Stability of a breathing K-V beam

Many explanations of halo formation in high current ion beams require the existence of particles which are outside the beams central core. We propose a mechanism which is capable of moving some particles outside the core. Specifically, we consider a 2-D KV beam which is started into a uniform density breathing oscillation by some mismatch in the transverse focusing pattern. We then consider perturbations with non-linear space charge density and find that they can be unstable against small oscillations for certain ranges of mismatch and tune depression. The stability limits in the mismatch/tune depression space have been computed for the first three azimuthally symmetric modes with non-linear charge density. It appears that even modest values of mismatch and tune depression can lead to instabilities which are capable of moving particles outside the core of the beam