Generation of chiral asymmetry via helical magnetic fields. (arXiv:2002.09501v1 [physics.plasm-ph])
<a href="http://arxiv.org/find/physics/1/au:+Schober_J/0/1/0/all/0/1">Jennifer Schober</a>, <a href="http://arxiv.org/find/physics/1/au:+Fujita_T/0/1/0/all/0/1">Tomohiro Fujita</a>, <a href="http://arxiv.org/find/physics/1/au:+Durrer_R/0/1/0/all/0/1">Ruth Durrer</a>
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
$langlemathcal{H}rangle + 2 langlemu_5rangle / lambda$ with
$langlemathcal{H}rangle$ being the mean magnetic helicity and
$langlemu_5rangle$ 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 $langlemathcal{H}rangle$ and vanishing $mu_5$. We
present analytic derivations for the time evolution of
$langlemathcal{H}rangle$ and $langlemu_5rangle$ that we compare to a
series of laminar and turbulent three-dimensional direct numerical simulations.
We find that the late-time evolution of $langlemathcal{H}rangle$ depends on
the magnetic and kinetic Reynolds numbers ${rm Re}_{_mathrm{M}}$ and ${rm
Re}_{_mathrm{K}}$. For a high ${rm Re}_{_mathrm{M}}$ and ${rm
Re}_{_mathrm{K}}$ where turbulence occurs, $langlemathcal{H}rangle$
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, $langlemu_5rangle$ always decays together with $k_mathrm{p}$,
i.e. $langlemu_5rangle approx k_mathrm{p}$, with a time evolution that
depends on whether the system is in the limit of low or high Reynolds numbers.
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
$langlemathcal{H}rangle + 2 langlemu_5rangle / lambda$ with
$langlemathcal{H}rangle$ being the mean magnetic helicity and
$langlemu_5rangle$ 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 $langlemathcal{H}rangle$ and vanishing $mu_5$. We
present analytic derivations for the time evolution of
$langlemathcal{H}rangle$ and $langlemu_5rangle$ that we compare to a
series of laminar and turbulent three-dimensional direct numerical simulations.
We find that the late-time evolution of $langlemathcal{H}rangle$ depends on
the magnetic and kinetic Reynolds numbers ${rm Re}_{_mathrm{M}}$ and ${rm
Re}_{_mathrm{K}}$. For a high ${rm Re}_{_mathrm{M}}$ and ${rm
Re}_{_mathrm{K}}$ where turbulence occurs, $langlemathcal{H}rangle$
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, $langlemu_5rangle$ always decays together with $k_mathrm{p}$,
i.e. $langlemu_5rangle approx k_mathrm{p}$, with a time evolution that
depends on whether the system is in the limit of low or high Reynolds numbers.
http://arxiv.org/icons/sfx.gif
