Optimum Optical Systems

The characteristics of complex optical systems required by modern accelerators and storage rings result from the optimization of many variable function, usually of c2-type. The search for the minimum of the function is very sensitive to the initial values of the variables. The route towards a safe determination of the initial conditions is described. First, fully analytical solutions for thin lens models are derived using symbolic computing. Then, for thick lens systems, the equations become transcendent and numerical techniques are applied. It is shown that, under rather general conditions, the optimization converges towards a single solution located in the neighbourhood of the thin lens approximation. The example of betatron matching with a doublet is described, as well as the case of an isochronous periodic structure.