# PAPER-for-ALL Repository

### PAPER-for-ALL Repository

**[A] 2024-05-02**:**Emma **| Strickland, N.M., Hoffmann, C. and Wimbush, S.C., 2014. “A 1 kA-class cryogen-free critical current characterization system for superconducting coated conductors“. Review of Scientific Instruments, 85(11).**SUPPORTING INFORMATION**:

https://qd-uki.co.uk/cryogenics/janis-4k-cryocoolers/ – website containing information on the cryocoolers

The Oxford Solid State Basics, Steven Simon, page 23 – derivation of the Wiedeman-Franz law and information about different metals and their properties

**Charles (H) **| Du, Qiang. “Discrete Gauge Invariant Approximations of a Time Dependent Ginzburg-Landau Model of Superconductivity“. Mathematics of Computation 67, no. 223 (1998): 965–86.*Du gives some nice geometric insight, cites earlier occurrences of the link-variable method than Gropp [1], considers gauges other than the temporal gauge, and proves the existence and uniqueness of solutions to the discrete equations*.**SUPPORTING INFORMATION**:

[1] Gropp, William D., Hans G. Kaper, Gary K. Leaf, David M. Levine, Mario Palumbo, and Valerii M. Vinokur. “Numerical Simulation of Vortex Dynamics in Type-II Superconductors“. Journal of Computational Physics 123, no. 2 (1 February 1996): 254–66.

**[B] 2024-01-11**:**Rollo **| Jeremy D Weiss *et al*, “Performance of low-loss demountable joints between CORC® cable-in-conduit-conductors at magnetic fields up to 8 T developed for fusion magnets“, 2023 Supercond. Sci. Technol. 36 085002.**SUPPORTING INFORMATION**:

1. Yeekin Tsui *et al*, “Soldered joints—an essential component of demountable high temperature superconducting fusion magnets”, 2016 Supercond. Sci. Technol. 29 075005.

2. P. K. Ghoshal et al., “Design and Evaluation of Joint Resistance in SSC Rutherford-Type Cable Splices for Torus Magnet for the Jefferson Lab 12-GeV Upgrade,” in IEEE Transactions on Applied Superconductivity, vol. 26, no. 4, pp. 1-4, June 2016, Art no. 4800304, doi: 10.1109/TASC.2016.2517922.

3. Hidetoshi Hashizume, Satoshi Ito, “Design prospect of remountable high-temperature superconducting magnet”, Fusion Engineering and Design, Volume 89, Issues 9–10, 2014, Pages 2241-2245, ISSN 0920-3796 – https://www.sciencedirect.com/science/article/pii/S092037961300728X?via%3Dihub**Daniel **| Godeke, A., ten Haken, B. and ten Kate, H, 2002, “The deviatoric strain description of the critical properties of Nb_{3}Sn conductors”, Physica C, 372–376, p. 1295 – 1298.**SUPPORTING INFORMATION**:

1. Ekin, Experimental techniques for low temperature measurements, Chapters 9.4.4 and 10.5.

2. Hydrostatic & Deviatoric Strains

**[A] 2023-09-28**:**Emma **| Li, X., Yang, Z., Xu, Y., Ren, L., Zhang, H., Ding, X. and Tang, Y., 2022. “Effects of bending and torsion behavior on Ic degradation and microstructure of ReBCO coated conductors.” Cryogenics, 126, p.103523.**SUPPORTING INFORMATION**:

https://web.mit.edu/course/3/3.11/www/modules/frac.pdf for information on the development of cracks in materials under stress

https://en.wikipedia.org/wiki/Environmental_scanning_electron_microscope For more information on ESEM microscopes

Poole – Superconductivity, chapter 8: For information on the microstructure of REBCO**Charles (H) **| Tajmar, M., and C. J. de Matos. ‘Extended Analysis of Gravitomagnetic Fields in Rotating Superconductors and Superfluids’. Physica C: Superconductivity and Its Applications 420, no. 1 (15 March 2005): 56–60.**SUPPORTING INFORMATION**:

The calculations in the paper are simple but for deeper background the following review paper seems OK:

Gallerati, Antonio, and Giovanni Alberto Ummarino. ‘Superconductors and Gravity’. Symmetry 14, no. 3 (March 2022): 554

