Nonlinear stabilization of cold beam-plasma instability

Nonlinear stabilization of cold beam plasma instability are studied on the basis of Dupree's theory of strong plasma turbulence. Calculations are carried out to second order in the perturbed electric field, and it is found that, for a narrow spectrum satisfying δκ/κ≪1, stabilization occurs for the trapping frequency ωT ť ∣qeκΕk/me∣½ ť γL the linear growth rate. Nonlinear frequency correction, and also the changes in the kinetic and thermal energy densities of the beam, are calculated as the waves grow. Some points of difference between the resonant and non-resonant instabilities are discussed.