In accelerator magnetic analyzing systems consisting of a beam analyzing system and a reaction product analyzing system, the total resolution of the system may be made, to first order, independent of target thickness or independent of the width of the beam on the target, by proper choice of target orientation angle. By proper choice of geometry, the two may be accomplished simultaneously for a given nuclear reaction, and suitable compromises give reasonably good results for a large variety of applications. In most cases, taking advantage of these effects allows an order of magnitude increase in intensity without affecting the resolution.