Functional dependence, broad-band fitting, and ancillary conditions

The ability to make multiple passes through a charged particle optical system, as a single step in a mathematical procedure, opens up new computational capa- bilities. At the simplest level, the functional dependence of any transfer matrix of any order, or any beam phase-space parameter can be plotted as a function of any other parameter used to describe the optical con#12;guration. Secondly, broad-band #12;tting can be done on aberrations, where all orders are considered simultaneously according to their importance on the #12;nal phase-space beam distribution. Finally, ancillary conditions may be imposed in the calculation of functional dependences. For example, the dependence of a matrix element on a beam line parameter may be calculated and plotted, subject to constraints imposed on other matrix elements. The computer program TRANSPORT now has these capabilities. Additional examples will be given.