• G. Bassi
  The University of Liverpool, Liverpool
• J.A. Ellison, K.A. Heinemann
  UNM, Albuquerque, New Mexico

We consider a 2D bunch represented by \mathcal N simulation particles moving on arbitrary planar orbits. The mean field of the bunch is computed from Maxwell's equations in the lab frame with a smoothed charge/current density, using retarded potentials. The particles are tracked in beam frame, thus requiring a transformation of densities from lab to beam frame. We seek improvements in speed and practicality in two directions: (a) choice of integration variables and quadrature rules for the field calculation; and (b) finding smooth densities from scattered data. For item (a) we compare a singularity-free formula with the retarded time as integration variable, which we used previously, with a formula based on Frenet-Serret coordinates. The latter suggests good approximations in different regions of the retardation distance, for instance a multipole expansion which could save both time and storage. For item (b) we compare various ideas from mathematical statistics and numerical analysis, e.g., quasi-random vs. pseudo-random sampling, Fourier vs. kernel smoothing, etc. Implementations in a parallel code with \mathcal N up to a billion will be given, for a chicane bunch compressor.