Effect of space charge forces on particle tracking and generation of high order maps

TOPKARK is a beam optics program consisting of two Fortran codes developed in parallel: a 3-D high-order mapping code and a particle tracking code; both utilize a space charge model which treats the particle bunch as a uniformly-filled 3-D ellipsoid. The map code uses the differential algebra library DA to generate an arbitrary-order Taylor map describing a given lattice, then the Lie algebra library LIELIB is used to obtain the Dragt-Finn factorization of the corresponding Lie polynomial. The Lie polynomial generated by TOPKARK without space charge has been successfully bench-marked through third order against MARYLIE 3.0 and through fifth order against TLIE. With space charge on, TOPKARK generates a linear map that agrees well with TRACE 3-D. The tracking code uses a symplectic integration scheme when space charge is off, and it includes a more general space charge model which assumes only ellipsoidal symmetry of the spatial distribution