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($p_{\perp }^2$,$p_z$) 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 $p_{\perp }$=p${^}_{\perp }$=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 ${\omega }_p^2$/${\omega }_c^2$, and electron energy.