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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.
Giuseppe Carleo, Riccardo Rossi, Julien Sebastian Gacon, Jannes Willy E. Nys, Stefan Woerner
Ardemis Anoush Boghossian, Benjamin Paul Johanès Gabriel Lambert, Alice Judith Gillen, Shang-Jung Wu, Afsaneh Taheri Telgari