Three dimensional δf simulations of beams in the SSC

A three dimensional δf strong‐strong algorithm has been developed to apply to the study of such effects as space charge and beam‐beam interaction phenomena in the Superconducting Super Collider (SSC). The algorithm is obtained from the merging of the particle tracking code Simpsons used for 3 dimensional space charge effects and a δf code. The δf method is used to follow the evolution of the non‐gaussian part of the beam distribution. The advantages of this method are twofold. First, the Simpsons code utilizes a realistic accelerator model including synchrotron oscillations and energy ramping in 6 dimensional phase space with electromagnetic fields of the beams calculated using a realistic 3 dimensional field solver. Second, the beams are evolving in the fully self‐consistent strong‐strong sense with finite particle fluctuation noise is greatly reduced as opposed to the weak‐strong models where one beam is fixed.