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Mark Kushner: Microphone. Yeah, I just turned it on.

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Mark Kushner: Hi, welcome to today's Epsi seminar. It's my pleasure to introduce Professor Nuno Lurio

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Mark Kushner: as today's Mitzi speaker.

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Mark Kushner: I know the director of Mit, you know, Mit is that little community college up in Boston.

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Mark Kushner: Nuno is director of Mit's Platinum Science Infusion Center.

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Mark Kushner: Professor of nuclear science and engineering, and the Herman Fenchbach, Professor of Physics at Mit

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Mark Kushner: Nuna. Ricci, received his master of Engineering and physics at the Institute of Superior technico in Lisbon and his Phd. In Physics at Imperial College, in London.

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Mark Kushner: He was a post re post doctoral researcher at Princeton, Clouds and Physics Lab and UK. Atomic Energy Association, golf Hand center, Fusion, energy

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Mark Kushner: and a Researcher at Isc. Lisbon, before joining Mit in 2,016,

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Mark Kushner: was the recipient of the American Physical Society, Thomas Dixon's outstanding Professor Award, twice

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Mark Kushner: recipient, opposed fellowship and the Nest Nsf. Career award.

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Mark Kushner: He was elected Fellow of American Physical Society of 2,022.

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Mark Kushner: We know's research interests are fundamental aspects of magnetized platform dynamics, such as magnetic reconnection, magnetic field generation and its amplification containment and transport and even platforms.

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Mark Kushner: It titles his seminar. Today, his mother's perspectives and challenges in magnetic connection.

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Mark Kushner: Thank you very much for making the trek to Ann Arbory, and please accept our token of appreciation. The mipsi mug. Thank you. Thank you, Mark.

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Mark Kushner: I had seen these mugs on people's shelves, and I was envious. I was envious that I didn't have one. So now I'm part of the club. Thank you. I appreciate it.

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Mark Kushner: Okay,

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Mark Kushner: so thank you for

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Mark Kushner: that kind introduction mark

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Mark Kushner: very happy to be here my 1st time visiting Ann Arbor and

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Mark Kushner: your university, and I'm excited by all the things I've seen here so far a lot going on.

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Mark Kushner: So it's

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Mark Kushner: exciting for me to be here.

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Mark Kushner: Okay. So

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Mark Kushner: I

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Mark Kushner: felt like I wanted to give a

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Mark Kushner: not very technical talk on magnetic reconnection. That's the area

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Mark Kushner: that I've worked on the most in my career. And

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Mark Kushner: this talk, you know, there's it will touch on several

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Mark Kushner: technical aspects. But the main goal here is to really to convey a sense of

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Mark Kushner: you know what I find is interesting as future research directions for someone who was excited about this field, and wants to know where things might be heading.

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Mark Kushner: Feel free to interrupt me as as you please. So let me just I. I was told that the

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Mark Kushner: the audience wouldn't necessarily be composed of reconnection experts. So that's sort of the the gist of of the talk.

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Mark Kushner: you're all here, because the word plasma means something to you, I guess right. And so you probably know that plasmas do interesting things

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Mark Kushner: waves, sharks, etc.

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Mark Kushner: Among the interesting things that they do is magnetic. Reconnection is one of the most well, I don't know that it's 1 of the most exciting. It's certainly one of the most exciting for me, but I think it's undisputed that it's 1 of the most fundamental nonlinear processes that magnetize plasmas

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Mark Kushner: can can do. Solar flares are

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Mark Kushner: the most popular manifestation. This is a movie that is not playing, but

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Mark Kushner: could be playing

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Mark Kushner: showing. You know, the typical thing that you've all seen magnetic activity in the solar corona leading to.

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Mark Kushner: you know, a a bright thing that we associate with with a solar flare.

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Mark Kushner: Now.

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Mark Kushner: so let's sort of be a little more specific about this. The sort of textbook definition of magnetic reconnection is that you have a magnetic field.

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Mark Kushner: and it undergoes a topological change. So in the the topological change that you see here in this movie

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Mark Kushner: is that you have blue lines, blue magnetic field lines, and you have

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Mark Kushner: red magnetic field lines. They didn't talk to each other, but now they do right.

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Mark Kushner: Sometimes I make a slightly risque joke where I say, you have the the Republican field line and the Democrat field line. And now they're talking to each other right? And I don't make this joke as much anymore, because that kind of dialogue doesn't tend to happen as much.

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Mark Kushner: We'll see

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Mark Kushner: all right. So so topological change is the key idea, right? That you know, something happens in the plasma that leads the magnetic field to change the way it was organized in a fundamental and irreversible way.

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Mark Kushner: Okay.

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Mark Kushner: and

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Mark Kushner: this reorganization process

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Mark Kushner: typically leads to

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Mark Kushner: the release of magnetic energy.

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Mark Kushner: and that magnetic energy is then transferred to the plasma in different ways. And so the brightening that you associate with solar flares is a reflection of that energy conversion. So you have energy stored in the magnetic field that got mapped to the plasma. And you know, maybe you got some radiation out of that.

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Mark Kushner: So on the left is a cartoon on.

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Mark Kushner: Sorry, on the right is supposed to be a movie that I can't play. But this is actual data from an experiment we used to have at Mit called Vtf. It was run by Jan Agadal, and what you would see if I had

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Mark Kushner: click. The right buttons on keynote is, you'd see these lines, that map magnetic field lines coming together just like in the cartoon and sort of reconnecting. Okay.

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Mark Kushner: so just the point here is simply to say that we have cartoon depictions of this, and we have actual data from experiments. That sort of maps very well to that

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Mark Kushner: part 2

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Mark Kushner: at least qualitatively.

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Mark Kushner: Oh, there we go.

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Mark Kushner: So this is actual data again. From from this on the left is current density, and on the right is an inferred quantity called reconnection rate.

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Mark Kushner: And this is sort of the

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Mark Kushner: current associated with outsources.

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Mark Kushner: Okay, so

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Mark Kushner: reconnection is as ubiquitous, as

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Mark Kushner: well, almost as ubiquitous as plasmas themselves. It seems like every time that you have a magnetized plasma.

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Mark Kushner: phenomena like reconnection happens in that plasma

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Mark Kushner: so typical places you go to find reconnection. Events are magnetically confined, laboratory plasmas, Tokamax, for example, but not only right, so they are. We have dedicated reconnection experiments that people set up in labs

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Mark Kushner: laser solid interactions, both sort of deliberately to to done, to study reconnection, but also as a byproduct of inertial confinement, fusion type of experiments. Earth's magnetosphere is a big one, and in that context the recent

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Mark Kushner: most exciting mission is NASA's Mms Mission. That's sort of a billion dollar Class 4 Satellite Mission, launched in 2016, I think, actually, same time as this paper that's specifically designed to measure the reconnecting environment in the Earth's

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Mark Kushner: magneto sheath and magneto tail.

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Mark Kushner: and then there's all sorts of

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Mark Kushner: flares. So we are familiar with solar flares. But in fact, many stars have flaring events, and then more exotic astrophysical environments, accretion disks, magnetars, blazars. They all have some sort of reconnection type activity that shapes the way that their magnetosphere works.

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Mark Kushner: Then magnetized turbulence. Solo wind ism. So the way that the turbine cascade unfolds

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Mark Kushner: tends to touch upon what tends to lead to the occurrence of reconnection, events that can then be critical in how that energy, turbine energy is transferred to the plasma, be it in terms of heating or in terms of particle acceleration

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Mark Kushner: turman, dynamo, space, weather, etc. So it's a it's a long list. And this is just to say that, you know, there's a lot of communities that are interested in reconnection. They come at it with slightly different angles, different different interests, right? But there's sort of an underlying topic which is to understand better how this highly nonlinear process works.

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Mark Kushner: Okay? So

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Mark Kushner: I just need to get some concepts

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Mark Kushner: in place so that I can start discussing the key questions and what the key challenges are.

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Mark Kushner: and I feel like

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Mark Kushner: the best way to do that is to introduce you to a textbook model of reconnection that you know. Sometimes you learn in plasma physics, classes, and that's called the Sweet Parker model of reconnection. It's called Sweet Parker, because it was invented or derived by Peter Sweet and Eugene Parker. So it became the sweet Parker model, late fifties.

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Mark Kushner: So this is a steady state model. It's 2D. Where you assume a geometry exactly like the one that I showed you in that cartoon of the Democrats and the Republicans. Okay.

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Mark Kushner: so here you have the unreconnected field lines in red. They're being brought in by arrows that depict plasma flows that are bringing them together.

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Mark Kushner: The topological change happens here. At the center, at a place called the X Point.

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Mark Kushner: You get the reconnected field lines in blue and you get plasma flows flowing outward along the current player.

