Hall current effects in mean-field dynamo theory

TL;DR

This paper explores how the Hall term influences large-scale dynamo action, revealing modifications to the alpha and beta coefficients that could enable dynamo activity even under alpha-quenching, with implications for astrophysical phenomena.

Contribution

It demonstrates that the Hall term alters the alpha and beta coefficients in mean-field dynamo theory, allowing dynamo action under conditions previously thought unfavorable, and compares these effects with existing models.

Findings

Alpha coefficient is altered and becomes zero at a double Beltrami state.

Beta coefficient is no longer positive definite, enabling dynamo action.

Potential mechanism for negative beta is proposed.

Abstract

The role of the Hall term on large scale dynamo action is investigated by means of the First Order Smoothing Approximation. It is shown that the standard $\alpha$ coefficient is altered, and is zero when a specific double Beltrami state is attained, in contrast to the Alfv\'enic state for MHD dynamos. The $\beta$ coefficient is no longer positive definite, and thereby enables dynamo action even if $\alpha$-quenching were to operate. The similarities and differences with the (magnetic) shear-current effect are pointed out, and a mechanism that may be potentially responsible for $\beta < 0$ is advanced. The results are compared against previous studies, and their astrophysical relevance is also highlighted.