Stochastic variational principles for the collisional Vlasov-Maxwell and Vlasov-Poisson equations

TL;DR

This paper reformulates collisional Vlasov-Maxwell and Vlasov-Poisson equations as coupled stochastic PDEs, deriving variational principles and proposing a stochastic particle method for structure-preserving numerical simulations.

Contribution

It introduces a novel stochastic variational framework for collisional plasma equations and develops a particle method based on this formulation.

Findings

Derived stochastic variational principles for collisional Vlasov equations

Proposed a stochastic particle method with variational characterization

Lays groundwork for stochastic structure-preserving integrators

Abstract

In this work we recast the collisional Vlasov-Maxwell and Vlasov-Poisson equations as systems of coupled stochastic and partial differential equations, and we derive stochastic variational principles which underlie such reformulations. We also propose a stochastic particle method for the collisional Vlasov-Maxwell equations and provide a variational characterization of it, which can be used as a basis for a further development of stochastic structure-preserving particle-in-cell integrators.