectrometer and a 35 MeV proton beam the MSU
K50 cyclotron, energy resolution as good as 1.5 keV was achieved in inelastic proton
scattering [N075]. This is similar to Ge detectors used in 7-ray studies. Spectrometers
allow coincidence experiments to be performed with a very selective reaction filter by
measuring a forward-going ion in the spectrometer and the coincident particles or

gamma rays in detector arrays surrounding the target.

In heavy ion research, such as takes place at the NSCL, the arguments for the
use of magnetic spectrometers are equally valid. A measure of their usefulness is the
large demand for the magnetic spectrometers at the two heavy ion laboratories in
the intermediate energy range of 10 to 100 MeV/nucleon, the NSCL and GANIL.
At the N SCL, the S320 spectrometer even with its limited solid angle and resolution

had consistently received 30 percent of the beam time and was used in 40 percent

1

2

of the approved experiments from 1983 to 1990 using the K500 cyclotron. Since
that time the A1200 fragment separator [Sh92] has been used as the primary NSCL
spectrometer and takes up to 80 % of the beam time. For the first few PACs at the
NSCL where 8800 experiments were considered 30 % of the beam time has gone to
the 8800. At GANIL, the SPEG spectrometer has consistently used more than 20

percent of the accelerator time since its completion in 1986 [Mu89].

The NSCL facility has unique capabilities for heavy ion studies. With the K1200
and K500 cyclotrons, experiments with beams from proton to Uranium and energies
of 2 to 200 MeV / u are possible. In addition, the A1200 beam analysis device for the
K1200 cyclotron is able to measure and define precisely the beam energy, and produce
separated radioactive beams which can be transported to any experimental device.

A layout of the facility, showing the position for the 3800 spectrometer is given in

Fig. 1.1.

With the energies and beams available at the N SCL, there is now a wide range
of very interesting experiments with the S800 which could be performed. Although
it is impossible to conceive of all the potential physics which will be carried out with
the spectrometer, the research will include four significant areas: Giant Resonances,
Charge Exchange, Direct Reaction Studies and Nuclear structure. A much more
detailed description of these areas is covered in A Proposal for Construction of the
S800 Spectrometer along with a discussion of why a magnetic spectrometer is essential

for these experiments [N089].

The 8800 spectrometer will be able to bend and analyze reaction products from
the K1200 and the K500 cyclotrons up to a K=800 dipole magnet field bending limit
(E/A(MeV) = K x (q/A)2). Hence, the S800 spectrometer will be able to bend onto
its focal plane any heavy ion extracted from the K1200 and stripped to its equilibrium

charge state by a target. For comparison of the S800 to other spectrometers, a figure of

.7.‘ ‘71-’27” ' 'm¢ _.. rm
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Figure 1.1: Floor plan of the NSCL showing the beam distribution system to allow
experiments with the K1200 and K500 cyclotrons.

merit, which will be discussed in more detail in Chapter 2, versus year of construction
for various magnetic spectrometers is shown in Fig. 1.2. The S800 spectrometer is
among the best in terms of its combination of large solid angle, large energy range,
and good energy resolution. This is possible because of the use of superconducting

technology and ray reconstruction techniques.

This thesis is organized as follows: The S800 spectrometer properties are discussed
in Chapter 2. The design and construction of the 8800 dipole are presented in Chapter
3. A detailed design and construction of high gradient, large aperture quadrupoles
for S800 spectrometer are given in Chapter 4. Chapter 5 shows the magnetic field
mapping and analysis for the S800 quadrupoles. Finally, a summary concludes the

thesis.

 

 

 

 

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1940 1950 1960 1970 1980 1990 2000
Year

Figure 1.2: Figure of merit versus year of construction for forty years of spectrometer
development.

Chapter 2

Optical Properties of the NSCL
Superconducting Spectrometer

To achieve the physics goals discussed in Chapter 1 in the most efficient manner, a
large acceptance, high resolution spectrometer has been designed and constructed.
As illustrated in Fig. 1.2, the S800 spectrometer has a large “figure of merit”, that
we have defined as the product of resolution, solid angle, energy range and magnetic
rigidity. It achieves these values, in part, because it is one of the first superconducting
high resolution magnetic spectrometers for nuclear physics. The spectrometer has a
design energy resolution E / AE of 10‘ for the entire 20 msr solid angle. This has been
demonstrated by raytracing and by a simulation of software corrections through the

use of the optimization computer code MOTER [Th79].

Since the appearance of the first magnetic spectrometers in 1948 continuous im-
provements in resolution, solid angle and range have been made. With the large
increase in accelerator energies, the bend radius of spectrometers has been increased
from 35 cm [Bu48] to 8.4 m [Ha89], since the practical limit in magnetic field for an
iron dominated dipole magnet is in the range of 1.5 to 1.8 T. Calculating an appro-
priate figure of merit for spectrometers involves solid angle, resolution, energy range,

and the particle rigidity, Bp. Additionally, normalization to a 1 mm object size allows

comparison between spectrometers matched to beams of various emittances, allow-
ing a comparison that is independent of the accelerator to which the spectrometer is
attached. Fig. 1.2 shows the historical development of spectrometers during the last

forty five years.

The unusual physical layout chosen for this spectrometer conveniently satisfies
several design goals, constraints and guidelines. Firstly, the combination of verti-
cal beamline dispersion, horizontal scattering, and vertical spectrometer dispersion
(VHV) decouples the momentum and scattering angle measurements. This is most
relevant for beam phase space matching to the spectrometer. For example, in the dis-
persive direction it is desirable to have a small incoherent spot size on target, which
implies a relatively large divergence, whereas in the seattering direction small beam

divergence, and consequently a relatively large spot size, is dictated.

The spectrometer mode was chosen to have the normal point-to-point imaging
in the dispersive direction, but parallel-to-point in the axial direction to facilitate
accurate scattering angle determinations. This is the system used at the LAMPF
HRS in Los Alamos [Mo]. Thus, in first order, the focal plane is two-dimensional
with x determining the particle’s momentum and y its scattering angle, where the
coordinate x is in the plane of bend of the central trajectory and the coordinate y

is perpendicular to the plane of bend of the central trajectory (using the standard

TRANSPORT notation).

The choice of first order resolving power, or (dispersion/ magnification) D/M, for
the system is directly related to the resolution specification. The quantity D/Mzo,
where so is the incoherent spot size, determines the first order resolution. It is
common to assume :co = 1 mm at the target so that (D/M), = 20 cm/% implies a
resolution of 20,000. However, in our case we chose to use a high resolving power

analysis line (D/M= 20 cm/%) to demagnify the beam by 0.6. Thus, a 1 mm spot at

the start of the analysis system is 0.6 mm at the target of the spectrometer and the
spectrometer need only a D /M of 12 cm/%. In the case of the S800 D/M = 12 cm/%.
This choice yields nearly a factor of two larger solid angle for a given dipole width
in the spectrometer while still permitting an overall momentum resolution of 20,000
at the spectrometer focal plane [R0]. The analysis line also allows for dispersion
matching. The dispersion matching condition specifies that the dispersion of the
beam at target must equal the D /M of the spectrometer or D = 12 cm/% on target
in this case. This implies M = 0.6 for the beam spot at the target since D/M = 20
cm/% for the beam, yielding an incoherent spot size of 0.6 mm at the target of the

spectrometer.

The previous considerations determined the selection of (D /M ) 3 , D3, and (D / M ) 3,
but they do not determine the spectrometer focal plane dispersion D5. This term
and the associated magnification M5 determine the spatial line width of the beam at
the focal plane and the length of the focal plane for a given spectrometer momentum
range 65. For the present spectrometer Ds = 12 cm/% and M5 = 0.74 were cho-
sen, giving a line width of 0.5 mm for momentum resolution of 20,000 and a detector
length of 60 cm for a momentum range of 5%. It is assumed that a detector resolution
of 0.2 mm F WHM for a 60 cm long detector is attainable, so that detector resolution

should not limit the system resolution.

The S800 beamline and spectrometer is shown in Fig. 2.1. The design goals and

physical parameters are summarized in Table 2.1.

The S800 beamline can operate at beam momenta of up to 1.6 GeV/c even though
stripping of the heavy ions at the target limits the maximum rigidity requirement of
the spectrometer to 1.2 GeV/c. The analysis system must be for the dispersion-
matched (energy-loss) spectrometer. The system must have a momentum resolving

power of at least 20,000 with a 1 mm object slit. It must also accept the K1200’s

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

mm
m
tram: mm
/—m

r am:
ma
rm m:

szmrar fl
/ I l [I I
mum mm

Figure 2.1: The view of the S800 beam analysis system and the spectrometer.

10

Table 2.1: Parameters of the S800 superconducting spectrometer.

 

 

Energy Resolution:

Energy range:

Solid angle:
Resolving power:
Radial dispersion:
Radial magnification:
Axial dispersion:
Angular resolution:

Focal plane size:
Focal plane tilt:

Magnetic rigidity limit:

Dipole fields:
Dipole gap:
Dipole size:
Weight of dipole:
Quad sizes:

Detector Requirements:

 

AE/E =10‘4 with 1 mm radial object size
for beam analysis system
AE/ E =10%
fl = 10-20 msr
D/M = 12.3
D = 12 cm/%
M = 0.74
R34 =0.88 mm/mr
A052 mr (Total of beam plus spectrometer
contributions)
50 cm (radial) x 15 cm (axial)
28.5°
Bp = 4 T-m
1.5 T (p =2.7 m)
D = 15 cm
3.5 m long x 100 cm wide
70 tons each
(1) 20.3 cm ID x 40 cm long
(2) 32.9 cm ID x 40 cm long
Two 2-dimensional detectors 1 m separation
(1) 50 cm x 15 cm
(2) 62 cm x 16 cm
Resolution: Radial 0.2 mm
Axial 0.4 mm

 

 

11

full phase space of at least 57r mm-mr (axially and radially) and 0.2% in beam energy
spread. When coupled to the spectrometer the whole system must be fully achromatic.
A TRANSPORT calculation for the entire system is shown in Fig. 2.2. Fig. 2.2 shows
the beam envelope and demonstrates the full achromat for a 63 = 0.1% momentum
spread in the beam and 57r mm-mr phase space. A more detailed discussion of the

beamline optics is given elsewhere [N081].

The two 45° bends are mechanically easier, and cheaper, to achieve by using
four 22.5° dipoles. The space between the dipoles allows for placement of sextupoles
which are used for second order corrections. Additionally, the smaller bend angle of
the individual magnets permit using the dipole magnet design as is used elsewhere in
the beam transport system. A more detailed discussion of the S800 beamline dipoles

and quadrupoles is given elsewhere [Ze95].

The spectrometer system chosen for the 8800 is a QQDD configuration. A strongly
focussing y-quad immediately after the target allows a large solid angle (20 msr) and
an x-focussing quad before the dipoles makes efficient use of the dipoles. The basic
layout of the spectrometer is shown in Fig. 1.1. and an enlarged version is shown
in Fig. 2.3. Table 2.2 and Table 2.3 the effects of misalignment on the resolution
using MOTOR and COSY INFINITY [Be93a] codes are shown. For each of the
four elements Q1, Q2, D1 and D2, we analyzed the sensitivity to unknown errors in
position in horizontal and vertical displacements, horizontal and vertical tilts, as well

as rotations of the element around the reference trajectory at its entrance, multipole

errors in Q1 and Q2.

The first order optics of the spectrometer were chosen to satisfy a complicated
set of requirements related to physics measurements, physical constraints. matching
to the accelerator beam, simplicity of tuning, and monetary considerations. These

considerations have been given elsewhere [No78, N079, Ze81]. The detailed design and

12

 

X(cm)

 

—Y (cm)
I
4:
l
I

 

 

 

-10 I I T I j l I I
O 5 10 15 20 25 30 35 4O 45
Z (m)

Figure 2.2: The x- and y-envelopes calculated by TRANSPORT for the S800 beamline

and spectrometer.

13

Figure 2.3: Side view of S800 showing position of magnetic elements.

14

construction of the S800 dipole and quadrupole magnets are discussed in following

chapters.

15

Table 2.2: Sensitivity analysis of misalignment and multipole errors. The energy
resolution is parts in 10,000.

 

 

 

 

 

 

 

Parameter Change %Change ERes ERes
(MOTER) (COSY)

Drift Before Q1 5 mm 0.83 1.12 1.10
Effective Length of Q1 10 mm 2.5 1.09 1.32
Field of Q1 0.011 T 1. 1.41 2.00
Aperture of Q1 0.5 mm 0.4 1.03 1.01
Drift Q1 - Q2 1 mm 0.5 1.22 1.22
Effective Length of Q2 0.5 mm 0.125 1.18 1.16
Field of Q2 0.0013 T 0.2 1.18 1.18
Aperture of Q2 0.8 mm 0.4 1.00 1.00
Drift Q2 - D1 5 mm 1. 1.26 1.22
Deflection Radius D1 5 mm 0.188 1.33 1.25
Deflection Angle D1 0.05 deg 0.07 1.23 1.22
Aperture of D1 5 mm 3.33 1.00 1.00
Entrance Edge Angle D1 0.1 deg — 1.20 —

Entrance Edge Curv. D1 — — - —

Exit Edge Angle D1 0.1 deg 0.33 1.43 1.82
Exit Edge Curv. D1 — — — —

Half Drift D1 - D2 10 mm 1.43 1.00 1.01
Deflection Radius D2 3 mm 0.11 1.27 1.45
Deflection Angle D2 0.05 deg 0.07 1.32 1.32
Aperture of D2 5 mm 3.33 1.01 1.00
Entrance Edge Angle D2 0.05 deg 0.167 1.16 1.85
Entrance Edge Curv. D2 — — — —

Exit Edge Angle D2 0.05 deg — 1.23 —

Exit Edge Curv. D2 — —- — —

Drift to Focal Plane 5 mm 0.19 1.27 1.20

 

 

16

 

 

 

 

 

 

 

Table 2.3: Sensitivity analysis of misalignment and multipole errors. The energy
resolution is parts in 10,000. -
Parameter Change %Change ERes ERIes
(MOTER) (COSY)
Hor. misalignment Q1 0.05 mm — 1.01 1.14
Ver. misalignment Q1 0.05 mm -— 1.00 1.18
Hor. tilt Q1 0.10 deg — 1.01 1.05
Ver. tilt Q1 0.024 deg —— 1.00 1.02
Rotation Q1 0.041 deg — 1.05 1.11
Hor. misalignment Q2 1.00 mm — 1.00 1.05
Ver. misalignment Q2 1.00 mm -— 1.00 1.20
Hor. tilt Q2 0.10 deg — 1.01 1.08
Ver. tilt Q2 0.05 deg — 1.00 1.09
Rotation Q2 0.05 deg — 1.05 1.11
Hor. misalignment D2 3.00 mm —— 1.12 1.00
Ver. misalignment D2 3.00 mm — 1.08 1.00
Hor. tilt D2 0.10 deg — 1.15 1.00
Ver. tilt D2 0.10 deg — 1.41 1.00
Rotation D2 0.09 deg — 1.01 1.05
Sextupole in Q1 0.0088766 T 0.7555 1.130 1.129
Octupole in Q1 0.0120890 T 1.0289 1.119 1.038
Decapole in Q1 0.0149080 T 1.2688 1.010 1.011
Dodecapole in Q1 0.0350980 T 2.9873 1.019 1.032
Sextupole in Q2 0.0026606 T 0.4089 1.024 1.006
Octupole in Q2 0.0047558 T 0.7310 1.001 1.005
Decapole in Q2 0.0084737 T 1.3024 1.003 1.002
Dodecapole in Q2 0.0127540 T 1.9603 1.004 1.001

 

 

Chapter 3

Design and Construction of Large
Superconducting Spectrometer
Dipoles

3.1 Why use superconducting coils in conventional
spectrometer magnets

The S800 is a large solid angle (20 msr) high resolution spectrometer which requires
two large gap (15 cm) dipoles with good field uniformity. The maximum field re-
quired in these dipoles is 1.5 T. This section is to compare the cost of construction
and operation of these dipoles with superconducting coils with those associated with

conventional copper coils.

