Effects of the space charge forces and the beam halo in an AVF cyclotron with intense beam currents

The equations of motion of particles in an AVF cyclotron in a curvilinear coordinate system are derived for the cases with and without space charge forces. Assuming a set of the parameter values in the equations, numerical calculations are carried out by using Lunge-Kutta methods in the case with space-charge forces. The results show that the formation of the beam halo is also a main reason of the beam losses, but the mechanism here is different from that in a linear accelerator. It is not given rise by resonance and chaos but the outward repellent motion and the vortex motion of the particles in the bunch