One of the challenges of the global closed orbit feedback of the Swiss Light Source is the modeling and simulation of the components of the feedback, done by a mix of numerical field calculation, circuit simulation and measurements fit to a discrete model. The feedback tries to stabilize the electron beam in the SLS storage ring by means of a chain of position
pickup, feedback controller, current controller and steering magnets. One of the major unknowns is the transfer function from the steering magnet input to the magnetic field seen by the beam. This can be split into two parts, one of them being the relation between magnet current and the magnetic field and the other the input impedance as seen by the power supply. The magnetic field calculation uses a linearized model of the magnet core. The frequency response is mainly influenced by eddy current losses in the sheet material of the magnet, which can be described analytically, and eddy current losses in the vacuum chamber containing the electron beam. Apart from the required dipolar field, also transient multi-polar field components were shown to exist, which were too weak for having a visible influence on the beam. For the simulation model, the numerical frequency domain data was fitted to an analytical
model.  Since the magnet current has to be extremely precise and fast, a fast power supply controller is required. This asks for well determined elements in the loop, one of them being the magnet impedance itself. The preferred description of the elements for the current controller design is linear.
Unfortunately the different types of magnets show a non linear behavior. As there are magnets with massive iron cores, as well as sheet metal cores, the variation of data as a function of the frequency is wide. In addition the capacitance of the wiring leads to another frequency dependence. To get a linear description a RLC-chain representation up to the order of 5 is used. With a numerical fit the elements are matched to the measured data for each magnet in the needed frequency range.