Theory of high power electron cyclotron resonance heating

Abstract

Electron cyclotron resonance heating has been successfully used on a series of experiments in an attempt to raise plasma temperatures beyond the constraints of the resistive dissipation which occurs with ohmic heating. Recently progress in gyrotron design has allowed for significant increases in applied microwave power and for the first time a free electron laser will generate high power pulsed radio frequency waves in the MTX experiment at Lawrence Livermore Laboratory in 1987. Classically the theory of ECRH has been considered by a Fokker-Planck approach and by a guasilinear approach. Both lead to a diffusion equation in velocity space for the distribution function but as the applied power increases the approximations made in these approaches are likely to become unsatisfactory. Adopting a test particle approach we firstly consider modifications to the velocity space diffusion co-efficient at high powers and then dispense with the diffusion equation completely. We begin by deriving averaged particle equations from a Lagrangian formulation which require less computer processor time to integrate than the exact Lorentz-force equations. These have been incorporated in a particle code to simulate ECRH in a tokamak. The results for this code are compared with analytic expressions derived for a modified diffusion coefficient and a probability function P(v,Δv). We show that for low fields the diffusive form is correct but for higher fields nonlinear effects become important.