WEBVTT 1 00:00:03.899 --> 00:00:04.830 Mark Kushner: I will be good to get. 2 00:00:06.000 --> 00:00:14.519 Mark Kushner: A welcome to the last 50 seminar for the fall semester I name is mark listener, I am the director of nitze. 3 00:00:15.150 --> 00:00:32.280 Mark Kushner: And it's my pleasure to introduce Professor can harness today's seminar speaker Ken received his PhD in aerospace engineering here at the University of Michigan and then been one of the first recipients of the graduate certificate and plasma science, engineering. 4 00:00:33.540 --> 00:00:46.170 Mark Kushner: 10 worked with invoice and while he was at the University of Michigan he was an empty fellow and winner of the best presentation award at the 2012 the FCC graduate symposium. 5 00:00:47.370 --> 00:00:54.510 Mark Kushner: Following graduate school check with a visiting research physicist at the plasma princeton plasma physics laboratory. 6 00:00:55.050 --> 00:01:00.540 Mark Kushner: And he served in that role as a Japan society for promotion of science postdoctoral fellow. 7 00:01:01.530 --> 00:01:16.230 Mark Kushner: He then joined the aerospace engineering department at Texas a&m university and is now a faculty Member in aeronautics and astronautics at Stanford university, where he directed the dynamics modeling laboratory. 8 00:01:17.040 --> 00:01:25.440 Mark Kushner: Professor for his research interests include electric propulsion low temperature plasmas and positive physics data driven modeling. 9 00:01:25.950 --> 00:01:39.270 Mark Kushner: plan so surface interactions in computational fluid and plasma dynamics he's a recipient of several awards, including the I triple A nuclear and plasma science society graduate scholarship award. 10 00:01:39.780 --> 00:01:49.020 Mark Kushner: The air force young investigator program award the Department of Energy early career award and the office of naval research, you know investigator program award. 11 00:01:50.130 --> 00:02:03.840 Mark Kushner: The title of ken's talk today is dynamics had low temperature magnetized plasmas self organization and anomalous electron transport but, before you start, we have. 12 00:02:05.130 --> 00:02:05.820 Mark Kushner: The MIPS enough. 13 00:02:08.220 --> 00:02:08.880 Mark Kushner: Finally. 14 00:02:11.010 --> 00:02:15.840 Mark Kushner: This is acknowledge things for you coming to get the seminar happy. 15 00:02:22.560 --> 00:02:23.790 Mark Kushner: Okay, very just. 16 00:02:31.230 --> 00:02:43.770 Mark Kushner: Right well Thank you so much, Professor Krishna for the introduction, so today, I wanted to give an overview of the low temperature man and dice plasma studies that we have been doing in my group. 17 00:02:44.910 --> 00:02:45.750 Mark Kushner: So. 18 00:02:48.240 --> 00:02:53.490 Mark Kushner: Is this Okay, or like is candlelight like be turned off like just for visibility. 19 00:02:57.540 --> 00:02:57.930 Mark Kushner: This way. 20 00:03:03.840 --> 00:03:11.100 Mark Kushner: I guess a little bit better so today my talk i'll introduce what low temperature monetize files mazhar and why I think. 21 00:03:11.700 --> 00:03:22.860 Mark Kushner: These are important for the entire plasma physics community and even the society i'll talk about the computational plasma modeling so where we are and why those are important as well, then i'll. 22 00:03:23.370 --> 00:03:35.010 Mark Kushner: Talk about physics in modeling of both instrumented vice plasmas specifically focusing on three areas, the first is kinetic theory and modeling of instabilities in turbulence, the second is our. 23 00:03:36.150 --> 00:03:42.330 Mark Kushner: New fluid modeling development for a low temperature main advice plasmas which I think are applicable to like other plasma. 24 00:03:42.810 --> 00:03:58.530 Mark Kushner: physics so really excited about the capability of this new fluid Code and the third one, is a our recent upgrade on data driven online estimation, specifically specifically i'm going to talk a little bit about applications to plasma chemistry and i'll conclude the talk. 25 00:04:00.030 --> 00:04:04.170 Mark Kushner: So, if you look into the entire plasma physics. 26 00:04:04.590 --> 00:04:14.670 Mark Kushner: area where research, then I think this plasma chart like you know everyone has their own like you know categorization, but this is kind of my understanding, so please correct me if i'm wrong. 27 00:04:14.970 --> 00:04:22.290 Mark Kushner: Or if i'm missing any important like you know plasma flows, but the X axis here is the plasma density and the y axis is the electron temperature. 28 00:04:22.650 --> 00:04:29.520 Mark Kushner: And if you look into our low temperature plasmas it's around like you know 10 to the 14 to 10 to the 18 per cubic. 29 00:04:29.970 --> 00:04:34.350 Mark Kushner: meter and it's around like room temperature to like penny via Max. 30 00:04:34.680 --> 00:04:42.570 Mark Kushner: If you look into like purple balls and like horrific thrusters it's a little bit on the edge of that low temperature plasma, so you can go a little bit higher density. 31 00:04:42.870 --> 00:04:46.830 Mark Kushner: And a little bit higher electron temperature so that's generated using the red circle. 32 00:04:47.400 --> 00:04:53.880 Mark Kushner: If you look into this orange circle, it is the atmospheric pressure plasmas it's lower temperature than like you know. 33 00:04:54.300 --> 00:05:01.020 Mark Kushner: electric propulsion devices, but it's higher plasma density, it can go up to like enter the 2010 to 2110 to 22. 34 00:05:01.590 --> 00:05:12.270 Mark Kushner: And this pink is what I recently started working on his pulse plasma so using like you know some hundred nanosecond like you know paul's. 35 00:05:12.540 --> 00:05:23.250 Mark Kushner: Then you can get the plasma densities and temperature to a little bit higher than the conventional little temperature plasmas so looking at these like three different types of applications and others. 36 00:05:23.580 --> 00:05:35.580 Mark Kushner: I feel like the importance of our research and also including other people in this room is that there is a gap between the low temperature plasma and the high temperature plasma field. 37 00:05:35.970 --> 00:05:45.300 Mark Kushner: and pushing that boundary of the low temperature plasma capabilities understanding the physics developing new predictive models can help the overall plasma physics community. 38 00:05:47.130 --> 00:06:02.100 Mark Kushner: So what is low temperature magnetized plasma is, in short, it's to use applied magnetic field that allows you to trap the electrons that otherwise diffuse to the walls, so this would allow the plasma to be higher electron temperature and higher plasma density. 39 00:06:03.240 --> 00:06:09.150 Mark Kushner: what's interesting about the low temperature main advice plasma was I list three things here one is multi scale. 40 00:06:10.080 --> 00:06:18.840 Mark Kushner: Here I the One example is high frequency oscillations that can include instabilities and also instability driven turbulence. 41 00:06:19.470 --> 00:06:27.900 Mark Kushner: Then the low frequency on the order of like 10s of killer hertz there's like breathing mode and ionization oscillations to like as immediately rotating spokes. 42 00:06:28.170 --> 00:06:38.250 Mark Kushner: which we can broadly categorize yourself organization, so how does this high frequency of low frequency oscillations interact and they are interacting like you know, can we understand them. 43 00:06:38.850 --> 00:06:53.610 Mark Kushner: The second point is multi physics, the gas is being fed and those are i&i so there's a collision or regime of the plasma, but once the plasma expands the gas density is lower so it's collision less. 44 00:06:54.030 --> 00:07:04.830 Mark Kushner: The collision or mechanisms such as like inner molecular collisions or wall collisions versus the collision less mechanisms such as a mom Estonian kinetic effects or even plasma ways and turbulence. 45 00:07:05.160 --> 00:07:09.300 Mark Kushner: How, these are all combined in a nonlinear way that's very challenging. 46 00:07:09.720 --> 00:07:16.020 Mark Kushner: The other part is probably most relevant to other conventional low temperature plasmas but it's multi species aspect. 47 00:07:16.320 --> 00:07:27.450 Mark Kushner: You have electrons ions which can can be singly politically charged and they're excited states of neutrals and like you know, an ions as well, so it's there's a lot of species to consider. 48 00:07:27.810 --> 00:07:35.790 Mark Kushner: Here i'm showing you two examples on the right one, is the hall effect thruster and the other is nine at RON discharge, these are just examples of low temperature plasma. 49 00:07:36.630 --> 00:07:41.400 Mark Kushner: field plasma devices mainly going to talk about our work on hall effect thruster. 50 00:07:41.730 --> 00:07:54.090 Mark Kushner: which has an anode and cathode that sets up an electric field into Axial direction there's a magnetic field in the cross direction that creates an e cross be and, as the musical direction, so the electrons are trapped and therefore you can maintain highlight contemporary. 51 00:07:55.800 --> 00:07:59.880 Mark Kushner: Now, in terms of the coupling if you take an example of a hall effect thruster. 52 00:08:00.180 --> 00:08:13.110 Mark Kushner: I want you to pay attention to the white fonts first, which is the anode and cathode it's a DC discharge, so the whatever you do near the anode can affect something on the castle and vice versa it's a DC. 53 00:08:13.530 --> 00:08:20.880 Mark Kushner: And within that DC there's a gas flow coming in from the animal side that's going to go through plasma reactions and ization. 