Implications of the strain irreversibility cliff on the fabrication of particle-accelerator magnets made of restacked-rod-process Nb3Sn wires

Abstract

The strain irreversibility cliff (SIC), marking the abrupt change of the intrinsic irreversible strain limit ε irr,0 as a function of heat-treatment (HT) temperature θ in Nb 3 Sn superconducting wires made by the restacked-rod process (RRP ® ), is confirmed in various wire designs. It adds to the complexity of reconciling conflicting requirements on conductors for fabricating magnets. Those intended for the high-luminosity upgrade of the Large Hardon Collider (LHC) at the European Organization for Nuclear Research (CERN) facility require maintaining the residual resistivity ratio RRR of conductors above 150 to ensure stability of magnets against quenching. This benchmark may compromise the conductors’ mechanical integrity if their ε irr,0 is within or at the bottom of SIC. In this coupled investigation of strain and RRR properties to fully assess the implications of SIC, we introduce an electro-mechanical stability criterion that takes into account both aspects. For standard-Sn billets, this requires a strikingly narrow HT temperature window that is impractical. On the other hand, reduced-Sn billets offer a significantly wider choice of θ , not only for ensuring that ε irr,0 is located at the SIC plateau while RRR ≥ 150, but also for containing the strain-induced irreversible degradation of the conductor’s critical-current beyond ε irr,0 . This study suggests that HT of LHC magnets, made of reduced-Sn wires having a Nb/Sn ratio of 3.6 and 108/127 restacking architecture, be operated at θ in the range of 680 to 695 °C (when the dwell time is 48 hours).

Effects of the initial axial strain state on the response to transverse stress of high-performance RRP Nb3Sn wires

“…Since then, different strategies have been developed for evaluating the impact of mechanics in the critical current (I c ) of Nb 3 Sn superconductors [31]. Related to accelerator magnet applications, they range from critical current measurements in full cables (or sub-scale cables) down to single wires, on which the conductor is subjected to the action of a certain type of load [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50].…”

Design Optimization, Cabling and Stability of Large-Diameter High Jc Nb3Sn Wires

“…The higher Jc of ERMC-1 relative to the MQXF wire is due mostly to its larger sub-element size and the higher ('standard') Sn stoichiometry. The former may not be acceptable for future accelerator magnets [4], and the latter increasingly compromises RRR (or requires a low heat treatment temperature, compromising Bc2 * [10] and strain performance [11]) as the sub-element size is reduced [7]. It has not been tested specifically in the present study, but it is also likely that this contributes to higher local RRR degradation at cable edges than would be obtained for 'reduced tin' wires like MQXF.…”

“…Heat treatment optimization to increase RRR or stability sacrifices a large part of the gain in Jc (relative to MQXF). It is therefore likely that the reduced tin formulation would be preferable in these applications, whilst also providing a larger parameter space for heat treatment optimization [11].…”

“…Literature data suggest that a reduction in temperature from 650 °C to 640 °C for similar RRP ® wires (132/169, reduced and standard tin) could reduce Bc2 * by ~1 T [10]: perhaps acceptable for the current 12 T application, but likely to have a disproportionately larger impact on Ic for future accelerator magnets at 14 T and above. There is also evidence that a precipitous decrease in the irreversible strain limit is approached on reducing the heat treatment temperature to ~640 °C for RRP ® wires of the standard tin stoichiometry: for two 108/127 wires with 52-55 µm sub-element diameter (ds), slightly smaller than ERMC-1, the acceptable window for heat treatment has been reported as (648 ± 3) °C or confined to ~640 °C [11]. It was therefore decided to evaluate only reductions in duration, not temperature.…”

Machine learning applied to X-ray tomography as a new tool to analyze the voids in RRP Nb3Sn wires

“…As matter of fact a clear quantitative correlation between voids and mechanical limits was obtained for Bronze route wires 21 while for the other types of internal tin wires, such as RRPs, the correlation has yet to be demonstrated. It was shown that varying the dopants (Ti or Ta) and the temperature of the heat treatment final plateau (600–750 °C), the axial irreversible limit of RRP wire changes 49 . Using the combination of x-ray tomography and unsupervised machine learning algorithm would be possible to completely characterize Nb 3 Sn wires and quantify the impact of the voids variation on the irreversible limit due to the different heat treatments.…”