Comparison between the Cauchy problem and the scattering problem for the Landau damping in the Vlasov-HMF equation

TL;DR

This paper compares the Cauchy and scattering problems for Landau damping in the Vlasov-HMF equation, introducing a new method to analyze their differences and the role of plasma echoes, including a non-perturbative result.

Contribution

It introduces a novel approach to compare Landau damping in the Vlasov-HMF equation for both problems, highlighting the influence of plasma echoes and providing a non-perturbative analysis.

Findings

Different influence of plasma echoes in the two approaches

A new method for the scattering problem similar to the Cauchy problem

A non-perturbative result for the scattering problem

Abstract

We analyze the analytic Landau damping problem for the Vlasov-HMF equation, by fixing the asymptotic behavior of the solution. We use a new method for this "scattering problem", closer to the one used for the Cauchy problem. In this way we are able to compare the two results, emphasizing the different influence of the plasma echoes in the two approaches. In particular, we prove a non-perturbative result for the scattering problem.