Magnetic Field Calculations in the End Sections of SSC Dipole Magnets

Abstract

In this work a full, three-dimensional magnetic field distribution is calculated throughout the end sections of a dipole magnet. The method of calculating the magnetic field is based upon a closed form series solution for a cylindrical shell of current inside an iron boundary. The effect of complex conductor geometries is represented as a summation of fields resulting from several current shells at different radial locations. The magnetic scalar potential is directly obtained in terms of its axial and angular Fourier coefficients throughout the entire magnet. The technique allows for periodic effects due to neighboring magnets and non-magnetic gaps along the axial length (i.e. termination of the iron yoke). The multi-pole coefficients are obtained in the end region as a function of axial position. The contribution from each of the six conductor blocks is shown separately. The results from the three-dimensional analysis near the center of the magnet compare well with those from a two-dimensional solution. An integration of the sextupole coefficient throughout the axial length is used as a measure of field quality in the entire region. The effect on the dipole and sextupole components of magnetic field due to terminating the iron yoke is also examined.