WEBVTT 1 00:00:58.840 --> 00:00:59.740 Yes, 2 00:01:02.850 --> 00:01:03.720 yes, 3 00:01:32.650 --> 00:01:33.580 Mark Kushner: this is, 4 00:01:39.790 --> 00:01:57.149 Mark Kushner: and to get money, and our company is equally officially important. So that was the form so many for you in the last like couple of weeks. 5 00:02:41.200 --> 00:02:55.829 Mark Kushner: I don't know if you're working too much, so we don't have to be with us. We we have, 6 00:05:36.480 --> 00:05:42.000 Mark Kushner: so she is so she's sick, so she didn't want to come in person. But she is. She's watching from home. 7 00:05:42.220 --> 00:05:45.660 Mark Kushner: Yeah, Hi, Kathy, 8 00:05:46.070 --> 00:06:01.929 Mark Kushner: it's my great pleasure to welcome home. 9 00:06:01.940 --> 00:06:09.689 Mark Kushner: Uh since then he's gone to the Naval Research Lab since two thousand and twelve, where he now is the head of one of the Research 10 00:06:09.700 --> 00:06:27.359 Mark Kushner: section uh long as many research interests feature it. Quite, very uh plasmid diagnostics, low temperature class, and this developing new class of sources for hypersonics. Research. And of course 11 00:06:27.370 --> 00:06:34.429 Mark Kushner: it's always closest to my heart. I think i'll make slides pretty well. My, which is he's he's always looking for recruits for this on any part of the world. 12 00:06:34.460 --> 00:06:45.159 Mark Kushner: So I think you had that information supplier. Um! With that, said I. I think it's a great pleasure to have you here, and 13 00:06:48.660 --> 00:06:57.650 Mark Kushner: also a privilege to be 14 00:07:04.340 --> 00:07:11.290 Mark Kushner: thanks. Well, that's why we give this to you. Look forward to talk after you. You should make sure I don't love it first. 15 00:07:16.480 --> 00:07:20.229 Mark Kushner: All right. So everyone hear me. Okay in here. 16 00:07:20.510 --> 00:07:44.850 Mark Kushner: All right. Well, uh thanks, everybody. Good afternoon uh It's a pleasure to be back at my old stopping grounds. I remember sitting in this audience watching Mixy talks myself uh ten or twelve years ago now. Uh so it's fun to come and tell you a little bit about what we're doing in Nrl. Uh, you know, building better mouse traps, and in particular i'll be talking about work we're doing on hollow cathode and a new plasma diagnostic uh called the plasma impedance probe. 17 00:07:45.250 --> 00:08:02.940 Mark Kushner: So when I was in your uh shoes I did not know much about Nrl. I think my thought was, There's a Naval Research lab. I hadn't really heard of it. But so for your reference. Weird Washington, Dc. Uh Nation's capital uh just uh south of the city proper. Uh. So we're on the river 18 00:08:02.950 --> 00:08:31.840 Mark Kushner: Here you can look up and see the Washington Monument. Uh, and next year we celebrate our one hundredth anniversary uh. So right after World War, I uh no less than Thomas Edison, said that the Government should maintain a great research laboratory devoted to naval technologies, and that's naval, not just navy. We actually have both navy and marine for uh applications that we serve. Uh, but from those humble beginnings today we have about a billion dollar top line organization, 19 00:08:31.850 --> 00:08:44.560 Mark Kushner: one thousand six hundred ish scientists and engineers. Over half of those are Phds doing research all the way from ocean floor to far reaches of space. So quite a lot happening at Nrl. 20 00:08:44.570 --> 00:09:01.960 Mark Kushner: Uh, and in particular in our group, the Naval Center for space technology. Uh, we have a number of different. You know better mouse traps we've tried to build over the years. So dating back to the fiftys when uh Project vanguard. As part of Nrl. Put the first Us. Satellite in orbit. 21 00:09:01.970 --> 00:09:25.220 Mark Kushner: Shortly thereafter Eisenhower would say that space should be a civil endeavor and start this organization. You might have heard of called Nasa, and about half these folks would go up the road to form Nasa Goddard Space Flight Center, but the rest would stick around uh and are still there. Seventy-five years later, uh in the sixtys we put up the first surveillance satellite grab one uh turned out. That space was a good place to both look and listen, 22 00:09:25.230 --> 00:09:55.060 Mark Kushner: and the seventies and eighties The timation satellites became the precursors to Gps Today during the nineties, not on the slide deck the Clementine Mission to image the moon was the first to detect ice on the moon's surface and then over the past a couple of decades. We've been doing a fair amount of different satellite applications, the most recently robotic servicing of geosynchronous satellites working with Northrop kind of Darpa Mission. 23 00:09:55.070 --> 00:10:00.170 Mark Kushner: You know but typically not the second that gets transitioned somewhere else. 24 00:10:00.620 --> 00:10:30.519 Mark Kushner: And in our plasma pulsing group in particular uh me and Logan been there the longest uh Marcel and Jack Marcel is a another Michigan grad. By the way, Marcel and Jack started as postdocs for us during Covid, and are now full time employees. Uh Nolan just started with us last month, and then Mitchell is our new postdoc. He started just this summer, i'm going to be presenting work from Marcel as well as Eric to Hero in our Plasma Physics Division, our collaborators, as well as some of our many interns over the last 25 00:10:30.530 --> 00:10:43.809 Mark Kushner: a few years. Um! I'll be presenting some work from Matt. Hello to Mark, Margaret Mooney, Hannah Watts and Oregon, Mergusian, and i'll just say, uh I two noises in the uh Yeah, there is a 26 00:10:44.370 --> 00:11:09.919 Mark Kushner: So So that's us. Uh, that's nrl in a nutshell. Feel free to ask me more. But this talk is going to have two main thrusts hollow cathode and plasma diagnostics. And i'm going to try and start this from an application area and then work by way. You know, kind of more fundamental. Uh from how we design and deal with uh hollow cathodes, the properties that go into modeling them, and eventually how we even measure those properties with diagnostics. 27 00:11:09.970 --> 00:11:39.769 Mark Kushner: So Catholics are a great place to start. If you are a uh, someone starting up a new research lab and plasma, you can test them in like ten to one hundred times smaller and cheaper facility than a hall thruster. Um! It's this bright central spike in many of the pretty hall thruster pictures you see, and in particular they share a lot of the physics of their bigger hall thrust or brethren. So the basic principle it'll be relevant to know is that we'll flow gas down a thermionic emitter. We'll use a heater to heat that thermody on a committer up to a temperature where it can boil off 28 00:11:39.780 --> 00:11:47.149 Mark Kushner: will apply voltage to a keeper, which is an auxiliary electrode for ignition. That seems the cathode lit. 29 00:11:47.160 --> 00:12:06.610 Mark Kushner: Uh, and then, once the cathode is lit, it'll sustain itself self heating through the plasma, and we can turn off the heater. So nice, elegant little system. Uh, unfortunately, if you push it too hard, drawing too much current, all right, too low a mass flow rate. Uh, you can drive instabilities in the plasma, and those instabilities can accelerate some ions that'll sputter your keeper over time. 30 00:12:06.620 --> 00:12:15.259 Mark Kushner: So in the worst case, uh Nasa, after fifteen thousand hours. So their keeper completely disappear. On the end-star greeted. I am thruster 31 00:12:15.270 --> 00:12:45.239 Mark Kushner: um, And you know there's recently some suggestive modeling work that uh to Jpl that pointed to a region in the near field zoom of the thrust of the cathode, where there were sharp gradients and plasma and neutral density that they thought might be triggering the instability. So we had an interesting idea. We thought maybe, could we broke that single keeper orifice into many, so one into many. We spread out the plasma, spread out the neutral efflux from the keeper, and maybe suppress that instability. 32 00:12:45.250 --> 00:12:51.849 Mark Kushner: Just some hand. Wavy reasons. We thought this might work, but it's also just a nice toy system to play with. 33 00:12:52.290 --> 00:13:08.340 Mark Kushner: So we went and tested some of these new designs. Um! Here is our cathode. You can see the anode here that we tested to a big cylinder. This is our about one meter size plasma test facility. It was our main test chamber up till earlier this year how we have another comparable size, 34 00:13:08.350 --> 00:13:23.710 Mark Kushner: and in this we tested three different designs, you know. So a single whole uh six and a twelve, and we keep the area constant over these same amount of neutral gas. Get out, and what we see just before and after testing, you know, went through some test matrices, 35 00:13:23.720 --> 00:13:42.649 Mark Kushner: you know the single whole one, you know. We started them all polished and shiny, This one Now it's from a hand bombardment, but the multiple whole cases actually look black now. Not only did they not scour away, they actually collected backs, butter from graphite and the facility. So they seem to a road less which is promising. 36 00:13:42.840 --> 00:13:56.359 Mark Kushner: And if we look at performance uh, so i'm going to show versus argon flow rate here on both these access. Ten to thirty Sccm. Our Anode voltage was lower in most cases with that multiple or this case, and uh, our 37 00:13:56.430 --> 00:14:13.359 Mark Kushner: oscillation magnitude. So the rms of our current that we were drawing steady state was fifteen. So this is Rms. We saw it lower, almost across the board with the multiple, and in particular we delayed the onset of a transition by about thirty or forty percent flow rate, so uh that 38 00:14:13.370 --> 00:14:29.840 Mark Kushner: at that instability on Set Point at eighteen Sccm. We were at lower power. Uh we supplied the current more stably, and we all said great. We did something good that it kind of worked. And now we only need to know why, uh, exactly at more than a hand wavy level. 