WEBVTT 1 00:00:02.170 --> 00:00:08.699 Mark Kushner: Try again. Good afternoon, everyone. It's my pleasure to introduce our speaker, Dr. Charles Starrett from Los Alamos. 2 00:00:08.930 --> 00:00:19.509 Mark Kushner: Dr. Starr got his PhD from Queen's University, Belfast, in 2007, studying the properties of quasitronium and its interaction with matter. 3 00:00:19.720 --> 00:00:34.460 Mark Kushner: After that, he did a postdoc at CA, which is the French Atomic Energy Division, for a few years before joining Los Alamos, where he's built his career studying, the materials, properties and atomic physics of 4 00:00:34.760 --> 00:00:38.690 Mark Kushner: Plasma is under extreme conditions, so extremely high densities and temperatures. 5 00:00:39.030 --> 00:00:46.909 Mark Kushner: I'm excited to hear about, your work today and your talk. And before you start, we have a little memento. 6 00:00:47.210 --> 00:00:49.970 Mark Kushner: A mug. Thank you so much. 7 00:00:50.130 --> 00:00:54.159 Mark Kushner: And I think we have to get a picture of this. So let me get you the 8 00:00:55.850 --> 00:01:04.100 Mark Kushner: Beautiful. Alright, and I'm supposed to tell you that is more rare than Nobel Prize. Excellent, thank you. 9 00:01:06.590 --> 00:01:16.270 Mark Kushner: Good afternoon, everybody. Thank you for coming to this talk, and thank you to Scott for organising it, and everyone else who organised it. 10 00:01:16.480 --> 00:01:20.110 Mark Kushner: I really appreciate the chance to talk about my research. 11 00:01:21.280 --> 00:01:26.319 Mark Kushner: I'm going to talk about the properties of hot, dense matter. 12 00:01:26.450 --> 00:01:33.480 Mark Kushner: My name is Charlie Starrett, Los Alamos. We care about this stuff we call warm, dense matter or hot, dense matter. 13 00:01:33.840 --> 00:01:42.789 Mark Kushner: This is a little AI schematic of what AI thinks warm does matter is, and it's pretty accurate. 14 00:01:42.900 --> 00:01:44.590 Mark Kushner: You can see that. 15 00:01:44.710 --> 00:01:48.839 Mark Kushner: on the Y axis here. Maybe I should use this pointer. 16 00:01:49.300 --> 00:01:53.089 Mark Kushner: We have temperature, so we're running here from about a thousand 17 00:01:53.720 --> 00:01:59.150 Mark Kushner: Kelvin up to, like, a billion Kelvins, so it's a huge range of temperature. 18 00:01:59.260 --> 00:02:10.720 Mark Kushner: 10 to the minus 8 grams per CC. So that's really low density, like vacuum space boards there, up to 10 to 6 grams per cubic centimeter. 19 00:02:11.260 --> 00:02:16.060 Mark Kushner: Nomal matter is is sort of around here, but lower temperature. 20 00:02:16.430 --> 00:02:20.699 Mark Kushner: Gas, which is down here. Plasma's all around here. 21 00:02:20.980 --> 00:02:32.130 Mark Kushner: and we care about these regions here in yellow and red, where you have densities about normal densities within a factor of 100 either way, say. 22 00:02:32.420 --> 00:02:34.760 Mark Kushner: And testers from Abidin. 23 00:02:35.040 --> 00:02:39.880 Mark Kushner: 10,000 Kelvin up to, say, 10 million or 100 million. 24 00:02:40.330 --> 00:02:49.820 Mark Kushner: What's going on here in nature is you can have the cores of giant planets at these rough reefs under these conditions. 25 00:02:50.240 --> 00:02:54.069 Mark Kushner: You can also have the solar cores up here. 26 00:02:54.340 --> 00:03:01.909 Mark Kushner: There's also white dwarf cores, which are much denser, but of course the envelope, the atmospheres of white dwarfs fall right through this regime. 27 00:03:02.460 --> 00:03:17.019 Mark Kushner: In inertial confinement fusion, which is a fusion scheme, the material heats up to these sorts of conditions, but of course, to get to these conditions, it's got to start down here. It goes through this warm and hot desk matter regime. 28 00:03:17.020 --> 00:03:24.769 Mark Kushner: So, if you want to understand any of these systems or these experiments, you have to understand the properties of warm dense matter. 29 00:03:26.330 --> 00:03:28.730 Mark Kushner: And… No. 30 00:03:29.510 --> 00:03:36.690 Mark Kushner: So, to accurately model these systems, people use these equations called the hydrodynamic equations. 31 00:03:36.920 --> 00:03:40.189 Mark Kushner: I don't know anything about this, so, 32 00:03:40.480 --> 00:03:55.490 Mark Kushner: don't ask you any questions. But there's these 3, these 3 equations they care about, and they just they're come from these contribution laws, the conservation of mass and measurement energy. And they solve these equations to model things like the sun. 33 00:03:55.700 --> 00:04:05.000 Mark Kushner: or fusion plasmas. And these equations are closed by materials data. Material data, including the equation of state. 34 00:04:05.460 --> 00:04:10.809 Mark Kushner: The equation state is something like the pressure or energy is a function of temperature and density. 35 00:04:13.030 --> 00:04:22.540 Mark Kushner: There's also opacity. This is how opaque the material is to photons, to light. So how does light travel through the material? 36 00:04:22.970 --> 00:04:28.889 Mark Kushner: And that, like, can be absorbed or emitted by the thing, so you can also have emission, not just opacity. 37 00:04:29.000 --> 00:04:33.349 Mark Kushner: And then you have particle transport stuff like the thermal connectivity. 38 00:04:33.760 --> 00:04:51.120 Mark Kushner: or viscosity, which I've labeled here. You can also have things like electron connectivity, which is more day-to-day. So how conductive is this wire? Well, you can measure it, but what if the wire is made out of a plasma? How conductive is that? That is what… that's the sort of thing we care about. 39 00:04:53.400 --> 00:04:56.840 Mark Kushner: So it's this stuff on the right that I that I care about. 40 00:04:57.840 --> 00:05:09.119 Mark Kushner: Now, I said the temperatures are like an EV and upwards. That's 10,000 Kelvin upwards. It's really hot. So, you know, a lot of people just think we're dealing with an ideal gas. 41 00:05:09.520 --> 00:05:14.420 Mark Kushner: But that's not the case. It turns out that, that 42 00:05:15.620 --> 00:05:19.990 Mark Kushner: I've got a figure here where we're looking at the average ionization 43 00:05:20.280 --> 00:05:22.699 Mark Kushner: Of iron, as an example here. 44 00:05:23.210 --> 00:05:32.420 Mark Kushner: So this is density on the X-axis, so very low density to very high density. And each of these lines here, these different colored lines, corresponds to a different temperature. 