Stabilization of ballooning modes with sheared toroidal rotation

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Abstract
Stabilization of magnetohydrodynamic ballooning modes by sheared toroidal rotation is demonstrated using a shifted circle equilibrium model. A generalized ballooning mode representation is used to eliminate the fast Alfvén wave, and an initial value code solves the resulting equations. The s−α diagram (magnetic shear versus pressure gradient) of ballooning mode theory is extended to include rotational shear. In the ballooning representation, the modes shift periodically along the field line to the next point of unfavorable curvature. The shift frequency (dΩ/dq, where Ω is the angular toroidal velocity and q is the safety factor) is proportional to the rotation shear and inversely proportional to the magnetic shear. Stability improves with increasing shift frequency and direct stable access to the second stability regime occurs when this frequency is approximately one‐quarter to one‐half the Alfvén frequency, ωA=VA/qR.