An approximate solution of the parallel whistler-mode dispersion equation in a weakly relativistic plasma

A new approximate solution of the parallel whistler-mode dispersion equation in a weakly relativistic plasma is obtained under the assumption that the real part of the wave refractive index, N, predicted by this solution is close to the value of N predicted by the solution of the corresponding non-relativistic dispersion equation. Both the values of N and the values of the increment of wave growth or damping are closer to those obtained by numerical solution of the weakly relativistic dispersion equation than previously suggested approximations. The accuracy of the obtained solution increases with decreasing electron density, and/or anisotropy of the electron distribution function, and/or electron energy. (Author)