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MAGNETS, FIELDS, AND FORCES

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Case Studies in Superconducting Magnets

In this chapter we study key topics related to magnets, fields, and forces. Magnets treated include: 1) solenoids, single and multiple, e.g., comprised of nested coils; 2) Helmholtz coils and high homogeneity magnets; 3) ideal dipoles; 4) ideal quadrupoles; 5) racetracks; and 6) ideal toroids. Two important solenoidal magnets for the generation of high magnetic fields, "Bitter" and "hybrid," are also discussed. Other issues such as "load lines," minimum volume magnets, superposition techniques, not included in the 1st Edition, are discussed in the PROBLEMS &DISCUSSIONS that follow this introductory section.

At the present time, .eld and force computations are generally performed with computer codes that for a given magnet configuration give accurate numerical solutions at any location. These codes can also compute the self and mutual inductances of coils comprising the magnet and Lorentz forces acting on the coils [3.1]. Analytical expressions derived in this chapter give field values only at specialized locations such as the magnet center; however, they illustrate subtle relationships among fields, forces, and magnet parameters.

In this introductory section, we .rst study the law of Biot-Savart that is basic to computation of a magnetic field generated by a current-carrying element in the absence of magnetic materials. Also presented in this section are rather extensive treatments of: 1) field analysis; 2) axial forces for “rings” and “thin” solenoids; 3) stresses and strains in solenoids; and 4) self and mutual inductances.

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References

  1. Many codes are available, created by individuals and institutions, e.g., SOLDESIGN (M.I.T.), and by commercial outfits, e.g., COMSOL, ANSYS, ANSOFT.

    Google Scholar 

  2. D. Bruce Montgomery, Solenoid Magnet Design (Robert Krieger Publishing, New York, 1980).

    Google Scholar 

  3. R.J. Weggel (personal communication, 1999).

    Google Scholar 

  4. Francis Bitter, Magnets: The Education of a Physicist (Doubleday, New York, 1959).

    Google Scholar 

  5. Milan Wayne Garrett, “Calculation of fields, forces, and mutual inductances of current systems by elliptical integrals,” J. Appl. Phys. 34, 2567 (1963).

    Article  Google Scholar 

  6. Based on a reformulation with new materials by Emanuel Bobrov (FBML) in 2005, with additional contribution by Seung-Yong Hahn (FBML), of a paper by E.S. Bobrov and J.E. Williams, “Stresses in superconducting solenoid” Mechanics of Superconducting Structures, F.C. Moon, Ed. (ASME, New York, 1980), 13–41.

    Google Scholar 

  7. Standard Handbook for Electrical Engineers, Ed. Archer E. Knowlton (McGraw-Hill Book, 1949).

    Google Scholar 

  8. Benjamin J. Haid (personal communication, 2003).

    Google Scholar 

  9. Hans-J. Schneider-Muntau and Mark Bird (personal communication, 2004).

    Google Scholar 

  10. John Peter Voccio, “Qualification of Bi-2223 high-temperature superconducting (HTS) coils for generator applications” (Ph.D. Thesis, Department of System Design Engineering, Keio University, 2007).

    Google Scholar 

  11. D.B. Montgomery, J.E.C. Williams, N.T. Pierce, R. Weggel, and M.J. Leupold, “A high field magnet combining superconductors with water-cooled conductors,” Adv. Cryogenic Eng. 14, 88 (1969).

    Google Scholar 

  12. M.J. Leupold, R.J. Weggel and Y. Iwasa, “Design and operation of 25.4 and 30.1 tesla hybrid magnet systems,”Proc. 6th Int. Conf. Magnet Tech. (MT-6) (ALFA, Bratislava), 400 (1978).

    Google Scholar 

  13. M.J. Leupold, J.R. Hale, Y. Iwasa, L.G. Rubin, and R.J. Weggel, “30 tesla hybrid magnet facility at the Francis Bitter National Magnet Laboratory,” IEEE Trans. Magn. MAG-17, 1779 (1981).

    Article  Google Scholar 

  14. M.J. Leupold, Y. Iwasa and R.J. Weggel, “32 tesla hybrid magnet system,” Proc. 8th Int. Conf. Magnet Tech. (MT-8) (J. Physique Colloque C1, supplément to 45), C1-41 (1984).