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Mark Kushner: Okay, so this is a cartoon picture you can write, and if you assume that this is in steady state, meaning that if you took, if you have this system and you take a picture of it now, and a moment later you wouldn't be able to tell which one is which. Right? It's steady state in that sense, but it is. It has flows, flows coming in flows, coming out. Okay.

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Mark Kushner: Now, you can derive interesting things about this system by just insisting on the conservation of things that you think ought to be conserved. For example, mass mass comes in, mass flows out. For example, energy. You can write down an energy balance equation, right? So if you conserve these things. It turns out that you can write.

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Mark Kushner: Well, pretty much everything you want to know about this system.

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Mark Kushner: So you everything comes in terms of this quantity called S, which is the Lundquist number.

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Mark Kushner: and it's a dimensionless quantity similar to the magnetic Reynolds number for those of you who are familiar with that.

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Mark Kushner: So it has depends on the length of the system which is macroscopic.

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Mark Kushner: It depends on the alpha and velocity.

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Mark Kushner: And it depends on the magnetic diffusivity.

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Mark Kushner: Okay, so it's like a Reynolds number like quantity. Okay?

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Mark Kushner: So using conservation of mass and momentum, you can derive that in this model, you expect the thickness of this flow channel.

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Mark Kushner: compared to its length.

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Mark Kushner: to scale, like Lundquist number, to the minus one half

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Mark Kushner: the inflow velocity compared to the outflow velocity which ends up being Alphanic also scales the same way, Lundquist number to the minus one half.

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Mark Kushner: And finally, the electric field that gets set up at this X point which is typically called the reconnection

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Mark Kushner: electric fields.

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Mark Kushner: also scales in

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Mark Kushner: adequately normalized

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Mark Kushner: as Lundquist number to the minus one. So it's very easy to remember the sweet Parker model, because everything, every dimensionalized quantity scales the same way. Okay, now, this is not an exact analytic solution of the problem. This is sort of a

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Mark Kushner: order of magnitude, sort of estimate of what things have to scale like. If you insist on conservation of basic quantities.

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Mark Kushner: Okay, so immediately, you stumble into

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Mark Kushner: one of the key questions.

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Mark Kushner: and that comes from

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Mark Kushner: realizing that the lumpus number.

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Mark Kushner: It's a number you can. You can measure or compute for your system.

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Mark Kushner: And that Lundquist number tends to be very large.

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Mark Kushner: So for the solar corona, for example.

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Mark Kushner: it it's between 10 to the 12 and 10 to the 14

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Mark Kushner: in the solar wind something like 10 to the 15. Okay? So it's a very large number in the fusion experiment, maybe like 10 to the 6 or 10 to the 7.th

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Mark Kushner: And so.

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Mark Kushner: because this is so large, that means that this electric field or this inflow velocity are very small.

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Mark Kushner: Right? So this would be the one over the square root of that. So this, you know, for the solar flares would be 10 to the minus 7.

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Mark Kushner: And so this tells you. So this electric field is basically the rate at which you're processing magnetic flux.

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Mark Kushner: So this tells you it's very slow.

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Mark Kushner: It will take a long time actually to have a solar flare going.

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Mark Kushner: So this immediately tells you that there's got to be something wrong with this model, because you cannot

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Mark Kushner: use this to predict the observed solar flare rates.

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Mark Kushner: So if you plug in numbers for the solar corona, you would come. You would predict that the solar flush should take like 2 months, whereas, in fact, it takes 15 min to an hour.

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Mark Kushner: Okay, so it's orders of magnitude of.

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Mark Kushner: But the key concepts have been introduced. So inflowing field lines, outgoing field lines inflows, outflows this notion that you can make some analytic progress, using, you know, a steady state picture and sort of assuming certain things about continuity of mass, continuity of energy.

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Mark Kushner: All right. So

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Mark Kushner: this allows me now to state the key questions that people work in this field want to address. Okay, so one is the question of reconnection rate.

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Mark Kushner: Okay, so we we in every reconnection environment that we observe or measure or simulate in our computer.

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Mark Kushner: we tend to find that the rate at which you're

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Mark Kushner: a processing flux through this narrow layer

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Mark Kushner: is is very fast. So it's fast in the sense that it is a time scale, or a rate that does not scale with that kinetic physics of your system. With the small parameters

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Mark Kushner: it is independent of resistivity. It is independent of

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Mark Kushner: how large your lama radius is.

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Mark Kushner: Okay. So it doesn't scale with small quantities, which is what allows it to be fast.

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Mark Kushner: But we don't have a good understanding of why that is right. So so what is it about this problem that allows for this process to occur in a way that's independent of the very mechanisms that allow it to happen.

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Mark Kushner: So actually, I didn't mention this. This is a a

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Mark Kushner: lapse on my part.

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Mark Kushner: you know, from introduction to plasma physics that in Mhd flux is conserved.

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Mark Kushner: And if you want to break flux conservation, you need resistivity. And so ideal Mhd. Conserves flux, it wouldn't allow change of topology. So to change the topology, you need to introduce a nonlinear and non-ideal effect like resistivity.

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Mark Kushner: So somehow you have reconnection, which in Mhc. Requires finite resistivity, but gives you a rate that doesn't actually depend on resistivity. And that's where that mystery comes from. In collisionless cases. You don't require resistivity. But you might require electron inertia.

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Mark Kushner: And the electron inertia is small and you have a rate that doesn't actually depend on electronic. Yes.

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Mark Kushner: Can you talk about this

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Mark Kushner: action rate. When do you

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Mark Kushner: start the timer? For when the reconnection has happened?

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Mark Kushner: Customer support team?

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Mark Kushner: Yeah, so you can, you can talk about this in sort of normalized units. Right? So you can. You can say it's really the the rate is, you know, I'm not talking about the timescale for the whole event, because that's going to depend on how big your fields are, but the rate at which you're processing flux per second.

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Mark Kushner: Right? So that that's that that rate is what is what we care about. So not the actual time duration of of the event.

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Mark Kushner: All right. So the other question is energy partition. So you have a certain amount of energy in principle available to you in the magnetic field.

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Mark Kushner: As you restructure that magnetic field, you release some of that energy. And you ask, Where does it go?

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Mark Kushner: Does it go into the ions? Does it go into the electrons?

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Mark Kushner: Does it accelerate them, or just heat them?

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Mark Kushner: Does it go into kinetic energy?

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Mark Kushner: What is the partition as a function of upstream plasma parameters?

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Mark Kushner: And can I predict this right? If you give me a plasma. And you tell me this is a plasma that has a certain beta, and it has. You know these and that other properties. Can I tell you a priori that this amount of magnetic energy is going to go into electrons. It's going to accelerate them rather than beat them. And this is going to be the power law, for example.

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Mark Kushner: And then a 3rd question, which is sort of the the one that's closest to the talk itself, is the question of onset. And this goes back to yours.

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Mark Kushner: So you know.

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Mark Kushner: if you're going to release a significant amount of magnetic energy.

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Mark Kushner: that means that you have processes in your plasma that build up that extra energy right? You cannot have an explosion if you don't 1st build up some energy.

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Mark Kushner: Okay, so what's happening in the plasma presumably is that there are plasma flows, or an evolution of a configuration that you started with. That brings the plasma into a state of discomfort. Let's call it that where, all of a sudden, you have this sudden release of energy.

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Mark Kushner: Okay? And so this onset is the transition between a period of energy accumulation

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Mark Kushner: to energy release

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Mark Kushner: right? And we'd like to be able to compute that transition. When does that happen? Right? Why does it happen? What are the processes that leave this transition to happen.

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Mark Kushner: So the question of that there are 2 timescales right? And what triggers this transition?

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Mark Kushner: All right. So let me

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Mark Kushner: discuss this question a little bit more, because, you know, I feel like

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Mark Kushner: everybody can sort of understand reconnection rate like, say, that's how fast you're bringing in flux and getting it out. And energy partition is also a familiar concept. Right? You have magnetic energy transferred to the plasma. But the onset is maybe not as clear. So

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Mark Kushner: imagine that this is this is a cartoon from a nice paper by Amitabha Bhattacharjee. Imagine that you're building this current by your plasma flows coming together. Okay, so building the current in what we call the current sheet right? This is so current as a function of time. And you might imagine that it's growing slowly, but then it sort of enters. This impulsive phase.

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Mark Kushner: and this growth period can be depends where you are right. This these numbers are for the magneto tail. It can be like the order of an hour. But then there's an impulsive event, that sort of minutes, minutes, time, scale that triggers this transition.

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Mark Kushner: and so like, I said, we'd like to understand how this transition occurs and what causes it.

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Mark Kushner: And I would argue that this transition question is

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Mark Kushner: much.

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Mark Kushner: much less understood than other aspects of reconnection, which themselves remain somewhat mysterious. But this, I think, is the most mysterious, or the one we've paid the least attention to

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Mark Kushner: all right. So

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Mark Kushner: the statement here is that one of the reasons it's deliberately well. One of the reasons that it's more mysterious than the others is that many studies deliberately bypass this stage. Okay.

