Analytical and numerical analysis of the generalized Shkarofsky function

• Published in: Astrophysics and space science Vol. 194; no. 2; pp. 173 - 196
• Main Authors: Temme, N. M., Sumner, A. E., Sazhin, S. S.
• Format: Journal Article
• Language: English
• Published: Dordrecht Kluwer 01.08.1992
• Subjects: Earth, ocean, space; Electrostatic and electromagnetic waves; Exact sciences and technology; External geophysics; Physics of the magnetosphere; Numerical analysis; Wave propagation; Magnetosphere; Whistler wave; Analytical method
• ISSN: 0004-640X; 1572-946X
• DOI: 10.1007/BF00643989

Analytical results for whistler-mode propagation in the earth's magnetosphere based on a code using the generalized Shkarofsky function are compared to numerical results. The analytical properties of the generalized Shkarofsky function are examined and subjected to an asymptotic analysis, and a numerical code is developed based on quadrature of the integral defining the Shkarofsky function. The numerical and analytical results are compared for a specific case of realistic parallel whistler-mode propagation and instabilities and the associated relativistic effects. Ideal approximations are derived for the Shkarofsky functions that can be used for qualitative analysis in many cases. The ranges of applicability are defined for the different approximations that are useful for analyzing relativistic effects of whistler-mode propagation and instability. (C.C.S.)