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.
Shaping effects of the E-fishbone in tokamaks are investigated. Coordinates related to the Solov＇ev configuration are used to calculate the precession frequency and kinetic contribu- tion. It is shown that elongation does not change the precession frequency and the kinetic energy. Growth rates of the E-fishbone vary with elongation which essentially has destabilizing effects. For elongated tokamaks, triangularity has a stabilizing effect on the modes which play a compensative role. The results may apply to Sunist.
Loss-cone instabilities are studied for linear fusion devices. The gyro-kinetic equation for such a configuration is rigorously constructed in terms of action-angle variables by making use of canonical transformation. The dispersion relation, including for the first time, finite bounce frequency is obtained and numerically solved. The loss-cone modes are found near ion-cyclotron frequency. The growth rates are greatly reduced and approaching zero with increasing beta value. The results suggest that loss-cone instabilities are unlikely to be threatening to linear fusion devices since a new longitudinal invariant is found and gives a constraint which helps confinement.
