Oscillatory regimes of the thermomagnetic instability in superconducting films

Abstract

The stability of superconducting films with respect to oscillatory precursor modes for thermomagnetic avalanches is investigated theoretically. The results for the onset threshold show that previous treatments of non-oscillatory modes have predicted much higher thresholds. Thus, in film superconductors, oscillatory modes are far more likely to cause thermomagnetic breakdown. This explains the experimental fact that flux avalanches in film superconductors can occur even at very small ramping rates of the applied magnetic field. Closed expressions for the threshold magnetic field and temperature, as well oscillation frequency, are derived for different regimes of the oscillatory thermomagnetic instability.PACS numbers: 74.25. Ha, 68.60.Dv, The irreversible electromagnetic properties of type-II superconductors are commonly explained in terms of the critical current density j c , as introduced by Bean [1]. In the corresponding critical state the distribution of magnetic flux is nonuniform and metastable. However, since j c is a decreasing function of temperature the metastable state can become unstable driven by the Joule heat generated during flux motion. In bulk superconductors this thermomagnetic instability gives rise to abrupt displacement of large amounts of flux, so-called flux jumps, which may cause the entire superconductor to be heated to the normal state [2][3][4][5][6]. In some cases, pronounced oscillations in magnetization and temperature have been detected prior to such jumps [7,8].In film superconductors experiencing an increasing transverse magnetic fields, the thermomagnetic instability gives rise to abrupt flux entry in the form of dendritic structures rooted at the sample edge [9]. Using magnetooptical imaging [10] the residual flux distribution left in the film after such avalanche events have been observed in many superconducting materials [11][12][13][14]. The experiments also show that there is a threshold magnetic field, H th , for the onset of avalanche activity, and that the unstable behavior is restricted to temperatures below a threshold value, T th , see Fig. 1. These thresholds have been explained on the basis of linear stability analysis of the nonlinear and non-local equations governing the electrodynamics of such films [15][16][17][18][19][20]. The theoretical works show that in order to trigger avalanches an electrical field in the range E = 30-100 mV/m is required.Experimentally, one finds in films of many materials, e.g., MgB 2 , Nb and NbN, that avalanches occur even when the magnetic field is ramped very slowly, e.g., below 1 mT/s [21], inducing correspondingly small E-fields. For a film placed in a magnetic field ramped at a rate of µ 0Ḣa the Bean model estimates [22] the E-field along the edge as E ∼ µ 0Ḣa w, where w is the half-width of the film. With a size of a few millimeters and a ramping rate of 1 mT/s the edge field is E ∼ 1 µV/m, i.e., several orders of magnitude below the theoretical threshold. Hence, thermomagnetic avalanches should not occur at such ramping rates, ...

Selective triggering of magnetic flux avalanches by an edge indentation

“…This result is in agreement with the theory in Ref. [35], which states that H th = dj c /π atanh(hT * /nadj c µ 0Ḣa ), where…”

Statistics of thermomagnetic breakdown in Nb superconducting films

“…It might come as a surprise to learn that as of today, there are neither theoretical predictions nor experimental investigations of the statistical distribution of H th . On the one hand, while theoretical simulations have been successfully used to emulate flux avalanches and deduce some of their properties 9,10 , they still fail to capture the stochasticity of the process. On the other hand, the lack of experimental information can be tracked back to the techniques used to estimate H th .…”

Anisotropic thermomagnetic avalanche activity in field-cooled superconducting films

“…Finally, note that in a recent work [27] the formulas above, represented in the graph of Fig. 4, were generalized by including in the linear stability analysis also modes with complex instability increments, i.e., scenarios of oscillatory precursor behavior were also considered.…”