A new approximate solution of parallel whistler-mode dispersion equation

A new approximation of the real part of the nonrelativistic plasma dispersion function ?Z 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 ?Z when d²?Z/dξ ₀ ² = 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 ?Z _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.