Exact solutions of macroscopic self-consistent electromagnetic fields and microscopic distribution of Vlasov-Maxwell system

TL;DR

This paper derives exact solutions for the Vlasov-Maxwell system, revealing that zero-temperature solutions are impossible and extending the BGK mode to electromagnetic cases.

Contribution

It provides the first exact solutions for the macroscopic electromagnetic fields and microscopic distribution in the Vlasov-Maxwell system, generalizing the BGK mode.

Findings

Zero-temperature solutions are mathematically impossible.

Exact solutions for macroscopic fields E, B, and fluid velocity u are derived.

Microscopic distribution extends the BGK mode to electromagnetic scenarios.

Abstract

Strict mathematics reveals that the strict solution of a Vlasov-Maxwell equation set cannot be of a zero-temperature mathematical form. This universal property of Vlasov-Maxwell system can lead to a closed equation set of three macroscopic quantities: selfconsistent fields E, B and fluid velocity u, and hence their exact solutions.Strict solution of microscoipc distribution governed by self-consistent electromagnetic fields is found to be a universal extension of well-known BGK mode, which corresponds to electrostatic case.