Skip to main content
SpringerLink
Log in

A Statistical Mechanical Model of Critical Currents in Superconductors

  • Original Paper
  • Published:
Journal of Superconductivity and Novel Magnetism Aims and scope Submit manuscript

Abstract

We present a statistical mechanical model for critical currents which is successful in describing both the in-plane and out-of-plane magnetic field angle dependence of J c . This model is constructed using the principle of maximum entropy, that is, by maximizing the information entropy of a distribution, subject to constraints. We show the same approach gives commonly assumed forms for J c (B) and J c (T). An expression for two or more variables, e.g. J c (B,T), therefore, follows the laws of probability for a joint distribution. This gives a useful way to generate predictions for J c (B,T) for the DC critical current in wires, cables or coils.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Jaynes, E.T.: Phys. Rev. 106, 620 (1957)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Jaynes, E.T.: Phys. Rev. 108, 171 (1957)

    Article  MathSciNet  ADS  Google Scholar 

  3. Jaynes, E.T.: In: Levine, R.D., Tribus, M. (eds.) The Maximum Entropy Formalism, pp. 15–118. MIT Press, Cambridge (1978)

    Google Scholar 

  4. Kapur, J.N.: Maximum-Entropy Models in Science and Engineering, New Age, 2nd revised edn. (2009)

    Google Scholar 

  5. Cover, T.M., Thomas, J.A.: Elements of Information Theory, 2nd edn. Wiley Series in Telecommunications and Signal Processing (2006)

    MATH  Google Scholar 

  6. Banavar, J.R., Maritan, A., Volkov, I.: J. Phys. Condens. Matter 22, 063101 (2010)

    Article  ADS  Google Scholar 

  7. Caticha, A.: Lectures on probability, entropy, and statistical physics. Max-Ent 2008 Sao Paulo, Brazil. arXiv:0808.0012

  8. Carazza, B.: J. Phys. A, Math. Gen. 9, 1069 (1976)

    Article  ADS  MATH  Google Scholar 

  9. Long, N.J., Strickland, N., Talantsev, E.: IEEE Trans. Appl. Supercond. 17, 3684 (2007)

    Article  ADS  Google Scholar 

  10. Long, N.J.: Supercond. Sci. Technol. 21, 025007 (2008)

    Article  ADS  Google Scholar 

  11. Wimbush, S.C., Long, N.J.: New J. Phys. 14, 083017 (2012)

    Article  ADS  Google Scholar 

  12. Clem, J.R., Weigand, M., Durrell, J.H., Campbell, A.M.: Supercond. Sci. Technol. 24, 062002 (2011)

    Article  ADS  Google Scholar 

  13. Harrington, S.A., et al.: Nanotechnology 21, 095604 (2010)

    Article  ADS  Google Scholar 

  14. Durrell, J.H., et al.: Phys. Rev. Lett. 90, 247006 (2003)

    Article  ADS  Google Scholar 

  15. Matsushita, T.: Flux Pinning in Superconductors. Springer, Berlin (2006)

    Google Scholar 

  16. Campbell, A.M., Evetts, J.E.: Critical Currents in Superconductors. Taylor & Francis, London (1972)

    Google Scholar 

  17. Varanasi, C.V., Barnes, P.N.: In: Bhattacharya, R., Paranthaman, M.P. (eds.) High Temperature Superconductors. Wiley–VCH, Weinheim (2010)

    Google Scholar 

  18. Jaynes, E.T.: Probability Theory, the Logic of Science. Cambridge University Press, Cambridge (2003)

    Book  MATH  Google Scholar 

  19. Jung, J., Yan, H., Darhmaoui, H., Abdelhadi, M., Boyce, B., Lemberger, T.: Supercond. Sci. Technol. 12, 1086–1089 (1999)

    Article  ADS  Google Scholar 

  20. Albrecht, J., Djupmyr, M., Bruck, S.: J. Phys. Condens. Matter 19, 216211 (2007)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The author acknowledges discussions with S.C. Wimbush and other members of the superconductivity team at IRL. Thanks to N.W. Ashcroft, Cornell University, for comments on an earlier version of this paper.

Author information

Authors and Affiliations

  1. Industrial Research Limited, P.O. Box 31-310, Lower Hutt, 5040, New Zealand

    N. J. Long

Authors
  1. N. J. Long
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. J. Long.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Long, N.J. A Statistical Mechanical Model of Critical Currents in Superconductors. J Supercond Nov Magn 26, 763–767 (2013). https://doi.org/10.1007/s10948-012-2063-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10948-012-2063-6

Keywords

Search

Navigation