Dependence of thermomagnetic instability on strong nonlinear <i>E</i>-<i>J</i> models in superconducting films

Abstract

The &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}$ E-J $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M4.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M4.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; relationship in conventional conductor generally satisfies linear Ohm's law. However, the &lt;inline-formula&gt;&lt;tex-math id="M5"&gt;\begin{document}$ E-J $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M5.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M5.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; model in superconductors presents strong nonlinear characteristics, which is significantly different from that of conventional conductor.With the nonlinear &lt;inline-formula&gt;&lt;tex-math id="M6"&gt;\begin{document}$ E-J $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M6.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M6.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; power law of superconducting materials by using the fast Fourier transform method (FFT), we quantitatively investigate the relationship between the magnetic-thermal stability and the nonlinear constitutive relation of superconducting films at different temperature, magnetic field ramp rate and critical current density. We find that the strong nonlinear electromagnetic constitutive model plays a crucial role in the onset and morphology (tree-like and finger-like) of the magneto-thermal instability of superconducting thin films. In addtion, the reason why similar magneto-thermal instabilities cannot be observed in conventional conductors is also explained. It can be found that the magnetic field on the border of the superconducting film increases rapidly for a larger creep exponent due to the enhancement of diamagnetism, which results in a large magnetic pressure and easily trigger flux avalanches. Therefore, the threshold field of flux avalanches in superconducting film decreases with flux creep exponent. Finally, we present the curves that can clearly divide the &lt;inline-formula&gt;&lt;tex-math id="M7"&gt;\begin{document}$ n_0-j_{c0} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M7.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M7.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; plane and &lt;inline-formula&gt;&lt;tex-math id="M8"&gt;\begin{document}$ n_0-\dot {H}_a $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M8.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M8.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; plane into magneto-thermal stability region and magneto-thermal stability regions for superconducting thin film with different levels of nonlinearity.