Phase space approach to charged beam analysis

In the design of devices using charged particle beams, often the effect of the charge on the electric field has to be taken into account. The distribution of the space charge in the beam can influence the electric field created by the electron optics significantly. The interaction between electrodes and space charge generated electric fields is described by the Poisson equation, the space charge is governed by the equation of motion. In this paper an interpolation scheme in phase space is presented speeding up the usual successive substitution algorithm considerably. The problem of finding the configuration space distribution from the phase space data is automatically solved, without integrating explicitly over the velocity space. The results obtained in several computational examples are discussed