Defect formation in long Josephson junctions

We study numerically a mechanism of vortex formation in a long Josephson junction within the framework of the one-dimensional sine-Gordon model. This mechanism is switched on below the critical temperature. It is shown that the number of fluxons versus velocity of cooling roughly scales according to the power law with the exponent of either 0.25 or 0.5 depending on the temperature variation in the critical current density.

Figure 1

(Color online) The average number of kinks versus quench time for the linear temperature dependence of the critical current $f\left(t\right)=\left[1-T\left(t\right)/T_c\right]$. The junction lengths are 2000, 1000, 800, 400 ${\lambda }_J$ (from top to bottom).

Figure 2

(Color online) The snapshots of the string evolution during the kink formation, see the explanation in the text.

Figure 3

(Color online) The average number of kinks versus quench time for the quadratic temperature dependence of the critical current $f\left(t\right)={\left[1-T\left(t\right)/T_c\right]}^2$. The junction lengths are 2000, 1000, 800 ${\lambda }_J$ (from top to bottom). By triangles the number of kinks is shown for an annular junction of the length $L=800$.

Figure 4

(Color online) The average number of kinks versus quench time for the linear, Eq. (5), (crosses) and quadratic, Eq. (6), (diamonds) temperature dependences of the critical current. Triangles and circles are experimental data from Refs. 1, 2.

Figure 5

(Color online) The average number of kinks versus quench time for the linear, Eq. (5), (light symbols) and quadratic, Eq. (6), (dark symbols) temperature dependences of the critical current and different levels of freezing $f\left(t\right)={10}^{-7}$—crosses, $f\left(t\right)={10}^{-6}$—triangles, $f\left(t\right)={10}^{-5}$—diamonds, and $f\left(t\right)={10}^{-4}$—stars. Circles—the experimental data from Ref. 2.