Effects of an External Magnetic Field on Landau Damping in Maxwellian Plasmas

Abstract

Landau damping of longitudinal electron oscillations in a boundless, Maxwellian, collisionless magneto-plasma is studied in an approximation which neglects the coupling to transverse oscillations. The longitudinal component of the electric field is explicitly developed as a superposition of exponentially damped sinusoidal oscillations for an initial perturbation sinusoidal in space and Maxwellian in velocity. A formula is derived for the minimum time for Landau damping, i.e., the time which must elapse before only the lowest frequency oscillation is significant. An analysis is presented for the strong magnetic field case in which ωc≫2π |sinθ| (λ/λD)ωp, where ωc is the cyclotron frequency, θ is the angle between the propagation vector and the external magnetic, λD is the Debye length, λ is the wavelength, and ωp is the plasma frequency. For this case the Laundau zeros move continuously along rays from their location in the absence of a magnetic field when the angleθ is zero to the origin as this angle approaches 90 deg. With this same variation of angle the minimum time increases from the null field value to infinity. These results are independent of the cyclotron frequency, provided that the above inequality is satisfied. For no external magnetic field the minimum time is found to increase with increasing wavelength and decreasing thermal spread of the initial perturbation when the spread is less than that of the unperturbed distribution.