Plasmoid instability — how current sheets fragment and speed up

24:18>> Instability of current sheets and formation of plasmoid chains. >> Yeah, this is the he So, he was at PPL at the time, prison prison plasma physics lab. Yes. >> Um PPPL at the time. And >> this is the one that puts him on the map of plasma physics cuz he solves this 50-year-old problem >> problem. >> Not bad. >> Not bad. Not bad. >> Not bad. >> And and for those who might not know, a lot of people tried to solve this problem. >> Yes. Yes. Yes. This was a known This was like a known problem. And he does it using just like >> good old-fashioned theoretical physics analytical theory. And it's like it's a technique that we've actually learned in

25:00um grad school, but he applies it to this in a very ingenious way. And I don't I'm I'm not going to go into the nitty-gritty detail, but effectively what he's doing is this. Okay, he says, "Okay, I've got a thin current sheet, right? >> Got this thin current sheet." And what's happening is when when I when I turn up the length scale of this guy and when I turn up the magnetic field of this guy, what's going to happen is that current sheet, which is the interface between the magnetic field going this way and this way, right? I want to I want to be able to reconnect it. And the problem is that that reconnection is happening way faster than I want it to. >> Right. Right. >> What what he shows is the the aspect ratio of that current sheet

25:41>> gets really small. >> Okay. >> Okay. At really high magnetic fields, the the width of this guy is really small compared to the length of this guy. >> Okay. >> Okay. And then what he says is >> meaning meaning it's like it's like a twizzler. >> Yeah. Yeah. >> Right. Versus >> and I'm like stretching it. I'm stretching it. Okay. It's a twizzler and I'm stretching it. Okay. >> Okay. And then what he does is he he he does something called perturbation. >> Yes. >> Which is he says, "Okay, suppose I have this twizzler and there's a tiny little bump. >> Tiny little instability for whatever reason." >> Sure. >> Okay. Can I trace what happens to that instability? >> Okay. If that instability goes down, >> if there's a restorative force, >> right? Then that instability is going to

26:22go up and down and it's going to become kind of like a harmonic oscillator. This is a very useful tool in graduate school physics is to understand perturbations and how those perturbations grow with time. >> Y >> but if there's an instability then that tiny little fluctuation is going to magnify >> and create some kind of bigger instability which will create a bigger instability. >> For for layman who might have seen the Asen Kutcher movie, it sounds a lot like the butterfly effect. >> Exactly. Right. Are we in this sort of chaotic regime where where it's going to break free and start doing some some random stuff? Right. Right. >> Right. >> Okay. >> And what ends up happening is he shows that when you have this long sheet of stuff, >> Yes.

27:03>> it breaks into chains of smaller little plasmoids, >> okay, >> is what he calls it. >> Okay. And they're these secondary sheets. And we've got a we've got a um a photo from exactly that, which is you've got this rubber band that you're stretching right? >> Yes. And as you stretch that twizzler, as you were saying, that twizzler as you stretch it, it's going to create little beads >> to maintain like its structure in some sense. >> Okay. >> Okay. >> And all of that stuff means that the time scale is going to be reduced by orders of magnitude. >> Okay. Got it. >> Right. Because now you're making the the system smaller in some sense. Right? You're like the system used to be this

27:43massive thing with a really large B field and a really large length scale. Now you're you're you're collapsing it into smaller and smaller length scales. >> So So as in this image, what we're seeing is at the top there is a again a long twizzler, quote unquote, and this example with small beads throughout it at at very varying sizes. >> And then as we go down, we see that those perturbations actually shorten the length. >> Yeah. >> Of what we're seeing. And then there's these those beads become more concentrated and larger. Yeah. Almost in their amplitude. Yeah. Right. Right. because we're basically moving it from like this big a system that's this big to becoming smaller and smaller. Right.

