Electron Self-Injection in Multidimensional Relativistic-Plasma Wake Fields

We present an analytical model for electron self-injection in a nonlinear, multidimensional plasma wave excited by a short laser pulse in the bubble regime or by a short electron beam in the blowout regime. In these regimes, which are typical for electron acceleration, the laser radiation pressure or the electron beam charge pushes out background plasma electrons forming a plasma cavity-bubble-with a huge ion charge. The plasma electrons can be trapped in the bubble and accelerated by the plasma wakefields up to very high energies. The model predicts the condition for electron trapping and the trapping cross section in terms of the bubble radius and the bubble velocity. The obtained results are in a good agreement with results of 3D particle-in-cell simulations.