45 00:05:32.690 --> 00:05:36.349 Mark Kushner: So this would be an iron plasma at 10,000 Kelvin. 46 00:05:36.670 --> 00:05:50.330 Mark Kushner: And about, oh, let's see, let's put it here, about 1 gram per cc. So this model, which we created, can tell you what the average number of free electrons per atom is at these conditions. So I'm not going to get into big… 47 00:05:50.480 --> 00:06:01.950 Mark Kushner: how we make that model, but the point I want to make is that even at these high temperatures, certain densities, it's not fully ionized. That means there are bound electrons 48 00:06:02.380 --> 00:06:06.619 Mark Kushner: in the plasma, even at these super high temperatures and super high densities. 49 00:06:06.810 --> 00:06:13.899 Mark Kushner: And you don't know a priori how many of these bound electrons there are, how many free electrons there are. 50 00:06:14.050 --> 00:06:19.139 Mark Kushner: So you have to have a model for that. And the model needs to be a quantum mechanical model. 51 00:06:19.390 --> 00:06:22.510 Mark Kushner: The Husky-find electrons are quantum mechanical objects. 52 00:06:23.490 --> 00:06:24.340 Mark Kushner: So. 53 00:06:24.600 --> 00:06:37.519 Mark Kushner: not only is it not an ideal gas, but you don't know many free electrons per atom there are. But beyond that you don't even know the more subtle details like, yeah, how these atoms are correlated, how the electrons are correlated. 54 00:06:37.530 --> 00:06:46.039 Mark Kushner: All the subtle details of this crude quantity, like Z bar glossed over, are completely, you need a quantum mechanical model. 55 00:06:46.170 --> 00:06:47.030 Mark Kushner: Get out. 56 00:06:48.630 --> 00:06:51.240 Mark Kushner: Okay, so that sort of sets the frame. 57 00:06:52.100 --> 00:06:55.130 Mark Kushner: of what I'm talking about. So we want these properties. 58 00:06:56.000 --> 00:06:58.860 Mark Kushner: Plasmids of interest are quantum mechanical. 59 00:06:59.040 --> 00:07:05.889 Mark Kushner: But it turns out they're also relativistic. So if you want to solve for these properties, you have to solve for the electronic structure. 60 00:07:06.350 --> 00:07:10.789 Mark Kushner: So to do that, we solve typically the time-independent Dirac equation. 61 00:07:10.970 --> 00:07:20.100 Mark Kushner: So, some of you will have done quantum mechanics where you probably did the Schrodinger equation, I'm guessing. So, Schrodinger equation is very similar to this. 62 00:07:20.510 --> 00:07:25.770 Mark Kushner: You just drop these first two terms, and you have, like, a momentum Operator? 63 00:07:26.130 --> 00:07:34.240 Mark Kushner: Dirac just allows you… it just includes relativity, it includes special relativity. You need that because it, as we'll see, for atoms. 64 00:07:34.450 --> 00:07:44.200 Mark Kushner: the atoms are very… the bound states are very deeply bound, and those electrons are relativistic. So if you want to get the properties of those bound states right, for certain properties, you need 65 00:07:44.540 --> 00:07:46.159 Mark Kushner: the the direct conclusion. 66 00:07:46.350 --> 00:07:51.940 Mark Kushner: For other things, you can just get away with Schrodinger's, but generally you need the Durac. 67 00:07:52.890 --> 00:08:00.970 Mark Kushner: So, here in this equation, the unknowns are these… these… these wave functions, or eigenstates, psi, I, 68 00:08:01.240 --> 00:08:12.169 Mark Kushner: and these eigenenergies, E, EI. So, you saw this equation for these, and the I labels which state you're talking about. There are multiple solutions, multiple eigenstates. 69 00:08:12.530 --> 00:08:22.739 Mark Kushner: And I runs from zero to infinity. There's infinitely many of these states. You can order them in energy. Zero would be the lowest energy one, and that's called the ground state. 70 00:08:24.250 --> 00:08:29.969 Mark Kushner: V contains all the interactions. So in this we're just considering electrons and nuclei. 71 00:08:30.250 --> 00:08:33.700 Mark Kushner: And this would be the Coulomb interaction between all those particles. 72 00:08:35.320 --> 00:08:43.069 Mark Kushner: Now, at zero temperature, or room temperature, it's basically zero temperature, as far as electronic structure is concerned. 73 00:08:44.680 --> 00:08:55.389 Mark Kushner: Turns out you really generally only need the lowest energy solution to this. If you've got a collection of ions and electrons, you just need the ground state, most of the time. Not always, but most of the time. 74 00:08:55.780 --> 00:09:02.269 Mark Kushner: and that will tell you all the the parameters you're interested in. But in in warm dense matter and hot dense matter. 75 00:09:02.890 --> 00:09:06.380 Mark Kushner: There's a whole host of these states that come into play. 76 00:09:06.640 --> 00:09:15.660 Mark Kushner: So there's something called the Boltzmann probability, which basically says the probability that an excited state will exist in a plasma is equal to this. 77 00:09:15.810 --> 00:09:20.009 Mark Kushner: Exponential of minus beta. Beta is 1 over the temperature. 78 00:09:20.200 --> 00:09:23.940 Mark Kushner: And F is basically the energy of that atom. 79 00:09:24.210 --> 00:09:25.730 Mark Kushner: We're that excited to see it. 80 00:09:27.510 --> 00:09:43.889 Mark Kushner: So you can see that at zero temperatures, only the lowest one of these will have a probability non-zero, and the probability will be one. But as temperature goes up, this function is going to spread out, and you're going to get a lot more of these excited states. 81 00:09:44.260 --> 00:09:56.239 Mark Kushner: So this is not only we need the ground state like you normally need in solid state physics. But you need all these excited states, not necessarily infinitely many of them, but a lot of them, and comes a formidable challenge. 82 00:09:56.760 --> 00:10:00.390 Mark Kushner: Well, it's a formidable challenge under normal conditions, as I say here. 83 00:10:00.500 --> 00:10:03.130 Mark Kushner: But you need all these excited states, too. 84 00:10:05.180 --> 00:10:06.000 Mark Kushner: Okay. 85 00:10:07.770 --> 00:10:10.110 Mark Kushner: So what do we do? Where do you start? Well. 86 00:10:11.390 --> 00:10:16.160 Mark Kushner: I would say one of the most popular tools in our field is density functional theory. 