Quasiperiodic magnetic flux avalanches in doubly connected superconductors

Magneto-optical imaging of Nb rings, open rings, and strips reveals that the topology affects the dendritic flux avalanches in the samples. In particular, dendrites crossing the entire width of the sample appear only in the rings. Such dendrites appear when the difference between the applied field and the average field inside the central hole reaches a certain threshold level $\mathrm{\Delta }{H}_{\mathrm{th}}$. With increasing applied field, this condition is reached quasiperiodically as a crossing dendrite creates momentarily a hot channel through which flux flows into the central hole, balancing the field inside the hole with that outside the ring. The threshold $\mathrm{\Delta }{H}_{\mathrm{th}}$ differs in magnitude from the onset field $H_{\mathrm{th}}$ of magnetic instability, and exhibits qualitatively different dependence on the rim width.

Figure 1

Magneto-optical images at $T=4.5\mathrm{K}$ of ring (a), open ring (b), and strip (c) in external fields of 56.7, 56.7, and 61.2 Oe, respectively. A long-range dendrite crossing the entire width from edge to edge (marked with red color) appears only in the ring.

Figure 2

The average field in the central hole of a ring from set 3 as a function of the external field at $T=5\mathrm{K}$. The solid red line is a guide to the eye. The stepwise increase in the field occurs when a dendrite crosses the entire rim of the ring. The dashed line describes the line $H_i=H_a$. Inset: The applied field $H_a^j$ versus the average field inside the hole $H_i^j$, both measured at the onset of the jumps. The solid line is a linear fit of the data to $H_a^j=H_i^j+\mathrm{\Delta }{H}_{\mathrm{th}}$.

Figure 3

The difference $\mathrm{\Delta }H$ between the applied field $H_a$ and the average field inside the hole $H_i$ as a function of $H_a$ at $T=5\mathrm{K}$, for the same ring as in Fig. 2. In each cycle $\mathrm{\Delta }H$ increases linearly to $\mathrm{\Delta }{H}_{\mathrm{th}}$ and then sharply drops to zero following the appearance of a crossing dendrite. The solid line is a guide to the eye.

Figure 4

Temperature dependence of the threshold fields for a ring (circles), an open ring (triangles), and a strip (stars) of the same width from set 3. Also shown is the threshold field $\mathrm{\Delta }{H}_{\mathrm{th}}$ (squares) for the appearance of a crossing dendrite in the same ring. The solid lines are a guide to the eye. The error bars for the data points of $H_{\mathrm{th}}$ are ∼5 Oe. In the $\mathrm{\Delta }{H}_{\mathrm{th}}$ data, the error bars are derived from the linear fit of the data to $H_a^j=H_i^j+\mathrm{\Delta }{H}_{\mathrm{th}}$.

Figure 5

Width dependence of the threshold field for rings (circles), open rings (triangles), and strips (stars), and $\mathrm{\Delta }{H}_{\mathrm{th}}$ (squares) at $T=5\mathrm{K}$. The solid lines are a guide to the eye. The error bars for the data points of $H_{\mathrm{th}}$ are ∼5 Oe. In the $\mathrm{\Delta }{H}_{\mathrm{th}}$ data, the error bars are derived from the linear fit of the data to $H_a^j=H_i^j+\mathrm{\Delta }{H}_{\mathrm{th}}$.

Figure 6

Schematic illustration of the mechanism for $\mathrm{\Delta }{H}_{\mathrm{th}}$. The green solid lines and the red dotted lines describe the induction just before and immediately after the appearance of a crossing dendrite, respectively.

Figure 7

Maps of current distribution at $T=4.8\mathrm{K}$ in an open ring (a) from set 2 in an external field of 36 Oe and in a ring from the same set in external fields of 34.6 Oe [(b) just before the appearance of the first crossing dendrite], 36 Oe [(c) immediately after the crossing], 53.3 Oe [(d) just before the appearance of the second crossing dendrite], and 58 Oe [(e) immediately after the second crossing].