Java Videos of Simulations of Vortex Motion in Superconductors

The videos show computer-simulated "top views" (views from above the sample, or "bird's views") of magnetic field lines penetrating superconductors, when the external magnetic field is slowly ramped up.
The motion of penetrating magnetic field lines in superconductors can exhibit "stick-slip" type motion and collective "jamming" that resembles transport in other systems (e.g., grains of sand, colloids, dielectric breakdown).

∗ These Java/QuickTime movies were created by Cynthia Olson and Jared Groth in 1996.
   Here's MP4s recording of those Java/QuickTime movies in 2021.

Avalanche vortex movies

Vortex Avalanches - Strong pinning

Vortices are represented by circles that are colored according to the instantaneous vortex velocity. Blue indicates vortices that are stationary inside pinning sites. Yellow vortices are moving at a moderate rate, and red vortices are moving quickly. An external field is being very slowly increased by adding a single vortex to the left edge of the sample each time the sample reaches mechanical equilibrium. All vortex motion is a result of vortex-vortex interactions and the gradient in vortex density; no uniform current is applied. Avalanche disturbances propagate from the dense left edge of the sample to the relatively less dense right edge. Vortices that reach the right edge of the sample are removed in order to maintain a constant average flux profile.

In most avalanches, chains of vortices move from pinning site to pinning site, with each vortex moving into the site vacated by a vortex to its right. The winding chains extend down the flux gradient and appear at different locations in different avalanches. Chain size varies from sample-spanning to just three or four vortices. Note that the avalanche disturbances propagate neither instantly nor at constant speed through the sample, but that they pulse through the sample, with most of the vortices involved stopping exactly one pinning site to the right of their initial positions. Events with longer lifetimes consist of more than one pulse of motion.

This sample has a high density of strong randomly placed pinning sites, with a pinning density of 5.93/lambda^2, and pinning strengths uniformly distributed from f_p = 0.6 to 3.0. The coloring of instantaneous vortex velocities has been scaled according to the maximum vortex speed attained during the movie; vortex velocities in this sample are typically higher than velocities in the sample with weak pinning sites shown in the other movie. Since the pinning is strong, avalanche motion tends to be in short-lived small bursts, with many avalanches involving only a tiny number of vortices. Vortices around a moving vortex chain are too strongly pinned to move, so most avalanches are narrow.

Parameters and Notes

• A_p = 3.0 (Pinning strength)
• N_p = 3700 (Number of pinning sites)
• r_p = 0.15 (Radius of pinning)
• Parabolic random pinning
• Time between vortex drops was not constant
• There are on average 1729 vortices in the system.

Vortex Avalanches - Weak pinning

Vortices are represented by circles that are colored according to the instantaneous vortex velocity. Blue indicates vortices that are stationary inside pinning sites. Yellow vortices are moving at a moderate rate, and red vortices are moving quickly. An external field is being very slowly increased by adding a single vortex to the left edge of the sample each time the sample reaches mechanical equilibrium. All vortex motion is a result of vortex-vortex interactions and the gradient in vortex density; no uniform current is applied. Avalanche disturbances propagate from the dense left edge of the sample to the relatively less dense right edge. Vortices that reach the right edge of the sample are removed in order to maintain a constant average flux profile.

In most avalanches, chains of vortices move from pinning site to pinning site, with each vortex moving into the site vacated by a vortex to its right. The winding chains extend down the flux gradient and appear at different locations in different avalanches. Chain size varies from sample-spanning to just three or four vortices. Note that the avalanche disturbances propagate neither instantly nor at constant speed through the sample, but that they pulse through the sample, with most of the vortices involved stopping exactly one pinning site to the right of their initial positions. Events with longer lifetimes consist of more than one pulse of motion.

This sample has a high density of weak randomly placed pinning sites, with a pinning density of 5.93/lambda^2, and pinning strengths uniformly distributed from f_p= 0.2 to 1.0. The coloring of instantaneous vortex velocities has been scaled according to the maximum vortex speed attained during the movie; vortex velocities in this sample are typically lower than velocities in the sample with strong pinning sites shown in the other movie. Since the pinning is weak, avalanche motion tends to be broad and vortices around a moving vortex chain are likely to also move.

Parameters and Notes

• A_p = 1.0 (Pinning strength)
• N_p = 3700 (Number of pinning sites)
• r_p = 0.15 (Radius of pinning)
• Parabolic random pinning
• Time between vortex drops was not constant
• There are on average 677 vortices in the system.

