Nonlinear transverse electron beam dynamics in a modified betatron accelerator

Abstract

The transverse electron beam dynamics in a modified betatron accelerator is studied using a new approach. This approach is based on the two exact constants of the motion and the potentials at the center of the beam. The main advantage of the present technique is that the ring orbits can be accurately determined over the entire minor cross section of the torus and not only near the minor axis. The results indicate that the electron ring orbits in the plane transverse to the toroidal magnetic field always close inside the vacuum chamber, and their topology is often substantially different than that predicted from the linear theory.