Influence of inner and outer walls electromagnetic properties on the onset of a stationary dynamo

Abstract

To study the onset of a stationary dynamo in the presence of inner or outer walls of various electromagnetic properties, we propose a simple 1D-model in which the flow is replaced by an alpha effect. The equation of dispersion of the problem is derived analytically. It is solved numerically for walls of different thicknesses and of electric conductivity and magnetic permeability different from those of the fluid in motion. We also consider walls in the limit of infinite conductivity or permeability.PACS. 47.65.+a Magnetohydrodynamics and electrohydrodynamics -91.25.Cw Origins and models of the magnetic field; dynamo theories

Impact of Impellers on the Axisymmetric Magnetic Mode in the VKS2 Dynamo Experiment

“…Moreover, the (FM) boundary condition yields significantly smaller thresholds. This observation agrees with previous results obtained in a different context [14,15]. Both curves can be represented by the scaling law Rm c jj ÿq , where q 0:67, suggesting that the dynamo process is similar for both types of boundary conditions.…”

Ambivalent effects of added layers on steady kinematic dynamos in cylindrical geometry: application to the VKS experiment

“…This negative influence of lid layers on the dynamo is quite in contrast to the well-known positive effect of side layers [22,23]. Since such lid layers are indeed present for technical reasons in the VKS2 experiment, it is interesting to examine their role in more detail.…”

Kinematic simulation of dynamo action by a hybrid boundary-element/finite-volume method

“…where the magnetic field components are the time centered predicted states interpolated at the edges as determined from Eqs. (4) & (5). The final update for the magnetic field is then performed as described by Eq.…”

“…Critical values that are necessary to obtain dynamo action in the laboratory are of the order Rm crit ∼ 30...100 which is already technically demanding. Therefore, essential efforts are concentrated on possibilities to reduce this critical value and to increase the actual Rm of the field producing flow.From numerical simulations it is known that the boundary conditions and also boundary layers of stagnant or somehow guided flow could possess supportive as well as obstructive impacts on the onset of dynamo action [5,6]. In the kinematic regime the backreaction of the field on the flow by the Lorentz force can be ignored so that the complexity of the underlying system of equations is significantly reduced because only the induction equation with a prescribed velocity field has to be solved numerically.…”