39 00:14:29.850 --> 00:14:44.469 Mark Kushner: And so, practically speaking, a single keeper or office. All you have is diameter to worry about. How big is the whole. But now we've opened up a whole can of worms, of how many holes should there be, and how big and where, and the design space kind of explodes. 40 00:14:44.480 --> 00:14:51.119 Mark Kushner: So Marcel Georgian came in uh in early two thousand and twenty to help try to put this on a firmer footing. 41 00:14:51.350 --> 00:15:18.459 Mark Kushner: And so Marcel's first work, saying, Well, let's systematize that investigation, said You know. Let's look at three different configurations, a single and a couple of multiple orifice cases. We'll scoot the anode down a little bit. We'll put some probes in the plume uh lang, your probe and miss a probe and ion saturation probes, and we'll use these to measure the fluid forces that are actually happening uh in the discharge. So we'll measure our electric and our pressure forces and infer our drag forces that we're seeing, 42 00:15:18.470 --> 00:15:29.770 Mark Kushner: and so that ends up. That's an Ohm's law formulation. It's a fluid approach, and what he end up seeing and uh see that I know. Yep. So in this paper that he put out last year, and she applied for his 43 00:15:30.380 --> 00:15:49.700 Mark Kushner: end up seeing for the single office case. I'm going to show two sets of plots. Um! They're the different vector forces, so electric pressure and drag forces and the radial direction and the axial. So this is ultimately a vector thing. But we're trying to split it up and show the two pieces of the vector without like really query, arrow plots. So 44 00:15:49.710 --> 00:16:02.119 Mark Kushner: So we look at the electric field magnitudes. Um in volts per meter again your domain here. This is the edge of your keeper. So actually back up to the domains clear. Uh, we're looking at this region here, right? So 45 00:16:02.560 --> 00:16:15.239 Mark Kushner: This is the keeper edge, and that's the keeper orifice. And then about, You know several tens of millimeters downstream. Here is the edges of the Anos we're looking at that gap between the cathode keeper and where the anode starts where we could fit a probe. 46 00:16:15.250 --> 00:16:28.709 Mark Kushner: And we see, you know, some significant or radio electric fields uh not too much in the pressure area, and then significant drag effects. So strong radio, electric and drag forces in the single or this case, 47 00:16:28.720 --> 00:16:40.579 Mark Kushner: we shift into the multiple orifice case. Uh, you can see now the shape of the keeper here has changed to show you where the holes were. Uh, you know, similar. We have radial forces, uh, and both 48 00:16:40.660 --> 00:16:52.590 Mark Kushner: electric field and drag, and our kind of takeaways are. We are still seeing those effects and electric and drag forces. But now we're also seeing a strong drag component in the axial direction. 49 00:16:52.600 --> 00:17:01.709 Mark Kushner: And as we go to our farthest out case, i'll flip through these a little faster. We've moved the orifices so far out, we've actually reversed the electric field direction. We've 50 00:17:01.790 --> 00:17:04.900 Mark Kushner: sourced all of our electron current out here. And there's kind of a 51 00:17:04.960 --> 00:17:16.689 Mark Kushner: field to refill the central region. Um. So the electric field is reversed there. The drag has been reduced, and maybe the biggest thing that we see is an axial pressure contribution dominating the plume. 52 00:17:16.700 --> 00:17:36.719 Mark Kushner: So i'm kind of showing this to show how we initially approach trying to break down force wise what's happening when we're seeing the lower potentials in the initial cases. I will say we we sort of broke the system, because you know the voltage trends we saw initially, Don't actually hold um for performance across these cases. But we can still talk about this force picture 53 00:17:36.730 --> 00:17:52.640 Mark Kushner: uh when we run a cathode, we don't actually control the electric field. We source so many amperes of current, and we let the power supply provide the volts it needs to overcome those the drag and pressure forces and make them balance. Um. So electric fields really a response, 54 00:17:52.650 --> 00:18:01.820 Mark Kushner: and what we saw is going from, You know the single orifice case to a wider and wider separation, moving ourselves from an electric field to a pressure-dominated regime 55 00:18:02.010 --> 00:18:06.880 Mark Kushner: and so we increase pressure, and reduce drag. As we moved in this direction the 56 00:18:07.150 --> 00:18:23.390 Mark Kushner: So So that's kind of a basic picture. And I wanted to show that to just show conceptually how these different forces are interplaying in the plume. Uh, but what Marcel then went and did next in our group was to try to take this another step deeper and focus on those drag forces in particular. 57 00:18:23.400 --> 00:18:41.180 Mark Kushner: So you know we we have this. You know some information about forces. We'd like to learn to manipulate them for future designs to make this better. Um. And so we're going to talk a little bit about how those forces actually get measured and implemented into cathode codes, which is ultimately where we do that design one. 58 00:18:42.230 --> 00:18:49.579 Mark Kushner: So i'm gonna go back to the cathode drawing board here. And you know we have our Catholic picture you saw before 59 00:18:49.680 --> 00:19:08.189 Mark Kushner: inside that cathode. Three fluid models do pretty well. Electron fluid Ion fluid neutrals. Uh we can describe what's happening internally. Um. Pretty well, but as you move out into the plume region. That picture sort of breaks down. So here I'm. Showing as a function of axial position the plasma potential, 60 00:19:08.200 --> 00:19:26.910 Mark Kushner: and that three fluid result, you know, compared to the data and circles and triangles, you know. Kind of doesn't do such a hot job out here. Um, that's maybe not surprising. It. It was suitable in a very collisional regime inside the cathode, and it's not going to be outside here where it's much less collisional and probably more collisionless 61 00:19:26.920 --> 00:19:36.520 Mark Kushner: um. Nevertheless, you can add in some artificial electron resistivity and get those models to match up better. So the question is, How do you do that? 62 00:19:36.530 --> 00:20:00.989 Mark Kushner: Uh, this is pretty well understood what mechanisms are happening here. Uh, this guy named Ben Jones did some work uh in the past ten years or so, and the technique was to look downstream of a cathode with a a pair of probes, and I saturation and use a dispersion relation to understand what kind of waves are present in the system, and it turns out to line up very nicely with an I and acoustic wave description. Um, So 63 00:20:01.000 --> 00:20:22.779 Mark Kushner: you can use that description to describe with. You know much math that ensues, for how this inverse land out damping effect takes place, you distort your distribution function shows up as this effective brag force. Um, and you get a effective collision. Frequency will come back to that. That's much much higher than that. Um, You know that that lower model that we showed in there, 64 00:20:23.010 --> 00:20:35.700 Mark Kushner: and you know, so we can. We can push things up. Um. So let's zoom in on that a little bit we talked about this picture. We have a pressure gradient that's going to push electrons from the cathode to the anode. 65 00:20:35.960 --> 00:20:56.509 Mark Kushner: Uh. We have some drag force due to this iron acoustic turbulence that slows them down, and then we have an electric field that's going to come in to conserve our discharge current. But you know, require as much more voltage as it needs to. And so this next section kind of follows a recently submitted paper of ourselves that just went out earlier this month, 66 00:20:56.520 --> 00:21:09.309 Mark Kushner: and so i'll do my best to represent what Marcel described here, because I wanted to talk about this uh this force balance, and in particular trying to incorporate the pressure. And this collisional drag term here. 67 00:21:09.860 --> 00:21:14.230 Mark Kushner: The problem is that this is a fluid description, and that turbulence is a kinetic effect, 68 00:21:14.560 --> 00:21:23.530 Mark Kushner: so that kinetic effect ends up getting treated with a Boltzmann formulation uh where you've got, you know, some collisional term here, and 69 00:21:23.540 --> 00:21:34.659 Mark Kushner: you can do a usual routine of adding a perturbation which has a waveform and doing a Fourier decomposition and time average to get. You know your time average quantities out of that. 70 00:21:34.670 --> 00:21:44.180 Mark Kushner: But that wave uh ends up, adding a new term, even though they're oscillatory effects there's a time average bit that shows up, and this is called the quasi-inear theory. 