Historical research guide · 1147 · 2015

Superconductivity for Magnets

R. Flükiger

In one minute

René Flükiger's brief at the CERN Accelerator School was the material itself: what an industrially available superconducting wire actually does when you ask it to carry current in a strong field. He gives niobium-tin its three numbers — a transition temperature of 18.2 kelvin, and an upper critical field between 25 tesla measured in the binary compound and 30 tesla once it is alloyed with titanium or tantalum — and explains that the alloying additives are there for exactly that reason. Then he turns to what limits a real wire rather than an ideal one: the Lorentz forces in a magnet squeeze and stretch the conductor, and the current it carries falls. His sharpest result is that when the pinning force is plotted against the field as a fraction of the upper critical field, every strained and unstrained measurement falls on one curve — the strain is not damaging the pinning, it is lowering the ceiling.

Connection

Chapter 11 needs a superconductor to be a material with numbers, not a word. This is where the transition temperatures and the upper critical fields of the two conductors that build every large magnet come from, along with the reason a magnet is a metallurgy problem: what holds the flux tubes still is grain boundaries 50 to 100 nanometres across.

From the source

Niobium-tin is cubic, has a transition temperature of 18.2 kelvin, and its upper critical field varies between 25 tesla measured in the binary compound and 30 tesla after alloying with about 1.5 atomic per cent titanium or about 3 atomic per cent tantalum — additives industrial wires always carry, specifically to reach the maximum upper critical field.Section 2, opening paragraph
Magnesium diboride has a transition temperature of 39 kelvin and a hexagonal lattice with a = 0.30834 nanometres; it is a two-gap superconductor and its properties are anisotropic, though far less so than in the high-temperature copper-oxide superconductors.Section 3, opening paragraphs; Section 3.2
In high-temperature superconductors an irreversibility field can be found that is markedly different from the upper critical field; in niobium-tin the two almost fall together. The two are read off a resistivity-versus-temperature measurement at conventionally chosen fractions of the normal-state resistivity, and Flükiger says plainly that the definition is somewhat arbitrary.Section 3.1
Normalized pinning force plotted against reduced field — the field as a fraction of the upper critical field — collapses onto a single universal curve for a niobium-tin wire whether or not uniaxial tensile strain is applied. Flükiger's reading: strain does not change the pinning mechanism, it changes the upper critical field, and the loss of current density follows from that.Section 2.1, paragraph beginning 'The question about the possible effect of uniaxial tensile stresses'; Fig. 7 caption
Measured critical currents for a named conductor: an Oxford Instruments RRP niobium-tin wire at 4.2 kelvin and zero applied strain, on the 0.1 microvolt per centimetre criterion, carries 278.4 amps at 12 tesla, 156.6 amps at 15 tesla, 95.9 amps at 17 tesla and 50.4 amps at 19 tesla.Fig. 6 caption
What to watch: Flükiger names the engineering ceiling and where it is being pushed. Small niobium-tin solenoids for nuclear magnetic resonance reach 23.5 tesla, while in the large dipoles and quadrupoles of an accelerator upgrade the achievable field is limited to 13 to 15 tesla by space, Lorentz forces and thermal stability — and the wire needed grows fivefold going from 12 to 20 tesla.Section 2.3, first and second bullets

The way in

https://arxiv.org/abs/1501.07146

Historical source-access record. This guide links to the original; it does not reproduce the paper text.

WHAT WAS READ. The author's PDF was downloaded from arXiv on 2026-09-12 and read as text; the file is 21 pages, sha256 a00051b5585742c61568d16a37bb2f909ca8c352f1c927acf5bb2b7fbe0f7a8a. The licence was checked on this item's own arXiv record, not inherited from the volume. TEXT. The abstract and the material passages this site needs are carried below under that licence; the lecture's treatment of Bi-2212 and R.E.-123 conductors is not reproduced and is at the source. The sixteen figures are not reproduced — the lecture is built around them and several carry numbers in their captions, so the captions that carry a number are quoted and the plots are described. Extraction flattened subscripts and the scaling-law equations; the scaling law is therefore described rather than reset, and its fitted constants are quoted from the running text.

How to cite it

R. Flükiger (2015) Superconductivity for Magnets arXiv:1501.07146

Where it sits in the curriculum

Gravity control and superconductors