87 00:10:17.340 --> 00:10:23.509 Mark Kushner: Density functional theory, can I have a quick show of hands who is familiar with density functional theory? 88 00:10:24.450 --> 00:10:27.149 Mark Kushner: So, maybe a third of the room, something like that. 89 00:10:28.330 --> 00:10:32.900 Mark Kushner: The basic idea is that you have this n-body problem. 90 00:10:33.390 --> 00:10:42.450 Mark Kushner: and you reduce it to an effective one-body problem. So we all know that you can solve the Schrodinger equation for hydrogen, right? That's a one-body problem, one electron. 91 00:10:43.110 --> 00:10:44.729 Mark Kushner: a one electron problem. 92 00:10:45.350 --> 00:10:57.059 Mark Kushner: But it turns out DFT turns any system with any number of electrons into an effective one-body problem. The one electron then moves in an effective field of all the other particles. 93 00:10:57.760 --> 00:11:07.630 Mark Kushner: So you can tell straight away that's going to be a super speed up. The M-body problem is totally intractable. Even if you have helium, you can't solve it exactly. And that's only got two electrons. 94 00:11:08.410 --> 00:11:16.810 Mark Kushner: If you've got uranium, you've got 92 electrons, so you've got no hope there. And of course, there's more than one ion in the problem, or nucleus. 95 00:11:16.950 --> 00:11:22.210 Mark Kushner: I've got those numbers, you know, 6 times 10 to the 23, so that's a lot of particles. 96 00:11:22.730 --> 00:11:27.799 Mark Kushner: So you're really hosed. But it turns out that if you use Dft. 97 00:11:27.920 --> 00:11:39.900 Mark Kushner: You can reduce it to this one electron problem, and it happens, you can reduce it, you can just assume there's only a few hundred or even a few tens of nuclei, and that seems to be good enough. 98 00:11:43.130 --> 00:11:44.840 Mark Kushner: But, as you know. 99 00:11:47.080 --> 00:12:01.099 Mark Kushner: We are interested… we're interested in a huge domain of temperatures and densities. I showed you that figure where we range from, like, 10 to minus 6 to 10 to the 6th in density, and… Huge range of temperatures. 100 00:12:01.570 --> 00:12:05.879 Mark Kushner: So, you need to make a model that works everywhere reasonably well. 101 00:12:06.110 --> 00:12:09.390 Mark Kushner: But it's also quick enough that you can get the data you care about. 102 00:12:09.800 --> 00:12:23.939 Mark Kushner: So, we often use this average atom approximations. Instead of using DFT for many, many centers, that's many nuclei, you say, well, I've only got one nuclei surrounded by an average plasma. 103 00:12:24.860 --> 00:12:33.139 Mark Kushner: and you just solve for this average atom model, and that may seem quite crude and quite severe, and I would agree with you. It does seem quite crude and severe. 104 00:12:33.370 --> 00:12:35.819 Mark Kushner: But it works quite well, as I'll show. 105 00:12:36.870 --> 00:12:42.969 Mark Kushner: And this is much faster to solve, as you could expect, after most cases of interest, it's accurate enough. 106 00:12:46.550 --> 00:13:02.629 Mark Kushner: Okay, so I'm going to take you through a few slides now. When I started at Los Alamos, I developed my own average atom model, and we looked at applications of it. I'm going to take you through these applications, and everything's going to look hunky-dory until it's not. 107 00:13:02.970 --> 00:13:04.750 Mark Kushner: We'll get to that in a minute. 108 00:13:05.460 --> 00:13:15.009 Mark Kushner: So, the first thing is the equation of state. So, it turns out you can measure the equation of state of these dense plasmas. You can do it on facilities like the National Ignition Facility. 109 00:13:15.280 --> 00:13:18.380 Mark Kushner: in Lawrence Livermore National Lab in California. 110 00:13:20.450 --> 00:13:22.269 Mark Kushner: So what you do, I mean. 111 00:13:23.450 --> 00:13:30.810 Mark Kushner: From my… I'm a theorist, right, so take this experimental description with a piece of salt, but basically. 112 00:13:31.010 --> 00:13:35.000 Mark Kushner: NIF has 192 laser beams. 113 00:13:35.150 --> 00:13:38.289 Mark Kushner: 2 megajoules, I believe it's the most powerful laser in the world. 114 00:13:38.800 --> 00:13:42.339 Mark Kushner: They shine into this hall room, which is like a gold tube. 115 00:13:42.700 --> 00:13:53.689 Mark Kushner: The lasers hit the gold and the gold heats up and emits X-rays. The X-rays bathe a target, which is like a roughly BB ball size pellet of material. 116 00:13:53.770 --> 00:14:09.430 Mark Kushner: and the X-ray is heated up and it compresses violently, and you launch a shock into the material, and you can measure the shock speed. But from that you can get something called a Hugoniot curve. So it measures the, it basically is the pressure versus compression of the material. 117 00:14:09.990 --> 00:14:19.189 Mark Kushner: So in 2020 and 2018, these groups based at Lawrence Livermore I've measured the… 118 00:14:19.620 --> 00:14:24.220 Mark Kushner: tugonio of plastic. That's C. 9, 8, 10. 119 00:14:24.880 --> 00:14:30.049 Mark Kushner: at these super high pressures. So this is in Megabar. This axis is in Megabar. 120 00:14:30.200 --> 00:14:44.209 Mark Kushner: One bar is about one room temperature. The megabar is a million… sorry, room… room pressure. So megabar is about a million times room pressure. And here they're measuring hundreds to nearly a giga. 121 00:14:44.280 --> 00:14:54.950 Mark Kushner: giga giga bar of a thousand bar. So this is really super high pressure. You can see the experiments in red and black, and the average atom model 122 00:14:55.130 --> 00:15:05.740 Mark Kushner: is in black. Sorry, the experiment's in blue and red, and the average animal model's in black. And it has this nice little kink that goes through both sets of data. 123 00:15:06.520 --> 00:15:11.929 Mark Kushner: So this was a really nice demonstration that 124 00:15:12.580 --> 00:15:20.329 Mark Kushner: these models are realistic, and these effects here are quantum mechanical effects. They're from the shells in the atom. 125 00:15:20.510 --> 00:15:22.520 Mark Kushner: Which the simpler models don't have. 126 00:15:23.670 --> 00:15:30.399 Mark Kushner: Okay, so that was one thing we did. Another thing you can look at is particle transport. 127 00:15:31.000 --> 00:15:38.060 Mark Kushner: So I told you we're interested in how thermal connectivity and stuff like that. We're also interested in diffusion. 