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Mark Kushner: so what happens is.

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Mark Kushner: let's say you're doing your incident reconnection. And you're you know, you're going to run a computer simulation.

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Mark Kushner: And the typical thing that you do is you prepare an initial condition

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Mark Kushner: that as soon as you switch on the code starts reconnecting immediately.

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Mark Kushner: Okay, so what you've done there is. You've bypassed the process by which the plasma would form that current sheet in the 1st place.

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Mark Kushner: and you are so confident in your ability to understand plasma physics that you say it doesn't matter. I know exactly what state the plasma would prepare, and that's going to be my initial condition. I'm going to save myself a lot of computing time by just coming up with this initial condition. That, I think, is where the plasma would take me

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Mark Kushner: if I had it

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Mark Kushner: if I have let it do that. Okay.

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Mark Kushner: so what's an example of this? An example is when your initial condition is designed to mimic exactly a sweet Parker type currency like I just explained. So you can

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Mark Kushner: literally write that in as your initial condition, and just let it go.

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Mark Kushner: And Street Park is just an example. You know, a pet check type. Configuration is another one you'll find in textbooks. You can write down an initial condition for that, and just

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Mark Kushner: let your simulation go from there.

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Mark Kushner: So

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Mark Kushner: this explicitly precludes investigating the onset because you're starting with an initial configuration that's already formed. It's already reconnecting. It's already in the deep stage of reconnection.

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Mark Kushner: Now, the so not only are you not addressing the onset question.

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Mark Kushner: you are assuming that the configuration you're starting your simulation with is realizable meaning. If you had followed the time history of your plasma

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Mark Kushner: from the beginning all the way to when you get this current sheet

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Mark Kushner: it would. You're you're sort of assuming it would get there. You would get the initial condition that you're preparing.

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Mark Kushner: So you're you're making a statement about the realizability of that system. You're saying I'm not following this entire time history, because I can't afford it. The computation is too

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Mark Kushner: time consuming. But I know that this is where it's going to get right. So this system that I'm starting with is realizable. The plasma could in principle get there.

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Mark Kushner: you know I don't know how many of you feel sufficiently confident in your understanding of nonlinear plasma physics that you can sort of make this leap of faith. But what I have learned is that plasmas are never your friends right, and you think they are going to do something, and invariably they don't, they do something else, and that this talk is a bit of a it's a story like that. Okay.

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Mark Kushner: it. It could be in an ideal.

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Mark Kushner: You know, Voltaire type world that realizability could be unrelated to the onset question. But in fact, they are not unrelated. These questions are actually very much related.

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Mark Kushner: And so when you bypass the onset stage and assume something, you're you basically

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Mark Kushner: throwing away a lot of your problem. And you might end up

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Mark Kushner: studying a system that no physical plasma can actually ever produce for you.

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Mark Kushner: And I think that's sort of a very interesting point.

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Mark Kushner: Okay.

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Mark Kushner: let's see

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Mark Kushner: there. So

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Mark Kushner: the story of the last well, a story of the last 15 years

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Mark Kushner: of reconnection theory is the realization that

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Mark Kushner: the the suite Parker type configurations that I described to you

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Mark Kushner: are actually highly unstable.

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Mark Kushner: So if you set one up like, I just told you not to do okay in a computer, what happens immediately. So this is a time sequence is that it is unstable to an instability. It forms these structures

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Mark Kushner: that this is the sort of a grown up one. We call them magnetic islands or plasmoids, and these structures

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Mark Kushner: become wider than the sheet you started with and destroy it, so that sheet

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Mark Kushner: destroys itself via

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Mark Kushner: its own instability in a time that's much faster than it would take to reconnect any flux

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Mark Kushner: and a significant amount of lights.

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Mark Kushner: So this instability, I guess, has come to be known as the plasmoid instability. It's very fast.

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Mark Kushner: It's much faster than the reconnection time scales completely destroys your system. That you started with right takes over and instead forms a structure that looks like this. So these things, this is a still. But these, these structures are moving. They're moving outward. They're constantly regenerating. They're talking to each other, they merge with each other. So it's a highly nonlinear system. And basically, it's a sort of a

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Mark Kushner: a form of turbulence. Right? So you get all these structures. They're all interacting with each other and sort of completely changing the the process that you have.

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Mark Kushner: If you measure what has happened to the reconnection rate, you find that

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Mark Kushner: when you have this instability your reconnection rate now becomes fast independent of the Lundquist number, so the existence of this instability breaks with the sweet Parker scaling.

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Mark Kushner: and actually shows that there is a way to have fast reconnection in resistive Mhd. You just have to be at large enough Lundquist numbers that you can access this instability, because, like all these instabilities, it has a threshold so same as you know water flowing down a pipe. If you want it to become turbulent, you need a Reynolds number that's like, I don't know 3,000.

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Mark Kushner: So here's similar to get this instability. You need a Lundquist number that's on the order of 10 to the 4.th

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Mark Kushner: Okay, but if you're there you get it. And then the reconnection rate becomes independent of the linguist.

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Mark Kushner: All right.

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Mark Kushner: But now let's go back to the previous thoughts.

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Mark Kushner: and the idea that this instability

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Mark Kushner: actually implies that sweet Parker current sheets would never actually form.

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Mark Kushner: So in the previous slide, I showed you what happens if I postulate one to my computer

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Mark Kushner: right? But the fact that it destroys itself immediately.

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Mark Kushner: actually tells you that if you were

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Mark Kushner: following the motions of a plasma that would ultimately lead to a sweet Parker current sheet.

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Mark Kushner: you would find that before you get there

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Mark Kushner: your sheet would be destroyed by the instability.

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Mark Kushner: So this is a cartoonish way of explaining this point.

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Mark Kushner: So imagine that you have. You're forming a current sheet, and I'm conceptualizing this by saying, the current sheet has a thickness, a and the length L,

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Mark Kushner: and if you're forming it. That means that A is shrinking, and L is getting longer. So the flow channel shrinking, getting longer right.

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Mark Kushner: And I'm plotting that ratio on the Y-axis as a function of time.

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Mark Kushner: and you know I start with no current sheet, and as a function of time

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Mark Kushner: it would eventually converge to something like Lundquist number to the minus one half. That's the sweet Parker prediction.

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Mark Kushner: if nothing were to happen to it.

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Mark Kushner: But I've just learned that if it were to get there.

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Mark Kushner: it would be unstable to an instability. I didn't tell you this, but it's very fast an instability whose growth rate scales with Lundquist number to the power of one quarter.

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Mark Kushner: Sure. Now.

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Mark Kushner: instabilities don't just materialize instantaneously out of nothing. Right? So as you're forming

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Mark Kushner: as you're evolving this background.

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Mark Kushner: you are making it progressively more unstable.

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Mark Kushner: Okay, so maybe you start with a stable situation, so the growth rate would be negative.

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Mark Kushner: But as you compress it and make it longer.

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Mark Kushner: you have to be making it more unstable, and at some point you transition to a situation where the growth rate is now positive.

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Mark Kushner: This is easy to understand.

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Mark Kushner: You guys have lawns, you water your lawn with a garden hose

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Mark Kushner: and think about what sweet parka means. It means that you're pumping water down your garden hose.

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Mark Kushner: The garden hose has an aspect ratio that's 10 to the 7. So its length, divided by its diameter, is 10 to the 7.

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Mark Kushner: You're pumping water down this hose at high pressure, and you expect the hose to start to stay straight.

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Mark Kushner: Does that strike you as a stable situation?

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Mark Kushner: No, okay, so same idea here, right?

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Mark Kushner: So as you're going this way.

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Mark Kushner: you're making your garden hose longer and longer at the same.

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Mark Kushner: and and thinner and thinner if you wish. So there is going to be a moment of time when it wants to start doing this.

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Mark Kushner: So that's sort of the

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Mark Kushner: gardener. Analogy to my instability here. Okay.

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Mark Kushner: now.

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Mark Kushner: the moment of time when the growth rate becomes positive, just slightly above 0, is itself not the most interesting moment of time. Maybe you have an instability, but it's very slow.

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Mark Kushner: So the background continues to evolve.

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Mark Kushner: Okay, so yeah, you compress and extend some more. And you're guaranteed right. I'm not showing you the math, but you can prove this.

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Mark Kushner: that there's going to be a moment of time when the growth rates

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Mark Kushner: is comparable to the timescale on which you're forming your current sheets.

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Mark Kushner: the timescale on which your garden hose is growing.

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Mark Kushner: So from that moment onward you can change the garden hose. But the instability is faster.

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Mark Kushner: Okay, so that's when your islands or plasmoids are going to show up and completely destroy your current sheet and take over.

