Generation of chiral asymmetry via helical magnetic fields

Abstract

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 $⟨\mathcal{H}⟩+2⟨{\mu }_5⟩/\lambda$ with $⟨\mathcal{H}⟩$ being the mean magnetic helicity and $⟨{\mu }_5⟩$ 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 $⟨\mathcal{H}⟩$ and vanishing ${\mu }_5$. We present analytic derivations for the time evolution of $⟨\mathcal{H}⟩$ 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 $⟨\mathcal{H}⟩$ depends on the magnetic and kinetic Reynolds numbers ${\mathrm{Re}}_{{}_{\mathrm{M}}}$ and ${\mathrm{Re}}_{{}_{\mathrm{K}}}$. For a high ${\mathrm{Re}}_{{}_{\mathrm{M}}}$ and ${\mathrm{Re}}_{{}_{\mathrm{K}}}$ where turbulence occurs, $⟨\mathcal{H}⟩$ 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 $k_{\mathrm{p}}\propto t^{-1/2}\ln \left(t/t_{\log }\right)$. After being rapidly generated, $⟨{\mu }_5⟩$ always decays together with $k_{\mathrm{p}}$, i.e. $⟨{\mu }_5⟩\approx k_{\mathrm{p}}$, with a time evolution that depends on whether the system is in the limit of low or high Reynolds numbers.

arXiv comment16 pages, 11 figures, accepted for publication in PRD

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