Helical magnetic effect and the chiral anomaly

TL;DR

This paper introduces the helical magnetic effect (HME), showing its coefficient is fixed by the chiral anomaly for massless Dirac fermions, and explores related plasma instabilities and their theoretical implications.

Contribution

It establishes a fixed relation between the HME coefficient and the chiral anomaly, and discusses conditions for helical plasma instability in chiral fluids.

Findings

HME coefficient is fixed by the chiral anomaly as C/2.

The magnetovorticity coupling coefficient relates to the chiral anomaly as C/2.

Conditions for helical plasma instability are identified.

Abstract

In the presence of the fluid helicity $\boldsymbol{v} \cdot \boldsymbol{\omega}$, the magnetic field induces an electric current of the form $\boldsymbol{j} = C_{\rm HME} (\boldsymbol{v} \cdot \boldsymbol{\omega}) \boldsymbol{B}$. This is the helical magnetic effect (HME). We show that for massless Dirac fermions with charge $e=1$, the transport coefficient $C_{\rm HME}$ is fixed by the chiral anomaly coefficient $C=1/(2\pi^2)$ as $C_{\rm HME} = C/2$ independently of interactions. We show the conjecture that the coefficient of the magnetovorticity coupling for the local vector charge, $n = C_{B \omega} \boldsymbol{B} \cdot \boldsymbol{\omega}$, is related to the chiral anomaly coefficient as $C_{B \omega} = C/2$. We also discuss the condition for the emergence of the helical plasma instability that originates from the HME.