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Mark Kushner: So let's think about what this means. It means that you have the systems

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Mark Kushner: that was just slowly accumulating energy, and nothing was stopping it.

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Mark Kushner: But you were slowly but surely driving it to criticality.

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Mark Kushner: and you pushed it, and it didn't want to go there. But you pushed it some more.

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Mark Kushner: And now you have an unstable system. And this instability is so fast that it's faster than the timescale in which you're forming things. It takes over and transitions your system from a period of energy accumulation to a period of energy release.

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Mark Kushner: And so we have suggested

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Mark Kushner: Dimitrios, Denski and I, that this may, in fact, be what the onset is right. So once the plasmoid chain develops its nonlinear evolution, right will quickly transition you from energy accumulation to a very fast state of energy release.

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Mark Kushner: And you can. You can do a lot of things with this with sort of analytical theory for this system. And one of the things you can prove is that, in fact, you would never reach the sweet Parker aspect ratio. You are at best going to go to something that scales with Lundquist number to a power of 1 3, rd which you know, asymptotically speaking, is much smaller.

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Mark Kushner: You can also prove that the time it takes to onset this instability is only weakly dependent on the Lundquist number itself. So basically, you're guaranteed that an onset exists. If you just let the plasma go.

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Mark Kushner: Okay.

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Mark Kushner: any questions so far.

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Mark Kushner: Yeah, just how fast is it? Is it like

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Mark Kushner: that that the

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Mark Kushner: apologies?

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Mark Kushner: Right? So that's going to depend on specific plasma parameters? Right? So if you want a number in seconds. That's going to depend very much on what plasma you're looking at. But you could be in a situation where the time it takes for the onset

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Mark Kushner: scales with a Lundqvist number in a way that's so strong that basically it would take forever it would never happen. But that's not the case. Right? So you're guaranteed at whatever Lundquist numbers you're at, you're guaranteed that this onset will occur in finite time. Basically.

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Mark Kushner: Okay.

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Mark Kushner: so this is sort of an interesting lesson in the sense that

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Mark Kushner: for many years people were studying.

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Mark Kushner: In in Mhd. People were studying reconnection. Assuming that this was going to be a sweet target kind of system.

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Mark Kushner: right? So that assumption was an assumption about you know how much you thought you understood plasma. Physics turns out you didn't right. It turns out that actually, that's not what the plasma does. The plasma will destroy that sheet before it ever gets to a street Parker State.

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Mark Kushner: And you know, there's arguments here about how that process is, in fact.

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Mark Kushner: related, and determines the onset of this transition between slow and fast.

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Mark Kushner: Now you can extend qualitatively, at least, you can extend these arguments to collisionless plasmas so plasmas that are not described by resistive Mhd.

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Mark Kushner: And there's several interesting conclusions. One of them is that this, the collisionless version of this instability

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Mark Kushner: always onsets before your sheet thickness gets down to kinetic scales like ion scale

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Mark Kushner: right? That it it will happen before.

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Mark Kushner: The other thing is that

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Mark Kushner: you know there's many instabilities in collisionless systems. And so this plasma instability is not the only game in town.

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Mark Kushner: So

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Mark Kushner: Matt Coons and and student Renato did a simulation of this problem for large, high beta plasmas.

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Mark Kushner: and what they saw is that actually, as the current sheet is forming you immediately trigger, mirror instability.

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Mark Kushner: and so you will eventually be reconnecting.

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Mark Kushner: and that you'll still get your plasmoids. But they're now plasmoids growing after out of

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Mark Kushner: magnetic fields that are infested by mirror instability.

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Mark Kushner: There's no way you could have predicted that initial configuration, and you can't actually very well specify it as an initial condition to your system, you just literally have to evolve and let the system do what it wants to do.

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Mark Kushner: But the interesting thing is that this completely changes the properties of the reconnecting plasma and of the reconnecting layer. And that's sort of a

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Mark Kushner: so an interesting realization.

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Mark Kushner: Okay.

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Mark Kushner: this is just very quickly. You can.

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Mark Kushner: just to just to flag that

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Mark Kushner: this chain of reasoning can be translated into turbulence theory.

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Mark Kushner: So if you say

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Mark Kushner: you know, I have now a turbulent system. It's a box which I'm stirring with a spoon. It's a plasma, right? And injecting energy. And now it's going to develop a turbulent cascade, and that energy is going to dissipate.

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Mark Kushner: So there's theories about how, in this turbulence you form reconnection sites, current sheets.

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Mark Kushner: And now you can say similar things right? You can say well.

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Mark Kushner: these currencies that you form they cannot be arbitrarily long. They cannot be of the sweet Parker kinds.

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Mark Kushner: Right? So I can. I can make statements about how long they can become until they are disrupted by the same instability.

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Mark Kushner: and that we so we did that with

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Mark Kushner: Stas, Bolderev and I. And and we worked on that problem. And the prediction was that there should be a transition

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Mark Kushner: in the. So this is a plot of energy, magnetic energy, spectrum as a function of wave number.

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Mark Kushner: and the prediction was that there should be a transition

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Mark Kushner: in the spectrum at scales like Lundquist's number to the minus 4 sevenths.

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Mark Kushner: And then Shuang Fei dong.

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Mark Kushner: did this heroic simulation. So you're looking at the output of a simulation that cost

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Mark Kushner: 200 million CPU hours.

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Mark Kushner: Okay, the simulation itself took over a year to do and 2 years to data mine.

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Mark Kushner: And this is the glorious result of it. It's the biggest Mhc. Simulation known to mankind.

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Mark Kushner: And lo and behold, you have a Mhd energy spectrum that comes in as something like minus 3 halves.

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Mark Kushner: and exactly at the scale that we predicted

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Mark Kushner: S to the minus 4 sevenths. It transitions to a spectrum that's K to the minus 11 fifths, which is also what we predicted.

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Mark Kushner: So this was, we were happy about this.

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Mark Kushner: Okay.

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Mark Kushner: so this is not sort of in the context of the reconnection theory itself. But it's how you can adapt the same sort of ideas

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Mark Kushner: to Mhd. Turbines, cascades

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Mark Kushner: cool.

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Mark Kushner: All right. So this brings me to part 2,

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Mark Kushner: which is really the thing that I've been more excited about over the last year, but I kind of needed to give you this context.

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Mark Kushner: Otherwise, part 2 wouldn't make any sense to you. Okay, so let me tell you a little bit about

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Mark Kushner: a proposal for

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Mark Kushner: Well, a proposal for actually being able to compute reconnection for realistic type parameters, which is something that we can't do right now.

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Mark Kushner: Alright, so

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Mark Kushner: One thing that's becoming clear via the arguments that I just took you through, and others that I didn't have time to go through. Is that given

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Mark Kushner: enough skill, separation? Right? So if you're truly in a

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Mark Kushner: naturally occurring plasma with very large Lundquist numbers very large scale separation between the outer scale and the electron inertia.

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Mark Kushner: There's no such thing as a Laminar magnetic reconnection layer. Right? So you set up a reconnecting system, and what you find is you find that this layer becomes turbulent. Maybe it's plasmoids. Maybe it's the mirror instability. Maybe it's a variety of other instabilities. But you're basically guaranteed that this layer becomes turbulent.

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Mark Kushner: Okay.

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Mark Kushner: this reconnection drives turbulence right? So plasmoids mirror, etc.

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Mark Kushner: But then the turbulence itself becomes critical in defining the properties of your reconnecting system.

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Mark Kushner: Right? So that turbulence is how you actually

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Mark Kushner: transfer energy to the electrons or the ions. It's what controls your reconnection rate. It's what controls particle acceleration. So the properties of these terms are absolutely essential to understand all the things that you want to measure in your reconnecting system.

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Mark Kushner: Now, I just told you about an Mhd. Simulation that cost 200 million CPU. Hours. That was a turbulence simulation.

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Mark Kushner: How many of those can

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Mark Kushner: anyone do per year?

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Mark Kushner: Well, you know, we're talking about one that mankind has run right? So

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Mark Kushner: not very many. Okay. But that's the sort of the the sort of scale that you're talking about. If you want to start simulating reconnection for realistic parameters.

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Mark Kushner: and you know that's not something that we can do on a routine basis. And that's why, you know, many studies of reconnection have been 2D. Rather than 3D. They compromise on all sorts of things, and I'm not criticizing anybody. I do this myself right. It's like, how much, how much can I? You know? How many months can I wait for there to be a result from my simulation. Well, I'm an impatient guy. I can wait. I don't know 2 weeks. Then I'm you know.

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Mark Kushner: Okay, so I'd like us to move into a state where actually doing simulations of reconnection becomes for anything approaching realistic parameters becomes more routine.

