Alternative representation of the dielectric tensor for a relativistic magnetized plasma in thermal equilibrium

Abstract

An alternative representation of the dielectric tensor εij(k, ω) for a relativistic magnetized plasma in thermal equilibrium is presented. This representation involves an infinite series expansion in powers of , as well as an asymptotic expansion for large Here ωc = eB0/mc is the nonrelativistic cyclotron frequency, k⊥ is the wavenumber perpendicular to the magnetic field B0êz, and α is the dimensionless parameter defined by α = mc2/KBT. The present work generalizes Shkarofsky's (1966) representation. Moreover, unlike Trubnikov's (1958) formal result, in which the k⊥ and kz dependences of εij(k, ω) are inexorably coupled, the present representation naturally separates the k⊥ and kz dependences of εij(k, ω). As an application, the general expression is simplified for the case of a weakly relativistic plasma, and the dispersion relation is obtained for electromagnetic waves, including first-order relativistic effects. The method developed in this paper can be used for other non-thermal distributions.