Halo formation and self-pinching of an electron beam undergoing the Weibel instability

The collisionless Maxwellization of the energy distribution of an electron beam undergoing Weibel filamentation instability in a dense background plasma is demonstrated. While binary collisions between discrete charged particles are usually responsible for establishing the Maxwell-Boltzmann distribution (MBD) of non-equilibrium plasmas, we demonstrate that the same effect is achieved through collective collisions between multiple beam filaments. The final state of the filaments' merger is a single pinched beam surrounded by a wide halo. An analytic model for the equilibrated beam is developed and used to estimate spatial profiles of the pinched beam and its halo, the temperature, and the magnetic field. Results of analytical theory agree well with those of particle-in-cell simulations. Deviations from the MBD are explained by incomplete Maxwellization of the electrons with high and low transverse energies.