Generation of chiral asymmetry via helical magnetic fields

It is well known that helical magnetic fields undergo a so-called inverse cascade by which their correlation length grows due to the conservation of magnetic helicity in classical ideal magnetohydro-dynamics (MHD). At high energies above approximately 10 MeV, however, classical MHD is necessarily extended to chiral MHD and then the conserved quantity is (H) + 2 mu(5)/lambda with H being the mean magnetic helicity and mu(5) being the mean chiral chemical potential of charged fermions. Here,. is a (phenomenological) chiral feedback parameter. In this paper, we study the evolution of the chiral MHD system with the initial condition of nonzero H and vanishing mu(5). We present analytic derivations for the time evolution of H and mu(5) that we compare to a series of laminar and turbulent three-dimensional direct numerical simulations. We find that the late-time evolution of H depends on the magnetic and kinetic Reynolds numbers Re-M and Re-K. For a high Re-M and Re-K where turbulence occurs, H eventually evolves in the same way as in classical ideal MHD where the inverse correlation length of the helical magnetic field scales with time t as k(p) proportional to t(-2/3). For a low Reynolds numbers where the velocity field is negligible, the scaling is changed to k(p) proportional to t(-1/2) ln (t/t(log)). After being rapidly generated, mu(5) always decays together with k(p), i.e., mu(5) approximate to k(p), with a time evolution that depends on whether the system is in the limit of low or high Reynolds numbers.