Reduced quasilinear treatment of energetic electron instabilities in nonuniform plasmas.

High-frequency kinetic instabilities can enhance scattering of the runaway electrons (REs) dramatically. This wave-induced scattering should be beneficial for RE mitigation.

Quasilinear theory of wave-particle interaction in uniform plasmas provides a convenient technique to describe enhanced scattering but it needs to be generalized  to cover the essential role of spatial nonuniformity in actual experiments. Indeed, the nonuniform density distribution creates cavities for whistlers and magnetized plasma oscillations. These modes remain trapped within the core plasma, interacting with the REs on a time scale that is significantly longer than the wave bounce time. Another subtlety concerns the helical structure of the magnetic field in a tokamak that brings the bouncing wave packets in and out of resonance with the particles.

In this work, we address the role of plasma nonuniformity for the RE driven waves within the quasilinear approach. The short wavelength of whistlers and magnetized plasma oscillations suggests the WKB approximation. We note that the bounce time within the core plasma cavity of the trapped wave packets is significantly shorter than the growth time of the unstable waves. This allows us to average the wave-particle interaction dynamics over the fast bounces of the waves within the plasma. One can thereby simulate the effect of nonuniformity numerically at a reduced cost of the calculation.