TRANSFORMATION GROUPS IN-BEAM OPTICS .1. GENERAL-THEORY

The motion of charged particle beams in a beam optical system can be described by means of the transformations of the phase space contours and particle distribution functions. These transformations comprise several groups: the beam transport (BT) group, contour preserving (CP) group, distribution preserving (DP) group, etc. The principal problems of beam optics can be reduced to the following: the determination of the eigen phase space contour of a transformation and the determination of the transformation in which the shape of a phase space contour can be preserved.