54 00:08:21.150 --> 00:08:29.850 Mark Kushner: Creating different species now electromagnetic fields would set up there's plasma wall and traction and potentially there's turbulence transport. 55 00:08:30.120 --> 00:08:41.580 Mark Kushner: Which is induced by instabilities and waves and, on top of that, if you do this plasma device, you know development you're going to test it and there is a vacuum Chamber facility effect. 56 00:08:41.880 --> 00:08:49.200 Mark Kushner: which may be different from how you operate in space so everything and different scales are lean not linearly come coupled. 57 00:08:50.490 --> 00:08:58.830 Mark Kushner: So that whole you know, I hope that that's a good enough introduction for the low temperature magnifies plasma so like to switch to the computational plasma modeling. 58 00:08:59.910 --> 00:09:05.220 Mark Kushner: Now, I just wanted to start, you know very basic because, like, I know that there are some students. 59 00:09:05.820 --> 00:09:12.930 Mark Kushner: But this was my question like when I started PhD and I finally got some resolution when I was writing my dissertation. 60 00:09:13.260 --> 00:09:18.570 Mark Kushner: When I was talking with Professor brown Valley, or whose marriage remember this professor in aerospace. 61 00:09:19.050 --> 00:09:28.500 Mark Kushner: So my question was why do we have to do computational modeling and through like several iteration was Professor van the year, this is the slide that I finally got approval from him. 62 00:09:28.860 --> 00:09:38.370 Mark Kushner: So if you take the physical truth, because, like you know people talk about hey you're doing similar simulation you're doing theory and you're doing experiment, as if, like we're doing something else. 63 00:09:38.640 --> 00:09:45.090 Mark Kushner: But all of us are trying to seek the physical truth with different perspectives, so I just wanted to lay out what the connections are. 64 00:09:45.360 --> 00:09:52.650 Mark Kushner: So theory is like mathematical like approximations the physical truth, then there's experimental or the measurement side. 65 00:09:53.130 --> 00:09:58.020 Mark Kushner: The simulation kind of lies in an interesting area because we rely on the theory. 66 00:09:58.590 --> 00:10:10.410 Mark Kushner: And we can get like two types of mathematical solutions, one is the analytic solution, so you know if you have analytics solution that doesn't mean that you don't have to do simulation right, but like it's very useful for verification. 67 00:10:10.920 --> 00:10:16.560 Mark Kushner: Now, if you don't have the analytic solution, then that's where the only tool to get solution is computational simulation. 68 00:10:17.040 --> 00:10:25.440 Mark Kushner: So that is the importance of computer simulation and the theory behind that now, you can do validation between the theory and experiment and experiment and computational simulation. 69 00:10:26.130 --> 00:10:31.710 Mark Kushner: Now, using all this verification and validation is very important for computational modeling and the. 70 00:10:32.370 --> 00:10:42.210 Mark Kushner: The final goal is so that we can provide design tool for the Community if you have a plasma thruster can you do have a predictive modeling tool that you can design. 71 00:10:42.450 --> 00:10:51.780 Mark Kushner: The next generation thrusters, so this is what I feel like why computation models are important now i'm stealing some information from Professor parishioners. 72 00:10:52.290 --> 00:10:58.770 Mark Kushner: Paper that I like to read a lot, so this is about the low temperature plasma models and it talks about the. 73 00:10:59.250 --> 00:11:03.870 Mark Kushner: Important like multi scale nature and what types of Sub modules you have to. 74 00:11:04.170 --> 00:11:16.440 Mark Kushner: Implement and how a couple of them so on the top right is the different time skills that are required from electromagnetic to plasma transport chemical in fluid transfer up to the surface chemistry that's often the slowest. 75 00:11:16.980 --> 00:11:23.670 Mark Kushner: On the bottom right is there's the electron energy distribution function that you need to solve, and that leads to chemistry. 76 00:11:23.910 --> 00:11:29.580 Mark Kushner: At least a plasma gas flow and that's coupled with electromagnetic flow and that needs to be iterated so it's just. 77 00:11:29.850 --> 00:11:42.750 Mark Kushner: You know I think this is a really good paper to read, if you haven't it talks about the different multi scale multi physics nature of little temperature plasmas now going a little bit more specific into plasma physics based modeling techniques. 78 00:11:43.800 --> 00:11:50.610 Mark Kushner: I like to categorize the physics based models is like three different methods First is the fluid or continuum models. 79 00:11:51.180 --> 00:12:02.550 Mark Kushner: which can include drift diffusion approximation and it can also include oil and have you stokes are like MSG to fluid equations which are used in various different like fields and the. 80 00:12:03.540 --> 00:12:13.230 Mark Kushner: advantage of fluid models in comparison to the other two is that it's numerically inexpensive because you only need to solve for the macroscopic quantities like density temperature in both philosophies. 81 00:12:14.190 --> 00:12:24.420 Mark Kushner: The second is particle based kinetic methods which, in which we use macro particle that represents like a bunch of real particles so it's an approximation to the actual physics. 82 00:12:25.110 --> 00:12:30.570 Mark Kushner: Some you know examples include particle and sell PICs direct simulation Monte Carlo and Monte Carlo pollution models. 83 00:12:31.080 --> 00:12:37.410 Mark Kushner: The third pillar is well was my PhD topic here in Michigan is a grid based direct kinetic method. 84 00:12:37.890 --> 00:12:49.500 Mark Kushner: This solves the kinetic equations directly so blast off equation is you know hyperbolic partial differential equations so you should be able to use the you know the numerical tools to solve PDS. 85 00:12:50.310 --> 00:12:57.720 Mark Kushner: The advantage of the direct kinetic simulation is that there's no statistical noise compared to the particle methods and inherently has statistical noise. 86 00:12:59.940 --> 00:13:07.350 Mark Kushner: So with these introduction I like to go into the details of the physics and modeling of low temperature magnetized plasma. 87 00:13:07.620 --> 00:13:14.640 Mark Kushner: And I first I would like to spend like 10 slides ish on the kinetic theory and modeling of instabilities and turbulence. 88 00:13:15.330 --> 00:13:24.060 Mark Kushner: Now I wanted to start from like some textbook information and it my plasma course I use the frank chance the introduction, or to plasma physics. 89 00:13:24.360 --> 00:13:30.000 Mark Kushner: So in Chapter five he talks about the anonymous transport effect in like one or two pages. 90 00:13:30.900 --> 00:13:43.980 Mark Kushner: in Chapter five he starts by saying, like using single fluid resistive mhc the fox associated with the fusion can be written as this, the gamma is a new number density Fox and is the number the cpu is the bulk philosophy. 91 00:13:44.400 --> 00:13:47.640 Mark Kushner: Which is related to the diffusion caution and the density great. 92 00:13:48.300 --> 00:13:58.800 Mark Kushner: This density this diffusion coefficient in the classical notation can be written as such, it comes from the one over Omega square where Omega is the hall parameter. 93 00:13:59.400 --> 00:14:09.450 Mark Kushner: And if you kind of like you know play around with this equation, you can also rewrite this as the collision frequency over the electrons momentum transfer collision frequency. 94 00:14:09.930 --> 00:14:21.180 Mark Kushner: of times like one over be saying so, this is the classical but then he talks about this deep purple scaling as be you know inverse of. 95 00:14:21.540 --> 00:14:26.730 Mark Kushner: One over be and all previous experiments, rather than the to the power minus two. 96 00:14:27.240 --> 00:14:35.790 Mark Kushner: Furthermore, the the perp was far larger than that given by the classical notation this is anomalous the poor magnetic confinement. 97 00:14:36.420 --> 00:14:46.050 Mark Kushner: First, noted by bone in 1946 and bone can diffuse sanity is known in this equation 511 so. 98 00:14:46.680 --> 00:14:58.290 Mark Kushner: The classical electron transport cross magnetic field is the first equation that I highlighted in blue, which has the one over B squared dependence and the anomalous is known to scale as one over be. 99 00:15:00.600 --> 00:15:11.790 Mark Kushner: The way we thought about the crossfield electron transport, specifically in the hall forestry community is that we can take like different program measurements, such as done and, like University of Michigan. 100 00:15:12.120 --> 00:15:21.720 Mark Kushner: Professor gallon or in Professor Jones this lab and also in jpl you can do like language pro measurements and get temperature or like you know the potential voltage like profile. 101 00:15:22.080 --> 00:15:28.380 Mark Kushner: And you can run a simultaneous like simulation of the same device and then what you find is that. 102 00:15:28.680 --> 00:15:37.350 Mark Kushner: If you look into the physical properties of the electron collision frequency, such as collect on neutral collision electron I included in an electron wall collisions. 103 00:15:37.740 --> 00:15:45.690 Mark Kushner: Feed that collision frequency into the mobility and then use that you get at this discrepancy between the simulation result and the experimental results. 104 00:15:46.050 --> 00:15:56.340 Mark Kushner: So that's why how we treated the electron transport in our Community is that you have the measurements and there needs to be a normal so electron transport. 