Superconductivity for Magnets

R. Flükiger (CERN), Superconductivity for Magnets, CERN Yellow Report CERN-2014-005, pages 247 to 267, a lecture to the CAS-CERN Accelerator School Superconductivity for Accelerators, Erice, Italy, 24 April to 4 May 2013, edited by R. Bailey. Preprint at arxiv.org/abs/1501.07146. Carried here under CC BY 3.0.

Abstract

The present state of development of a series of industrial superconductors is reviewed in consideration of their future applications in high field accelerator magnets, with particular attention on the material aspect. The discussion is centred on Nb₃Sn and MgB₂, which are industrially available in a round wire configuration in kilometre lengths and are already envisaged for use in the LHC Upgrade (HL-LHC). The two systems Bi-2212 and R.E.-123 may be used in magnets with even higher fields in future accelerators: they are briefly described.

Keywords: systems, Nb₃Sn, MgB₂, Bi-2212, R.E.-123, superconducting wires, critical current densities.

2. Multifilamentary Nb₃Sn wires

Nb₃Sn is in the cubic phase, with Tc = 18.2 K, and belongs to the category of Low-Temperature Superconductors (LTS). Its upper critical field Bc2 varies between 25 T (measured in binary Nb₃Sn) and 30 T (after alloying with Ti or Ta). Industrial Nb₃Sn wires always contain a certain content of additives (about 1.5 at.% Ti or about 3 at.% Ta) in order to achieve a maximum value of Bc2.

(Flükiger then compares the three industrial routes — the bronze route, Powder-In-Tube, and the internal-tin RRP process — and reports that CERN retained the two with the highest transition temperatures, RRP wire from Oxford Instruments and PIT wire from Bruker, in wires 0.7 to 1.0 mm in diameter with copper to non-copper ratios of 1.15 to 1.25 and unit lengths reaching 800 m.)

2.1 Uniaxial tensile stress

Fig. 6 caption: Normalized Ic vs. applied strain for a RRP Nb₃Sn wire at T = 4.2 K and for different fields. Ic behaves reversibly in the shown strain window (εm = 0.25%). The critical currents at zero applied strain (0.1 µV·cm⁻¹) are marked by the dashed line: 278.4 A (12 T), 156.6 A (15 T), 95.9 A (17 T), 50.4 A (19 T).

The question about the possible effect of uniaxial tensile stresses on flux pinning can be answered by representing the normalized pinning force Fp/Fp,max as a function of the reduced magnetic field b = B/Bc2; as shown for a RRP wire, all data fall on a universal curve, reflecting that the pinning mechanism is not influenced by the application of uniaxial tensile strain (see Fig. 7). This confirms that the effects of uniaxial stress on Jc are essentially due to the change of Bc2.

(The lecture's scaling law for Nb₃Sn writes the critical current density as a function of field, temperature and strain, with the upper critical field and the transition temperature each carrying their own strain dependence. Extraction flattened the equation and it is not reset here; its fitted constants are given in the text as αNb₃Sn = 900 for ε = −0.003, Tc0m = 18 K, Bc0m = 24 T, and CNb₃Sn,0 = 60 800 A·T^½·mm⁻², for a value of Jc = 3000 A·mm⁻² at 4.2 K and 12 T.)

2.2 Effect of transverse stresses

The effect of transverse stress on the superconducting properties, and in particular on the current-carrying capability, is much stronger than that of uniaxial stress. It is clearly seen that a maximum of Ic/Ic0 is reached for transverse stresses of the order of 20 MPa, in contrast to uniaxial stresses, where the maximum is observed at 150 MPa. Three load cases were studied at the University of Geneva: a wire pressed between two parallel walls (the worst possible case, never encountered), a wire simultaneously pressed by four walls without epoxy, and the same with epoxy, simulating the stress on a wire in a Rutherford cable. The epoxy has a very beneficial effect, rendering the stress distribution more hydrostatic, thus reducing the transverse stress acting directly on the wires in the Rutherford cable.

2.3 Conclusions about Nb₃Sn wires

• Small solenoids for NMR based on Nb₃Sn can reach 23.5 T (1 GHz). In large dipoles or quadrupoles (e.g. for LHC Upgrade), the achievable field is limited to 13–15 T, due to the limited available space, large Lorentz forces, and thermal stability requirements.
• The amount of Nb₃Sn wire in a magnet increases strongly with the produced field: at 20 T, it is five times more than for 12 T.
• The critical current density at small fields is dictated by flux pinning due to A15 grain boundaries (size: 50–100 nm). At high fields, Jc is mainly influenced by the value of Bc2.
• Both internal Sn (RRP) and Powder-in-Tube (PIT) wires satisfy or almost satisfy the conditions for LHC Upgrade accelerator magnets: Jc = 1500 A·mm⁻² at 4.2 K/15 T. Bronze route wires do not reach these high Jc values, but are best suited for the 'persistent mode' operation of NMR magnets.

3. The MgB₂ system

The MgB₂ phase (Tc = 39 K) crystallizes into a hexagonal lattice, with a = 0.30834 nm.

3.1 The irreversibility field, Birr

An 'irreversibility field' Birr can be found in high-temperature superconductors which is markedly different from the value of the upper critical field Bc2. This is not the case for Nb₃Sn, where Birr and Bc2 almost fall together. The determination of Birr can be based on the measurements of the electrical resistivity R(T). The definition is somewhat arbitrary: usually, the values are taken at 10% and 90%, or at the normal-state resistivity value Rn, for Bc2 and Birr, respectively.

3.2 The anisotropy of Bc2 in MgB₂

The physical properties of MgB₂ show a marked anisotropy. The value of Bc2 perpendicular to the ab planes is markedly lower than the value parallel to ab. In carbon alloyed MgB₂, the anisotropy is lowered. At sufficiently high carbon contents (too high for the optimization of the critical current density) it disappears.

(Figure 14 of the lecture, not reproduced here, plots the upper critical field against temperature for Nb−Ti, Nb₃Sn and alloyed MgB₂ single crystals on one pair of axes — the direct visual comparison of the three conductors' field ceilings.)