Analytical Solutions of Eddy-Current Problems in a Finite Length Cylinder
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Abstract
Magnetic field and eddy currents in a cylinder of finite length are calculated by separation of variables. The magnetic field outside the cylinder or inside the bore of the hollow cylinder and shell is expressed in terms of Bessel functions. Both axial and transverse applied fields are considered for the solid and hollow cylinders. The equations for the vector potential components are transformed in one-dimensional equations along the radial coordinate with the consequent integration by the method of variation of parameters. The equation for the scalar electric potential when required is also integrated analytically. Expressions for the magnetic moment and loss are derived. An alternative analytical solution in terms of scalar magnetic potential is derived for the finite length thin shells. All formulas are validated by the comparison with the solutions by finite–element and finite-difference methods.
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References
J. Lameraner and M. Štafl, Eddy currents. London: Iliffe Books Ltd., 1966.
H. E. Knoepfel, Magnetic fields. New York–Toronto, John Wiley&Sons, Inc., 2000.
V. V. Batygin and I. N. Toptygin, Problems in Electrodynamics, London,U.K., Academic, problems 368 and 371, 1976.
R. Grimberg, E. Radu, O. Mihalache, A. Savin, Calculation of the induced electromagnetic field created by an arbitrary current distribution located outside a conductive cylinder, J. Phys. D: Appl. Phys. 30 2285 30, pp.2285–2291, 1997.
E. H. Brandt, Superconductor disks and cylinders in an axial magnetic field. I. Flux penetration and magnetization curves, Phys. Rev. B, vol. 58, no. 10, pp. 6506–6522, 1998.
H. S. Lopez, M. Poole, S. Crozier, Eddy current simulation in thick cylinders of finite length induced by coils of arbitrary geometry, Journal of Magnetic Resonance, 207, pp.251–261, 2010.
J. R. Bowler and T. P. Theodoulidis, Eddy currents induced in a conducting rod of finite length by a coaxial encircling coil, J. Phys. D: Appl. Phys. 38, pp. 2861–2868, 2005.
M. Perry, T. Jones, Eddy current induction in a solid conducting cylinder with a transverse magnetic field, IEEE Trans. on Magn., vol. 14, No 4, pp.227-231,1978.
T.H. Fawzi, K. F. Ali, P. E. Burke, Eddy current losses in finite length conducting cylinders, IEEE Trans. on Magn. vol.19, No 5, pp.: 2216 – 2218, 1983.
T. Morisue, M. Fukumi, 3-D eddy current calculation using the magnetic vector potential, IEEE Trans. on Magn., vol. 24, No. 1, pp. 106-109, 1988.
Q. S. Huang, L. Krahenbuhl, A. Nicolas, Numerical calculation of steady-state skin effect problems in axisymmetry, IEEE Trans. on Magn., vol. 24, No. 1, pp. 201-204, 1988.
L. R. Turner et al, Results from the FELIX experiments on electromagnetic effects of hollow cylinders", IEEE Trans. on Magn., vol. 21, No. 6, pp.2324-2328, 1985.
International Electromagnetic Workshops: Test Problems, April 1986. Available online: https://www.osti.gov/scitech/servlets/purl/7179128
R. P. Feynman, Feynman lectures on physics. Volume 2: Mainly electromagnetism and matter. Reading, MA.: Addison-Wesley, 1964.
G. A. Grinberg, The Selected Problems of Mathematical Theory of Electric and Magnetic Phenomena. Moscow-Leningrad, Russia: Acad Sci USSR, 1948.
W. Rosenheinrich, Tables of some indefinite integral of Bessel functions of integer order, 2017. Available online: http://web.eah-jena.de/~rsh/Forschung/Stoer/besint.pdf
Opera 2D, User Guide and Opera 3D, User Guide. Cobham Technical Services, Vector Fields Software, Kidlington, UK, Mar. 2016.
I.E. Tamm, Fundamentals of the theory of electricity, Moscow : Mir Publishers, 1979.
A. A. Samarskiy, Theory of Finite Difference Schemes, Moscow: Nauka, 1977.
Y. Zhilichev, Superconducting cylinder of finite length in transverse magnetic field, Latvian Journal of Physics and Technical Sciences, No5, pp.14-21, 2001.
B. Ancelle, A. Nicolas, and J. C. Sabonnadiere, A boundary integral equation method for high frequency eddy currents, IEEE Trans. on Magn., vol. 17, No. 6, pp.2568-2570, 1981.
J. Poltz and K. Romanowski, Solution of quasi-stationary fields problems by means of magnetic scalar potential, IEEE Trans. on Magn., vol. 19, No. 6, pp.2425-2428, 1983.
M. Filtz and H. Bussing, Screening attenuation of conducting and ferromagnetic hollow cylinders of finite length, Electrical Engineering, vol. 90, pp.469-478, 2008.