105 00:15:56.640 --> 00:16:06.570 Mark Kushner: That you need to like play around in tune, so that you get the simulation results that agree with the measurement result right and that comes from the notation that we start. 106 00:16:07.500 --> 00:16:11.370 Mark Kushner: Discussing the electron transport by using the drift diffusion flux. 107 00:16:12.060 --> 00:16:18.420 Mark Kushner: That has the drift and the fusion terms and by using this you can rewrite it to get the electron mobility. 108 00:16:18.660 --> 00:16:29.430 Mark Kushner: Right, so all just like gamma either like from flux, the any the electron density electric field, these can be obtained by the measurements that can get you the electron ability and that. 109 00:16:29.850 --> 00:16:37.860 Mark Kushner: gives you to terms collision all term that comes from the physics and something else, and that something else is known to be anonymous electron transport. 110 00:16:40.320 --> 00:16:44.160 Mark Kushner: Now, in recent theoretical and measurement advancements have. 111 00:16:44.610 --> 00:16:52.380 Mark Kushner: revealed that there's plasma ways in these devices, if you near the cathode even you know the plume like even inside the discharge channel. 112 00:16:52.680 --> 00:17:00.840 Mark Kushner: So I just wanted to like you know start from very basic thing if you take the equation emotion for any charge species, this is an equation emotion. 113 00:17:01.290 --> 00:17:08.520 Mark Kushner: And if you have a fixed electric field and fixed magnetic field, and you can do single particle trajectory calculations, this is what you get. 114 00:17:08.910 --> 00:17:12.990 Mark Kushner: Right like there is a generation and there's a cross the drift in the y direction. 115 00:17:13.500 --> 00:17:21.630 Mark Kushner: Well, you can notice here is that this solution does not have any crossfield transport right because the electrons are trapped around the magnetic few. 116 00:17:22.230 --> 00:17:28.200 Mark Kushner: Now, if you have an electric field that's oscillating in the direction of the ethos, the drift. 117 00:17:28.590 --> 00:17:34.710 Mark Kushner: i'm just assuming the static like you know scientists oil electric field and do the same thing, what happens it's pretty interesting. 118 00:17:35.190 --> 00:17:41.640 Mark Kushner: Not all the particles, but some particles exhibit this like chaotic like behavior because it's a non linear equation. 119 00:17:42.120 --> 00:17:48.720 Mark Kushner: that's why I wrote down in the equation motion the electric field is a function of X right, so the X is nonlinear. 120 00:17:49.140 --> 00:17:56.130 Mark Kushner: So, even with the simple single particle trajectory calculation, we can show that these single particle trajectories can be nonlinear. 121 00:17:56.400 --> 00:18:05.070 Mark Kushner: And the presidents of plasma wave and, incidentally, you can see that the guiding Center shifts in the Left direction for some particular particles. 122 00:18:05.730 --> 00:18:18.330 Mark Kushner: Now, so why is this important, so this is a collision less electron transport mechanism across the magnetic fields via the plasma waves or the plasma turbulence and the question is like is it same in one day two year three. 123 00:18:20.010 --> 00:18:25.020 Mark Kushner: So what we did, is in the Community, led by john furrier booth and lauren greig in. 124 00:18:25.590 --> 00:18:34.410 Mark Kushner: France, they propose a test case to do a benchmarking because, like there's many people that have the pin code, but like you know, can we trust all the results, there needs to be. 125 00:18:34.620 --> 00:18:41.970 Mark Kushner: A benchmark taste, that we can you know all get together and show that we get good agreement, so this is what we did as a Community, and I was part of it. 126 00:18:42.300 --> 00:18:53.580 Mark Kushner: We have an anode and cathode and there's a fixed magnetic field profile and the actual direction we fixed ionization right just to get the steady state quicker, which allows the runtime to be like 30 microseconds. 127 00:18:53.910 --> 00:19:01.440 Mark Kushner: Otherwise, you have to wait for the slow noodles so this significantly accelerates the simulation, and these are some like details of the calculation. 128 00:19:01.740 --> 00:19:12.780 Mark Kushner: But I want to highlight here that this test case was proposed to only use a single charge the NIH Okay, and it takes like 32 processes for like one or two weeks or on one case. 129 00:19:14.160 --> 00:19:22.230 Mark Kushner: Right, so what what kind of results that you get is quite fascinating so recall that there is an hour and castles so there's a DC you know potential drop. 130 00:19:22.500 --> 00:19:26.940 Mark Kushner: And there is the magnetic field into the page, which creates a cross be in the y direction. 131 00:19:27.480 --> 00:19:42.420 Mark Kushner: So this equal speed drift generates this plasma wave and it's already pretty complicated, there is a small, like you know small scale feature near the anode but then it transitions into a little bit longer like wavelengths modes in the plume and. 132 00:19:42.900 --> 00:19:56.400 Mark Kushner: So what we can see is that due to the E cross the drift, this is what's known as the electron Cyclotron drift instability, the electron psycho strong will be resonant with the plasma wave and create these structures and. 133 00:19:57.630 --> 00:20:04.350 Mark Kushner: What we wanted to do further was take this test case and study other physics, the first thing we did was we my. 134 00:20:04.860 --> 00:20:10.470 Mark Kushner: collaborator saving that Scotland cnrs who gave him if see talk, a few months ago, one year ago. 135 00:20:11.370 --> 00:20:15.840 Mark Kushner: She was instrumental in developing a Thompson scattering measurement. 136 00:20:16.200 --> 00:20:24.000 Mark Kushner: which suggests that by tuning that way vector of what you can measure she measured Axial mode and as a nice little right. 137 00:20:24.180 --> 00:20:33.930 Mark Kushner: recall that in the previous slide talked about the as municipal mode in the direction of the cross feed her if she tilted at 90 degrees and still found that there is an axiom or that no. 138 00:20:34.230 --> 00:20:40.530 Mark Kushner: I mean, nobody really predicted so there's a coupling between the Axial and, as you saw mode and this is an experimental evidence. 139 00:20:40.800 --> 00:20:48.990 Mark Kushner: And the evidence is also that, if you look into the phase velocity of that wave, it was higher than the velocity of the singly charged ions. 140 00:20:49.260 --> 00:20:56.460 Mark Kushner: So this was suggesting that some other mechanism had to like drive this plasma way that's faster than the single charge giants. 141 00:20:57.000 --> 00:21:06.990 Mark Kushner: This led us to study the I, and I, and to Stream is stability, so what mean what I mean by the eye and to streaming disability is we accounted for the lovely charged ions species. 142 00:21:07.290 --> 00:21:13.380 Mark Kushner: And it's free parameter here is the double charged iron fraction which I define here just the density ratio. 143 00:21:13.620 --> 00:21:19.410 Mark Kushner: In the you know the theory but it gets like pretty complicated right like this is a 2d dispersion relation. 144 00:21:19.710 --> 00:21:31.680 Mark Kushner: That comes from the xenon plus and xenon two plus which both have like you know cold assumption call diane assumption, but the electrons, this is a 2d description of the magnetized electrons that has like a bernstein kind of you know. 145 00:21:33.270 --> 00:21:42.090 Mark Kushner: i'm telling you also the results of this, if you look only for the CDI the single charge I am, this is the you know the resonance that you get in the y direction. 146 00:21:42.390 --> 00:21:49.980 Mark Kushner: And you get the Iit si only case and the combination becomes pretty complicated, although, in this case it's just like a superposition of the two. 147 00:21:51.180 --> 00:22:01.230 Mark Kushner: So we published this in last year's of physical review he, and this is the result from adding the w charged ions into this PIC simulation. 148 00:22:01.770 --> 00:22:08.460 Mark Kushner: The last movie is the same as the one I showed you a few slides ago but the right has 20% double charged ions. 149 00:22:08.760 --> 00:22:20.340 Mark Kushner: In the simulation so what's interesting is that the electron Cyclotron drift instability is still there, creating the motivation and the y direction but in addition to that there's the Axial X. 150 00:22:20.640 --> 00:22:26.190 Mark Kushner: wave that you can see that's evident from the structures in the you know the right side of this movie. 151 00:22:27.300 --> 00:22:38.880 Mark Kushner: Now this is all good by like while we are chasing after is like you know the transport mechanism right, so the simulation can you know, diagnose like you know electron volts velocity which may be difficult, with measurements. 152 00:22:39.180 --> 00:22:43.920 Mark Kushner: But this is the result for the electron both philosophy in the crossfield direction. 153 00:22:44.430 --> 00:22:49.590 Mark Kushner: So the zero percent are the 2% you know results or when it singly charged I am dominant. 154 00:22:49.890 --> 00:22:56.790 Mark Kushner: And then, as I increase the double charged I on notice that the velocity is you know negative because the electrons are going from the right to the left. 155 00:22:57.120 --> 00:23:05.130 Mark Kushner: But what I want to for what I want you to focus here is the absolute value increasing as we increase the w charged ions fraction. 