Coulomb interactions in microfocussed electron and ion beams

Using established theories for calculating statistical Coulomb interactions in electron and ion beams, the effect of these interactions on the performance of practical instruments is estimated. The analysis concentrates on low voltage (1 kV) electron probe forming instruments and intermediate voltage (30 kV) focussed ion beam instruments. The approach is to first calculate the optimized probe size-probe current relations for these instruments in the absence of Coulomb interactions. As a function of probe size, it is then calculated how much current is really allowed in the probe before the Coulomb interactions significantly contribute to the probe size. The result is a comprehensive representation of instrument parameter values at which Coulomb interactions become important. The absolute maximum current ever obtainable in a given probe size is derived.