Scaling laws of the plasma velocity in visco-resistive magnetohydrodynamic systems
Résumé
We consider a visco-resistive magnetohydrodynamic modeling of a steady-state incompressible tokamak plasma with a prescribed toroidal current drive, featuring constant resistivity η and viscosity ν. It is shown that the plasma velocity root-mean-square behaves as η f (H) as long as the inertial term remains negligible, where H stands for the Hartmann number H ≡ (ην)-1/2 , and that f (H) exhibits power-law behaviours in the limits H ≪ 1 and H ≫ 1. In the latter limit, we establish that f (H) scales as H 1/4 , which is consistent with numerical results.
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