NEOCLASSICAL INTERNAL KINK MODES IN TOKAMAKS

The authors draw attention to the fact that the majority of theoretica l papers dealing with internal kink modes in a tokamak and initiated b y experimental observations of both saw teeth and ''fishbones'' do not provide an adequate description of the experiments. This is related t o the fact that the neoclassical banana regime is present in the exper iments, while these neoclassical effects are neglected in the mentione d papers. It is shown that the hydrodynamics plasma approach incorpora tes neoclassical effects through the longitudinal viscosity terms in t he description of the singular layer of perturbations. The need for th e consistent development of the neoclassical theory of internal kink m odes is justified. As a first step in developing such a theory, a revi ew of the previous fragmentary studies of the neoclassical theory of p lasma instabilities is presented and the basic statements of the gener al neoclassical theory of internal kink modes with a simple singular l ayer are formulated. Novel results of this paper include the following . First, the equation of the small-amplitude oscillations in the regio n of the singular layer is derived, which takes into account both the conventionally incorporated and the neoclassical effects. Second, a ge neral analysis of the neoclassical effects, on the basis of this equat ion, is carried out in application to the problem of internal kink mod es. For some particular mode types, the neoclassical modification is s tudied. For all types of kink modes, it is shown that the ''plane'' ef fect of the transverse viscosity, which is often incorporated in the t heoretical papers, is negligible compared to the effect of the neoclas sical viscosity. The ''residual'' neoclassical instability of the idea l mode m = 1, for which there is stabilization due to the effect of th e finite Larmor radius, is studied. In the analysis of the resistive m odes, the main attention is paid to the drift tearing (reconnection) m ode that has a frequency close to the electron-drift frequency. It is shown that this instability growth rate depends substantially on the n eoclassical viscous-resistive effect. It is noted that the electron vi scosity results in the magnetic hump effect. Quantitatively, the elect ron viscosity effect exceeds the effect of the usual magnetic hump.