    Google Scholar 

  15. M.J. Leupold, Y. Iwasa, J.R. Hale, R.J. Weggel, and K. van Hulst, “Testing a 1.8 K hybrid magnet system,”Proc. 9th Int. Conf. Magnet Tech. (MT-9) (Swiss Institute for Nuclear Research, Villigen), 215 (1986).

    Google Scholar 

  16. M.J. Leupold, Y. Iwasa, and R.J. Weggel, “Hybrid III system,” IEEE Trans. Magn. MAG-24, 1070 (1988).

    Article  Google Scholar 

  17. Y. Iwasa, M.J. Leupold, R.J. Weggel, J.E.C. Williams, and Susumu Itoh, “Hybrid III: the system, test results, the next step,” IEEE Trans. Appl. Superconduc. 3, 58 (1993).

    Article  Google Scholar 

  18. Y. Iwasa, M.G. Baker, J.B. Coffin, S.T. Hannahs, M.J. Leupold, E.J. McNiff, and R.J. Weggel, “Operation of Hybrid III as a facility magnet,” IEEE Trans. Magn. 30, 2162 (1994).

    Article  Google Scholar 

  19. K. van Hulst and J.A.A.J. Perenboom, “Status and development at the High Field Magnet Laboratory of the University of Nijmegen,” IEEE Trans. Magn. 24, 1397 (1988).

    Article  Google Scholar 

  20. Jos A.A.J. Perenboom, Stef A.J. Wiegers, Jan-Kees Maan, Paul H. Frings, “First operation of the 20 MW Nijmegen High Field Magnet Laboratory,” IEEE Trans. Appl. Superconduc. 14, 1276 (2004).

    Article  Google Scholar 

  21. S.A.J. Wiegers, J. Rook, J.A.A.J. Perenboom, and J.C. Maan, “Design of a 50 mm bore 31+ T resistive magnet using a novel cooling hole shape,” IEEE Trans. Appl. Superconduc. 16, 988 (2006).

    Article  Google Scholar 

  22. Y. Nakagawa, K. Noto, A. Hoshi, S. Miura, K. Watanabe and Y. Muto, “Hybrid magnet project at Tohoku University,” Proc. 8th Int. Conf. Magnet Tech. (MT-8) (Supplément au Journal de Physique, FASC. 1), C1-23 (1984).

    Google Scholar 

  23. K. Watanabe, G. Nishijima, S. Awaji, K. Takahashi, K. Koyama, N. Kobayashi, M. Ishizuka, T. Itou, T. Tsurudome, and J. Sakuraba, “Performance of a cryogenfree 30 T-class hybrid magnet,” IEEE Trans. Appl. Superconduc. 16, 934 (2006).

    Article  Google Scholar 

  24. H.-J. Schneider-Muntau and J.C. Vallier, “The Grenoble hybrid magnet,” IEEE Trans. Magn. MAG-24, 1067 (1988).

    Article  Google Scholar 

  25. G. Aubert, F. Debray, J. Dumas, K. Egorov, H. Jongbloets, W. Joss, G. Martinez, E. Mossang, P. Petmezakis, Ph. Sala, C. Trophime, and N. Vidal, “Hybrid and giga-NMR projects at the Grenoble High Magnetic Field,” IEEE Trans. Appl. Superconduc. 14, 1280 (2004).

    Article  Google Scholar 

  26. A. Bonito Oliva, M.N. Biltcliffe, M. Cox, A. Day, S. Fanshawe, G. Harding, G. Howells, W. Joss, L. Ronayette, and R. Wotherspoon, “Preliminary results of final test of the GHMFL 40 T hybrid magnet,” IEEE Trans. Appl. Superconduc. 15, 1311 (2005).

    Article  Google Scholar 

  27. K. Inoue, T. Takeuchi, T. Kiyoshi, K. Itoh, H. Wada, H. Maeda, T. Fujioka, S. Murase, Y. Wachi, S. Hanai, T. Sasaki, “Development of 40 tesla class hybrid magnet system,” IEEE Trans. Magn. 28, 493 (1992).

