The role of energy and momentum conservation in nonlinear beam-plasma interaction

Theoretical and numerical results concerning the nonlinear interaction of an initially cold beam with a single wave (ω ≈ k v_b) in either magnetized or field- free plasma are presented and discussed. By using the energy and momentum conservation laws, the equations describing the development of the wave amplitude and phase, both in the temporal and spatial problem, are derived and then solved numerically together with the equations of motion of the beam particles. The fundamental role of an absorption (or transformation) of the wave in its interaction with a beam modulated at a frequency belonging to the upper branch of the electron plasma oscillation is recognized in two model situations.