Dynamo generation of a magnetic field by decaying Lehnert waves in a highly conducting plasma

Abstract

Random waves in a uniformly rotating plasma in the presence of a locally uniform seed magnetic field and subject to weak kinematic viscosity ν and resistivity η are considered. These “Lehnert” 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. A mean electromotive force proportional to ν-η is derived, demonstrating the conflicting effects of the two diffusive processes. Attention is then focussed on the situation η=0, relevant to conditions in the universe before and during galaxy formation. An α-effect, axisymmetric about the rotation vector, is derived, decaying on a time-scale proportional to ν-1; this amplifies a large-scale seed magnetic field to a level independent of ν, this field being subsequently steady and having the character of a “fossil field”. Subsequent evolution of this fossil field is briefly discussed.