Modeling and numerical simulation of space charge dominated beams in the paraxial approximation

This work is devoted to the modeling of space charge dominated particle beams in the paraxial approximation with several types of external focusing fields (uniform, periodic and alternating gradient). A solid mathematical background for numerical beam simulation is established. The Kapchinsky-Vladimirsky (KV) distribution which can be matched exactly or numerically to the focusing channel is first studied. Then the matched KV beam is used to approximately match arbitrary beams. Moreover, Waterbag and Maxwell-Boltzmann beams are studied to give analytical solution for code validation. Finally, numerical simulations are presented in different configurations.