New longitudinal space charge algorithm

We describe a new, improved longitudinal space-charge electric field calculation for particle beams with periodic modulation of the charge density. Whereas the usual method assumes long bunches with constant transverse cross-section, the new algorithm applies to long or short bunches with arbitrary binomial transverse distribution and incorporates dynamical corrections to the usual static approximation. The algorithm has been coded in Fortran and been made an option of the particle tracking program LONG1D. Based on tracking studies, it is concluded that these improvements to the physics model are most important for short bunches with high synchrotron frequency and high-order longitudinal multipole content