Kinetic description of coupled transverse oscillations in an intense relativistic electron beam-plasma system

Abstract

The stability properties of an intense relativistic electron beam propagating through a collisionless background plasma are investigated within the framework of the Vlasov–Maxwell equations. It is assumed that νj/γj<<1, where j=b,e,i denote beam electrons, plasma electrons, and plasma ions, respectively, and νj and γjmjc2 are Budker’s parameter and the characteristic energy, respectively, of the plasma component j. The analysis is carried out for the class of rigid-rotor equilibrium distribution functions in which all particles of plasma component j have the same value of energy in a frame rotating with angular velocity ωj and the same value of axial canonical momentum. From the stability analysis for coupled transverse oscillations between the beam electrons and the plasma electrons, it is found for a low density beam (ω2pb/ω2cb≲0.5) that perturbations with azimuthal harmonic numbers l⩾2 are the most unstable modes. Moreover, the fundamental mode (l=1) is completely stabilized whenever the conducting wall is sufficiently close to the plasma boundary. The ion resonance stability properties are also investigated, including the interaction of the beam electrons with the plasma ions. It is shown that the instability domain for the ion resonance instability extends to large values of axial wavenumber kz for high harmonic numbers l.