# Generation of chiral asymmetry via helical magnetic fields

###
Jennifer Schober, Tomohiro Fujita, Ruth Durrer

**21/2/20**Published in : arXiv:2002.09501

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 magnetohydrodynamics (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⟨μ5⟩ / \lambda with ⟨H⟩ being the mean magnetic helicity and \langle\mu_5\rangle being the mean chiral chemical potential of charged fermions. Here, \lambda 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 μ5. We present analytic derivations for the time evolution of ⟨H⟩ and ⟨μ5⟩ 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 ReM and ReK 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_\mathrm{p} \propto t^{-2/3}. For a low Reynolds numbers where the velocity field is negligible, the scaling is changed to k_\mathrm{p} \propto t^{-1/2}\mathrm{ln}\left(t/t_\mathrm{log}\right). After being rapidly generated, ⟨μ5⟩ always decays together with kp, i.e. ⟨μ5⟩ \approx k_\mathrm{p}, with a time evolution that depends on whether the system is in the limit of low or high Reynolds numbers.