128 00:15:38.470 --> 00:15:45.870 Mark Kushner: And one of the first things we did was work out how to calculate the interatomic forces with these average atom models. 129 00:15:46.370 --> 00:15:52.999 Mark Kushner: That might be slightly counterintuitive, because if you've only got one atom in the plasma, how could you have an interatomic force? 130 00:15:53.140 --> 00:15:57.010 Mark Kushner: But we we figured out how to do it, and it turns out to work out pretty well. 131 00:15:57.220 --> 00:16:01.540 Mark Kushner: So these are these are molecular dynamic simulations of 132 00:16:01.970 --> 00:16:10.020 Mark Kushner: our model compared to one of these many atom models. So you don't make the average atom approximation. You have the many ions in your box. 133 00:16:10.330 --> 00:16:21.330 Mark Kushner: But it still does see functional theory. Our model was pseudoatom molecular knowledge compared to the many atom, which is labeled PFND, agrees very well. 134 00:16:22.530 --> 00:16:24.139 Mark Kushner: resistance for aluminum. 135 00:16:24.990 --> 00:16:29.569 Mark Kushner: And these are 2 different densities. And you can see we're going up a range of temperatures here. 136 00:16:30.620 --> 00:16:36.360 Mark Kushner: I guess what I'm trying to get at here is that it works well compared to the other Dft models. 137 00:16:36.660 --> 00:16:39.789 Mark Kushner: There's also this experiment where they measured this thing. 138 00:16:40.460 --> 00:16:45.960 Mark Kushner: This is again at… oh, not again, this was at the LCLS, which is the linear… the. 139 00:16:46.180 --> 00:16:48.809 Mark Kushner: It's a free electron laser in Stanford. 140 00:16:49.240 --> 00:16:56.209 Mark Kushner: They heated up a block of aluminium and compressed it to these conditions and measured, like, the X-ray scattering 141 00:16:57.630 --> 00:17:00.139 Mark Kushner: It's called an elastic scattering feature. 142 00:17:00.450 --> 00:17:05.279 Mark Kushner: But it turns out that you can break that from our model, from the average out of model, and we got this great agreement. 143 00:17:05.859 --> 00:17:15.659 Mark Kushner: So, I mean, I haven't given you a lot of detail here, but what I'm telling you is that, you know, not only does it agree with the more sophisticated models, but it agrees with experiments, so it's looking good. 144 00:17:16.420 --> 00:17:21.329 Mark Kushner: We worked with Scott Ballard, Professor Ballard here. 145 00:17:21.650 --> 00:17:31.889 Mark Kushner: back in 2016. And instead of using molecular dynamics to predict these transport quantities, you just use kinetic theory. So, you don't have to go to all the complication of molecular dynamics. 146 00:17:32.200 --> 00:17:36.530 Mark Kushner: You just plug it into your equation and it spits out the transport quantity. 147 00:17:36.810 --> 00:17:44.190 Mark Kushner: And here's some examples of, again, this is hydrogen and iron. There's the densities, about 8 grams. 148 00:17:44.470 --> 00:17:47.099 Mark Kushner: We're looking at a huge range of temperatures again. 149 00:17:47.660 --> 00:17:52.669 Mark Kushner: And, we're comparing to the many atom DFT. 150 00:17:54.030 --> 00:17:55.729 Mark Kushner: which is the circles here. 151 00:17:56.500 --> 00:18:06.989 Mark Kushner: And then that's our models. And the PAMD model is the molecular dynamics model is the dashed line, and it agrees well with the PFMD, which is the many atom simulation. 152 00:18:07.330 --> 00:18:12.360 Mark Kushner: And EPT plus AA is just… it's… Tiberium, but it's a. 153 00:18:12.460 --> 00:18:17.830 Mark Kushner: It's Professor Baldwin's kinetic theory coupled to our average atom model. 154 00:18:17.970 --> 00:18:23.410 Mark Kushner: and it agrees very well for most of the regime, and we understand why it doesn't agree down here. 155 00:18:23.810 --> 00:18:28.109 Mark Kushner: So… So you can do really well for these transport properties of this model. 156 00:18:28.790 --> 00:18:32.180 Mark Kushner: And the last thing I'm going to show you, I think it's the last thing. 157 00:18:32.440 --> 00:18:37.040 Mark Kushner: proves… that I think proves that our Horizontal models are doing well is this. 158 00:18:37.540 --> 00:18:45.740 Mark Kushner: There's a stopping power calculation that my postdoc, who just became staff at Lothian, Zach Johnson, has a paper on. 159 00:18:46.160 --> 00:18:59.329 Mark Kushner: Here he's looking at stopping power, so this is like if you fire a proton into a block of, of, of, Tungsten? Metal? How's that energy deposited in the tungsten? How quickly does it slow down? 160 00:18:59.500 --> 00:19:02.360 Mark Kushner: This is, like, the energy loss per unit distance here. 161 00:19:02.620 --> 00:19:07.169 Mark Kushner: This is… this is not warm dense matter, this is just room temperature and density. 162 00:19:07.540 --> 00:19:09.999 Mark Kushner: The IAEA has a database. 163 00:19:10.210 --> 00:19:11.510 Mark Kushner: It's done. 164 00:19:12.050 --> 00:19:21.280 Mark Kushner: ZAC model is a high velocity model, and it agrees very well with high velocities. Some difference down here, but we don't really expect it to work there. 165 00:19:21.490 --> 00:19:32.479 Mark Kushner: And the sort of standard model where you only look at free electrons is here. The difference being that in the average atom model, you have these bind electrons, and you get this extra stopping power. 166 00:19:32.930 --> 00:19:34.580 Mark Kushner: So that seems to work there. 167 00:19:34.990 --> 00:19:41.719 Mark Kushner: My final thing here is an application. This is an application to white dwarfs. 168 00:19:42.450 --> 00:19:48.570 Mark Kushner: So we looked at, we recalculated the thermal conductivity of of hydrogen. 169 00:19:48.680 --> 00:19:50.949 Mark Kushner: In the swarm that's moderating. 170 00:19:51.270 --> 00:19:54.989 Mark Kushner: And we looked at what was in the… 171 00:19:55.130 --> 00:19:59.869 Mark Kushner: The White Dwarf modeling code, I think it's called MESA. 172 00:20:00.380 --> 00:20:12.369 Mark Kushner: And I think this is pronounced Yoffy. This institute in Russia has their own model for thermal conductivity, and it was being used by all these people modelling stars. 173 00:20:13.150 --> 00:20:23.349 Mark Kushner: Well, our model predicted some differences and we put this table in. A postdoc called Simon Blouin put this into these white dwarf models. 