Three-dimensional magnetic engineering: The programs magnus and epilog

Abstract

We present the post-processor EPILOG for the well established finite element program MAGNUS for three-dimensional magnetic engineering. MAGNUS solves problems of magnetostatics with nonlinear magnetic materials, permanent magnets and electric currents, for any 3-D geometry. The two-scalar-potentials formulation of magnetostatics used by MAGNUS combines numerical accuracy and computational efficiency, and is considered state of the art. The well known program KUBIK is used as a pre-processor to describe the geometry and finite element mesh. KUBIK is highly interactive and allows the user to effectively control all geometric details.The needs of magnetic engineers, however, go far beyond the simple availability of a mathematical solution. Once the solution has been obtained by MAGNUS in the form of a continuous magnetic scalar potential function defined at every point in the solution domain, those needs are met by EPILOG. EPILOG is command operated. Commands are independent of each other and can be used in any order, or not used at all. The purpose of each command is to use the solution for the calculation of a derived quantity or the production of a plot or table. The following derived quantities can be obtained: the magnetic energy in specific regions, the magnetic force on specified conductors in space, the magnetic torque on specified conductors, the magnetic flux across a given surface in space, the inductance of a circuit, and a variety of line integrals for specified lines in space. A useful facility is the automatic calculation of harmonic multipoles averaged along the beam direction for accelerator magnets, essential for end analysis and the integral effect of the magnetic field on the beam.Graphical facilities include color plots of the shapes of the conductors, the geometry, field lines and surfaces of constant magnetic scalar potential in specified regions of space. EPILOG produces a device independent graphical metafile, which can be seen on any device by running the Graphical Kernel System GKS or some other graphics package. Another important feature of EPILOG is its ability to produce tables of quantities such as the scalar potential, the total field, the field of conductors alone, the magnetic permeability, etc. Editing options allow the user to specify where the quantities are to be tabulated, such as on equispaced points on a line or arc in space. One useful application is the evaluation of the maximum field inside conductors for superconducting magnets.The ability of EPILOG to accurately provide the magnetic field components at any given point in space is convenient for its use as input to particle tracking programs. EPILOG can easily be interfaced to such a program. EPILOG is appropriate for complicated 3-D geometries, common in wigglers and undulators, or for the analysis of ends of bending magnets, as required in the design of synchrotron light sources.