Energy Conservation and the Chiral Magnetic Effect

TL;DR

This paper investigates the energy conservation aspects of the chiral magnetic effect in plasmas, showing that chiral asymmetry can induce plasma instability but is unlikely to explain stellar magnetic fields.

Contribution

It constructs an effective potential for helical electromagnetic perturbations and clarifies the role of electron Fermi energy asymmetry in plasma instability.

Findings

Negative curvature in the potential indicates plasma instability due to chiral asymmetry.

A nonzero electron mass allows excited states with nonzero helicity to relax to the ground state.

Chiral plasma instability is unlikely to explain stellar magnetic fields under typical conditions.

Abstract

We analyze the chiral magnetic effect in a homogeneous neutral plasma from the point of view of energy conservation, and construct an effective potential for the growth of maximally helical perturbations of the electromagnetic field. We show that a negative curvature at the origin of the potential, indicating instability of the plasma, is induced by a chiral asymmetry in electron Fermi energy, as opposed to number density, while the potential grows at large field value. It follows that the ground state for a plasma has zero magnetic helicity; a nonzero electron mass will allow an excited state of a plasma with nonzero helicity to relax to that ground state quickly. We conclude that a chiral plasma instability triggered by weak interactions is not a viable mechanism for explaining magnetic fields in stars except possibly when dynamics drives the system far from equilibrium.