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Heating finite betas (relative to low beta) tokamak plasmas by Aljven waves i s studied b y means of a linearized kinetic model which takes i n t o account i o n sound and transit time magnetic pumping as well as the efect considered by preceding authors. I n cylindrical geometry, a set of three second-order differential equations i n r for the perturbed fields E,, EL, and Ell i s solved numerically.The results lead to a significant conclusion that Alfoen wave heating may be an cdvanced way of heating plasmas i n future tokamaks.

A quasi-linear formalism is developed for relativistic particles. It is self-consistent including spatial diffusion. An attempt is made to simulate the process of electron cyclotron resonant heating (ECRH) and electron cyclotron current drive (ECCD) for the HL-2A tokamak. Temperature oscillating regimes in Tore Supra diagnosed by MHD activity seem to be reproduced in the simulation. The special feature in this paper is to see the resonance in the long time scale for relativistic plasma.

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The main topics concerning lower hybrid wave heating (LHH) and lower hybrid current drive (LHCD) in tokamak systems are presented. The inherent properties of tokamak systems give the 'gap' filling on Brambilla's spectrum, which are conducive to LHCD, but, on the other hand, induce a consumption of wave energy by the trapped electrons, which reduce the current drive efficiency. The methods for the enhancement of the current drive efficiency may be derived from detailed analyses by drawing upon the ray tracing technology on toroidal geometry and the Fokker-Planck theory on velocity space.

Effects of the m = 0 harmonics on the early quasi-linear stage of m = 1 double tearing modes are investigated. The numerical calculation with the harmonics m = 0 included shows that the effect of the m = 0 harmonics on the mode is negligible in the linear stage. As the mode begins to grow nonlinearly, both the current and flow profiles are pinched due to the m = 0 harmonics. To make a comparison we also carry out the calculation with m = 0 harmonics turned off. The profiles of the total current, poloidal magnetic field, and poloidal shear velocity in the cases with or without the m = 0 harmonics are compared and discussed. In addition, the formation of a poloidal velocity shear is found and its mechanism is investigated.

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