<span style="font-variant:small-caps;">PSI</span>

supervised by

Michael Ehrlichman

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Summer 2015

Introduction
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In order to meet the needs of users in fields ranging from biophysics to material science, it is necessary to develop a new generation of synchrotron light sources. An ideal light source provides a diffraction-limited photon beam, requiring an emittance, imprecisely speaking the spread of a particle beam in phase space, on the order of 1 pm$\cdot$rad. A myriad of storage ring magnet component configurations, called lattices, exist which are designed with ultra-low emittance [@Intropaper]. Reference [@compact] outlines the design of such a lattice in the context of the pending Swiss Light Source (SLS) upgrade, SLS2, using longitudinal gradient bending magnets. In particular, the authors calculate the ideal bending component of a magnetic field (that is, the $B_y$ component) which minimizes emittance. Presently, in simulating the behavior of an ultra-low emittance lattice, the LGB bending field component is modeled by a series of homogeneous field bend magnets (otherwise called a *stack of S-bends* or just a *stack*). However, any physical magnet used to generate the desired longitudinally varying bend field profile will inevitably have a $B_x$ component and a $B_z$ component as well, which the stack does not properly 