WEBVTT

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Mark Kushner: All right, now we are set. Very good.

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Mark Kushner: So, yes, the title of my talk is Breaking Newton's Third Law, so just remembering that Newton's Third Law says that for every action, there is an equal and opposite reaction. And what we found in dusty plasma experiments is there were unequal

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Mark Kushner: And so the question is, how do you break Newton's law? Something else must really be going on, because Newton's laws actually work very well.

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Mark Kushner: So, to get started, I'm going to tell you a little bit about what a dusty plasma is. Most of you are probably familiar with plasmas.

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Mark Kushner: And then, so that you understand what's going on, to talk about once you put dust in a plasma, how does the dust become charged? And we'll focus on just spherical grains. As physicists, we love spheres.

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Mark Kushner: And after they're charged, look at what is some of the observed behavior that we've seen in laboratory experiments, and then we'll talk about the ion flow and the ion wakes, which help explain what we observe by creating these non-reciprocal interactions. And so, how do we model those wakes to determine what

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Mark Kushner: what they're doing. So plasma, as you know, you create when you add enough energy to a gas to actually free some electrons from the atom so that you have positive ions and negative electrons.

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Mark Kushner: And a dusty plasma, you just put dust into the plasma. This is any type of solid particle. It can range in size from nanometers

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Mark Kushner: to, in space, plasma is up to a centimeter, but on Earth, we're usually looking at micrometer-sized particles. So remember, the diameter of a human hair is about 100 microns, and we usually use 2 to 10 micron size particles.

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Mark Kushner: But the electrons and ions in the plasma run into the dust, and the dust collects these charges, and because the electrons are more mobile, being lighter, they collide more frequently at first, and the dust becomes negatively charged.

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Mark Kushner: This means that the dust will attract the positive ions and repel the negative electrons, and so we have this characteristic distance in the plasma called the Debye length, and this is the characteristic shielding distance, such that the plasma rearranges itself to shield the negative charge of the dust grains.

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Mark Kushner: So, when we talk about the potential of a charged dust grain, instead of the normal Coulomb potential, which is just 1 over 4 pi epsilon naught times Q over r, we have this extra exponential term, the e to the negative r over the Debye length, and so it falls off faster than a Coulomb potential.

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Mark Kushner: So, where do we find dusty plasmas?

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Mark Kushner: Well, they're everywhere in space, and this is where the field of dusty plasma has got its start. If you look at the regions of giant molecular clouds, this is where star and planet formation is taking place. So what happens is you see these little permont trees that are sticking out.

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Mark Kushner: These are extra-dense parts of the molecular cloud. These really bright stars are evaporating the clouds, because they're putting off X-rays and gamma rays.

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Mark Kushner: But where it's really dense, it doesn't evaporate, and that's where you have stars forming. So the stars collapse, and as they collapse, the cloud will start to spin faster and faster, and the star ignites, and it has an outflow that blows off the top and the bottom, and you're left with a disk. And so these are cross…

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Mark Kushner: section images of disks that were first discovered after the Hubble Space Telescope was launched in the early 90s, and so that was great. We predicted that there should be disks around stars, and there actually are disks around stars.

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Mark Kushner: When I started, I was also looking at the dynamics of Saturn's F ring, which is a very dynamic, dusty ring. You can see you get these knots and these kinks. It has shepherding moons, this is Prometheus. Out here is Pandora, that helps shape the… the rings.

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Mark Kushner: But then, in the mid-90s, the silicon chip manufacturers had a real problem with dust in their plasmas. And they were spending billions of dollars on clean rooms to get rid of all the dust.

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Mark Kushner: Because when the dust falls down on your computer chips, about 30% of the chips would be bad, because they would be shorted out by these dust particles.

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Mark Kushner: So this, is a billion dollar industry worth a lot of money, so they needed to study this process, and so then they created what is called the GEC, Gaseous Electronics Conference RF, radio frequency.

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Mark Kushner: reference cell, so that everybody could do the same experiment. And the dusty plasma physicist said, hooray! We have a platform! And so we put dust in it on purpose.

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Mark Kushner: But we buy very expensive desks so that it's all the same size and perfectly spherical. And then I have to show you this picture, because this is actually from the NASA SOFIA telescope.

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Mark Kushner: So these, swirls here.

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Mark Kushner: actually map the magnetic field around the black hole at the center of our galaxy. So what is happening here is that the dust particles that are charged, they're not spherical dust particles, but, you know, maybe they're ellipse flatal.

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Mark Kushner: But because they're charged, they have this dipole moment, so that they interact with the magnetic field, and they all line up in the same direction, and so the light that passes through the dust field is then polarized, and they can use this polarization then to map the galactic magnetic field lines.

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Mark Kushner: So, that's a pretty cool application of dusty plasmas.

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Mark Kushner: So let's talk about how the dust does become charged. So if you have a dust screen, and you have, electrons and ions, those can run into the dust, and we call those the primary charging currents. And so we just assume that if an electron or ion hits the surface, it sticks.

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Mark Kushner: But then you can have secondary electron emissions, so if you have a very high energy electron, it'll actually penetrate the surface of the grain, and then it can knock off electrons all along its path, and it can knock off more than one electron, so it can be a positive charging current.

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Mark Kushner: And then you can have photoelectric emission, where you have a high-energy photon that comes in and excites an electron and knocks it off, and that's also a positive charging current. So those are often active in astrophysical environments, but in laboratory conditions, we are usually only concerned with the primary charging currents. So electrons and ions hitting the grain.

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Mark Kushner: So if we want to know what the grain charge is, what we can do is we can sum up all the currents to the grain.

