Onset of Dendritic Flux Avalanches in Superconducting Films

We report a detailed comparison of experimental data and theoretical predictions for the dendritic flux instability, believed to be a generic behavior of type-II superconducting films. It is shown that a thermomagnetic model published very recently [Phys. Rev. B 73, 014512 (2006)] gives an excellent quantitative description of key features like the stability onset (first dendrite appearance) magnetic field, and how the onset field depends on both temperature and sample size. The measurements were made using magneto-optical imaging on a series of different strip-shaped samples of ${\mathrm{MgB}}_2$. Excellent agreement is also obtained by reanalyzing data previously published for Nb.

Figure 1

(a) Three MO images of flux penetration in ${\mathrm{MgB}}_2$ taken during repeated identical experiments. (b) Image obtained by adding the 3 complementary colored images above. In the sum image the gray tone regions are those of repeated behavior, whereas colors show where there is no or only partial overlap. Strong irreproducibility is seen in the dendrite shapes, while the penetration near the edge and along static defects is reproducible. The dendrites tend to nucleate at preferred sites along the edge, which is due to small edge cavities giving local field amplification. The experiments were performed after cooling to 9.2 K and applying a magnetic field of 20 mT.

Figure 2

MO image showing flux distribution in ${\mathrm{MgB}}_2$ strip-shaped samples at 4 K and 15 mT applied field. The image brightness represents the local flux density. Both the number and size of the dendrites are larger for the wider samples.

Figure 3

Threshold magnetic field for onset of the dendritic instability in ${\mathrm{MgB}}_2$ strips of different width (symbols) plotted together with a fitted theoretical curve (full line), which diverges at a finite $w$ indicated by the dashed asymptote.

Figure 4

Temperature dependence of the threshold magnetic field. Experimental data obtained for the 5 mm wide ${\mathrm{MgB}}_2$ sample and for a 1.8 mm wide Nb film [10] are plotted as ● and ▴, respectively. The full lines are theoretical fits. The dashed lines show the limiting temperature above which the instability vanishes.

Figure 5

Theoretical stability diagram predicting the threshold temperature $T_{\mathrm{th}}$ for different film width. The curve is plotted for parameter values corresponding to ${\mathrm{MgB}}_2$ films.