Large-scale dynamo action driven by forced beating waves in a highly conducting plasma

Abstract

The aim of this short paper is simply to demonstrate the effect of interactions between distinct waves induced by an oscillatory forcing on generation of the large-scale electromotive force (EMF) in a highly electrically conducting plasma in the dynamical regime, i.e. when the back reaction of the Lorentz force on the flow is included. The mean EMF is induced by waves with distinct but close phase speeds, which are called ‘beating waves’ by analogy with the acoustic effect of ‘beat’, in the presence of a locally uniform seed magnetic field. These waves may have either positive or negative helicity, and it is supposed that waves of a single sign of helicity are preferentially excited by a symmetry-breaking mechanism. The formula for the mean EMF in a highly conducting plasma is derived, conditions relevant to those of the early universe before and during galaxy formation. Within the scope of the weak magnetohydrodynamic turbulence dominated by the linear waves an$\unicode[STIX]{x1D6FC}$-effect, that is generation of the large-scale EMF is studied, which leads to amplification of the seed mean magnetic field. Possible subsequent equilibration due to quenching resulting from the presence of the Lorentz force is briefly discussed.