Energy Conservation and the Chiral Magnetic Effect

Understand

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.