Alfvén wave cascades in a tokamak

Experiments designed for generating internal transport barriers in the plasmas of the Joint European Torus [JET, P. H. Rebut et al., Proceedings of the 10th International Conference, Plasma Physics and Controlled Nuclear Fusion, London (International Atomic Energy Agency, Vienna, 1985), Vol. I, p. 11] reveal cascades of Alfven perturbations with predominantly upward frequency sweeping. These experiments are characterized by a hollow plasma current profile, created by lower hybrid heating and current drive before the main heating power phase. The cascades are driven by ions accelerated with ion cyclotron resonance heating (ICRH). Each cascade consists of many modes with different toroidal mode numbers and different frequencies. The toroidal mode numbers vary from n=1 to n=6. The frequency starts from 20 to 90 kHz and increases up to the frequency range of toroidal Alfven eigenmodes. In the framework of ideal magnetohydrodynamics (MHD) model, a close correlation is found between the time evolution of the Alfven cascades and the evolution of the Alfven continuum frequency at the point of zero magnetic shear. This correlation facilitates the study of the time evolution of both the Alfven continuum and the safety factor, q(r), at the point of zero magnetic shear and makes it possible to use Alfven spectroscopy for studying q(r). Modeling shows that the Alfven cascade occurs when the Alfven continuum frequency has a maximum at the zero shear point. Interpretation of the Alfven cascades is given in terms of a novel-type of energetic particle mode localized at the point where q(r) has a minimum. This interpretation explains the key experimental observations: simultaneous generation of many modes, preferred direction of frequency sweeping, and the absence of strong continuum damping.