Development and Application of Adjoint Methods in the MICHELLE Beam Optics Code

We present progress on the application of an adjoint approach to determine sensitivity functions for the design of charged particle optics in the presence of both electric and magnetic static fields. The methodology is applied by implementing techniques in the MICHELLE beam optics code whereby a minimal number of time-reversed simulations enables the determination of a variety of figures of merit resulting from small, but arbitrary, property changes. Such changes may include geometric electrode shapes, magnetic field patterns, electrode voltages, emission properties, etc. The use of these sensitivity functions to determine manufacturing alignment and assembly tolerances to maximize production yield as well as in optimization algorithms will be discussed. Applications to beam transport in magnetic fields will be presented.