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Numerical Simulation of Phase Transitions in Type-II Annular Superconductor Using Time-dependent Ginzburg-Landau Equations

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Abstract

Time-dependent Ginzburg-Landau equations were solved by finite element method in two-dimensional space for order parameter and energy components of the annular superconducting sample in steady magnetic fields. Vortices preferred to penetrate from the inner surface of the annulus due to lesser energy required at the concave surface. A transition magnetic field strength was observed in spatial averages of carrier concentration and energy components, showing small bumps and abrupt variations, indicating phase transition from a non-vortex to vortex state. These effects were observed to repeat with every subsequent entry of a set of vortices into the sample; transition magnetic field strength was found to depend inversely on the annular width of the sample. The present work gives a better understanding of energy variations during phase transition from non-vortex to vortex state and predicts that vortex state can be avoided by tuning the wire thickness in practical applications, e.g., superconducting electromagnets.

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Acknowledgments

This work was supported by National Science Foundation of China grant numbers 11174030 and 11504020. Author HMJ acknowledge Higher Education Commission of Pakistan for PhD scholarship.

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Authors and Affiliations

  1. Department of Physics, University of Science and Technology Beijing, Beijing, 100083, China

    Hasnain Mehdi Jafri, Xingqiao Ma, Congpeng Zhao, Houbing Huang & Zhuhong Liu

  2. ASIC, China Center for Information Industry Development, Beijing, 100083, China

    Congpeng Zhao

  3. Energy Research Centre, COMSATS Institute of Information Technology, Lahore, Pakistan

    Tauseef Anwar

  4. Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA, 16802, USA

    Long-Qing Chen

Authors
  1. Hasnain Mehdi Jafri
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  2. Xingqiao Ma
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  3. Congpeng Zhao
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  4. Houbing Huang
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  5. Tauseef Anwar
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  6. Zhuhong Liu
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  7. Long-Qing Chen
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Correspondence to Xingqiao Ma.

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Supplementary Information

Supplementary Video S1 showing entrance of vortices into the annular sample is available as supplementary information, can be found at https://youtu.be/Z1mEor3TWi0.

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Jafri, H.M., Ma, X., Zhao, C. et al. Numerical Simulation of Phase Transitions in Type-II Annular Superconductor Using Time-dependent Ginzburg-Landau Equations. J Supercond Nov Magn 31, 3445–3451 (2018). https://doi.org/10.1007/s10948-018-4586-y

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