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Mark Kushner: especially right if we're in a situation where there are surprises from

360
00:41:02.510 --> 00:41:09.920
Mark Kushner: from plasma physics for us like, you know, who would have guessed that there's a threshold when Lundquist numbers 10 to the 4 right?

361
00:41:10.180 --> 00:41:26.640
Mark Kushner: 10 to the 4 is a large number. Right? You thought, well, I'm simulating a thousand. Isn't that large enough? Isn't that asymptotic enough? Turns out it isn't right that 10 to the 4 is a threshold where you go from Laminar to turbulent right. Who's to say that there isn't another threshold? At 10 to the 8.th I don't know. I can't prove that.

362
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Mark Kushner: So I think we need to move to more realistic cases, but we are very limited by what we can fit into our computers.

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Mark Kushner: So

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Mark Kushner: I would like to be in a situation where I can study anything that even vaguely looks like a reconnecting, a realistic reconnecting system. So I'd like it to be 3D. I'd like to have realistic mass ratio. I'd like to have something approaching asymptotic skill separation between the system size and the kinetic skills.

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Mark Kushner: It's very hard, right? And you know what we can do on a brute force approach is very limited.

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Mark Kushner: So what you do is you make these decisions that can sort of

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Mark Kushner: bring you to an initial condition or a simulation that I would argue can be worryingly unreal. Right. So we can fall into the situation where you're setting up an initial condition that actually can't exist. You will never get there, right? So you know, and maybe we should move beyond that.

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Mark Kushner: So I think you know.

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Mark Kushner: we could just sit here and say, Well, aren't computers getting better all the time?

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Mark Kushner: Yeah, just not fast enough, right? So I remember the simulations I could do when I was a grad student. I know what simulations I can do now. Maybe they're better by a factor of 2. But we're not talking factors of 2 here, right? We're talking about decades. We need factors of 10 of hundreds to become actually interesting access, interesting regimes.

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Mark Kushner: Okay.

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Mark Kushner: so

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Mark Kushner: let me just recap some things for you. So let's imagine this is sorry I drew these. It's obvious they're not very good. Okay, but the the key ideas are here. So let's imagine you have a forming current sheet again. My, A and my L.

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Mark Kushner: No, this is across, and this is along right. And

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Mark Kushner: it's going to go from something like this to something like this, right? So it's getting my garden hose is getting longer and thinner.

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Mark Kushner: Right?

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Mark Kushner: No.

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Mark Kushner: when you start you're in a situation where your gradients are below critical. Right? So you don't have an instability drive right. It's stable.

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Mark Kushner: But eventually you do trigger this instability.

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Mark Kushner: The instability drives turbulence, and the service then starts back reacting on your plasma, right on your incoming plasma, and eventually the 2 have to reach some sort of understanding, some sort of equilibrium. Right? You have incoming plasma flows, but you have this terminus in the layer that wants to diffuse and expand.

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Mark Kushner: And so eventually you will have a system which is quasi steady state, where these 2, the incoming energy and the energy in the layer are sort of in agreement with each other.

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Mark Kushner: So that would be a quasi, steady state that's eventually reached.

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Mark Kushner: Okay, so here's a better. Better plot still, a cartoon just

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Mark Kushner: done in new plot. So it looks a little better.

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Mark Kushner: Nobody knows what the new plot is anymore. But you know, and that's how old I am. So this is again, aspect ratio. This is time. Let's just focus on the red line. You imagine you're forming current sheets. So that's this line coming down

386
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Mark Kushner: eventually, it reaches a critical

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Mark Kushner: value. It triggers an instability that makes it expand right? It can't stay where it is right, because now he has to accommodate, accommodate all disturbing power.

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Mark Kushner: And eventually it settles onto something that's like the mean aspect ratio.

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Mark Kushner: Now, that's a very interesting thing because

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Mark Kushner: because of mass continuity.

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Mark Kushner: The mean aspect ratio is also the reconnection rate. So it's, you know, the

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Mark Kushner: like in Sweet Park, right? The width divided by the length is the same thing as the inflow divided by the outflow, and that's the reconnection rate.

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Mark Kushner: So this aspect ratio that it converges to is, in fact, this

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Mark Kushner: fancy R, and that's the reconnection rates.

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Mark Kushner: These are all cartoons. Okay.

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Mark Kushner: this is the same idea. But, viewed from the point of view of turbulent emf. So the turbulent electric field. Okay, so this axis is the aspect ratio A over L, you start at something over the unity, and time moves you this way. So you're making it thinner and longer.

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Mark Kushner: Eventually you hit the critical value that

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Mark Kushner: raises the turbulent power from nothing to something that turbulent power expands, and as it expands the current sheets you're losing drive because your gradients are now becoming shallower, and eventually you converge to some critical value.

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Mark Kushner: All right. So let's talk about this mean field decomposition.

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Mark Kushner: So these termed fluctuations. They only exist in the current player.

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00:46:31.350 --> 00:46:38.510
Mark Kushner: and they're very fast. So they evolve on this time scale called the authentic timescale or faster.

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00:46:38.840 --> 00:46:51.560
Mark Kushner: Okay, so these could be plasmoids. How long does a plasmoid stay in the reconnection layer? Well, it's being affected by the mean fields, and it takes this time to go from the center of the layer out

403
00:46:52.140 --> 00:47:00.190
Mark Kushner: right? So this is the longest that it can exist in the layer, for it can be, it can be destroyed, it can be absorbed. But that's roughly how long it will stay there, for

404
00:47:01.960 --> 00:47:02.890
Mark Kushner: now

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00:47:03.250 --> 00:47:08.530
Mark Kushner: the advantage is that the reconnection time is much longer than that.

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Mark Kushner: So the reconnection time is, you know, the reconnection rate, or one over times the often time, and even if this number is like 0 point 1, that's still a factor of 10.

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Mark Kushner: And you know I'm a theorist. So a factor of 10 is plenty for me to do asymptotic analysis on right. So for me, this is

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Mark Kushner: much larger, right? So there's a timescale separation between the reconnection time and the timescale of the fluctuations.

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Mark Kushner: The reconnection time is the timescale on which the background fields are evolving, and the often time is the timescale on which the fluctuations are evolving. The fact that the 2 are separated now allows me to do some analytic theory.

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Mark Kushner: So what you can do is you can say, Huh.

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Mark Kushner: that's very interesting, so I can take any of my fields, magnetic field or density.

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Mark Kushner: and I can say that it is the sum of a mean field

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Mark Kushner: and the fluctuation on top of that.

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Mark Kushner: And this mean field is just the time average of the actual fields

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00:48:09.650 --> 00:48:16.139
Mark Kushner: averaged over times that are longer than the fluctuations, but shorter than the reconnection time.

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00:48:19.430 --> 00:48:22.839
Mark Kushner: Great. So if I do that, so here's

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00:48:23.010 --> 00:48:24.216
Mark Kushner: this is

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00:48:24.910 --> 00:48:30.400
Mark Kushner: This is a plot from this nice paper by Yemen Wong, and emit Ava

419
00:48:30.440 --> 00:48:42.689
Mark Kushner: in this paper they were doing. They were doing direct numerical simulations and just then post-processing the data to see what it would look like if you averaged. Okay? So

420
00:48:42.790 --> 00:48:50.689
Mark Kushner: if you take just this, this is an actual snapshot from their simulation, it's a turbulent system. If you average it.

421
00:48:50.740 --> 00:48:54.109
Mark Kushner: you get this thing which would be your mean flow.

422
00:48:54.730 --> 00:49:01.229
Mark Kushner: So I'm talking about the analytic version of this right where you say this is what the actual full field looks like.

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00:49:01.270 --> 00:49:11.999
Mark Kushner: If I time average it, I will get this. So my full field can be described as the average plus the fluctuation. So whatever I need to add here to make that image.

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00:49:12.160 --> 00:49:19.880
Mark Kushner: So so the idea that there is a mean flow, it's well defined, and on top of that we'll live. These fluctuations that are very fast

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Mark Kushner: cool, so

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00:49:23.840 --> 00:49:30.029
Mark Kushner: we can make a little bit of progress. Not very much, or not as much as I'd like, but still some.

427
00:49:30.080 --> 00:49:31.690
Mark Kushner: So you can write

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Mark Kushner: equations now, mh, equations for the mean fields, and you can write them for the fluctuations like people do in.

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00:49:37.720 --> 00:49:39.689
Mark Kushner: I don't know dynamo series, for example.

430
00:49:39.940 --> 00:49:42.250
Mark Kushner: So you write the mean field? Ohm's law.

431
00:49:42.320 --> 00:49:44.289
Mark Kushner: That's the topic question there.

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00:49:44.360 --> 00:49:54.380
Mark Kushner: that now includes this term, which is what I was calling the turbulent Emf. So this is the effect of the fluctuations on the mean fields.

