On Chern–Simons corrections to magnetohydrodynamics equations

Abstract

This paper studies the effect of a (3+1)-dimensional Chern–Simons (CS) electrodynamic on the equations governing the dynamics of magnetized plasma and fields. In this model, the CS part consists of a dynamical pseudo-scalar field whose space–time derivatives couple with the electromagnetic field. The paper explores the CS corrections to the evolution equation for the magnetic field in a plasma with non-zero electrical resistivity. We revisit Cowling's theorem in this context and observe that the CS corrections lead to possibly small but non-zero source terms for the axisymmetric magnetic field. The scalar product of electric and magnetic fields plays the role of the source of the pseudo-scalar field, and therefore, pulsars are likely astrophysical candidates to generate propagating pseudo-scalar waves. Although an aligned electric field gets shorted out by flowing charges in large parts of the magnetosphere, there are vacuum gaps in the vicinity of pulsars where strong is expected to be present. A wave solution for the pseudo-scalar field generated by the time-varying associated with a pulsar is derived.