Oscillations in a Relativistic Plasma

Abstract

The linear oscillations in a hot plasma which is representable by the relativistic Vlasov equation with the self‐consistent fields are investigated. The generalization of Bernstein's method for the relativistic case is used to obtain the formal solution of the linearized problem. Particular attention is given to the case when the system initially is in the relativistic equilibrium state. The dispersion equation is derived and studied for the case when the propagation is along the direction of the unperturbed magnetic field, considering the spatial dispersions explicitly. The asymptotic expansions are developed corresponding to the dispersion relations of the cases studied. It is found that transverse waves propagating along the unperturbed field are Landau damped if ν2 ≥ 1 − Ω2∕ω2, ν and Ω being the index of refraction and the gyrofrequency, respectively. In the absence of the external field the cutoff frequency, which is found to be the same for both longitudinal and the transverse modes, is shown to be a monotonically decreasing function of the temperature