improving the design and analysis of superconducting magnets for particle accelerators thesis

343 Pages·2000·6.4 MB·English

IMPROVING THE DESIGN AND ANALYSIS
OF SUPERCONDUCTING MAGNETS
FOR PARTICLE ACCELERATORS
THESIS
SUBMITTED TO THE
University of Rajasthan
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
(PHYSICS)
by
Ramesh Chandra Gupta
The University of Rajasthan and Brookhaven National Laboratory
Under the supervisions of
Prof. N.K. Sharma
Emeritus Scientist (CSIR)
The University of Rajasthan, Jaipur 302004, INDIA
and
Dr. G.H. Morgan
Senior Scientist
Brookhaven National Laboratory, Upton, NY 11973, USA
November 1996
THESIS
DEDICATED
TO
MY FAMILY
In particular to my wife Manju who always encouraged me
and took care of my obligations towards our children Ankur and Anjeli
while I was busy working on evenings and weekends for several years.
0
SUPERVISOR S CERTIFICATE
This is to certify that the thesis entitled \IMPROVING THE DESIGN AND
ANALYSISOFSUPERCONDUCTINGMAGNETSFORPARTICLEACCEL-
ERATORS" describes the original work done by Ramesh Chandra Gupta, under our
supervision for the degree of Doctor of Philosophy of the University of Rajasthan, Jaipur,
India. Mr. Ramesh Chandra Gupta has ful(cid:12)lled the required formalitiesas per the univer-
sity rules known to us.
(N.K. Sharma)
Emeritus Scientist (CSIR)
Department of Physics
University of Rajasthan
Jaipur 302004 INDIA
(G.H. Morgan)
Senior Scientist
Building 902
Magnet Division
Brookhaven National Laboratory
Upton, NY 11973 USA
ACKNOWLEDGMENTS
It is my honor to use this opportunity to acknowledge Prof. N.K. Sharma for inspiring
me to become a physicist and for providing a basic training in scienti(cid:12)c methods since I
wasin high school. I thank myothersupervisor Dr. G.H.Morganforencouraging metobe
thorough while allowing an independent style of working to be developed. I also thank Dr.
Morgan for spending a large amountof timein criticallyexamining the manuscriptand for
proposing several corrections to it, in particular to chapter 1.
The thesiswasalsoreviewedbyDr. E.Willenwhomadeseveralsuggestionsforwriting
itinaclearerand moreprofessionalmanner. DiscussionswithDr. S. Khan, Dr. G.Morgan
and Dr. P. Thompson were very valuable in developing various techniques presented here.
A signi(cid:12)cant amount of work on RHIC (Relativistic Heavy Ion Collider) magnets has been
done in collaboration with Dr. Thompson and on SSC (Superconducting Super Collider)
magnets with Dr. Morgan.
I also thank Dr. A. Jain and Dr. P. Wanderer for discussions on various topics related
to magnetic measurement, testing and analysis. Most of the test data and several (cid:12)gures
related to test results have been provided by Dr. Jain.
Advice on (cid:12)eld quality improvementsfrom the machine physics point of view was pro-
vided by Dr. H. Hahn, Dr. M. Harrison, Dr. S. Peggs and Dr. J. Wei. A close interaction
between accelerator physicists and magnet builders was important in leading (cid:12)eld quality
improvementsin the direction most critical to the performance of machine.
Discussions with the engineers in RHIC magnet production group, in particular with
Mr. M. Anerella and Mr. E. Kelly, were importantin incorporatingvarious design features
in magnet construction in an e(cid:14)cient manner. Several drawings in this manuscript are
provided by the design o(cid:14)ce.
I would like to thank the University of Rajasthan, Jaipur, India for agreeing to accept
the research work performed at the Brookhaven Nation Laboratory (BNL), USA, towards
a Ph.D. degree after a long gap since completing my M.Sc. course work there. Finally I
would like to thank the RHIC management(Drs. A. Greene, S. Ozaki, P. Wanderer and E.
Willen)at BNL for their continuous support and encouragementtowardsthe completionof
this work. This work was supported by the U.S. Departmentof Energy under contract No.
DE-AC02-76CH00016.
Ramesh Chandra Gupta
LIST OF PUBLICATIONS BY THE CANDIDATE
The following is the list of external publications (i.e. the papers that are published as the
conference proceedings, etc.) whicharerelatedtotheresearchworkdescribed inthisthesis.
A copy of them is attached at the end of the thesis.
