Numerical study on nonlinear stage of cyclotron-focusing instability

Ion beam acceleration by a cyclotron wave producing in an electron rectilinear beam is being investigated. Nonlinear wave motion with captured particles whose phase velocity increases as the propagation proceeds is known as ''acceleron''. The relativistic electron beam propagating in a shielding tube has been confined in the state of equilibrium by the longitudinal magnetic field and by the space charge field of an initially stationary ion beam. Time dependences are given of perturbations of the electron beam radius, ion density, ratio of the number of captured ions to their total number, and the average velocity of captured ions. The presented calculation shows a good agreement with the hypothesis of existence of an ''acceleron'' - a self-accelerating wave with captured particles