Vlasov Simulations of Electron Plasma Waves: self-focusing and modulational instability*

Vlasov simulations of nonlinear electron plasma (EPW) waves are presented in 2D (2 space and 2 velocity dimensions) with LOKI (Banks et al, Phys. Plasmas 18, 052102 (2011)). EPWs are created with an external traveling wave potential with a transverse envelope of width $\Delta y$ such that thermal electrons transit the wave in a ``sideloss'' time, $t_{sl} \sim \Delta y/v_e$ where $v_e$ is the electron thermal velocity. The plasma wave field envelope and associated self-consistent quasi-steady distribution of trapped electrons are studied after the external drive is turned off. For sufficiently short times and large enough wave amplitudes, the magnitude of the negative frequency shift from trapped electrons is a local function of electrostatic potential and the phase of the wave on axis lags the off axis phase. Analysis and simulations are presented of the damping and trapped-electron-induced self-focusing (H. Rose, Phys. Plasmas 12, 012318 (2005)) of the finite-amplitude EPW. The onset of trapped electron modulational instability (S. Brunner and E. Valeo, PRL 93, 145003 (2004)) both along and transverse to the direction of propagation is studied as a function of the wave amplitude and the system length.