Effect of electron-ion collisions on the nonlinear state of the relativistic two-stream instability

The analysis outlines conditions for the hydrodynamic interaction, including foil scattering and beam self-magnetic field effects. For the hydrodynamic interaction, the oblique coupling coefficient model is extended to include the effect of a finite electron-ion collision rate on the nonlinear state. Partial numerical simulation results are found to be in agreement with the model. Limitations due to temperature inhomogeneity along the deposition length and to increased deposition length are also discussed. It is found that an intense relativistic electron beam can couple its energy via the two-stream instability to a high density 1017–1020 cm−3 plasma. It is required that the plasma be fully ionized, with an initial electron temperature of ≳10 eV for 1017 cm−3, 10–20 eV for 1018 cm−3, 15–50 eV for 1019 cm−3, and ∼100 eV for 1020 cm−3.