Collisionless filamentation, filament merger and heating of low-density   relativistic electron beam propagating through a background plasma
  A cold electron beam propagating through a background plasma is subject to filamentation process due to theWeibel instability. If the initial beam radius is large compared with the electron skin depth and the beam density is much smaller than the background plasma density, multiple filaments merge many times. Because of this non-adiabatic process, the beam perpendicular energy of initially cold beam grows until all filaments coalesce into one pinched beam with the beam radius much smaller than initial radius and smaller than the electron skin depth. It was shown through particle-in-cell simulations that a significant fraction of the beam is not pinched by the magnetic forces of the pinched beam and fills most of the plasma region. The resulting electron beam energy distribution in the perpendicular direction is close to a Maxwellian for the bulk electrons. However, there are significant departures from a Maxwellian for low and high perpendicular energy (deeply trapped and untrapped electrons). An analytical model is developed describing the density profile of the resulting pinched beam and large low-density halo around it. Based on this analytical model, a calculation of the energy transfer from the beam longitudinal kinetic energy to the transverse beam kinetic energy, the self-magnetic field, and the plasma electrons is performed. Results of analytical theory agree well with the particle-in-cell simulations results. 
Vladimir Khudik, Igor Kaganovich, and Gennady Shvets
physics.plasm-ph