A Three-Dimensional Field Program

The high-energy microtrons studied at Argonne National Laboratory (ANL) require complicated magnetic field shapes. A three-dimensional infinite-permeability magnetic field program was written to show that poles and coils can be devised to produce these fields. The program is in Hewlett-Packard 9845B BASIC, which limits the active mesh to about 30 000 points. In some problems the number of useful points can be greatly increased by placing virtual points one plane beyond the active mesh. The regular cubic mesh is described by three arrays. One is a scalar potential array, H, which is derived from ampere-turns by using current cuts. Another is an information array, I, and the third is a list, L, containing other data. This data structure is similar to the Carnegie Magnet - Program. An element from I usually contains a bit string with directions for calculating the corresponding H. However, if more data are required, then the word from I is interpreted as the address in L where the required data are stored. Parts of L can be reused when two or more points require the same data. The organization of the data is shown in Fig. 1. This organization minimizes memory requirements and makes the calculation fast for most points. The program has four parts: (1) prepare the problem description file, (2) load the starting mesh, (3) relax the mesh, and (4) output results. Preliminary results indicate that the magnet edge can be quite "hard" and suggest that the required field shapes can be produced.