IMPLEMENTATION OF TPSA IN THE MATHEMATICA CODE LieMath

摘要

The Lie Algebra package LieMath written in the Mathematica language constructs the beamline map in a singleexponent Lie generator form. The algorithm (a BCH-based map concatenation) has been recently enhanced with Truncated Power Series Algebra (TPSA) techniques. The polynomials produced by the series expansion of the Hamiltonian are replaced with arrays of coefficients (derivative structures) and the Poisson bracket and BCH are defined as operations on such structures. We have confirmed the statement that using automatic differentiation instead of symbolic operations increases the speed by least an order of magnitude. The code is equipped with a MAD parser and a normal form block allowing it to extract nonlinear chromaticity and amplitude detuning. The notebook was applied in FFAG studies and may be useful for the linear collider final focus or collimation systems.