    Article  Google Scholar 

  28. John R. Miller, “The NHMFL 45-T hybrid magnet system: past, present, and future,” IEEE Trans. Appl. Superconduc. 13, 1385 (2003).

    Article  Google Scholar 

  29. M. Bird, S. Bole, I. Dixon, Y. Eyssa, B. Gao, and H. Schneider-Muntau, “The 45T hybrid insert: recent achievement,” Phys. B, 639 (2001).

    Google Scholar 

  30. J.R. Miller, Y.M. Eyssa, S.D. Sayre and C.A. Luongo, “Analysis of observations during operation of the NHMFL 45-T hybrid magnet systems,” Cryogenics 43, 141 (2003).

    Article  Google Scholar 

  31. J.R. Miller (Personal communication, 2003).

    Google Scholar 

  32. E.S. Bobrov (Personal communication, 2003).

    Google Scholar 

  33. Juan Bascuñán, Emanuel Bobrov, Haigun Lee, and Yukikazu Iwasa, “A low- and high-temperature superconducting (LTS/HTS) NMR magnet: design and performance results,” IEEE Trans. Appl. Superconduc. 13, 1550 (2003).

    Article  Google Scholar 

  34. Haigun Lee, Juan Bascuñán, and Yukikazu Iwasa, “A high-temperature superconducting (HTS) insert comprised of double pancakes for an NMR magnet,” IEEE Trans. Appl. Superconduc. 13, 1546 (2003).

    Article  Google Scholar 

  35. J. Allinger, G. Danby, and J. Jackson, “High field superconducting magnets for accelerators and particle beams,” IEEE Trans. Magn. MAG-11, 463 (1975).

    Article  Google Scholar 

  36. A.D. McInturff, W.B. Sampson, K.E. Robins, P.F. Dahl, R. Damm, D. Kassner, J. Kaugerts, and C. Lasky, “ISABELLE ring magnets,” IEEE Trans. Magn. MAG-13, 275 (1977).

    Article  Google Scholar 

  37. W.B. Fowler, P.V. Livdahl, A.V. Tollestrup, B.F. Strauss, R.E. Peters, M. Kuchnir, R.H. Flora, P. Limon, C. Rode, H. Hinterberger, G. Biallas, K. Koepke, W. Hanson, and R. Borcker, “The technology of producing reliable superconducting dipoles at Fermilab,” IEEE Trans. Magn. MAG-13, 275 (1977).

    Google Scholar 

  38. G. Ambrosio, N. Andreev, E. Barzi, P. Bauer, D.R. Chichili, K. Ewald, S. Feher, L. Imbasciati, V.V. Kashikhin, P.J. Limon, L. Litvinenko, I. Novitski, J.M. Rey, R.M. Scanlan, S. Yadav, R. Yamada, and A.V. Zlobin, “R&D for a single-layer Nb3Sn common coil dipole using the react-and-wind fabrication technique,” IEEE Trans. Appl. Superconduc. 12, 39 (2002).

    Article  Google Scholar 

  39. L. Rossi, “The LHC main dipoles and quadrupoles towards series production,” IEEE Trans. Appl. Superconduc. 13, 1221 (2003).

    Article  Google Scholar 

  40. L. Bottura, D. Leroy, M. Modena, M. Pojer, P. Pugnat, L. Rossi, S. Sanfilippo, A. Siemko, J. Vlogaert, L. Walckiers, and C. Wyss, “Performance of the first LHC pre-series superconducting dipoles,” IEEE Trans. Appl. Superconduc. 13, 1235 (2003).

    Article  Google Scholar 

  41. T Doi, H. Kimura, S. Satō, K. Kuroda, H. Ogata, M. Kudō, and U. Kawabe, “Superconducting saddle shaped magnets,” Cryogenics 8, 290 (1968).

    Article  Google Scholar 

  42. J.L. Smith, Jr., J.L. Kirtley, Jr., P. Thullen, “Superconducting rotating machines,” IEEE Trans. Magn. MAG-11, 128 (1975).

    Article  Google Scholar 

  43. T. Ohara, H. Fukuda, T. Ogawa, K. Shimizu, R. Shobara, M. Ohi, A. Ueda, K. Itoh, and H. Taniguchi, “Development of 70MW class superconducting generators,” IEEE Trans. Magn. 27, 2232 (1991).

