Natural Alfven oscillations of plasma cylinder with an ion beam

Stability of natural Alfven oscillations of plasma cylinder with ion beam is studied. A collision heterogeneous plasma with free boundary is considered. Effective variant of the method of differential run in order to study Alfven oscillations of plasma cylinder is suggested. The calulation technique is developed. Spectrum of small perturbations is analyzed for parabolic profiles of plasma density and eigenfunctions are plotted. Critical parameters neutral curves and increments are determined. It is found out that the spectrum of Alfven orcillations of plasma cylinder includes near-axis and near-interface disturbances. With the growth of the Reynolds number the near-axis disturbances are located in the near-axis region of a plasma, and interface disturbances - in the vicinity of the plasma boundary. Both near axis and interface. Alfven oscillations can become incremenating depending on ion beam parameters. The localization effect of near-axis disturbances is expressed in a plasma cylinder more distinctly than in a flat layer of the plasma