Abstract
Magnetic field synthesis problems have been discussed at length in scientific literature but they still remain as a topic of research in electrical engineering, physics and medical applications. In these disciplines, there is often a need to design an electromagnetic arrangement which can generate a magnetic field of required distribution. Such an arrangement can also work as an active shield. The aim of an active shield is to generate a specified magnetic field which counteracts the external magnetic fields in a protected region. The idea of active shielding is to construct a suitable arrangement of coils, excited with currents that generate an opposite magnetic field sufficient to cancel out the unwanted external fields. The opposite field must have the same frequency and amplitude as the external field. If the incident field presents a wide bandwidth, the final aim is to generate an opposite field in the same frequency range or at least in a range as large as possible. Two independent methods of magnetic fields synthesis, i.e. iteratively regularized Gauss–Newton method and Genetic Algorithm coupled with Bezier curves-based method, are discussed and compared in this paper.
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References
Ishiyama A, Hondoh M, Ishida N, Onuki T (1989) Optimal design of MRI magnets with magnetic shielding. IEEE Trans Magn 25(2): 1885–1888
Kidane TK, Edelstein WA, Eagan TP, Taracila V, Baig TN, Cheng YuN, Brown RW (2006) Active–passive shielding for MRI acoustic noise reduction: network analysis. IEEE Trans Magn 42(12): 3854–3860
Celozzi S, Araneo R, Lovat G (2008) Electromagnetic shielding. IEEE Press John Wiley, Italy
Ziolkowski M, Gratkowski S (2009) Active, passive and dynamic shielding of static and low frequency magnetic fields. In: XV International Symposium on Theoretical Electrical Engineering ISTET, June 22–24, Lubeck, Germany
Ziolkowski M, Gratkowski S (2011) A comparison of two formulations for magnetic field synthesis on a cylindrical solenoid’s axis. Int J Appl Electromagn Mech (in press)
Sikora R, Purczynski J, Adamiak K (1978) The magnetic field synthesis on a cylinder solenoid axis by means of Tichonov’s regularization method. Archiv fur Elektrotechnik 60: 83–86
Tikhonov AN, Goncharsky AV, Stepanov VV, Yagola AG (1995) Numerical methods for the solution of ill-posed problems. Kluwer Academic Publishers, Dordrecht
Adamiak K (1980) Synthesis of homogeneous magnetic field in internal region of cylindrical solenoid. Archiv fur Elektrotechnik 62: 75–79
Zhou P (1993) Numerical analysis of electromagnetic fields. Springer, Berlin
Adamiak K (1977) Tichonov’s regularization method applied to the magnetic field on a solenoid axis synthesis. Archiv fur Elektrotechnik 59: 19–22
Engl HW, Kugler P (2005) Multidisciplinary methods for analysis optimization and control complex systems. Springer, Berlin. Springer link Chapter: Nonlinear inverse problems: theoretical aspects and some industrial applications, see http://www.ipam.ucla.edu/publications/invtut/invtut_hengl_pkugler.pdf
Doicu A, Schüssler O, Loyola D (2010) Constrained regularization methods for ozone profile retrieval from UV/VIS nadir spectrometers. J Quant Spectrosc Radiat Transf 111: 907–916
Hansen PC (1992) Analysis of discrete ill-posed problems by means of the L-curve. SIAM Rev 34: 561–580
Ziolkowski M, Gratkowski S, Palka R (2009) Solution of three dimensional inverse problem of magnetic induction tomography using Tikhonov regularization method. Int J Appl Electromagn Mech 30: 245–253
Golub GH, Heath M, Wahba G (1978) Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21: 215–223
Park H, Shin S, Lee HA (1999) Tikhonov regularization scheme for system identification of continuous structures. In: Transactions of the 15th International Conference on Structural Mechanics in Reactor Technology (SMiRT-15), Seoul, Korea
Vogel C (1996) Non-convergence of the L-curve regularization parameter selection method. Inverse Probl 12: 535–547
Zeb A, Ingham DB, Lesnic D (2008) The method of fundamental solutions for a biharmonic inverse boundary determination problem. Comput Mech 42: 371–379
Piegl L (1993) Fundamental developments of computer aided geometric design. Academic Press, San Diego
Ziolkowski M, Gratkowski S (2008) Genetic algorithm and Bezier curves based shape optimization of conducting shields for low frequency magnetic fields. IEEE Trans Magn 44: 1086–1089
Haupt RL, Haupt SE (2004) Practical genetic algorithms, 2nd edn. Wiley, New York
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Ziolkowski, M. Comparison of two methods for magnetic field synthesis on a solenoid’s axis. Electr Eng 93, 227–235 (2011). https://doi.org/10.1007/s00202-011-0208-4
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DOI: https://doi.org/10.1007/s00202-011-0208-4