New compact and singularity free formulations for the magnetic field produced by a finite cylinder considering linearly varying current density

Abstract

This paper presents new compact analytical expressions for the magnetic field calculation produced by a finite cylindrical sheet. A linearly varying surface current density between the ends of the cylindrical sheet has been assumed as current source. The expressions presented in this work are substantially more compact if compared with the ones currently available in the literature. Since the solutions are given in terms of complete elliptic integrals of the first, second and third kind, and the last two ones diverge at certain arguments, the field expressions also diverge at these critical points, even though the field solution is finite. These singular points are located at the ends of the current sheet cylinder. New analytical expressions are also presented for these critical points avoiding the singularities in an elegant way. The radial component of the magnetic field strength is separately discussed, and it has been proven that its solution at singular points diverges. To improve the computational performance on the evaluation of magnetic field at critical points, an alternative formulation is presented, where complete elliptic integrals of the second and third kind are replaced with alternative functions. Numerical algorithms for the computation of these functions are also presented.

Keywords

Current carrying cylinder elliptic integrals magnetic field singularity

Get full access to this article

View all access options for this article.

References

Díaz Flórez

G.A.

and Mombello

E.E.

, Magnetic vector potential and magnetic field intensity due to a finite current carrying cylinder considering a variable current density along its axial dimension, International Journal of Applied Electromagnetics and Mechanics, (ISSN 1383-5416), IOS Press 40(2) (2012), 133-147.

Díaz Flórez

G.A.

and Mombello

E.E.

, Semianalytic integral method (SAIM) for fast solution of current distribution in foil winding transformers, IEEE Transactions on Magnetics, (ISSN: 0018-9464) PP(99)(2015), DOI: 10.1109/TMAG.2015.2440360.

Abramowitz

and Stegun

, Handbook of mathematical functions with formulas graphs and mathematical tables, Dover Publications Inc., New York, 1970.

Olver

F.W.J.

, Lozier

D.W.

, Boisvert

R.F.

and Clark

C.W.

, NIST handbook of mathematical functions, 2010.

Byrd

and Friedman

, Handbook of elliptic integrals for engineers and scientists, Springer Verlag, Heidelberg Berlin, 1971.

et al., Calculation and control of stray losses in power transformer, International Journal of Applied Electromagnetics and Mechanics, (ISSN 1383-5416), IOS Press 39(1-4) (2012), 835-841.

Adel

, A new model of rotor eccentricity in induction motors considering the local air-gap over-flux concentration, International Journal of Applied Electromagnetics and Mechanics, (ISSN 1383-5416), IOS Press 42(4) (2013), 519-537.

Feng

Z.X.

, The treatment of singularities in calculation of magnetic field by using integral method, IEEE Transactions on Magnetics 21(6) (1985), 2207-2210, DOI: 10.1109/TMAG.1985.1064259.

Gurel

and Ergul

, Singularity of the magnetic-field integral equation and its extraction, IEEE Letters on Antennas and Wireless Propagation 4 (2005), 229-232. DOI: 10.1109/LAWP.2005.851103.