Approach to Chandrasekhar-Kendall-Woltjer State in a Chiral Plasma

TL;DR

This paper investigates the evolution of magnetic fields in chiral plasmas, establishing conditions under which the system reaches the Chandrasekhar-Kendall-Woltjer state using spherical harmonic analysis.

Contribution

It introduces a measure for the CKW state in chiral plasmas and derives conditions on initial spectra for the system to evolve into this state.

Findings

Non-zero chiral magnetic conductivity is necessary.

Growth rate of electric resistivity and conductivity product is crucial.

Numerical examples confirm the proposed conditions.

Abstract

We study the time evolution of the magnetic field in a plasma with a chiral magnetic current. The Vector Spherical Harmonic functions (VSH) are used to expand all fields. We define a measure for the Chandrasekhar-Kendall-Woltjer (CKW) state, which has a simple form in VSH expansion. We propose the conditions for a general class of initial momentum spectra that will evolve into the CKW state. For this class of initial conditions, to approach the CKW state, (i) a non-vanishing chiral magnetic conductivity is necessary, and (ii) the time integration of the product of the electric resistivity and chiral magnetic conductivity must grow faster than the time integration of the resistivity. We give a few examples to test these conditions numerically which work very well.