LIEMAP: a program for extracting a one-turn single exponent Lie generator map

A method for computing a one-turn map for a storage ring is presented. Each element of the lattice is represented by a matrix for a linear element followed by a Lie generator for a nonlinear multipole kick. All matrices are moved to the front of the lattice and multiplied to form a single matrix. This rearrangement also changes each nonlinear Lie operator by a similarity transformation. The Campbell-Baker-Hausdorff (CBH) theorem is used to combine successive nonlinear generators into one generator which is then expressed as a perturbative series in the multipole strengths. In principle, the program can be used to compute the CBH series in any desired order. Routines from a differential algebra library ZLIB are used to perform all operations.<
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