A new approximate solution of parallel whistler-mode dispersion equation

Abstract

A new approximation of the real part of the nonrelativistic plasma dispersion function ℜZ of a real argument ξ₀ is proposed: namely,

$$\Re Z_A (\xi _0 ) = \frac{{2\xi _0 }}{{1 - 2\xi _0^2 }}.$$

This approximation gives the exact value for ℜZ when d²ℜZ/dξ ²₀ = 0 and gives the correct expressions for the first two terms of its expansion for large ξ₀. On the basis of this approximation, a new approximate expression for whistler-mode refractive index is derived for the case of wave propagation parallel to the magnetic field in a hot anisotropic and dense plasma. Under certain conditions this expression is more convenient for practical applications in magnetospheric and/or astrophysical conditions than other approximate expressions. The approximation ℜZ _A was also used in deriving the approximate expression for whistler-mode instability or damping (γ), although in this case it seems to have little merit when compared with the previously used expressions for γ.