Beam Transport Limits and the Core Particle Model
S. Chilton (UCB-NE)

Ideally, optimizing beam focusing would involve focusing beams 
as strongly as possible, packing in as much space-charge as possible.  
However, in reality, single-minded devotion to maximizing space-charge 
and focusing strength is insufficient to ensure stable beam transport, 
as real beams contain particles outside their statistical radii r_x and
r_y in the KV model.  In some regions of parameter space, stable beam
transport is impossible.  The simplest of these regions, the so-called
envelope bands, are fairly well-understood.  However, experiments have
shown that in other parameter space regions, higher-order effects
result in beam emittance growth and unstable transport.  Modeling
these effects has proven quite challenging in accelerator physics.

Here, we derive a core particle model that attempts to explain why
higher-order instabilities manifest themselves where they do in
parameter space.  We then develop a Mathematica program (based in part
on the envelope matching scheme described last semester) and use
it to map our parameter space for instabilities and, by extension,
transport limits.  The results of our simulations agree reasonably
well with experiments.