Causality and Collisionless Damping in Plasma

Hee J Lee,Mi Young Song

doi:10.4236/jmp.2013.44077

Abstract

We derive the collisionless Landau damping in a plasma by satisfying the causal requirement that the susceptibility function of the plasma for time t should be nil. The causality condition should be satisfied by the susceptibility function of a plasma no matter what equations we employ to describe the plasma. Thus we conclude that the fundamental reason of the collisionless damping can be traced to the causality. As an example, we derive the collisionless damping of ion acoustic wave in a plasma by employing fluid equations.

Highlights

Lim and Lee [2] derived the Landau damping from the Kramers-Kronig relations, and concluded that the fundamental reason of the collisionless damping of plasma waves can be traced to the causality
We have shown that Im as obtained by the Landau contour follows from the causal requirement expressed by Equation (3), t 0 0
The collisionless damping of plasma waves appears to be universal because the causality prevails regardless of the way of describing plasmas

Summary

Introduction

We show that the Landau damping can be derived from the causal requirement that must be satisfied for the dielectric permittivity function. The causal requirement is mathematically expressed by Equation (3), and should be satisfied always in electrodynamics no matter what way it is derived. Its physical meaning is that the response of the medium must follow the cause; the cause cannot be precedent to the effect By enforcing this causality condition, the velocity integral in Equation (1) is shown to be equivalent to the integral along the Landau contour. Lim and Lee [2] derived the Landau damping from the Kramers-Kronig relations, and concluded that the fundamental reason of the collisionless damping of plasma waves can be traced to the causality. SONG vation clearly shows that the causal requirement is responsible for the collisionless damping

Evaluation of Susceptibility from the Causal Requirement

Ion Landau Damping Derived from Fluid Equations

Discussion