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Mark Kushner: And you know that a current is just a change in charge, so we say the sum of the currents is equal to the change in charge over time, and at equilibrium, the charge is no longer changing.

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Mark Kushner: But the currents are a function of the surface potential of the grain, and the charge is also a function of the surface potential of the grain. So there's some particular surface potential for which this equation is satisfied. So that's our question, is what is the surface potential of the grain?

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Mark Kushner: So, the way that we do this is you actually calculate flux. This is a big, scary equation, but it's simply flux. And remember that flux is the area multiplied by the speed of the particles that are incident on the area, multiplied by the cosine of the angle that they make with the normal to the area.

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Mark Kushner: So we're going to add up flux, but then the particles can be coming in with a whole distribution of speeds. So this could be a Maxwellian distribution, say. And so we need to add up all the possible,

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Mark Kushner: velocities that they can be coming in, and all the possible directions, so we're going to integrate over the 3D velocity space.

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Mark Kushner: And there's a couple of things here, is that some particles don't have enough energy to reach a charged surface. So if you have a negatively charged grain, it can repel very slow electrons, and meanwhile, the ions would be attracted. And also, we have this effective cross-sectional area that we get from conservation of angular momentum, because if you have a positively charged ion that's approaching a negatively charged grain.

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Mark Kushner: Its trajectory will be bent.

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Mark Kushner: And so, towards the grain, and so you get a large effective cross-sectional area, whereas an electron that's approaching the grain, it's going to be repelled from the dust grain, and so it has a smaller effective cross-sectional area to hit the dust grain. And so we just calculate that using conservation of energy and conservation of angular momentum.

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Mark Kushner: So you do all this for a spherical grain, you can just do the integration.

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Mark Kushner: And if you have a negatively charged dust grain, you can get the electron current that is going to fall off exponentially.

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Mark Kushner: And for the ion current, because this E times phi is going to be negative, or a negative dust charge here, E is just, a positive number. But the ion current, since the E phi is positive, this is going to increase linearly with the charge.

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Mark Kushner: So, our best way to solve two nasty equations is just to graph them and see where they cross. And if we make some assumptions, like, okay, we have spherical grains, the temperature of the electrons is equal to the temperature of the ions.

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Mark Kushner: The number density of the electrons is equal to the number density of the ions. We have a hydrogen plasma.

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Mark Kushner: You can simplify your equation, and we have the exponential part, and we have the linear part, or if we moved this whole thing to the other side of the equation, we can plot that line and look where it crosses zero.

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Mark Kushner: And the potential is negative 2.51 KT per E, and this is what is known as the Spitzer result. So this is… all grains, regardless of their size, charge up to the same potential.

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Mark Kushner: We don't always have hydrogen plasmas, so you can do this for other types of plasma, and the thing is, as the ions get more and more massive, the potential becomes more and more negative.

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Mark Kushner: And also in the lab, often the temperature of the electrons and the ions are not equal. The electrons are usually hotter than the ions, and as the electron temperature increases, you also get a more negative grain. So that's how we calculate the charge on our grain.

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Mark Kushner: So, now that we know that all of our grades are charged up negatively, and they're all charged to the same potential, how do they actually interact with each other?

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Mark Kushner: Well, the first experiment that they did back in the 90s was to create a dust crystal. So, this is actually a movie of the crystal. You can see it's quite stable. Oh, here's a little guy who's flying around the outside.

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Mark Kushner: And you see them winking in and out, because they're moving slightly in and out of the laser, the plane of the laser that's illuminating them. So we can establish these very stable structures, just exactly what you would expect if they all are going to repel each other, and then we can find them.

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Mark Kushner: Except sometimes, they're not repelling each other. This is what we call a plasma torsion, and you can see that these two grains are attracted to each other. And so, how on earth does that happen with our negatively charged dust grains?

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Mark Kushner: Or this is another view. So this is a dust cloud, and we're looking at a slice, a vertical slice to the cloud. And what you see is that all of the particles are actually lined up in these chains. So this is not what you would expect for, like, a crystalline solid lowest potential behavior here.

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Mark Kushner: What's causing them to charge up in, line up in these chains?

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Mark Kushner: And here's another view of… this is a dust crystal where we're looking at it edge-on, and we have two layers, and this is probably just a cluster of about, you know, 12 particles.

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Mark Kushner: But you can see these grains in the vertical direction are very much coupled to each other and move together. So, we said they're all negative, they should all repel each other, and yet they're obviously attracting each other.

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Mark Kushner: And another curious thing is…

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Mark Kushner: Here's an example. So we start with these particles in a vertical chain, this is going to loop, and we hit this bottom particle with the laser. And when we hit that particle, only it moves until it hits the other particles.

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Mark Kushner: So, we can knock this particle out of the chain, and it has no other effect on the other particles. Whereas if you had done a different experiment where we knocked out an upper particle, it would drag the lower particle with it. So we have these very non-reciprocal interactions.

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Mark Kushner: And then finally, if we're doing these experiments in the cell, and, typically we'll use a glass box to provide very strong horizontal confinement, because the sides of the glass box will charge up negatively and squish everything to the middle.

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Mark Kushner: Very, very small changes in the plasma power will cause the structure to jump to a new configuration. So we started out with a single… this is the top view, and you can see it's just a single particle in this long vertical chain.

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Mark Kushner: Increase the power slightly, and now we get two chains side by side, and you can see the two particles from the top. And then we can go to a three-chain configuration, 4 chains, 5 chains, 7 chains.

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Mark Kushner: 8 chains, etc. But these changes in structure are very sharp. It's not like they just kind of wiggle around a little bit. They stay in one particular structure, and then suddenly they will snap to the next structure.