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00:49:54.610 --> 00:50:01.760
Mark Kushner: So the mean fields act on the fluctuations, the fluctuations act back on the mean fields, and that's how they do it. They give you a turbulent electric field.

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Mark Kushner: Now you can do very simple arguments. You can say, well, if I'm away from the current sheet. There's no turbulence there, right? All the term is localized to the current sheet itself. So if I go away, no turbulence, so that equation away from the current sheet just gives me that term.

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00:50:18.210 --> 00:50:21.829
Mark Kushner: and that's inflow velocity. Times. Inflow magnetic field.

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00:50:22.860 --> 00:50:34.050
Mark Kushner: If I go to the center of the current sheet. Then that's where the turbulent Tmf dominates. So there the electric field is just given by the actual turbulence fluctuations.

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00:50:34.780 --> 00:50:40.270
Mark Kushner: Now, if I'm in approximate steady state. This is just the sweet Parker argument, but now, with turbulence on it.

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Mark Kushner: these 2 electric fields have to be the same.

439
00:50:42.770 --> 00:50:46.120
Mark Kushner: because a steady state is one where the electric field is constant.

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00:50:46.770 --> 00:50:55.029
Mark Kushner: And so, if you equate these 2 things, you finally have a prescription for the reconnection electric field in terms of the fluctuations.

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Mark Kushner: Now, you don't know what the inflow velocity is, and you don't know these fluctuations. So this isn't actually the solution to anything right. But it's a constraint between macroscopic fields and fluctuations.

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Mark Kushner: and then you can figure out more things you can say. Well, if these fluctuations are plasmoid like, then I know that their amplitude should be like the upstream field, which allows me to conclude immediately that the incoming flow

443
00:51:20.060 --> 00:51:24.800
Mark Kushner: mean flow is like the Rms velocity of the fluctuations.

444
00:51:25.270 --> 00:51:27.270
Mark Kushner: That's sort of a nice conclusion.

445
00:51:29.130 --> 00:51:30.060
Mark Kushner: So

446
00:51:31.980 --> 00:51:34.860
Mark Kushner: that was just to sort of lay out the formalism.

447
00:51:35.040 --> 00:51:38.909
Mark Kushner: But now I can make it make an interesting conjecture, I can say.

448
00:51:39.080 --> 00:51:46.059
Mark Kushner: consider a large scale field where a current sheet is forming, like I was talking to you about in previous slides.

449
00:51:46.260 --> 00:51:52.980
Mark Kushner: And now I can conjecture that in transition to turbulence, so the thickness at which this turbulence is triggered

450
00:51:53.300 --> 00:51:55.840
Mark Kushner: is actually, when

451
00:51:55.970 --> 00:51:58.870
Mark Kushner: the current sheet is still on Mht. Scales.

452
00:52:00.060 --> 00:52:02.600
Mark Kushner: it hasn't gotten down to kinetic skills.

453
00:52:03.120 --> 00:52:07.480
Mark Kushner: So I can't prove this in general. But it is true for every case I've looked at.

454
00:52:07.990 --> 00:52:10.770
Mark Kushner: Okay. So that's why it's a conjecture and not a theorem.

455
00:52:11.100 --> 00:52:11.930
Mark Kushner: Alright.

456
00:52:12.280 --> 00:52:15.520
Mark Kushner: Now, if this is true, it has a very powerful conclusion.

457
00:52:15.530 --> 00:52:24.810
Mark Kushner: It means that I can treat the mean fields just with Mhd. Formalism, and I only need kinetic equations for the fluctuations.

458
00:52:26.790 --> 00:52:34.920
Mark Kushner: So this is the plot that goes with it. We've you've seen it before. The idea is that this threshold at which you trigger the turbulence

459
00:52:35.080 --> 00:52:41.679
Mark Kushner: is, you know, is still on Mht. Scales. You haven't yet gotten down to iron skin, depth or iron Lamarines.

460
00:52:44.280 --> 00:52:56.059
Mark Kushner: Okay, so the proposal here is that you can do this decomposition, and you can evolve the mean fields just with the mean field. Mht. Equations. Even in collisionless cases.

461
00:52:56.820 --> 00:53:01.820
Mark Kushner: and you need a kinetic description only for the current sheet to solve for the fluctuations.

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Mark Kushner: So, for example, I know there are people in the audience that are interested in using coupling between Mhd and pick

463
00:53:08.710 --> 00:53:31.619
Mark Kushner: for solving this problem. I think these sort of arguments actually put this sort of coupling in a very firm ground, and tell you that you can actually be very bold about this right? You actually just need Mht equations for the mean fields that you are justified in doing timescale decomposition in doing time averages for your kinetics, for your kinetic fluctuations.

464
00:53:32.920 --> 00:53:37.804
Mark Kushner: This isn't proof, but it's consistent. It's a nice paper by Jacob Percy, who is

465
00:53:38.360 --> 00:53:55.080
Mark Kushner: a graduate student at Mit working with Shiang Lee. This is a laser plasma experiment, I think, done on Omega laser a reconnection experiment, and not only did he get plasmoids in this layer, but he was able to measure as a function of time the thickness of the current sheet.

466
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Mark Kushner: and at the earliest time that he was

467
00:53:58.040 --> 00:53:59.530
Mark Kushner: accessing.

468
00:53:59.630 --> 00:54:01.670
Mark Kushner: There's already plasmoids there.

469
00:54:01.710 --> 00:54:13.279
Mark Kushner: but the layers larger than the ion skin depth, right? So this suggests that, you know, maybe these plasmoids form even when you're still at Mhc scales, like, I was just just talking about.

470
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Mark Kushner: Okay, I don't want to run out of time, and I want to make sure I leave time for questions. So let me just very quickly say that this suggests, for example, that the very minimal model for reconnection. Capturing kinetic effects might actually just require a clever form of an anomalous resistivity like people have been doing before.

471
00:54:37.190 --> 00:54:44.209
Mark Kushner: But you need to inform that enormous resistivity with more knowledge, I think, than what's been done before.

472
00:54:46.100 --> 00:54:53.879
Mark Kushner: Let me tell you very quickly how we're trying to approach this question. So we're saying, is there a subgrid like model

473
00:54:53.960 --> 00:54:55.109
Mark Kushner: that can

474
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Mark Kushner: tell me about what's happening with the fluctuations and capture the effect of the fluctuations on the mean fields.

475
00:55:03.910 --> 00:55:07.600
Mark Kushner: And so this is just to show you that actually, you can do very well

476
00:55:07.730 --> 00:55:12.129
Mark Kushner: and or not depending on what you care about. So there's many curves here.

477
00:55:13.364 --> 00:55:19.880
Mark Kushner: Different curves are different values of an enormous resistivity.

478
00:55:20.240 --> 00:55:23.290
Mark Kushner: and the actual real simulation is the blue one.

479
00:55:23.830 --> 00:55:34.519
Mark Kushner: And so, if I am free to play with the value of the resistivity. I can get the curve that looks exactly from an Mhc. Simulation that looks exactly like a kinetic simulation.

480
00:55:35.190 --> 00:55:39.539
Mark Kushner: But when you look at what the fields look like, they look nothing like each other.

481
00:55:39.560 --> 00:55:48.169
Mark Kushner: So this is the actual simulation, and this is the one that gave you me exactly the same curve in terms of reconnected flux, but the fields look completely different.

482
00:55:48.780 --> 00:55:56.259
Mark Kushner: So if all you care about is the reconnection rate, I can tell you how to do that right. But if you care about morphology, then it becomes a little more interesting.

483
00:55:57.390 --> 00:56:01.090
Mark Kushner: So this is work by Alex Felberg, who is a grad student in my group

484
00:56:01.120 --> 00:56:03.230
Mark Kushner: is taking this further.

485
00:56:03.902 --> 00:56:10.929
Mark Kushner: So is develop is sort of essentially implementing these ideas about having mean fields

486
00:56:10.980 --> 00:56:17.710
Mark Kushner: and then talking about the effect of the small scales on the mean fields. But what he's doing now is he's saying.

487
00:56:17.730 --> 00:56:22.539
Mark Kushner: let me have an asset. The assets is that the

488
00:56:22.730 --> 00:56:28.539
Mark Kushner: turbulent fluctuations can be expressed only as function of the mean fields.

489
00:56:28.600 --> 00:56:31.860
Mark Kushner: I can't prove. Nobody can prove this right. It's an ances.

490
00:56:32.210 --> 00:56:35.099
Mark Kushner: And then you can use data to learn

491
00:56:35.630 --> 00:56:38.390
Mark Kushner: this this anomalous term.

492
00:56:38.930 --> 00:56:44.850
Mark Kushner: And so this is a plot of an example of you can actually do this right. So the actual

493
00:56:45.030 --> 00:56:52.249
Mark Kushner: data is the blue line that's under the orange line, which is the neural network prediction that you got from

494
00:56:52.320 --> 00:56:54.619
Mark Kushner: just doing this sort of analysis.

