Interaction of blowing hollow electron beam with a finite length plasma cylinder

One of the most important problems for collective ion accelerators is that of providing stable transport of a high-current relativistic electron beam. The cause of instability can be beam interaction with a plasma produced by residual gas ionization. That is why it becomes interesting to find the instability development in beam-plasma systems of different configurations. The given work is dealing with interactions of a monoenergetic hollow electron beam with a blow off plasma cylinder of finite length. The plasma and beam are enclosed into a metallic waveguide. An external longitudinal magnetic field is applied to the system magnetizing electron beam motion. The plasma electron motion is assumed to be either magnetized (a strong magnetic field) or not in the least magnetized (a weak magnetic field). It is assumed that the electron beam has a hollow configuration with infinitely thin walls