Use of a minimum-ellipse criterion in the study of ion-beam extraction systems

Ion-beam extraction systems may be optimized by ray-tracing codes. As a general criterion for comparing the geometry-dependent phase-space distributions, we first calculate the minimum-area ellipse that encloses all particles of any given two-dimensional phase-space distribution. Then, the relation between ellipse area and contained beam fraction is established by systematically finding and eliminating those particles that contribute most heavily to the emittance. Prescriptions for finding the minimum ellipse and beam fractions are presented. The minimum and rms ellipses are compared for two code-calculated distributions that represent ion-beam extraction geometries