The influence of the Al stabilizer layer thickness on the normal zone propagation velocity in high current superconductors

TL;DR

This paper presents a 2D numerical model and analytical formula to study how the thickness of the aluminum stabilizer layer affects the normal zone propagation velocity in high-current NbTi superconductors, considering thermal and magnetic effects.

Contribution

It introduces a comprehensive 2D numerical model and an analytical formula that account for the stabilizer layer thickness, thermal diffusion, and current redistribution in predicting normal zone propagation.

Findings

Cladding acts as a heat sink beyond a certain thickness.

The model accurately predicts propagation velocity across different regimes.

Good agreement with experimental data validates the approach.

Abstract

The stability of high-current superconductors is challenging in the design of superconducting magnets. When the stability requirements are fulfilled, the protection against a quench must still be considered. A main factor in the design of quench protection systems is the resistance growth rate in the magnet following a quench. The usual method for determining the resistance growth in impregnated coils is to calculate the longitudinal velocity with which the normal zone propagates in the conductor along the coil windings. Here, we present a 2D numerical model for predicting the normal zone propagation velocity in Al stabilized Rutherford NbTi cables with large cross section. By solving two coupled differential equations under adiabatic conditions, the model takes into account the thermal diffusion and the current redistribution process following a quench. Both the temperature and magnetic field dependencies of the superconductor and the metal cladding materials properties are included. Unlike common normal zone propagation analyses, we study the influence of the thickness of the cladding on the propagation velocity for varying operating current and magnetic field. To assist in the comprehension of the numerical results, we also introduce an analytical formula for the longitudinal normal zone propagation. The analysis distinguishes between low-current and high-current regimes of normal zone propagation, depending on the ratio between the characteristic times of thermal and magnetic diffusion. We show that above a certain thickness, the cladding acts as a heat sink with a limited contribution to the acceleration of the propagation velocity with respect to the cladding geometry. Both numerical and analytical results show good agreement with experimental data.