I. R.C. Gupta, G.H. Morgan, A Design for a High Field Combined Function Superferric
Magnet, Proceedings of the 1985 Particle Accelerator Conference, Vancouver, Canada;
IEEE Transaction on Nuclear Science, Volume NS-32, Oct 1985, pp. 3687-88 (1985).
II. R.C. Gupta, Modi(cid:12)cations in the AUTOMESH and other POISSON Group Codes,
Proceedings ofthe WorkshopinElectromagneticFieldComputations,Schnectady, NY,
pp. H38-H42 (1986).
III. R.C. Gupta, Improvements in the Mesh Generator of the POISSON Group Codes,
Proceedings of the 1987 Particle Accelerator Conference, Washington DC, pp. 1449-
1451 (1987).
IV. R.C. Gupta, G.H. Morgan, P.A. Thompson, A Single Layer Coil Superconducting
Magnet for SSC, Proceedings of the 1987 Particle Accelerator Conference, Washington
DC, pp. 1413-1415 (1987).
V. R.C. Gupta, G.H. Morgan, P.J. Wanderer, A Comparison of Calculations and Mea-
surements of the Iron Saturation Characteristic of the SSC Design D Dipole Magnet,
Proceedings of the 1987 Particle Accelerator Conference, Washington DC, pp. 1405-
1407 (1987).
VI. R.C. Gupta, G.H. Morgan, Collarless, Close-in, Shaped Iron Aperture Designs for
the SSC Dipole, Proceedings of the 1989 Particle Accelerator Conference, Chicago, pp.
500-502 (1989).
VII. R.C. Gupta, S.A. Kahn and G.H. Morgan, Coil and Iron Design for SSC 50 mm
Magnet, Proceedings of the 1990 American Society of Mechanical Engineers (ASME)
Winter Annual Meeting in Dallas (1990).
VIII. R.C. Gupta, S.A. Kahn and G.H. Morgan, A Comparison of Calculations and Mea-
surements of the Field Harmonics as a Functionof Current in the SSC Dipole Magnets,
Proceedingsofthe1991IEEEParticleAcceleratorConference,SanFrancisco,pp. 42-44
(1991).
IX. R.C. Gupta, et al., RHIC Insertion Magnets, Proceedings of the 1991 IEEE Particle
Accelerator Conference, San Francisco, pp. 2239-2241 (1991).
X. R.C. Gupta, S.A. Kahn and G.H. Morgan,SSC 50 mm Dipole Cross section,Proceed-
rd
ings of the 3 InternationalIndustrial Symposiumon Super Collider(IISSC), Atlanta,
pp. 587-600 (1991).
XI. R.C. Gupta, Correcting Field Harmonics after Design in Superconducting Magnets,
th
Proceedings of the 4 International Industrial Symposium on Super Collider (IISSC),
New Orleans, pp. 773-780 (1992).
XII. R. Gupta, et al., Large Aperture Quadrupoles for RHIC Interaction Regions, Proceed-
ings of the 1993 Particle Accelerator Conference, Washington, D.C., pp. 2745-2747
(1993).
XIII. R.C.Gupta,A.K.Jain,Variationina1 saturationinSSCColliderDipoles,Proceedings
of the 1993 Particle Accelerator Conference, Washington, D.C., pp. 2778-2780 (1993).
XIV. R. Gupta, et al., Field Quality Improvements in Superconducting Magnets for RHIC,
Proceedings of the 1994 European Particle Accelerator Conference, London, UK, pp.
2928-2930 (1994).
XV. R. Gupta, et al., Field Quality Control Through the Production Phase of RHIC Arc
Dipoles, Proceedings of the 1995 International Particle Accelerator Conference, Dallas,
Texas (1995).
XVI. R. Gupta, et al., Tuning Shims for High Field Quality in Superconducting Magnets,
Proceedings of the Fourteenth International Conference on Magnet Technology (MT-
14), Tampere, Finland, June 11-16 (1995).
XVII. A. Jain, R. Gupta, et al., Skew Quadrupole in RHIC Dipole Magnets at High Fields,
Proceedings of the Fourteenth International Conference on Magnet Technology (MT-
14), Tampere, Finland, June 11-16 (1995).
XVIII. R.Gupta,EstimatingandAdjustingFieldQualityinSuperconductingAcceleratorMag-
nets, Proceedings of the LHC CollectiveE(cid:11)ects Workshop, Montreux,1995; Submitted
to the Particle Accelerators (1995).
