Trapping and acceleration in nonlinear plasma waves

The trapping and acceleration of a test electron in a nonlinear plasma wave is analyzed in one dimension using Hamiltonian dynamics. The plasma wave is described by a nonlinear, cold fluid model. The maximum energy gain and the minimum energy required for trapping of the test electron are determined. The separatrix is plotted for several values of plasma wave amplitude. In the large wave amplitude limit, the maximum energy of a trapped electron scales as 2γ2pE2z, where γp is the relativistic factor associated with plasma wave phase velocity and Ez is the electric field amplitude of the nonlinear plasma wave. This is in contrast to the well-known results for a sinusoidal wave, in which the maximum energy scales as 4γ2pEz. As the nonlinear plasma wave approaches wavebreaking, the maximum energy is given by γmax→4γ3p−3γp, where γmax is the relativistic factor of the trapped electron.