Decay law of magnetic turbulence with helicity balanced by chiral fermions

TL;DR

This paper investigates how magnetic turbulence decays in plasmas with balanced helicity and chiral fermions, revealing a new decay law governed by a modified Hosking integral through high-resolution simulations.

Contribution

It introduces a novel decay law for magnetic turbulence with balanced helicity and chiral fermions, supported by high-resolution numerical simulations.

Findings

Magnetic energy density decays with time as in nonhelical turbulence.

Magnetic helicity density scales as t^{-2/3}.

Chiral chemical potential decays similarly to helicity, much slower than exponential decay.

Abstract

In plasmas composed of massless electrically charged fermions, chirality can be interchanged with magnetic helicity while preserving the total chirality through the quantum chiral anomaly. The decay of turbulent energy in plasmas such as those in the early Universe and compact stars is usually controlled by certain conservation laws. In the case of zero total chirality, when the magnetic helicity density balances with the appropriately scaled chiral chemical potential to zero, the total chirality no longer determines the decay. We propose that in such a case, an adaptation to the Hosking integral, which is conserved in nonhelical magnetically dominated turbulence, controls the decay in turbulence with helicity balanced by chiral fermions. We show, using a high resolution numerical simulation, that this is indeed the case. The magnetic energy density decays and the correlation length increases with time just like in nonhelical turbulence with vanishing chiral chemical potential. But here, the magnetic helicity density is nearly maximum and shows a scaling with time $t$ proportional to $t^{-2/3}$. This is unrelated to the $t^{-2/3}$ decay of magnetic {\it energy} in fully helical magnetic turbulence. The modulus of the chiral chemical potential decays in the same fashion. This is much slower than the exponential decay previously expected in theories of asymmetric baryon production from the hypermagnetic helicity decay after axion inflation.