Macroscopic and microscopic models for the relativistic beam-plasma instability: A comparison

The relaxation of a relativistic electron beam is studied in one space dimension by two different codes: (a) by a hybrid code where the fluid equations for the background plasma are integrated according to the pseudospectral method, and the beam particle equations by the particle-in-cell method; (b) by a pure particle-in-cell code. Thermal energy remains small in both simulations, which indicates that the fluid description is adequate to study the interaction. Beyond that, a quantitative comparison of the results shows good agreement; code (a) is more accurate due to the lower noise level, but it is also more sensitive to numerical instabilities. Finally, we show that simpler models like the single-wave model and its derivatives are in conflict with the correct wave--particle dynamics