The collective energy loss of the relativistic electron beam propagating through background plasma

We have developed a reduced computational model¹ describing beam-plasma interaction between kinetic beam particles and ambient plasma fluid. Using conservation of the canonical momentum for beam and plasma electrons in long beam pulses, we have numerically studied the dynamics of collisionless Weibel (filamentation) instability (WI) in the regime of very underdense electron beam. A physical model describing the structure and coalescence energetics of the beam/return current filaments produced as a result of the WI was developed. We emphasize the strongly nonlinear stage of the instability, during which the beam density of filaments is compressed to the background plasma density, and the ambient plasma is fully evacuated. Our analytic and numerical results using LSP code demonstrate that the beam filaments can carry super-Alfvenic currents with hollow current density profiles similar to the Hammer-Rostoker equilibrium. This has profound implications for the long-term evolution of the magnetic field and beam current and explains the long-standing puzzle: why magnetic field energy initially increases, but eventually decreases during the collisionless Weibel instability.