**[A] 2023-06-15**:**Emma **| Senatore, C., Barth, C., Bonura, M., Kulich, M. and Mondonico, G., 2015. Field and temperature scaling of the critical current density in commercial REBCO coated conductors. Superconductor Science and Technology, 29(1), p.014002**SUPPORTING INFORMATION**:

Poole – Superconductivity, pages 495 – 497**Charles (H) **| Scott G. B. and Springford M., “The Fermi surface in niobium,” 1970 Proc. R. Soc. Lond. A320115–130.**SUPPORTING INFORMATION**:

A B Pippard, “Experimental analysis of the electronic structure of metals,” 1960 Rep. Prog. Phys. 23 176

**[B] 2023-01-19**:**Brad **| Abrikosov, A. A. (1957). On the magnetic properties of superconductors of the second group. *Soviet Physics-JETP*, *5*, 1174-1182.**SUPPORTING INFORMATION**:

1) Tilley + Tilley: Sec 8.5 (Main results for us: Equation 8.78 and 8.79)

2) Correction from square to hexagonal/triangular lattice: Kleiner, W. H., Roth, L. M., & Autler, S. H. (1964). Bulk solution of Ginzburg-Landau equations for type II superconductors: upper critical field region. *Physical Review*, *133*(5A), A1226.

3) Alexander Blair’s thesis (2022) – Sec. 2.3.5**Rollo **| TBA**SUPPORTING INFORMATION**:

TBA

**[A] 2023-01-19**:**Emma **| Hartnett, W.N., Ramirez, J., Olson, T.E., Hopp, C.T., Jewell, M.C., Knoll, A.R., Hazelton, D.W. and Zhang, Y., 2021. Characterization of edge damage induced on REBCO superconducting tape by mechanical slitting. Engineering Research Express, 3(3), p.035007**SUPPORTING INFORMATION**:**For information on delamination**: Majkic, G., Galstyan, E., Zhang, Y. and Selvamanickam, V., 2013. Investigation of delamination mechanisms in IBAD-MOCVD REBCO coated conductors. IEEE transactions on applied superconductivity, 23(3), pp.6600205-6600205. **Structure and manufacturing processes of REBCO tapes**: Trillaud, F., Dos Santos, G. and Gonçalves Sotelo, G., 2021. Essential material knowledge and recent model developments for REBCO-coated conductors in electric power systems. Materials, 14(8), p.1892. **Etching process of REBCO**: Turenne, M., Johnson, R.P., Kahn, S., Hunte, F., Ye, L. and Schwartz, J., 2010, December. Characterization of REBCO coated conductors for high field magnets. In 1st International Particle Accelerator Conference, IPAC 2010 (pp. 400-402).**Charles (H) **| Fleckinger-Pelle, J. and Kaper, H.G., 1995. Gauges for the Ginzburg-Landau equations of superconductivity (No. ANL/MCS/CP-87416; CONF-9507214-1). Argonne National Lab.(ANL), Argonne, IL (United States).**SUPPORTING INFORMATION**:

Landau and Lifshitz, Course in Theoretical Physics Vol. 2: Classical Theory of Fields, 3.18: Gauge Invariance This book is available online via the Durham library.

**[B] 2022-09-29****Rollo **| Yeekin Tsui, Elizabeth Surrey and Damian Hampshire, “Soldered joints—an essential component of demountable high temperature superconducting fusion magnets“, 2016 Supercond. Sci. Technol. 29 075005**SUPPORTING INFORMATION**:

Pool, Ch2.*Info on solders for superconductors*:

R.W. Fast, W.W. Craddock, M. Kobayashi, M.T. Mruzek, Electrical and mechanical properties of lead/tin solders and splices for superconducting cables, Cryogenics, Volume 28, Issue 1, 1988, Pages 7-9, ISSN 0011-2275, https://doi.org/10.1016/0011-2275(88)90223-8.

Y. Tsui, R. Mahmoud, E. Surrey and D. Hampshire, “*Superconducting and Mechanical Properties of Low-Temperature Solders for Joints*,”in IEEE Transactions on Applied Superconductivity, vol. 26, no. 3, pp. 1-4, April 2016, Art no. 6900204, doi: 10.1109/TASC.2016.2536806.