71 00:21:44.250 --> 00:22:12.729 Mark Kushner: And if you further integrate uh that first moment of that, you end up with an expression for your electric force in terms of density and potential also uh density and electric field oscillations, I should say. But we're going to measure the plasma potential. So I I included this kind of busy pot, just because I really wanted to get to this point to say Um, what we're actually going to measure, to look at the kinetic side of this and and complement to the fluid we did earlier. We'd really like to know. How does that fluid picture match up with the kinetic side? 72 00:22:13.510 --> 00:22:14.880 Mark Kushner: So, to do that 73 00:22:14.890 --> 00:22:44.880 Mark Kushner: take a very similar setup to what we did before. With the fluid approach, micro density, temperature, and plasma potential um and those weren't so hard. But for this quasi-linear theory. We actually need these density oscillations and the plasma oscillations on the potential measured synchronously. So we can get the phasing between them. So we can understand the transport contribution so to do that. Marcel got out his jeweler's loop and made this nice little pro. This is a quarter inch diameter alumina. This is actually an sem tip that he adapted to use it, 74 00:22:44.890 --> 00:22:54.630 Mark Kushner: and a missive probe, which is kind of cool. So that's a lab. Six crystal at the tip of your usual hairpin wire, and it helped it last a lot longer in the chamber until we still broke it. 75 00:22:54.640 --> 00:23:21.440 Mark Kushner: Um, but and then You've got the the makings of a triple probe in there, too, with your floating probe and your ion saturation pro along with your plasma potential. So we're able to get these different quantities out. The four your amplitudes and the phase delay we needed to get at that kinetic formulation of what this drag force is, and we're going to look at the two and see how they line up, and you know, rest assured it turns out they lay line up pretty Well, the problem is later shoehorning back into a fluid approach. 76 00:23:21.450 --> 00:23:38.510 Mark Kushner: So Marcel measured all this uh along axis of our cathode uh in this setup here. So you can see we now have a mesh anode to let the neutral gas out better and not build it up inside you some operating conditions. So before we did two d. Now we're really just going to do on d uh kind of simplify the picture, 77 00:23:38.850 --> 00:23:55.209 Mark Kushner: and we can indeed. Um, i'm looking at the product here now of our density and potential oscillations together. Uh, we can plot our Fourier amplitudes. We can look in the right frequency, resume regime for the iet to be expected to be taking place, you know. Maybe 78 00:23:55.220 --> 00:24:16.349 Mark Kushner: half a megahertz to five megahertz ish i'd have to look and see exactly where he drew the bounds. Uh, we also get the phasing. There's a little bit of phasing offset, because our probes aren't perfectly aligned. Um. It's tough because they're small, and where they fit in that aluminum tube. Um. But Marcel is able to do a simple, fitting routine to try to correct for that. So we get a phase delay we can look at, 79 00:24:16.360 --> 00:24:17.350 Mark Kushner: and 80 00:24:17.690 --> 00:24:46.079 Mark Kushner: I'm not going to belabor this slide so much, just showing that you know the Ohm's law picture looks very much like it did before. Uh, you know we could dig into it and say, you know, there's an electric field that pulls the electrons out as we move down the axis till eventually switches sign uh about one hundred millimeters downstream. The pressure is always pulling things out. Stuff happens sharper near the cathode than farther away. This is all very consistent with the plots we saw before. Um so similar similar uh looks like I initially had some 81 00:24:46.090 --> 00:24:47.870 Mark Kushner: animations there. 82 00:24:47.950 --> 00:25:00.679 Mark Kushner: What I wanted to show actually is the comparison between the fluid formulations and the kinetic. Because this is ultimately getting these different ways of looking at the problem. To agree is how you try to make progress on designing better devices. 83 00:25:00.690 --> 00:25:19.159 Mark Kushner: So i'm going to show drag on the uh y-axis position on the x-axis in our cathode down the axis uh and down here I've got our fluid version where we're inferring the drag as the difference between our uh pressure term uh and our electric field term 84 00:25:19.570 --> 00:25:25.799 Mark Kushner: up here we have the kinetic version um, and in particular this is assuming no ion drift. 85 00:25:25.940 --> 00:25:41.880 Mark Kushner: So if you remember, this is a the idea of this ion acoustic stuff, is It's a streaming instability. It's electrons whizzing by the relatively stationary ions, and you know, kicking up a potential wave in their wake that the ions then experiencing. So it's the relative velocity we need to consider, 86 00:25:41.890 --> 00:25:54.590 Mark Kushner: and the ions aren't actually perfectly still. So you can make some reasonable assumptions to try to get at the Ion dri, and when you correct for that uh it, it brings everything into quite a bit closer agreement. Um, you know, throughout more of the plume. 87 00:25:54.770 --> 00:26:03.820 Mark Kushner: So maybe our takeaways here are excellent agreement near the cathode within our error Bars, which are, you know, large, because probes have, you know, reasonable uncertainties, 88 00:26:03.830 --> 00:26:22.499 Mark Kushner: and you know, improved agreement, at least downstream. Uh, when you account for that, I on drift. So this is this is good. It says that the picture that we have for what is causing these kinetic effects seems to give you estimates that are, you know, in line with what you get when you just use fluid to measure the other parts 89 00:26:22.540 --> 00:26:24.809 Mark Kushner: and look for what's missing. So it 90 00:26:24.880 --> 00:26:32.090 Mark Kushner: has a lot of measurement and a lot of calculation to say that we think we probably have the right approach uh, which maybe was not in doubt before, 91 00:26:32.230 --> 00:26:36.459 Mark Kushner: but really where we want to go with this is, then Marcel is still trying to figure out 92 00:26:36.830 --> 00:26:51.440 Mark Kushner: a good way for how once you got these, do you really shoe Horn in a good method to get what you just measured laboriously with your time resolved probes synchronously between potential and density. How do you shoe horn that into this fluid 93 00:26:51.450 --> 00:27:03.189 Mark Kushner: case, where you have a product of an electron velocity and some anomalous collision frequency. And so that anomalous collision frequency is often what we really kind of care about in this field 94 00:27:03.880 --> 00:27:07.389 Mark Kushner: uh that one right there. And so it's actually, 95 00:27:07.630 --> 00:27:14.239 Mark Kushner: maybe at the tail end of our talk. I'll, you know, mention some ideas we have to try to more directly. Get at that funny quantity. 96 00:27:14.310 --> 00:27:41.849 Mark Kushner: Um! I should pause to make a brief note. We Marcel did also try to get at our velocity terms. And this work um, and estimate the electron mach number. And what he found was that, you know, you could pretty confidently say we were in an iron acoustic regime near the cathode, up to a certain point where he thought it might be crossing over into a different regime, where you know. Maybe that explains some of the larger divergence we see downstream. Um, So i'm not going to belabor that point too much, because I wanted to end 97 00:27:41.860 --> 00:27:50.969 Mark Kushner: at this final piece to show how hard it is to get some of these different terms to line up and models. So this is a plot of that 98 00:27:51.030 --> 00:28:05.879 Mark Kushner: collision frequency term, And I remember hearing a lot when I was in grad school about these collision frequencies are made up, and this is the problem. And, In fact, they're a lot less made up now than they were then. Uh, but it's still hard to link them together. 99 00:28:06.020 --> 00:28:15.059 Mark Kushner: But you have this classical collision for classical meal on where you get this cool and collision frequency electron to I on down here. And then we're going to look at a bunch of other different ways to do it. 100 00:28:15.070 --> 00:28:30.129 Mark Kushner: This is what we get with that Ohm's law formulation, and so uh, you know, rapid fall as you leave the cathode, but you know it's still higher than the classical case by a lot Uh, this is what we get with that kinetic approach. So this is the you know agreements. I was just showing 101 00:28:30.140 --> 00:28:44.729 Mark Kushner: this hump is actually caused by the electric field going through zero turns out that dividing by zero causes problems and data so ignore that. Fill that in with your eyeball goes across. Um! These are actually two other cases where 102 00:28:44.740 --> 00:29:08.859 Mark Kushner: he tried to calculate these quantities, using just one pro, which is maybe a more typical way. People would do it when they don't go full hog and try to measure everything synchronously and with different. You know what he thought were reasonable assumptions. You get pretty wildly varying estimates. Those are described more in the paper. I'm not going to go into them. The last bit is uh this sag dev model, which is a a saturated uh growth model that ends up showing up in um 103 00:29:08.870 --> 00:29:28.220 Mark Kushner: how this currently gets shoehorned into our fluid codes and the the takeaway I really want to get you here is first measuring all these quantities is experimentally laborious. You are all grad students majority of you. So you know that experimental labor often falls on you. Thank you. Uh, and and also that you know that's like a 104 00:29:28.230 --> 00:29:46.469 Mark Kushner: fifty to a hundred times difference on this log scale between some of these different methods here. Um. So there are certainly large variations in this anomalous collision frequency. I would say that this, maybe to me, is a motivation that I always wish I had better plasma diagnostics to at least cut the error bars on my measurements. 