Fig. 3.1 shows the results of a POISSON calculation for a dipole using a super-
conducting coil. This dipole has a 15 cm gap and a useful field width of 70 cm as
required by the spectrometer. It has two small superconducting coils, one above and
one below the median plane, which carry 130,000 amp-turns each to produce a 1.5
T field. The top and side pieces are fairly thin (40 cm and 37 cm, respectively) and
run at 2.1 ~ 2.2 T when the central field is 1.5 T. The 15 cm gap would require
only 100,000 amp—turns if the top and side pieces were much thicker. The resulting
dipoles are relatively lightweight, less than 75 tons each for a central path length of

17

18

3.5 m. A similar design optimized for a conventional copper coil would be about 50%
more massive because the top and side pieces would be thickened to reduce the power

requirements.

The total costs of both systems are compared [N081b]. The superconduting ver-
sion of these dipoles wins by about a factor of 2 in both initial cost and operational
cost. The savings are substantial, several hundred thousand dollars. This comparison
has been done for one specific dipole design, but generalization to other cases is fairly
easy. The costs of the copper coil system scale very rapidly with the gap of the mag-
net, whereas the costs of the superconducting coil scale very slowly with the magnet
gap. Hence, for large gap magnets, e.g. 20 to 30 cm or more, there is absolutely no
question that superconducting coils are much more cost effective than conventional
coils. The construction of the CEBAF high momentum spectrometer dipole magnet

demonstrates this principle [3093].

On the other hand, scaling the present estimates down to smaller gaps, e.g. 5
to 10 cm, the cost advantages of the superconducting coils for this style dipole tend
to go away. For such smaller dipoles, however, other magnet designs may be more
cost effective. We have done preliminary studies of 5 cm Window-frame dipoles
with superconducting saddle coils. By using cold steel in these designs very compact
systems can be built. In any case, before concluding that superconducting coils are

not cost effective for small dipoles, various options must be considered.

It is very clear that any large solid angle, high resolution spectrometer for momenta

above 1 GeV/c superconducting coils can permit substantial savings in both initial

cost and operational cost.

19

3.2 Design parameters of 8800 dipoles

The specified resolving power, momentum range, and solid angle of the spectrometer,
combined with the chosen first order 8800 optics, determines the volume of “good”
magnetic field required in the 8800 dipoles. The choice of dipole to achieve the volume
of good field then to a large extent determines the cost of the 8800 system. If the
dipoles are over designed, they can easily cost two to three times more than necessary.
However, if they are under-designed or poorly constructed the system will not meet
the resolution specifications at the designed solid angle. (It will have good resolution

if the solid angle aperture is stopped down far enough.)

In a system, such as the 8800, where focal plane measurements of .1: f, y f, 0; and
of are made for physics reasons and aberration corrections, the dipole good field
specifications can be greatly reduced. For example, it is certainly not necessary to
specify a field flatness of 1 in 20,000 in order to obtain a momentum resolution of
20,000. It is essential that the dipole fields not have small scale or fine structure, but
slowly changing field across the dipole widths can be accounted for via the focal plane

measurements in the same way as the intrinsic aberrations discussed above.

Quantitative consideration must be given to the upper limit of field gradients
which can be accommodated with the focal plane measurements. For example, the
following analysis shows that in the present design field gradients of up to 1 gauss
per cm in the radial direction can be corrected via focal plane angle measurements.
Consider a ray with the central momentum which leaves the target with angle 0, and
hits the focal plane at position x, with angle 0}. This ray passes through the dipole

with an average radial displacement ED given by:

ED = (x/0)0,

20

When ($70) is the average value of the matrix element (rs/9) within the dipoles.
Since a change or error in the magnetic field is equivalent to the same percentage
change in momentum, then a field variation AB changes the x-coordinate at the

focal plane by:

Ax; = (AB/BIIx/é)

_ (___B- Bo)
— B ———(a:/6)

Assume the actual dipole field B is given by
B = B($D)

Such that

dB =de( D)
d6 dz: We)

 

These equations can be combined to give the uncertainty in focal plane x-coordinate

69:; as a function of the uncertainty 60: in the initial angle at the target:

5., = (,1, :73) (woo/(5)60.

Finally, the uncertainty in m; is converted to momentum uncertainly 6 (AP/ P) by
dividing by the dispersion (:r/6), and the uncertainty in 0: is related to the uncertainty
in the measured quantity 0f by the magnification M9: M1,“, yielding:

6(AP/P)= M ,1:( To) (1131118)“f

For our system M3 = 0.8 and (m) = 0.7 cm/mr, so if the angular measurement
uncertainty 60f is 1 mr, then a gradient of 1 G/cm at 15 kG yields:

0.8(0.7)(0.1) 1

MAP/P) 15 000

 

21

= 1/27, 000

In other words, field gradient of as much as 1 part in 15,000 per cm can be tolerated
in the dipoles if the focal plane is measured to 1 mr uncertainty and the magnitudes

of these gradients are measured [No81a].

When the design goal is a gradient specification instead of a flatness requirement,
the iron can be driven into saturation. Superconducting coils, with their higher
current densities, provide cheap amp-turns, allowing reduced iron mass and larger
dipole gaps (increased solid angle). When one already has a liquid helium refrigerator
and the superconducting magnet experience, the choice is much easier still. The
saturation level of the yoke has been kept low enough to avoid stray fringing fields

which may interfere with detectors near the target.

The simplest configuration is a window frame with a compact superconducting
coil. This was the first extensively studied design [Ze79, Ze80, Ze81a], which although
it gives the most compact design for a given volume of good field (a gradient of :l:
1 G/cm), it requires a complex superconducting saddle coil. We have chosen to
concentrate on the alternate magnet type, the H-frame. Two strategies were used to
maximize the region of good field: (1) improving the infinite permeability solution,
and (2) improving the finite permeability solution. The infinite permeability solution
is improved by the addition of a trim coil on the median plane with current in the
same direction as the main coil. Because the field in the H-frame magnet decreases as
the edge of pole tip is approached, a coil on the median plane has the effect of keeping
the field from decreasing as rapidly. The addition of the return coil directly above, on
the pole tip, also improves the field profile and makes assembly easier. The trim coils

are normal conductors, carrying approximately 0.7% of the main coil ampere-turns.

22

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

'091L
+.

 

 

 

 

 

E1311

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.1: 8800 H-frame dipole POISSON calculation.

The field profile is kept reasonable over a wide dynamic range (with finite perme-
ability) by using a tapered gap behind the pole tip which is 1 cm high at the midline
and 1/2 cm at a distance of 40 cm . It does not extend all the way across the pole.
The basic design is shown in Fig. 3.1 and Fig. 3.2. Fig. 3.1 shows a calculation for
1.5 T and Fig. 3.2 gives the basic dimension. The dipole bending limit gives K=800
MeV for the central ray at a field of slightly less than 1.5 T, but the dipoles can be

run up to fields of 1.6 T if necessary for slightly more rigid particles.

The effects of the trim coil at low field where the iron is closest to infinite per-

meability is seen in Fig. 3.3 and Fig. 3.4. The degree of field uniformity at 5 kG

23

for several trim coil settings are shown in Fig. 3.3. The volume of good field needed
is out to 35 cm. The optimized trim coil current is 0.7 % of the main coil. The
infinite permeability solution is also shown for comparison, required for the infinite
permeability case. The permeability curve used in the calculations is for 1003 iron,

supplied by the vendor (Japan Steel). Fig. 3.4 shows the gradients for the same cases.

For field levels where significant saturation of the iron occurs, as around the normal
1.5 T range, the effects of the filter are seen. The filter is tapered to provide a variable
reluctance so that the field stays uniform with increasing excitation. It is seen in
Fig. 3.5 that the volume of good field has been increased by several centimeters by
the combination of trim coils and filters. This is seen more readily in Fig. 3.6, which
shows the gradients for the same cases. Note that the infinite permeability case has

trim coils turned on.

Since the operating range of the dipoles is designed to be from 0.5 to 1.6 T,
the magnet must meet the gradient requirements at all excitations. The gradient
requirements are actually a percentage of central field, ie., 1 G / cm at 1.5 T, 0.33 at
0.55 T, and 1.06 at 1.6 T. The field profiles are shown in Fig. 3.7. With the corrections

described the dipole meets the gradient requirements.

In order to insure reliable operation of the superconducting coils, a low current
density, cryostable coil configuration was chosen. A current density of about 4 kA/cm2
(about the same as the NSCL K1200 cyclotron) will be used. Although this is con-
siderably less than the 18 kA/cm2 used in the beamline dipoles, the stored energy is
much greater. The :l:16° dipoles have only 35 kJ, while each 8800 dipole has 1.1 MJ.
The magnetic field in the coil package of the 8800 never exceeds the gap field. The
choice of a cryostable coil, while it should never quench since the Steckley parameter
is < 1 [R683], does require the use of a dump resistor to protect the coil in case of

a massive heat pulse sufficient to remove all the liquid helium. Both the K500 and

24

 

40

64.13

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.2: 8800 dipole showing dimensions in cm.

K1200 cyclotrons are equipped with a fast dump (emergency) and a slow dump re-
sistor for energy removal. Quench calculations have been done which show the coils
will survive a quench when the dump switch is used in a timely manner [Ze86]. In
this case, the calculated hot spot temperature is only 75 K. Additionally, the dump
should not cause a quench. This has been experimentally verified by high current

dumps. A summary of the coil and wire specifications is given in Table 3.1.

25

 

 

 

 

(J I T l l I I l l l
B ____ 5 kG TCS optlmlzed
10 — 0 o \ ..
CF ' ’ °
2 O 1 + + + + + +' + + + + + + + a + + j ‘ + . O .—
>< M, ’ .
v I //°
0—10 L TCs lowered by 14% . + ‘3:
0” TC's lowered by 797. /*
\—20 —- / a
E} TC's off .
—30 1 -—
-4O 1 L l L I I L L I f
O 4 8 12 16 20 24 28 32 36 4O

Radius ( cm )

Figure 3.3: Deviations of the field from the central field at low field as a. function of

charge in trim coil currents.

26

r)
(J I l l I I l l l

 

0 Optimized TC's

E

o

\ . l I ° 0

”00/ /: o

_ U * .
v—l “ TC's lowered by 14% /. 1.
m +
<1 2 - TC's lowered by 79% '-
3 TC's off / *

0
l I l l l l I

O 4 8 12 16 2O 24 28 32 36
Radius ( cm )

 

 

l
4:.

 

Figure 3.4: Deviations of the gradients from the central field at low field as a function
of charge in trim coil currents.

27

 

50 I I f I I I I I I
40 * ssoo Dipole 14.8 kG ‘
A 30 — _

20— 4

/ B (X10
0 '55
T
I‘ O
I "U
. SI
- E?
I: :1.
D (D
Q.
Rilogd

 

 

 

—10‘— Aim/3:23:30
m—ZO _ Nofilter 'A
<1—30 — _ No TC’s /' —

—4O _ No Filter nor TC's \: _

_50 l l l l l l l l J

0 4 81216 2024 28 323640
Radius ( cm)

Figure 3.5: Deviations of the fields at 14.8 kG for several cases showing the effects of
trim coils and filters.

28

 

 

 

 

 

2 T I I I I I I j
A 1
E

O
\
.U ' o o +
v_1 _ No filter /A 0 O 047
a: ' A i
<‘_2 _ No TC's / 4
\ .
m . / i
<I_3 — No TC's, no fllter A 4

_4 1 1 l l 1 i 1 l

O 4 8 12 16 20 .24 28 32 36
Radius ( cm )

Figure 3.6: Deviations of the gradients at 14.8 kG for several cases showing the effects
of trim coils and filters.

29

 

50 I I I I I 1 I I I
40 — -
30 _ S800 Dipole .4

N

O
I
p...
C."
x
Q

91.

O ( x 10-4)
H
O O
I
I?
ID
0
ID
ID
10
{IO
‘0
$0
(’0
{*0
(I0
I» o 01
1+ O
to 0 w
“I O Q
fir O
.0 O
00 0
CI? 0
O I- O
I- o
> O
. O
+ O
0
file!— -

 

 

 

 

m
—10 — / + -
\ 16 kG / ,q
m—ZO »- fl... 4
<1—30 — 4
_4O _. .4
_50 l l l l L l l l l

O 4 8 12 16 2O 24 28 32 36 4O
Radius ( cm)

Figure 3.7: Deviations of the fields over the dynamic range needed for spectrometer
operation.

30

 

 

 

 

 

 

2 I I I l I I F I
1 _ 8800 D1pole 5 kG (X3) _"
A \
CE.) 0 o 0 ° ° 0 o o o o 0 ° ° 0 o
O ‘ g“;w - r u o o o . . \OJZ
\ . 7. . ' o e
-0_1_ 15kG ”.91
{.13 . / II
-2 _ .16 k0 (X 0.94) -
\
m Required radius =>
<I_3 - _
_4 1 I I I I I I I
O 4 8 12 16 20 24 28 32 36

Radius ( cm )

Figure 3.8: Deviations of the gradients over the dynamic range needed for spectrom-
eter operation, scaled to the 1.5 T field.

31

Table 3.1: 3800 dipole conductor and coil specifications.

 

 

 

 

Conductor

type: NbTi in copper matrix
Copper to Superconducting Ratio: 15:1

Size: 1.981 X 3.25 mm2
Im-t @ 2 T measured as Z 1400 A
10,," @ 1.6 T central field 420 A

Coil

Number turns per coil : 350

Weight of conductor per coil: 250 kg

Inductance: 10 H

Stored energy: 1.1 MJ

Protection resistor: 0.25 D

 

 

 

 

3.3 S800 Dipole Construction

Because the cost of the spectrometer is strongly determined by the mass of the dipoles,
the size must be kept to a minimum, consistent with the required good field region.
Additionally, as the spectrometer is designed to disperse in the vertical plane, a
lighter set of magnets means the support structure does not have to be as massive.
Minimizing the mass requires the construction of a dipole with coils that follow the
beam sagitta, that is, a kidney shaped magnet. The result is a coil with one negative
curvature side. We have kept the number of turns to a minimum, consistent with
liquid helium consumption and power supply costs. This necessitates going to a
cryostable coil for this relatively low field (1.6 T in the gap) device and running at
higher current (420 A) [Ze93].

