中国物理B ›› 2010, Vol. 19 ›› Issue (4): 44101-044101.doi: 10.1088/1674-1056/19/4/044101

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Analytical solutions to the electromagnetic field in a cylindrical shell excited by external axial current

吴静, 肖春燕   

  1. School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China
  • 收稿日期:2009-09-11 修回日期:2009-11-09 出版日期:2010-04-15 发布日期:2010-04-15
  • 基金资助:
    Project supported by the State Key Lab of Power Systems, China (Grant No.~SKLD09KM06).

Analytical solutions to the electromagnetic field in a cylindrical shell excited by external axial current

Wu Jing(吴静)† and Xiao Chun-Yan(肖春燕)   

  1. School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China
  • Received:2009-09-11 Revised:2009-11-09 Online:2010-04-15 Published:2010-04-15
  • Supported by:
    Project supported by the State Key Lab of Power Systems, China (Grant No.~SKLD09KM06).

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摘要： The solutions to the electromagnetic field excited by a long axial current outside a conductive and magnetic cylindrical shell of finite length are studied in this paper. The more accurate analytical solutions are obtained by solving the proper boundary value problems by the separation variable method. Then the solutions are simplified according to asymptotic formulas of Bessel functions. Compared with the accurate solutions, the simplified solutions do not contain the Bessel functions and the inverse operation of the singular matrix, and can be calculated out fast by computers. The simplified solutions are more suitable for the cylindrical shell of high permeability and conductivity excited by a high frequency source. Both of the numerical results and the physical experimental results validate the simplified solutions obtained.

Abstract: The solutions to the electromagnetic field excited by a long axial current outside a conductive and magnetic cylindrical shell of finite length are studied in this paper. The more accurate analytical solutions are obtained by solving the proper boundary value problems by the separation variable method. Then the solutions are simplified according to asymptotic formulas of Bessel functions. Compared with the accurate solutions, the simplified solutions do not contain the Bessel functions and the inverse operation of the singular matrix, and can be calculated out fast by computers. The simplified solutions are more suitable for the cylindrical shell of high permeability and conductivity excited by a high frequency source. Both of the numerical results and the physical experimental results validate the simplified solutions obtained.

Key words: analytical solution, electromagnetic field, ferrite shell, axial current

中图分类号:  (Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems)

  • 41.20.Gz
41.20.Cv (Electrostatics; Poisson and Laplace equations, boundary-value problems) 02.30.Gp (Special functions) 02.60.Lj (Ordinary and partial differential equations; boundary value problems)