Calculation of Space Charge Effects in Isochronous Cyclotrons

An introduction to the problems related to space charge calculations in isochronous cyclotrons is followed by the presentation of a new computer simulation model for the longitudinal space charge effects. The new model uses an analytical tansformation to reduce from three to two dimensions and a particle-in-cell method to calculate the charge distribution as a function of time. The new computer program enabled us to study the "spiralling instability", which can evoke filamentation in the phase-plane related to energy and RF-phase of the particles. While this instability is most important at low energies, there is also a steady increase of energy spread in the beam pulses during the acceleration. Also this second effect causes an increase of the beam losses at extraction, therefore both can limit the beam current that can be handled.