Space charge effects in plasma particle analyzers

The effects of space charge on the energy resolution obtainable with deflection type analyzers have been considered previously for cylindrical beams. In the present analysis the problem of the electric field in a retarding potential analyzer is considered. This electric field is larger than the transverse field which causes radial expansion. Extension of the analysis to two dimensions in a simple case shows, however, that the longitudinal field is much reduced when the beam has a diameter small compared to its length.