Internal kink stabilization by high-energy ions with nonstandard orbits

Abstract

A generalized energy principle that takes into account the nonstandard, potato-shaped particle orbits of high-energy ions in the central region of a tokamak is derived. It is shown that, in the limit of zero orbit width, this energy principle reduces to the one formulated by Van Dam et al. [Phys. Fluids 25, 1349 (1982)]. The modification of hot particle stabilization theory when such orbit effects are important is investigated. In particular, a model distribution function is chosen to describe high-energy trapped ions produced by ion cyclotron resonant frequency (ICRF) heating applied near the axis of a tokamak. Standard banana orbit theory predicts that, for fixed total stored energy of energetic particles peaked about the magnetic axis, the stabilizing influence on internal kink modes is inversely proportional to the spatial spread of the hot particles. However, this scaling saturates when the spatial spread of the distribution function approaches the width of a typical nonstandard orbit. Hence, ICRF heating is most efficient in producing stabilization when the heating zone is comparable to the orbit width, while the tendency to stabilize does not improve if the heating zone is narrower than the orbit width. Further, it is shown that, if particle orbits can extend close to the q=1 surface, the tendency for stabilization is inhibited.