Fluid models for computation of the physics of intense charged particle beams

Traditionally, calculation of radial and longitudinal dynamics of intense, relativistic, charged particle beams has used either envelope models, which calculate the time development of the beams r.m.s. radius, or particle models, which follow detailed particle orbits. Envelope models are simple and require little computer time but cannot model phenomena such as phase-mixed damping of beam radial oscillations that derive from particle kinetic effects. Computational particle models do reproduce kinetic phenomena but are very costly and yield no analytic results. This work describes two intermediate fluid models that are both simple and yet display phase mixed phenomena. Each model is developed in detail and is used to compute beam radial damping. These results are compared to the results of a traditional particle calculation. The models are found to agree well and reproduce all significant phenomena. The models are then used to compute the evolution of the beam hollowing instability in two dimensions as a demonstration of their utility. Finally, extensions of the models are discussed for three-dimensional calculations