Mechanism Of Relaxation In The Electron Bump-On-Tail Instability Beyond The Quasilinear Approximation

The electron bump-on-tail instability, a classic model problem to understand collisionless relaxation processes and anomalous resistivity, is studied numerically using high-order discontinuous Galerkin methods applied to both quasilinear theory and direct Vlasov-Poisson simulation. Quasilinear diffusion is initially in good agreement with a direct simulation but later underestimates turbulent momentum flux. Enhanced flux occurs as the phase space eddy turnover time in the largest amplitude wavepackets becomes comparable to the wavepacket transit time of resonant phase fluid. In this regime eddies effectively turn over during wavepacket transit so that phase fluid predominately disperses by eddy phase mixing rather than by randomly phased waves. The result is an enhanced rate of relaxation above quasilinear predictions. These findings provide a means to understand the physics behind comparisons of quasilinear diffusion theories and observed fluctuations in space and laboratory plasmas.