The coils of the dipoles have 350 turns, arranged in 28 layers. Layer—to—layer
climbs are made alternately on the straight ends. This results in 12.5 turns per layer.
Insulation for each layer is provided by winding the turns into slots machined in

thin G10 pieces. Cross cuts and small gaps between pieces provide additional helium

32

passageways and flexibility in going around corners.

Winding the negative curvature side of the coil is difficult because any tension in
the winding pulls the wire out of its insulation groove. The first few layers can be
done by first clamping the wire at the corner then passing the wire around a cylinder
to form it to the right curvature. The wire can then be rolled into the grooves. It
can then be clamped at the other end to hold it in place. However, after a few layers
the accumulated tension begins to separate the layers. We have solved this problem
by the straightforward method of using many clamps along the negative curvature
side. More clamps are required for the additional layers because of the accumulated
tension which makes the coil package act like a big spring. A pneumatic arm is used
to keep the same force on the coil regardless of coil thickness to which is attached a
roller for the negative side. This roller bends the wire to the required radius so that
the wire lays in the groove. The clamps are removed ahead of the arm and replaced
after it has gone by. The procedure requires two people to operate efficiently. In
addition to winding, insulation strips and climb pieces must be positioned, resulting

in taking nine hours per layer.

Because of the manufacture’s wire lengths, two or three splices were made in each
coil. These are accomplished by milling one half of the width of each piece for a
length of two twist pitches (about 6 cm) and soldering them together so that the
width and height are the same as the original conductor. Added cross channels in
the G10 insulation pieces are used near the splices to ensure that any helium vapor

bubbles formed can escape. A test joint showed a resistance of S 2 n0.

Once all layers have been wound, nonmagnetic spring assemblies are placed on
the outside of the coil. These provide for thermal contraction compensation and to
compress the coil to prevent movement when the coil is energized. Assembly of the

outer wall and top of the bobbin on the negative side necessitates the removal of all

33

of the clamps at once. Fortunately, it was found the time constant for loosening of
the coil after it has been clamped for several days is about two hours. Therefore, it is
possible to remove all the clamps, place the covers in place and re-clamp them before
the coil relaxes. After carefully welding the first coil closed, it was leak checked and

the bobbin prepared for winding the second coil.

Since the magnet operates at a relatively low field, the magnetic field shape is
predominately determined by the iron, with coil contributing only twenty percent even
at high field. However, the field uniformity requirement is one part in a thousand,
so coil placement cannot be neglected. The shape of the coil is such that forces are
much larger on one side of the arc than the other, and the bobbin is not stiff enough
to resist excessive deflections on it own. The deflections of the bobbin, which is a
box structure of 1.9 cm thick 316 Stainless Steel, would result in asymmetries in the
field if they were not properly restrained. Three dimensional force calculations were
used to determine the required support structure [Ze92] and more support links were
used than would be required to simply restrain the bobbin. A set of five tension links
and a compression link is used to minimize deflection in the radial direction. Smaller
pairs of links at each corner support any axial force due to off centering across the

median plane.

The tension links are constructed from S-glass unidirectional tape. Because of
the stress concentrations in the bushings and attachment points due to the small
space requirements, titanium (Ti-6Al-4V ELI) was used for these parts. The links
have been tested to beyond the maximum calculated loads. Additionally, each link
assembly is proof tested to at least its calculated load. The compression link is made
of a Randolite PD43 tube with Ti fittings. To insure the link would not fall apart if
it went into tension, a small Ti rod holds the link assembly together. This link has

also been extensively tested. At the room temperature end of the links is a spherical

34

bearing, which combined with the orthogonal clevises at the coil end, takes up the
motion during cool down. The calculated heat load at 4 K from all the links is less

than one watt.

The $800 dipole magnet consists of five major pieces: the two top slabs, the inner
and outer side yokes and the pole tip assembly. The pole tip assembly is made up of
the pole tips , which are connected together with precision stainless steel spacers, and
the coil cryostat. The cryostat was handled as a unit. With the carriage in place on
the track, first one of the top slabs was lowered into 10 meter deep pit and attached
to the supports. Next, the bottom side yoke was mounted to the top slab. The pole
tip/ cryostat assembly was then carefully lowered into position and moved to the top
slab. Because the compression support link on the negative curvature side has to stick
out of the inner side yoke, a key way was cut in the inner yoke. The inner yoke was
then slid into place on the assembly. The clearance between the support structure
and the link assembly did not allow the remaining top yoke slab to be simply lowered
into place, so another crane was placed into the pit to pick up the now connected
four pieces (50 t). Then the in house 40 t crane picked up the last top slab while
the other crane lifted the other assembly straight up. Then both were brought close
together and lowered at the same rate. They were then bolted together to complete
the assembly. Once all the pieces were in place, the lead/dewar box was connected
to the magnet. The liquid helium feed circuit brings liquid through a heat exchanger
at the top of the magnet before delivering high quality liquid into the bottom of the
coils. Each coil is fed separately and the overflow fills the dewar to provide cooling for
the incoming liquid. Liquid nitrogen is supplied at the bottom of each side (the inner
and outer arcs) and conducted through 0.95 cm diameter copper tubing soldered in
a serpentine path along the shield. Aluminum tape provides the necessary thermal

radiation protection between 4 K and 77 K [Ze94]. Superinsulation is used between

35

the nitrogen shield and the cryostat walls. The current leads consist of five strands

each of a cabled superconductor (147 wires of 0.25 mm diameter).

The power supply is capable of providing 600 A at :I:20 V. The nominal current for
the maximum field of 1.6 T is about 420 A. However, the current leads and the support
links are capable of operating at 468 A for peak field of 1.7 T [Ze95a]. Although the
magnetic field profile at this field will not be good enough to allow the full solid angle
and momentum acceptance to be used, it will allow more rigid beams to be analyzed.
Coil protection is achieved with a 0.25 I! dump resistor which is activated when a
potential difference between the coils of greater than 0.5 V is detected. Additionally,

the dump switch is activated if the helium vessel rupture disk is used.

3.4 Commissioning of the $800 Dipole Magnets

During final leak checking, and before the first magnet cryogenic connections were
completed, a small helium leak on the bobbin was discovered. Since disassembly of
the magnet to try to find and fix the leak would result in a six month delay, the pump-
ing option was accepted. It was felt the leak was small enough to allow operation
of the magnet, so two holes were added to the dewar box and the cryostat to allow
the placement of vacuum pumps. The magnet was then cooled down successfully,
although the heat load was twice as high as anticipated. After adjusting the support
links, the magnet successfully ran to the required central field of 1.6 T. No training
nor unbalanced coil voltages were observed. All support links were well below their
limits and their loading agreed well with calculations. The field of the first dipole
as a function of coil current in the 15 cm gap is shown in Fig. 3.9. The fields were
measured with a Hall Gaussmeter, and later confirmed with NMR. The maximum

field of 1.6 T is achieved at 420 A, while the current estimated to give this field based

36

on two dimensional POISSON calculation is 498 A. Three dimensional calculations
were not used to estimate the transfer function because the tapered “Purcell filter”
could not be put in the calculation due to node limitations. The discrepancy between
the POISSON calculations and the measured data could be the result of an under-
estimation of the saturation magnetization or because the truly three dimensional
structure of the iron yoke: The inner and outer side yoke have different areas to keep
the saturation constant of either side of the middle. However, more iron is available
to return the flux, due to the longer length of the outer slab. Therefore, a lower
level of saturation is achieved and hence, less current is required to achieve the higher
fields. The magnet is designed to have significant saturation, so that the expected
gradient in the field is constant over the operating range of 0.5 to 1.6 T. This satura-
tion, together with the tapered filter provide the required field quality. Measured and
POISSON calculations of the deviations of the field gradient are shown in Fig. 3.10
[Ca]. The deviations of the mapping field gradients are less than 1 Gauss/ cm which
reached the spectrometer requirements. More field mapping results of D1 and D2 will

be in J. Caggiano’s thesis.

In order to try to reduce the heat load due to the helium leak, the magnet was
warmed up and more pumping was added. Additionally, holes were cut through the
superinsulation blanket to reduce the pumping impedance from the bobbin to the
pumps. The magnet was again been cooled down. The insulation vacuum is now
improved, but the heat load is still high although it should be sufficient for operation.
It is possible that part of the heat load is due to the nitrogen shield making contact
with the bobbin in some location. Since the shield has its own support links, it can
be adjusted independent of the bobbin, which must be adjusted to optimize the field
quality and minimize the forces. The heat load of the first dipole magnet is 12 W.

Fig. 3.11 shows the heat load as a function of helium background pressure in the

37

cryostat.

Based upon our initial operating experiences with the first dipole, D1, some small
modifications were made to the second dipole, D2, during its assembly. The cavities
in the bobbin on either long, curved side between the two coils were left open to the
insulating vacuum on D1. Concerns about the potential of helium leakage from the
coil packages into this space caused these volumes to be sealed and lines run to allow
independent evacuation of the these spaces on D2. Also, a number of G-lO composite
bumpers were added to the surface of the bobbin to prevent any possibility of direct
contact between the 4 K bobbin and the 77 K nitrogen shield around it. The heat

load of the D2 magnet is only 5.5 W.

38

2.0 l l l l

 

E"
U‘
I

 
 
  
 
  

Magnetic Field (T)
p—s
b:
l

P
01
l

 

 

(L0

 

I I I I
O 100 200 300 400 500
Current (A)

Figure 3.9: Central magnetic field as measured by a Hall Gaussmeter as function of
current.

39

 

p—s
I
I

O
l
’1
/
I

———*—— POISSON Calculation
—fi——— Measured, No TC
—--0— Measured, with TC

AB/AR (Gauss/cm)
.I.‘ .L
I l
I I

I
CD
I
I

 

 

 

I
uh

I I I I T I
12 16 2O 24 28 32 36
Radius (cm)

0
4:
CD

Figure 3.10: Measured and POISSON calculation deviations of the field gradient with

trim coil on and off. The data were measured at the center of D1 as a function of
radius.

40

 

 

 

 

40 I I I I 4 l _
3?
CU 30+ -
E
“U
‘6
O
u—l
1320- __
a)
:13
10 I I I I I I
2 3 4 5 6 7 8 9

Pressure (10'6 Torr)

Figure 3.11: The heat load of the first dipole magnet as a function of insulation
vacuum pressure.

Chapter 4

Design and Construction of High
Gradient, Large Aperture
Quadrupoles for the 8800

4.1 Magnetostatics of quadrupoles

From the Biot-Savart law of magnetostatic we find
V - B = o (4-1)
V x B = 1161.1 (4.2)

where B and J are the magnetic field and the current density. The current density
is zero inside quadrupoles, therefore V x B = 0 permits the expression of the vector
magnetic induction B as the gradient of magnetic scalar potential and hence, B =
—V (PM. Then the basic differential laws of magnetostatics reduces to the Laplace

equation for (PM, namely

 

 

 

2 _ —— .—
V (DM- 1' 61‘ r2 020 + 622 0 (4'3)

1 0 BQM 1620M 62(1))” _
rar

Cylindrical coordinates have been chosen since they are most suitable for quadrupole

magnet geometries. We attempt a solution by the method of separation of variables

41

42

and assume that
(PM(r, 0, z) = R(r)O(0)Z(z) (4.4)

Then, upon substituting this expression into eq. (4.3) the complete solution in cylin-

drical coordinates becomes [Ma65]

 

<I>M(r, 0, 2) ~ Z[Aann(kr) + anNn(kr)]eiinoeikz (4.5)
where
_ kr " °° (-1)"‘ kr 2'"

is a Bessel function of order n and NnUcr) is a Neumann function of order n. Since
Neumann functions become -oo at r=0, we choose only the Jn(kr) to treat problems
which involve the origin. The values of n, m and k are in principle arbitrary, although
11 must be an integer (or zero) in order to insure the singlevaluedness of 9(0). There
are an infinite number of solutions which, apart from an arbitrary angular phase and

assuming that z=0 is the center of a quadrupole magnet, may be written as [Na91]

QM(r,0,z) = isin(n9)<l>n(r,z)

: :2 {sin(n0) (5.3)“ ":20 [W (5;) 2,1} (4.7)

where r0 is the pole radius. (If k = 0 , then there is no dependence on 2 and
the Laplace’s equation becomes two dimensional case. (PM is just proportional to

r"sin(n0).) In cylindrical coordinates, the radial component of the magnetic field is

 

B,(r, 0, z) = —a§:4
= — g {sin(n0) (I—o)n-l ":0 [bm,n(z) (%)2m]}
: — i0: sin(n0)B,.,,,(r, 2) (4-8)

n=0

43

where

B.,..(r,z) = (1)“1 i [bm,,,(z) (1)21 (4.9)

To m=0 7‘0
The n=2 term corresponds to the quadrupole component of the magnetic field and
has a sin(20) angular dependence. By Fourier analyzing a magnetic field, it is possible

to extract each multipole component of the magnetic field, which is used to judge the

quality of the field.

For an ideal quadrupole, Br,2 would be proportional to r and would have no
2 dependence inside a quadrupole magnet. Outside the quadrupole magnet, 8,;
would be zero, and B”, would be zero everywhere for n9E2. However, there is always
a gradual decrease in the field near the end of the quadrupole magnet, and it is
impossible to completely remove every higher order multipole, so the main goal for
the design of the quadrupole magnet is primarily to attempt to minimize the higher
order multipoles, while maximizing the quadrupole term of the magnetic field. With
perfect symmetry, not every term in the magnetic field expansion is present. The

quadrupole magnet has fourfold symmetry and
<I>M(r,0, z) = —<I>M(r, 0 + 1r/2,z)

so only the n = 2, 6, 10, 14, . ~ 2(1+2k) terms are allowed. Substituting equation

(4.7) into equation (4.3) and using the orthogonality relation, we obtain

 

 

 

(2m + n)bm,,,(z) _ nzbm,n(z) 1 dzbm_1,,,(z) _ 0
rme-I-n—l) (2m + n)r(()2m+n—l) (2m + n _ 2)r(()2m+n—3) (122 _
This equation yields [Ha96]
2 d’bm- n
bm,n(z) = — m + n 1’ (z) (4.10)

4m(m + n)(2m + n — 2) dz2

44

where m 2 1. From equation (4.5) we know that bmm are linear combinations of e,”

-kz

and e which meets the boundary condition. The 2 component of the magnetic

field, Bz(r,0,z), must vanish at z =2 0 and z = 00 or

 

=0 at 2:0 and 2:00 (4.11)

Since the spectrometer mainly depends on the integrals of the transverse components

along a path parallel to the beam axis, we have

j: B.,..(r, z)dz = (for-1 :0 (53)” f0” bm,,,(z)dz

and using equation (4.10) and (4.11), we find that only the m = 0 term contributes.
Therefore,

[Om B.,..(r,z)dz = (—)"-l [om bo,,,(z)dz (4.12)

r
7‘0
which shows that the integral is proportional to 1"“, and that only the leading term

of the integral in the radial expansion is important.

4.2 Quadrupole types

Quadrupole magnets are the primary focusing elements in an accelerator beamline.
The design for the high resolution spectrometer at the NSCL requires two quadrupole
magnets, Q1 and Q2. These magnets are required to have high field gradients and
large apertures as compared with typical beamline magnets. Room temperature
magnet designs were found to be too power hungry and could not have been fit

within the space available. This necessitated the use of superconducting magnets.

