Magnetic fields calculated by INTMAG compared with analytical solutions and precision measurements

Abstract

Abstract The computer program INTMAG [R. Becker, Nucl. Instr. and Meth. B42 (1989) 303] calculates magnetostatic fields by integrating the contributions of real filaments, which result from splitting up solid windings, and of assumed filaments on the surface of iron pieces, in order to simulate the behaviour of the iron-air interface. The currents of the surface filaments are determined in succeeding steps by an iterative procedures, which saves memory at the expense of computing time, but allows to use as much as 999 filaments in a problem, even on a PC. Due to the integration calculus, the results are more accurate and much more “smooth” than from any finite difference or finite element method program. For the use in trajectory-optics programs such as EGN2 [W.B. Herrmannsfeldt, SLAC-331 (1988)], where radial expansion of axial data is a common procedure, the results of INTMAG do not need any “Maxwellisation”, because they are exact solutions of Maxwell's equations. New features added to INTMAG comprise a finite permeability, rectangular coordinates, and mirroring to save numerical work in the case of mirror or angular symmetry as well as an improvement of the integration over the discretised boundary filaments. The PC versions of INTMAG is compiled with MS-Fortran 5.0 (Microsoft Corp., Redmont, WA, USA) which allows to use NAMELIST input, making the input file easy to read and easy to set up. Besides explaining the new features added, the emphasis of this paper is on the comparison of INTMAG calculations with analytical solutions, namely the magnetisation of iron ball and sphere in the case of axisymmetric coordinates and of iron rod and cylinder in rectangular coordinates for different values of permeability. As a further example in rectangular coordinates, a quadrupole is calculated, demonstrating the option of mirroring. Also a comparison is made with precision measurements (B. Langenbeck, private communication) in the gap of a bending magnet of the ESR [B. Franzke, Nucl. Instr. and Meth. B24 (1986) 18] ring at GSI. For this example, POISSON (POISSON, group of programs at GSI) calculations can be included into the comparison.