28:23And and so now we're making like smaller and smaller systems with smaller Lquitz numbers. Got it. Right. And and now the what he what he effectively showed is that the scaling that happens at this physics is no longer like one over the square root of the Lungquist number, but instead like the number to the power of something. So it's not like a diminishing, it's actually a growing thing, right? And this was just from first principles. It's a beautiful paper, right? That that that he showed this. Um and so now he he can he can resolve that giant discrepancy between time scales that we see. Right? Because actually the thing that we're worried about, this is no longer a stable thing.

29:03As we make this thing bigger, it's going to it's going to sort of collapse into smaller things. And as those smaller things become bigger, it's going to collapse into into even smaller things. It's like this weird fractally kind of self- similar thing where like the more you stretch the smaller the beads become and then and then you're going to make more beads the more you stretch, right? And and you have this like fractally self similar effect that's happening and this explains a bunch of stuff that we've noticed >> like that insight in and of itself. >> Yeah. >> Right. Um >> and and the rigorous way in which he showed it in that 20 2007 paper, it was very rigorous because he realized that one of the assumptions that Sweden

29:43Parker had made is no longer true. Right? If I actually put in the dependence, he realized that there's this one term in the equation that they assume to be constant. But that term is actually dependent on the number itself, right? And when I put that in and I and I go through this perturbation analysis, >> doesn't quite work. So a previously static variable was proven to be dynamic. Yes. And obviously because it was not static but was dynamic that was the key. It was a key unlock to then actually understanding the effects that we're trying. >> Yes. Exactly. And it and it mattered for these big scales. >> Yeah. And similar to our hypersonics thing. It's like it didn't matter when you were at small scale and so you could ignore it. But as soon as you start

30:25things that we label as constant constants for simplicity in order to be able to just keep the math simple no longer can be applied and have consistent observable effects. >> Mhm. >> Okay. >> Yeah. Yeah. It's it's a very cool paper again cited multiple times and it and it applies to astrophysical plasma. For example, this is um a picture of the Venus >> tooid. So this is what happens when the solar wind goes and impacts Venus which has its own magnetic field. And what you can see is you've got the stretching of the magnetic field because of the solar wind and on the top you've got a magnetic field going this way and on the bottom you've got a magnetic field going

31:05this way. So what's going to happen? You're going to get a little plasmoid, >> you know, because because those magnetic field lines want to sort of >> mesh together. They don't they don't want to fight, right? And so you get the little plasmoid that we were talking about. And you can see when when we talk about the Venus Express, which is the probe that took measurements close to Venus versus the Pioneer Venus Express, which took measurements all the way out, >> it matches the fact that there's a strong magnetic field here and a weaker magnetic field there. And and the mathematics works out, right? So it shows that in astrophysical plasma this

31:46hypothesis by Nuno is true. >> So just to double click on that the the point being Nuno's theory on paper that can be proven mathematically on paper had matching observable data from two different Mars pro uh Venus excuse me probes from different distances of where they measured. And that was in uh uh important in being able to show that it actually worked because we had two in two reference points of distance where the measurements were coming in from. And then so we could use the math that Nuno sort of established and say does the math match at this farther distance from the PVO this closer distance from VEX. And it

32:27>> and it did and it was great. And crucially this is like on top of the fact that his theory >> reproduces the time scales that we see on the sun. >> Ah right on yeah the solar solar measurements also track. >> Yeah the solar measurements the fact that it takes hours to minutes for this reconnection to happen on the surface of the sun in the solar corona and things like that that's already taken care of. And on top of that, he's now he's now talking about the magnetic field around planets. And also in Tacomamax, we've like literally seen this. So in Tacamax, which is a takamac is like a donut shaped thing where we try to confine plasma. Yes. >> And in those tacamax, you can see little

33:08plasmoids that form, >> right? And they form at the the the scale. Yes. >> That he suggests with this theory. And and it lasts as long as what he suggests in the theory. And this becomes extremely useful when we are trying to replicate the sun on earth for fusion