**[A] 2022-09-15**:**Emma **| Jiamin Zhu, Shuiliang Zhen, and Zhijian Jin, “Development of A Novel Method to Efficiently Measure Critical Bending Diameter of 2G HTS Tapes” IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 32, NO. 7, OCTOBER 2022**SUPPORTING INFORMATION**:

He, R., Tan, Y., Huang, Z., Xie, Y., Wang, G., Wang, Y., Wu, Q. and Wei, J., 2021. Bending and uniaxial tensile strain effects on the critical current of REBCO coated conductor tapes. *Cryogenics*, *116*, p.103285. (For information on bending strain mathematics)

https://www.superpower-inc.com/specification.aspx (For information on the structure of REBCO tape)**Charles (H) **| Choi, H., Roundy, D., Sun, H. *et al*. “The origin of the anomalous superconducting properties of MgB_{2}” Nature 418, 758–760 (2002).

MgB_{2} is one of few superconductors with a simple enough electronic structure to support a first-principles calculation of *T*_{c} in the phonon-mediated theory.**SUPPORTING INFORMATION**:

A B Pippard 1960 Rep. Prog. Phys. 23 176 https://iopscience.iop.org/article/10.1088/0034-4885/23/1/304/meta. This is basically a tutorial on Fermi surfaces, electronic structure, etc.**Charles (G)** | T. Suzuki, S. Awaji, H. Oguro & K. Watanabe “Applied Strain Effect on Superconducting Properties for Detwinned (Y, Gd)BCO Coated Conductors” IEEE Trans. Appl. Supercond. Vol. 25 p. 8400704, 2015**SUPPORTING INFORMATION**:

Single crystal measurements for comparison to the detwinned tape: Fietz W H, Weiss K-P and Schlacter S I (2005) *Supercond. Sci. Technol. ***18 **S332-7

Strain behaviour in conventional (twinned) REBCO: van der Laan D C, Abraimov D, Polyanskii A A, Larbalestier D C, Douglas J F, Semerad R and Bauer M (2011) *Supercond. Sci. Technol. ***24 **115010

**[B] 2022-06-16**:**Brad **| C. S. Owen and D. J. Scalapino, “Vortex Structure and Critical Currents in Josephson Junctions” Phys. Rev. 164, 538, 1967**SUPPORTING INFORMATION**:

This paper is a highly cited seminal paper detailing the maths involved when considering wide junctions (larger than the Josephson penetration depth)

The details of the calculations are not too important here – instead, the resulting behaviour of the critical current in field (c.f. Fig 4 and Fig 5) is the focus*Also see*:

Barone and Paterno – Sec 1.7 – Electrodynamics of the Josephson Junction

Poole – Chapter 15 – Sec VIII – Magnetic Field and Size Effects

S. V. Kuplevakhsky and A. M. Glukhov (Phys. Rev. B 73, 2006)

S. V. Kuplevakhsky and A. M. Glukhov (Phys. Rev. B 76, 2007)

**Rollo **| P. K. Ghoshal et al., “Design and Evaluation of Joint Resistance in SSC Rutherford-Type Cable Splices for Torus Magnet for the Jefferson Lab 12-GeV Upgrade,” in IEEE Transactions on Applied Superconductivity, vol. 26, no. 4, pp. 1-4, June 2016, Art no. 4800304, doi: 10.1109/TASC.2016.2517922**SUPPORTING INFORMATION**:

Poole Ch. 2.

Info on solders for superconductors – R.W. Fast, W.W. Craddock, M. Kobayashi, M.T. Mruzek, “*Electrical and mechanical properties of lead/tin solders and splices for superconducting cables*,” Cryogenics,Volume 28, Issue 1,1988,Pages 7-9,ISSN 0011-2275

Y. Tsui, R. Mahmoud, E. Surrey and D. Hampshire, “*Superconducting and Mechanical Properties of Low-Temperature Solders for Joints*,”in IEEE Transactions on Applied Superconductivity, vol. 26, no. 3, pp. 1-4, April 2016, Art no. 6900204, doi: 10.1109/TASC.2016.2536806.

