Nonlinear Frequency Shift of a Plasma Mode

The nonlinear frequency shift of an electron plasma mode is calculated without restriction to part of the electrons. A time‐dependent dispersion equation solved numerically in the time‐asymptotic limit yields, for phase/thermal velocity ratios $\text{≳4}$ , frequency shifts significantly larger than previously calculated. The relative contribution of trapped and untrapped electrons to the frequency shift varies widely with the wave amplitude and the phase/thermal velocity ratio.