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Mark Kushner: So our question was, what causes these structures to be stable?

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Mark Kushner: Oh, except sometimes they're not stable. This is a system… it's like a two-particle chain, and it says, no, I want to be a one-particle chain, but then it goes back to a two-particle chain, and I've clipped this video, but it does this… I think it did this for, I don't know, half an hour, as long as they wanted to look at it. It just sat there and did that.

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Mark Kushner: So, we get these interesting behaviors. So, here's the meat of the talk.

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Mark Kushner: This is the ion flow and the ion wakes, which are causing these non-reciprocal interactions.

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Mark Kushner: So, let's go back and look at our plasma. We know that in the bulk of the plasma, the plasma is a conducting fluid, and inside of a conductor, the electric field is zero.

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Mark Kushner: And this occurs because the number density of our electrons is equal to the number density of our… of the ions, so we have this quasi-neutral.

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Mark Kushner: Conducting fluid.

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Mark Kushner: But…

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Mark Kushner: All surfaces in a plasma will charge up negatively, not just our dust particles. So inside of our experiment, the walls of the chamber and the lower electrode also charge up negatively.

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Mark Kushner: So, you've got this negative surface, and the electrons are going to be repelled from the negative surface, and their distribution is going to be given by a Boltzmann distribution.

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Mark Kushner: The ions are accelerated from the bulk plasma, and, as they travel down to the lower electrode, their density is roughly determined by continuity of flow, so that, if you're up…

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Mark Kushner: Occupying a small section up here as it moves faster and faster to keep the same number of particles, you have to have a bigger volume to keep the same number of particles.

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Mark Kushner: So if we plot the number density of the electrons and the number density of ions as a function of the distance from the bulk plasma to the lower electrode, these are not the same.

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Mark Kushner: Let's turn it on the side so that you can see that the number density of the electrons falls off faster than the number density of the ions.

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Mark Kushner: So in our plasma sheath, we don't have equal electrons and ions, and this allows an electric field to exist in the sheath of the plasma that points from the bulk down to the lower electrode.

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Mark Kushner: So when we put a dust grain in, the dust grain is negative, so the net electric force is upward, which is great, because then we can levitate the grains against the force of gravity.

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Mark Kushner: And if we put another dust grain in, it's also going to levitate at the same height, because it has roughly the same charge, but it'll exert a force. All of our dust grains would just fall off the lower electrode if we didn't have something else to confine them, so often what we do is we put this little indentation in the lower electrode, it's like a circle.

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Mark Kushner: And so now our particles will float above that indentation.

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Mark Kushner: Okay, so they're in the sheath, but there's an electric field in the sheath, and I said that the ions are flowing downward. So, as the ions flow down past the dust grain, the negative dust grain is going to deflect their paths.

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Mark Kushner: And this is just a little cartoon showing that the ions tend to build up downstream of the dust grain. And the amount to which they build up depends on how fast are the ions flowing. What is the charge on the dust grain? Are there other dust grains around?

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Mark Kushner: So, what that happens then is when they build up downstream of the dust screen, we can treat that as an extra bit of positive charge that hangs out downstream of the dust.

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Mark Kushner: So, the forces between the two charged dust grain are reciprocal.

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Mark Kushner: But the force between a dust grain and the other ion wake are not reciprocal, because it depends on how close one dust grain is to the other dust grain's ion wake. And so then the apparent total force on the dust grains

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Mark Kushner: are not equal and opposite. And of course, it's the dust grains that we see moving around.

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Mark Kushner: So this is why we think that they're not behaving as if they're obeying Newton's third law.

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Mark Kushner: It's because we have to treat the whole system, and it's really the ions plus the dust that are obeying Newton's laws.

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Mark Kushner: Okay, so how do we actually model this behavior to, see what's going on?

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Mark Kushner: So my group, we have software that we've written called DRIAD, which stands for the Dynamic Response of Ions and Dust.

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Mark Kushner: And it's an in-body simulation where we resolve the dynamics of the ions and the dynamics of dust on their independent timescales. So the ions are moving on a timescale that's microseconds.

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Mark Kushner: And the dust is moving on a timescale that's milliseconds. So we have to move the ions, freeze them, move the dust kind of thing. So it's like a pick simulation where usually we are moving the electrons, freeze them, move the ions. We assume that the electrons are Boltzmann distributed because they're on the eco-second timescale.

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Mark Kushner: So…

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Mark Kushner: we just let them do their thing. So the ion motion, we have to add a baller of our forces. So we have the ion-ion force, which is a Yukawa force, because of the electrons.

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Mark Kushner: We have the dust ion force. So the force that the dust exerts on the ions, we only assume is a Coulomb force, because ions that are very close to the dust grain are in a region where the electrons have moved away.

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Mark Kushner: And ions that are far away from the dust are screened by the other ions in the system. So it's the ions that provide the screening for the negatively charged dust grains.

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Mark Kushner: Then we have, say, the sheath electric field, or any other electric field that's in the plasma.

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Mark Kushner: We have to take into account the boundary forces, so when we model this, we're usually modeling a very small region, and we're assuming that we have ions uniformly distributed outside that region that would exert

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Mark Kushner: electrostatic forces on the ions inside of our region. And then we account for ion-neutral collisions, which provide a drag force on the ions that are being accelerated in the electric field.

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Mark Kushner: So if we do a model, and we'll do a model, say, with 100,000 ions, and this just has one dust grain, you can see that as the ions are flowing, there's an electric field that's pointing down, so the ions are flowing down, and they… the density is built up downstream of the dust. So this is what the ion wake would look like.