**[A] 2022-05-12**:**Charles**| ten Haken B, Godeke A and ten Kate H H J, “The Influence of Compressive and Tensile Axial Strain on the Critical Properties of Nb_{3}Sn Conductors” 1995 IEEE Trans. Appl. Supercond. Vol. 5 pp. 1909-12**SUPPORTING INFORMATION**:**1**) Basic introduction to deviatoric strain: Gerya, T. (2019). Stress and strain. In Introduction to Numerical Geodynamic Modelling (pp. 50-59), chapter 4. Cambridge: Cambridge University Press. doi:10.1017/9781316534243.005*More detail about strain in Nb _{3}Sn*:

**2**) D. M. J. Taylor and D. P. Hampshire – The scaling law for the strain-dependence of the critical current density in Nb3Sn superconducting wires – Supercond. Sci. Tech 18 (2005) S241-S252

**3**) Arbelaez D, Godeke A and Prestemon “An improved model for the strain dependence of the superconducting properties of Nb

_{3}Sn.” 2008 Supercond. Sci. Technol. 22 025005

**Mark**| Lu, J., et al. (2021). “Oxygen out-diffusion in REBCO coated conductor due to heating.” Superconductor Science & Technology 34(7): 10.

This paper deals with an important issue for experimentalists dealing with HTS materials that inevitably require soldering i.e. the application of heat for various time periods. It also addresses the conflicting behaviours of HTS and copper that are joined together at elevated temperatures.

SUPPORTING INFORMATION:

See Jack Ekin, Chapter 8 that, in part, deals with some associated HTS contact issues

**[B] 2022-03-24**:**Brad **| Josephson, B. D. “Coupled superconductors.” Reviews of Modern Physics 36, no. 1 (1964): 216.**SUPPORTING INFORMATION**:

Barone and Paterno – Sec 1.7 – Electrodynamics of the Josephson Junction

Poole – Chapter 15 – Sec VIII – Magnetic Field and Size Effects

**Charlie**| Carver A. Mead, “Collective electrodynamics I“, Proceedings of the National Academy of Sciences, vol. 94, no. 12, pp. 6013-6018, (1997)

**[A] 2022-03-03**:**Charles**| A. A. Babaei Brojeny, and J. R. Clem, “Self-field effects upon the critical current density of flat superconducting strips” Supercond. Sci. Technol. Vol. 18, 2005, pp. 888-895**SUPPORTING INFORMATION**:

An example of self-field effects causing losses in ac-transport current carrying conductors can be found on p1391 of the Handbook of Superconducting Materials, Volume I: Superconductivity, Materials and Processes**Mark**| Zhang, P. X., Y. Feng, X. H. Liu, C. G. Li, K. Zhang, X. D. Tang, and Y. Wu. “Microstructure and superconducting properties comparison of bronze and internal tin process Nb_{3}Sn strands for ITER.” Physica C: Superconductivity 469, no. 15-20 (2009): 1536-1540

This paper analyses the physical and superconducting characteristics of Bronze Route and Internal Tin strands designed for use in the ITER magnet system that were fabricated by Western Superconducting Technologies.**SUPPORTING INFORMATION**:

Wilson, “Superconducting Magnets”, Ch. 12.3 starting on p293

100 Years of Superconductivity – Ch 11.3 “History of Nb_{3}Sn and related A15 Wires”

**[B] 2022-01-**27:**Brad **| D. Saint-James and P. G. de Gennes, “Onset of superconductivity in decreasing fields,” Phys. Lett., vol. 7, no. 5, pp. 306-308, 1963.**SUPPORTING INFORMATION**:

Tinkham, “Introduction to Superconductivity”, 2nd Ed. – Section 4.9

Saint James, “Type II Superconductivity” – Section 4.2 (a) **Charl**ie| Lee, P. J., and D. C. Larbalestier. “Determination of the flux pinning force of α-Ti ribbons in Nb46. 5wt% Ti produced by heat treatments of varying temperature, duration and frequency.” Journal of materials science 23.11 (1988): 3951-3957.**SUPPORTING INFORMATION:**

Superconducting Magnets by Wilson – Ch 12.2 p286 “Niobium Titanium”