    Article  Google Scholar 

  44. J. Kerby, A.V. Zlobin, R. Bossert, J. Brandt, J. Carson, D. Chichili, J. Dimarco, S. Feher, M.J. Lamm, P.J. Limon, A. Makarov, F. Nobrega, I. Novitski, D. Orris, J.P. Ozelis, B. Robotham, G. Sabbi, P. Schlabach, J.B. Strait, M. Tartaglia, J.C. Tompkins, S. Caspi, A.D. McInturff, and R. Scanlan, “Design, development and test of 2 m quadrupole model magnets for the LHC inner triplet,” IEEE Trans. Appl. Superconduc. 9, 689 (1999).

    Article  Google Scholar 

  45. T. Nakamoto, T. Orikasa, Y. Ajima, E.E. Burkhardt, T. Fujii, E. Hagashi, H. Hirano, T. Kanahara, N. Kimura, S. Murai, W. Odajima, T. Ogitsu, N. Ohuchi, O. Oosaki, T. Shintomi, K. Sugita, K. Tanaka, A. Terashima, K. Tsuchiya, and A. Yamamoto, “Fabrication and mechanical behavior of a prototype for the LHC low-beta quadrupole magnets,” IEEE Trans. Appl. Superconduc. 12, 174 (2002).

    Article  Google Scholar 

  46. R. Burgmer, D. Krischel, U. Klein, K. Knitsch, P. Schmidt, T. Trtschanoff, K. Schirm, M. Durante, J.M. Rifflet, and F. Simon, “Industrialization of LHC main quadrupole cold masses up to series production,” IEEE Trans. Appl. Superconduc. 14, 169 (2004).

    Article  Google Scholar 

  47. S.H. Minnich, T.A. Keim, M.V.K. Chari, B.B. Gamble, M.J. Jefferies, D.W. Jones, E.T. Laskaris, P.A. Rios, “Design studies of superconducting generators,” IEEE Trans. Magn. MAG-15, 703 (1979).

    Article  Google Scholar 

  48. A.S. Ying, P.W. Eckels, D.C. Litz, W.G. Moore, “Mechanical and thermal design of the EPRI/Westinghouse 300 MVA superconducting generator,” IEEE Trans. Magn. MAG-17, 894 (1981).

    Article  Google Scholar 

  49. W. Nick, G. Nerowski, H.-W. NeumüllerM. Frank, P. van Hasselt, J. Frauenhofer, and F. Steinmeyer, “380 kW synchronous machine with HTS rotor windings—development at Siemens and first test results,” Physica C: Superconductivity 372–376, 1470 (2002).

    Google Scholar 

  50. Greg Snitchler, Bruce Gamble, and Swarn S. Kalsi, “The performance of a 5 MW high temperature superconductor ship propulsion motor,” IEEE Trans. Appl. Superconduc. 15, 2206 (2005).

    Article  Google Scholar 

  51. H. Ichikawa and H. Ogiwara, “Design considerations of superconducting magnets as a Maglev pad,” IEEE Trans. Magn. MAG-10, 1099 (1974).

    Article  Google Scholar 

  52. Bruce Gamble, David Cope, and Eddie Leung, “Design of a superconducting magnet system for Maglev applications,” IEEE Trans. Appl. Superconduc. 3, 434 (1993).

    Article  Google Scholar 

  53. Kenji Tasaki, Kotaro Marukawa, Satoshi Hanai, Taizo Tosaka, Toru Kuriyama, Tomohisa Yamashita, Yasuto Yanase, Mutuhiko Yamaji, Hiroyuki Nako, Motohiro Igarashi, Shigehisa Kusada, Kaoru Nemoto, Satoshi Hirano, Katsuyuki Kuwano, Takeshi Okutomi, and Motoaki Terai, “HTS magnet for Maglev applications (1)— coil characteristics,” IEEE Trans. Appl. Superconduc. 16, 2206 (2006).

    Article  Google Scholar 

  54. A. den Ouden, W.A.J. Wessel, G.A. Kirby, T. Taylor, N. Siegel, and H.H.J. ten Kate, “Progress in the development of an 88-mm bore 10 T Nb3Sn dipole magnet,” IEEE Trans. Appl. Superconduc. 11, 2268 (2001).