174 00:20:23.470 --> 00:20:33.070 Mark Kushner: and find that using the Yaffe model, he got the black luminosity curve. So this is the luminosity of the white dwarf as a function of 175 00:20:33.750 --> 00:20:46.120 Mark Kushner: of years, how old it is essentially. So you can see, it gets about 12 billion years, it gets this luminosity. And if you change the thermal conductivity, you get this very different answer by about a billion years here. 176 00:20:46.400 --> 00:20:52.279 Mark Kushner: So it makes a difference to these real world properties doing a proper treatment of these quantities. 177 00:20:52.790 --> 00:21:01.999 Mark Kushner: And I would just like to add that I don't think this picture is settled yet. Our model we used there was somewhat crude, although better than the Yaffe model, in my opinion. 178 00:21:02.180 --> 00:21:05.579 Mark Kushner: But I think there's still work to be done there. 179 00:21:06.550 --> 00:21:10.710 Mark Kushner: So okay, so I've just convinced you that AIA models are 180 00:21:10.890 --> 00:21:14.600 Mark Kushner: wonderful. They can solve any problem in dense plasmas. 181 00:21:14.950 --> 00:21:20.410 Mark Kushner: And, despite their crudeness, right? Because, I mean, they're just one atom in a plasma. 182 00:21:21.250 --> 00:21:27.389 Mark Kushner: But then we started to look at Opacity, and this is where things started to go very wrong. 183 00:21:28.050 --> 00:21:29.539 Mark Kushner: So if you just 184 00:21:30.140 --> 00:21:41.759 Mark Kushner: Oh, well, okay, so there was this paper in 2015, I believe, a higher than predicted measurement of iron capacity at solar interior conditions. 185 00:21:42.310 --> 00:21:54.149 Mark Kushner: This measured the opacity of iron at about 180 EV, so that's 180 million Kelvin, I think, and a density of about a 20th of that of solid. 186 00:21:54.300 --> 00:21:56.669 Mark Kushner: That data is shown in the middle plot here. 187 00:21:57.540 --> 00:22:04.830 Mark Kushner: So the measurement is in… in red and Aragon marvelous in green. 188 00:22:04.940 --> 00:22:08.209 Mark Kushner: These do not look like the same thing. Agree with that. 189 00:22:08.940 --> 00:22:15.669 Mark Kushner: There was a follow-up paper in 2019 from the same group where they looked at chromium and nickel. 190 00:22:16.160 --> 00:22:21.149 Mark Kushner: And here you can see we're doing slightly better, but it's still not great. 191 00:22:21.680 --> 00:22:25.950 Mark Kushner: So, let me describe what some of these features are in this plot here. 192 00:22:26.120 --> 00:22:28.520 Mark Kushner: So this is photon wave length. 193 00:22:29.130 --> 00:22:31.440 Mark Kushner: Which is essentially the photon energy. 194 00:22:31.980 --> 00:22:33.850 Mark Kushner: Unless it's the opacity. 195 00:22:34.540 --> 00:22:35.920 Mark Kushner: on the Y-axis. 196 00:22:36.130 --> 00:22:38.750 Mark Kushner: This region here, you can see, is fairly flat. 197 00:22:38.980 --> 00:22:45.699 Mark Kushner: And this is called the bound-free region. So this is where you have an electron in your atom, in the plasma. 198 00:22:45.890 --> 00:22:51.970 Mark Kushner: It's bound to the atom, a photon comes in, gives it enough energy that it's free to escape the atom. 199 00:22:52.350 --> 00:23:04.960 Mark Kushner: So there's now a continuous process, right? You can get a wee bit more energy and it'll still escape the atom, or a wee bit less and it'll still escape the atom. But the cross-section for that turns out, the opacity for that looks like this straight line here. 200 00:23:05.250 --> 00:23:09.159 Mark Kushner: So the quasi continuum, we're doing quite well here and here. 201 00:23:09.670 --> 00:23:11.029 Mark Kushner: Not so much here. 202 00:23:11.540 --> 00:23:13.460 Mark Kushner: And then these 203 00:23:13.750 --> 00:23:32.979 Mark Kushner: this region here is dominated by bound-bound opacities, so this is where your photon comes in, have a bound electron, and it gets excited to another bound state. So it's not free to leave the atom, it's just another bound state. It's an excitation, but it's not a bound state excitation, and this leads to lines in the plasma. 204 00:23:33.180 --> 00:23:36.279 Mark Kushner: And you can see that in the average atom model here. 205 00:23:36.740 --> 00:23:41.039 Mark Kushner: The lines are very strong and very few. 206 00:23:41.390 --> 00:23:47.859 Mark Kushner: Whereas in the experiment, there's a lot more of these lines and they make it look a lot more smooth. 207 00:23:48.900 --> 00:23:54.560 Mark Kushner: That means there's a lot more broadening of these fine bound lines than there is in the average animal. 208 00:23:56.640 --> 00:24:01.570 Mark Kushner: So So… 209 00:24:02.020 --> 00:24:04.380 Mark Kushner: We looked at two things to start with. 210 00:24:05.390 --> 00:24:11.340 Mark Kushner: So why is the average agent model doing so poorly here when it does so well for all these other quantities we talked about? 211 00:24:12.140 --> 00:24:25.410 Mark Kushner: Well, we're using density functional theory, and people in my field love density functional theory, but they would tell you straight away, they would ask me, how are you calculating the opacity? And I would have told them I'm using the independent particle approximation. 212 00:24:25.890 --> 00:24:31.829 Mark Kushner: And they would say, well, that's wrong. You're supposed to use time-dependent density functional theory to calculate the quantities. 213 00:24:32.770 --> 00:24:36.130 Mark Kushner: calculate quantities like capacity. So we did that. 214 00:24:36.240 --> 00:24:44.169 Mark Kushner: We knew it wouldn't make a large difference, but we did it anyway, and you can see the plot here. This is the iron opacity. So this is this case here. 215 00:24:44.750 --> 00:24:47.290 Mark Kushner: The independent particle is in black. 216 00:24:47.450 --> 00:24:49.929 Mark Kushner: And that's the same as the green line here. 217 00:24:50.440 --> 00:24:53.890 Mark Kushner: or roughly the same, you should say, maybe slight differences. 218 00:24:54.390 --> 00:25:03.919 Mark Kushner: And then we did time-dependent DFT, and that is in red. And you can see this does not qualitatively change the picture. So it is not time-dependent DFT that's the problem. 219 00:25:04.330 --> 00:25:07.469 Mark Kushner: Right? What is time-dependent DFT giving you physically? 220 00:25:08.400 --> 00:25:18.739 Mark Kushner: Well, independent particle says that if you get an excitation, the atom, all the other electrons in the atom stay the same. That's wrong, right? Because the other electrons will respond once you excite 221 00:25:19.130 --> 00:25:26.970 Mark Kushner: your active electrode. We call it relaxation. They'll relax to the position of the new the new electoral position. 