Current limits in linear accelerators

In recent years considerable interest has developed in the use of linear accelerators for various high-current applications (radiation testing facilities, neutron spallation sources, heavy-ion fusion, etc.). The beam dynamics and current limits in a linear accelerator are determined largely by the periodicity and phase-space acceptance of the external focusing system and the particle oscillation frequencies (or phase shifts per focusing period), both without the space-charge forces and with the space-charge forces of the particle bunch. General formulas for the transverse and longitudinal current limits in terms of these fundamental quantities are derived. The relationships with the actual accelerator and particle beam parameters are examined for strong (quadrupole) and weak focusing field configurations. As a practical illustration, the results are applied to a drift-tube linac with quadrupole focusing in the transverse direction and rf phase focusing in the longitudinal direction.