Avalanches injecting flux into the central hole of a superconducting $\mathrm{Mg}{\mathrm{B}}_2$ ring

Magneto-optical imaging was used to observe dendritic flux avalanches connecting the outer and inner edges of a ring-shaped superconducting $\mathrm{Mg}{\mathrm{B}}_2$ film. Such avalanches create heated channels across the entire width of the ring, and inject large amounts of flux into the central hole. By measuring the injected flux and the corresponding reduction of current, which is typically 15%, we estimate the maximum temperature in the channel to be $100\mathrm{K}$, and the duration of the process to be on the order of a microsecond. Flux creep simulations reproduce all the observed features in the current density before and after injection events.

Figure 1

(Color online) (a) A field map of the sample at $T=6.2\mathrm{K}$ and $B_a=13\mathrm{mT}$. Bright pixels correspond to positive magnetic field, while dark pixels correspond to negative. Pixels in the Meissner region indicate the zero level. (b) The difference in field between the map shown here and the subsequent map in the sequence after a dendrite has perforated the ring and injected a large amount of flux into the central hole. Bright and dark pixels indicate flux has entered or left, respectively. Again the Meissner state indicate the zero level. While the most conspicuous feature is the large flux increase in the central hole, one can also observe a reduction in the field around the outer edge. In the superconducting material there is very little change in the field. The arrows superimposed on the field map show the current distributions before and after the perforation.

Figure 2

(Color online) Measured flux within $r_p$ as a function of applied field showing the crossover from complete screening to a linear increase following the applied field. The flux jumps are small and frequent at low temperature, becoming rarer and larger when the temperature approaches $T_{\mathrm{th}}$. The oblique grid lines have slope $A_{r<r_p}$, with the line through the origin representing the contribution to ${\Phi }_{r<r_p}$ from the applied field. The contribution to the flux from the ring currents ${\Phi }_{\text{self}}$ is illustrated for one of the curves. The solid black line is the result of a simulation with a Kim model for the critical current (see Sec. 5).

Figure 3

(Color online) (top) The evolution of the current along the radial profile and for the same experiment shown in Fig. 1. (bottom) The total ring current obtained by integrating the current density across the ring width.

Figure 4

(Color online) Field (top) and current (middle) profiles just prior to and just after a simulated perforation. The perforation field was 0.19 ${\mu }_0{J}_{c}d$, the creep exponent $n=30$, the blocking parameter $\alpha =0.13$, and a field independent $J_c$ was used. (Bottom) The change in current due to a perforation. The solid gray (red online) line is results from a simulation, and the black line is experimental points. The plot shows that the simulations reproduce the change well. In particular, the change in current grows as one gets closer to the inner edge.

Figure 5

Flux jump size versus perforation field from simulations and experiments. The filled squares show experimental first jumps, and the solid line shows results from simulations with $\alpha =0.13$. The simulations reproduce the experimental fact that the current is reduced by a smaller amount than ${\Phi }_{r<r_p}$