On the role of resonant absorption in the electromotive force of dynamic dynamos

Mattias Brynjell-Rahkola (University of Cambridge)

Wednesday 12th November 15:00-16:00
Maths 311B

Abstract

Large-scale dynamos refer to processes in which a magnetic field is generated and maintained on the system scale by fluid motion. The common prototype for such dynamos is the alpha-Omega dynamo, in which a toroidal field is induced from a weak poloidal field by differential rotation, and the electromotive force (EMF) provides a feedback from the toroidal to the poloidal field that closes the loop. In this model, the main theoretical challenge is to describe the non-linear feedback due to the EMF, and to this end various models have been proposed.

In the seminar, a situation will be discussed where the EMF stems from three-dimensional waves on a neutrally stable background. This is likely to characterise non-linear lower branch dynamo solutions in e.g. stellar interiors and accretion discs that are susceptible to the 'kink' and the magnetorotational instability (MRI), respectively. Assuming that the background magnetic field is spatially varying, the system features a continuous Alfvén spectrum. Consequently, if the frequency of a perturbation falls within this Alfvén continuum, the wave will be absorbed in a narrow Alfvén resonant layer where its amplitude diverges. The details of this resonant absorption will be outlined during the talk, and to illustrate the feedback on the background state by such singular modes, an analytic expression for the EMF in the vicinity of Alfvén resonance will be presented. This expression is then applied to a one-dimensional global model of an accretion disc, which offers insight into the conditions under which a persistent EMF may be expected. Finally, the analysis is extended to a two-dimensional local disc model capable of supporting dynamo activity. In that case, the resonant layers correspond to curves around which the wave dynamics is organised.

Add to your calendar

Download event information as iCalendar file (only this event)