Methods of finding the parameters of ideal current loops for computer simulation of magnetic fields

Methods are described for finding the position, radius, and strength of ideal current loops to represent the magnetic field of 1) a partially immersed convergent electron gun, 2) a short solenoid, using the Helmholtz concept extended to triplets and quadruplets, and 3) a periodic permanent magnet (P.P.M.) focusing stack for a TWT. The parameters of the coils then constitute a complete description of the magnetic field with no paraxial approximation.