The choice of superconducting quadrupoles is limited to three basic types: a)

cos(20) type, where the field is shaped by the coil, b) Panofsky type [Ha59], which

45

is a square or rectangular current sheet approximation, and c) iron dominated type

(also called superferric) [Ze84], where the field is shaped primarily by the iron pole

tip.
4.2.1 Cos(26l) quads

Cos(20) quads, which produce highly uniform gradients of up to 50 T/m over a large
volume, have been built [C083] at Fermi Lab, CERN and other places. However, this
type is convenient only if the conductor is a flat cable (approximating a current sheet)
which requires high current operation (1,000-5,000A). Vapor-cooled current leads for
1,000 A consume liquid helium at a rate of 2.8 litres per hour. In recent years, Cos(20)
magnets have been used as spectrometer elements at CEBAF’s experimental ball A
[A195]. One of the quadrupoles has a 30 cm warm bore and a 1.6 m length. The peak
gradient of 8.3 T / m is produced by epoxy-impregnated coils operating at 3250 A. The
maximum stored energy is 130 kJ and the effective length is only 92 cm. The other
two quadrupoles have 60 cm warm bores and 3 m lengths, which have used a 3 sector,
2 layer coil construction operating at a peak current of 1850 A. The stored energy is
592 kJ and the effective length is only 1.8 m. Each of the Cos(20) quadrupoles costs
about 1.1M$. Engineering and construction of a Cos(20) magnet was considered to
be quite expensive. In addition, they have an effective length less than their physical

length, requiring even higher field gradients to offset this condition.

4.2.2 Panofsky quads

The Panofsky quad, while easy to build, suffers from two problems. First, the field
in the corners of a square quad is \/2 times the field at pole faces. The means that
the superconducting wire parameters are dominated by a region of wasted field. The

second problem is that Panofsky quads which have been built have achieved the

46

desired field uniformity only by very careful construction and attention to where each

individual wire is placed.

4.2.3 Iron dominated quads

The third type of superconducting quadrupole is the iron dominated quad which was
developed for the N SCL standard beamlines. It differs from the other two in that
the field shaping is done primarily by iron poles; in this sense it is similar to classical
iron dominated quadrupoles but with some important differences. The resulting iron
and coil cross section and calculated field lines are shown in Fig. 4.1 for a 12.7 cm
inside diameter quad. The fraction of useful bore of this magnet is quite good when
compared to room temperature magnets. Mathematically this performance can be
understood by conformal mapping this and the standard geometries into equivalent
dipoles. In the infinite permeability limit, a window-frame dipole produces a perfect
field up to the coil, and such a dipole conformally mapped into a quadrupole geometry
is also perfect. This is not true for the H dipole magnet; typically, 0.5 to 0.75 gaps
are lost inside of the pole edge with a commensurate loss in the mapped quadrupole.
Room temperature magnets are forced into the mapped H geometry by virtue of the
large number of ampere-turns needed by the typical magnet and the limited current
density available with copper. The magnets simply need the space to get all the
ampere-turns packed in. The pole fields are also limited by saturation of the iron.
The pole does not grow in cross section to contain the additional flux which enters
it with increasing radius; in some magnets the cross section even decreases in order
to permit a large coil to be used. The mapped window-frame magnet does not suffer
from this disadvantage since the pole cross section increases until the return iron is
reached. According to conformal mapping, the coil surface should be hyperbolic and

the current density would not be uniform. Since an accurately non-uniform current

47

 

 

 

 

 

 

1

15.24 cm

 

 

IF

 

Figure 4.1: Octant of the NSCL beamline quadrupole with magnetic field lines using
the POISSON code.

density coil would be difficult to achieve, the nonuniformity is compensated for by

repositioning the exposed surface of the conductor.

4.3 Physical parameters of Q1, Q2 and a sex-
tupole as related to the 8800

We decided against cos(20) quadrupoles because of the high current operation and its
helium requirements. We also investigated superconducting Panofsky quadrupoles.

A Panofsky design was not chosen due to the sensitivity of the field quality to er-

48

Table 4.1: The physical parameters of Q1 and Q2 magnets.

 

 

 

 

 

 

Item Q1 Q2
Length of iron 0.34 m 0.30 m
Pole tip diameter 0.24 m 0.42 m
Peak gradient 19.7 T/m 7.5 T/m
Effective length (nominal) 40 cm 40 cm

 

rors in conductor placement and the construction problem. Our conclusions from
these studies and from experience with our cold-iron, iron dominated superconduct—
ing beamline quads is that a larger version of the latter type is our choice for both
Q1 and Q2 quadrupoles. The design goals and physical parameters of Q1 and Q2

magnets are summarized in Table 4.1.

According to the beam optics calculation for S800 spectrometer, the dominant
aberration in the focal plane is x/02. This results in a very large line width, even in
the absence of any momentum spread. Sometimes it is desirable to physically stop
intense elastically scattered particles just before the detector, while permitting low-
lying excited states to pass. A sextupole has been used to correct the x/02 term. The

best place for the sextupole is in Q2.

4.4 Magnetostatic calculations

4.4.1 Magnetic field calculation of Q1

The original Q1 design was based on two dimensional magnetic field calculations
performed with POISSON. Q1 is a large version of the N SCL’s standard cold beamline
quads. The beamline quadrupole pole tip radius is 6.35 cm and Q1 is 12 cm. A sketch
of one eighth of this design is shown in Fig. 4.2. However, the compromise coil design

and the finite length that include the coil return at the ends may introduce significant

49

higher order multipoles to the field, even with ideal placement of all components. The
end effects were studied with a three dimensional magnetostatic code, TOSCA [To].
We used six 20-node bricks and two straight bars to model the Q1 coil [Zh96]. The
cross section shape of the straight bar is same as in Fig. 4.2. Since the cross section
of the NSCL standard beamline quad coil end is irregular in shape, it is impossible
to precisely model the real coil end using TOSCA. We used three 20-node bricks to
approximately model the end of Q1 coil and kept the cross section area of the 20-node

brick coil the same as the straight bar’s. The coils and iron are shown in Fig. 4.3.

The code TOSCA computes three-dimensional magnetic fields in the presence
of arbitrary current distributions including the presence of nonlinear materials. In
regions of space where the current density is zero, the magnetic field is defined in
terms of a scalar potential which solves Laplace’s equation. In regions where currents

are present, the code calculates the magnetic field directly using the Biot-Savart law.

The mesh used in the r0 plane of the magnet is shown in Fig. 4.4. Boundary
conditions are <1) = constant along the horizontal and Emma; = 0 along the symmetry
edge running through the center of the pole face. This mesh is replicated in z with
the granularity shown in Table 4.2. This results in a total of 25,323 mesh points. The
magnet iron ends abruptly at z = 17 cm with no shaping and chamfer. The problem

takes roughly 3 hours of CPU time on a ALPHA 3000-400 undergoing 15 iterations.

We use the three-dimensional finite element analysis program TOSCA to calculate
the scalar potential and the magnetic field. For fixed radii r and axial positions 2, the
individual multipole components are extracted using a straightforward Fourier anal-
ysis. Table 4.3 shows the peak multipole components and the integrated multipole
components for Q1 magnet at a current of 86 A. These quantities are important, and
will have different significance when the S800 spectrometer is operating in different

modes. Fig. 4.5 shows the various multipole components as a function of z, the dis-

50

'0'

 

 

 

 

 

Figure 4.2: Octant of Q1 with magnetic field lines calculated by POISSON.

51

LY4o.o

   

 
 
 
     
  
 
  
    

     
   
   
     

  
  

  
    
  

             
 

   

   
 
   
 
    
 
      
      
  

 
   

         
      
 
 
 
 
 
     

     

  
 
 

    
   
  

 
 
   
  

09
'0'...
«a .Iouo
_ If. 55‘ “‘é‘g‘fi x400
== EE=:'.' ‘ ‘
==’ ‘ /==...
69 flu"-
v’v’é "~‘-‘:‘
Vic, ‘ 4°66».
"'::"IIIIII\“::‘::%
«ans-sees
.:..llIII“ “
'l-IIIII‘

Figure 4.3: Q1 coils and iron geometry used for TOSCA calculations

52

101 0.0

 

Figure 4.4: Details of the Q1 mesh used in the r0 plane for the TOSCA calculation.

53

Table 4.2: Longitudinal granularity for Q1 used in the TOSCA calculations.

 

 

2 (cm) Number of divisions Type
0 Z z 2 17 8 quadratic
17 2 z 2 25 4 quadratic
25 2 z 2 35 4 quadratic
35 2 z 2 45 4 quadratic
45 2 z 2 60 5 quadratic
60 2 z 2 100 10 quadratic
100 2 z 2 200 12 linear
200 2 z 2 300 8 linear

 

 

 

 

 

tance from the center of the Q1 magnet along the beamline axis. As expected, the
field inside the Q1 magnet is dominated by straight section of the coils, producing
an almost pure quadrupole field. Near the ends of the Q1 magnet , the higher order
multipole fields increase greatly in strength. We have plotted the integrals of these
functions, integrated up to the plotted value of z, to show their development and
convergence. There is rather long tail to large z, but the contribution to the integral
past z z 30 cm is rather small. Note that these components change sign at the end
of the Q1 magnet iron, yielding a significant cancellation effect in the final field inte-
gral. Numerical programs which calculate the magnetic field by some finite difference
method solution of eq. 4.3 can not be expected to give highly reliable results near the
interface of empty space and a highly nonlinear material such as the iron pole tip.
However, since the field integrals depend only on the coefficients b0," it is possible
to determine then at lower radii and extrapolate to r=ro. The results for Q1 are
summarized as follows:

1 oo oo
5 B,,2(12cm, z)dz :/ B,,2(12cm, z)dz = 0.49 T - m
—00 0

/00 B,,6(12cm, z)dz = (2.0 x 10'3) x 0.49 T - m
o

54

Table 4.3: Q1 multipole analysis results for half of the magnet at a radius of 8.8 cm.

 

 

n Maximum | B”, | (T) f; B,,,,dz(T - m)
2 1.754 0.358

6 8.54 X10"3 5.35 X10-4
10 1.63 x10‘3 1.17 x10-4
14 3.76 X10"4 6.38 X10"5

 

 

 

 

 

Table 4.4: The calculated parameters of the Q1 magnet.

 

Operation current 86 A
Stored energy 68 kJ
Inductance 18.4 H

 

 

 

 

foo B.,,o(12cm,z)dz = (—6.1 x 10“) x 0.49 T . m

0

[00 Br,l4(12cm,z)dz = (—4.5 X 10'4) x 0.49 T - m
0

The calculated parameters for Q1 are given in Table 4.4. The calculated gradients

for Q1 as a function of current are shown in Fig. 4.7.

A significant consideration in construction is the magnetic force on the coils. The
magnetic field exerts a force F = JxB per unit volume of current carrying coil
and in superconducting magnets, where the field and current density are both high,
this force can be very large. Such forces can cause severe problems in the design
and construction of superconducting magnets. They can cause structural failure and
destroy the magnet, or they can damage the superconductor or insulation. Perhaps
the most serious problem, because it is so difficult to predict, is the degradation of
magnet performance which may be caused by the sudden release of mechanical energy.
Calculations of force and stress demand knowledge of the magnetic field throughout

a winding. Many of the field computing programs are now being used in conjunction

55

TOSCA Calculations for Q1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.0 T T I I I 0.006 T r I
0.004 r ..
1.5 ~ .I
0.002 I- -
A 1.0 " _, A 0.000 '- -I
E: E:
,3 :-0.00Z *- a
m P-
05 4 m -o.004 ~ 4
-0.006 7' —I
0.0 *- a
-04008 b d
_0.5 I L I I I _0.010 I I I I I
.0 1 . .3 5 .6 .0 1 .3 5 .6
z (m) z (m)
5 I T I I j 1 I I fi' fi I
o - — -o . ~
7" I"
2 2
‘5 ‘5 " 'l 5’1 '- "
E—Io — ~ E—z - 4
2. a.
mu. ma.
-15 ~ I -3 ~ ~
~20 I I I I I _4 I I I I I
.0 .2 .3 5 .8 0 .3 5 6
2 (m) 2 (m)

Figure 4.5: Multipole components of the Q1 radial field for the quadrupole (n=2)
term and the first three allowed terms (n=6,10 and 14) are plotted as functions of z,
the distance along the beamline axis from the center of the Q1 magnet at r = 8.8 cm.

56

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TOSCA Calculatlons for Q1
4 I I r I T .0010 r I T I
.0008
A 3 I- “ A
E E
P p .0006
N .2 ~ 2 N
“U '0
In m
k. 1 _ k.
’ .0002
o 1 I 4 1 4 .0000 1
.0 1 .3 .5 .0 5
Z (m)
0 T I I I T O I I I I
F -2 — . .p—I -
2 9.
x ”—2 -
v _4 __ 4 V
A A_3 I-
E —6 _ j E
E: *4 P-
N N
v -8 '- “ '6
2. $5 ”
In” In”
\‘10 ” ‘ 's—6 F a
_12 L I I I 1 _7 J l l l
.0 1 5 .6 0 1 5

.3
2 (m)

 

Figure 4.6: Integrated multipole component of the Q1 radial field I; bmdz for n=2,

6, 10 and 14 at r = 8.8 cm.

 

 

57

 

(\‘J
01
I—
i.—
——
I—
P—--
—-
I——
I—

N
O
I

I

     
  

H
U‘
I

Gradient (T/m)
8
l

 

 

 

I I I

I I
0 10 2O 30 4O 50 6O '70 80 90
Current(A)

Figure 4.7: TOSCA calculations of the Q1 gradient as a function of current.

58

with finite element stress programs to calculate stress with considerable precision.

The forces on each coil of Q1 are calculated by TOSCA which integrates the body
forces on the source conductors using J XB. Each section of each coil is represented
by an 8 or 20 node finite element. Gaussian quadrature integration with a selectable
number of Gauss points is used to calculate the forces. The program calculated
the force acting at the centroid of each section of each conductor. Since the fields
produced near the straight section of the coils are stronger than the fields produced
near the ends of the coils, the force acting on the straight section of the coils is larger.
Fig. 4.8 shows the forces per unit length that act on the straight section of the Q1
coil. The strongest component of field is in the y direction and produces an outward

x direction force on the conductors.

4.4.2 Magnetic field calculation of Q2 and the sextupole

The Q2 magnet design is similar to the Q1 magnet, but is a large version of the
NSCL’s standard beamline quads. The pole tip radius of Q2 is 21 cm which is three
times larger than the NSCL’s beamline quad’s radius. As mentioned before, the
dominant aberration of the beam optics at the focal plane of S800 spectrometer is
3/02. According to the beam optics calculation, the best place for a sextupole to
correct this aberration is in Q2. The original Q2 and the sextupole designs, based on
the two-dimensional magnetostatic code, POISSON, are shown in Fig. 4.9. However,
the calculations assume that the iron and coils are infinitely long along the beam axis.
Of course, the iron has a finite length and the coil must return, therefore the magnetic
field can’t be calculated precisely due to this loss of symmetry. It is necessary to use

a three-dimensional magnetostatic code like TOSCA.

