Low-Frequency Analytical Model of Superconducting Magnet Impedance

A superconducting magnet for particle accelerators is often modeled as an ideal inductor, as it indeed exhibits a completely negligible resistance; this is fully satisfactory, as an example, for control purposes, as the time constant formed by the magnet inductance and the resistance of normal conducting cables connecting it to the power converter accurately describe the essentially dominant dynamics of the circuit. Such a model would however fail to correctly represent the noise attenuation mechanism at play in practical superconducting magnets, which also include a vacuum pipe or a beam screen in the inner part of the aperture, an iron yoke on the outer part, and, potentially, a stainless steel or aluminum collar in between. Even at relatively low frequencies, a more accurate model is therefore needed. A sufficiently general one is proposed and illustrated.