Trapping, dark current, and wave breaking in nonlinear plasma waves

The trapping of thermal electrons in a nonlinear electron plasma wave of arbitrary phase velocity is investigated. Using a model based on single-particle dynamics, various thermal effects are calculated, such as the evolution of the plasma temperature. Assuming a broad (one-dimensional) plasma wave driver, the threshold plasma wave amplitude for electron trapping is calculated, thereby determining the fraction of trapped plasma electrons and the expected dark current in a plasma-based accelerator. It is shown that the trapping threshold is increased within the region of the laser pulse. The laser intensity required to excite plasma waves of sufficient amplitude to trap background electrons is determined. The hydrodynamic wave breaking field amplitude is recovered from particle trapping considerations. Implications for experimental and numerical studies of plasma accelerators are discussed.