Vortex plastic motion in a sample with a Periodic Array of Pinning Sites (PAPS)

Periodic Array of Pinning Sites - High matching fields

The movie illustrates the higher matching fields for a square array of pinning sites. Vortices enter the pinning region at the left and right edges of the sample, increasing the vortex density inside the sample. Circles represent vortices.

The parabolic pins in this sample are in a square array at a density of n_p = 0.19 (Pinning site density) and are all of strength f_p = 5.0 (Pinning site strength) Higher matching fields, up to and including the fourth matching field, are shown. At the higher fields, domains of different vortex lattice orientation can be seen moving through the sample, with domain boundaries marked by dislocations.

Parameters and Notes

• A_p = 5.0 (Pinning strength)
• r_pin = 0.25 (Pinning radius)
• N_pin = 247 (Number of pinning sites)
• Square array of pinning sites.
• Reached approximately 1148 vortices, somewhere above the 4 1/2 matching field.
• Vortices dropped every 300 md steps.
• Movie was written every 650 md steps

Periodic Array of Pinning Sites - Low matching fields

The movie illustrates the low matching fields for a square array of pinning sites. Vortices enter the pinning region at the left and right edges of the sample, increasing the vortex density inside the sample. Circles represent vortices.

The parabolic pins in this sample are in a square array at a density of n_p = 0.46 (Pinning site density) and are all of strength f_p = 0.45 (Pinning site strength) The first two matching fields, along with matching fields of less than one, are shown.

Parameters and Notes

• A_p = 0.45 (Pinning strength)
• r_pin = 0.15 (Pinning radius)
• N_pin = 600 Number of pinning sites
• Parabolic triangular pinning
• Reached approximately 2200 vortices, somewhere past the second matching field.
• Vortices dropped every 400 md steps.
• Movie was written every 650 md steps

Dynamic phases of vortices in samples with periodic pinning

Interstitial Flow (region II) - Periodic Array of Pinning Sites

Disordered Flow (region III) - Periodic Array of Pinning Sites

1D Incommensurate Flow (region IV) - Periodic Array of Pinning Sites

Plastic motion of vortices in samples with different pinning landscapes

Plastic Vortex Motion - Strong, sparse pinning

The movie shows the initial penetration of a flux front into a sample with a low density of strong pinning sites. We add vortices at a constant rate to an unpinned region at the left edge of the sample, creating a gradient in vortex density that drives the vortices into the pinned region. Circles represent vortices, and lines are drawn tracing the path each vortex follows through the sample.

The randomly placed parabolic pins in this sample are at a density of n_p = 0.64 (Pinning site density) and are all of strength f_p = 3.0 (Pinning site strength) Since the pinning is strong, vortices that fall into pinning sites remain trapped for the remainder of the movie, and repel the other vortices moving through the sample. As a result, the vortices quickly form channels that wind between the pinning sites. These channels are easily distinguished by the high density of vortex trails within them. Vortices moving inside the channels never interact with pinning sites, but instead are guided by the repulsion from the pinned vortices.

Parameters and Notes

• A_p = 3.0 (Pinning strength)
• r_pin = 0.15 (Pinning radius)
• N_pin = 400 (Number of pinning sites)
• Parabolic random pinning
• Vortices dropped every 40 md steps.
• Up to 600 vortices dropped, total.
• Movie was written every 20 md steps.

Plastic Vortex Motion - Intermediate strength pinning

The movie shows the initial penetration of a flux front into a sample with an intermediate density of intermediate strength pinning sites. We add vortices at a constant rate to an unpinned region at the left edge of the sample, creating a gradient in vortex density that drives the vortices into the pinned region. Circles represent vortices, and lines are drawn tracing the path each vortex follows through the sample.

The randomly placed parabolic pins in this sample are at a density of n_p = 1.92 (Pinning site density) and are all of strength f_p = 1.0 (Pinning site strength) The pinning sites are strong enough to trap vortices for a long period of time, but it is possible for a vortex to be pushed out of a pinning site by vortices entering the sample behind it. Although the pinning density is too high to permit a vortex to cross the entire sample without hitting a pinning site, some paths through the sample intersect fewer pinning sites than others, and these paths are favored by the vortices. Temporarily pinned vortices serve to repel the other vortices moving through the sample, and help guide the vortices into the paths of easiest flow.

Parameters and Notes

• A_p = 1.0 (Pinning strength)
• r_pin = 0.15 (Pinning radius)
• N_pin = 1200 (Number of pinning sites)
• Parabolic random pinning
• All the pinning sites are the same strength.
• Vortices dropped every 40 md steps.
• Up to 600 vortices dropped, total.
• Movie was written every 20 md steps.