105 00:29:46.640 --> 00:29:56.329 Mark Kushner: But nevertheless, for this first half of my talk I want to leave you with the following: Takeaways first understanding: Anomalous electron transport is important, 106 00:29:56.340 --> 00:30:20.859 Mark Kushner: and maybe I should have added, not trivial. Uh, it's really important, for you know our cathode lifetime and performance prediction, and we'd like to know. Our devices can last for thousands of hours, And it's also, you know, important in other plasma systems. I don't really think it's too far a stretch to say understanding how the electrons move, and they can find or not, is kind of fundamental In just about every plasma application that we have. 107 00:30:21.010 --> 00:30:26.609 Mark Kushner: Uh, the measurements look like this fluid, almost picture a fluid onslaught picture. 108 00:30:26.750 --> 00:30:31.859 Mark Kushner: It's pretty well represented by the kinetic quasi linear theory, so I I think it. 109 00:30:32.260 --> 00:30:46.050 Mark Kushner: We experimentally measured our electric and pressure forces, we inferred right. We then go and try to measure, drag as directly as we can these probes, and see how it matches up, and we get pretty good agreement. Uh. But 110 00:30:46.090 --> 00:30:52.720 Mark Kushner: casting these into this anomalous collision frequency um, we get a lot of spread, and so it 111 00:30:52.940 --> 00:30:59.590 Mark Kushner: at least to me it's not yet clear how fast to shoe horn this effect into the fully fluid framework. 112 00:30:59.640 --> 00:31:00.630 Mark Kushner: Uh, 113 00:31:01.180 --> 00:31:02.290 Mark Kushner: maybe 114 00:31:02.430 --> 00:31:04.139 Mark Kushner: the answer is 115 00:31:04.280 --> 00:31:14.509 Mark Kushner: better diagnostics. If you create a better microscope to look at the world. Um. New physical insights will ensue. And so that is maybe the motivation for the second half of my talk. 116 00:31:14.980 --> 00:31:16.180 Mark Kushner: So 117 00:31:17.010 --> 00:31:21.769 Mark Kushner: part two is the plasma impedance probe. And uh, 118 00:31:21.990 --> 00:31:26.709 Mark Kushner: I think everyone's familiar with the language pro in this room. Oh, no, Oh, no, I've 119 00:31:27.020 --> 00:31:28.590 Mark Kushner: oh, thank goodness! 120 00:31:29.200 --> 00:31:43.100 Mark Kushner: So I think everyone familiar with the line, your pro, the the original plasma diagnostic this. You know. It's over a century old, probably by now, but it's very elegant in its simplicity. You shove a wire into plasma. You sweep through the bias voltage, 121 00:31:43.110 --> 00:32:01.619 Mark Kushner: and you can get out of that. You know some estimates of many of our plasma properties. In particular, we use the flux to that uh probe to compute a density uh, really that flux as a function of potential and density and temperature, and I guess probe size and uh species. And 122 00:32:01.630 --> 00:32:13.339 Mark Kushner: you know the scroll is getting longer. It's affected by beams and your distribution function. And is there a magnetic field, and how big was the sheet compared to the probe? And you know the number of effects you have to consider actually gets long. 123 00:32:13.730 --> 00:32:19.259 Mark Kushner: But in principle it's really simple uh hardware. Wise. You just pay for it in the complexity on the back end. 124 00:32:19.580 --> 00:32:26.340 Mark Kushner: And if you ask most people who work with these. I often hear a sheepish kind of factor of two, 125 00:32:26.350 --> 00:32:44.399 Mark Kushner: for when people say how accurate is the density measurement, you get out of it, certainly you see, tighter numbers quoted that. But look, they are often statistical uncertainties, they say, given how many measurements I made in my errors on my measurement circuit here is, statistically my cloud of uncertainty. Not where does that relate to the true value underneath? 126 00:32:44.480 --> 00:32:45.550 Mark Kushner: Um, 127 00:32:45.760 --> 00:33:02.909 Mark Kushner: if you think about most things that we measure with high degrees of precision. They often have some mis traceable um calibration. It's often timing and length, you know, speed of light and interferometry, and this lets you build up and bootstrap yourself to a bunch of other fundamental quantities. So 128 00:33:02.920 --> 00:33:27.869 Mark Kushner: uh, this actually a picture of the standard kilogram which I was sad to see, was retired in twenty, nineteen Um! And now they just measure that with, you know, planks constant that am pure balances, too. Um! But there's no such thing as a like standard kilogram. There's no such standard candle of a ten to the ten per cubic centimeter plasma that you can pull off a shelf and put your probes in and say, Oh, good! I got the right answer. My probes right. I can go measure other things. 129 00:33:27.880 --> 00:33:37.080 Mark Kushner: Um, and that's unfortunate. And So what we wonder is, could you maybe use the plasma frequency instead as a timing signal to get at this measurement 130 00:33:37.090 --> 00:33:56.009 Mark Kushner: so plasma frequency, you know I thou shalt have a plasma, and it will have free charges, and I will reach out. I will pluck an electron and let it vibrate. And you know the frequency at which it vibrates is related to that surrounding uh plasma density. And you can. You can derive that um, and get at, you know, some fundamental quantity. 131 00:33:56.040 --> 00:34:24.799 Mark Kushner: And so this impedance pro we're showing here a palette that went up to Space Station in two thousand and nineteen, with nrl's uh plasma impedance probe on it. It's about this big big dipole antenna. This one was designed to get um up to ten to the eight per cubic centimeter density, which is, you know, about one hundred. Megahertz is plasma frequency, and it would do that maybe ten times a second. So that's actually still up there getting good data. Um. But looking at that, I really wonder could you use them for higher density? Plasmas? 132 00:34:24.810 --> 00:34:38.100 Mark Kushner: Yeah, could you get something like ten to the ten at least maybe higher. And could you get like hundred kilohertz? Is time resolution. That'd be great, too, because all thrusters breathe, You know, you know, ten, twenty kilohertz I'd love to look at that. 133 00:34:38.110 --> 00:34:47.710 Mark Kushner: And uh, it turns out that's that's a big focus for a lot of the other work we've been doing in our group for the past couple of years. It's just trying to develop this fundamental diagnostic and see how far we can push it. 134 00:34:48.370 --> 00:34:49.620 Mark Kushner: So 135 00:34:49.870 --> 00:34:58.080 Mark Kushner: am Peter's. Pro. I sort of claimed it did things I'm gonna try a little bit to motivate, if not completely explain how it does things uh 136 00:34:58.090 --> 00:35:15.449 Mark Kushner: at the plasma frequency your plasma impedance, so complex resistance. Um complex quantity linear resistors, I put in V, and I get I right at the same time complex, you know, impedance, I put in V, and I get I a little bit later or a little bit earlier. Uh, but the impedance is complex quantity 137 00:35:15.460 --> 00:35:21.450 Mark Kushner: at the uh plasma frequency, or in A. B field. The upper hybrid frequency is going to have this nice poop peak 138 00:35:21.490 --> 00:35:31.209 Mark Kushner: and the impedance magnitude, and it's also. It's a resonance. So It's going to have a nice ph phase shift in the um imaginary part. Uh sorry. This is the phase um. So 139 00:35:31.890 --> 00:36:01.130 Mark Kushner: choose your desired way to represent complex things, Cartesian with real and imaginary polar, with magnitude and phase, I will switch back and forth. So apply coordinate corrections appropriately. Uh, but anyway, just is you get two shots in this impedance spectrum to figure out what your upper hybrid or your plasma density, your your plasma frequency is, and if you know your B field. You know your density to these relations, and the way we actually do it is we put the dipole antenna, or sometimes a model antennas will see in the plasma, 140 00:36:01.140 --> 00:36:08.339 Mark Kushner: and we excite it, and we pick off um the current voltage components with transformers. So So this 141 00:36:08.350 --> 00:36:24.670 Mark Kushner: is a new-ish diagnostic certainly being applied to higher density. Plasmos, Their questions are always Is it accurate? That's like the hardest one, so we'll get to that at the end. Uh, can you measure a useful density range we'll show. Yes. Can you get good spatial resolution and time resolution? Um, 142 00:36:24.680 --> 00:36:34.859 Mark Kushner: yes, on time we'll see on space. Can you it cheaply. Certainly not yet. Sorry still working on that. Uh, but we're gonna go through those over these next few slides. 143 00:36:35.070 --> 00:36:36.810 Mark Kushner: So first um! 144 00:36:36.860 --> 00:36:48.819 Mark Kushner: You may have experienced this already, but certainly at at like the grad school level. Rf. Is just a magical black box like things happen, and it doesn't match your physical intuition. Um, practically speaking, uh 145 00:36:48.830 --> 00:37:02.769 Mark Kushner: calibration is really key in these systems. So choose an intended design that you might like this is a dipole. These are the two legs of our tiny little dipole. Here's an Sm. A connector. Here's our uh penny for scale a Lincoln, and 146 00:37:02.780 --> 00:37:11.540 Mark Kushner: what you're gonna do is you're gonna take that antenna, and you're gonna hook it up to some line like going through your vacuum chamber, or whatever to measure your plasma and hook it up to a Dax system. 