The space/time evolution of the nonlinear two-stream instability

A cold electron beam penetrating a cold plasma is electrostatically unstable. The instability produces a growing electric field that saturates when the beam electrons are suddenly trapped by a single wave. During trapping a significant amount of energy is transferred from the beam to the field and ultimately to the plasma. At Los Alamos experiments are being performed that demonstrate this anomalous beam-driven plasma heating. The heating efficiency is a function of the phase velocity of the trapping wave. According to our generalization of a previous calculation, the instability is absolute and its wave form evolves in both space and time. Modifying trapping theory to account for the space and time evolution of the two-stream instability, we find that the heating efficiency should change in time. This prediction is in agreement with results from one-dimensional PIC simulations.