We used two straight bars to model the straight section of the Q2 coil. The cross

section shape of the straight bar is the same as indicated in Fig. 4.9. However, the

59

AIR

IRON

AIR v Fx/L = 2_13 kN/m

I, Fy/L = —88 kN/m

 

 

 

 

 

Figure 4.8: The x- and y-components of force per unit length on the straight section

of the Q1 coil are calculated with the program TOSCA at I = 86A.

60

Table 4.5: Longitudinal granularity for Q2 used in the TOSCA calculations.

 

 

 

2 (cm) Number of divisions Type

0 2 z 2 15 15 quadratic
15 2 z 2 25 5 quadratic
25 2 z 2 30 1 quadratic
30 2 z _>_ 50 1 quadratic
50 _>_ z _>_ 200 2 quadratic
200 2 z 2 300 1 linear

 

 

 

 

end of the Q2 coil is a more complex shape, especially in areas which involve a change
in cross section. We used three 20-node bricks to approximately model one end of Q2
coil and also kept the cross sectional area of the 20-node brick coil the same as the

straight bar’s.

The sextupole coil is wound on the surface of a cylinder. It is best to model the
sextupole coil using “the constant perimeter end”. We assume it is made up of two
straight sections parallel to the beamline axis. The half length of the central filament
of these sections is 15 cm. The cross section of the sextupole is almost rectangular,
the thickness is 1 cm in the radial direction and the width is 3.5 cm in the azimuthal
direction. The ends of the sextupole conductor form a smooth curve over the cylinder.

Fig 4.10 shows the Q2 iron, the Q2 and sextupole coils..

The mesh used in the r0 plane of Q2 and the sextupole are shown in Fig 4.11.
Boundary condition are (I) = constant along the horizontal and Emma; = 0 along the
symmetry edge running through the center of the pole face. This mesh is replicated in
z with the granularity shown in the Table 4.5. This results in a total of 25,323 mesh
points. The magnet iron ends abruptly at z = 15 cm with no shaping and chamfer.

The problem takes roughly 2 hours of CPU time on a ALPHA 3000-400 undergoing

15 iterations.

61

 

 

 

 

II'

45 <:m-—-——-———'-I

Figure 4.9: Octant of Q2 and the sextupole with field lines calculated by POISSON.

62

     
 
  
    
 
 

 
    
   
    

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‘3’" . "5'0.

   
  
 

  
  
 

  

 

‘~

 

Figure 4.10: Computer simulation for Q2 and the sextupole magnets using TOSCA.

63

 

 

 

 

' . n r .0 100.0

 

 

 

 

 

 

Figure 4.11: Details of Q2 and the sextupole mesh used in the r0 plane for the TOSCA
calculation.

64

We use the three dimensional numerical integration program TOSCA to calculate
the scalar potential and the magnetic field. For fixed radii r and axial positions z, the
individual multipole components are extracted using a straightforward Fourier anal-
ysis. Table 4.6 shows the peak multipole components and the integrated multipole
components for a Q2 magnet current of 90 A. Both of these two quantities are impor-
tant, and will have different significance when the S800 spectrometer is operating in
different modes. Fig. 4.12 shows the various multipole components as a function of z,
the distance from the center of the Q2 magnet along the beamline axis. As expected,
the field inside the Q2 magnet is dominated by straight section of the coils, produc-
ing an almost pure quadrupole field. Near the ends of the Q2 magnet, the higher
order multipole fields increase greatly in strength. We have plotted the integrals of
these functions, integrated up to the plotted value of z, to show their development
and convergence. There is a rather long tail to large 2, but the contribution to the
integral past 2 z 30 cm is rather small. Note that these components change sign at
the end of the Q2 magnet iron, yielding a significant cancellation effect in the final
field integral. Since the field integral depends only on the coefficients 50m, it can be
determined for the field integral and extrapolated to r = re. The results for Q2 are

as follows:

00

%/00 B,,2(21cm,z)dz =/ Br,2(210m,z)dz = 0.33 T-m
—oo 0
[00° B,,6(2lcm,z)dz = (6.1 x 10") x 0.33 T - m
/°° B.,,0(21cm, z)dz = (—4.2 x 10*) x 0.33 T . m
0

f0” B.,,,(21cm, z)dz = (—8.8 x 104) x 0.33 T - m

65

Table 4.6: Q2 multipole analysis results for half of the magnet at a radius of 8.8 cm.

 

 

n Maximum | Br,” I (T) f0Z Br,ndz(T - m)
2 0.6493 0.14

6 0.48 x10'4 3.5 x10’5
10 1.01 ><10'5 1.0 X10-6
14 1.17 ><10'5 9.0 x10“8

 

 

 

 

 

TOSCA Calculations for 02

0.1 W I I I I

 

 

at] (T)
c':
(a)
I
I
O u-o N an IF 0

3,,(1') (x 10")

I
.0
a

I

I

I
“

 

 

 

 

I
O
«I
L... I-
I—
I
N

 

 

 

.3
Z (In)

 

p.
0
d
—I
p
O
-I
.I

 

10b 7

O
I
I
O
m
I

a 10m (210*)
0'

B M('1') (210")
O O

I
0‘
l
I
.—
O
I
l

 

 

 

 

 

 

 

I
g
o

o
H”

p

-

h

bu~
I

p

at

P

_

P
h-

.3 .3
Z (m) 2 (In)

Figure 4.12: Multipole components of the Q2 radial field for the quadrupole (n=2)
term and the first three allowed terms (n=6,10 and 14) are plotted as functions of z,
the distance along the beamline axis from the center of Q2 magnet at r = 8.8 cm.

66

TOSCA Calculations for Q2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.00 6 I 1 I f I
—0.02 1 {‘5 _ _
'2
A —0.04 a
E 54 I ~
E; -0.06 ~ A
s 83 _ .
.1 h
{0.08 v
m "2 _ —
-~. ~0.10 ~ ‘1,
03"1 _ .
—0.12 - k.
—0.14 0 1 g 1 1
. 6 .0 1 2 .3 4 .5 6
2 (m)
0 0 I I
05‘ _ _. 9"
I2 2 Ig_1 _‘
x x
v _4 -I V
A A"2 "
E —6 q E
3.1 E:
-3 .-
3 —a ‘ 3
9, 32
In L
m__ ,, Ila-4 ‘
H 1° 4.
_12 I I I I I _5 I I
.0 1 .2 .3 .6 4 .5 6
Z (In)

 

Figure 4.13: Integrated multipole component of the Q2 radial field I; b,,,,dz for n=2,
6, 10, and 14 at r = 8.8 cm.

67

Table 4.7: The calculated parameters of the Q2 magnet.

 

Operation current 90 A
Stored energy 132 kJ
Inductance 32.8 H

 

 

 

 

Table 4.8: The calculated parameters of the sextupole magnet.

 

Operation current 3 A
Stored energy 103 J
Inductance 22.8 H

 

 

 

 

The calculated parameters for Q2 are given in Table 4.7. The calculated gradient
of Q2 as a function of current are shown in Fig. 4.14. The claculated parameters for

the sextupole magnet are given in Table 4.8.

The forces on the coils of Q2 magnet are also calculated by TOSCA. The only
difference between Q1 and Q2 is that there is a sextupole inserted in Q2. If the
sextupole current is zero, the force on the straight section of the Q2 coil is indicated
in Fig. 4.15. Only a low current in the the sextupole is necessary to correct the
33/02 aberration since the sextupole field is very weak at Q2 coil position, the total
forces acting on the Q2 coils are only slightly changed. However, the forces acting
on the straight section of sextupole conductor are more complicated. Depending on
the location of the coil, the force can be radially inward, outward, or in an azimuthal
direction, as shown in Fig. 4.16. The coil clamping method must take this distribution

into account.

68

j—n
O
I—
.—
_-
I—
I—
I.—
p—
p—
—

 

m
I
1

Gradient (T/m)

 

 

 

 

I I I I I I I I I
0 10 20 30 40 50 60 70 80 90 100
Current(A)

Figure 4.14: TOSCA calculation for Q2 gradient as a function of current.

69

AIR

IRON

A'R P Fx/L = 170 kN/m

IFy/L = -63 kN/m

 

 

 

 

 

 

 

Figure 4.15: The x- and y-components of force per unit length on the straight section
of the Q2 coil are calculated with the program TOSCA at 192 = 90A and Lump“, =
0A.

70

Fr/L - 6.4 kN/m

Fr/L - -6.4 kN/m Ft’L ' 8'3 kN/m

Ft/L - 8.3 kN/m Fr/L . 3.5 kN/m
Fr/L - -3,5 kN/m Ft/L - 10.5 kN/m
Ft/L - 10.5 kN/m '

' Fr/L - -9.2 kN/m Fr/L - 9.2 kN/m
Ft/L - -2.IkN/m Ft/L - '2.1kN/m

 

 

\ /

Figure 4.16: The radial and azimuthal components of force per unit length on the

straight section of the sextupole coils are calculated with the program TOSCA at
[sextupole = 3A and qu 37- 90A.

71

4.5 Quench simulations

An evaluation of the quench behavior is needed for coil safety. In this case a dump
resistor was not used for quench protection because a high field and small coil size
make the quench propagation extremely fast, and the energy spreads more uniformly
throughout the coil. However, the higher stored energy requires larger wire and higher
operating current for protection in case of a quench. The code QUENCH [Wi68] has
been used to evaluate the worst case scenario. Fig. 4.17 shows the internal voltage
of Q1 increasing to 637 volts after quenching, which is still lower than the voltages
of the NSCL standard beamline quads or the 8800 beamline quads. Since the NSCL
standard beamline quads have survived hundreds of quenches and the S800 beamline

quads dozens of quenches without damage, no problem was anticipated for Q1 or Q2.

Since the sextupole coils are inside Q2, mutual inductance in the coils is significant

and must be evaluated. We consider the total energy of the system
1 L 12 1 L 12 M I I
E=§Q2Q2+§Us+ 02.

where ng and L, are the self-inductances of Q2 and the sextupole which are given
in table 4.7 and table 4.8, and where M is the mutual inductance. We calculated the
total energy by using TOSCA with both of the magnets on. Using above equation, the
mutual inductance has been calculated to be 10.7 H. The worst case is Q2 quenching
first, and the energy from Q2 transferring to the sextupole with a one second time
delay, as seen in Fig. 4.18. The internal voltages for Q2 and the sextupole are shown

in Fig. 4.19 and are not excessive.

72

 

 

 

 

.— I I I I I I I I I l I I I I 1 I T I I I I I I 4
Z n 1
800 “- / \ —*
\
A - _ _ — _ S800 BL Quads ‘
\E/ " ’/\\ \ ‘
_ I ..
._. ,/ \ \ —————— NSCL Standard BL Quads
CU I' , / \ _
"" 600 .._ \ _-
+> I /
CI I— l/ \ Q1 ..
CD _ I \ \ e
+2 / I
0 I ’ \ \ ‘
D-I r I/ \ \ -
c0 _ I \ _
E . I \ \ _
q) - I, \ \ -I
+2 _ I \ \ J
E. 200 —- ,’/ ‘\ \ —
_ I \ \ ..
I" I \ \ \ ..
e \ \\ -
\ -.
0 I 1 I l L I l I l I I 1 >4 I 1 l l I L
0 2 4 6 8
Time(s)

Figure 4.17: The comparison of the internal voltages in Q1, N SCL standard beamline
quads and 8800 beamline quads after quenching.

Current (A)

73

 

   

 

 

 

L- T I I I I I I f I I I I I 17 r T r I
80 —‘
60 Q2 d

------ Sextupole 4

40 ‘—

_J

20 — —d

O'- rfll’ll L i L 1 1 T‘ir-i—q-.L_L____. L ‘
0 5 10 15

Figure 4.18: Decay of currents in Q2 and the sextupole after quenching.

Internal Potential (V)

600

400

200

74

 

I I

 

   

Q2

Sextupole

 

Figure 4.19: Internal voltages in Q2 and the sextupole after quenching.

 

75

4.6 Heat load calculations

Heat load is an important parameter for superconducting magnets. A high precision
stainless steel spacer positions Q1 and Q2 with respect to each other. All elements
are assembled into the same cryostat (Q1 / Q2 doublet cryostat). A section view of
the assembly showing the main features is given in Fig. 4.20. To minimize the overall
liquid helium consumption load on our refrigeration system, and to cryogenically
decouple devices during operation, a batch-fill mode of operation can be used. The
break even point over a continuous flow system required a minimum holding time for
liquid helium between fills. The length of this time period depends on the system
and operation parameters. In order to fulfill this condition, and to keep the reservoir
a reasonable size, careful attention must be payed to all sources if heat acting on
the helium vessel. Since much of the liquid nitrogen shield is cooled by conduction
through the copper to a pool of boiling liquid nitrogen at the center of the device,
temperature gradients exist in the shield. The shield temperatures was measured
with type T thermocouples; the highest temperature of the nitrogen shield is 95 K
which was used for the heat load calculation. The heat load for the cryostat mainly
comes from support links, radiation, the vent pipe, and the feed and return lines.

Subsequent sections treat these four sources of heat load contributions in detail [De].

4.6.1 Support link heat loads

A support link for 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. The

N SCL standard beamline quads built in this lab have employed the epoxy fiberglass

CRY OSTAT

O-l YOK E
O-I POLE TIP
0-/ COIL

76

ELECTRICAL LEADS

VERTICAL LINK

"" """ 02 YOKE
oz POLE TIP
02 COIL

HE X APOLE
' /—BORE TUBE

 

 

 

 

 

 

 

 

 

 

NITROGEN SHIELD
HEUUM VESSEL

SPACER

Figure 4.20:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

HORIZONTAL UNK

View of a longitudinal section of Q1, Q2 and sextupole.

77

composite G-lO (E-glass) for their links. In Q1 /Q2 doublet, the 8 horizontal links

have also used G-10.

The distance between the Q1 / Q2 doublet and the first S800 spectrometer dipole
(D1) is very short and they produce overlapping magnetic fields, so there is a strong
interaction between the Q1 / Q2 doublet and D1. To reduce the Q1 / Q2 doublet dis-
placement due to D1, we have employed titanium for the 2 vertical links of the doublet.

The total heat loads of the support links is

Qlinka = QG—IO + QTitanium

where the cross section area is 1.06 cm2 for the titanium links and 0.7 cm2 for
G—10 links; both links are 12.7 cm long. Also, we know that If; AdT = 2.905 W/cm
for titanium [Jea] and If; AdT = 0.272 W/cm for G-lO [Nbs]. We obtain

 

. 95 95
Qlinks = 2 X AT: AridT + 8 X iglo- AG-iodT
IT.- 4.2 10-10 4.2
= 0.61W (4.13)

Even though the heat load of titanium is ten times bigger than G-lO’s, the calcu-

lation result shows using titanium for the vertical links is still acceptable.

4.6.2 Radiation heat loads

To reduce radiation, we have used a high conductivity aluminum tape, 3M #425
(from 3M Corporation) as coatings on both the 4K and 95K surfaces. We assume all
the helium vessel and shield of Q1/Q2 doublet are two long concentric cylinders. We
calculate that the bore tube surface area of the helium vessel is 12,000 cm2 and the
rest surface area of the helium vessel is 39,000 cmz. If we assume 1.27 cm clearance

between the helium vessel and the nitrogen shield, we can calculation that the bore

78

tube surface area of the nitrogen shield is 11,000 cm2 and the rest area of the nitrogen

shield is 40,000 cmz.

