Large scale distributed parameter model of main magnet system and frequency decomposition analysis

Large accelerator main magnet system consists of hundreds, even thousands, of dipole magnets. They are linked together under selected configurations to provide highly uniform dipole fields when powered. Distributed capacitance, insulation resistance, coil resistance, magnet inductance, and coupling inductance of upper and lower pancakes make each magnet a complex network. When all dipole magnets are chained together in a circle, they become a coupled pair of very high order complex ladder networks. In this study, a network of more than thousand inductive, capacitive or resistive elements are used to model an actual system. The circuit is a large-scale network. Its equivalent polynomial form has several hundred degrees. Analysis of this high order circuit and simulation of the response of any or all components is often computationally infeasible. We present methods to use frequency decomposition approach to effectively simulate and analyze magnet configuration and power supply topologies.