ATAP Science Brief
by Ian Pong
November 2022
Superconductors convey electrical current with essentially no resistance. This capability is used primarily to make powerful electromagnets, which are key to applications ranging from high-energy physics to magnetic resonance imaging to fusion energy. Understanding how their performance varies with temperature is an important part of advancing these applications. An international team that includes a researcher in ATAP’s Superconducting Magnet Program has found a more accurate way to characterize performance across a range of temperatures using the quicker, easier, less expensive “magnetization” technique. Their approach uses one standard current-transport measurement as the “anchor” for a data set composed mostly of considerably easier magnetization measurements.
Superconducting magnet materials work within certain combinations of the current (in the figure the vertical axis shows the “pinning force” (the product of the critical current and the magnetic field) that they carry; the applied magnetic field; and the temperature. Ways of measuring their performance include measuring the current that they actually transport (purple), and the quicker, easier approach of measuring magnetization (green), but neither method alone using standard specialized equipment gives a complete predictive assessment of transport performance in accelerator magnets for high energy physics (blue). The authors explain the basis for differences in the two types of methods, and outline a way to use one transport measurement as the “anchor” for a series of magnetization measurements.
Each material is superconductive only below a certain “critical temperature” or Tc. There are two other such critical parameters: the current density in the wire, Jc, and the upper limit on field strength Bc2. These three parameters are interrelated in a way that can be described by a “critical surface” in a 3D plot. (Note that in the figure, Jc is replaced by the pinning force F which is the product of Jc and B.) The penalty for violating these limits is that the wire becomes normal-conducting, and the vast current it carries, suddenly facing a resistive load, turns into heat—which is very undesirable inside a deeply cryogenic magnet with a large amount of stored energy.
Jc and Bc2 are at their maximum at absolute zero (superconducting magnets typically operate not far above this point; the Large Hadron Collider, for instance, runs at 1.9 kelvin) and vanish at Tc. At no point in that operating space may any of those parameters may be exceeded. Knowing the temperature dependence of a superconductor’s performance is critical in superconducting magnet design because it gives the temperature margin for safe operation.
For perspective, a wire made of niobium-three-tin (Nb3Sn), a high-field material beginning to be used in particle accelerators, with a cross sectional area of just 1 mm2 can carry well over 1,000 A at liquid helium temperatures (4.2 K) amid a magnetic field of 12 tesla (several hundred thousand times the Earth’s magnetic field strength). For comparison, a familiar normal-conducting, room-temperature wire—the conductor in the power cord of a TV set—with a 2 mm2 cross section might be rated at about 10 A.
The most difficult situation is measuring the limit of a superconductor’s current-carrying ability at temperatures above 4.2 K. Magnet developers need to explore this part of the Tc, Jc, Bc2 parameter space depicted above in order to understand the temperature margin, even though the magnet will be operated at lower temperatures. However, measurements above this temperature involve gaseous helium, which has lower cooling capacity than liquid helium. Therefore, fully and accurately characterizing the temperature dependence of any high-current, high-field superconductor’s performance requires world-class experts with specialized equipment.
It is an expensive endeavor. Mapping the Jc dependence of a piece of wire over a moderate range of magnetic fields and temperatures with the gold-standard transport technique takes days and can cost tens of thousands of dollars. Instead of transport measurements, where one passes a large current through the superconductor and measures the voltage, the new approach uses one such measurement as an anchor for a series of magnetization measurements, which are much easier and cheaper, using a vibrating sample magnetometer (VSM) or superconducting quantum interference device (SQUID).
Ian Pong, lead author of the paper. [Thor Swift/Berkeley Lab)
Magnetization measurements use comparatively short samples, can be performed in a matter of hours, and cost only a tenth as much as transport measurements. The parameter space in which they work is complementary to that of transport measurements. But there is a catch: the temperature dependencies of a given Nb3Sn wire determined by the two measurement methods don’t always match.
In a recent paper published in the journal Superconductor Science and Technology, Pong (the lead author) and colleagues from NIST, ATI Vienna, CERN, and the National High Magnetic Field Laboratory identify the issues underlying this discrepancy in temperature dependence measurements and propose a procedural solution for reconciling the temperature dependence difference in NbcSn superconducting wires. By taking one standard transport measurement at 4.2 K as an ‘anchor’, with this procedural solution it becomes possible to combine the simplicity and economy of quick magnetization measurements at different temperatures with the accurate prediction of transport properties in extrapolated temperature ranges.
The work has led to a new understanding of the reasons why transport and magnetization techniques give different readings, so that the respective strengths of these methods can now be combined. During the peer review process, the journal commented that “This manuscript may be a definitive article on the temperature scaling law of critical current in Nb3Sn superconducting wires.”
