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

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.

RevTex 4, 15 pages, 6 figures. Typos in paragraph 1 and 2 in the introduction of the published version are corrected. These typos have no effects on the result of the paper. The typos in paragraph 2 are in Eq. (1) and in the inline formula in the second to last line