Constraints on dynamo action in plasmas

TL;DR

This paper establishes upper bounds on magnetic energy growth via dynamo action in various plasma models, highlighting the necessity of collisions or kinetic mechanisms to break magnetic moment conservation for magnetic field amplification.

Contribution

It provides a hierarchy of constraints on dynamo action across different plasma models, emphasizing the role of magnetic moment conservation in limiting magnetic energy growth.

Findings

Dynamo action is constrained in models conserving magnetic moment.

Small seed magnetic fields cannot be significantly amplified without collisions.

External forcing that conserves magnetic moment does not lead to dynamo amplification.

Abstract

Upper bounds are derived on the amount of magnetic energy that can be generated by dynamo action in collisional and collisionless plasmas with and without external forcing. A hierarchy of mathematical descriptions is considered for the plasma dynamics: ideal MHD, visco-resistive MHD, the double-adiabatic theory of Chew, Goldberger and Low (CGL), kinetic MHD, and other kinetic models. It is found that dynamo action is greatly constrained in models where the magnetic moment of any particle species is conserved. In the absence of external forcing, the magnetic energy then remains small at all times if it is small in the initial state. In other words, a small "seed" magnetic field cannot be amplified significantly, regardless of the nature of flow, as long as the collision frequency and gyroradius are small enough to be negligible. A similar conclusion also holds if the system is subject to external forcing as long as this forcing conserves the magnetic moment of at least one plasma species and does not greatly increase the total energy of the plasma (i.e., in practice, is subsonic). Dynamo action therefore always requires collisions or some small-scale kinetic mechanism for breaking the adiabatic invariance of the magnetic moment.