Application of Resistance Network Analogues to the Design of Synchrotron Magnet

Abstract

Resistance networks have been used for the design of the magnet in the 40 GeV proton synchrotron project in Japan, because of their high accuracy, simplicity, high speed of operation and very low operation cost. In this paper, first, the analogies between the electrical potential in the network and the vector and scalar potentials in two dimensional magnetic problem are described. Next, the leakage factor, inductance and effective lengths of flux density and its gradient, which are necessary for the design of the magnet, are estimated by the use of networks and the results are in agreement with those on model magnets constructed for studies of the synchrotron magnet. Also, the magnetic field distribution in the gap of the synchrotron magnet with infinite permeability is obtained with an accuracy of less than 0.3%, and furthermore, the pole shape of the synchrotron magnet is investigated taking account of the saturation effect and it is found that there exists an optimum pole shape for a fixed pole width. Last, the results of systematic analysis for conventional quadrupole magnet are shown.