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A cold electron beam propagating through a background plasma is subject tofilamentation process due to theWeibel instability. If the initial beam radiusis large compared with the electron skin depth and the beam density is muchsmaller than the background plasma density, multiple filaments merge manytimes. Because of this non-adiabatic process, the beam perpendicular energy ofinitially cold beam grows until all filaments coalesce into one pinched beamwith the beam radius much smaller than initial radius and smaller than theelectron skin depth. It was shown through particle-in-cell simulations that asignificant fraction of the beam is not pinched by the magnetic forces of thepinched beam and fills most of the plasma region. The resulting electron beamenergy distribution in the perpendicular direction is close to a Maxwellian forthe bulk electrons. However, there are significant departures from a Maxwellianfor low and high perpendicular energy (deeply trapped and untrapped electrons).An analytical model is developed describing the density profile of theresulting pinched beam and large low-density halo around it. Based on thisanalytical model, a calculation of the energy transfer from the beamlongitudinal kinetic energy to the transverse beam kinetic energy, theself-magnetic field, and the plasma electrons is performed. Results ofanalytical theory agree well with the particle-in-cell simulations results.

Collisionless filamentation, filament merger and heating of low-density relativistic electron beam propagating through a background plasma