Monte Carlo simulation of a nonlaminar DC beam including the influence of self-fields

We present a method to simulate the transport of a nonlaminar DC beam under the influence of self-fields. The simulation randomly populates an initial phase space distribution with n particles. These particles are propagated in steps through the transport region, and the particle positions at each step are used in an unbinned maximum likelihood fit for the beam profile distribution. The self-fields at the position of each particle are calculated using the fitted beam profile distribution. The total computation required by the simulation scales linearly with n. The simulation for an electron beam with a phase space given by the Kapchinskij-Vladimirskij distribution is in good agreement with the beam profile predicted by the Kapchinskij-Vladimirskij envelope equations.