Hamiltonian model for plasma electron trapping and acceleration in multidimensional plasma wake field

Abstract

We present a simple model (piecewise model) for electron self‐injection in nonlinear, multidimensional plasma waves excited by short laser pulse in the bubble regime. In this model fields are assumed to be constant in quarters that yields an extra integral of the electron motion and allows us to obtain analytical expressions for the electron trajectories. In the framework of this model we derive the condition of the electron trapping in the bubble. The developed theory predicts the trapping cross section in terms of the bubble radius and the bubble velocity and reveals key features of electron trapping in three‐dimensional regime.