222 00:25:27.560 --> 00:25:36.799 Mark Kushner: classically speaking. So PDDAT is giving you that relaxation, so that changes the energy slightly, and, like, here you can see it changes the energies. 223 00:25:37.050 --> 00:25:44.299 Mark Kushner: And it can shift things up or down a little, but it's not a dramatic change, right? Still fairly similar. 224 00:25:45.710 --> 00:25:52.410 Mark Kushner: Okay, so… Anyone got any other guesses, given how I described the average atom model? 225 00:25:52.910 --> 00:25:55.669 Mark Kushner: Of what, what we could be missing. 226 00:25:58.510 --> 00:26:03.099 Mark Kushner: The one… okay, we've got one. Interactions between the… Bout with them. 227 00:26:09.820 --> 00:26:16.439 Mark Kushner: I guess that's partially right. I guess that's partially right. They're a little vague, but I think you're on to something there. 228 00:26:16.580 --> 00:26:20.960 Mark Kushner: What I was hoping you would say was, well, the one atom in the plasma thing. 229 00:26:21.270 --> 00:26:29.369 Mark Kushner: So the average atom is one average atom in plasma. So we thought, well, obviously we need better plasma physics. We need more atoms in the plasma. 230 00:26:30.860 --> 00:26:36.189 Mark Kushner: So we checked out. This took a while, right? It's not easy to do this. We developed this multi-center model. 231 00:26:36.610 --> 00:26:41.090 Mark Kushner: Based on something called AKR or the multiple scattering method. 232 00:26:41.440 --> 00:26:50.269 Mark Kushner: And I worked on this for many years, and a postdoc of mine, Nathaniel Schaefer, developed a very sophisticated way to calculate the opacity 233 00:26:50.600 --> 00:26:52.469 Mark Kushner: of these dense plasmas. 234 00:26:52.750 --> 00:27:07.309 Mark Kushner: based on multi-center system. Now, I haven't given you a lot of details there, but basically, you start out with a plasma with, say, a few tens of atoms, and you… each one feels the effects of the other plasma, other ions and electrons in the plasma. They all interact. 235 00:27:07.820 --> 00:27:11.090 Mark Kushner: But it's still density functional theory. 236 00:27:11.860 --> 00:27:16.189 Mark Kushner: And this is this is what we get again. This is the iron case here. So you can compare this to here. 237 00:27:16.540 --> 00:27:21.420 Mark Kushner: We have this on a different scale. Unfortunately, this is photon energy instead of wave length. 238 00:27:21.830 --> 00:27:24.219 Mark Kushner: But it's the same experimental data. 239 00:27:24.350 --> 00:27:29.039 Mark Kushner: The one thing is, like, Low photon energy means high, high… 240 00:27:29.480 --> 00:27:36.799 Mark Kushner: number of angstroms and high number of, high photon energy means low number of angstroms. So it's, they're sort of flipped. 241 00:27:37.050 --> 00:27:43.369 Mark Kushner: Need to flip this plot over. This is the quasi-continuum on this side, and on this plot, it's on this side. 242 00:27:44.850 --> 00:27:46.539 Mark Kushner: So you can see, again. 243 00:27:46.780 --> 00:27:53.630 Mark Kushner: We're comparing Tartarus, which is our one centre model in red to the multi-centre model in blue. 244 00:27:54.980 --> 00:27:58.529 Mark Kushner: doesn't really improve the picture, right? I mean, we have this 245 00:27:59.490 --> 00:28:06.270 Mark Kushner: We have this broadening, which is called stark broadening, and we have that in there correctly now. 246 00:28:06.870 --> 00:28:08.999 Mark Kushner: or close to being correct. 247 00:28:09.420 --> 00:28:17.789 Mark Kushner: It doesn't actually improve the… agreement with the experiment, you know, in any meaningful sense. 248 00:28:18.950 --> 00:28:23.120 Mark Kushner: So Anyone else got an idea of what we're missing? 249 00:28:27.090 --> 00:28:30.810 Mark Kushner: Good, I'm glad I'm not the only one, it took me a long time to figure out. 250 00:28:31.410 --> 00:28:37.890 Mark Kushner: So, what we're missing is something called configurational broadening. 251 00:28:39.250 --> 00:28:50.119 Mark Kushner: So I told you in the independent particle approximation, you have this excitation of your active electron. It absorbs a photon, gets excited, and all the other electrons stay the same. 252 00:28:50.580 --> 00:28:52.750 Mark Kushner: And even if you allow them to relax. 253 00:28:53.230 --> 00:28:55.509 Mark Kushner: That's time dependent Dft. 254 00:28:56.900 --> 00:29:02.580 Mark Kushner: But what is actually happening is in real plasmas you have 255 00:29:02.800 --> 00:29:13.460 Mark Kushner: you have this excitation, and you have your other electrons, but the other electrons can start out in different energy states. They're not always in this average energy state that 256 00:29:13.670 --> 00:29:15.460 Mark Kushner: Dft says they're in. 257 00:29:16.650 --> 00:29:24.660 Mark Kushner: So… Yeah. So you have in our little picture here you have this energy transition right? 258 00:29:24.870 --> 00:29:29.109 Mark Kushner: and you have one spectator electron. So let's say this is helium. 259 00:29:31.350 --> 00:29:43.289 Mark Kushner: Well, in this case here, let's not make helium. Let's do another atom. Let's do iron. You've got this excitation here and you've got one spectator electron. But in this case here, you have two spectator electrons. 260 00:29:43.570 --> 00:29:51.789 Mark Kushner: So your ionisation of the atom is different. It's the same transition, right? The same hydrogenic transition. Say we level this as a 1s to 2p. 261 00:29:52.450 --> 00:29:55.889 Mark Kushner: If you remember your hydrogenic transition labels. 262 00:29:56.100 --> 00:30:13.339 Mark Kushner: So you have the same transition, but you get different numbers and different configurations of electrons in the bound states that are in there, and even the free states can change. So these… the other electrons are in different energy states. You're looking at the same transition, but the other electrons are in different energy states. 263 00:30:14.000 --> 00:30:16.360 Mark Kushner: And this leads to configurational broadening. 264 00:30:16.530 --> 00:30:18.910 Mark Kushner: in in density, functional theory. 265 00:30:19.220 --> 00:30:27.190 Mark Kushner: In the way I'm doing it, you do not have this because these are all averaged over and have firmly direct occupations. 