Nonlinear Theory of the Instability of a Modulated Electron Beam of Low Density in a Plasma. III. Derivation of Nonlinear Equations for the Time‐ and Space‐Problems (Single Wave Model)

Abstract

AbstractIn this paper it is shown that there are, in dependence on the properties of the system, several systems of nonlinear equations for the description of the nonlinear “hydrodynamical stage” of the beam‐plasma instability. It becomes evident that the well known system of equations for the resonant wave instability in beam‐plasma systems is not applicable for the case of strong dissipation of the wave energy in the plasma and for the case of the excitation of nonresonant waves. As well for the time‐problem as for the space‐problem there are derived three different systems of nonlinear equations. An energetic analysis of the nonlinear stage of the excitation of resonant waves is given. Anomalous growth of the amplitude of resonant waves by interaction with strong modulated electron beams is examined.