The radiation heat load can be written as [H081]

0A1(T1“ — T2")
A
2‘: + a: G. -1)

where a is the proportionality constant and is called the Stefan — Boltzmann con-

 

Qradiation (4.14)

stant with the value of 5.669 x 10‘12 W/cm2 - K4. 6 is the emissivity for aluminum.
£1 and 62 are 0.038 and 0.011 at 95 K and 4.2 K [Le80]. Now we use eq.(4.14) to

calculate the radiation heat load.

Qradiation = 02 W (4.15)
4.6.3 Vent pipe heat loads

The safety vent pipe is 1.59 cm in outer diameter, 0.04 cm wall thickness and 19
cm long of 304 stainless steel, its diameter and length based on calculations for safe
venting to prevent liquid helium container overpressure. There are two kinds of the
heat loads associated with this vent pipe. One is the pipe wall thermal conduction
heat load. The other is the helium gas conduction heat load within the vent pipe. We
know that If; KwaudT = 4.525 W/cm [Jeb] and [3319...” = 0.053 W/cm [Ak50].

Therefore, the vent pipe heat flux is determined below:

A1 95 A2 95
i c = _ wa dT —/ as
Qpp LAgK u + L 43K, dT

= 0.05 W (4.16)

4.6.4 Feed and return line heat loads

During isolated operation, that is, when additional liquid helium is not being fed to the

device, only the feed line contributes if the return line is open and gas cooled. We use

79

Table 4.9: Calculation heat loads for the Q1 / Q2 doublet.

 

 

 

Item LHe (liter/ hour)
Support links 0.92
Radiation 0.30
Vent pipe 0.08
Feed and return lines 0.29
Total 1.59

 

 

 

 

Invar tubing which is 1.27 cm in diameter and 0.089 cm thick. We assume the length of
the tube from helium vessel to the vacuum break is 61 cm and has no liquid nitrogen
intercept. We know that If?) AwaudT = 35 W/cm and [432° Aga,dT = 0.264 W/cm.

We obtain:

A1 300 A2 300
inc = — Awa dT —/ A asdT
Q, L [1.2 u + L 4.2 g

0.193 W (4.17)

4.6.5 Total heat loads for the Q1 / Q2 doublet

From eq.(4.13), eq.(4.14), eq.(4.16) and eq.(4.17), we can easily calculate the total
heat loads for Q1/ Q2 doublet. During normal magnet operating, the helium pressure
is around 1.2 atm. We can convert the heat load units from Watts to liters of liquid
helium consumption per hour. 1 Watts = 1.513 liters/hour. The calculated boilofi'
rate is listed in Table 4.9. The actual measured heat load is 2 W for the Q1 / Q2
doublet.

80
4.7 Construction of Q1, Q2 and the sextupole

4.7.1 Coil winding

The coil is the most delicate component of a superconducting magnet. All of the
Q1, Q2 and sextupole coils were random- and wet-wound with Stycast epoxy on a
semi-automatic winding table. The number of turns was counted with two counters.
A mechanical ruler was used to measure the length of the wire used. The Stycast
epoxy was mixed with 4.5 % of Catalyst 11 by weight and poured into the epoxy
bath. During the winding process, the epoxy bath was cleaned and refilled with fresh
epoxy every two hours and warmed to 158° F 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. During winding many turns crossed over each other
at the corner where there was a transition between the straight sides and the end arc.
If the shape of the end form was not correct, shorted turns would occur. Additionally,
the angle of the end form from the bottom of the winding must be adjusted so that
turns did not crowd up at the top or bottom of the end form. One of the Q2 coils
with 2160 turns of 0.85 mm conductor was wound in three hours; winding one of the

Q1 coils with 1680 turns of 0.7 mm wire took the same amount of time.

Since the cross section of the sextupole coil is about 1 cm thick and 3.5 cm wide and
the wire is very small, it was difficult to make this kind of coil. During the sextupole
coil winding process, we reduced the wire tension to prevent the wire from breaking,
therefore the wire had to be packed in place every 200 ~ 300 turns to maintain a
high packing factor. Especially when coil winding nears the finish number of turns,
winding speed was slowed down to allow additional wire packing. It was found that

2160 turns of 0.3 mm wire can be wound to produce a sextupole coil in four hours. A

81

total of eleven sextupole coils been wound. Four of the coils were wound during the
winding development process and were not seen as usable for various reasons such as

variance in number of turns and shorted turns, etc.

Each of the coils for Q1, Q2 and the sextupole was oven cured. It took two hours
at 212° F followed by a four hours post cure at 3000 F. The electrical insulation of
the Q1 , Q2 and sextupole wire was provided by formvar. During the coil winding
process, the electrical insulation sometimes became damaged and several turns could
be shorted. After we finished each coil, the resistance, inductance, and dissipation

[M079] of the coil were measured to verify that there were no turn-to—turn shorts.

4.7 .2 The Q1, and Q2 coils testing

The low carbon iron for the pole tips and yokes of Q1 and Q2 was machined with
numerically controlled machines. In total, the magnet proved to be inexpensive and
straight forward to build. This was aided because the field was shaped primarily by
the iron and conductor placement was less important. Both Q1 and Q2 have cryogenic
Hall generators mounted on the pole tips, to allow measurement and setting of the
magnetic field. In section 4.4.1 and section 4.4.2, we discussed the force acting on
the Q1 and Q2 coils. At the Q1 and Q2 coils location, the strongest components of
the field are in the azimuthal direction and produce the biggest force in the outward
radial direction. The forces in the outward radial direction are nearly three times
larger than the forces in azimuthal direction. The coils of Q1 and Q2 are shimmed
against the pole tip first, then against each other by using titanium spacers and G-
10 shims. The reason we used titanium spacers was because titanium has a smaller
thermal contraction than iron and (31-10. The titanium spacers were held in place by
G-10 keepers. On the one end of the Q1 and Q2 magnets, the bus bars and G-10

stand offs were fixed on the yoke steel, as shown in Fig. 4.21 The current leads of all

82

Table 4.10: Inductances of the Q1 and Q2 magnets.

 

Magnet Lmeasured (Henry) Lcalculation (HCDI‘Y)
Q1 20.1 18.4
Q2 34.0 32.8

 

 

 

 

 

 

coils were soldered with a bigger superconducting wire to increase the stiffness and

to prevent the wire breakage, then connected to the bus bars.

A high precision stainless steel yoke spacer positions the Q1 and Q2 magnets with
respect to each other. The Q1 and Q2 magnets were tested before being installed in
their permanent cryostat in order to ensure basic coil performance before undertaking
the procedures involved in assembly of the cryostat. The leads were connected, and
level gages installed. The whole assembly was installed in a large commercial dewar
which is a 1.83 m in diameter and 3.65 m long cylinder. Two relatively long current
leads (4 meters each) were needed to make a connection from the Q1 and Q2 magnets

to the existing 500 A commercial current leads at the dewar top.

In the first Q2 coil test run, the Q2 magnet quenched at 61 A. But in the second
run, the Q2 magnet current reached 90.1 A which is our design value. However the
Q1 magnet performance was quite different from the Q2 magnet. The Q1 magnet
quenched at 57, 64, 65, 66 A; about 75% of our design value. One of the reasons Q1
coils quenched at a low current is that the Q1 magnet was on top of the Q2 magnet
and the Q1 coils were not covered 100 % by liquid helium. After refill to almost cover

the magent, the Q1 magnet current reached our design value, 86 A.

During the testing process, the inductances of the Q1 and Q2 magnets were mea-

sured, Table 4.10 shows the measurement results and TOSCA calculations.

83

 

Figure 4.21: Q1 and Q2 coils assembly.

84

4.7 .3 The Q1, Q2 and sextupole magnet assembly

The sextupole magnet was mounted to the helium vessel bore tube which is shown
in Fig. 4.22. In section 4.4.2 we discussed stress on the sextupole coils. The forces
acting on the straight section of the sextupole coil are complicated. Depending on the
location of the coil, the force can be radially inward or outward, or in an azimuthal
direction. The maximum force per unit length on the straight section of the sextupole
coil is 11 kN/m. The six G-10 locating spacers for the sextupole were fixed on the
helium vessel bore tube. The G-10 spacers prevented the coils moving in azimuthal
direction. The straight sections of the sextupole coils were held in position with
stainless steel bands. Even though the forces acting on the end of the coils were much
smaller than the straight sections, B stage fiberglass tape was wound around the coil
and cured. The bus ring was attached on the helium vessel bore tube. Before the
current leads were soldered to the bus ring, the leads of each coil were soldered with
bigger superconducting wires, to increase the stiffness and to prevent the wire from

breaking.

After the sextupole was in position, the end bell of helium vessel on Q2 side and
the helium vessel bore tube were aligned and welded together in vertical position on
the assembly table. We used a crane to picked up the Q1, Q2 iron and coil assembly
from the testing dewar and drop in the helium vessel bore tube. Since the clearance
between the pole tip of Q2 and the sextupole fixture was very small (0.032 in), several

people helped to guide this installation and to prevent the coils from being damaged.

85

 

Figure 4.22: Sextupole coils assembly.

Chapter 5

Magnetic Field Mapping and
Analysis

5.1 Introduction and need for quality maps

S800 spectrometer offers a large phase space acceptance, with solid angles of more
than 20 msr and energy acceptance of greater than 10%. Such a large solid angle and
high resolution spectrometer requires careful consideration and correction of aberra-
tions. The large phase space makes the correction process considerably more difficult
and complex. The conventional correction of aberrations with higher order hardware
(such as dipole edge curvatures, sextupoles, octupoles, etc) will cure second order or
third order terms, but these terms will eventually limit the maximum solid angle and
energy acceptance for a given resolution. The superconducting sextupole in Q2 will
be used to reduce the :1:/02 term, for a limited solid angle and for special cases (to
allow the use of a shadow bar in the focal plane). For the rest of the aberrations, we
will use the optimization computer code COSY INFINITY to do software corrections.
In order for the calculations to work, precise and accurate magnetic field maps of the
Q1 / Q2 doublet, D1 and D2 dipoles, and 8800 beamline quadrupole triplets are nec-
essary to achieve high resolution using ray reconstruction [Be93]. This chapter will

discuss the mapping and results for the spectrometer quadrupole magnets.

86

87

5.2 Quadrupole mapper

A mapper used for magnetic field measurement is based on a 486 PC computer,
with an Animatics 5000 Stepper Motor Controller and F.W. Bell 9903 series 3 axis
gaussmeter. The control program was written using Borland Turbo Pascal compiler

version 7.0.

Two different types of superconducting magnets were mapped with this apparatus:
the S800 beamline quadrupole triplets and the S800 spectrometer doublet. A complete
map requires motion in three dimensions. Azimuthal (0) movement of the probe is
achieved through the use a NEMA 34 servo motor and encoder. The increments are
applied through an 80 tooth gear and worm drive, with a resolution of 0.09 degrees.
Along the beamline axis (2), movement of probe is achieved through a non-magnetic
Thompson slide rail assembly equipped with a NEMA 23 servo motor and encoder.
This allows for z direction movement of the probe at programmable speeds up to
1 cm per second. The radial positioning of the probe is done with non-magnetic
threaded rod inside the probe holder box. The center of rotation is captured and
held in position by means of an aluminum machined frame which is flat to plus or

minus 0.0127 cm over entire 76.2 cm length.

The gaussmeter utilizes the Hall effect to measure magnetic field. The instrument
has a range of 10 pG to 2.9999 MG at sampling frequencies up to 50 kHz. The
maximum field produced by any of the magnets is 2 Tesla. The three axis Hall probe
of the gaussmeter has been calibrated using an N MR system. Figure 5.1 shows the
magnetic field difference between the gaussmeter and N MR measurements for one of
the three channels. The lines through the data are fourth order polynomial fits. The

fitting coefficients are shown in Table 5.1.

AB=a+ng+cB§+dB§+eBg

88

 

AB (Gauss)

 

 

 

 

—50 l I 1 Er
-1.5 -l.0 -0.5 0.0 0.5 1.0 1.5
N MR Measurments (T)

I

Figure 5.1: The magnetic field difference between the NMR and gaussmeter measure-
ments for one channel. The solid lines through the data are fourth order polynomial

fits.

where 89 is the gaussmeter field measurement.

Channel one of the probe measures the radial component of the magnetic field.
Channel two measures 0 component, or tangential component. Channel three mea-
sures the 2 component, which is component of the field along the beamline axis. The
data acquired by the meter are transmitted through the instrument’s RS-232 serial

port to the PC.

The design of the gaussmeter makes it best suited for situations where the probe
is in a fixed position during data acquisition. The feature conflicts with the desire to
measure the field as quickly as possible. The commands to acquire data, MExx, with
varying timing criteria. Thus, some measurement were in error when the probe was

moved before the new field was accurately read.

In order to synchronize the field data with respect to the position, the design

engineer at Bell was contacted for alternate solutions. A command that was imple-

Table 5.1: The fourth order polynomial fitting coefficients for the field differences

89

between N MR and Gaussmeter measurements.

 

 

 

 

 

 

 

Coefficient Negative field Positive field
a1 -0.72951 -0.25016

bl 2.35420 x10‘3 -2.64737)<10’3
c1 1.70199x10‘7 3.18635x10'7
d1 1.06793x10‘ll -3.90871x10'11
61 —5.82006X10'17 1.15326x10’15
a2 0.28693 -0.32442

52 3.39651 x10“3 -2.58475 x10‘3
c2 2.26697 x10'7 -2.46902x10'7
d2 1.80889x10‘ll -1.81681x10‘11
e2 1.82584 x10"16 2.23829 x10"16
a3 -0.28672 -0.70295

()3 3.83656 x10"3 -4.04085 x10‘3
c3 -2.46902x10‘7 -3.29303x10‘7
d3 -1.47827 x 10'11 2.87842x10‘ll
63 -l.47622><10‘16 -7.82781><10‘16

 

 

mented during development, but not released for customer use, allows control over
the sampling period. This command, ADxx, acquires data for 200 ms when issued.
Processing and correcting for probe errors takes 2 seconds, before the data are trans-
mitted through the instrument’s serial port. Using this command allowed the motor
to incrementally position the probe to each location and take data while the probe

was in a fixed position, ensuring synchronization.

The two axes of motion, 0 and z, are independently driven by stepper motors
controlled through the Animatics 5000 interface. This interface directs commands
through its RS-232 serial port into COMl on the PC. Commands to control motion
are stored in data files in the same directory as the main program according to their

function.

The z-axis pertains to the motion along the beamline. During mapping of the

quadrupoles, the motion will consist simply of 1 cm increments. Opto—sensors deter-

90

mine the absolute position of the probe for reproducible results at a fixed radius. The

location of the radius is determined by an adjustment of the gaussmeter Hall probe

holder.

The 0 direction of motion is along the circumference of the beamline. This cir-
cumference is divided into discrete location, either 120, 180 or 360 depending on the
chosen resolution. Each data sample consists of the probe being position at the precise
location, while the control program allows the gaussmeter to sample data. After data
sampling, the probe position is incremented until the index opto-sensor is actuated

when the revolution is complete.

