Perturbation treatment of linear beam optics of combined function magnets

In this paper, a perturbation theory is developed for calculating the 6D transfer matrix of a combined function magnet. Starting from the linear part of the Hamiltonian, the transfer matrix M is decomposed into an infinite sum over matrices M_n, which represent an n-fold interaction of the beam with the quadrupole content of the magnet. Given the magnetic field in the vicinity of the reference path, each matrix M_n can be calculated either analytically or by numerical integration. As an example, the transfer matrix is calculated of the 90° bending magnet of the double sided microtron HDSM at the MAMI-C electron scattering facility, which so far has been possible only by means of particle tracking.