Resummed hydrodynamic expansion for a plasma of particles interacting with fields

TL;DR

This paper introduces a resummed moments approach to kinetic theory that unifies hydrodynamic and non-hydrodynamic modes, enabling higher-order, efficient descriptions of particle-field interactions, validated against exact solutions.

Contribution

It develops a novel resummed moments formalism that extends hydrodynamics to higher orders and is particularly effective for particles interacting with fields, maintaining convergence and accuracy.

Findings

Accurately reproduces exact solutions of Boltzmann-Vlasov-Maxwell equations.

Maintains fast convergence similar to traditional moments methods.

Identifies a new truncation condition valid far from equilibrium.

Abstract

A novel description of kinetic theory dynamics is proposed in terms of resummed moments that embed information of both hydrodynamic and non-hydrodynamic modes. The resulting expansion can be used to extend hydrodynamics to higher orders in a consistent and numerically efficient way; at lowest order it reduces to an Israel-Stewart-like theory. This formalism is especially suited to investigate the general problem of particles interacting with fields. We tested the accuracy of this approach against the exact solution of the coupled Boltzmann-Vlasov-Maxwell equations for a plasma in an electromagnetic field undergoing Bjorken-like expansion, including extreme cases characterized by large deviations from local equilibrium and large electric fields. We show that this new resummed method maintains the fast convergence of the traditional method of moments. We also find a new condition, unrelated to Knudsen numbers and pressure corrections, that justifies the truncation of the series even in situations far from local thermal equilibrium.