Theory of the Laser Wake-Field Accelerator Revisited: Wake Overtaking,   Localized Spectrum and Ponderomotive Acceleration
  The electron and positron acceleration in the first cycle of a laser-driven wakefield is investigated. Separatrices between different types of the particle motion (confined, reflected by the wakefield or ponderomotive potential and transient) are demonstrated. The ponderomotive acceleration is negligible for electrons but is substantial for positrons. An electron bunch, injected as quasi-monoenergetic, acquires a localized energy spectrum with a cut-off at the maximum energy. 
T. Esirkepov, S. V. Bulanov, M. Yamagiwa, T. Tajima