Plastic Vortex Motion - Clustered pinning

The movie shows the initial penetration of a flux front into a sample with clustered pinning sites. We add vortices at a constant rate to an unpinned region at the left edge of the sample, creating a gradient in vortex density that drives the vortices into the pinned region. Circles represent vortices, and lines are drawn tracing the path each vortex follows through the sample.

The parabolic pins in this sample are placed in randomly located clusters. The density of an equal number of uniformly placed pins is n_p = 0.80 (Pinning site density) and the pins are all of strength f_p = 3.0 (Pinning site strength) Vortices that fall into the very strong pinning sites remain pinned for the rest of the movie and repel the other vortices moving through the sample. Vortices fill the pinning sites on the outer edges of the clusters of pins and prevent other vortices from reaching the pinning sites in the center of the pinning clusters. As a result, a large number of the pinning sites are ineffective and empty. The large spaces between pinning clusters offer routes of unimpeded vortex motion, and all moving vortices follow these broad channels, guided by the repulsion from the vortices pinned at the edges of the clusters.

Parameters and Notes

• A_p = 3.0 (Pinning strength)
• r_pin = 0.15 (Pinning radius)
• N_pin = 500 (Number of pinning sites)
• Parabolic clustered pinning
• All the pinning sites are the same strength.
• Vortices dropped every 40 md steps.
• Up to 600 vortices dropped.
• Movie was written every 20 md steps.

Plastic Vortex Motion - Triangular pins

The movie shows the initial penetration of a flux front into a sample with a triangular array of pinning sites. We add vortices at a constant rate to an unpinned region at the left edge of the sample, creating a gradient in vortex density that drives the vortices into the pinned region. Circles represent vortices, and lines are drawn tracing the path each vortex follows through the sample.

The parabolic pins in this sample are in a triangular array at a density of n_p = 0.44 (Pinning site density) and are all of strength f_p = 1.5 (Pinning site strength) Vortices that fall into the strong pinning sites remain pinned for the rest of the movie and repel the other vortices moving through the sample, creating channels of vortex motion between the rows of pinning sites.

Parameters and Notes

• A_p = 1.5 (Pinning strength)
• r_pin = 0.35 (Pinning radius)
• N_pin = 275 (Number of pinning sites)
• Parabolic triangular pinning
• All the pinning sites are the same strength.
• Vortices dropped every 40 md steps.
• Up to 600 vortices dropped, total.
• Movie was written every 20 md steps.

Plastic Vortex Motion - Triangular pins: Steady state motion

The movie shows the steady-state motion of vortices through a sample with a triangular array of pinning sites. We add vortices at a constant rate to an unpinned region at the left edge of the sample, creating a gradient in vortex density that drives the vortices into the pinned region. Circles represent vortices.

The parabolic pins in this sample are in a triangular array at a density of n_p = 0.44 (Pinning site density) and are all of strength f_p = 1.5 (Pinning site strength) Half of the vortices shown are sitting in the regular array of pinning sites, and oscillate in the pinning sites without becoming depinned or moving through the sample. The other half of the vortices are located between rows of pinned vortices, and are following channels of vortex motion between the rows of pinning sites. Note the correlations among the channels of moving vortices.

Parameters and Notes

• A_p = 1.5 (Pinning strength)
• N_p = 275 (Number of pinning sites)
• r_p = 0.15 (Radius of pinning)
• Parabolic triangular pinning
• All pinning sites were the same strength.
• Time between vortex drops = 80 md steps.
• The movie was written out every 20 md steps.

Additional VIDEO CLIPS of Vortex Dynamics

Bose glass vortex movies - Sample with strong pinning (interstitial flow)

Defect sites are indicated by open circles, vortices are shown as filled dots, and the paths followed by the vortices are indicated by lines. As the magnetic field outside the sample is increased, vortices enter the sample from the left edge of the frame. The vortices follow interstitial paths which move around regions with flux lines that are strongly pinned at defects.

Bose glass vortex movies - Sample with weaker pinning (pin-to-pin flow)

The weaker pinning in this sample produces a different manner of vortex transport. Pin-to-pin vortex motion, as well as interstitial motion, is possible and the previously narrow vortex trails become considerably broader.

Twin Boundary vortex Movie - Vortex flame movie

The left panel of the movie shows the averaged flux density as the magnetic field outside the sample is increased; the right panel shows the actual vortex locations. Vortices enter the sample from the bottom of the figure. The sample contains a single twin boundary which acts as an easy-flow channel for flux motion. Vortices escape from the twin boundary, producing the flame pattern.