HIGHER ORDER SYMPLECTIC INTEGRATION OF COLLECTIVE EFFECTS

Long time tracking simulations of intense beams requires a proper account for the collective effects. Many tracking codes allow the number of space charge kicks, for example, to be determined by the end user. This makes no guarantee that the integration is second order accurate in the step size. In this proceeding, we present results on the proper second- and fourth-order symplectic integration of the Hamiltonian dynamics of particles under collective interactions using a model Hamiltonian with collective space charge forces to illustrate the underlying principles.