Two-dimensional Vlasov simulation of electron plasma wave trapping, wavefront bowing, self-focusing, and sideloss

Two-dimensional Vlasov simulations of nonlinear electron plasma waves are presented, in which the interplay of linear and nonlinear kinetic effects is evident. The plasma wave is created with an external traveling wave potential with a transverse envelope of width Δy such that thermal electrons transit the wave in a “sideloss” time, tsl~Δy/ve. Here, ve is the electron thermal velocity. The quasisteady distribution of trapped electrons and its self-consistent plasma wave are studied after the external field is turned off. In cases of particular interest, the bounce frequency, ωbe=keϕ/me, satisfies the trapping condition ωbetsl>2π such that the wave frequency is nonlinearly downshifted by an amount proportional to the number of trapped electrons. Here, k is the wavenumber of the plasma wave and ϕ is its electric potential. For sufficiently short times, the magnitude of the negative frequency shift is a local function of ϕ. Because the trapping frequency shift is negative, the phase of the wave on axis lags ...