Computation of Lattice Maps Using Modular Bch and Similarity Composition Rules

A beam line map construction method for linear and circular high-energy colliders is described which avoids truncated power-series maps through systematic use of a two-term Baker-Campbell-Hausdorff (BCH) formula in combination with similarity transformations. The beam line map ultimately assumes the form of a product of a linear map and a single-exponential Lie-operator map. The method i) provides insight into map generator sources, ii) is accurate, iii) is complete in that all effects, such as edges and soft fringes, mis-alignments and mis-powerings, multipole errors, and input beam errors can be simply included, iv)permits faster map computation times, and v) bypasses truncated power-series map methods allowing for higher order, and even non-polynomial generators.