100 Years of Superconductivity – Ch 11.2 “Nb-Ti”

**[A] 2021-12-16**:**Brad **| D. Saint-James and P. G. de Gennes, “Onset of superconductivity in decreasing fields,” Phys. Lett., vol. 7, no. 5, pp. 306-308, 1963.**SUPPORTING INFORMATION**:

Tinkham, “Introduction to Superconductivity”, 2nd Ed. – Section 4.9

Saint James, “Type II Superconductivity” – Section 4.2 (a) **Charles**| W. H. Fietz, K. P. Weiss, and S. I. Schlachter, “Influence of intrinsic strain on Tc and critical current of high-Tc superconductors,” (in English), Superconductor Science and Technology, Article; Proceedings Paper vol. 18, no. 12, pp. S332-S337, Dec 2005, doi: 10.1088/0953-2048/18/12/018.**SUPPORTING INFORMATION**:

Brief introduction to REBCO & oxygen doping:

Tilley & Tilley (1990) Superfluidity and Superconductivity, 11.2 -“Resistive transitions and crystal structures”, pp.427-433

Poole *et al *(2007) Superconductivity, 2nd edition – 8.IV – “Aligned YBa2Cu3O7”, pp.202-208 **Mark**| C. Suryanarayana, “Mechanical Alloying and Milling,” *Progress in Materials Science, *vol. 46, pp. 1-184, 2001

This is a long paper that I haven’t read myself for over a decade. However, it provides a very good overview of mechanical ball milling, which is a process that was a prominent experimental tool in the Group when I joined and one I used myself to fabricate nanocrystalline niobium carbonitride. The milling equipment we have in the Group is discussed in sections 4.2.1 (Spex shaker mill) and 4.2.2. (planetary ball mill). There’s no need to read the whole paper in detail, but looking through the contents list will give some idea of the scope of the process and then a slightly more detailed look through section 4.3 and 12 should suffice.**SUPPORTING INFORMATION**:

For an overview of this paper with an emphasis on milling in the Group see the Archive at “Group Meetings+Talks+Posters\Group Meeting+problem solving+conference talks\Old talks\MJR-early talks\**MJR 090721 Milling in the Superconductivity Group.ppt**“.

**[B] 2021-11-11**:**Charlie**| D. Dew-Hughes, “Flux pinning mechanisms in type II superconductors,” Philosophical Magazine, vol. 30, no. 2, pp. 293-305, 1974

Dew-Hughes determines the field-dependence of the volume-averaged pinning force by simple consideration of the interaction strength and range, and the total pinned fluxon length.**SUPPORTING INFORMATION**:

Chapters 6 and 7 of Matsushita discuss material which is relevant to this paper. They are quite advanced by comparison but they do contain some helpful diagrams

**[A] 2021-10-14**:**Brad **| M. Machida and H. Kaburaki, “Direct simulation of the time-dependant Ginzburg-Landau equation for Type-II superconducting thin film: Vortex dynamics and V-I characteristics,” Physical Review Letters, vol. 71, no. 19, pp. 3206-3209, 1993

This paper gives some nice context for understanding 2D simulations. I think it gives a very nice overview of the methods and outputs for the TDGL 2D code. In particular, it illustrates how a transport current is simply simulated by fixing the fields at the edges – with the useful interpretation that the superconductor does not distinguish between different ’types’ of fields.**SUPPORTING INFORMATION**:

GL Theory – Poole, Superconductivity, Chapter 8

Intro/origin for TDGL Equations: Kopnin, *Theory of Non-equilibrium Superconductivity*, Introduction**Charles**| C. Tarantini et al., “Anisotropy of the irreversibility field for Zr-doped (Y,Gd)Ba_{2}Cu_{3}O_{7} thin films up to 45 T,” Physical Review B, vol. 84, no. 22, p. 224514, 2011**SUPPORTING INFORMATION**:*Introduction to resistivity measurements in REBCO* – Tilley & Tilley: Superfluidity & superconductivity (1990), Chapter **11.3 **(High *T*_{c} superconductors: Critical fields and critical currents), pp 433-442*Anisotropic B*_{c2} Klemm: Layered Superconductors, vol. 1 (2012), chapter **7.1.1 **(Upper critical fields: The anisotropic Ginzburg-Landau model: Anisotropic three-dimensional systems), pp. 223-226 **Mark**| N. Mitchell, M. Breschi, and V. Tronza, “The use of Nb_{3}Sn in fusion: lessons learned from the ITER production including options for management of performance degradation,” Supercond. Sci. Technol., Article vol. 33, no. 5, p. 21, May 2020**SUPPORTING INFORMATION**:

Superconducting Magnets by Wilson – Chapter 12: Superconducting Materials and their Manufacture and Chapter 13: Magnet Construction: Some Practical Details.

