Quasi-linear analysis of whistler waves driven by a relativistic runaway beam in Tokamaks

Abstract

A beam of highly relativistic runaway electrons can be generated during the current quench in a Tokamak disruption. Having energy of several MeV, these energetic electrons can cause damage to the inner wall of a Tokamak vessel. Concerning this dramatic event, a diffusion of runaway electrons toward a lower velocity is desirable. In this study, an investigation of the secondary runaway electrons diffusion caused by whistler waves is carried out. First, an instability growth rate for whistler waves due to the Doppler resonance with runaway electrons is obtained. In addition, a quasi-linear equation for the runaway electrons velocity distribution function is formed and its solution is given for mode number 1 by using the whistler wave dispersion relation and growth rate. Finally, the validity of the solution for a range of the electron energy is investigated.