An Asymptotic Method for the Vlasov Equation. III. Transition from Amplitude Oscillation to Linear Landau Damping

抄録

The nonlinear behaviour of Landau damping is investigated numerically. The basic equations are able to describe the amplitude oscillation, linear Landau damping, and intermediate regions of wave behaviour. If q≡γ_L⁄ω_B, where γ_L is the linear Landau damping coefficient and ω_B the bouncing frequency of electron trapped in the wave, we find that for q<<1 a plateau is formed in the time dependence of the amplitude of the electric field D, while for q\lesssim0.5 a plateau may also be formed. Another kind of plateau appears for q≈0.77, but for q<0.77 the wave is damped (not necessarily Landaudamped). The time evolution of the number of “trapped” electrons and also of the distribution of resonant electrons is obtained. It is found that even when D reaches its constant asymptotically for q<<1 the corresponding distribution of resonant electrons is not necessarily uniform in the trapped regions.