266 00:30:27.480 --> 00:30:32.020 Mark Kushner: So, each one of these atoms absorbs a photon. 267 00:30:32.300 --> 00:30:47.650 Mark Kushner: for the same transition, but it's at a slightly different energy. So each of these corresponds to a different energy, and that leads to a broadening of the lines. So you saw how our average atom lines were far too narrow and too strong. Well, this would lead to them broadening out. 268 00:30:48.410 --> 00:30:51.439 Mark Kushner: So in Dft configurational broadening is missing. 269 00:30:51.800 --> 00:30:55.559 Mark Kushner: In practice, I would say. In principle, it should be in this 270 00:30:55.840 --> 00:31:03.300 Mark Kushner: exchange and correlation term, which I didn't tell you about, but those of you that know DFT will know this is where all the unknown physics goes. 271 00:31:03.590 --> 00:31:10.469 Mark Kushner: Part of that unknown physics is configurational broadening, but it is not in any of the exchange coordination potentials that exist. 272 00:31:11.010 --> 00:31:12.340 Mark Kushner: as far as I know. 273 00:31:14.150 --> 00:31:15.619 Mark Kushner: Okay, so you get that. 274 00:31:18.980 --> 00:31:20.959 Mark Kushner: Okay, so what's the solution then? 275 00:31:21.080 --> 00:31:23.409 Mark Kushner: Well, you got to come up with a better model. 276 00:31:24.010 --> 00:31:28.179 Mark Kushner: So if Dft doesn't cut it, then you've got to improve upon Dft. 277 00:31:29.470 --> 00:31:32.790 Mark Kushner: So in Dft, the free energy is 278 00:31:33.530 --> 00:31:39.340 Mark Kushner: is given by this simple expression. Free energy equals energy minus temperature times the entropy. 279 00:31:39.780 --> 00:31:50.470 Mark Kushner: Now, this… this… this doesn't tell you a lot, but this is approximated with this effective one-electron model I talked about, like this hydrogenic one-electron model. 280 00:31:50.740 --> 00:31:55.039 Mark Kushner: We have one electron moving an average potential of all the other particles. 281 00:31:55.500 --> 00:31:58.489 Mark Kushner: And it includes this exchange correlation term. 282 00:31:58.780 --> 00:32:02.920 Mark Kushner: and Merman was the guy that extended this to finite temperature. 283 00:32:03.130 --> 00:32:09.559 Mark Kushner: And in his system, you use Fermi-Dirac occupations for the orbitals. 284 00:32:09.840 --> 00:32:16.470 Mark Kushner: So instead of there being… So instead of being an orbital with one or zero electron in it. 285 00:32:16.830 --> 00:32:29.700 Mark Kushner: there's, like, 0.37, 0.95, 0.24, so you get these fractional occupations. That's because there's not supposed to be a real electron in there, it's just an average number of electrons in your orbital. 286 00:32:30.820 --> 00:32:39.540 Mark Kushner: But that's exactly why it doesn't have the configurational broadening naturally, right? Because you've got these average numbers of electrons in your orbitals. 287 00:32:40.250 --> 00:32:42.840 Mark Kushner: jay: or is you actually in reality have one or 0. 288 00:32:43.630 --> 00:32:45.420 Mark Kushner: So we thought, well, why don't we just… 289 00:32:45.610 --> 00:32:48.250 Mark Kushner: Just do that. We could put one or zero in. 290 00:32:48.810 --> 00:32:50.480 Mark Kushner: So we extended this. 291 00:32:51.320 --> 00:33:03.370 Mark Kushner: this… this, free energy approximation to just say, well, I'm gonna use a DFT-like approximation for each excited state in the plasma. 292 00:33:04.010 --> 00:33:07.660 Mark Kushner: So each excited state now gets approximated by its own 293 00:33:08.090 --> 00:33:13.960 Mark Kushner: Dft, like energy expression here. So X here labels the excited states. 294 00:33:14.810 --> 00:33:19.629 Mark Kushner: And then each of these excise states will have a probability, W, WX. 295 00:33:20.200 --> 00:33:23.910 Mark Kushner: And there's… it turns out there's also this extra entropy term that comes along. 296 00:33:24.570 --> 00:33:30.480 Mark Kushner: Due to energy degeneracy, because you have different excited states with the same energy. 297 00:33:31.480 --> 00:33:32.340 Mark Kushner: So 298 00:33:32.540 --> 00:33:39.270 Mark Kushner: So what are we doing here? Well, each excited state is approximated by the one electron model, just like in DFT. 299 00:33:39.670 --> 00:33:45.120 Mark Kushner: But now we use integer occupations of each of the orbitals instead of Fermi-Diracs. 300 00:33:45.410 --> 00:33:52.410 Mark Kushner: And these… this set of integer occupations defines an excited state. So different excited states will have different 301 00:33:52.900 --> 00:33:54.980 Mark Kushner: Sets of integer occupations. 302 00:33:55.090 --> 00:33:58.309 Mark Kushner: See if I go back to this picture here. 303 00:33:58.480 --> 00:34:00.550 Mark Kushner: You've got this list of orbitals. 304 00:34:00.780 --> 00:34:04.450 Mark Kushner: and then and you could pick out this electron and put in one orbital. 305 00:34:04.640 --> 00:34:06.720 Mark Kushner: But you could also, in our model. 306 00:34:06.970 --> 00:34:11.459 Mark Kushner: pick out these 2 electrons and put them in in orbitals as well, whereas 307 00:34:11.590 --> 00:34:22.600 Mark Kushner: DFT, as it's normally done, averages over these two. So you'd get 2, 1 plus 2 divided by 2, which is 1.5 electrons in that orbital, right? 308 00:34:23.460 --> 00:34:29.980 Mark Kushner: So, we've got both these pictures now, explicitly, whereas DFT would just sum them up and average over them. 309 00:34:32.440 --> 00:34:36.119 Mark Kushner: Okay, so does that make sense to you guys? I know it's a bit tricky. 310 00:34:36.429 --> 00:34:41.659 Mark Kushner: But, you know, get a few head nods, so… 311 00:34:41.969 --> 00:34:47.290 Mark Kushner: Okay, so don't worry. There won't be a whole load of equations here. This is sort of like for those that 312 00:34:47.570 --> 00:34:54.180 Mark Kushner: understand a bit about DFT, the way it works is you have this free energy and you minimise it with respect to the electron density. 313 00:34:54.360 --> 00:35:01.860 Mark Kushner: In DFT, you get this equation without the X's. So there's one of these Cone-Sham-Mermin equations. 314 00:35:01.980 --> 00:35:04.390 Mark Kushner: This just looks like the Schrodinger equation, right? 315 00:35:04.730 --> 00:35:06.440 Mark Kushner: Here you have the potential. 