Cold phase fluid model of the longitudinal dynamics of space-charge-dominated beams

Abstract

The dynamics of a longitudinally cold, charged-particle beam can be simulated by dividing the beam into slices and calculating the motion of the slice boundaries due to the longitudinal electric field generated by the beam. On each time step, the beam charge is deposited onto an (r, z) grid, and an existing (r, z) electrostatic field solver is used to find the longitudinal electric field. Transversely, the beam envelope equation is used for each slice boundary separately. In contrast to the g-factor model, it can be shown analytically that the repulsive electric field of a slice compressed to zero length is bounded. Consequently, this model allows slices to overtake their neighbors, effectively incorporating mixing. The model then effectively describes a cold fluid in longitudinal z, vz phase space. Longitudinal beam compression calculations based on this cold phase fluid model showed that slice overtaking reflects local mixing, while the global phase space structure is preserved.