Closed-form analytical model of the electron whistler and cyclotron maser instabilities in relativistic plasma with arbitrary energy anisotropy.

Abstract

Detailed properties of the cyclotron maser and whistler instabilities in a relativistic magnetized plasma are investigated for a particular choice of anisotropic distribution function F(${p}_{\ensuremath{\perp}}^{2}$,${p}_{z}$) that permits an exact analytical reduction of the dispersion relation for arbitrary energy anisotropy. The analysis assumes electromagnetic wave propagation parallel to a uniform applied magnetic field ${B}_{0}$e${^}_{z}$. Moreover, the particular equilibrium distribution function considered in the present analysis assumes that all electrons move on a surface with perpendicular momentum ${p}_{\ensuremath{\perp}}$=p${^}_{\ensuremath{\perp}}$=const and are uniformly distributed in axial momentum from ${p}_{z}$=-p${^}_{z}$=const to ${p}_{z}$=+p${^}_{z}$=const (so-called ``waterbag'' distribution in ${p}_{z}$). This distribution function incorporates the effects of a finite momentum spread in the parallel direction. The resulting dispersion relation is solved numerically, and detailed properties of the cyclotron maser and whistler instabilities are determined over a wide range of energy anisotropy, normalized density ${\ensuremath{\omega}}_{p}^{2}$/${\ensuremath{\omega}}_{c}^{2}$, and electron energy.