Also see (with historical context) *100 Years of Superconductivity* – Chapter 11: Wires and Tapes (particularly 11.2 Nb-Ti and 11.3 Nb_{3}Sn) and Chapter 12: Large Scale Applications

**[B] 2021-08-12**:**Simon**| M. Coleman and S. McIntosh, “*BLUEPRINT: A novel approach to fusion reactor design*,” Fusion Engineering and Design, vol. 139, pp. 26-38, 2019**Charlie**| N. R. Werthamer, “Theory of a Local Superconductor in a Magnetic Field,” Physical Review, vol. 132, no. 2, pp. 663-668, 10/15/ 1963

**[A] 2021-07-15**:**Brad**| J. R. Clem, “Josephson junctions in thin and narrow rectangular superconducting strips,” Physical Review B, vol. 81, no. 14, 2010**Charles**| M. Lao, J. Bernardi, M. Bauer, and M. Eisterer, “Critical current anisotropy of GdBCO tapes grown on ISD-MgO buffered substrate,” Supercond. Sci. Technol., Article vol. 28, no. 12, p. 8, Dec 2015**Mark**| S. S. Fetisov et al., “Residual Resistance Ratio in Nb_{3}Sn Strands During ITER TF Conductor Manufacture and After SULTAN Tests,” (in English), IEEE Transactions on Applied Superconductivity, Article vol. 24, no. 3, p. 5, Jun 2014

**[B] 2021-03-31**:**Jack**| S. Kirkpatrick, “Percolation and Conduction,” Reviews of Modern Physics, vol. 45, no. 4, 1973**Simon**| D. Uglietti, R. Kang, R. Wesche, and F. Grilli, “Non-twisted stacks of coated conductors for magnets: Analysis of inductance and AC losses,” Cryogenics, vol. 110, 2020**Charlie**| V. G. Kogan and R. G. Mints, “Interaction of Josephson junction and distant vortex in narrow thin-film superconducting strips,” Physical Review B, vol. 89, no. 1, 2014

**[A] 2021-02-18**:**Jack**| H. Hilgenkamp and J. Mannhart, “Grain boundaries in high-T_{c} superconductors,” *Reviews of Modern Physics, *vol. 74, no. 2, pp. 485-549, 2002**Jack**| A. Gurevich and E. A. Pashitskii, “Current transport through low-angle grain boundaries in high-temperature superconductors,” *Physical Review B, *vol. 57, no. 21, pp. 13878-13893, 1998**Simon**| A. J. Creely et al., “Overview of the SPARC tokamak,” Journal of Plasma Physics, vol. 86, no. 5, 2020**Brad**| H. J. Fink, “Supercurrents through superconducting-normal-superconducting proximity layers. I. Analytic solution,” Physical Review B, vol. 14, no. 3, pp. 1028-1038, 1976**Charlie**| W. M. Nevins, “A Review of Confinement Requirements for Advanced Fuels,” Journal of Fusion Energy, vol. 17, no. 1, pp. 25-32, 1998/03/01 1998**Charles**| D. C. van der Laan et al., “Anisotropic in-plane reversible strain effect in Y_{0.5}Gd_{0.5}Ba_{2}Cu_{3}O_{7-d} coated conductors,” (in English), Supercond. Sci. Technol., Article vol. 24, no. 11, p. 8, Nov 2011**Mark**| F. Liu et al., “Properties of Toroidal Field Nb_{3}Sn Strands Made for the ITER Chinese Domestic Agency,” (in English), IEEE Transactions on Applied Superconductivity, Article vol. 29, no. 5, p. 4, Aug 2019