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Calculations and measurements for the SLAC SLC positron return quadrupole magnet

Computational Results The three-dimensional magnetostatic computer program TOSCA, running on the NMFECC CRAY X-MP computer, was used to compute the integral of gradient length for the SLC type QT4 positron return line quadrupole magnet. Since the bore diameter of the magnet is 12.7 centimeters, and the length is only 10.16 centimeters, three dimensional effects are important. POISSON calculations were done on a two-dimensionalmodel to obtain magnetic shimming which assured enough positive twelve pole to offset end effects, while TOSCA was used to estimate the effective length of the quadrupole. No corrections were required on the magnet as built. Measurements showed that the required integrated gradient was achieved for the given current, and that integrated higher harmonics were generally less than 0.1 percent of the quadrupole component. A drawing of the quadrupole is shown in Fig. 1. The short length was dictated by space requirements in the beam line. The TOSCA model was initially made two-dimensional by the use of periodic boundary conditions in order to compare the resulting field distributon with POISSON results. The POISSON runs were used to shim the magnet for a positive three percent twelvepole component in two dimensions. These runs were also used to check that the mesh density in the two-dimensional TOSCA runs was sufficient, and finally, to check that approximating the quadrupole poleface by only three line segements did not cause significant error. This scheme worked because the shim was a line, tangent to the hyperbolic surface and occupied most of it. One sixteenth of the problem was set up to take full advantage of symmetry. The element configuration for the base plane is shown in Fig. 2. This mesh was generated by XMESH, a pre-processor written by John Stewart of LLNL.’ The three