Two-stream instability in the presence of longitudinal magnetic field

A multiple sclaes perturbation theory has been applied to investigate the nonlinear behaviour of beam-plasma system near a marginally stable state in the presence of longitudinal magnetic field. The perturbation method leads to a nonlinear Schrödinger equation for the finite amplitude. The coefficients of this equation show that only if the beam is compressed isothermally can there exist a range of wavenumbers for which stabilization might occur. The stable region increases with the applied magnetic field.