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Mark Kushner: Looking at the ion density.

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Mark Kushner: The forces are going to be governed by the electric potential in the system. So if we take the dust grain, it's a negatively charged dust grain, this is what the potential would look like from a negatively charged dust grain.

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Mark Kushner: And then if you look at this ion density, the positive potential from the ion density, looks like this. So we get a positive that's downstream of the dust, and when we add these two together, we get something that looks very much like a dipole. So we have this negatively charged dust, and then we have this positively charged

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Mark Kushner: wake that's downstream. And so, this led people to develop the point wake model, where we model the wake just as a positive point charge that it is at a fixed distance below the dust screen.

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Mark Kushner: And this actually works pretty well for a lot of the crystal dynamics that we see, where all of the dust is floating at the same layer, and they're all roughly the same distance apart.

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Mark Kushner: But we're interested to see what happens when the dust is moving around, so we can do the same thing and look at the forces that are acting on the dust.

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Mark Kushner: So, we have a gravitational force acting on the dust,

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Mark Kushner: Yeah, that's what I thought would happen. Okay. With the gravitational force acting on the dust, we have the vertical electric field in the sheath, which is the QE. We have a dust-dust force, which is,

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Mark Kushner: a Coulomb force, because we have all of the ions in between that are doing the shielding. We have the dust ion force, so this is the force on the dust from the ions, and we use a eucalo force. So this is asymmetric. We use the Coulomb force for the force of the dust on the ions, and we use a UCOLO force for the force of the ions on the dust, where the electrons are providing the shielding.

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Mark Kushner: For the back reaction on the dust. And then we have neutral drag, a thermal bath, anything else we needed to add in.

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Mark Kushner: So, if we just look at two dust grains here.

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Mark Kushner: this is what two dust grains are doing. So we had two dust grains, we hit the bottom one with the laser, they did all sorts of crazy things.

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Mark Kushner: And this is kind of what we see in experiments, when we just have two dust screens. That's all you can tell what's going on. But with the dryad simulation, now with the dust density, I mean, the ion density, you can see how the ion density changes as the two particles approach each other.

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Mark Kushner: And we can also turn that into the potential, and you notice these dipole potentials… Are not always dipoles.

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Mark Kushner: So, when they're perfectly aligned, we just get one kind of dipole below the other one, or we might get a very weak dipole beneath the upper grain, and a stronger dipole beneath the lower grain.

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Mark Kushner: So, this leads us to ask, you know, what are these wakes actually doing as two dust grains are interacting with each other?

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Mark Kushner: So we did a very systematic investigation of the wakes, where we just held the dust still and modeled the ion wakes. And sometimes you get them well separated, so you have two wakes that have two defined peaks.

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Mark Kushner: Sometimes you have one combined wake, but it still has two peaks in the ion density, and sometimes you just get one big combined wake that only has one peak in the ion density.

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Mark Kushner: So we can map out all of these wakes for, you know, different horizontal separations between the grains, and for different vertical separations between the grains. And as they move further apart, you get two independent wakes, but all this stuff here in the middle, you get

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Mark Kushner: very interesting combined wakes. And so the potential map, you also see this occurring in the potential map, where even here, where we saw the density in the ion wakes, they looked the same. You can see that the potentials are actually quite different.

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Mark Kushner: So, this leads us then to investigate, say, our energy configurations. We can actually calculate what is called the configuration energy, and you know that systems like to tend to the lowest potential energy state. That's the most stable.

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Mark Kushner: So, in the configuration energy, we have two parts. One is a harmonic potential well, which accounts for the confinement forces. And so, there's some confinement in the horizontal direction, which here is the X direction, and it will have some characteristic frequency, omega X.

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Mark Kushner: And then you can have vertical confinement in a Z direction, which can be a very different frequency, because it's a different set of forces that are confining it.

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Mark Kushner: And then you can have the potential energy, which is, the charge on one dust grain multiplied by the electric potential of all the other dust grains, and you sum that up for all of the dust grains in your system.

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Mark Kushner: So we're looking at that interaction energy between the dust grains. So for our two dust grain sim… Two dust grain system, this is actually a little bit simpler. One, okay, we've got this

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Mark Kushner: The harmonic potential will, that's the confinement force.

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Mark Kushner: And then we have the configuration energy of the dust. Here we have the dust potential, which we have the Yukawa shielding from the electrons. And then we have the dust interacting with the ion potential. And the ion potential we actually calculate numerically at points

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Mark Kushner: In the simulation cylinder to know what the ion density is at every point, and then we use that to sum up on the dust.

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Mark Kushner: And then also, we look at the configuration energy of the ions. So, if you have ions at this particular point in space, what is the potential,

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Mark Kushner: Energy from all of the other ions in the simulation.

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Mark Kushner: And when you add these up, and we don't concern ourselves with any confinement, we get a picture that looks like this. And let me explain what this picture is showing you. So imagine that you have one dust screen that's sitting here in the upper right-hand corner. Each of these circles represents the position of the second dust screen.

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Mark Kushner: And the color tells you the potential energy.

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Mark Kushner: of…

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Mark Kushner: the system when the dust grain is at that spot. So you can see that the lowest potential energy is at a point about right here. So the lowest potential energy for two isolated dust grains is that they're going to line up vertically, not right on top of each other, but at a certain distance, and no lower, no higher.

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Mark Kushner: So, what happens then when we change the boundary conditions and we change this term over here?

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Mark Kushner: Well, if our horizontal confinement, WX, is small, omega X, is small compared to our vertical confinement, then you find that this minimum is going to shift so that the dust particles sit next to each other horizontally.

