Electric fields at finite temperature

TL;DR

This paper derives temperature-dependent equations for electric potential incorporating quantum corrections, enabling analysis of electric fields in thermal environments with various statistical and magnetic effects.

Contribution

It introduces a unified formalism for electric potential equations at finite temperature, including quantum and thermal effects, applicable to different plasma conditions.

Findings

Quantum corrections modify classical equations like Poisson-Boltzmann.

Temperature dependence affects electric field screening in plasmas.

The formalism accommodates different statistics and magnetic fields.

Abstract

Partial differential equations for the electric potential at finite temperature, taking into account the thermal Euler-Heisenberg contribution to the electromagnetic Lagrangian are derived. This complete temperature dependence introduces quantum corrections to several well known equations such as the Thomas-Fermi and the Poisson-Boltzmann equation. Our unified approach allows at the same time to derive other similar equations which take into account the effect of the surrounding heat bath on electric fields. We vary our approach by considering a neutral plasma as well as the screening caused by electrons only. The effects of changing the statistics from Fermi-Dirac to the Tsallis statistics and including the presence of a magnetic field are also investigated. Some useful applications of the above formalism are presented.