Kinetic study of the sausage mode of a resistive instability of a relativistic electron beam

The nonlinear problem of the growth of the sausage mode of the resistive instability of a relativistic electron beam propagating without collisions through a tenuous plasma is solved. The plasma conductivity is assumed to be high, so that the wave phase velocity is low in comparison with the velocity of light. A kinetic approach is taken to the description of the beam. A numerical solution of the problem shows that this instability occurs in a cold, uniform beam. In the nonlinear stage of the instability the beam goes through states with a hollow structure. Suppression of the instability is found for a beam with a Bennett distribution function. The stabilization results from phase mixing of the beam particles.