The General Solution to Vlasov Equation and Linear Landau Damping

TL;DR

This paper derives a comprehensive solution to the linearized Vlasov equation for plasma waves, revealing a continuous diffusion coefficient and reaffirming Landau damping, thus advancing understanding of plasma oscillations.

Contribution

It provides a general solution to the linearized Vlasov equation that aligns with Landau's treatment and introduces a continuous diffusion coefficient.

Findings

Diffusion coefficient is continuous in omega.

The solution confirms Landau damping.

Equivalence to Landau's plasma oscillation treatment.

Abstract

A general solution to linearized Vlasov equation for an electron electrostatic wave in a homogeneous unmagnetized plasma is derived. The quasi-linear diffusion coefficient resulting from this solution is a continuous function of omega in contrast to that derived from the traditional Vlasov treatment. The general solution is also equivalent to the Landau treatment of the plasma normal oscillations, and hence leads to the well-known Landau damping.