XIX. R. Gupta, Field Quality in the Superconducting Magnets for Large Particle Accelera-
tors,Proceedingsofthe1996EuropeanParticleAcceleratorConferenceatSitges,Spain
(1996).
i
CONTENTS
1. REVIEW OF THE FIELD . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. Physics Potentials and Goals of RHIC . . . . . . . . . . . . . . . . . . 2
1.3. Overview of RHIC Machine . . . . . . . . . . . . . . . . . . . . . . . 5
1.4. Superconducting Magnets . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4.1. Introduction to the Magnet Geometry . . . . . . . . . . . . . . . 8
1.4.2. Superconducting Cable . . . . . . . . . . . . . . . . . . . . . . 10
1.4.3. Cryogenic System . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4.4. Mechanical Design . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.5. Magnetic Design . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4.6. Magnet Construction . . . . . . . . . . . . . . . . . . . . . . . 16
1.4.7. Magnet Measurements . . . . . . . . . . . . . . . . . . . . . . . 17
1.5. Magnetic Field Analysis in Accelerator Magnets . . . . . . . . . . . . . 22
1.5.1. Basic ElectromagneticField Equations . . . . . . . . . . . . . . . 22
1.5.2. Field Harmonic De(cid:12)nitions . . . . . . . . . . . . . . . . . . . . 26
1.5.3. Analytic Expressions for Accelerator Magnets . . . . . . . . . . . 31
1.5.3.1. Field and Vector Potential due to a Line Current . . . . . . . 31
1.5.3.2. Line Current in a Cylindrical Iron Cavity . . . . . . . . . . . 36
1.5.3.3. Line Current in a Cylindrical Iron Shell . . . . . . . . . . . . 40
1.5.3.4. Field and Harmonics due to Current Blocks in Air . . . . . . 44
1.5.3.5. Field Harmonics due to Current Blocks in a Cylin-
drical Iron Shell . . . . . . . . . . . . . . . . . . . . . . . . 47
1.5.3.6. COS(m(cid:18)) Current Distribution for Ideal Fields . . . . . . . . 48
1.5.3.7. COS(m(cid:18)) Current Distribution in a Cylindrical
Iron Shell . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
1.5.3.8. Intersecting Circles with a Constant Current Densi-
ty for Ideal Fields . . . . . . . . . . . . . . . . . . . . . . . 57
ii
1.5.4. Complex Variable Method in 2-d Magnetic Field Calcula-
tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
1.5.4.1. Field due to an array of Line Currents . . . . . . . . . . . . 62
1.5.4.2. Beth’s Current Sheet Theorem . . . . . . . . . . . . . . . . 63
1.5.4.3. Example { Cos(m (cid:18) ) current distribution . . . . . . . . . . 65
1.6. Methods Investigated for Improving Field Quality . . . . . . . . . . . . 66
1.6.1. Improvementsin the Computationaland Analysis Meth-
ods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
1.6.2. Field Quality Improvementsthrough Yoke Design . . . . . . . . . . 67
1.6.3. Field Quality Improvementsthrough Coil Design . . . . . . . . . . 67
1.6.4. Field Quality Improvementsafter Construction . . . . . . . . . . . 68
1.6.5. Optimized Cross section Designs . . . . . . . . . . . . . . . . . . 69
2. IMPROVEMENTS IN THE COMPUTATIONAL AND ANALYSIS
METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
2.2. Computer Aided Cross-section Measurement and Analysis . . . . . . . . 71
2.3. IMPROVEMENTS IN THE POISSON GROUP CODES . . . . . . . . . 78
2.3.1. Upgraded AUTOMESH { Input Method No. 1 . . . . . . . . . . . 79
2.3.2. Upgraded AUTOMESH { Input Method No. 2 . . . . . . . . . . . 83
2.3.3. Upgraded AUTOMESH { Input Method No. 3 . . . . . . . . . . . 88
2.4. Conclusions on the Improvements in the Computationaland
Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3. FIELD QUALITY IMPROVEMENTS THROUGH YOKE DESIGN . . . . . . 92
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.2. Reduction in Saturation Induced Allowed Harmonics . . . . . . . . . . . 102
3.2.1. Varying the yoke inner radius . . . . . . . . . . . . . . . . . . . 103
3.2.2. Varying the yoke outer radius . . . . . . . . . . . . . . . . . . . 111
3.2.3. Varying the location of the helium bypass hole in the
yoke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
iii
