Hall current effects in mean-field dynamo theory

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 $α$ coefficient is altered, and is zero when a specific double Beltrami state is attained, in contrast to the Alfvénic state for MHD dynamos. The $β$ coefficient is no longer positive definite, and thereby enables dynamo action even if $α$-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 $β< 0$ is advanced. The results are compared against previous studies, and their astrophysical relevance is also highlighted.

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