The design of accelerator lattices involves evaluating and optimizing Figures of Merit (FoMs) that characterize a beam’s properties. These properties—hence the FoMs—depend on the many parameters that describe a lattice, including the strengths, locations, and possible misalignments of focusing elements. Often what is required is the gradient of the FoM with respect to each of the parameters. For systems that require numerical simulation, a naïve computation of a gradient requires one simulation for the “base case”, plus one additional simulation for each parameter of interest—a daunting effort in the case of computationally demanding simulations with many parameters. Adjoint techniques allow one to extract gradient information from one base-case simulation plus an additional one or two carefully prepared simulations. We demonstrate these techniques using the accelerator simulation code WARP, and we present our proof-of-concept results using several different FoMs as the basis for adjoint analyses of a simple beamline with multiple parameters.
Abell et al. (Thu,) studied this question.