General kinetic solution for the Biermann battery with an associated pressure anisotropy generation

TL;DR

This paper presents a kinetic analytic model for the Biermann battery effect that predicts magnetic field growth and pressure anisotropies, validated by particle-in-cell simulations showing consistent development of the Weibel instability.

Contribution

It introduces a general kinetic solution for the Biermann battery that accounts for arbitrary density and temperature gradients, linking anisotropy generation to magnetic field growth.

Findings

Analytic predictions match PIC simulation results.

Temperature anisotropies lead to Weibel instability.

Magnetic fields grow as predicted by the model.

Abstract

Fully kinetic analytic calculations of an initially Maxwellian distribution with arbitrary density and temperature gradients exhibit the development of temperature anisotropies and magnetic field growth associated with the Biermann battery. The calculation, performed by taking a small order expansion of the ratio of the Debye length to the gradient scale, predicts anisotropies and magnetic fields as a function of space given an arbitrary temperature and density profile. These predictions are shown to qualitatively match the values measured from particle-in-cell simulations, where the development of the Weibel instability occurs at the same location and with a wavenumber aligned with the predicted temperature anisotropy.