Beat-Wave Excitation of Plasma Waves Based on Relativistic Bistability

A nonlinear beat-wave regime of plasma wave excitation is considered. Two beat-wave drivers are considered: intensity-modulated laser pulse and density-modulated (microbunched) electron beam. It is shown that a long beat-wave pulse can excite strong plasma waves in its wake even when the beat-wave frequency is detuned from the electron plasma frequency. The wake is caused by the dynamic bistability of the nonlinear plasma wave if the beat-wave amplitude exceeds the analytically calculated threshold. In the context of a microbunched beam driven plasma wakefield accelerator, this excitation regime can be applied to developing a femtosecond electron injector.

Figure 1

Steady-state solutions of a driven plasma wave as a function of the beat-wave amplitude $a$. Solid lines 1, 2: stable equilibria for $\omega =0.95$; dashed line: unstable equilibrium for $\omega =0.95$; dot-dashed line: resonant excitation with $\omega =1$.

Figure 2

Excitation of a plasma wave by a Gaussian beat-wave pulse (dotted line), $a(\tau )=a_0\exp [-{\tau }^2/{\tau }_L^2]$, ${\tau }_L=150$. Solid line: $\omega =0.95$, above-threshold excitation with $a_0=0.023>a_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}=0.02$; dashed line: resonant excitation with $\omega =1$ and $a_0=0.023$; dot-dashed line: $\omega =0.95$, below-threshold excitation with $a_0=0.018<a_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}$.

Figure 3

(a) Excitation of a plasma wave by a pair of identical Gaussian beat-wave pulses (dot-dashed line) separated by the delay times ${\tau }_d=920$ (solid line: wake depleted by the second pulse) and ${\tau }_d=980$ (dashed line: wake unperturbed by the second pulse). Pulse parameters: same as in Fig. 2: $a_0=0.023$, $\omega =0.95$, and ${\tau }_L=150$. (b) Sequence of phase lockings and phase releases for ${\tau }_d=920$.