156 00:23:05.400 --> 00:23:11.370 Mark Kushner: Right, so this suggests that the electron mobility is affected by the Presidents of the w charged ions. 157 00:23:11.730 --> 00:23:20.490 Mark Kushner: You can also kind of see like you know there's kind of a tilting of this like plateau area it's kind of indicates that there is a nonlinear coupling between the two instabilities. 158 00:23:20.730 --> 00:23:27.330 Mark Kushner: This is something that like you know we haven't really spent too much time analyzing but you know it's kind of numerical evidence that there may be something. 159 00:23:27.750 --> 00:23:34.500 Mark Kushner: Now the right figure here is the actual I am velocity so i'm showing you the single charge and the charge on first thing I wanted to show this. 160 00:23:35.010 --> 00:23:43.620 Mark Kushner: Due to these double recharge diane you can see significant deceleration of the dog, which are giant in a slight acceleration of the single charge audience. 161 00:23:45.870 --> 00:23:51.900 Mark Kushner: Now, if you take a look at the plasma wave, which is shown with this, a call you know orange light colored map. 162 00:23:52.470 --> 00:24:06.840 Mark Kushner: The amplitude of the electric field, again, the Left figure is only singly charge and the right figure is 80% singly charged and 20% w charged right, so you can see that the left is only Axial as an insult, but in the right there's a 2d plasma way. 163 00:24:07.500 --> 00:24:14.370 Mark Kushner: Now what i'm showing you with the black solid lines are the time averaging time average electron streamlines. 164 00:24:14.730 --> 00:24:22.800 Mark Kushner: And this clearly shows that there are some changes in the electron transport and what I want to focus on here is this arrow that i'm showing. 165 00:24:23.070 --> 00:24:35.160 Mark Kushner: On the left and the right, you know the cathode, which is where they inject the electrons right so here, if you look into the vector on the Left there's you know the significant portion is going downwards, which suggests that there's. 166 00:24:35.670 --> 00:24:39.990 Mark Kushner: You know less like crossfield transport but more like you know why direction transport. 167 00:24:40.470 --> 00:24:55.590 Mark Kushner: On the right it's the contrary, because this apparel you know gets 90 degrees sifted and it's mostly excellent transport right, so this is kind of the first evidence that the plasma wave structures can affect the cross to the electron transport. 168 00:24:56.910 --> 00:25:00.750 Mark Kushner: And we think that this is, you know, due to the fluctuation based electron transport. 169 00:25:01.590 --> 00:25:10.140 Mark Kushner: This is just wanted to show two more slides, this is a new results that we got so the further use this code and added Tripoli charge I am because I was just curious. 170 00:25:10.380 --> 00:25:16.410 Mark Kushner: And I added Tripoli charge I in and my previous post provide was very instrumental in this. 171 00:25:16.740 --> 00:25:25.650 Mark Kushner: The similar plot is shown on the left is the Axial where the crossfield electron Bob philosophy here when I when we increase the Tripoli charge I on. 172 00:25:25.980 --> 00:25:31.440 Mark Kushner: We you know we were thinking that okay like electron transport can be enhanced you to the addition of the AAA charge. 173 00:25:31.740 --> 00:25:37.410 Mark Kushner: But what we saw was the contrary, the electron transport got reduced by adding more Tripoli charged ions. 174 00:25:37.710 --> 00:25:48.480 Mark Kushner: And the correlation that we found was that if you add people charged ions and if you analyze this plasma wave structure, you see a significant reduction of the plasma waves amplitude. 175 00:25:48.810 --> 00:25:57.270 Mark Kushner: by the addition of the AAA charge because you have singly doubling and tripling charged ions if you can you know have multi mosaic, and like you know beat together. 176 00:25:57.510 --> 00:26:04.230 Mark Kushner: That can reduce the amplitude of the plasma wave, which we think is you know attribute it to the reduce the electron transport. 177 00:26:04.950 --> 00:26:14.520 Mark Kushner: So this electron transport is decreased with the trip recharge and due to the damping of the plasma way, this is just our hypothesis, based on the simulation results. 178 00:26:15.270 --> 00:26:20.100 Mark Kushner: final result here this trip recharge study was that we can also take a look at the Ion. 179 00:26:20.670 --> 00:26:26.850 Mark Kushner: Ion and electron velocity distribution functions here i'm showing you the Axial I am velocity distribution functions. 180 00:26:27.090 --> 00:26:32.700 Mark Kushner: In the upstream where you, you know where we ionizing thing and the downstream when ions are all accelerated. 181 00:26:33.030 --> 00:26:39.630 Mark Kushner: And these are the plots for the y direction you know facebook's right, so the particle is going in the direction of the process be dressed. 182 00:26:39.960 --> 00:26:47.730 Mark Kushner: Well, we found interesting was that the xenon plus is there were not many trapping like you know, because the plan once you have the plasma wave. 183 00:26:47.970 --> 00:26:55.920 Mark Kushner: From the plasma, in theory, we know that the particles that are trapped has to satisfy you know it has to be smaller than the plasma potential amplitude right. 184 00:26:56.310 --> 00:27:07.470 Mark Kushner: So the xenon two plus and three boss, because the Z factor there allows them to have a higher or larger trapping velocity We found that the trapping signature were more more. 185 00:27:08.130 --> 00:27:19.530 Mark Kushner: found in the web and Tripoli charge and we couldn't find them in the single charge I am which may be an important takeaway for experimentalists if you're doing a lie on singly charged ions you may not see diane tracking. 186 00:27:20.040 --> 00:27:23.550 Mark Kushner: So this is what I thought, like you know, maybe it's you know, going to be helpful. 187 00:27:25.170 --> 00:27:33.480 Mark Kushner: Right so part one, I guess, I have to take my time, but um so So this was about the kinetic instability, so what I wanted to show was the. 188 00:27:33.720 --> 00:27:39.870 Mark Kushner: coupling between different instabilities and these players on ways will lead to the cross the electron transport. 189 00:27:40.350 --> 00:27:51.480 Mark Kushner: Well, as the interesting is that both the xenon to blessing xenon three studies suggest that the crossfield electron transport or the fusion is affected by the amplitude of the plasma wave. 190 00:27:51.720 --> 00:28:00.030 Mark Kushner: And notice here that we only did two D plasma always simulations what's going to happen in 3D great question that's what we want to focus on in the next coming years. 191 00:28:00.510 --> 00:28:03.060 Mark Kushner: Our recent simulation which was which we're going to. 192 00:28:03.570 --> 00:28:11.640 Mark Kushner: present in the coming site deck in a double a is that we also changed a few different parameters that allowed us to change the wavelength. 193 00:28:11.910 --> 00:28:25.800 Mark Kushner: Of the plasma waves and that also showed some effect to the crossfield electron transport, so the takeaway here is that the amplitude and the wavelength, of the plasma waves may be important to understand the crossfield electron transport. 194 00:28:28.170 --> 00:28:37.260 Mark Kushner: Second topic fluid models so i'm here i'm, I just wanted to introduce the phenomena that we see as low frequency plasma oscillations. 195 00:28:37.590 --> 00:28:45.570 Mark Kushner: We see like as a monthly rotating spokes that you can find from these like plasma balls like moving in the direction of the cross P direction. 196 00:28:46.350 --> 00:28:52.950 Mark Kushner: Re cosima researcher and university token, I worked on this rotating spokes like three years ago. 197 00:28:53.430 --> 00:29:06.690 Mark Kushner: in which we use the hybrid pick electron fluid model that you know presented this rotating sports very stable for very long time, we were able to resolve some numerical issues and achieve this stable lead rotating spoke. 198 00:29:07.290 --> 00:29:12.360 Mark Kushner: On the right is like the mall transition that involves ionization oscillation. 199 00:29:12.930 --> 00:29:25.650 Mark Kushner: which I, you know worked tremendously with mike's a character, when we were both together a PhD students in Michigan and breathing mode like you know, was also analyzed using like high speed language or probes available in pebble. 200 00:29:27.480 --> 00:29:36.900 Mark Kushner: So these are like the two low frequency plasma stations that we care about in the hall, for us, or community now, I just wanted to give one side of the theory foundation. 201 00:29:37.800 --> 00:29:46.890 Mark Kushner: The kinetic equations are listed, you know, using this boltzmann equation, or like any general kinetic equation, where F is the velocity distribution function. 202 00:29:47.400 --> 00:29:53.130 Mark Kushner: If you take the moments of this velocity goes up the kinetic equation, you can dry the fluid equations right. 203 00:29:53.370 --> 00:30:02.100 Mark Kushner: So people you know don't really appreciate this because you see the fluid equations and Connecticut ways in separately, but the fluid equations conference, the kinetic equations right. 204 00:30:02.400 --> 00:30:10.380 Mark Kushner: And the main assumptions that we use for like oil or Nadia stokes mhc to fluid equations is mostly in how we treat the closure problem. 205 00:30:10.770 --> 00:30:16.200 Mark Kushner: And the closure problem typically usually refers to this nsf topic pressure sensor. 