Interaction of a magnetic island chain in a tokamak plasma with a resonant magnetic perturbation of rapidly oscillating phase

An investigation is made into the interaction of a magnetic island chain, embedded in a tokamak plasma, with an externally generated magnetic perturbation of the same helicity whose helical phase is rapidly oscillating. The analysis is similar in form to the classic analysis used by Kapitza [Sov. Phys. JETP 21, 588 (1951)] to examine the angular motion of a rigid pendulum whose pivot point undergoes rapid vertical oscillations. The phase oscillations are found to modify the existing terms, and also to give rise to new terms, in the equations governing the secular evolution of the island chain's radial width and helical phase. An examination of the properties of the new secular evolution equation reveals that it is possible to phase-lock an island chain to an external magnetic perturbation with an oscillating helical phase in a stabilizing phase relation provided that the amplitude, epsilon, of the phase oscillations (in radians) is such that vertical bar J(0)(epsilon)vertical bar << 1, and the mean angular frequency of the perturbation closely matches the natural angular frequency of the island chain. Published by AIP Publishing.