We begin by defining our global Cartesian coordinate system as shown in Figure 1. All surfaces and particle trajectories are defined in this coordinate system. Here, we shall use capital letters to denote quantities in the global Cartesian system and bold notation to denote vectors. Thus: , defining node N as shown.
Figure 1: Global Cartesian Triad.
Further, we shall be dealing with two-dimensional prismatic geometries which are infinite in Z. Thus, we define surfaces as shown in Figure 2, comprised of straight lines connecting nodes and (linear surfaces are used to simplify particle tracing calculations---curved surfaces must be approximated by a number of linear segments). Note that, the surfaces, although mathematically described in two dimensions, are actually three-dimensional.
Figure 2: Details of Surface L.