206 00:30:16.590 --> 00:30:22.620 Mark Kushner: Which is exact like form right like you know you take the velocity difference between the particle velocity and. 207 00:30:22.920 --> 00:30:31.380 Mark Kushner: velocity for different directions multiply with the velocity distribution function, you can get an isotopic pressure tensor if it's not next line. 208 00:30:32.370 --> 00:30:39.000 Mark Kushner: Now if to make our life easier and if it's delusional, we know that, and I said Tropic pressure turns become zero. 209 00:30:39.570 --> 00:30:45.780 Mark Kushner: And then these equations can reduce to like boiler equations that you know where we can use ideal gas law. 210 00:30:46.350 --> 00:30:53.760 Mark Kushner: So anesthetic pressure sensor is one of the closer problems, the other closer problem is a heat flux, which is like the third order. 211 00:30:53.940 --> 00:31:06.420 Mark Kushner: You know tensor that we get from the moments of the kinetic equation, so we have to deal with the pressure and heat flux to deal with the fluid equations correctly and there's a conditional terms if you have like you know self collisions or like inner molecular collisions. 212 00:31:07.890 --> 00:31:10.680 Mark Kushner: So what are the fluid modeling strategies on. 213 00:31:11.220 --> 00:31:20.700 Mark Kushner: The first category, I think, is the drift diffusion flux model, which has been used in the low temperature plasma models, including our own electric Poles and community. 214 00:31:21.000 --> 00:31:28.650 Mark Kushner: So, within this drift diffuse and models, there can be Father neutral drift diffusion model and the non neutral dress diffuser model. 215 00:31:29.040 --> 00:31:41.370 Mark Kushner: The quantity info drifter fusion model allows us to simplify the process on the equation, and you know get the fields, from like different like you know electron fluid equations, and I say like you know a few like you know notable papers. 216 00:31:42.180 --> 00:31:47.070 Mark Kushner: In the low temperature plasma Community outside of electric propulsion Community like. 217 00:31:47.550 --> 00:31:53.010 Mark Kushner: Professor Krishna has been instrumental in designing these are neutral drift diffuse of models. 218 00:31:53.340 --> 00:32:01.860 Mark Kushner: A sama include using the sharp ferragamo scheme and like you know you have to deal with like timestamp and like explicit versus implicit modeling, but these are like you know. 219 00:32:02.370 --> 00:32:04.170 Mark Kushner: used in the low temperature models. 220 00:32:05.160 --> 00:32:12.300 Mark Kushner: So drift diffuser model for the closet mutual we use this like continuity equation that connects the iron current and the electron crane. 221 00:32:12.480 --> 00:32:18.990 Mark Kushner: From what you can get an equation for the electric field, or the potential, so this is the equation, we solve instead of the plus sign equation. 222 00:32:19.500 --> 00:32:28.440 Mark Kushner: The Non neutral diffusion equation, we use the drift diffusion equation and put it into the electron continuity equation solve the electron density. 223 00:32:28.710 --> 00:32:34.920 Mark Kushner: And then you can solve the parsons equation so it's a little bit more complicated than the closet neutral drift diffusion model. 224 00:32:35.640 --> 00:32:40.530 Mark Kushner: The third model that I want to talk about today is what I call the full fluid moment model. 225 00:32:41.100 --> 00:32:55.860 Mark Kushner: And the reason why I named this moment model is because, in the previous slide show that it's the moment that you're taking from the kinetic equations so here the equation becomes free the difference because now, you have to solve for the conservation equations just like we do in CFC. 226 00:32:57.450 --> 00:33:02.310 Mark Kushner: So one proof that I wanted to show very quickly is that. 227 00:33:03.510 --> 00:33:12.420 Mark Kushner: In this paper that I presented in psst in two years ago, if you take a look at the energy equation for the total energy and the internal energy. 228 00:33:12.840 --> 00:33:20.610 Mark Kushner: And you can you know, look at the right hand side, the total energy has a J dot E, which is the energy input to the plasma right. 229 00:33:20.970 --> 00:33:31.770 Mark Kushner: But for the internal energy it's not the jaded eat it is the friction between the internal energy and kinetic we're drifting right so that is trances the friction term mostly. 230 00:33:32.280 --> 00:33:41.100 Mark Kushner: Now, if you have no man no dice plasma, which means that the kinetic or drift energy is small or zero, then you can recover this right hand side heat. 231 00:33:41.700 --> 00:33:49.350 Mark Kushner: And term and the friction term to be equal so that means that the total energy and the internal energy equation becomes identical. 232 00:33:49.620 --> 00:33:57.840 Mark Kushner: And you can prove that the drift diffusion equation can be exactly recovered by this process, but if you have nine advice last one, where you have drift. 233 00:33:58.140 --> 00:34:07.500 Mark Kushner: than this K, is no longer zero so this s heat and the friction term are no longer the same, which means that you cannot use drift diffuse and approximation. 234 00:34:07.800 --> 00:34:20.520 Mark Kushner: So that led us to develop the full fluid moment model, accounting for these nonlinear inertia terms, here I just highlight a few like you know numerical you know details me as a fine I volume models for all species. 235 00:34:20.880 --> 00:34:23.670 Mark Kushner: Currently, we have one day to the into the to the results. 236 00:34:24.240 --> 00:34:31.800 Mark Kushner: there's a five moment equation with gloss on we use something like you know flux plating scheme and time averaging seen, we also think that this kinetic. 237 00:34:32.070 --> 00:34:41.520 Mark Kushner: flux boundary condition is quite useful for many plasma applications so we're also working on this and we're using like parallel computing for 2d problems. 238 00:34:42.900 --> 00:34:53.670 Mark Kushner: Now, the first test case that I wanted to show is one of the cross field plasma discharge so here I haven't relatively simplified hall thruster kind of model, where I have this magnetic field. 239 00:34:53.940 --> 00:35:00.150 Mark Kushner: And the electric field and i'm just looking into the plasma formation in the X direction along the actual direction. 240 00:35:00.690 --> 00:35:06.900 Mark Kushner: it's very simplified and it's you know I have an almost transports as a fudge factor to get steady state plasma. 241 00:35:07.170 --> 00:35:15.990 Mark Kushner: But this allowed us to study the difference between the drift diffusion models and the flu food models of food moment models and the result is shown on the right. 242 00:35:16.230 --> 00:35:21.600 Mark Kushner: If you take a look at the number densities some results like you know don't like you know so any. 243 00:35:22.410 --> 00:35:30.480 Mark Kushner: significant differences, but especially like near the anode sheath you can see that the closet neutral just diffusion because we're not resolving the sheath. 244 00:35:30.810 --> 00:35:39.540 Mark Kushner: Like you know it goes up to that like you know less self Center and for non neutral adrift diffusion and full fully moment model we can resolve this and on sheath. 245 00:35:39.930 --> 00:35:43.290 Mark Kushner: By like you know there's some difference between the two results. 246 00:35:44.160 --> 00:35:55.560 Mark Kushner: And the results, the differences come from the treatment of the bulk velocity because in the drift diffusion model where we're neglecting is the inertia term which i'm showing you on the right hand side here. 247 00:35:55.890 --> 00:36:06.750 Mark Kushner: it's like taking the partial partial partial partial why right, that is a nonlinear inertia term So if you take a look at the results that we get from all the four different like you know models. 248 00:36:07.320 --> 00:36:15.210 Mark Kushner: The Axial bog velocity is kind of okay good agreement so that's why the plasma densities we're not like significantly different than the previous slide. 249 00:36:15.450 --> 00:36:24.360 Mark Kushner: But you can see that the as a nice about the aussie shows pretty significant differences, especially near the end or the or the plasma discharge, so the. 250 00:36:24.870 --> 00:36:33.300 Mark Kushner: The black and the green or the full fluid moment model, the FM and the red is the qd and blue is the NDP, so there are some like anonymous. 251 00:36:33.660 --> 00:36:42.390 Mark Kushner: As a municipal both the law see that, like you know the derivative user model, you know shows that led to some of the plasma density discrepancies in the previous slide. 252 00:36:42.900 --> 00:36:50.550 Mark Kushner: Now, using this weekend now take the gradient of the bulk velocities from the FM results, and these are the results that shown. 253 00:36:51.750 --> 00:37:04.230 Mark Kushner: For the actual car, I want to mention that there is a significant axle acceleration here the analog cheese right because the electrons are just being sucked into the animals so there's acceleration from a fluid element point of view. 254 00:37:04.620 --> 00:37:14.400 Mark Kushner: And the as a musical share because there's a significant a prospect drift near the Center of this there's a huge density sorry the velocity of shared gradient that we get. 255 00:37:15.090 --> 00:37:18.570 Mark Kushner: This was gave us some you know really interesting results. 256 00:37:19.260 --> 00:37:23.130 Mark Kushner: And if you take a look into the electron momentum equation and reformulate. 257 00:37:23.430 --> 00:37:33.330 Mark Kushner: You can get that he crossed the drift and the dynamic dress but because of the inertia term there's an additional term that contributes to the bulk velocity in the crossfield transport. 