Chiral fermion asymmetry in high-energy plasma simulations
  The chiral magnetic effect (CME) is a quantum relativistic effect that
describes the appearance of an additional electric current along a magnetic
field. It is caused by an asymmetry between the number densities of left- and
right-handed fermions, which can be maintained at high energies when the
chirality flipping rate can be neglected, for example in the early Universe.
The inclusion of the CME in the Maxwell equations leads to a modified set of
MHD equations. We discuss how the CME is implemented in the PENCIL CODE. The
CME plays a key role in the evolution of magnetic fields since it results in a
dynamo effect associated with an additional term in the induction equation.
This term is formally similar to the $\alpha$ effect in classical mean-field
MHD. However, the chiral dynamo can operate without turbulence and is
associated with small spatial scales that can be, in the case of the early
Universe, orders of magnitude below the Hubble radius. A chiral $\alpha_\mu$
effect has also been identified in mean-field theory. It occurs in the presence
of turbulence but is not related to kinetic helicity. Depending on the plasma
parameters, chiral dynamo instabilities can amplify magnetic fields over many
orders of magnitude. These instabilities can affect the propagation of MHD
waves, which is demonstrated by our DNS. We also study the coupling between the
evolution of the chiral chemical potential and the ordinary chemical potential,
which is proportional to the sum of the number densities of left- and
right-handed fermions. An important consequence of this coupling is the
emergence of chiral magnetic waves (CMWs). We confirm numerically that linear
CMWs and MHD waves are not interacting. Our simulations suggest that the
chemical potential has only a minor effect on the non-linear evolution of the
chiral dynamo.
