Numerical model of a plasma with a monoenergetic relativistic electron beam

Abstract

The possibility of converting the energy of a low-density relativistic electron beam into the energy of a narrow Langmuir wave packet is demonstrated by numerical integration of the Vlasov and Poisson equations. It is shown that a small perturbation stops growing exponentially because the beam electrons are trapped by the wave, so that the wave-field energy is partially converted back into beam energy. Then, the beam slips out of resonance with the wave, and the energy exchange with the wave terminates almost completely. A detailed comparison is made between the results obtained in a one-dimensional (hydrodynamic) model of the beam instability with allowance for the plasma nonlinearity and the results of numerical simulations. The computed time evolution of the field energy is found to deviate substantially from the theoretical evolution, which is attributed to the decay of the primary oscillation spectrum in the numerical model. However, even with allowance for the internal kinetic processes in the plasma, the single-mode and numerical models give nearly the same energy losses of the beam in the asymptotic limit \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) (where ωp is the plasma frequency).