258 00:37:33.810 --> 00:37:41.850 Mark Kushner: So this is a metric that we chose that show the differences, the most we took the difference between the as the municipal and the actual. 259 00:37:42.120 --> 00:37:54.480 Mark Kushner: fluxes which is effectively like a hall parameter it tells you about you know the electron crappy so there seems to be some differences that we found and we attribute this to the sheer driven you know share that magnetic just. 260 00:37:56.370 --> 00:38:01.770 Mark Kushner: Very quickly, I wanted to show some recent results is a 2d application of this FM result. 261 00:38:02.040 --> 00:38:11.400 Mark Kushner: What I what we did, is that then i'm sort of my senior student set up this to the box, which has like four walls which are like zero potential and we. 262 00:38:11.670 --> 00:38:16.650 Mark Kushner: You know, put back the like ions that go to the wall back into the domain, so that we get steady state plasma. 263 00:38:16.950 --> 00:38:24.060 Mark Kushner: And i'm just showing you the magnetized case, proving that like you know, there is no, you know we're like numerical oscillations it's a very smooth. 264 00:38:24.330 --> 00:38:27.870 Mark Kushner: And people are like plasma that we get right now what i'm going to show in the. 265 00:38:28.260 --> 00:38:38.280 Mark Kushner: Next slide is that going to impose a magnetic field into the page right so that's going to create a cross be drift and the diamond medic first in the as a musical direction. 266 00:38:38.850 --> 00:38:45.690 Mark Kushner: We wanted to see whether we can you know, create rotating spokes from this new food model So these are the results. 267 00:38:46.230 --> 00:38:55.140 Mark Kushner: The Left is the plasma density plot and the right is, we can play everything, but like I learned his show, he asked me so electron both velocity. 268 00:38:55.710 --> 00:39:05.520 Mark Kushner: And here, you can see that the initial phase, there is already a spoke form and there's like n equals eight or like m equals 12 like you know, for, say, you can see that rotating. 269 00:39:06.030 --> 00:39:19.080 Mark Kushner: around like five microsecond which we're approaching it kind of becomes like m equals four right and as n equals four is I think there's just a numerical artifact because we have you know you know Cartesian box so it's like for most like you know that's like you know. 270 00:39:20.460 --> 00:39:24.450 Mark Kushner: forcing the plasma to the M equals four, but if we run it longer. 271 00:39:24.960 --> 00:39:36.480 Mark Kushner: The plasma oscillation becomes strong enough and there's a decay of this n equals four into n equals one type of mode, which you hope we can see like especially near the core right. 272 00:39:36.900 --> 00:39:40.800 Mark Kushner: And what's interesting more is that around like a microsecond which we pass. 273 00:39:41.040 --> 00:39:52.260 Mark Kushner: there's also radio non uniform me right, so the first like 10 microseconds it was just asking me so rotation, but now you see that it's like you know heavily like shifted even in the radial direction. 274 00:39:52.590 --> 00:40:00.480 Mark Kushner: Which is kind of a feature of the procedure if, like in the stroke dating spokes so this you know we you know submitted this is the space. 275 00:40:00.930 --> 00:40:09.480 Mark Kushner: To a paper, and you know, hopefully we can discuss more about the simulation results, but now the full fully mom mommy model is used to study rotating spokes. 276 00:40:10.080 --> 00:40:20.610 Mark Kushner: Now the summary of the fluid model is that we wanted to go, step by step, and showing that the drift diffusion model, maybe invalid for magnetized plasmas where the drift is large. 277 00:40:20.910 --> 00:40:25.290 Mark Kushner: That led us to developing the full fluid moment model that has an inertia terms. 278 00:40:25.590 --> 00:40:41.280 Mark Kushner: We did want the into the simulations we're also extending this to different applications, including high power microwave which i'm really excited about and we are also you know started to develop some 10 moment you know finite sorry a full full fully moment models. 279 00:40:42.900 --> 00:40:52.710 Mark Kushner: So hopefully in the future, I can talk more about this right, the final few slides is about the data driven model, so this is just a you know summary slide of what data driven model means. 280 00:40:53.370 --> 00:40:57.420 Mark Kushner: You have the physics based model on the right, which needs some input parameters. 281 00:40:57.660 --> 00:41:06.360 Mark Kushner: And from that you can get the simulation results, what we do is we compare that resolved with the experimental results, and we call that validation or right or like you know calibration. 282 00:41:07.080 --> 00:41:13.770 Mark Kushner: Then you compare them and if the agreement is not good you go back to psalm like you know the fudge factor, or the input parameters. 283 00:41:14.040 --> 00:41:24.720 Mark Kushner: and change that and rerun the simulation again to get the new simulation results when you get good agreement you claim victory and then say that we found that fudge factor that you know reproduces experimental result. 284 00:41:25.440 --> 00:41:39.870 Mark Kushner: Now for data driven model, this is what I want to call the offline validation because you need the simulation results compared repeated again get this amazing result compare again right, so this is kind of a after you get the simulation results like you know validation. 285 00:41:41.460 --> 00:41:50.100 Mark Kushner: So what we've started doing and I know that i'm running out of time, but so what we started doing is what I call the online estimation. 286 00:41:50.520 --> 00:41:57.900 Mark Kushner: or real time estimation real time destination, has been used for like spacecraft tracking or autonomous vehicle or even robotics. 287 00:41:58.260 --> 00:42:08.430 Mark Kushner: You measure something, and you acquire the information around you, you have some like low fidelity model, but you augment that estimate, based on the measurement and do the control theory right. 288 00:42:08.640 --> 00:42:16.380 Mark Kushner: So these will include like common variety of common filters that are very common in like you know controls and robotics community. 289 00:42:16.830 --> 00:42:26.670 Mark Kushner: Well i'm going to talk about here in the next few slides is we developed the extended conduit for plasma application, but we can also do like particle filters which, in their work for nonlinear systems. 290 00:42:26.970 --> 00:42:30.390 Mark Kushner: You can use like you know feeding functions or you can use like neural nets. 291 00:42:30.810 --> 00:42:37.710 Mark Kushner: You know there's a variety of like different tools, but here I want to talk about using the extended column and filter for plasma oscillations. 292 00:42:38.010 --> 00:42:45.510 Mark Kushner: So not going too much in detail what we wanted to do is take a low fidelity model which is zero the plasma global model. 293 00:42:45.840 --> 00:42:51.210 Mark Kushner: For like I neutral, you know reactions which gives you like you know predator prey kind of oscillations. 294 00:42:51.630 --> 00:42:57.000 Mark Kushner: And then, in the literature there's like you know different people doing different measurements of hall thruster. 295 00:42:57.270 --> 00:43:03.510 Mark Kushner: Very magnetic field varying like this church conditions and they found like you know different discharge modes right, so this is. 296 00:43:03.780 --> 00:43:12.570 Mark Kushner: This charge premium versus time, so what we did in this framework is take the publisher result that has the unsteady discharge kind of oscillation. 297 00:43:13.290 --> 00:43:22.080 Mark Kushner: Feed that back into the model so essentially doing an inverse problem and Kelly sm a the unknown parameter which we defined to be here the electronic temperature. 298 00:43:24.360 --> 00:43:31.830 Mark Kushner: So just very short extended column filter is quite unique and very impressive it took me some time to learn this on my own. 299 00:43:32.070 --> 00:43:38.880 Mark Kushner: I hope that, like, I took some control theory classes, when I was in Michigan so if there's anyone who's like thinking about it, I highly recommend. 300 00:43:39.570 --> 00:43:49.170 Mark Kushner: What we're trying to do is there's two phases, the physical space like you know prediction, and then they experiment or measurement like correct right so it's like a predictor correct or model. 301 00:43:49.800 --> 00:44:02.730 Mark Kushner: So this all in line on the bottom left shows that it's a prediction step right and then there's this discontinuities and the times steps that you augment that you know prediction, based on the experimental results. 302 00:44:03.150 --> 00:44:11.760 Mark Kushner: what's really fascinating about the extended common filter is that they will look into the measurements, which is the white tilda and what you have, as the estimate. 303 00:44:12.180 --> 00:44:19.980 Mark Kushner: Looking this difference and the common filter would tell you how much you have to correct that date, so this is, you know, describing this calming game. 304 00:44:21.960 --> 00:44:30.060 Mark Kushner: And not going into much detail, but this is the result that we did so they using the publish result of like discharge current oscillation in time. 305 00:44:30.450 --> 00:44:40.620 Mark Kushner: While we can estimate is like the electron temperature, which we know nothing about in this physical space model, and we have iron density and neutral density like you know low fidelity model. 