Our approach to ion beam modeling breaks down the complex interplay of competing elementary processes into a series of independent consecutive steps. Thus, both in methodological development and computational modeling, the main effort can be directed towards the processes which are of greatest relevance in the context given. Moreover, employment of the special software available allows for comprehensive and efficient optimization of multigrid ion sources for low ion beam divergence and long lifetime, even in a personal computer environment. Here, for our Kaufman-type two-grid ion source RR-ISQ 76 some ion beam characteristics in their dependence on geometrical two-grid configuration are calculated and discussed, first of all in terms of shape and area of the plasma sheath. These dependencies are used to optimize this particular ion source for a low beam divergence. ©1998 American Institute of Physics.