Phase space acceptance and emittance in beam transport with application to tandem accelerators

Phase space acceptance and emittance ellipse areas for a region bounded by beam-limiting apertures of half widths r1 and r2 are shown to be πr1r2/mod(a12) and πr1r2D/mod(a12), respectively, for linear beam transport in which D is the determinant of the basic 2x2 portion of the standard beam transport matrix and a12 is the matrix element which transforms initial divergence into final displacement. A technique of analysis using these and related results is demonstrated for typical beam transport components. Examples are given for analyzing and optimizing beam transport through tandem electrostatic accelerators. (Auth.)