306 00:44:40.890 --> 00:44:48.270 Mark Kushner: But we don't know whether that's correct right so what's the what the calf is doing is taking the measurement data in real time. 307 00:44:48.690 --> 00:45:00.750 Mark Kushner: estimating using the low fidelity model, along with them measurement correction and then surprisingly shows like very nice like you know plasma density and neutral density oscillations. 308 00:45:01.140 --> 00:45:11.130 Mark Kushner: Even we can see that the electron temperature nice to like you know follow that like you know sign a soil type oscillations so that this discharge permanent is oscillating as such. 309 00:45:11.850 --> 00:45:20.610 Mark Kushner: We extended this for like you know different conditions i'm showing you on the left, so you know, Christine grieve my PhD student in Texas a&m. 310 00:45:21.210 --> 00:45:31.530 Mark Kushner: She has been working on this and we are also preparing for another paper and there's other paper is applying the ETF to a post inductive the couple plasma. 311 00:45:32.070 --> 00:45:43.050 Mark Kushner: So you have these like plasma density experiment that you get from pulse, you know ICP and you know, while we treat it as an unknown was the electron power of sorts. 312 00:45:43.590 --> 00:45:52.260 Mark Kushner: Right, because there are some literature talking about like hey, you have the rf power How much is it going to go into the ions How much is it going to go to heat the materials and how much is it going to go to the electronic. 313 00:45:52.860 --> 00:46:01.740 Mark Kushner: This ETF allowed us to just use the plasma density time variation without knowing anything about the electron power absorption. 314 00:46:02.070 --> 00:46:09.750 Mark Kushner: This is what the ekg predicted, so the Ek didn't know about the duty cycle approach as a priority to this month modeling. 315 00:46:10.050 --> 00:46:25.770 Mark Kushner: But it's still recover the on phase in the office of the duty cycle, which I found really exciting and electron temperature is also shown on the bottom here that shows like you know, three V electron temperature drops to like 1.5 or even sometimes like around zero electron volts. 316 00:46:27.360 --> 00:46:33.330 Mark Kushner: So this is a summary of the data driven model what we're trying to do is model data fusion to do the real time estimation. 317 00:46:33.570 --> 00:46:42.930 Mark Kushner: Taking real time measurement data that has noise and uncertainty, but that's the beauty of the common filter how that filter filters all those noise and you know retains the. 318 00:46:43.170 --> 00:46:49.200 Mark Kushner: Important physical dynamics and we're applying that ETF to variety of things, including Plaza and chemistry. 319 00:46:49.560 --> 00:47:00.420 Mark Kushner: What we are excited about is applying this one in 2d like you know partial differential equations, which is, I think, a fundamental like cfd problem which I couldn't find in literature so we're excited to do this. 320 00:47:00.780 --> 00:47:03.630 Mark Kushner: And we're also going to try to apply this electric propulsion system. 321 00:47:03.930 --> 00:47:11.160 Mark Kushner: So in conclusion, what we're trying to do is we're trying to tackle this nonlinear multi scale coupling between different mechanisms. 322 00:47:11.400 --> 00:47:19.200 Mark Kushner: from small scale high frequency to the lowest frequency large scale structures for this, I wanted to like talked about like three different modeling techniques. 323 00:47:19.470 --> 00:47:29.190 Mark Kushner: One is a fluid model, the second is the kinetic model which sometimes we need to you know use high performance computing capabilities, the third one was our recent studies using data driven model. 324 00:47:29.730 --> 00:47:37.770 Mark Kushner: That this is my conclusion we're developing like different types of you know models and I just wanted to thank some of my important collaborators. 325 00:47:38.280 --> 00:47:39.780 Mark Kushner: Saving that Scott that has been really. 326 00:47:40.230 --> 00:47:48.960 Mark Kushner: A you know a good friend and very helpful and advancing the sciences and a few more people, especially wanted to thank my advisor who moved and CU boulder and boyd. 327 00:47:49.170 --> 00:47:59.730 Mark Kushner: and Professor or Krishna and Professor alligator or who are my you know Casey readers and also you know the mitzi opportunities, where amanda says the students so i'm really happy that i'm giving this talk here. 328 00:48:00.060 --> 00:48:10.950 Mark Kushner: I just wanted to also thank the funding agencies supporting my work and, if you have any questions here's the website and use an email address, so please let me know if you have any questions Thank you so much for your attention. 329 00:48:17.070 --> 00:48:19.710 Mark Kushner: Thank you very much, questions. 330 00:48:24.300 --> 00:48:27.030 Mark Kushner: I was curious about was application of columns filter to. 331 00:48:28.290 --> 00:48:34.260 Mark Kushner: kill yeah so in this in this is an example if you're trying to infer just one variable in your state vector. 332 00:48:34.680 --> 00:48:39.480 Mark Kushner: And so you might want to use this to say given some discharge current solutions and a suitably good one, the model. 333 00:48:39.540 --> 00:48:48.810 Mark Kushner: I mean for time are short timers all novelists pledge and frequency profiles, or something like that yeah would you just have the state vector be every single spatial point with you so. 334 00:48:49.530 --> 00:48:58.380 Mark Kushner: Great question, so the question was about one year application for UK and then that is the question though we're like you know constantly discussing was Christine. 335 00:48:58.740 --> 00:49:04.800 Mark Kushner: So, like you know you have like let's take 200 cells that has like plasma ncaa like on temperature and electric field. 336 00:49:05.250 --> 00:49:14.910 Mark Kushner: You can theoretically do that he gave on individual macroscopic quantities at individual cells, but the key here is that uncertainty, p. 337 00:49:15.360 --> 00:49:28.860 Mark Kushner: The tensor where the covariance right here, so this P is what's important for this common game what's the uncertainty that you have, therefore, you need to correct your data or trust that you know low fidelity physics based model. 338 00:49:29.280 --> 00:49:41.100 Mark Kushner: This key becomes so enormous when you have all those leads and all those cells, so what we're thinking as a starting point is do the you know low fidelity model and 200 cells are so let's just time. 339 00:49:41.370 --> 00:49:52.830 Mark Kushner: spatially average that quantity do like a zero D E, F try to get that back into the one D or tried to do like to median or three year vision model and then like step by step, like you, don't get to that full like Monday. 340 00:49:53.190 --> 00:49:58.560 Mark Kushner: So even one E, F is like super computationally challenging I was looking at I read a little while it was like. 341 00:50:00.060 --> 00:50:05.400 Mark Kushner: Oh yeah if you have any ideas, let me know yeah yeah, thank you for eating yeah thanks for the questions. 342 00:50:08.400 --> 00:50:19.470 Mark Kushner: So I have a question on this as well, so my will be quite naive questions because i'm great, but so it looked like the the the online. 343 00:50:20.910 --> 00:50:35.850 Mark Kushner: model algorithm was is essentially fitting to its optimizing the fat to actual experimental data So how do you get new physics inside if if you just fell into that data and you're starting with. 344 00:50:36.660 --> 00:50:43.350 Mark Kushner: physics equation that sort of fixed, how do you get physics inside and yeah interested right right. 345 00:50:44.130 --> 00:50:49.560 Mark Kushner: yeah absolutely the question was about what kind of physical and it's like can we get from these like data your models. 346 00:50:49.980 --> 00:51:00.900 Mark Kushner: So one thing that's important is that you can use this like common filter for high fidelity models like you know theoretically right well let's start from the low fidelity because that's easier to model and a quick run. 347 00:51:01.380 --> 00:51:07.080 Mark Kushner: So then, if you do the low fidelity model we can leave that terrible andhra and also electron transport as a parameter. 348 00:51:07.560 --> 00:51:18.780 Mark Kushner: right which is unknown like we don't know anything about that physics mathematically there's that term right as long as there's a term in that equation, we can estimate that equation augmented by the measure. 349 00:51:19.230 --> 00:51:24.300 Mark Kushner: So what you get is that and we I think we're getting somewhere, but you again like you know. 350 00:51:24.720 --> 00:51:34.530 Mark Kushner: If you look into the next slide like here's just like you know electron temperature is density and neutral density, but imagine you have that on our most electron transport, mobility, moving in time. 351 00:51:35.310 --> 00:51:49.260 Mark Kushner: So you can get that kind of information which will tell us like you know whether the crossfield electron transport is dynamically changing, which is something that like you know, our committee is working on oh just a follow up just going on with that yeah. 352 00:51:51.240 --> 00:51:56.040 Mark Kushner: yeah let's see do the robot be charged species has on their anomalous. 353 00:51:56.730 --> 00:52:06.090 Mark Kushner: Transport as anyone look better experiments to counterbalance on that because, at least with the it look like damping of those of the way was important. 