Estimation of the Instantaneously Dissipated Hysteresis Losses in Superconductors

Cables in superconducting magnets are subjected to field-dependent losses, i.e., induced interstrand and interfilament coupling losses, and superconductor hysteresis losses. For the two kinds of induced eddy currents, analytical and numerical models are available, allowing calculating the dissipated power under various operating conditions. For the losses stemming from the superconductor magnetization, the literature only gives formulas for the dissipated energy over closed excitation cycles. We derive an expression for the instantaneously dissipated hysteresis losses during an arbitrary ramp profile using a simplified geometry and hysteresis model. This allows estimating the losses dissipated in nonclosed excitation loops.