147 00:37:12.090 --> 00:37:28.289 Mark Kushner: The plasma frequency uh is going to have a certain behavior where uh, you know, it causes a peak in the impedance. That's what you see way up here, but through your circuit board here through your line, everything else, your data acquisition system won't. See that? So you have to calibrate it. 148 00:37:28.300 --> 00:37:47.589 Mark Kushner: So here we're just showing a board where we put um little smas with a fifty Ohm resistor and an inductive piece and a capacitor piece, so we could put this on the end, and then we could calibrate. What do Rl and C loads look like at the end, too, and see if we could predict a combination Rlc. Circuit. And so your goal is to move what you call a calibration plane, 149 00:37:47.600 --> 00:37:53.230 Mark Kushner: where you know what things look like in terms of impedance as close to your plasma system as you can. 150 00:37:53.450 --> 00:38:08.200 Mark Kushner: So we start doing that. Uh, it turns out we run into problems. We calibrate all the way up to the end of that. Sm. A. But I can't stick in Sm. A. Down here. I need my antenna, and so this piece. This is a little transformer called a balance. It transitions your 151 00:38:08.210 --> 00:38:21.739 Mark Kushner: balanced dipole to your unbalanced grounded coax, and this thing has its own Rf. Properties, you know they call them S. Or scattering parameters. It will uh transmit some. It will reflect some, and 152 00:38:22.280 --> 00:38:25.010 Mark Kushner: you have to somehow get rid of that effect. 153 00:38:25.020 --> 00:38:44.389 Mark Kushner: It turns out uh knowing those s parameters, you can analytically apply a correction on top of the calibration you've already done, and to check your math uh what we end up doing was just to make sure i'll come back to this resonance. Id in a minute. We We checked by building a back to back version of these, and confirming we could remove two of them. Then we felt like confidently we could remove one. 154 00:38:44.400 --> 00:38:57.350 Mark Kushner: But what that Ballin did with that extra stuff, that extra impedance effects was, it would create a nice little resonance in our impedance that wasn't there in the ideal model that we had, residents are terrible to try to get out with calibration, 155 00:38:57.360 --> 00:39:14.209 Mark Kushner: because you're trying to subtract two large numbers and look at the small number that's left over, and it is a recipe for not goodness. So that was lesson. Number one was, you know. Try to avoid resonances in your frequency, range of interest, and the balance is one place it could happen. 156 00:39:14.430 --> 00:39:43.279 Mark Kushner: Uh, for the next thing I apologize because I I should. The color schemes here, and i'm going to again. I'm showing the same data I did, but now it's up here with some more stuff. We had our balance. We had the ideal case uh we deemed it. We remove that balance, and it made the blue thing look like the orange thing which kind of has the right shape now. Um, and you can. We could also separately see if we could move the ideal green impedance down to a fit, and that's the red, and that difference turns out to be capacitance. 157 00:39:43.290 --> 00:39:58.509 Mark Kushner: So um! This is the same data you saw up here. But now, instead of stopping at a thousand Megahertz, it goes all the way up to one thousand five hundred. You can see that these ideal curves really just had their resonance way farther downstream, and the balance moved it up. 158 00:39:58.560 --> 00:40:01.489 Mark Kushner: So this is important for two reasons. One 159 00:40:01.520 --> 00:40:05.530 Mark Kushner: we could see that that parasitic capacitance drove a five hundred Megahertz shift, 160 00:40:05.540 --> 00:40:33.479 Mark Kushner: so as we'll see in the next measurement, like not correcting for that made the measurements garbage, so the next measurements will be garbage. But there will be data More importantly, looking ahead to using this someday on, you know, dense plasma, This is kind of cool that the line effects moved. A resonance uh the capacitance moves. The resonance to lower frequency. Lower frequency is actually a lot easier to handle in Rf. And this means that maybe the upper limits of the density ranges. You can interrogate with this kind of diagnostic 161 00:40:33.490 --> 00:40:55.270 Mark Kushner: aren't really limited by your Rf. Hardware, maybe, uh what you know. A resonance at the plasma frequency looks like way down in some dense, even fusiony plasma could, through the line length, be projected down to some lower frequency. You can access with cheap hardware. So anyway, we'll come back to this extra capacitance problem and a couple of slides uh I got fifteen minutes left, which feels like right if you get through. Oh, yeah. 162 00:40:55.280 --> 00:41:19.380 Mark Kushner: So this uh we thought we're good enough. We've. We've got some pieces. Let's see if we see anything plasma like with this diagnostic. So we took um our cathode that you saw before. Put a magnetic field on it to extend the plasma which the density downstream, and then we put our pip and our lang, your probe way down there, so you can see that experimentally here, and this is our, you know, pretty plasma. This is why we do this field because the plasma is pretty sorry. 163 00:41:19.390 --> 00:41:34.449 Mark Kushner: Um! So we plot plasma density versus magnet current. We turn up the magnet. We're going to collimate the plasma. We're going to push density downstream um The lang here prob in orange shows that you know we are increasing density as we do that, and our pip, hey? 164 00:41:34.470 --> 00:41:48.170 Mark Kushner: On the bright side we are seeing the right trend. We are only a factor of three off on this thing that I tell you is going to improve by accuracy. But but I know I know I know what the problem is, It's the capacitance. So we're going to. We're going to deal with the capacitance next. 165 00:41:48.570 --> 00:41:49.720 Mark Kushner: So 166 00:41:49.810 --> 00:42:03.670 Mark Kushner: uh a lot of that capacitance was like we have a circuit board underneath this little dipole antenna, and it's hard to characterize all that stuff. So let's move to a simpler system. Let's go from Dipole to a ball on a stick uh monopole. 167 00:42:03.680 --> 00:42:23.969 Mark Kushner: This is much more analytically tractable, uh simpler, to model those parasitic effects is actually really heavily developed before they went to dipoles on Space station. But whereas in a low density plasma sorry in a high density, plasma like thrusters, we can be um pretty sure that we're going to couple back into the coax shield here, 168 00:42:23.980 --> 00:42:37.839 Mark Kushner: and the low-density plasma they were seeing on station or in sounding rockets where they wanted to use this. They were like, never quite sure. Where is this monopole going to couple to out in the rest of the universe? So it would go to dipoles, because, you understand each side's coupling to the other better. But we use this ball in a stick. 169 00:42:37.930 --> 00:42:52.179 Mark Kushner: Um, If you recall, there was a lesson that resonances in your frequency range of interest are bad. So you probably don't want to start with a six inch length of Cox uh, which has a nice resonance right in the heart that you want to look at. You want to make it really really short. 170 00:42:52.620 --> 00:43:11.990 Mark Kushner: Um. Nevertheless, once you do that, we end up with a ball on a stick type impedance probe uh that i'll talk about. We get. We found about a ten to the third dynamic range that we're able to measure with it, we'll see that it looks okay compared to some. 171 00:43:12.770 --> 00:43:17.410 Mark Kushner: So uh, we're not there yet, though we had a couple of problems remaining. 172 00:43:17.720 --> 00:43:31.420 Mark Kushner: So first, you know. So here is our ball on a stick uh simulated and console blue is E-field magnitude black is saturated so really really dark blue, strong e fields, you know, so strong fields in the Cox. Uh, and we'll look at 173 00:43:31.430 --> 00:43:39.010 Mark Kushner: two different cases. One is a magical mall floating freely in plasma, and the other is the true ball on a stick with the cox 174 00:43:39.330 --> 00:43:42.520 Mark Kushner: in vacuum. Those give actually great agreement 175 00:43:42.920 --> 00:43:55.569 Mark Kushner: when you start simulating the case for a plasma, they really disagree, and in particular um. First, they disagree because the impedance peak is just in the wrong spot. It turns out that even with like an inch of Cox, 176 00:43:55.850 --> 00:44:09.370 Mark Kushner: that has some impedance properties, and you need to analytically de embed the impedance effect. So that coax uh, you can do that, and you can largely fix this left right error. There's still the up and down error on this magnitude. So where we're halfway there, 177 00:44:10.670 --> 00:44:14.320 Mark Kushner: I will make an aside which will become relevant in time. 178 00:44:14.580 --> 00:44:16.349 Mark Kushner: Is that uh, 179 00:44:16.520 --> 00:44:28.030 Mark Kushner: i'm showing here data for two different plasma, then two different plasma densities. So uh different plasma frequencies. And what i'll say also, without really justifying it, is two different dampings, 180 00:44:28.040 --> 00:44:43.149 Mark Kushner: the idea being that if you know you put an Rf. Excitation into a plasma, it should go away over time. How rapidly does it do? That is a damping phenomenon is that damping phenomena on the same as a effective collision frequency for the electrons. 181 00:44:43.160 --> 00:44:58.939 Mark Kushner: So it's a great topic for future work, I don't know. Uh. Nevertheless, we expect between the real and imaginary parts to have the same plasma frequency. But i'm going to orient you to orange data and the yellow fit to it first. So orange data, yellow is a fit 182 00:44:58.970 --> 00:45:09.849 Mark Kushner: Here's our plasma frequency orange data, yellow as a fit. The phase shift is not where it should be. I go over to the high damping case. Orange data, yellow. Here's the plasma frequency 183 00:45:09.920 --> 00:45:16.440 Mark Kushner: Orange. Oh, my God! What happened? There's no anything that looks like anything. Um! So 184 00:45:16.820 --> 00:45:33.980 Mark Kushner: I did not talk about in blue. This is the vacuum impedance that we got before we turn on plasma, for reasons that we're not immediately clear. Um! If we just take that vacuum impedance and subtract it off all of a sudden we get the green things, and everything looks amazing. 