Ballooning mode stability in high β tokamaks with a q=1 magnetic island

Abstract

The secondary stability of ballooning modes in a high β tokamak plasma with a q=1 magnetic island is calculated numerically. As the island grows, the temperature gradient around the X point of the island steepens. Resistive ballooning modes grow more rapidly in the presence of the island, but ballooning modes are unstable even in the absence of the island. When the safety factor at the magnetic axis q0=0.8 and the width of the island is equal to the radius of the q=1 flux surface, the ballooning mode growth rate is twice as large as the growth rate in the absence of the island. The connection length along a magnetic field line from the outside of the torus, where the magnetic curvature is unfavorable for stability, to the inside of the torus, where the curvature is favorable, is shorter when q is smaller. The shorter connection length at smaller q provides greater stability at q=1 than at larger q, and somewhat mitigates the effect of the steep temperature gradient generated at the X point of the magnetic island.