5.3 8800 beamline quadrupole triplet mapping

An integral part of the S800 spectrometer is the analysis line which consists of fif-
teen superconducting quadrupoles and four superconducting dipoles. The beamline
brings the beam from grade level into the spectrometer, which is situated in a ten
meter deep pit. The quadrupoles are larger version of the NSCL’s standard beamline
quadrupoles. The standard quadrupoles have a 12.7 cm diameter inscribed circle and
S800 beamline quadrupoles are 20.3 cm in diameter. The beamline quadrupoles are
arranged into triplets with 3 magnets in a common cryostat. To achieve the required
energy and angular resolution for nuclear physics experiments, the magnetic fields

must be accurately known.

Data are stored on the internal hard drive until they are loaded to another com-
puter for processing. At one degree step size, each revolution takes 14.35 minutes and
produce a 15 kB data file. A Z-axis step of 1 cm will require 210 revolutions in order
to adequately measure the length for the triplet and fringe fields. The total data file

for each of these maps is 3.15 MB. A one degree map takes 51 hours to complete, with

91

Table 5.2: Mapping Time and File Size for S800 Beamline Quadrupole Triplet.

 

Parameter 1°Steps 2°Steps 3°Steps

 

Triplet Mapping Time 51 hours 34 hours 17 hours

Data File Size 3.15 MB 2.1 MB 1.05 MB

 

the mapping process requiring minimal operator supervision. Table 5.2 lists mapping

times and file sizes.

Figure 5.2 shows the radial component of the magnetic field for the triplet when
the currents for the three quadrupoles are 5, 15 and 10 A respectively [Zh95]. The
optics for fragment separation mode have fifteen adjustable parameters so tuning
the beam is only practical if the gradients are accurately known. On one pole tip of
each quadrupole magnet a cryogenic Hall generator was mounted to provide reference
for setting the magnetic field. The Hall generator was calibrated with the mapper
gaussmeter at a known radius with a calibrated power supply. The measured gradients
as a function of current for one quadrupole are shown in Figure 5.3. Each quadrupole
will have its own calibration of gradient versus current (by reference to the cryogenic
Hall generator). The cold Hall generator voltage and field gradient versus current for

one of the magnets is given in Table 5.3.

5.4 Magnetic field analysis of the $800 beamline
quadrupoles

Since the S800 beamline magnets are large versions of the NSCL’s standard beamline
magnets which are cold iron, iron dominated superconducting magnets, they differ

from Panofsky and C0820 in that the field shaping is done primarily by iron poles.

92

1
,, I17 1, .1 7,1
1111111111
II,1,777777II 1,
37,;11:7\\\
117,7I17‘I
77’1,,‘01,1“,1\“’ ”II/7 77”! ’I
’II” ”’17’

\l
1771 777, 77711777 77,
7 7717,, 7717777771 177171,,“ 1111
77777777 N.7,77777 77777,, 77777771777777
7717777717,,7

. 77
7717137777711,
\‘1/77

1“ \ 7, I117,‘/
{177 “1 7,, 1 .111,
,I.‘,1 \ 3771/ 11,
777777 ,777777777777777711377 71 11,, 1“ 7,77 7,17 711177777177,
77777 777,771,,71,:,\,‘7‘,17‘,77.777, \,‘,77777777’I7777,I,
\\\\l 77““, $1777II7’3’ I1I1777’ 7 ’ / ”’ , \li”””’ II’II”

I“ ’I ‘ \ \)

"7'71 ”I” \,1

77,11

 

Figure 5.2: The radial component of the magnetic field for the triplet when the
currents for the three quadrupoles are 5, 15 and 10 A respectively.

 

Gradient (T/m)

 

 

 

I If I I I T
5 IO 15 20 25 30 .35 4O 45
Current (A)

Figure 5.3: The gradient produced in a quadrupole as a function of current.

Table 5.3: The Hall generator voltages and gradients of a S800 beamline quadrupole

as function of current.

93

 

 

 

 

 

 

Power Supply (A) Shunt Current Hall Generator Gradient (T/m)
Current (A) (A) Voltage (V) (T/m)
5.0 5.164 1.261 4.484
10.0 10.130 2.342 8.525
15.0 15.114 3.279 12.519
17.0 17.098 3.601 14.023
20.0 20.084 4.029 16.128
23.0 23.070 4.379 18.021
25.0 25.062 4.571 19.114
27.0 27.052 4.740 20.046
30.0 30.032 4.904 21.350
32.0 32.024 5.035 22.032
35.0 35.008 5.158 23.088
37.0 36.996 5.289 23.755
39.0 38.990 5.380 24.411
40.0 39.982 5.405 24.730
41.0 40.972 5.434 25.043
42.0 41.972 5.476 25.360
43.0 42.534 5.507 25.536

 

 

94

Effective Length for 8800 Beamline Quadrupole
45 l l l l l l l l

 

44- —

A43 "‘ '-
E

0
v

442.. _.

 

 

 

 

4O

_4

T l

T T l l l
o 5 1o 15 20(§5 30 35 4o 45
| A

Figure 5.4: The effective length of the 8800 beamline quadrupole as a function of
current.

The effective length of the S800 beamline quadrupoles as a function of current is

shown in Figure 5.4.

The radial component of magnetic field at the center is shown in Figure 5.5.
Figure 5.6 shows a map and the harmonic content at a radius of 7.43 cm. The
sextupole error is about 0.3 parts in a thousand of the quadrupole field. Note that
only the N=6 and 10 terms are theoretically allowed, and the rest of the terms must

result from construction errors, and /or mapper errors.

5.5 Q1, Q2 and sextupole magnet field mapping

The Q1, Q2 and sextupole magnets are mapped by using the same mapper. A z-
axis step of 1 cm requires 180 revolutions in order adequately measure the length
of the Q1, Q2 and sextupole magnets and fringe fields. A one degree map takes 43

hours to complete, with the mapping process requiring minimal operator supervision.

95

Magnetic Field Hormonic Anolysis
1.5 l l l l l l l

 

1.0 - —

0.5 -l _

0.0 d '-

Br (T)

—O.5 — '-

 

 

 

—1.5 I r

l l l j l
O 45 90 135 180 225 270 315 360
Q (degree)

Figure 5.5: The radial component of magnetic field at the center at a radius of 7.43
cm.

Mognetic Field Hormonic Anolysis

 

 

 

050 l l l l l l
a?
V 0.25“ _
m
a)
.0
.3
2;; 0.00 m m m ® m m
<
a)
.2
:6 —o.254 -
a)
QC
-O.5O l l l T l

 

 

j
3 4 5 6 7 8 9 10
Hormonic Number

Figure 5.6: Fourier analysis of the radial component of the field in Figure 5.5.

96

Table 5.4: Mapping Time and File Size for the Q1 / Q2 Doublet.

 

Parameter 1°Steps 2°Steps 3°Steps

 

Doublet Mapping Time 43 hours 29 hours 14 hours

Data File Size 2.7 MB 1.8 MB 0.9 MB

 

Table 5.4 listed mapping time and file size for the Q1 / Q2 doublet.

Maps for different sets of currents have been done. Figure 5.7 shows the radial
component of the magnetic field for the Q1 / Q2 quadrupole doublet when the currents
for the doublet are 84 and 70 A respectively. On two poles of the Q1 and Q2 magnets
a cryogenic Hall Generator was calibrated with the mapper gaussmeter at a known
radius with a calibrated power supply. Each quadrupole has its own calibration of
gradient versus current (by reference to the cryogenic Hall generator). Table 5.5 and

Table 5.6 lists the power supply current, shunt current, cryogenic Hall voltage and

field gradient for Q1 and Q2.

The sextupole was mapped when the Q1 and Q2 magnets were on or off. F ig-
ure 5.8 shows the radial component of the magnetic field of the sextupole magnet
when the currents of Q1 and Q2 are zero. Table 5.7 shows the sextupole shunt cur-

rents, cryogenic Hall generator voltages and field strengths for different power supply

currents.

5.6 Magnetic field analysis of Q1, Q2 and the sex-
tupole

The Q1 and Q2 magnet gradients have been measured using the quadrupole map-

per [Zh97]. Figure 5.9 and Figure 5.10 show the gradient differences between the

97

0”,,“ I,‘.‘:\

['6‘ \l\\ \
lI/,III,:I,0:\ \\\\\l\\\w\\\\ \\
’I’"Inl‘\\\ ‘llll
WI,’I”\\\\
In" Ml) I
“Chi‘ENIoI'I I W“ 0‘
\ I ’I H“ N
:S\\\\‘\‘ H...” III], ”I; o \\ \\\\\\\\\\
\\\\\H IIIIIII ‘\l\\S\l\\\\ \ll ,
,“lhl‘l III,’ I W\\ \\\\\\\ \
I’II ’I’Il'“ \\\\ \l
,I, 11,,II, I, 09‘“ S\“\\\l\:\\\

,II, III
‘u’I II

“I I‘ll
IIIIIIIII
\M‘l‘“ \\ IIII

‘\ \l\ ,1:\\\\\\“”Ill

 

Figure 5.7: The radial component of the magnetic field for the Q1 / Q2 doublet when
the currents for Q1 and Q2 are 84 and 70 A respectively.

Table 5.5: The measurements of Q1 shunt current, cryogenic Hall generator voltage
and field gradient.

 

 

Power Supply Shunt A Hall Generator B Hall Generator Gradient

Current(A) Current(A) Voltage (V) Voltage (V) (T/m)
9.200 10.005 0.972 0.973 2.955—
19.500 20.006 1.941 1.936 5.906
29.600 30.006 2.912 2.898 8.848
34.700 35.002 3.393 3.375 10.240
40.100 40.008 3.863 3.840 11.734
45.200 45.009 4.313 4.284 13.100
50.200 50.003 4.727 4.695 14.354
55.300 55.000 5.058 5.026 15.380
60.500 60.003 5.331 5.291 16.257
65.500 65.006 5.563 5.522 17.050
70.600 70.012 5.784 5.735 17.787
80.800 80.049 6.201 6.146 19.143
85.800 85.036 6.394 6.332 19.772

 

 

 

 

 

 

 

98

Table 5.6: The measurements of Q2 shunt current, cryogenic Hall generator voltage
and field gradient.

 

 

Power Supply Shunt A Hall Generator B Hall Generator Gradient
Current(A) Current(A) Voltage (V) Voltage (V) (T/m)
9.800 10.008 0.597 0.582 1.216
19.800 20.000 1.162 1.124 2.423
29.800 30.008 1.676 1.623 3.517
34.800 35.003 1.898 1.839 3.985
39.800 40.009 2.094 2.029 4.397
44.900 45.010 2.281 2.210 4.785
49.900 50.000 2.462 2.386 5.158
54.900 55.000 2.640 2.559 5.519
59.900 60.012 2.814 2.729 5.869
64.900 65.010 2.984 2.894 6.203
70.000 70.015 3.144 3.049 6.511
80.000 80.000 3.420 3.318 7.046
90.050 90.007 3.666 3.557 7.534

 

 

 

 

 

 

 

   
  

    
     
  
 

0“” “l‘
4598“ \\

      
  

     
    
     

111 \“ \“‘\
. , \l“““\ “‘1
“‘1, llll,‘3‘\ll\\\“ll\l<;ss:szs§
‘11; 11:1 I‘ M 11‘)

   

 
 

   

‘0‘:
.W‘
::o..

   
  

9» \\\\\l“;1}l
“4,111 ”III/I

Figure 5.8: The radial component of the magnetic field for the sextupole when the
sextupole current is 3 A, Q1 and Q2 are off.

99

Table 5.7: The measurements of the sextupole shunt current, cryogenic Hall generator
voltages and field gradient.

 

 

 

 

 

 

 

PS Shunt A Hall Generator B Hall Generator Sextupole
I (A) I (A) Voltage (V) Voltage (V) strength (T/mz)
1.350 1.001 0.100 0.040 0.829
2.800 2.005 0.167 0.146 1.642
4.280 3.002 0.234 0.169 2.468
5.740 4.002 0.302 0.234 3.281
7.200 5.002 0.369 0.299 4.107
8.660 6.002 0.437 0.364 4.920
10.140 7.001 0.504 0.429 5.733
11.600 8.003 0.572 0.494 6.546
13.070 9.002 0.639 0.559 7.359
14.540 10.000 0.707 0.624 8.172

 

 

measurements and TOSCA calculations. The results of the mapping indicate that
the magnets are in close agreement with TOSCA model predictions and the required

specification for the 3800 spectrometer.

The measured and TOSCA calculations of the effective lengths as a function of the
gradients are shown in Figure 5.11 and Figure 5.12. The effective lengths of Q1 and
Q2 decrease when the magnetic fields increase like beamline quads, the Q1 effective
length differs by less a 1 % from the TOSCA calculations. For Q2 the effective length

has a 2 % difference at low field, but gives close agreement at high currents.

For an ideal quadrupole, Br; would increase linearly with r and would have no
2 dependence inside the magnet. Outside the magnet, B7,; would be zero. Br,“
would be zero everywhere for n¢2. However, there is always a gradual decrease
in the field near the end of the magnet. It is not possible to completely remove
every higher order multipole. Figure 5.13 and Figure 5.14 show the harmonic content
at the center and end of Q1 and Q2 at a radius of 8.8 cm. Note that only N=6

and 10 terms are theoretically allowed, and the rest of the terms must result from

100

‘LN
O
_
._
_
_
_.
__
_

 

[‘3
01
l
r

!\>

O
1
l

b
l
r

Gradient Difference (7o)
63
l
l

.O

U'1
1
I

 

 

.0
o

 

T l l l l l l
10 20 3O 4O 50 60 7O 80
01 Current (A)

0

Figure 5.9: The Q1 gradient differences between the measurements and TOSCA

calculations versus current.

 

30 l l l 1 l 1 L l
g 2.5 - -
0) I
g 2.0- —
8
m
g; 15- —
Q
E 1.0— r
'6
E
o 0.5- F
0.0 T

 

 

 

l l l l I l T
O 10 20 3O 4O 50 60 7O 80 90
02 Current (A)

Figure 5.10: The Q2 gradient differences between the measurements and TOSCA

calculations VCI'SllS current.

101

 

 

 

 

45 4 1 1
E? -—.—- MEASURED
044* ~
v + TOSCA
5

943— —
Q)
_l

(1)
E424 —
U
.93
C]
_ 41 4 —
O

40 1 l l

O 5 10 15 2O

01 Gradient (T/m)

Figure 5.11: The Q1 effective length differences between the field measurements and
TOSCA calculations versus gradient.

 

 

 

 

47 1 l L
846% + MEASURED _
V + TOSCA
:E
945— _
(I)
_J
3
'5 44 — b
O
.93
:3 L—
N 43 —
O

42 i l i

0.0 2.5 5.0 7.5 10.0

02 Gradient (T/m)

Figure 5.12: The Q2 effective length differences between the field measurements and
TOSCA calculations versus gradient.

