High order optics of multipole magnets

The authors have developed a new capability to compute third and fifth order Lie algebraic transfer maps for a family of realistic multipole magnets, including dipoles. The general Hamiltonian is expanded symbolically to arbitrary order. The vector potential off axis, for a given multipole symmetry, is determined from the appropriate magnetic field gradients and their longitudinal derivatives on axis. Subroutines to compute the required gradients are available for Halbach REC quadrupoles, and for general multipoles, with the current distribution on a cylindrical surface specified by a shape function. This function can be supplied by the user, or selected from internal options. Both the reference trajectory, and the map about it are calculated by numerical integration through the general magnetic field, using modular GENMAP software. This allows the calculation of curved reference trajectories in a general dipole magnet, as well as offset reference trajectories needed for misalignment tolerance studies. These new calculational capabilities have been added to the MARYLIE Lie Algebraic beam optics design code