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

The equations of motion of particles in an AVF cyclotron in a curvilinear c oordinate system are derived for the cases with and without space charge fo rces. Assuming a set of the parameter values in the equations, numerical ca lculations are carried out by using Lunge-Kutta methods in the case with sp ace-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 ch aos but the outward repellent motion and the vortex motion of the particles in the bunch.