102

construction errors, or mapper errors. The N=6 terms at center of the magnets have
big differences with those terms at end of the magnets. This is due to the coil return
at ends which introduces significant higher order multipoles in the magnetic field.
Fig. 5.15 and Fig. 5.17 show the various multipole components as a function of z,
the field inside the Q1 and Q2 magnets is dominated by straight section of the coils,
producing an almost pure quadrupole field. Near the ends of the Q1 and Q2 magnets,
the higher order multipole fields increase greatly in strength. We have plotted the
integrals of these functions in Fig. 5.16 and Fig. 5.18, integrated up to the plotted
value of z, to show their convergence. Note that these components change sign at
the ends of the Q1 and Q2 magnet iron, yielding a significant cancellation effect
in the final field integral. Table 5.8 shows the peak multipole components and the
integrated multipole components for the Q1 magnet current of 80 A and Q2 magnet
current of 90 A. Table 5.9 and Table 5.10 list the multipole components of Q1 and
Q2 for different currents. When the currents of the Q1 and Q2 magnets change, the
sextupole, octupole and decapole components remain almost constant. However, the
dodecapole components are strongly current dependant and are much larger at the

ends of the magnets than at their centers.

We also mapped Q2 with the sextupole magnet on and off. Fig. 5.19 shows the
multipole components for Q2 and the sextupole magnet at center of the magnets. As
can be seen the sextupole magnet does not disturb the Q2 field, but does allow the

addition of an n=3 component, as needed.

During mapping process, the field interaction between Q1 and Q2 has been mea-
sured. The field at the center of each magnet is independent of the other throughout

the whole dynamic range.

The contribution to the magnetic field uncertainties from the mapping apparatus

have been studied. The major error source likely comes from mapper/magnet mis-

103

 

Center
7 End

Q1 Relative Amplitudes (%)

 

 

 

5 6 7 8 9 1O
Harmonic Number

Figure 5.13: Fourier analysis of the radial component of the field in Q1 magnet at I
= 45 A.

alignment. When we installed the mapper into the Q1 / Q2 doublet, alignment was
done using as optical transit. However, mapper/magnet alignment was extremely
difficult and the difference between centers of less than :l: 0.0127 cm could not be
achieved. This error produces 0.1 % systematic error. Also, the Hall probe' is tem-
perature dependent with a temperature coefficient of i 0.02%/ C [Bell]. Once the
mapper achieved thermal equilibrium in the bore of the doublet it changed little dur-
ing mapping process. Therefore the relative contributions are very small, this does,

however, limit the absolute field calibration of the magnets to d: 0.04%.

 

104

 

0.4

o
a
1

Center
End

\\\\\\\‘ \\
//// //

\\\\
W/fl/

02 Relative Amplitudes (%)
_o o
d N
l
\\\\\\\\\\ \\\\
/%////’/////// ////4/////////

/’.,///

 

 

 

2
2
/
%

4W%

0 / w , ,,, , ,, :~, , .
3 4 5 6 7 8 9 1O
Harmonic Number

Figure 5.14: Fourier analysis of the radial component of the field at the center and
end of Q2 at I = 45 A.

Table 5.8: Q1 and Q2 multipole analysis results at a radius of 8.8 cm.

 

 

 

Q1 (1:80 A) Q2 (1:90 A)

11 Max Q," 1 (T) f; B.,,.dz(:r . m) Max | B.,,. | (T) ff, 3,..sz . m)
2 1.687 0.685 0.663 0.286

3 2.8 )»:10"'3 -4.4 x10“ 1.9 ><10’3 7.9 x10“

4 2.6 x10"3 -2.9 x10“ 7.4 x10" 2.0 x10“

5 2.0 ><10'3 -6.0 x10“ 2.9 x10“ 1.2 x10“

6 7.1 x10"3 -9.9 x10“ 1.1 x10'3 1.3 x10“

10 1.8 x10‘3 -2.5 x10“ 1.3 x10“ 4.4 ><10'5

14 2.2 ><10"4 1.4 x10‘5 1.2 X10'4 4.0 X10'5

 

 

 

 

 

 

 

105

Q1 data analysis

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.0 I I I Y 0.0“ I I T I
0.002
1.5 '- -
0.000 ‘
E E
51.0 >- ‘ ‘-0.002
m m
-0.004
0.5 '- a
-0.006
0.0 ‘ ‘ 4 -0.008 1 1 l '
0.0 0.2 4 0. 0 8 1 0 0.0 0 2 0.4 0.0 0.8 1.0
2 (m) z (m)
5 T V I f 2 fl 1 I I
0 1 - -‘
f‘ f‘
° 2
a _5 .. u 5 o -
E—m e . 5-1 + .
a. 2!
In" a:
_15 p- -1 —2 r- -
_20 1 _1 _L 1 _ 1 l l J—
0.0 0 0.4 0. 0 8 1 0 0.0 0 0.4 0.6 0.8 1 0
Z (11:) 2 (m)

Figure 5.15: Multipole components of the Q1 radial field for the quadrupole (n=2)
term and the first three allowed terms (n=6,10 and 14) are plotted as functions of z,
the distance along the beamline axis at r = 8.8 cm and I = 80 A.

106

Q1 data analysis

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7 T ‘1 I 2 T I T l
.8 " "f 7" 0 _ _
S
A .5 _ -«
E 5 _2 h- -(
‘54 ~ ~ A
N a '4 " ‘1
“‘1 3 r 4 3:
m.‘ u —e l- -1
'U
s. .2 - « 1,
a:
1 E — s ‘3 F ‘
o g 1 1 _lo 1 1 1
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
Z (m) Z (111)
5 T T I T 3 I fir fi I
F — _‘ A
N N
V _5 _- _‘ V
E—10 r a
£3 E:
N a 0 ‘
'U—15 ,. —< '6
g 3.
“:20 ~ - an“
'\ \
_25 1 1 1 1 _2 1 1 1 1
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
Z (m) 2 (m)

Figure 5.16: Integrated multipole component of the Q1 radial field f0” bmdz for n=2,
6, 10 and 14 at r = 8.8 cm and I: 80 A.

107

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

analys1s
lo I T r T I
s — 1
r
E -5 - 1
:
Q
-10 1 1 1 1 L
0 0 0.2 0 4 0.0 0.8 1.0 1.2
2 (In)
14 Y T I I T 12
12 10 a
10 a 8 -‘
s c
3 a i 3 ° ‘
6 .4 A ‘ ..
E 4 5 2 '1
a as
m 2 -< fl 0 -4
o 1 -2 -
_2 _‘ l l l l l
0.0 0.2 0 4 0.8 1.0 1.2 0.0 0.2 0.4 0.8 1.0 1.2

0.6
2 (m)

Figure 5.17: Multipole components of the Q2 radial field for the quadrupole (n=2)
term and the first three allowed terms (n=6,10 and 14) are plotted as functions of z,
the distance along the beamline axis at r = 8.8 cm and I = 90 A.

108

Q2 data analysis

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.05 T I I I I 15 I I I j j
0.00 " g‘
lg 10 .. _1
E -0.05 ‘ 5
‘3 -0.10 - E 5 f 7
S :—
2-0.15 " v _O _‘
m N
~. —o.2o - "’q
m" -5 ~ A
—O.25 -‘ H
-0.30 ---10 1 1 1 1 1
12 0 0 0.2 0 4 0.8 0.8 1.0 1.2
2 (m)
5 I T I I I 5 I I r I I
1" 4 q 7" 4 ~ J
9. 2
X N
V V 3 ,_ .1
A3 '1 A
a e 2 L _
E: E:
2 .1
S S 1 - .
mcl a m”- .
‘1 K‘ 0
o _1 k L 1 1 1
0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0 8 10 1.2
2 (m) 2 (m)

Figure 5.18: Integrated multipole component of the Q2 radial field I; bundz for n=2,
6,10 and 14 at r = 8.8 cm and I = 90 A.

Table 5.9: Harmonic components of the field at the center and end of Q1 at a radius

109

of 8.8 cm for several currents. The numbers are defined by Bn/Bz in ‘70.

 

 

 

 

 

 

 

 

 

 

 

 

n=3 n=4 n=5 n=6

Current (A) Center End Center End Center End Center End
10 0.097 0.107 0.135 0.107 0.117 0.172 0.263 2.571

20 0.108 0.131 0.124 0.166 0.099 0.156 0.256 2.553

32.5 0.124 0.165 0.128 0.175 0.121 0.173 0.270 2.291

45 0.093 0.154 0.093 0.234 0.095 0.149 0.278 1.626

57.5 0.100 0.179 0.106 0.235 0.103 0.180 0.255 1.093

70 0.080 0.149 0.077 0.282 0.075 0.153 0.155 0.701

80 0.082 0.134 0.044 0.295 0.095 0.180 0.139 0.432

 

Table 5.10: Harmonic components of the field at the center and end of Q2 at a radius

of 8.8 cm for several currents. The numbers are defined by Bn/Bz in %.

 

 

 

 

 

 

 

 

 

 

 

 

n=3 n=4 n=5 n=6
Current (A) Center End Center End Center End Center End
10 0.271 0.307 0.053 0.073 0.074 0.059 0.026 0.192
20 0.233 0.295 0.022 0.033 0.036 0.036 0.005 0.175
32.5 0.318 0.367 0.074 0.094 0.058 0.068 0.015 0.167
45 0.277 0.347 0.049 0.066 0.064 0.067 0.025 0.162
57.5 0.321 0.383 0.078 0.107 0.058 0.081 0.020 0.145
70 0.257 0.327 0.030 0.060 0.042 0.043 0.049 0.112
80 0.256 0.338 0.018 0.067 0.043 0.046 0.052 0.111
90 0.285 0.370 0.024 0.065 0.063 0.055 0.054 0.091

 

 

 

110

 

 
 

 
 

 

 

 

5
§
7; 4 *- s
m § 0
'5 § the sextupole magnet IS off
= _. § .
CE:- 3 § the sextupole magnet IS on
< s
o §
.2 2 — §
‘6 s
a s
1:: §
N l 7 §
0 §
\
a
o / l§ 4L 1 _1_ 1

3 4 5 6 7 8 9 1O
Harmonic Number

Figure 5.19: The Q2 and sextupole magnet multipole components at center of the
magnets at 102 = 70A and Lamp“, = 3A.

Chapter 6

Conclusion

This thesis describes the characteristics of the superconducting magnets for the NSCL
spectrometer. In order to study the properties of the single particle states popu-
lated in reactions, the $800 spectrometer with energy resolution E/AE of 10,000 has
been designed and constructed. The spectrometer design is based on a quadrupole-
quadrupole-dipole-dipole layout and computer-optimized magnetic fields. The spec-
trometer magnets, along with the beam analysis line magnets, are superconducting

magnets. The decision to use superconducting magnets was based on a cost analysis.

Considerable consideration went into the design and construction of the S800
dipole magnets. A two dimensional computer code has been used for the dipole
design. To achieve the spectrometer requirements with the least amount of iron two
features have been added to the basic H-frame magnet for the dipoles: The addition
of resistive trim coils attached to the pole tip and at the median plane and the use of
a tapered air gap behind the pole tip. The construction of the 8800 dipole magnets
with a negative side went well and the dipoles have achieved their design goals. The
cryostable coils consist of 350 turns each and operate at 500 A. Both dipoles (D1 and
D2) have been operated at full field. The forces on the D1 and D2 links are well within
operational limits and are close to the calculated values. Detailed mapping of the S800

dipole magnets was performed using special mapping systems. The dipole mapping

111

112

system was based on the induced emf in a moving search coil. The deviations of the

field gradients are less than 1 Gauss / cm, the spectrometer design requirements.

Two high gradient, large aperture quadrupoles (Q1 and Q2), for use as spectrom-
eter elements, have been designed and constructed. Three basic type quadrupoles
were considered for the design: a) cos(20) type, where the field is shaped by the coil,
b) Panofsky type, which is a square or rectangular current sheet approximation, and
c) iron dominated type, where the iron pole tip primarily shapes the field. We de-
cided against the cos(20) quadrupoles because of the high current operation and its
helium requirements. We also investigated superconducting Panofsky quadrupoles.
A Panofsky design was not chosen due to the sensitivity of the field quality to errors
in conductor placement and construction problem. From these studies and from ex-

perience with our standard beamline quadrupoles the iron dominated type had been

chosen for Q1 and Q2.

This thesis presents the magnetic field calculations for Q1, Q2 and the sextupole
using two- and three-dimensional computer codes. The individual maltipole compo—
nents are extracted using a straightforward Fourier analysis. TOSCA was used to
compute the total magnetic force on each coil. The code QUENCH was used to eval-
uate the quench behavior of these magnets. The calculations for these potted coils

indicate that they are still conservatively designed.

All coils of Q1, Q2 and the sextupole are random and wet wound with epoxy on a
simple winding table. After curing, the coils of Q1 and Q2 are shimmed against the
poles tip first, then against each other by using titanium and G-10 spacers. Both Q1
and Q2 have cryogenic Hall generators mounted on the pole tips, to allow setting the
magnetic field. Before being put into the liquid helium container, Q1 and Q2 were
rigidly connected together so that alignment was maintained. The sextupole coils are

held in position with G-10 spacers and stainless steel bands. Q1 and Q2 have been

113

operated at full field. The measured total heat load on the cryogenic container is 2

Watts, which is consistent with our calculation.

To achieve the required energy resolution and angular resolution for nuclear physics
experiments, the magnetic fields must be accurately known. The quadrupole mapper
consists of a gaussmeter and a dual axis motor controller. The three axis hall probe of
the gaussmeter has been calibrated to absolute field with N MR measurements. Maps
for different sets of currents have been done. The cryogenic Hall generators were
calibrated with the mapper gaussmeter at a known radius with a calibrated power
supply. Each quadrupole has its own calibration of the gradient versus current by

reference to the cryogenic Hall generator.

The results of the mapping indicate that the magnets are in close agreement with
TOSCA models predictions. The integral contribution of the 12-pole of Q1 and Q2
relative to the quadrupole terms, respectively, are 1.4 x10‘3 and 4.5 x10'4. The
sextupole magnet in Q2 operated up to its design value, 5.7 T/m2 , with both Q1

and Q2 magnets running at maximum operation currents.

Initially, the CTI-1400 liquefier (40 l/hr or 100 Watt) alone was available to op-
erate the spectrometer system of D1, D2, Q1 / Q2 doublet, it was impossible to use
continuous feed mode for all magnets due to the elevated pressure in the return gas
stream. It was found that operating D1 and D2 in continuous feed mode and filling
the Q1 / Q2 doublet once daily would allow continuous operation on the order of a week
before having to shut down to replenish liquid in the storage dewar. The estimated
heat load of operating the spectrometer system in continuous feed is approximately
100 Watts. This is the mode of operation since bringing on line a new liquefier which
first produced liquid on Dec. 3, 1996. With the new liquefier in operation the spec-
trometer magnets remain full and at the same time liquid is accumulated in a 2500

liter dewar which is then also used to perform the daily bath filling operation of the

114

S800 beamline magnets.

The S800 spectrometer was completed and commissioned in September 1996.
Without computer software correction, the energy resolution obtained was 1 part
of 5,000. This is a very good value for a first attempt, and within a factor of two of
the design resolution. The quadrupole map data have been processed and processing
continues on the dipole data. The next significant challenge is to use COSY INFIN-
ITY and the measured magnetic field data to determine the coefficients in the ray

reconstruction.

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