3.2.4. Additional Saturation suppressor holes in the iron yoke . . . . . . . 123
3.2.5. Yoke-yoke alignment keys . . . . . . . . . . . . . . . . . . . . . 129
3.2.6. Yoke collaring keys . . . . . . . . . . . . . . . . . . . . . . . . 132
3.2.7. Tooth at the midplane of the yoke aperture . . . . . . . . . . . . . 135
3.2.8. Cutout or Bump in the iron aperture . . . . . . . . . . . . . . . . 139
3.2.9. Elliptical iron aperture . . . . . . . . . . . . . . . . . . . . . . 145
3.2.10. Two radius aperture yoke . . . . . . . . . . . . . . . . . . . . . 149
3.3. Saturation Induced Allowed Harmonics in RHIC Arc Dipoles . . . . . . . 153
3.4. Reduction in the Saturation-induced Non-allowed Harmonics . . . . . . . 169
3.4.1. b1 saturation | Cross talk . . . . . . . . . . . . . . . . . . . . . 170
3.4.2. a1 saturation | Cryostat and other sources . . . . . . . . . . . . 176
3.5. a1 Saturation in SSC Dipole Magnets . . . . . . . . . . . . . . . . . . 182
3.5.1. (cid:14)a1 variation with axial position within a magnet . . . . . . . . . . 182
3.5.2. Magnet to magnet variations in the integral (cid:14)a1 . . . . . . . . . . 185
3.5.3. Compensation of the saturation induced a1 in SSC mag-
nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
3.6. a1 Saturation in RHIC Dipole Magnets . . . . . . . . . . . . . . . . . 190
3.6.1. Magnet to magnet variation in a1 saturation . . . . . . . . . . . . 190
3.6.2. Reduction in a1 saturation in RHIC dipoles . . . . . . . . . . . . 194
3.7. Conclusions on the Field Quality Improvements through Yoke
Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
4. FIELD QUALITY IMPROVEMENTS THROUGH COIL DESIGN . . . . . . . 206
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
4.2. Sources of Harmonics Allowed by the Magnet Geometry . . . . . . . . . 209
4.3. Reduction in the Allowed Harmonics through Wedges . . . . . . . . . . 210
4.4. Reduction in the Allowed Harmonics in RHIC Arc Dipoles by
Changing the Midplane Gap . . . . . . . . . . . . . . . . . . . . . . 212
4.5. Reduction in b3 in RHIC Quadrupoles with Midplane Gaps . . . . . . . . 214
iv
4.6. Coil Cross-section Iterations without Changing Wedges . . . . . . . . . . 216
4.7. Conclusions on the Field Quality Improvements through Coil
Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
5. FIELD QUALITY IMPROVEMENTS AFTER CONSTRUCTION . . . . . . . 220
5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
5.2. Tuning Shims in Magnet Body for Extra High Field Quality . . . . . . . 222
5.2.1. Tuning Shims in the RHIC Interaction Region
Quadrupoles . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
5.2.2. Tuning Shim and the Magnet Design . . . . . . . . . . . . . . . . 224
5.2.3. Procedure for Implementing the Tuning Shim Correction . . . . . . 227
5.2.4. Calculations for Tuning Shim Corrections . . . . . . . . . . . . . 229
5.2.4.1. Approximate Analytic Expressions for Low Field
Estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
5.2.4.2. Numerical Calculations for Low Field Correction . . . . . . . 233
5.2.4.3. Numerical Calculations for High Field Correction . . . . . . . 243
5.2.5. Symmetriesin the Harmonics Generated by Tuning
Shims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
5.2.6. Independent and Coupled Changes in Harmonics Correc-
tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
5.2.7. Comparison with the Measurements . . . . . . . . . . . . . . . . 250
5.2.8. Tuning Shim Correction Vs. External Correctors . . . . . . . . . . 255
5.3. Tuning Yoke Length at Magnet Ends for Field Correction . . . . . . . . . 258
5.3.1. Yoke Length for Integral a1 Correction . . . . . . . . . . . . . . . 260
5.3.2. Yoke Length for Integral Transfer Function Correction . . . . . . . 262
5.4. Conclusions on the Field Quality Improvements after Construc-
tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
6. OPTIMIZED CROSS SECTION DESIGNS . . . . . . . . . . . . . . . . . . 265
6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
6.2. SSC 50 mmAperture Collider Dipole Magnet Cross-section . . . . . . . . 266