Collective processes in a tokamak with high-energy particles: nonlinear theory of beam-Alfven instability

The author studies the quasilinear relaxation of high-energy ions under interaction with the Alfven waves excited by them and the nonlinear interaction of the beam with a monochromatic wave. The author assumes that the quasilinear relaxation occurs faster than the Coulomb one. The author assumes that the quasilinear processes are important for a tokamak with high-energy particles and he presents, in an appendix, a derivation of the quasilinear equations with allowance for the effects of inhomogeneity. The nonlinear evolution both of the beam distribution function and the wave amplitude are considered. The high-energy particles are assumed to be moving along the magnetic field