  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.
