Cause of multiple paths of electrical breakdown?

[Diane Wilbor]

When a voltage gradient across a dielectric becomes too large, the material will break down and become conductive, mostly because of plasma ionization. Thus we get lighning, static electricity fingertip shocks, and tesla coil shows. But often during such breakdowns, there are multiple, simultaneous, breakdown paths. Why? Once one path is created, isn't that now-conductive path far superior for current to flow through? That is what causes the arc itself to extend almost instantly since the now-conductive partial arc is even closer to the opposite electrode/ground and thus the same potential difference has a shorter separation, creating higher field which causes even more runaway arcing until the spark joins the two.

But once such a conductive path exists, why would another one occur simultaneously? For example, a bolt of forked lightning? After thought, I imagine it would be because one or both of the opposing potentials is resistive and can't handle the current and thus it accumulates charge (like a capacitor) until the resistive Earth near the stroke is effectively at a high potential, until an alternative path to a different patch of Earth is also a candidate. In the limit this would happen multiple times, and recursively, giving path branches like this.

But this doesn't explain why you'd get lighning branches that terminate inside the nonconducting dielectric itself. Why does lightning fork into tendrils that do not reach the ground? Surely the air cannot accumulate charge locally! Unless it's accumulating on raindrops? But that's not true, you see this with http://www.thinkgeek.com/images/products/zoom/iqim_tinytesla_musical_coil_kit.jpgWhere is the current going? Surely there's not one air molecule at the end of each tendril accumulating coulombs of charge!

And also unexplained is how there would be multiple paths between highly conductive materials like metal electrodes. Here it's really clear that there's no local resistance to allow any local charge accumulation. Why are there multiple small arc paths instead of one big path?

My thought that would help explain this itself is that the air (or dielectric in the plexiglass example) itself has limited current carrying capability, especially after it's heated so much that it has expanded into lower density. But then why wouldn't the breakdown just keep enlarging the plasma tube (which is easy) instead of breaking down in a brand new path?

I suspect the answers involve plasma dynamics and the effect of spatial charge in the arc itself pushing the arcs apart, but I can't get even a qualitative feeling why that would create multiple paths between conductive electrodes.

 

[Cutter Ketch]

I can't answer your question, but I want to say that it is a fun one to think about. My intuition is opposite of yours: I think the discharge should be messy, and I would be surprised to see a nice steady plasma tube. On the other hand that's an easy position to take when we all already know that lightning forks. And I sympathize with your point that an established plasma path seems easier than forging a new path. However, that must not be the case.

 

[davenn]

But this doesn't explain why you'd get lighning branches that terminate inside the nonconducting dielectric itself. Why does lightning fork into tendrils that do not reach the ground? Surely the air cannot accumulate charge locally!

http://stormhighway.com/cgdesc.php

not sure if that fits for the Tesla coil and art patterns. I suspect for the Tesla coil, it quite probably does

what you may not realize is that, all this forks are heading out at pretty much the same time. All "seeking" that path to the ground or oppositely charged area within a cloud.
Usually only one of those leaders finds a leader coming up from the ground ( other section of the cloud)and initiates the main discharge channel. But all those other unconnected paths are still there and can be seen.Dave

 

[ZapperZ]

When a voltage gradient across a dielectric becomes too large, the material will break down and become conductive, mostly because of plasma ionization. Thus we get lighning, static electricity fingertip shocks, and tesla coil shows. But often during such breakdowns, there are multiple, simultaneous, breakdown paths. Why? Once one path is created, isn't that now-conductive path far superior for current to flow through? That is what causes the arc itself to extend almost instantly since the now-conductive partial arc is even closer to the opposite electrode/ground and thus the same potential difference has a shorter separation, creating higher field which causes even more runaway arcing until the spark joins the two.

But once such a conductive path exists, why would another one occur simultaneously? For example, a bolt of forked lightning? After thought, I imagine it would be because one or both of the opposing potentials is resistive and can't handle the current and thus it accumulates charge (like a capacitor) until the resistive Earth near the stroke is effectively at a high potential, until an alternative path to a different patch of Earth is also a candidate. In the limit this would happen multiple times, and recursively, giving path branches like this.

But this doesn't explain why you'd get lighning branches that terminate inside the nonconducting dielectric itself. Why does lightning fork into tendrils that do not reach the ground? Surely the air cannot accumulate charge locally! Unless it's accumulating on raindrops? But that's not true, you see this with http://www.thinkgeek.com/images/products/zoom/iqim_tinytesla_musical_coil_kit.jpgWhere is the current going? Surely there's not one air molecule at the end of each tendril accumulating coulombs of charge!

And also unexplained is how there would be multiple paths between highly conductive materials like metal electrodes. Here it's really clear that there's no local resistance to allow any local charge accumulation. Why are there multiple small arc paths instead of one big path?

My thought that would help explain this itself is that the air (or dielectric in the plexiglass example) itself has limited current carrying capability, especially after it's heated so much that it has expanded into lower density. But then why wouldn't the breakdown just keep enlarging the plasma tube (which is easy) instead of breaking down in a brand new path?

I suspect the answers involve plasma dynamics and the effect of spatial charge in the arc itself pushing the arcs apart, but I can't get even a qualitative feeling why that would create multiple paths between conductive electrodes.

Actually, I would be surprised if the arc itself is "long and straight". This is because of the mean free path of electrons in air. The electrons that ionizes the medium is the source that creates this electrical discharge. Since there is a finite mean free path, one expects there to be multiple collisions and thus, a more jagged trajectory. In dielectric medium, this trajectory is even more jagged since the mean free path is even shorter than in air.

This might also explains why there can be multiple paths, because the collisions can easily cause more than one energetic electrons to fly off in different directions.

Zz.

 

[nsaspook]

This is something we typically see on plastic high voltage insulators that breakdown.
https://en.wikipedia.org/wiki/Lichtenberg_figure

Electrical treeing often occurs in high-voltage equipment prior to causing complete breakdown. Following these Lichtenberg figures within the insulation during post-accident investigation of an insulation failure can be useful in finding the cause of breakdown. An experienced high-voltage engineer can see from the direction and the shape of trees and their branches where the primary cause of the breakdown was situated and possibly find the initial cause. Broken-down transformers, high-voltage cables, bushings and other equipment can usefully be investigated in this manner. The insulation is unrolled (in the case of paper insulation) or sliced in thin slices (in the case of solid insulating materials). The results are then sketched or photographed to create a record of the breakdown process.

 

[Diane Wilbor]

Thanks for the references!

I can understand the idea of initial ionization appearing randomly and causing multiple branches. But if those branches do not terminate at a current sink (like a lower potential cloud, or literally to ground), then why (and how) does massive current travel down those branches, and where does it GO? We know the current is beyond significant.. it's enough to generate incandecent plasma at 10,000 degrees or more.