Synthesis of the magnetic field using transversal 3D coil system


  • Bartlomiej Garda AGH University of Science and Technology 30 Mickiewicza Av. 30-059 Krakow Poland
  • Zbigniew Galias


Magnetic field is usually generated using magnets realized as a set of simple coils. In general, those magnets generate magnetic field with nonzero components in all directions. Usually during the design process only one component of the magnetic field is taken into account, and in the optimisation procedure the currents and positions of simple coils are found to minimize the error between the axial component of the magnetic field and the required magnetic field in the ROI. In this work, it is shown that if the high quality homogeneous magnetic field is generated then indeed one may neglect non-axial components. On the other hand, if the obtained magnetic field is not homogeneous either due to design requirements of too restrictive constrains, then all other components may severely deteriorate the quality of the magnetic field. In the second part of the paper, we show how to design a 3D transversal coil system to solve problems which are intractable in the 1D case.

Author Biography

Bartlomiej Garda, AGH University of Science and Technology 30 Mickiewicza Av. 30-059 Krakow Poland

Department of Electrical Engineering,

asystent proffesor


P.J. Leonard, A.M. Connor, Pole Shape Optimisation Using a Tabu Search Scheme, IEEE Transactions on Magnetics, vol. 36, no. 4, July 2000.

R.Turner, A target field approach to optimal coil design, Journal of Physics D: Applied Physics, no.8 vol.19, pp.~147--151, 1986.

T. Ohnishi, N. Takahashi, Effective Optimal Design of 3-D Magnetic Device Having Complicated Coil Using Edge Element and Biot–Savart Method, IEEE Transactions on Magnetics, vol. 38, no. 2, March 2002.

Q. Wang, Practical Design of Magnetostatic Structure Using Numerical Symulations, John Wiley and Sons Singapore Pte. Ltd, 2013

Jianming Jin, Electromagnetic Analysis and Design in Magnetic Resonance Imaging. CRC Press, 1998.

M. Poole, P. Weiss, H. S. Lopez, M. Ng, S. Crozier Minimax current density coil design, Journal of Physics D: Applied Physics, vol. 43, no. 9, 2010,

K. Adamiak. On Fredholm Integral Equations of the First Kind Occurring in Synthesis of Electromagnetic Fields. International Journal for Numerical Methods in Engineering, 17(8), pp. 1187–1200, 1981.

F. Rom´eo and D. I. Hoult. Magnet Field Profiling: Analysis and Correcting Coil Design. Magnetic Resonance in Medicine, 1(1), pp. 44–65, 1984.

M. J. E. Golay. Field Homogenizing Coils For Nuclear Spin Resonance Instrumentation. Review of Scientific Instruments, 29(4), pp. 313–315, 1958.

B. Garda, Linear algebra approach and the quasi-Newton algorithm for the optimal coil design problem , Przeglad Elektrotechniczny, vol. 8, no. 7a, pp. 261-264, 2012.

M.W. Garrett, Thick cylindrical coil systems for strong magnetic fields with field or gradient homogeneities of the 6th to 20th order, J. Appl. Phys., vol. 38, no. 6, pp. 2563--2586, May 1967.

B. Garda and Z. Galias, Is the radial component negligible in the design of magnetic resonance imaging devices?, In proceedings of the International Conference on Signals and Electronic Systems : Poznan, Poland, 11–13 September 2014

Xu Hao, S.M. Conolly, G.C. Scott, A. Macovski, Homogeneous magnet design using linear programming, IEEE Transactions on Magnetics, vol.36, no.2, pp. 476-483, Mar 2000.

H.S. Lopez, C.G. Salmon, C.C. Mirabal, H. Saint-Jalmes, Designing an efficient resistive magnet for magnetic resonance imaging, IEEE Transactions on Magnetics , vol.~40, no.~5, pp. 3378-3381, Sept. 2004.

B.H. Suits and D.E. Wilken, Improving magnetic field gradient coils for NMR imaging, Journal of Physics E: Scientific Instruments, vol. 22, no. 8, pp. 565--573, 1989.

B. Garda and Z. Galias, Comparison of the linear algebra approach and the evolutionary computing for magnetic field shaping in linear coils, In proceedings of NOLTA 2010 International symposium on Nonlinear Theory and its Applications, Krakow, Poland, September, 2010

B. Garda and Z. Galias , Non-negative least squares and the Tikhonov regularization methods for coil design problems, In Proc. Int. Conference on Signals and Electronic Systems, ICSES'12, Wroclaw, 2012.






Signals, Circuits, Systems