Principle of Helical \& Nonhelical Dynamo and $\alpha$ effect in Field Structure model

TL;DR

This paper presents a field-structure model explaining both helical and nonhelical dynamo processes, illustrating energy cascades and the $ ext{α}$ effect, supported by qualitative simulations and semi-analytical methods.

Contribution

It introduces an intuitive field-structure model for dynamo processes, including the $ ext{α}$ effect, with qualitative simulation verification and semi-analytical coefficient derivation.

Findings

Nonhelical kinetic energy cascades to smaller eddies.

Helical magnetic energy inversely cascades to larger eddies via the $ ext{α}$ effect.

Semi-analytical calculation of $ ext{α}$ and $eta$ coefficients from magnetic energy and helicity.

Abstract

We explain the (non)helical dynamo process using a field-structure model based on magnetic induction equation in an intuitive way. We show how nonhelical kinetic energy converts into magnetic energy and cascades toward smaller eddies in a mechanically forced plasma system. Also, we show how helical magnetic energy is inversely cascaded ($\alpha$ effect) toward large scale magnetic eddies in a mechanically or magnetically forced system. We, then, compare the simulation results with the model qualitatively for the verification of the model. In addition to these intuitive and numerical approaches, we show how to get $\alpha$ and $\beta$ coefficient semi-analytically from the temporally evolving large scale magnetic energy and magnetic helicity.