185 00:45:33.990 --> 00:45:52.860 Mark Kushner: It is a Christmas miracle, and we have not very much idea why, like mathematically, it didn't really seem like this should work um or do anything but it. So let's come back at that. Put a pin in that. This work from an experimental standpoint that's great, because you can like You don't need a special console model to just measure with no plasma. That's easy. 186 00:45:53.720 --> 00:46:05.850 Mark Kushner: But back to our our regular programming. Um the embedding the stem help. But it was not enough In particular. The sphere Models capacitance was really low, and it made the overall impedance look really low 187 00:46:06.280 --> 00:46:22.139 Mark Kushner: when we look for where the extra capacitance is. Um, uh, look where the field strengths are strong. You know where field strengths are strong. It tells you that you've got capacitance, you know, energy being stored in your system electrically. And so this multiple like the top half, is what a field a sphere looks like, 188 00:46:22.150 --> 00:46:39.070 Mark Kushner: and the bottom half is uh, or what the perfect sphere in space would look like. The bottom half is a ton of coupling to this coax. So really, what's happening is we're coupling to our coax line. We're getting a lot of extra capacitance there and cute sphere models Just don't cut it um. 189 00:46:39.080 --> 00:46:55.959 Mark Kushner: So this kind of a busy chart, but historically dating back to like two thousand and five. This work developed an nrl. They would kick their monopole, and they'd say it has a sheath, and they have some plasma around it, and it couples to some ground plane a distance. See away. And uh, we'll just take C to the infinity close to the chamber itself. 190 00:46:55.980 --> 00:47:07.760 Mark Kushner: Um, in practice what we really should have been doing was saying. A couples to this Cox down here, and let there be some in this simple picture, some effective. See? That's a fit that comes much closer. 191 00:47:07.770 --> 00:47:18.400 Mark Kushner: And what accounting for that did is it took all of our um in solid line data models with different levels of damping or simulations and models where we're like getting 192 00:47:18.410 --> 00:47:44.809 Mark Kushner: real versus complex impedances, where we don't predict the same plasma frequency, and you know, letting that um C term get corrected um, using actually the real capacitance, we would calculate um using the full geometry. It made everything start to line up again nicely. So uh this was nice. Um, I will note there are some other findings too small for this margin to contain um such that it's best to let your pro radius be bigger than to by length, 193 00:47:44.820 --> 00:48:04.319 Mark Kushner: and you know we we think that the effective probe size that you're sampling spatially is probably like three times this monopole diameter. But i'm not going to justify that in this talk, Uh, Nevertheless, another quick data look uh, we actually took our uh pip and compared it to a bigger Langmere probe downstream of a cathode again. 194 00:48:04.330 --> 00:48:23.769 Mark Kushner: And in this case, you know, before we off by a factor of three. Now we are, you know, over this, you know, seven to twelve inches downstream region, you know, up to about four or five times ten to the eighth, and you're looking pretty good, and it's not immediately obvious to me that, like it's not gradient effects that are causing us to diverge more as we get into a higher density regime 195 00:48:23.780 --> 00:48:47.470 Mark Kushner: so separately. I'm showing data here with the cathode running at a relatively high-ish current higher density separately. We saw a similar agreement down to the mid ten of the sixes, so we you know felt like at at least one hundred X, and maybe the three order of Magnitude X region where we were getting pretty good agreement as we swapped out different light in your probes to access the new plasma density regime. So that was nice 196 00:48:47.580 --> 00:48:59.179 Mark Kushner: um going forward, you know we're We're now comfortable enough to go back to the dipoles, which have, you know, some benefits of their own, and we're comparing some larger area. Plasma is like larger um spatial extent 197 00:48:59.190 --> 00:49:09.369 Mark Kushner: and lower gradient uh our impedance probe a dipole to a double langmier probe to a couple of different varieties of single langmier probe to kind of try to pin this down further. 198 00:49:09.920 --> 00:49:13.080 Mark Kushner: All right. So so some rules of thumb um 199 00:49:13.270 --> 00:49:27.699 Mark Kushner: size. Your monopole sufficiently large that you know your pro radius is bigger at least than your to by length. This is actually pretty pretty forgiving. Um! You should move your calibration clean as close to the pip as possible and d embed whatever is left that you can, 200 00:49:27.710 --> 00:49:37.449 Mark Kushner: and you know potentially subtract off the vacuum impedance. If you don't have some great, you know, nonlinear or console model for what the true uh impedance is going to be 201 00:49:38.540 --> 00:49:43.270 Mark Kushner: so. That was all that was all static. So I I did promise something about time, resolution. 202 00:49:43.300 --> 00:50:01.889 Mark Kushner: Um! There is a world where conceptually it's really simple to imagine measure impedance as a function of frequency by applying a frequency and measuring the impedance, move to a new one and measure the impedance and do it again and again. You can do this with a vector network analyzer. It's great. It's just slow, you know. You're going to get like 203 00:50:02.140 --> 00:50:21.980 Mark Kushner: maybe a kilohertz with like a really really fancy V, and a most of the time it's going to be like a several seconds to a minute kind of measurement. What you can do instead is send in a pulse that has a lot of different frequency content. And look at the response to that pulse. So we send in a Gaussian Mono pulse. Um! And then the fft of that is nice because it's actually a Gaussian and fft space. 204 00:50:22.660 --> 00:50:36.799 Mark Kushner: And so you get A. This is a voltage that we measure with these little transformers on one of our boards, and this is a current. So we send in Rf. To the antenna. Your antenna goes over here, and then we take off current and voltage, or maybe voltage and current. Um. But anyway, 205 00:50:36.810 --> 00:50:44.049 Mark Kushner: when we get our currents and voltages. We can take our ffts, and then their ratio is a impedance, 206 00:50:44.060 --> 00:50:59.099 Mark Kushner: and we can compare what you get with the V and a sweep in black from what is this zero to? Uh a gigahertz? So we get pretty good agreement with the red, which is the fft version up to in this case, you know, five or six hundred megahertz. 207 00:50:59.110 --> 00:51:06.100 Mark Kushner: So this is great Uh, almost from the get go. We were getting of order one hundred kilohertz resolution. 208 00:51:06.110 --> 00:51:19.590 Mark Kushner: Um! We've done some experiments where we see something like a one to four-ish Megahertz um type signals that we can resolve um, but they're you know are they super clean yet. No, and it's still still coming. 209 00:51:20.080 --> 00:51:26.979 Mark Kushner: So uh one of the last things I want to talk about and get to that plasma density standard candle I mentioned. 210 00:51:27.410 --> 00:51:45.589 Mark Kushner: We initially looked at this as a drop in for lang your probe a thing you shove in the plasma replaced by another thing. You shove in the plasma. Make a local measurement. So line your pro collected flux Here we're going to use our little antenna to transmit out into the plasma and see, uh what you know transmits well, and get a local measurement. 211 00:51:45.780 --> 00:51:57.090 Mark Kushner: And the antenna, though, can also receive. So you could ask what if I put the antenna out there, and I put something else to see how that signal travels through the plasma. Instead of looking at self impedance, 212 00:51:57.100 --> 00:52:15.170 Mark Kushner: Could I look at mutual impedance, and in particular you could look at an array of those things. So uh, we'll talk here about a simulation case where we have eight antennas uh each of forty-five degree, you know, arc uh fifty centimeters across, and then consider a pixel size of like one centimeter for what follows 213 00:52:15.260 --> 00:52:31.850 Mark Kushner: we can at least in simulation, where you know you are God, and you may put plasma where you wish. We can add a some plasma in each pixel and see what it does to these impedance effects. And so we can build up the mutual impedance sensitivity, maps from antenna, one to itself, 214 00:52:31.860 --> 00:52:42.959 Mark Kushner: antenna one to two. Um, you know, all the way across from antenna, one to five, and so on. And I I believe you know mathematically, these are actually like Jacobians. Um, that figure into the math 215 00:52:43.060 --> 00:52:55.890 Mark Kushner: for the pseudo-inverse that they compute. But, practically speaking, I look at these as like basis functions. These, are, you know, fundamental shapes. I'm going to use to ultimately try to reconstruct the plasma perturbation that I have inside, 216 00:52:55.930 --> 00:53:12.349 Mark Kushner: and so you can put in some different shapes. Um like here is, you know, a a vessel mode basically like what you might expect to see from some sort of rotating, you know, uh behavior. And you can get a picture where this is all simulation, right? But it looks like we could make things out. 217 00:53:12.640 --> 00:53:30.199 Mark Kushner: Uh I pulled some example photos from um Eric's latest presentation at the magnet meetings, like I even still have the subject here. So we put some plasma top hats at different