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Mark Kushner: On the other extreme, if our horizontal confinement is really strong compared to the vertical confinement, omega Z, then the dust particles are going to line up vertically.

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Mark Kushner: But then we have these interesting cases that are in between. In particular, look at this case.

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Mark Kushner: And you can see that this minimum in the potential energy is not well defined, and there's this whole region of space that's kind of this trough.

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Mark Kushner: Of potential energy.

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Mark Kushner: And here's a simulation where we fixed the upper dust grain and we pinged that lower dust grain, and as it comes back to equilibrium, notice that it spins a long time

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Mark Kushner: in this region.

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Mark Kushner: And so you get this quasi-stable state, where you have this, potential energy trough. Here, the ratio of omega X to omega Z is about 0.8. So we've got that trough. And they see this in experiments as well, and they didn't understand why you could get a dust grain that kind of just hung out here at an angle. What is going on?

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Mark Kushner: So, that was 2 dust grains. Now, let's go to 3 dust grains.

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Mark Kushner: And that makes our lives a lot more complicated. So, if we took our two dust screen simulations, and we looked at the configuration energy, of those two dust screens.

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Mark Kushner: The potential energy, configuration energy, would be given by these contours, and these yellow dashed lines are circling the minimum and the potential energy for the two dust grains for these various positions.

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Mark Kushner: And so you would predict that if you added a third dust grain, it would go and sit in that

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Mark Kushner: Minimum energy spot.

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Mark Kushner: But that's not what happens. When you put in the third dust grain, and you calculate the configuration energy, the place where the third dust grain wants to hang out is marked by these yellow diamonds.

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Mark Kushner: And so you notice that it's in between the two dust grains, and could be close to them, it could be down beneath them.

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Mark Kushner: And this does explain something that we see in experiments.

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Mark Kushner: We'll get to that on the next slide. But this, this, this, shows you visually.

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Mark Kushner: what the potential energy maps look like, if the third dust grain was at the predicted minimum energy location versus when the third dust grain is at the actual location for the minimum energy. And you can see that there's really big asymmetry

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Mark Kushner: If it's just sitting at its potential energy, and you get much, much stronger wigs, so it's not the lowest energy configuration from when it actually hangs out here.

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Mark Kushner: But in a lot of experiments, you actually see this. So the… at the end of, say, a two-particle chain, you'll see that the bottom ones kind of hang out in between the two chains. You see it here in this chain.

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Mark Kushner: And this is a completely different experiment, and what's different about this experiment is this is not a vertical chain, this is a horizontal chain that's confined in a trough.

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Mark Kushner: And so they have changed the, omega X and omega Z by the shape of their trough.

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Mark Kushner: And, you can see that once again, as it's unzipping into a 2D zigzag chain, you get these particles that hang out on the end. That's the minimum energy spot.

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Mark Kushner: Okay.

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Mark Kushner: So, we know that it's weird.

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Mark Kushner: And it looks like the wake's changed a lot, and there's a lot of conditions where this point wake model really doesn't work that well.

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Mark Kushner: So we said, well, maybe we can do better. How can we model this wake? Because if you notice, this positive energy wake is not really a point charge, it's this big, diffuse cloud of ions.

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Mark Kushner: So we're going to model the electric potential of the dust grain and the wake in two parts. We're going to go ahead and let the potential of the dust just be a shielded Yukawa potential.

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Mark Kushner: And one other thing is that we're going to define this coordinate system where the angle theta is given by the deviation from the electric field. So theta equals zero is going to point in the direction of the electric field, and theta equals 180 degrees is going to point opposite the electric field.

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Mark Kushner: And so now we want to model the wake, and for the wake, we're going to use a Gaussian.

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Mark Kushner: And…

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Mark Kushner: the magnitude of the positive wake potential is going to be set by, some fraction of the desk charge, so alpha times the dust charge. And then it also depends on how fast

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Mark Kushner: The ions are flowing, and that we characterize by the Mach, so the fraction of the sound speed of the ions in the plasma.

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Mark Kushner: So, as, as the mock number increases, these wakes get longer and longer and more diffuse.

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Mark Kushner: And this exponential, this has this lovely… this is the Gaussian part, it's this lovely expression here, and what we're looking at is X naught and Z naught kind of sets the location for the maximum of the wake, and these coefficients on the outside,

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Mark Kushner: depend on sigma X and sigma Z, and you can kind of picture sigma X as setting the width in the horizontal direction, and sigma Z as setting the length in the vertical direction, and then this theta is, a twist.

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Mark Kushner: That you get for your… for your Gaussian. So, if you just have one dust grain, it's always going to be perfectly aligned with the electric field, but if you have two dust grains, the wakes are going to twist towards each other. So then we have the other coefficients for B and C.

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Mark Kushner: So, here are the weights, that we get for the Dryad simulation, where we're actually modeling all of the ions are flowing at 3 different ion flow speeds. So this is Mach of 0.6,

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Mark Kushner: Mach of 0.9 and Mach of 1.35, and these correspond to electric fields, heath electric fields, of 4,000, 8,000, and 16,000 volts per meter. And you can see that the wakes get much more elongated.

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Mark Kushner: And then, if we fit them with our Gaussian wake model, this is what the analytic solution produces for the potential maps. And this is the difference between

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Mark Kushner: our wake model map and the Dryad simulation potential map. And so, they're… they're, very close, except in regions really, really close to the dust grains.

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Mark Kushner: And then we can do a similar thing for our two dust grain simulations. So this is what the Dryad simulation would give for the potentials, and this is the Gaussian wake that matched it, and then looking at the potential maps.

