Cylindrical harmonic analysis of the magnetic field in the aperture of the superconducting winding of an electromagnet

Authors

DOI:

https://doi.org/10.15587/1729-4061.2018.123607

Keywords:

particle beam, dipole electromagnet, quadrupole winding, cylindrical harmonic, magnetic induction

Abstract

It is of practical interest to create such models of the electromagnetic field of an electromagnet that help correct the mean integral coefficients of the harmonics of magnetic induction by the geometric parameters of the magnet. The aim of the study was to obtain analytical expressions for the coefficients of the mean integral lengths of the cylindrical harmonics of magnetic induction created by the current in the superconducting winding inside the aperture of a dipole or quadrupole direct electromagnet on the basis of the geometric parameters of the winding. The analytical solution found is based on the sectorial spherical harmonics of the internal solution of the Laplace equation for the scalar potential of the magnetic field and allows associating them with a series of polar harmonics. The study shows the proportionality between the mean integral contributions to the magnetic induction, produced by uncharacteristic harmonics, and the mean integral value of the ground field. It has been determined that the contribution to the mean integral values of the harmonics coefficients from the end elements of the winding appears only in the presence of the iron framework as a result of its saturation. The received analytical representations make it possible to calculate necessary correction of geometrical parameters of a current winding when optimizing the magnetic field inside the aperture of dipole and quadrupole electromagnets with given mean integral factors.

Author Biography

Andriy Getman, National Technical University "Kharkiv Polytechnic Institute" Kyrpychova str., 2, Kharkіv, Ukraine, 61002

PhD, Senior Researcher

Department of Theoretical Electrical Engineering

References

  1. Russenschuck, S., Tortschanoff, T. (1994). Mathematical optimization of superconducting accelerator magnets. IEEE Transactions on Magnetics, 30 (5), 3419–3422. doi: 10.1109/20.312673
  2. Russenschuck, S. (2010). Differential Geometry Applied to Coil-End Design. Field computation for accelerator magnets. Wiley-VCH Verlag GmbH & Co. KGaA, 609–636. doi: 10.1002/9783527635467.ch19
  3. Russenschuck, S., Auchmann, B., Perez, J. C., Ramos, D., Fessia, P., Karppinen, M. et. al. (2011). Design Challenges for a Wide-Aperture Insertion Quadrupole Magnet. IEEE Transactions on Applied Superconductivity, 21 (3), 1674–1678. doi: 10.1109/tasc.2011.2105453
  4. Fischer, E., Khodzhibagiyan, H. G., Kovalenko, A. D. (2008). Full Size Model Magnets for the FAIR SIS100 Synchrotron. IEEE Transactions on Applied Superconductivity, 18 (2), 260–263. doi: 10.1109/tasc.2008.922261
  5. Kovalenko, A., Agapov, N., Alfeev, A. et. al. (2008). Full size prototype magnets for heavy ion superconducting synchrotron SIS100 at GSI: status of manufacturing and test at JINR. EPAC’08. Genoa, 2443–2445.
  6. Fischer, E., Schnizer, P., Kurnyshov, R., Schnizer, B., Shcherbakov, P. (2009). Numerical Analysis of the Operation Parameters of Fast Cycling Superconducting Magnets. IEEE Transactions on Applied Superconductivity, 19 (3), 1266–1269. doi: 10.1109/tasc.2009.2018746
  7. Yang, W., Zhang, X., Han, S., Yang, J., Pei, C., Yang, L. et. al. (2014). Magnetic Field Measurement for Synchrotron Dipole Magnets of Heavy-Ion Therapy Facility in Lanzhou. IEEE Transactions on Applied Superconductivity, 24 (3), 1–4. doi: 10.1109/tasc.2013.2289953
  8. Yao, Q. G., Ma, L. Z., Zhang, X. Q., He, Y., Wu, W., Moritz, G. et. al. (2010). Magnetic Field Design of the Dipole for Super-FRS at FAIR. IEEE Transactions on Applied Superconductivity, 20 (3), 172–175. doi: 10.1109/tasc.2009.2038890
  9. Schnizer, P., Schnizer, B., Akishin, P., Fischer, E. (2008). Magnetic Field Analysis for Superferric Accelerator Magnets Using Elliptic Multipoles and Its Advantages. IEEE Transactions on Applied Superconductivity, 18 (2), 1605–1608. doi: 10.1109/tasc.2008.920636
  10. Vanderlinde, J. (2005). Classical electromagnetic theory. Springer, 420. doi: 10.1007/1-4020-2700-1
  11. Wolff, S. (1992). Superconducting accelerator magnet design. AIP Conference Proceedings, 249. doi: 10.1063/1.41989

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Published

2018-02-14

How to Cite

Getman, A. (2018). Cylindrical harmonic analysis of the magnetic field in the aperture of the superconducting winding of an electromagnet. Eastern-European Journal of Enterprise Technologies, 1(5 (91), 4–9. https://doi.org/10.15587/1729-4061.2018.123607

Issue

Section

Applied physics