  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.