    Article  Google Scholar 

  55. G. Ambrosio, N. Andreev, S. Caspi, K. Chow, V.V. Kashikhin, I. Terechkine, M. Wake, S. Yadav, R. Yamada, A.V. Zlobin, “Magnet design of the Fermilab 11 T Nb3Sn short dipole model,” IEEE Trans. Appl. Superconduc. 10, 322 (2000).

    Article  Google Scholar 

  56. A.R. Hafalia, S.E. Bartlett, S. Caspi, L. Chiesa, D.R. Dietderich, P. Ferracin, M. Goli, S.A. Gourlay, C.R. Hannaford, H. Higley, A.F. Lietzke, N. Liggins, S. Mattafirri, A.D. McInturff, M. Nyman, G.L. Sabbi, R.M. Scanlan, and J. Swanson, “HD 1: design and fabrication of a 16 tesla Nb3Sn dipole magnet” IEEE Trans. Appl. Superconduc. 14, 283 (2004).

    Article  Google Scholar 

  57. J.E.C. Williams, L.J. Neuringer, E.S. Bobrov, R. Weggel, and W.G. Harrison, “Magnet system of the 500 MHz spectrometer at the FBNML: 1. Design and development of the magnet,” Rev. Sci. Instrum. 52, 649 (1981).

    Article  Google Scholar 

  58. Haigun Lee, Emanuel S. Bobrov, Juan Bascuñán, Seung-yong Hahn and Yukikazu Iwasa, “An HTS insert for Phase 2 of a 3-phase 1-GHz LTS/HTS NMR magnet,” IEEE Trans. Appl. Superconduc. 15. 1299 (2005).

    Article  Google Scholar 

  59. Juan Bascuñán, Wooseok Kim, Seungyong Hahn, Emanuel S. Bobrov, Haigun Lee, and Yukikazu Iwasa, “An LTS/HTS NMR magnet operated in the range 600–700 MHz,” IEEE Tran. Appl. Superconduc. 17, 1446 (2007).

    Article  Google Scholar 

  60. D.S. Easton, D.M. Kroeger, W. Specking, and C.C. Koch, “A prediction of the stress state in Nb3Sn superconducting composites,” J. Appl. Phys. 51, 2748 (1980).

    Article  Google Scholar 

  61. J.W. Ekin, “Strain scaling law for flux pinning in practical superconductors. Part 1: Basic relationship and application to Nb3Sn conductors,” Cryogenics 20, 611 (1980).

    Article  Google Scholar 

  62. J.W. Ekin, “Four-dimensional J-B-T-ε critical surface for superconductors,” J. Appl. Phys. 54, 303 (1983).

    Article  Google Scholar 

  63. S.L. Bray, J.W. Ekin, and C.C. Clickner, “Transverse compressive stress effects on the critical current of Bi-2223/Ag tapes reinforced with pure Ag and oxide-dispersion-strengthened Ag, J. Appl. Phys. 88, 1178 (2000).

    Article  Google Scholar 

  64. J.W. Ekin, S.L. Bray, N. Cheggour, C.C. Clickner, S.R. Foltyn, P.N. Arendt, A.A. Polyanskii, D.C. Larbalestier and C.N. McCowan, “Transverse stress and fatigue effects in Y-Ba-Cu-O coated IBAD tapes,” IEEE Trans. Appl. Superconduc. 11, 3389 (2001).

    Article  Google Scholar 

  65. F. Bitter, “The design of powerful electromagnets Part IV. The new magnet laboratory at M.I.T.,” Rev. Sci. Inst. 10, 373 (1939).

    Article  Google Scholar 

  66. George R. Harrison and Francis Bitter, “Zeeman effects in complex spectra at fields up to 100,000 gauss,” Phys. Rev. 57, 15 (1940).

    Article  Google Scholar 

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  1. Francis Bitter Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, MA, USA

    Yukikazu Iwasa

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Iwasa, Y. (2009). MAGNETS, FIELDS, AND FORCES. In: Case Studies in Superconducting Magnets. Springer, Boston, MA. https://doi.org/10.1007/b112047_3

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  • DOI: https://doi.org/10.1007/b112047_3

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