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Mark Kushner: Okay, so this was for one particular experiment. It seems to work pretty well, but what about other kinds of experiments? Does this only work in the sheath of a GEC conference cell, or can we apply it to other experimental conditions?

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Mark Kushner: So, on the International Space Station, there is a dusty plasma experiment. Dusty plasma experiment was actually the first experiment that was put on the International Space Station more than 20 years ago, and PK4 is the fourth iteration of the dusty plasma experiment.

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Mark Kushner: And this is what it actually looks like.

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Mark Kushner: You notice it looks like a neon tube.

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Mark Kushner: That's because it is a neon tube. This is a neon plasma, and what they do is, this is a DC-generated plasma, so you just have this really big direct current between the two electrodes.

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Mark Kushner: And if you just had a DC plasma, the dust would all flow one direction and then be lost from the experiment. So to get around that, it's a DC plasma that is

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Mark Kushner: flip-flopped at 500Hz.

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Mark Kushner: So, I just want to call that a DC plasma. Okay, but it's really AC.

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Mark Kushner: But at 500Hz, the dust particles can't move fast enough, and so they're just kind of jittering in space, and this is how you actually freeze the dust cloud in front of the cameras. Meanwhile, the ions can respond on the 500 Hz timescale, and so the ions are sloshing back and forth.

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Mark Kushner: Past the dust screens.

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Mark Kushner: And the interesting thing here is that the dust grains like to line up in these long chains.

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Mark Kushner: So, the question is, you know, what is going on that we get this change from a uniform dust cloud to these long chains?

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Mark Kushner: So what's going on is the wake is changing. In our GEC cell, the electric field pointed in one direction, so we got a wake just downstream of the grain. But in the PK4 experiment, the electric field is flip-flopping back and forth, so we get awake both upstream and downstream of the dust grain, and so we have a very different interaction potential. So when we look at this one.

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Mark Kushner: M.

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Mark Kushner: We thought that was all there is, but no, the plasma is doing weird things. So when you look at that beautiful, neon tube, you just see a uniform glow. But actually, PIC models of this DC plasma showed that it's not a nice static plasma. You actually have blobs of plasma. These are ionization waves.

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Mark Kushner: that are, you know, moving very fast. They pass a point, say, every 40 microseconds.

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Mark Kushner: So this is simulated emission in the PICC form… in the PIC model, and this is actual data taken from the experiment in the Baylor replica in the CASPER lab, where they used a very high-speed camera in a very dark room, running at about a

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Mark Kushner: 1,000 frames per second.

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Mark Kushner: maybe faster than that, maybe 100,000. I always, you know, you lose a couple of zeros there. And you actually see these blobs of plasma moving. So we really do have these plasma blobs. And the interesting thing, then, is that the electric field here, you can see you have these

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Mark Kushner: big electric fields, which can change by a factor of about 10. So here, everything is normalized to 1, which is the maximum for whatever characteristics. So the electric field and the associated flow of the ions changes a lot in these ionization waves.

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Mark Kushner: And the number density of the electrons and ions changes in these blobs of plasma.

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Mark Kushner: And there are actually points you can't tell on the scale, but there's actually a slight difference between the density of the electrons and the density of the ions, and that's what allows these big electric fields to exist between these blobs.

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Mark Kushner: So part of the thing is now we have these changing boundary conditions. We have to account for this changing ion flow.

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Mark Kushner: And the ionization waves that you get are different at different gas pressures. So Peter Hartman, who's our colleague from the Wigner Institute in Hungary, he does these PICC simulations and provides the boundary conditions at different gas pressures in the PK4 experiment. And so we wanted to look at what is the difference in the wakes at 40 pascal and 60 pascal.

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Mark Kushner: And so these are just static dust configurations with the dust at different distances.

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Mark Kushner: And looking at the potential in the system. And we can use machine learning, then, to figure out what are all the coefficients that define the Gaussian wakes, the symmetric Gaussian wakes, now, about each dust particle as a function of the particle separation.

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Mark Kushner: And these are the maps that we get, or my graduate student gets, after doing all of the matching and getting all of the coefficients. And these are the difference maps between the simulation results from the Dryad simulations and our analytic results. And notice that here.

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Mark Kushner: This is on the scale of, like, 15 millivolts, and the dust is at negative 15 millivolts, but remember, the dust surface potential is on the order of volts.

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Mark Kushner: And the differences here are much, much less than 1 millivolt that we're getting.

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Mark Kushner: Over here, so it seems to match pretty well. Well, that's great, but we trained this on data where all the particles are in a chain and at certain distances, so does it work if we extrapolate?

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Mark Kushner: And so here are results where we have single dust chains, but the particles are further apart.

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Mark Kushner: And we have 6 particles in the chain, and here's results where the particles are not lined up, but at a zigzag or two zigzag chains. And so, you can see that the potential maps are still pretty good. We're still matching to less than, say, 1 millivolt for most of this space.

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Mark Kushner: So, now that we know this anisotropic potential, can we model the interactions between the dust screens without modeling the ions?

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Mark Kushner: And so here's a little toy model of just about 8 grains, and the only forces here are the dust-dust forces that are these anisotropic forces that we learned, some Brownian motion, and then some gas friction to slow them down.

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Mark Kushner: And you can see, without any confinement forces, these particles actually line up in a chain.

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Mark Kushner: Great! We did something good.

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Mark Kushner: The 60… this is the 40 pascal data. The fun thing is that with the 60 pascal data, we don't really get very anisotropic interactions. They're a little bit more spherical. Those particles do not line up in chains. We cannot make them line up in chains.

