Critical Initial Amplitude of Langmuir Wave Damping

By one-dimensional Vlasov-Poisson simulation,the critical initial state marking the transition between the Landau scenario,in which the electric fields definitively damped to zero and the O'NEIL scenario,in which the Landau damping is stopped after a certain damping stage,is studied.It is found that the critical initial amplitude ε can only exist when the product of the wave number(k m) and the electron thermal velocity(v th) is moderate,that is,0.2 < k m v th < 0.7.Otherwise,no critical initial amplitude is found.The value ε increases with the increase in k m for a fixed v th,and also increases with the increase in v th for a fixed k m.When k m v th is fixed,the value ε also changes with the wave number and the electron thermal velocity,even though the damping rate and the oscillation frequency are the same in this case.