spots inside the array. Uh, here's one in the center, one off center. Here we have two of them. 218 00:53:30.390 --> 00:53:42.370 Mark Kushner: These are not super impressive. Right? Like It's great that you see something like It's amazing. The universe works this way. But this is not a super, you know, awesome picture, but this is, I think, only for one frequency. So bear that in mind. 219 00:53:42.710 --> 00:53:44.029 Mark Kushner: Um. 220 00:53:44.040 --> 00:54:06.779 Mark Kushner: Eric also gets asked a lot. Uh I asked him a lot all the time. I think he must have been talking about me when he made this slide. That's all anyone ever wants to know is your spatial resolution turns out you get a lot better spatial resolution near your antennas and um, and it kind of suffers as you move in farther away toward the center. Which kind of makes sense when you look at some of the sensitivity maps um, but it's it's hard to pick out exactly what your resolution is going to be. 221 00:54:06.930 --> 00:54:09.569 Mark Kushner: It's particularly hard, because 222 00:54:09.950 --> 00:54:39.590 Mark Kushner: when you add more frequencies, you get more. I won't. Call them lines of site curves of site that the microwaves can use through the plasma. So you're going to have different regions. The plasma that are above. Cut off that you can't go through at all. You're going to have different levels of diffraction moving through the lower density effects, 223 00:54:39.600 --> 00:54:46.560 Mark Kushner: photos would suggest, although we don't for sure know how much, yet I think I have only like two or three slides left. So let me 224 00:54:46.640 --> 00:54:48.910 Mark Kushner: move towards closing thoughts. 225 00:54:48.990 --> 00:55:01.019 Mark Kushner: A final thing I want you to think about is that uh these pips don't really measure density uh they're really getting you with this specimen toward a dielectric constant. 226 00:55:01.030 --> 00:55:28.209 Mark Kushner: So this is what the impedance of an antenna might look like versus frequency. A a resonant dipole, and you'll have a peak at some resonance point, and to the left, your capacitive to your right, your inductive. We purposely make the dipole like really really short, and it kicks this way off screen to the right um by making them super short. So we're really only looking at capacitive effects. So our Dipole impedance looks a lot like the capacitance of it to the rest of the universe 227 00:55:28.220 --> 00:55:36.229 Mark Kushner: and vacuum. And in plasma it looks like that same sort of thing, but corrected with a plasma dielectric uh constant right here. 228 00:55:36.350 --> 00:55:38.179 Mark Kushner: And so uh, 229 00:55:38.320 --> 00:55:50.560 Mark Kushner: that's kind of interesting. You can actually look at how that files mode dielectric is uh related to your density, your uh plasma frequencies, And also this damping frequency I've mentioned before, but this is interesting because 230 00:55:50.640 --> 00:55:56.910 Mark Kushner: it's really hard to get a standard plasma density. But you know we can get materials of known dielectric 231 00:55:56.920 --> 00:56:17.899 Mark Kushner: quite a bit more easily. Uh, In fact, this is a Mcmaster car rod of Polycarbonate Um. And while this one is Mcmaster car spec, one could certainly put it in a resonant, microwave cavity, and precisely measure the dielectric constant of if we wanted. So what we're looking at now is, can We, um, you know, make a plasma density standard candle 232 00:56:18.030 --> 00:56:48.020 Mark Kushner: without the plasma. Uh, just just the candle. Uh, can we take different plastics, Teflon courts, glass, And with those different dielectric constants resolve. How well we can see them within these arrays, you know, make a nice, beautiful step function, which gosh! Is hard to do with a plasma, and can we move it around? Can we uh add different dielectric constants in there, and start to use this as a way to get towards something that we can truly, intrusively calibrate for the accuracy of the system. So we've just started to make these measurements um recently, 233 00:56:48.030 --> 00:56:49.009 and are trying to 234 00:56:49.200 --> 00:56:51.430 Mark Kushner: back out the calculations on them. 235 00:56:51.590 --> 00:57:11.939 Mark Kushner: Finally. Um! It's still exciting to test with plasma, too. This is the Space chamber uh and Rl's Plasma Physics division. It is a big chamber designed to make textbook plasma. Thou shalt have a uniform axial beefield with you big old solenoids. Um! They've got a giant array of Thor to tons of filaments on one end cap that to make electron be 236 00:57:11.950 --> 00:57:30.950 Mark Kushner: zoom down the chamber so you can block off parts of those to make nice uniform electric radio fields again for your textbook problem. Here. They're making one of those, and we're actually running it through our tomography array and starting to look at how well we can resolve a plasma column uh and do some time varying measurements with that, too. 237 00:57:31.200 --> 00:57:43.889 Mark Kushner: So uh some closing thoughts, and they all wrap up here if you can do static tomography. Could you do time? Resolve pictures, too? Could you like fire each one of these like a little Gatling gun and move around while the others listen. 238 00:57:43.990 --> 00:58:00.060 Mark Kushner: The answer is definitely, maybe, uh, in theory it looks like it should work uh. And so we're. We're trying that for sure. And the other thing is when you actually watched one of those pulse pip uh pulse pip shots. You know we fire in some voltage pulse, and we measure some current pulse. Um! 239 00:58:00.070 --> 00:58:09.910 Mark Kushner: And if this were like undamped, you would just see this kind of ring for a long time, right? But instead, this is not a great platform, but you know there's some kind of envelope for which it rings down, 240 00:58:09.920 --> 00:58:34.199 Mark Kushner: and you could fit an envelope there and call a characteristic damping frequency, and I I find myself really curious how that relates to those anomalous collision frequencies that we end up calculating when we shoot horn things into the fluid framework for the cathode. Um, It is, you know, for that measurement that was a factor of ten to one hundred different between all the different methods. We're definitely within a factor of ten. Uh, so 241 00:58:34.270 --> 00:58:48.769 Mark Kushner: so could we use this as another way to infer some of those quantities in the plasma. It doesn't get you the full velocity collision frequency product you need in the fluid formulations you need like Thompson scattering or something there. But it might get you part of the way. 242 00:58:48.780 --> 00:59:14.520 Mark Kushner: Um. So with that i'll close by noting that. Uh, we do have our internship application cycle open through November first. I think you saw earlier. We've had a whole bunch of interns in the past. We'd love to have a bunch More uh applications are here. We also have postdoc opportunities uh quarterly definitely reach out like before you apply to that. It's a lot of work, Um! And then, you know, some are faculty positions as well, coming up in December for applications if anyone was interested there to talk. 243 00:59:14.530 --> 00:59:15.540 Mark Kushner: Thanks, 244 00:59:22.440 --> 00:59:26.839 Mark Kushner: uh, thank you very much for that great Webinar there. Questions. 245 00:59:27.320 --> 00:59:46.230 Mark Kushner: But yes, uh, I was curious earlier. The first time to talk with this happened. It's magnetized or not, Mac. Uh, for the most, I think almost, I think entirely Those are on magnetized. I was just looking with the B field off. If i'm. If i'm wrong, Marcel will hear me and correct me and make me correct you as well. 246 00:59:46.290 --> 00:59:47.160 Yeah. 247 00:59:48.560 --> 01:00:03.530 Mark Kushner: Uh. So I have two questions. First of all, based on the the first half of the talk. Um, i'm curious. If you guys have any thoughts of why, when there may be a transition to the unemployment regime, that the causes of your theory would not agree as well with. 248 01:00:03.870 --> 01:00:22.070 Mark Kushner: I don't have a great answer for that, as well as sort of surprised when Marcel brought it up and focused on it. I I know that the electron mach number, you know, plays in there, and the analysis. But I don't have the, you know, detailed understanding to know which particular assumptions we're breaking down. Um, I I do know that, he 249 01:00:22.080 --> 01:00:43.990 Mark Kushner: he told me, and I read through that like paragraph and a half in his paper. Um! And so I probably the easiest thing to do is to send you the pre-print of the paper, and then my other question was, what's that the lower limit of the density you can measure with these antiques 250 01:00:44.000 --> 01:01:13.979 Mark Kushner: started, realizing we could correct for the damping that would we? We would see the um imaginary part where you get the second look at the plasma frequency, you know, in the face of disappear, and that would happen around the time that the probe radius hit the to biling um. It would kind of be worse there, so that that's one link, is the pro. Just. I think it's just getting too small, but maybe we could correct for that if we accounted for the um passive effects. The other thing is that your balance in the dipole cases you need to make sure that they have good low frequency, 251 01:01:13.990 --> 01:01:35.539 Mark Kushner: sensitivity. They've all got different frequency properties, and you can. You can muck yourself up if you think you're targeting one density regime. But then say, all those line effects push the resonant frequency you thought you were looking at down into somewhere. Your balance doesn't work anymore. So So those those are the kind two things I think she's effects and um some sensitivity effects in your circuit. 