  We investigate limits on the current of the PSI Injector II high intensity
separate-sector isochronous cyclotron, in its present configuration and after a
proposed upgrade. Accelerator Driven Subcritical Reactors, neutron and neutrino
experiments, and medical isotope production all benefit from increases in
current, even at the ~ 10% level: the PSI cyclotrons provide relevant
experience. As space charge dominates at low beam energy, the injector is
critical. Understanding space charge effects and halo formation through
detailed numerical modelling gives clues on how to maximise the extracted
current. Simulation of a space-charge dominated low energy high intensity (9.5
mA DC) machine, with a complex collimator set up in the central region shaping
the bunch, is not trivial. We use the OPAL code, a tool for charged-particle
optics calculations in large accelerator structures and beam lines, including
3D space charge. We have a precise model of the present production) Injector
II, operating at 2.2 mA current. A simple model of the proposed future
(upgraded) configuration of the cyclotron is also investigated.
  We estimate intensity limits based on the developed models, supported by
fitted scaling laws and measurements. We have been able to perform more
detailed analysis of the bunch parameters and halo development than any
previous study. Optimisation techniques enable better matching of the
simulation set-up with Injector II parameters and measurements. We show that in
the production configuration the beam current scales to the power of three with
the beam size. However, at higher intensities, 4th power scaling is a better
fit, setting the limit of approximately 3 mA. Currents of over 5 mA, higher
than have been achieved to date, can be produced if the collimation scheme is
adjusted.