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Mark Kushner: It's kind of interesting. And this is what you see in the real experiment, is you hit certain conditions, and suddenly you get chains, and then you change your conditions, and they go away. So…

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Mark Kushner: you know, these are the questions we're trying to answer. What are the conditions that lead to a change in the behavior and lead to a change in the structure? And the answer is, you can't just model the dust, you've got to model the dust and the plasma, and the back reaction… so the plasma affects the dust, but then the dust is actually also affecting the plasma in turn.

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Mark Kushner: So… There we have it. Our third law of violation is actually explained by the dust and the ions.

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Mark Kushner: And it matters very much how your dust grains are aligned with each other and aligned with the flow. And you have to look at this changing potential energy landscape as you're changing the position of the dust and changing the number of the dust, so it becomes this very nonlinear model.

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Mark Kushner: Which makes it really fun to keep turning more knobs and trying new things.

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Mark Kushner: And I would like very much to thank all of my collaborators. This has been going on for years, so collaborators have come and gone. I've had undergraduate students, I've had graduate students, I have had postdocs, I have collaborators at other universities, and, it's…

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Mark Kushner: truly been an interesting time, as everybody has added their own unique features to what we've been doing. So, thank you very much for your attention, and I'm happy to answer any questions.

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Mark Kushner: Thank you very much. Are there questions?

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Mark Kushner: Hi, Laura. Yeah, thank you for the fascinating talk. So, for the ion wake, does that only form in the plasma sheath region?

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Mark Kushner: So, the experiments on the space station are designed to be done in the bulk, so that is in the plasma bulk.

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Mark Kushner: What if the plasma is a DC plasma? It's, like, a real DC plasma? So if it were a real DC plasma, if you had a long enough DC plasma, yes, you would have dust grains flowing one way and ions flowing the other. And so, in that case, yes, you would get a

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Mark Kushner: one direction… unidirectional wake behind the dust screens. Okay.

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Mark Kushner: Yeah, thank you. Very graciously.

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Mark Kushner: Yeah, so with the dust crystals, I was wondering how they are constructed, and if you're able to calculate some sort of modified Madeline number that uses the Debye length.

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Mark Kushner: Okay, remind me what the Madeline number is, measure of. A functional crystal, it's sort of the potential that an individual charge in the lattice would feel. Oh, okay, okay, yes. So you can calculate local potentials, and it'll do that by perturbing a single particle and looking at the oscillations.

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Mark Kushner: And then trying to map that potential well. So there have been experiments done that. So the way that they actually form the crystal.

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Mark Kushner: is, usually, if you want to get a big crystal, you have your lower electrode, and you put this indentation on the lower electrode. Some people actually put a ring on top of the electrode. And then you simply drop the dust in from the top.

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Mark Kushner: and you let it spread out, and if you have multiple layers in your crystal, usually we want a single 2D crystal. What you can do is you can change the power slightly and drop the particles, and the particles on the bottom will become unstable and fall out of the crystal, and then you turn it back up and you check and see if your crystal is flat.

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Mark Kushner: And so you can do that a couple of times and get a single monodispersed layer of your crystal. Okay.

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Mark Kushner: Thank you.

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Mark Kushner: And then you have to have some way to perturb. So, the way to measure that potential, some people would use a laser to perturb a single particle, some would just sit there and watch the thermal jitter of the particles and try to determine a potential,

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Mark Kushner: And then some experiments will, like, just take two particles and maybe pull one particle back, and then let it go, so you've got the two particles interacting, and then try to back it out.

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Mark Kushner: It's not…

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Mark Kushner: It sounds easy, but then it turns out to be quite hard on all of this, because you can never just measure the potential, it's… you measure the force, which is the potential times the charge on the other particle, and we can't measure them independently.

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Mark Kushner: Yeah, I… in some situations, you had the mock number, which was higher than 1. I was wondering, is there an equivalent collisionless shock you can generate in these kind of…

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Mark Kushner: systems, because I didn't see it in the… Right, so this, mock… Yes.

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Mark Kushner: So there are shocks in dusty plasmas. I've never studied shocks in dusty plasmas. There's all sorts of waves and instabilities in dusty plasmas. So to enter the sheath, the traditional sheath theory is that for the ions to enter the sheath, they need to be traveling at least Mach 1, and that's defined by the BOEM criteria, which is the certain velocity you need to,

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Mark Kushner: Move from the bulk to the pre-sheath to the sheath.

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Mark Kushner: If the particle's moving faster.

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Mark Kushner: Yeah, then that sounds… so the…

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Mark Kushner: Do you know the answer to this one, Mark? Have you done any, shocks and dusty plasmas?

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Mark Kushner: Shocks and dusty plasmas, or shocks? Because, well, it's really the ions that are moving faster, yeah. And that's just not something that I look at a lot.

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Mark Kushner: But yes, there are… there are shocks and instabilities.

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Mark Kushner: The, surface potential on a, on a dust particle.

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Mark Kushner: surface sharing… Yes and no.

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Mark Kushner: So we assume that it's uniform, and of course, if you had a conducting grain, it would be uniform.

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Mark Kushner: And if the plasma is isotropic, you assume that it's uniform, because the currents are the same from all directions, but you can have… real dust grains will not be spherical, and so that's a lot of my research, is looking at irregular dust screens.

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Mark Kushner: They could be built up out of spherical bodies, or they could be flakes, and then you will have a distribution of charge over the surface. Or…

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Mark Kushner: If you have

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Mark Kushner: very small charges on your desk screens, like you're in space astrophysical environments where you only have one or two electrons. You know, if they're sitting on different parts of the surface, then, of course, it's not.

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Mark Kushner: Smoothly distributed.

