containing a stack representation of the ideal LGB bending magnetic field mentioned in the introduction. In order to fairly compare the differences between tracking through the map models for each LGB and tracking through a stack, we developed individual simulation lattices containing stack representations of the bending fields for both the C-shaped and canted solenoid LGB prototypes. For both LGB’s, our general method was to track particles through a lattice containing a stack representation, copy the lattice, switch the stack representation for our map model, and repeat the simulations. Thus, we had four lattices in total, since we had two LGB’s, and two models for each LGB.

In the process of switching out the stack representations for map models, we had to make modifications to the lattices. In particular, we isolated the LGB’s and appended patch elements to either end of the map models. Patch elements are not physics and exist in simulation lattices only. Their purpose is to change adjust the reference trajectory and time [@bmad] within the lattice. In our simulations, the patch elements were oriented so that the simulated particle would displace an angle of $2\pi$ upon completing one revolution in the complete lattice. Because the bending 