The Determination of Beam Transport Manufacturing Parameter Sensitivities Using Adjoint Methods in the Presence of Static Fields With Michelle

New advances in the application of adjoint methods [1] to determine beam transport sensitivities to device parameters using the MICHELLE [2] , [3] code are presented. Such sensitivities are due to manufacturing assembly tolerances, field errors from components, including how both may vary over the lifetime of a device. Understanding the sensitivities to alignments, for example, informs the assembly process of the effect of misalignments. 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 wide 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. Each of the adjoint method simulations are made on the original geometry and computational mesh, and replaces multiple such direct simulations where geometries may be changed and the resultant mesh changed. Not changing the mesh using the adjoint method improves the sensitivity of the simulation differences and improves result fidelity. The development and 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 to illustrate the effectiveness of the technique.