495
00:56:55.020 --> 00:57:16.169
Mark Kushner: That's when it was trained on. This is on the training simulation. It then applies it to a simulation that this thing had never seen, and gets reasonable agreement. So this looks pretty promising in terms of using combination of machine learning techniques with what I would argue is a proper formulation of the problem from a theoretical

496
00:57:16.600 --> 00:57:23.710
Mark Kushner: theoretical standpoint. Right? You! You just have to know what it is that you're training for and cast your problem in that way.

497
00:57:26.048 --> 00:57:28.081
Mark Kushner: Let me skip this.

498
00:57:28.970 --> 00:57:30.470
Mark Kushner: let me skip this.

499
00:57:31.871 --> 00:57:46.209
Mark Kushner: This is beautiful. So the only is a student that I stole from you guys is in my group. And and he's a joy to work with. And last night he did this for me. Let's see if I can

500
00:57:47.470 --> 00:57:55.099
Mark Kushner: here. So these are 2 simulations they are exactly the same, except in one aspect.

501
00:57:55.490 --> 00:58:01.619
Mark Kushner: that one starts with a current layer that has a thickness that's like the iron skin, that.

502
00:58:01.990 --> 00:58:08.649
Mark Kushner: And this one has a current layer that has a thickness like the electron skin depth. Otherwise they're exactly the same.

503
00:58:09.300 --> 00:58:14.489
Mark Kushner: Okay. And now what do you see? You see that these systems evolve in completely different ways.

504
00:58:15.560 --> 00:58:19.500
Mark Kushner: Okay, so this shows you the importance of the initial conditions.

505
00:58:19.970 --> 00:58:25.580
Mark Kushner: Okay? So this, the plasma conditions are exactly the same, everything's the same. The box is the same, everything's the same. Okay.

506
00:58:25.770 --> 00:58:27.290
Mark Kushner: But this system.

507
00:58:27.410 --> 00:58:36.630
Mark Kushner: you know, the one on the left doesn't actually evolve to something that looks like the one on the right and the one on the right doesn't evolve to something that looks like the one on the left.

508
00:58:36.750 --> 00:58:43.369
Mark Kushner: So if you were studying this thing. Assuming you know what the initial condition is, you'd be studying a system that again doesn't exist

509
00:58:43.530 --> 00:58:45.930
Mark Kushner: because this one doesn't converge to that.

510
00:58:52.550 --> 00:59:02.559
Mark Kushner: Okay, I'll just say these words, and you can ask me. We think we've solved election only reconnection. If this means anything to you, you can ask me about this, or you can read this paper.

511
00:59:03.200 --> 00:59:17.810
Mark Kushner: and this is more work by Dion. We got very interested in this idea of what happens in reconnection. If you have a very large temperature difference between ions and electrons. So let's say you have cold ions

512
00:59:17.870 --> 00:59:19.609
Mark Kushner: compared to the electrons.

513
00:59:19.670 --> 00:59:31.210
Mark Kushner: and we got interested in this, because earlier, we were studying ion acoustic instability which is triggered when this happens and the ion acoustic instability can be very efficient at keeping the ions.

514
00:59:31.590 --> 00:59:41.059
Mark Kushner: So if you have a reconnecting system where ions are colder than than electrons, what you can show is that actually, you get the instability developed

515
00:59:41.340 --> 00:59:46.080
Mark Kushner: very strongly, and then it can very efficiently heat the ions.

516
00:59:46.100 --> 00:59:52.909
Mark Kushner: And you know we're wondering if this is a contending mechanism for iron heating in the solar wind, for example.

517
00:59:53.300 --> 00:59:54.120
Mark Kushner: So

518
00:59:54.430 --> 00:59:56.680
Mark Kushner: this is unpublished. We're still working on this.

519
00:59:57.160 --> 01:00:00.243
Mark Kushner: So let me conclude I took you through a lot of things.

520
01:00:00.830 --> 01:00:05.480
Mark Kushner: so key idea is that the onset question in reconnection

521
01:00:05.974 --> 01:00:10.589
Mark Kushner: is a painful one in the sense that it forces you to

522
01:00:11.060 --> 01:00:22.330
Mark Kushner: follow the evolution of the plasma rather than just assume that you know what the initial condition is going to be. But if you do this, you get rewarded right, because you actually discover

523
01:00:22.370 --> 01:00:29.310
Mark Kushner: what are the mechanisms that can trigger the transition from a slow energy accumulation to a fast energy release.

524
01:00:29.660 --> 01:00:30.550
Mark Kushner: Now.

525
01:00:31.290 --> 01:00:48.649
Mark Kushner: you know whatever aspects, whatever plasma configuration you're looking at, if you're asymptotic enough in your parameters. You tend to find that there are instabilities in the current sheet. So there is no such thing, really, as a Laminar reconnection layer. Okay, so you have to embrace this turbulence. It's part of it. Okay?

526
01:00:48.950 --> 01:00:54.382
Mark Kushner: And the proposal here is that there is a self regulating

527
01:00:55.600 --> 01:00:56.390
Mark Kushner: and

528
01:00:56.910 --> 01:01:05.030
Mark Kushner: mechanism. Between the turbo single layer and the actual mean fields of the incoming fields, they self-regulate to reach a quasi-steady state.

529
01:01:06.110 --> 01:01:18.470
Mark Kushner: Fortunately there is a timescale separation between the fluctuations and the background fields. And I think this allows you to construct a what I call the mean field, or a transport like approach

530
01:01:18.550 --> 01:01:24.599
Mark Kushner: to the problem of reconnection which might actually allow you to compute this efficiently right. All you have to do is

531
01:01:24.690 --> 01:01:33.560
Mark Kushner: Do Mhd. On the mean fields, and use a kinetic description, or maybe a machine learning description in the layer to capture the effect of of the fluctuations.

532
01:01:34.050 --> 01:01:37.360
Mark Kushner: You know realistic. You may not agree with me.

533
01:01:37.430 --> 01:01:49.459
Mark Kushner: But brute force is not going to be how we are going to solve this problem. So if you don't agree with me, that's fine. But come up with something that actually allows you to compute reconnection in realistic systems.

534
01:01:49.990 --> 01:01:52.060
Mark Kushner: And that's all I'd like to say. Thank you.

535
01:01:58.390 --> 01:02:01.330
Mark Kushner: Thank you very much. Are there questions

536
01:02:01.710 --> 01:02:02.340
Mark Kushner: oops

537
01:02:03.290 --> 01:02:04.100
Mark Kushner: home.

538
01:02:04.930 --> 01:02:06.020
Mark Kushner: Would you say that.

539
01:02:06.110 --> 01:02:15.040
Mark Kushner: as in general, all reconnection regimes are characterized by an instability in the current chain? And it's just a question of which instability

540
01:02:15.410 --> 01:02:29.360
Mark Kushner: all as long as you have enough scale separation between the size of your fields and the kinetic scales or the rest or the resistive scale. Yeah, yeah.

541
01:02:29.430 --> 01:02:36.210
Mark Kushner: at the same. Yeah, there should be a plasma instability. Yeah, some sort of instability for sure.

542
01:02:37.620 --> 01:02:39.989
Mark Kushner: And this is so.

543
01:02:44.700 --> 01:02:45.550
Mark Kushner: so

544
01:02:46.310 --> 01:02:52.229
Mark Kushner: anytime that you get to a large scale aspect ratio, you're going to be plasmoid, unstable.

545
01:02:52.480 --> 01:02:55.120
Mark Kushner: So if there's nothing else, at least there is that

546
01:02:55.670 --> 01:03:03.769
Mark Kushner: unless there is so so that. But you also have a current beam, right? So if you shrink down your current channel all the way down to electron skin depth.

547
01:03:04.020 --> 01:03:08.050
Mark Kushner: right, you have a very intense current. So there's a large electron ion drift

548
01:03:08.120 --> 01:03:10.359
Mark Kushner: which also drives instabilities.

549
01:03:10.700 --> 01:03:11.640
Mark Kushner: So

550
01:03:12.190 --> 01:03:16.379
Mark Kushner: the only way that this could fail is if you have

551
01:03:16.630 --> 01:03:24.040
Mark Kushner: stabilization mechanism. So if you have a plasma on one side of your reconnection layer that's so different from the plasma on the other side.

552
01:03:24.120 --> 01:03:30.699
Mark Kushner: so there might be a very intense density, gradient across or gradients that could stabilize some of these instabilities.

553
01:03:30.760 --> 01:03:36.070
Mark Kushner: maybe. But then maybe you trigger some others. It was like drift waves. So I think it's I

554
01:03:36.220 --> 01:03:46.150
Mark Kushner: I you know honestly, I I can't think of a system where you wouldn't be unstable, a naturally occurring system, reconnected systems that where you wouldn't be unstable to something.

