The methods of numerical simulation of particle optics problems are examined with respect to their accuracy and stability. Principles of space-charge optics and of beam formation are recalled to address questions like the general validity of the 3/2-power law and the Pierce angle. For the simplest mathematical model of the plasma sheath the ''correct'' shape of the wall electrode is calculated analytically and compared with numerical simulations. The result will be used to establish engineering rules for the extraction of ion beams from a plasma with minimum aberration. The compensation of ion beams by electrons and the influence of this on ion-beam formation is discussed both from the viewpoint of theoretical analysis of compensation as well as on the basis of experimental evidence. (C) 1996 American Institute of Physics. References: 23
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