Critical Current Metrology for Nb3Sn

The main focus of the project is to develop standard techniques for the measurement of critical current of high-temperature and low-temperature superconductors. Some applications for which these types of measurements are crucial include: magnetic-resonance imaging, research magnets, fault-current limiters, magnetic energy storage, motors, generators, transformers, transmission lines, synchronous condensers, high-quality-factor resonant cavities for particle accelerators, and superconducting bearings. One area in which superconductors have the potential for making a significant impact is in fusion energy. Fusion energy is a potential, virtually inexhaustible energy source for the future. It does not produce CO2 and is environmentally cleaner than fission energy. Superconductors are used to generate the ultra-high magnetic fields that confine the plasma in fusion energy research. Electronic and Electrical Engineering Laboratory (EEEL) staff measure the magnetic hysteresis loss and critical current of marginally stable, high-current Nb3Sn superconductors for fusion and other research magnets.

There are three main aspects of this project supported by the Statistical Engineering Division (SED). 

1. Develop an algorithm to determine the irreversible strain limit    of Nb3Sn superconductors.
2. Fit the non-linear strain scaling, temperature scaling, and unified    temperature/strain scaling models to critical current data.
3. Investigate methods of estimating the residual resistivity ratio (RRR).

1. Irreversible Strain:
   A superconducting wire is sensitive to many environmental conditions during measurement, including the amount of strain applied to the wire. A small amount of strain may not effect the performance of the wire, however if a wire is exposed to too much strain (compressive or extensive) the damage is irreparable. Knowing the physical properties of a superconducting wire is invaluable to the development of high quality devices. SED staff have developed an algorithm that quantifies the strain at which the wire is permanently damaged, called the irreversible strain limit.  
2. Unified Scaling: 
   EEEL staff have completed the construction and testing of a variable-temperature and variable-strain, or unified, apparatus for measuring critical current.
   
   
   
   
   
   
   

   The top photograph (apparatus2.jpg) shows the new high-current apparatus constructed at NIST to measure the critical-current dependence on strain, temperature and magnetic field. The worm-wheel that torques the spring can be seen through the small, round window. The lower photograph (spring.jpg) shows the CuBe spring with a helical sample soldered to the spring.  Three pairs of voltage taps cover the three central turns of the spring.  The current contacts are made at each end of the spring.

   
   The apparatus combines world class capabilities in variable-temperature and variable-strain measurements and is expected to be the highest-current apparatus of its type in the world. The new apparatus will help answer fundamental questions about the performance of strain sensitive superconductors. Measurements taken on the new apparatus facilitate the investigation of scaling models. Scaling models are nonlinear functions of magnetic field, temperature and strain versus pinning force, or critical current (Ekin, 2006). There are many scaling models currently in use, so a long-term objective of this project is to provide some guidance to the superconducting community regarding the best scaling models. SED staff have succeeded in fitting the three unified scaling models (temperature, strain, and combined temperature and strain) to critical current data. The data and subsequent model fits will be used to verify or determine the limits of scaling laws. Such information would greatly reduce the amount of data and liquid helium required to measure new samples in the future.  
3. Residual Resistivity Ratio: 
   Accurate measurement of RRR of niobium samples is important to assure that critical material-purity specifications are met in the construction of superconducting radio-frequency cavities. We have compared methods for estimating RRR of high-purity niobium samples and investigated the effects of using different functional models on the final value. RRR is typically defined as the ratio of the electrical resistances measured at 273 K (the ice point) and 4.2 K (the boiling point of helium at standard atmospheric pressure). However, pure niobium is superconducting below about 9.3 K, so the low-temperature resistance is defined as the normal-state (i.e., non-superconducting state) resistance extrapolated to 4.2 K and zero magnetic field. Thus, the estimated value of RRR depends significantly on the model used for extrapolation. We examined three models for extrapolation based on temperature versus resistance, two models for extrapolation based on magnetic field versus resistance, and a new model based on the Kohler relationship that can be applied to combined temperature and field data. We also investigated the possibility of re-defining RRR so that the quantity is not dependent on extrapolating an arbitrary model. We have summarized our findings in the paper, "A Comparison of Methods for Computing the Residual Resistivity Ratio of High-Purity Nb Samples."