The inadequacy of a magnetohydrodynamic approach to the Biermann Battery

TL;DR

This paper demonstrates that the traditional magnetohydrodynamic approach to modeling the Biermann battery is inadequate when electron distributions deviate from Maxwellian, leading to significant inaccuracies in magnetic field predictions.

Contribution

The study shows that MHD models fail under non-Maxwellian conditions and highlights the importance of kinetic simulations for accurate magnetic field generation modeling.

Findings

Electron pressure gradient distortions reduce the Biermann electric field by about 50%.

Flux limiters in MHD models produce unphysical electric field predictions.

MHD models can significantly overestimate magnetic field generation in laser-plasma interactions.

Abstract

Magnetic fields can be generated in plasmas by the Biermann battery when the electric field produced by the electron pressure gradient has a curl. The commonly employed magnetohydrodynamic (MHD) model of the Biermann battery breaks down when the electron distribution function is distorted away from Maxwellian. Using both MHD and kinetic simulations of a laser-plasma interaction relevant to inertial confinement fusion we have shown that this distortion can reduce the Biermann-producing electric field by around 50\%. More importantly, the use of a flux limiter in an MHD treatment to deal with the effect of the non-Maxwellian electron distribution on electron thermal transport leads to a completely unphysical prediction of the Biermann-producing electric field and so results in erroneous predictions for the generated magnetic field.