Numerical determination of ray tracing: a new method.
A practical method for tracing rays in a gradient-index medium (electron rays in a potential field) is described. First, the Euler equation is transformed into a convenient form of four first-order differential equations. Next, a standard numerical technique is used for solving the resulting equations that contain at most two first-order spatial derivatives of a refractive index. A comparison of this method with previous methods is made. Some special distributions of the refractive index and the potential of a spherical field capacitor have been used as a verification of the proposed method.
Puchalski
J
J