252 01:01:36.900 --> 01:01:59.790 Mark Kushner: Any other question. Yeah. So a quick two to two part. Let's see. The first one is you. You compare the um, the plasma with the the the the the the the so my question is so it's not kind of those which ones right. 253 01:01:59.800 --> 01:02:29.650 Mark Kushner: I I get this question all the time, like you claim this density die, or this diagnostic is better through it, you know, like they're different. How do we know the old one is not right, and this is a totally fair question, and it vexes me. That's why I was so excited to at least like come up with the idea that we could look at some known dielectrics and say, how close are we there? 254 01:02:29.660 --> 01:02:40.290 Mark Kushner: And can we use that? And then look at some density, You know measurements with other probes in that regime, and and see if we could answer that question better. Um! That that, said I, 255 01:02:41.190 --> 01:02:50.389 Mark Kushner: I, I am biased toward the impedance probe at this point it would be right, because they they could both be wrong also. Yeah, this is also fair. 256 01:03:03.930 --> 01:03:32.930 Mark Kushner: Uh, that's pretty good question. I wouldn't expect similar mission. The plasma should be much more dense on orifice, because that's where it's generated from the the tube. Um, you know. So in in this case, in this case, I guess they are uh sorry they are. They are all equally spaced from the center. Uh, we had to Ipc paper where Jack Brooks was looking at a high speed video, and you could see there would be some hopping around in it, and he was trying to um, you know. Figure out what that might tell you about wave structure downstream of the pilot. So 257 01:03:32.940 --> 01:03:46.830 Mark Kushner: actually, I can say, based on that, you do see hopping and non uniform emission. Um! There does appear to be a little bit of rotation, even with no B Field applied. Yeah, that was the recent one. That was the Uh. 258 01:03:46.960 --> 01:03:49.379 Mark Kushner: Yeah, the one just the same. 259 01:03:50.520 --> 01:03:51.759 That's perfect 260 01:03:51.920 --> 01:04:05.390 Mark Kushner: um in in your demographic approach. Uh the uh projections. The number of projection is fairly sparse. If I think of uh, an actual demographic method, can can you comment on uh 261 01:04:05.620 --> 01:04:06.560 one. 262 01:04:06.570 --> 01:04:29.009 Mark Kushner: Why it works with so few projections, and how you make it work. Uh, why do we only have eight antennas instead of like a lot more so. You mean Why, you only date. If I take of of of of network, you need many more projections to get a a high quality, you know a local uncertainty uh reconstruction here with aid. It looks like you're aim. No, Perhaps you're able to do a a fairly good week construction. Uh, 263 01:04:29.280 --> 01:04:57.130 Mark Kushner: so i'll i'll tackle the the why so few from a practical standpoint. First, you know, each of those things requires two high speed that channels per antenna to get your Rf current and your Rf. Voltage at a speed relevant to the plasma frequencies you're trying to observe, so that ends up being, you know, a bunch of scope cards. That's why I said like right now it is. It is not especially cheap. Um! And we need to do some work to figure out how to get over that hump of complexity to some simple or cheaper implementation. But 264 01:04:57.140 --> 01:05:08.159 Mark Kushner: eight is the most like sixteen channels, is, like, you know, a nice round number, and beyond that the cost was just going to keep getting higher. Um! As for why, it seems to do as good as it does 265 01:05:08.300 --> 01:05:17.250 Mark Kushner: my best guess there is that it's related, at least for some of the ones I showed um with. Like the Bessel mode type shape, 266 01:05:17.260 --> 01:05:30.910 Mark Kushner: I think that's related to the fact that that one was including multi-frequency um information. So you're not just getting the you know what is n squared minus n like the fifty-six mutual impedances at one frequency. You're getting them across like 267 01:05:30.920 --> 01:05:46.649 Mark Kushner: one hundred or one thousand different frequencies, each of which has a little bit of information, so so that can help you, because those things are not all the same. Um, the same repeated. But you also looks like you were using a projection. Basically you had a set of basis function to use with any construction. You were not 268 01:05:46.660 --> 01:05:52.909 Mark Kushner: trying to even imagine you in shape. 269 01:05:53.050 --> 01:06:04.240 Mark Kushner: There was. There were many slides that I cut out of this, involving large bunches of matrix math. And uh, you know, Penrose pseudo inverses and um things of this nature that I feel like, 270 01:06:04.260 --> 01:06:06.859 Mark Kushner: I would have to answer your question better offline 271 01:06:10.050 --> 01:06:13.580 Mark Kushner: any other questions. Yeah, 272 01:06:13.810 --> 01:06:29.100 Mark Kushner: one maybe detailed one, which is when you do the calculation uh for the the quasi when you're dragged. It's great. You do this measures by the way it's great to do you? You have potential measurements right? And then you're trying to convert that to electric field. 273 01:06:29.370 --> 01:06:38.720 Mark Kushner: So uh, this will be a lot too missing pro. You have to assume, like what the way number is already convert those potential measurements to. 274 01:06:39.170 --> 01:06:40.140 Uh, 275 01:06:42.030 --> 01:06:48.440 Mark Kushner: yeah, And i'm trying to figure out how Marcel would have done that if you had just taken the fact that we have the two 276 01:06:48.480 --> 01:06:54.020 Mark Kushner: density uh I saturation probes and assumed it was the same one. Uh at that time. 277 01:06:54.160 --> 01:07:00.660 Mark Kushner: I I don't know how he squared that circle. I'd have to look back 278 01:07:01.530 --> 01:07:04.830 that that that that's really might be breaking down. 279 01:07:12.890 --> 01:07:28.999 Mark Kushner: Yeah, I I I don't have a I don't have a good answer about how he implemented that I was, I was already, you know, horrified enough at wanting to use a like eight hundred dollar sem tip for an emissive pro versus like a five dollar um, you know school of the rate of tungsten, 280 01:07:36.870 --> 01:07:38.229 Mark Kushner: and then we broke it. 281 01:07:38.710 --> 01:07:39.740 Of course. 282 01:07:42.690 --> 01:08:03.140 Mark Kushner: Um! Some of the that you were talking about reminded me of um a little bit of optical subway links, imaging in the sense that um you take a physical object which is smaller than a way like the like, to localize the response. And it seems like that's kind of what you're doing. I think the pro is much smaller than the wavelength of the microwave source you're using. 283 01:08:03.150 --> 01:08:18.429 Mark Kushner: You confirm that. And then also, my second part of the question is, Um, what would be the advantage of having the um receiver in the plasma versus like scattering like you could do. Just put a physical probe to scatter. 284 01:08:18.630 --> 01:08:21.039 Mark Kushner: I have signal to the other probes. 285 01:08:21.210 --> 01:08:50.409 Mark Kushner: So let me. Let me let me start with the the wavelength uh question. See? I remember. You know, thirteen megahertz was like a twenty meter. So yeah, we we're we're we're way way smaller than. And in fact, I I mentioned we're. We're purposely making the antennas really electrically short, which means they're they're way under quarter wavelength size. So yes, uh So if that is enough to tell you whether or not we are analogous to um the optical techniques that you're referring to. I'm. I'm not familiar with um. Hopefully, that's enough. 286 01:08:50.420 --> 01:09:15.139 Mark Kushner: And then your your second question was about It sounded like, maybe putting some additional electrode, maybe in the center of the tomographic region of interest, or something to scatter. I'm. Not sure. So what's the manage versus just putting some object to scatter, because that's essentially what they do in like um. These These imaging approaches I mentioned is, you have like a pro tip which is much smaller than a wavelength of light, and you can get coupling optical coupling on a very simple 287 01:09:15.149 --> 01:09:23.970 Mark Kushner: dimension in a very small dimension. And so I can imagine a similar thing here where you have just a scattering object which is very small in size 288 01:09:24.130 --> 01:09:26.480 Mark Kushner: uh to help localize the response. 289 01:09:27.830 --> 01:09:29.359 Mark Kushner: I 290 01:09:30.220 --> 01:09:35.089 Mark Kushner: don't know that there's anything a priori. I would object to about that. What I would say is that 291 01:09:35.100 --> 01:10:05.080 Mark Kushner: for the moment we've, you know, looked a lot in our investigations at the places we felt were, you know, tractable conceptually. And so I'm. I'm. Far from wanting to say that what we've done is a like Platonic ideal of you know. Simplicity or of you know low cost um for result. And we weird. There's like this hump, you know. Right of it gets, you know, more and more complex. So you figure out how to simplify the inversions right now are taking, like, you know, days to low end weeks to do, but like 292 01:10:05.090 --> 01:10:18.809 Mark Kushner: we know, there's mathematical techniques that are going to come and cut that down, and I could totally believe there's a similar learning curve on the experimental side. So if if I could steal something from the optical folks. I am happy to steal it. Yeah, 293 01:10:20.800 --> 01:10:22.880 Any last questions 294 01:10:24.020 --> 01:10:27.980 Mark Kushner: I've got to quickly check the chat. 295 01:10:28.430 --> 01:10:29.760 Yeah. 296 01:10:31.040 --> 01:10:33.120 Mark Kushner: One 297 01:10:34.690 --> 01:10:44.180 Mark Kushner: just for my sister, hey? Sis, alright, bye,