Eciency of a Boris-like integration scheme with spatial stepping

The Boris integration scheme, familiar in plasma simulation, is modified to use a spatial variable as the independent variable. This is important for beam simulations, where using the distance along the beam axis as the inde-pendent variable simplifies particle tracking through a beamline. The modi-fied Boris scheme is second-order accurate, requires only one force calculation per particle per step, and preserves phase space structure more accurately than a Runge-Kutta integration scheme. The new scheme is implemented in the ICOOL code for simulation of muon cooling. Two ICOOL simulations demonstrate the advantages of the Boris integrator: (i) for a single particl