Excitation of turbulence by a relativistic electron beam

The two-stream instability as it passes from the initial state to turbulent regime is analyzed by an extension of the methods of O'Neil et al. (1971). In the extension, more than one mode is allowed, the effect of beam temperature is taken into account, and relativistic effects are included. A study of autocorrelation and trapping times shows that the system relaxes toward a partially coherent state. For hot relativistic beams the results are significantly different from the predictions of Thode and Sudan (1975). It is also found that cold relativistic beams tend to yield a rather weakly turbulent final state. The quasilinear theory is found to be valid even when the trapping time is of the same order as the autocorrelation time.