Analysis of higher order optical aberrations in the SLC final focus using Lie algebra techniques

The SLC final focus system is designed to have an overall demagnification of 30:1, with a β at the interaction point (β*) of 5 mm, and an energy band pass of ~0.4%. Strong sextupole pairs are used to cancel the large chromaticity which accrues primarily from the final triplet. Third-order aberrations limit the performance of the system, the dominating terms being U₁₂₆₆ and U₃₄₆₆ terms (in the notation of K. Brown). Using Lie algebra techniques, it is possible to analytically calculate the size of these terms, in addition to understanding their origin. Analytical calculations (using Lie algebra packages developed in the Mathematica language) are presented of the bandwidth and minimum spot size as a function of divergence at the interaction point. Comparisons of the analytical results from the Lie algebra maps and the results from particle tracking (TURTLE) are also presented