Determination of the electromechanical limits of high-performance Nb$_3$Sn Rutherford cables under transverse stress from a single-wire experiment

TL;DR

This study investigates how transverse stress affects the critical current of Nb$_3$Sn wires used in high-field accelerator magnets, revealing field-dependent irreversible stress limits crucial for magnet design.

Contribution

It provides the first detailed analysis of the stress dependence of Nb$_3$Sn wire performance under high magnetic fields, linking single-wire tests to Rutherford cable behavior.

Findings

Irreversible stress limit depends on magnetic field strength.

Critical current reduction is permanent beyond a certain stress threshold.

Results help predict cable performance under operational stresses.

Abstract

The development of high-field accelerator magnets capable of providing 16 T dipolar fields is an indispensable technological breakthrough needed for the 100 TeV energy-frontier targeted by the Future Circular Collider (FCC). As these magnets will be based on Nb$_3$Sn Rutherford cables, the degradation of the conductor performance due to the large electro-magnetic stresses becomes a parameter with a profound impact on the magnet design. In this work, we investigated the stress dependence and the irreversible reduction of the critical current under compressive transverse load in high performance Powder-In-Tube (PIT) Nb$_3$Sn wires. Tests were performed in magnetic fields ranging between 16 T and 19 T on wires that were resin-impregnated similarly to the wires in the Rutherford cables of accelerator magnets. The scope was to predict the degradation of the cable under stress from a single-wire experiment. Interestingly, the irreversible stress limit, $\sigma_{irr}$, defined as the stress level corresponding to a permanent reduction of the critical current by 5$\%$ with respect to its initial value, was found to depend on the applied magnetic field. This observation allowed us to shed light on the mechanism dominating the irreversible reduction of the wire performance and to compare and reconcile our results with the irreversible limits measured on Rutherford cables, typically tested at fields below 12 T.