On the role of the Hartmann number in magnetohydrodynamic activity

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Abstract
Magnetohydrodynamic activity near the threshold of instability is studied numerically for resistive equilibria in periodic cylinders. Attention focuses on the role of the viscosity (and its reflection in the Hartmann number) in determining the existence and nonlinear evolution of instabilities. Three identical axisymmetric resistive equilibria without flow are investigated, with three viscosities. The highest viscosity leads to stability of the axisymmetric state. The intermediate value leads to a helically deformed equilibrium with flow, with an (m,n)=(2,1) deformation. The lowest viscosity leads to a 'mixed' helically deformed, final, approximately steady state with flow, with (m,n)=(2,1) and (3,2) deformations and their harmonics, plus other, adjacent, modes near m=2n. It is concluded that it is likely that the numerical value of the viscosity, and possibly the form of the viscous stress tensor, must never be ignored in discussions of near-threshold incompressible MHD activity in driven, dissipative MHD plasmas.