# Landau damping in the multiscale Vlasov theory

## TL;DR

This paper extends the Vlasov kinetic theory by introducing an extra distribution function to model micro-turbulence, demonstrating how this leads to Landau damping through Fokker-Planck type effects while preserving key physical properties.

## Contribution

It introduces an extended Vlasov framework with an additional state variable, providing a novel explanation for Landau damping within a Hamiltonian, entropy-conserving setting.

## Key findings

- Extended Vlasov theory maintains reversibility and Hamiltonian structure.
- Fokker-Planck type damping explains Landau damping.
- Extension applied to fluid mechanics as well.

## Abstract

Vlasov kinetic theory is extended by adopting an extra one particle distribution function as an additional state variable characterizing the micro-turbulence internal structure. The extended Vlasov equation keeps the reversibility, the Hamiltonian structure, and the entropy conservation of the original Vlasov equation. In the setting of the extended Vlasov theory we then argue that the Fokker-Planck type damping in the velocity dependence of the extra distribution function induces the Landau damping. The same type of extension is made also in the setting of fluid mechanics.