Phase speed of electrostatic waves: The critical parameter for efficient   electron surfing acceleration
  Particle acceleration by means of non-linear plasma wave interactions is of great topical interest. Accordingly, in this paper we focus on the electron surfing process. Self-consistent kinetic simulations, using both relativistic Vlasov and PIC (Particle In Cell) approaches, show here that electrons can be accelerated to highly relativistic energies (up to 100 m_e c^2) if the phase speed of the electrostatic wave is mildly relativistic (0.6c to 0.9c for the magnetic field strengths considered). The acceleration is strong because of relativistic stabilisation of the nonlinearly saturated electrostatic wave, seen in both relativistic Vlasov and PIC simulations. An inverse power law momentum distribution can arise for the most strongly accelerated electrons. These results are of relevance to observed rapid changes in the radio synchrotron emission intensities from microquasars, gamma ray bursts and other astrophysical objects that require rapid acceleration mechanisms for electrons. 
M E Dieckmann, N J Sircombe, M Parviainen, P K Shukla and R O Dendy