Ultrafast magnetic flux dendrite propagation into thin superconducting films

We suggest a theoretical model allowing one to find analytically the velocity of a magnetic flux dendrite penetration into thin superconducting films. The key assumptions for this model are based upon experimental observations. We treat a dendrite tip motion as a propagating flux jump instability. Two different regimes of dendrite propagation are found: A fast initial stage is followed by a slow stage, which sets in as soon as a dendrite enters into the vortex-free region. The theoretical results and experimental data obtained by a magneto-optic pump-probe technique are compared and a good agreement between the calculations and measurements is found.

Figure 1

(Color online) Magneto-optic images of a dendritic flux pattern in a YBCO film with the thickness $d=330\mathrm{mm}$ subjected to a field of $B_a=15\mathrm{mT}$. (a) Final state (after $\approx 10\mathrm{s}$) of a dendritic flux pattern with superimposed current distribution shown by the arrows. The length of the arrows is proportional to the local current density. (b) The absolute value of the current density is shown. The bright areas indicate high current densities.

Figure 2

Current lines for the straight-line magnetic flux dendrite. The full line to the left marks the strip edge.

Figure 3

(Color online) Shown is the magnetic flux distribution in our superconducting sample measured perpendicular to the edge. The measured data are shown as circles, whereas the solid line represents a least-squares fit. This fitting function given by Eq. (12) was used as $B_{\mathrm{out}}\left(s\right)$.

Figure 4

The time dependence of the length of a magnetic flux dendrite, $s\left(t\right)$. The solution of Eqs. (14, 15) with $s_0=0.1\mathrm{mm}$ and $\alpha =1.67$ is shown by the solid line; the experimental data are shown by the solid dots (Ref. 15). The dependence $s\left(t\right)$ for the first $15\mathrm{ns}$ is shown in the inset.

Figure 5

The dependence of the flux dendrite velocity on the sample thickness $v\left(d\right)$. The dashed line is a fit of $v\propto 1∕d$ revealing the dependence given by Eq. (11) and the solid dots are the experimental data (Ref. 35).