Finding self-consistent distributions of beam particles interacting with each other via the space charge force is one of the challenges of accelerator physics. Exactly solvable models are used for simulation benchmarks, instability threshold calculations, etc. Since such distributions have been found only in one and two dimensions (Kapchinsky-Vladimirsky distribution), it is not possible to apply them to a general three-dimensional motion. The talk presents new sets of self-consistent distributions, extending even to the three dimensional case. 3D distributions can be used in linacs. A subset of new 2D distributions can be injection-painted into an accumulator ring to produce periodic space charge conditions. The periodic condition guarantees zero space-charge-induced halo growth and beam loss during beam accumulation and transport.


Talk Slides: (slides)