555
01:03:47.990 --> 01:03:48.760
Mark Kushner: Stop.

556
01:03:49.070 --> 01:03:57.820
Mark Kushner: I was wondering if you could talk about observational constraints or experimental constraints on this onset mechanism. So you're saying

557
01:03:57.970 --> 01:04:04.520
Mark Kushner: current sheets forming some instability like plasmoid. That explains the onset. Why, there's a build up

558
01:04:04.540 --> 01:04:05.680
Mark Kushner: disruption.

559
01:04:05.800 --> 01:04:16.559
Mark Kushner: so does it work out. The timescales work out with the observation. Can that explain this a little bit better? Yeah. So right? So in in the so Dmitry Wozniski and I have a paper on this in 2016,

560
01:04:16.610 --> 01:04:17.970
Mark Kushner: where

561
01:04:18.440 --> 01:04:24.960
Mark Kushner: we try to. We foolishly maybe try to actually plug in some numbers for the solar corona

562
01:04:24.980 --> 01:04:28.029
Mark Kushner: right? And the time scales come actually come out, okay.

563
01:04:28.110 --> 01:04:37.440
Mark Kushner: that might be a coincidence, or it might not right, because to actually plug in numbers, you need to have a model for your current sheet formation.

564
01:04:38.090 --> 01:04:52.380
Mark Kushner: And then, right? So you have to have some fields that are evolving as a function of time. Analytically right. And you know, the model that we used is a very simple, naive, toy model. Chapman Kendall collapse. Right? That's not actually what's happening in the solar corona.

565
01:04:52.530 --> 01:05:00.159
Mark Kushner: And you know, to the extent that the differences between a a simple time model and the real system don't matter.

566
01:05:00.180 --> 01:05:05.949
Mark Kushner: you know. Maybe the numbers come out okay, right? But you know, to actually trust this, you would have to be looking at

567
01:05:06.140 --> 01:05:14.290
Mark Kushner: magnetic geometries that pertain to the solar corona. Evolve them in time and compute things for that kind of geometry. We we haven't done that.

568
01:05:14.940 --> 01:05:20.021
Mark Kushner: How about lab experiments? So for Sawtooth, for Sawtooth, it also kind of works out

569
01:05:20.480 --> 01:05:24.815
Mark Kushner: for other lab experiments. The ones that we have data for

570
01:05:26.580 --> 01:05:28.570
Mark Kushner: you know. So you're either.

571
01:05:29.380 --> 01:05:45.459
Mark Kushner: You tend to be in a regime where you don't have a lot of plasmoids. Right? You're like for Mrx, for example, you know you're not actually truly asymptotic, and you might get one plasma there. But you're not truly asymptotic in in the sense that I talk about here. So there! It's sort of harder to, I think.

572
01:05:45.490 --> 01:05:46.930
Mark Kushner: make this argument.

573
01:05:49.300 --> 01:05:50.000
Mark Kushner: Yes.

574
01:05:50.518 --> 01:05:54.001
Mark Kushner: so plasmoids seem like a pretty natural consequence of reconnection.

575
01:05:54.420 --> 01:06:03.220
Mark Kushner: is there much be? Do you know much work about relating sort of the distribution of plasmoids you generate? Given the reconnection conditions like

576
01:06:03.400 --> 01:06:06.699
Mark Kushner: the number and the flex content of them. Is that

577
01:06:06.850 --> 01:06:15.870
Mark Kushner: so? There is work on predicting what the plasma distribution functions are as a function of upstream quantities.

578
01:06:16.000 --> 01:06:16.694
Mark Kushner: But

579
01:06:18.410 --> 01:06:28.339
Mark Kushner: most of that work is in the Mhd. Limits, and I think there isn't as much in the collision less limits right that people do have predictions for, you know.

580
01:06:28.470 --> 01:06:35.429
Mark Kushner: plasmoid size, distribution and plasmoid flux distribution as a function of upstream parameters. Yeah.

581
01:06:35.720 --> 01:06:36.890
Mark Kushner: that exists.

582
01:06:40.400 --> 01:06:43.109
Mark Kushner: Any other questions. Yes.

583
01:06:43.240 --> 01:06:45.500
Mark Kushner: So you talked about modeling from on sale.

584
01:06:46.010 --> 01:06:49.810
Mark Kushner: I did not sort of assume that we did have a suite of record.

585
01:06:52.291 --> 01:07:00.639
Mark Kushner: What initial conditions do you choose? If you want? How do you reduce the charge? Charge layers?

586
01:07:01.830 --> 01:07:05.789
Mark Kushner: Yeah. Great question. So

587
01:07:05.980 --> 01:07:10.049
Mark Kushner: the I mean, there's different ways. You can do this. But the key one is

588
01:07:10.070 --> 01:07:17.029
Mark Kushner: you shouldn't start a system that has a very long and thin current player already formed.

589
01:07:17.140 --> 01:07:19.410
Mark Kushner: so you can take through flux bundles

590
01:07:19.500 --> 01:07:23.970
Mark Kushner: like circular fox bundles and just have them sufficiently apart.

591
01:07:24.000 --> 01:07:27.530
Mark Kushner: so that you know the current between them is.

592
01:07:27.590 --> 01:07:36.610
Mark Kushner: you know, irrelevant. Basically they will. You can nudge them. They will start coming together. That will form a current sheet. Just let it go right.

593
01:07:36.720 --> 01:07:43.780
Mark Kushner: or you can start. You know what people call a Harris sheet. But so the hyperbolic tangent and

594
01:07:43.830 --> 01:07:54.159
Mark Kushner: you can make it unstable to mild it. Mild instability. It will bring it together and form a current, a current sheet. Naturally. So there! There are ways to do this.

595
01:07:54.280 --> 01:07:57.149
Mark Kushner: And the the reason that people don't do this is

596
01:07:57.380 --> 01:08:13.109
Mark Kushner: because, you know, this process can be very slow. Right? So if you're already stretching the limits of your pick simulation with all the parameters that you chose. You don't want to waste a lot of time in this process, right? That turns out that you might. You might just have to.

597
01:08:13.640 --> 01:08:16.740
Mark Kushner: So you're you're saying that you need to choose

598
01:08:17.880 --> 01:08:25.460
Mark Kushner: has to be slow enough. So if you do them. If you do, if you

599
01:08:25.689 --> 01:08:30.710
Mark Kushner: you don't have to force that right, if you just set it up in what I would argue is a

600
01:08:31.408 --> 01:08:37.450
Mark Kushner: unbiased way. It will be slow compared to the for initially, and we'll just do exactly what I told

601
01:08:37.479 --> 01:08:38.640
Mark Kushner: told you about.

602
01:08:40.720 --> 01:08:41.550
Mark Kushner: Yes.

603
01:08:41.729 --> 01:08:53.590
Mark Kushner: I know you've already just kind of touched on this. But I was wondering if you could talk about what specifically a magnet magnetic reconnection experiment might look like, or what kind of there are to

604
01:08:53.840 --> 01:09:11.159
Mark Kushner: do this experimentally. Yeah, so experiments exist. Right? So one of the ones that might be closer to here is when you take, let's say, 2 laser beams, you, you shine them at solid targets that gives you a Beermann field right from the vape.

605
01:09:11.240 --> 01:09:18.890
Mark Kushner: expanding plasma cloud self magnetized by Beermann Fields and those come together, and you reconnect the Beermann fields.

606
01:09:18.899 --> 01:09:26.669
Mark Kushner: This is yeah. And and so that's a reconnection experiment. It's in a very particular parameter regime. Right? So very high densities. And all these things right?

607
01:09:26.810 --> 01:09:32.970
Mark Kushner: And then people have dedicated reconnection experiments in the lab typically with magnetic confinement systems

608
01:09:33.069 --> 01:09:52.339
Mark Kushner: where you know, one way or another, you engineer Fields, that will sort of come together and reconnect. And so, Mrx, at Princeton is one example. The Vtf. Experiment we had at Mit was another one, the big red ball in Wisconsin, so different concepts. And you know usually what the thing that

609
01:09:52.510 --> 01:09:57.639
Mark Kushner: changes between these experiments is, what plasma parameter regime they're operating in.

610
01:10:00.130 --> 01:10:02.180
Mark Kushner: Yeah, let's thank our speaker again.

611
01:10:07.270 --> 01:10:08.980
Mark Kushner: The chat. See if you know.

612
01:10:09.354 --> 01:10:11.300
Mark Kushner: Say, I didn't look at this.

613
01:10:12.883 --> 01:10:15.849
Mark Kushner: Thank you all. If you have one

614
01:10:16.110 --> 01:10:18.330
Mark Kushner: post. Thank you. Question here

615
01:10:25.290 --> 01:10:26.000
Mark Kushner: this.