Two- and three-dimensional tokamak equilibrium modifications driven by the localized ponderomotive force of applied radio frequency waves

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Abstract
Large ponderomotive forces can occur when waves in the ion cyclotron range of frequencies (ICRF) are employed in stabilization or high power heating schemes. It is shown that the magnetohydrodynamic (MHD) equilibrium of the plasma is modified when the rf antenna is localized poloidally and/or toroidally. In the two‐dimensional (2‐D) problem (toroidally uniform rf) a modified Grad–Shafranov equation describes ponderomotively driven magnetic surface distortions. At electric field strengths of interest for ICRF stabilization, the equilibrium distortions are small provided that Lrf≪a and the poloidal localization of the rf is not severe. The character of the 3‐D problem (toroidally and poloidally varying rf) depends on whether or not the ponderomotive force couples to rational surfaces within the plasma. For the case without rational surfaces, the 3‐D component of the distortions is found to be small by 1/q2a relative to the 2‐D component. In the case where rational surfaces are excited, magnetic islands result. A threshold condition for island overlap determines the rf electric field at which ergodicity may be expected. It is shown that ergodicity of the edge plasma may occur for some cases of interest for heating and stabilization, but should be controllable.