Lumped-Element Dynamic Electro-Thermal model of a superconducting magnet

Abstract

Modeling accurately electro-thermal transients occurring in a superconducting magnet is challenging. The behavior of the magnet is the result of complex phenomena occurring in distinct physical domains (electrical, magnetic and thermal) at very different spatial and time scales. Combined multi-domain effects significantly affect the dynamic behavior of the system and are to be taken into account in a coherent and consistent model.A new methodology for developing a Lumped-Element Dynamic Electro-Thermal (LEDET) model of a superconducting magnet is presented. This model includes non-linear dynamic effects such as the dependence of the magnet's differential self-inductance on the presence of inter-filament and inter-strand coupling currents in the conductor. These effects are usually not taken into account because superconducting magnets are primarily operated in stationary conditions. However, they often have significant impact on magnet performance, particularly when the magnet is subject to high ramp rates.Following the LEDET method, the complex interdependence between the electro-magnetic and thermal domains can be modeled with three sub-networks of lumped-elements, reproducing the electrical transient in the main magnet circuit, the thermal transient in the coil cross-section, and the electro-magnetic transient of the inter-filament and inter-strand coupling currents in the coil's superconductor. The same simulation environment can simultaneously model macroscopic electrical transients and phenomena at the level of superconducting strands. Preprint submitted to CryogenicsSeptember 18, 2015The model developed is a very useful tool for reproducing and predicting the performance of conventional quench protection systems based on energy extraction and quench heaters, and of the innovative CLIQ protection system as well.

Modeling of Interfilament Coupling Currents and Their Effect on Magnet Quench Protection

“…This approach was used in a stand-alone application with the same name and in the TALES software [7], [15], [28], [29], and has been routinely validated against experimental results [15], [30]- [32]. 1 This formula corrects the one proposed in [7], [15].…”

“…when the magnetic field changes rapidly with respect to τ if , a more detailed characterization of P if is required [7], [25]- [27].…”

“…The LEDET method allows modeling the electro-magnetic and thermal transients in a superconducting magnet by means of networks of lumped-elements [7], [15]. This approach was used in a stand-alone application with the same name and in the TALES software [7], [15], [28], [29], and has been routinely validated against experimental results [15], [30]- [32].…”

“…A modeling technique named LEDET (Lumped-Element Dynamic Electro-Thermal) was recently proposed, which is based on the representation of coupling-loss effects by means of an equivalent network of lumped-elements [7], [15]. The LEDET method is applied to efficiently simulate the complex electro-magnetic and thermal transient occurring during a magnet discharge and assess the impact of inter-filament coupling loss on the quench protection performance.…”

Quench Protection of a Nb$_3$Sn Superconducting Magnet System for a 45-GHz ECR Ion Source

“…The alternative protection system based on CLIQ [5]- [7] is investigated for the sextupole magnet protection. The analysis is performed with the LEDET (Lumped-Element Dynamic Electro-Thermal) program [5], [8], [9], which includes non-linear effects such as inter-filament coupling loss, quench-back, and reduction of the differential inductance due to coupling currents.…”