354 00:52:06.450 --> 00:52:14.010 Mark Kushner: And like neutral injection to look at, to see if that has an effect, I know it's complicated experiment, but are you are you collaborating when you tell. 355 00:52:15.030 --> 00:52:26.790 Mark Kushner: someone like like doing experiments it, you can do with other other in other ways right, the question was about experimental evidence, so the wealthy for charged ions and. 356 00:52:27.180 --> 00:52:32.220 Mark Kushner: selena has done like you know Tom says caring for different conditions like with different species. 357 00:52:32.580 --> 00:52:42.060 Mark Kushner: One of the things that started this activity was that she added hydrogen ions into like a xenon flow and that had like tremendous effect in terms of the waves that she was measuring. 358 00:52:42.600 --> 00:52:49.650 Mark Kushner: We tried to do that simulation wise, but what we found was that adding hydrogen Ion would also change the equilibrium solution right. 359 00:52:49.980 --> 00:53:02.340 Mark Kushner: So it's kind of a tricky question without we happy to discuss with you more by adding something you're going to change the equilibrium solution, so you have to set kind of a good test case that you know that you're not producing that you know city state yeah. 360 00:53:07.980 --> 00:53:10.170 Mark Kushner: you've done the conservation equations yes. 361 00:53:11.520 --> 00:53:17.010 Mark Kushner: Could you describe what you how you model, the transport, so are you a model once your closure model. 362 00:53:18.030 --> 00:53:28.020 Mark Kushner: I say yes, the closure model so far for the five moments is the same as the like you know the boiler equation, which is using the ideal gas law. 363 00:53:28.290 --> 00:53:41.970 Mark Kushner: So the rotating spoke simulation that I was showing was basically similar to boiler equation so just using like P equals NKVD but, like you know, in the 10 moment model, for instance, like, why is this showing well. 364 00:53:43.140 --> 00:53:47.040 Mark Kushner: So i'm just i'm just looking at the zoom screen so i'm just going to leave at home. 365 00:53:48.900 --> 00:53:56.100 Mark Kushner: i'm just going to leave it like this, so that in the DEMO model what we're trying to do is you can formulate the second moment. 366 00:53:56.430 --> 00:54:02.910 Mark Kushner: Not the total energy but individual like you know, and I said proper pressure sensor elements so that's going to you know. 367 00:54:03.660 --> 00:54:14.310 Mark Kushner: be interesting, because this is going to be P P bar bar is going to be exact, because there is an equation for that there's an additional closer problem for that, like you know pressure tensor equations. 368 00:54:14.580 --> 00:54:27.750 Mark Kushner: So how do you close that we have some idea we try to formulate like a Chapman escalade kind of closure, which is very similar to how you get like you know the shear stress viscous your stress and like and have you stokes, so I think we have some idea to close it. 369 00:54:29.160 --> 00:54:30.420 Mark Kushner: Sure didn't have any inclusion. 370 00:54:31.530 --> 00:54:39.240 Mark Kushner: No yes yeah in the results that I showed like you know it was collision less but, like the ESTA ionization to create that steady state Plaza. 371 00:54:39.630 --> 00:54:55.470 Mark Kushner: yeah and assuming ideal gas law, yes, so whether that model is applicable to real physics that's another question, I think we have some ideas that it may be relevant, but yes, like you know how to like understand that fluid formulation versus a kinetic is still ongoing question. 372 00:54:57.690 --> 00:54:59.550 Mark Kushner: I guess a related question to that so. 373 00:55:00.690 --> 00:55:06.120 Mark Kushner: Unless if you do included and enhance mobility in the diffusion equation. 374 00:55:07.290 --> 00:55:13.470 Mark Kushner: arguments about inertia are those as important, or do you think when you do include enhanced. 375 00:55:15.600 --> 00:55:24.660 Mark Kushner: Still was important in Hall for us from yeah right okay yeah So the question was if you add the inertia term in the presence of the collisions with inertia terms, so the important. 376 00:55:25.350 --> 00:55:33.780 Mark Kushner: I think, based on the measurements, which are often time average just using that and I have it in my PhD dissertation that I did some calculation. 377 00:55:34.110 --> 00:55:39.780 Mark Kushner: So sheer gradient terms can be pretty comparable or larger than the collision frequency. 378 00:55:40.380 --> 00:55:48.990 Mark Kushner: So that's why I started thinking about this and how to formulate it so because, like the collision frequency is like maximum of 10 to the seven hertz right. 379 00:55:49.440 --> 00:55:59.490 Mark Kushner: Like in like in our classically right, but like, if you take, like the velocity gradients then it can be on door to like 10 to the eight like you know, even with the time average results. 380 00:56:00.210 --> 00:56:07.020 Mark Kushner: yeah, so I think the interesting thing is that if that's still like you know the steady state plasma discharge. 381 00:56:07.290 --> 00:56:18.900 Mark Kushner: What happens if it's on see right like you know that sheer gradient is moving in time and space and how is that going to you know, create like a reasonable stress as a time average term that's kind of the interesting part, I think. 382 00:56:20.580 --> 00:56:24.570 Mark Kushner: I have one question on the chat So can I just answer this or. 383 00:56:26.190 --> 00:56:40.410 Mark Kushner: miracle thanks for the question in part one, you are considering opportunity simulations if you weren't the extended 3D simulation would you maintain similar structures, asking, because on city turn excellent question, so the question was about to Eve vs 3D effects. 384 00:56:41.670 --> 00:56:45.210 Mark Kushner: This is why i'm trying to develop a fluid model, starting from 2d. 385 00:56:45.570 --> 00:56:52.500 Mark Kushner: Because like in the fluid term last Community people do to 2d like turbulence simulation and then they saw like a inverse cascade. 386 00:56:52.800 --> 00:56:57.810 Mark Kushner: But then, if you do 3D then there's no and there's cascade and there's always a cascade to the smaller scale. 387 00:56:58.260 --> 00:57:08.970 Mark Kushner: which I think would apply to our plasma cases So if you do 2d there's like you know if you do the theory there's resonances that locks that mode to certain wavelength and frequency. 388 00:57:09.270 --> 00:57:16.170 Mark Kushner: If you do 3D which we also are working on and we're working on some publication growth rate structure changes drastic. 389 00:57:16.680 --> 00:57:19.500 Mark Kushner: And it becomes more broadband like an acoustic model. 390 00:57:19.830 --> 00:57:28.890 Mark Kushner: So yes, like you know, there is going to be differences in the 2d 3D but the rotating spoke, for example, is a lower frequency like fluid structure, so I think like you know. 391 00:57:29.160 --> 00:57:44.280 Mark Kushner: Some of them will still be there, even in 3D simulations and john for one core also asked the question, thank you john ability effects was totally charged ions perhaps different driven by differences in Q amp m just may be related to work by her school and later bye well rude. 392 00:57:45.510 --> 00:57:51.720 Mark Kushner: And multi species transport yeah absolutely in this paper that I worked on with city not Scott. 393 00:57:52.350 --> 00:57:59.910 Mark Kushner: We cited and we read you know mania of US scott's earlier work about the w charged ions were outside the different charts species. 394 00:58:00.870 --> 00:58:10.410 Mark Kushner: leading to is to stream to stream instability that can like you know thermal is is species So yes, i'm aware of that and I think we're seeing the similar thing. 395 00:58:10.740 --> 00:58:21.480 Mark Kushner: What we are kind of you know, adding on to like Scott and all his work is that what is that way, the effect to the cross field electron transport so john, thank you for the comment. 396 00:58:24.120 --> 00:58:24.390 Mark Kushner: You. 397 00:58:26.940 --> 00:58:28.020 Mark Kushner: know you always are. 398 00:58:30.330 --> 00:58:36.270 Mark Kushner: So, in your simulations of great keep nerds pulse plasma dyson. 399 00:58:38.220 --> 00:58:50.250 Mark Kushner: There was some information that you didn't use it you couldn't have you, yes, and that was that the power goes to zero, in the interim false yes. 400 00:58:51.660 --> 00:58:56.100 Mark Kushner: What would the outcome me I can force that swoosh. 401 00:58:57.600 --> 00:59:00.840 Mark Kushner: interesting idea I haven't done that. 402 00:59:04.860 --> 00:59:12.810 Mark Kushner: I think I am happy with the results so far, even if there's like oscillation patterns that you can see that's purely numerical because, like. 403 00:59:13.080 --> 00:59:23.160 Mark Kushner: It kind of overshoot and like when it's negative like we just need to reinforce it back to like positive so that's why there's a numerical oscillation but time average wise like it's only like two three Watts. 404 00:59:23.550 --> 00:59:28.170 Mark Kushner: So, like it's very close to zero so i'm kind of happy with the results so far. 405 00:59:30.750 --> 00:59:40.320 Mark Kushner: Because we didn't know like if the ETF would predict that, like you know near zero condition, but if we already appropriate up a priori know that it's zero was. 406 00:59:40.710 --> 00:59:51.060 Mark Kushner: Then, that would lead make some room to change other parameters so like that's an interesting idea yeah we can set the shape of the pulse and let's say. 407 00:59:51.360 --> 01:00:04.320 Mark Kushner: If you don't know about like you know this reaction like pending ionization raid, then we can you know leave that as an unknown and use these experimental data to study the reaction rate box that's not one other idea okay.