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Mark Kushner: Is there work to incorporate magnetic fields into the dusty platform? Absolutely, and so that's what another of my grad students is looking at, because that changes the charging currents, depending on if the electrons and ions are magnetized.

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Mark Kushner: And in high magnetic field limits, it changes the charging, because it's no longer isotropic, it's coming from certain directions, so if you have electrons tied to the magnetic field lines, they can only come from, say, above and below. And so that changes the charging a lot. And then you would have uneven charge distribution if you have insulating grains.

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Mark Kushner: one back here. So, that, are they always equally spaced when they align vertical chin complex, or non-chin?

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Mark Kushner: They're close, but not exactly equal. And so a lot of that is we still don't understand… so these experiments are done in a glass box.

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Mark Kushner: And we don't really understand the sheath inside the glass box, because we have the sheath from the lower electrode, and then we have sheaths from the walls.

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Mark Kushner: And they're overlapping in a nonlinear fashion. And so often you will see… and then the charges, a dust particle that's in the wake of another charge will have a smaller charge, because it has increased ion current.

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Mark Kushner: And so, depending on where it is in the chain, you can get unequal spacing, and it depends very much on the chain and other conditions. How about the simulation result?

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Mark Kushner: Yes, in simulation results, depending on the boundary conditions, you might see a difference from the center of the chain to the outer ends of the chain.

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Mark Kushner: Thank you.

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Mark Kushner: Scott.

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Mark Kushner: Question, Jaya, as unneutral collisions.

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Mark Kushner: So I was curious, how are those implemented? So… Like, what is the… what's the gas pressure on them?

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Mark Kushner: Okay, so Zolt and Donko, pioneered what's called the null collision method, so that you're not having to do a Monte Carlo test on every single particle. Instead, based on a maximum collision rate, you say a certain fraction

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Mark Kushner: of the ions would have a collision, and then you take that fraction of the ions, and you do a Monte Carlo on those to determine what the collision… if they collide, and you use the collision cross-sections from the LexCAT process… LexCAT

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Mark Kushner: project, there we go. And so they have the ion-neutral collisions and the charge exchange collisions cross-section. So you look at the energy of your ion, do the Monte Carlo, come up with a collision.

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Mark Kushner: outcome.

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Mark Kushner: If you change the gas pressure in a couple of the… Right, so if you change the gas pressure, it will change that collision rate, and so the gas pressure goes into that collision rate calculation. What effect does that make?

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Mark Kushner: Mmm… So, yes, it… there will be some damping of the wakes, and also it changes the drift velocity.

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Mark Kushner: of the ions for a certain electric field. So the drift velocity is usually a function of basically E over N, so the electric field over the number density

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Mark Kushner: Of, of the plasma.

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Mark Kushner: Any last questions?

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palther1: Hi, I had one question, first, Dr. Matthews, it's a great presentation.

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palther1: I hope everyone can hear me fine.

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Mark Kushner: Have these same models been done using non-uniform dust? If so, how much of a factor does the variation in particle size have?

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Mark Kushner: Yes, we have done, simulations with non-uniform dust, like, let's say, dust aggregates. Oh, let's see.

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Mark Kushner: That's okay, it doesn't… yeah, we can close that one. And let me escape. I can show you some dust aggregates.

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Mark Kushner: Okay, this one doesn't show the charge. Here, this one will show the charge. And this also answers your question about the charge in a magnetic field.

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Mark Kushner: So, you can see, this is, the dust aggregates charging up, and here's with zero magnetic field, and you can see most of the charge goes to the extremities of that aggregate, and then this one is with a magnetic field that's pointing down at 4 Teslas.

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Mark Kushner: And so, what you'll see here is that these particles here are kind of shielded from the electrons, and so they don't collect as much charge. And so, ultimately, what happens is that changes the dynamics, so the particle will want to rotate because of these dipole moments.

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Mark Kushner: And so you can see this plot over here shows the charge on the individual monomers as a function of time. So you can see that there's this,

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Mark Kushner: time factor to the charge. And the particles tend to want to align such that the dipole… if you have an electric field.

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Mark Kushner: They want to align.

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Mark Kushner: Let's see, it might be easiest to do it this way.

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Mark Kushner: So that the dipole moment will point… so the net dipole moment is the red P right here, and it wants to point along the Z direction.

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Mark Kushner: And, you can also look at the principal moments of inertia of the aggregate, and the smallest principal moment is the one that usually is aligned with the electric field, because the charge wants to go to the extremities, and so the dipole moment points along the longest axis.

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Mark Kushner: So this will change your transport, you know, how does your aggregate rotate in the electric field and align, and how does that affect the drag and the flow and transport?

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Mark Kushner: With all particles having the same potential, is there a way to create an environment where they're… with different ratios of the density of the dust to the plasma, where you could have…

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Mark Kushner: ions, like, moving through a fluid dust? Yes, you can have different densities, and you can actually create environments where the dust do have different potentials, because if you have, say, secondary electron emission, small particles and large particles can then charge up to different potentials, because small particles, the electrons can escape in all directions, where for a large particle.

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Mark Kushner: it can really only escape from the closest side. So, there are some ways to get differential charging, and then you can get differential dust populations.

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Mark Kushner: Thank you very much. You're very welcome.

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Mark Kushner: Right, yeah, it didn't take off. So, in that case…

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Mark Kushner: My heart was still… was still moments within Miss Beasts whenever someone mentions sexual.

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Mark Kushner: Was I gonna have a strong, I always…

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Mark Kushner: Yeah, right. She goes to a different school.

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Mark Kushner: It's a traumatic experience to lose a kid like that. After writing the paper, it is traumatic.