Space charge induced beam loss on a high intensity proton synchrotron

High intensity proton synchrotrons provide beams for several types of facility around the world, including spallation neutron sources and high energy physics experiments. The defining feature of these particle accelerators, that of intense beams, is tightly coupled to what limits the intensity, which is the controlled loss of beam particles.
Many different factors contribute to beam loss. Beam will be lost on injection to a synchrotron and may be lost on extraction or in transfer lines. Non-linearities in the accelerator lattice can introduce driving terms for resonant beam behaviour. Collective effects between the beam particles and with the beam environment modify the single particle behaviour considerably.
High intensity loss that occurs in the transverse plane, due to space charge and image fields, was investigated. The rapid cycling synchrotron at the ISIS Spallation Neutron Source in the UK was the focus for all of the work. The ISIS Synchrotron has many particular features which were described. One such feature is the conformal rectangular vacuum vessel, which takes the shape of the design beam envelope with certain modifications. This vacuum vessel has a complex effect on beam image fields.
Numerical tools to study the space charge and image fields at ISIS were created and reported. The tools included two Poisson solvers to study space charge and images which were benchmarked against commercially available algorithms. A two dimensional particle-in-cell tracking code was created using the space charge solvers in combination with either a smooth focusing lattice model or one which generated Twiss matrices. A variety of diagnostic tools were available.
A survey of existing analyses for pencil beams in parallel plate and rectangular geometry was made. Results from the analysis were then compared with two dimensional simulations with round uniform beams in rectangular geometry. Differences and extensions to the analysis were summarised. Coefficients for higher order image terms were defined and tabulated. The two dimensional nature of the image field was discussed and values for the coefficients for certain higher order terms identified in the plane orthogonal to the beam offset.
Solutions for closed orbits produced with single and harmonic kicks at low and high intensity were discussed and simulated. A model was proposed which included the higher order image coefficients produced by the closed orbits. A single particle model was then explored which obtained resonance conditions from the closed orbits and image coefficients. The effect of self-consistent coherent motion on the results was discussed.
Particle-in-cell beam tracking simulations were used to explore the results of this analysis numerically. Image resonances were found and described for a variety of simulation parameters starting with a smooth focusing lattice and uniform density beam, then progressing to more realistic cases including waterbag beams, alternating gradient lattices and conformal vacuum vessels. Image resonances described by the models were reported as were others that needed further explanation. Their possible impact for ISIS was discussed.
New experiments with coasting beams at ISIS were carried out to explore the relationship between tune and beam loss at low intensity. Such experiments are a vital first step to understanding high intensity behaviour. It was shown that ISIS has existing lattice nonlinearities (some known, some unknown) which will need to be taken into account for high intensity experiments and simulations.
Finally this work was put into context by examing specific transverse space charge effects for a proposed ISIS upgrade and including ideas developed throughout the thesis. Estimates were made of the strength of space charge effects and emittance scaling using conventional methods. The particle tracking tools developed for the thesis were then used to study beam behaviour with lattice gradient errors, the effects of closed orbits and changes to the working point. The transverse calculations and simulations suggested that the upgrade was feasible.

Keywords: Space charge
High intensity
Images
Advisor: Warsop, C
Peach, K