316 00:35:06.710 --> 00:35:09.599 Mark Kushner: With interactions between the electrons and the ions. 317 00:35:09.940 --> 00:35:17.980 Mark Kushner: Here you have your wave function, here you have your eigenenergy, so it's exactly the same as the Dirac equation, or Schrodinger equation, that I showed you earlier. 318 00:35:19.010 --> 00:35:23.690 Mark Kushner: And then in DFT, what you do is you take these orbitals and you sum them up. 319 00:35:24.280 --> 00:35:28.229 Mark Kushner: sum over all the orbitals, and multiply by their Fermi-Dirac occupancies. 320 00:35:29.100 --> 00:35:33.800 Mark Kushner: And that's where these are. This picture of average occupations comes from. 321 00:35:34.420 --> 00:35:37.309 Mark Kushner: In our world and in our Excise Dates version. 322 00:35:37.530 --> 00:35:40.900 Mark Kushner: We have a different density for each excited state. 323 00:35:41.770 --> 00:35:48.250 Mark Kushner: These Fs are the one electron occupation factors that we set, we choose to set to start with. 324 00:35:48.360 --> 00:35:50.100 Mark Kushner: C's are ones or zeros. 325 00:35:50.800 --> 00:35:53.970 Mark Kushner: And then you get the total density by summing up. 326 00:35:54.460 --> 00:35:58.219 Mark Kushner: Overall excited states with a probability W for that. 327 00:35:58.510 --> 00:35:59.630 Mark Kushner: electrical test. 328 00:36:00.800 --> 00:36:09.599 Mark Kushner: And if you minimize with respect to the probabilities, you get back Boltzmann probability. So that comes out of the model, rather than being imposed. 329 00:36:10.040 --> 00:36:11.939 Mark Kushner: And it's exactly the same form. 330 00:36:12.110 --> 00:36:20.650 Mark Kushner: I should say Z here for those that are interested is the partition function, which just serves to keep the probabilities between zero and one. 331 00:36:22.050 --> 00:36:23.419 Mark Kushner: Okay, so that's it. 332 00:36:23.570 --> 00:36:29.980 Mark Kushner: That's the new model. You have one of these equations for each excited state you choose in your 333 00:36:30.360 --> 00:36:35.740 Mark Kushner: be in your plasma. You have to choose to start with what excited states you want to model. 334 00:36:35.880 --> 00:36:40.489 Mark Kushner: So you create a list, you solve this equation for each of these excited states. 335 00:36:40.920 --> 00:36:45.139 Mark Kushner: You get their energies out, and then you get their probabilities from this. 336 00:36:47.520 --> 00:36:49.170 Mark Kushner: Okay, so how does it do? 337 00:36:49.580 --> 00:36:54.400 Mark Kushner: Well, oh, well, we have a couple of papers in this if anyone's interested. This was the first one. 338 00:36:54.820 --> 00:36:59.630 Mark Kushner: Then we had a nice one by, this was a student, a summer student we had, Trinity Thelen. 339 00:36:59.930 --> 00:37:05.870 Mark Kushner: Actually, she wasn't summer student, she was a post-bac. She came to work with us after she did her bachelor's degree. 340 00:37:06.200 --> 00:37:09.800 Mark Kushner: And she did a very nice job writing this paper. 341 00:37:10.380 --> 00:37:15.619 Mark Kushner: I thought she was taking too long, but the referee agreed with her, not me. 342 00:37:16.150 --> 00:37:20.050 Mark Kushner: It was a very, very warm review. 343 00:37:24.540 --> 00:37:28.009 Mark Kushner: So, and the third one here is where we calculate the opacity. 344 00:37:29.290 --> 00:37:34.050 Mark Kushner: Okay, so how do we do? Well, there's average Adam on the left, that's what we saw before. 345 00:37:34.430 --> 00:37:51.979 Mark Kushner: And this is the excited state method on the right. So you can see it's an improvement. Let's not look at the middle figure here, iron, because it's awful. Here, for chromium, we're definitely doing better than average atom, though it's not perfect, right? I think that's fair to say, but, like, it's definitely improved. 346 00:37:52.930 --> 00:37:57.079 Mark Kushner: For nickel, again, it's an improvement. 347 00:37:57.840 --> 00:38:01.550 Mark Kushner: I would say a dramatic improvement, but still not perfect. 348 00:38:02.000 --> 00:38:09.799 Mark Kushner: But it turns out that the reason I don't want you to look at this is because this data has been revised, and 349 00:38:10.930 --> 00:38:20.779 Mark Kushner: Although it's 10 years old, they have revised it a number of times now, and I believe they're preparing a new shipper. They've presented it at conferences, and their numbers do come down a lot. 350 00:38:21.620 --> 00:38:26.320 Mark Kushner: I don't know. I haven't been able to compare it to the new model, but I suspect it'll agree a lot better. 351 00:38:26.770 --> 00:38:39.939 Mark Kushner: And similarly, they have a new statistical analysis method which does change these two, although I haven't seen the results. So it's a little inconclusive that that rug's sort of been pulled. 352 00:38:40.040 --> 00:38:53.820 Mark Kushner: pulled out from us, but once we get the new data, we'll compare to it. However, this group is an excellent group out of Sandia National Labs, and they have published another experiment on oxygen at solar interior conditions. 353 00:38:54.320 --> 00:38:56.950 Mark Kushner: And they used the new analysis method on it. 354 00:38:57.550 --> 00:38:59.409 Mark Kushner: But here's here's the result. 355 00:39:00.030 --> 00:39:07.639 Mark Kushner: So this is oxygen at 148 eV, so that's 1.5 million degrees. 356 00:39:08.220 --> 00:39:09.400 Mark Kushner: Let's see. 357 00:39:09.640 --> 00:39:11.599 Mark Kushner: Fairly low density. 358 00:39:12.890 --> 00:39:17.950 Mark Kushner: This is… I've split this up, this is the way they present it in the paper. This is the bind-free region. 359 00:39:18.280 --> 00:39:32.110 Mark Kushner: And then these are the different bind-bind transitions. This is 1s to 2p. So this is mostly hydrogen like oxygen in this plasma. That means that oxygen, instead of having eight electrons, typically has one bind electron. 360 00:39:32.530 --> 00:39:35.460 Mark Kushner: So this is an excitation where you get one. 361 00:39:35.800 --> 00:39:38.960 Mark Kushner: and your Ys, which is the grindstead up to the 2 P. 362 00:39:39.350 --> 00:39:47.090 Mark Kushner: You have 3P, 4P, 5P, and this is the bind-free, where the electron has enough energy to leave the system. 363 00:39:48.840 --> 00:39:56.740 Mark Kushner: So you can see iphone, which is our multi, our new model based on this excited state methodism in red. 364 00:39:56.970 --> 00:40:01.130 Mark Kushner: Partners is the old average outer model, and Blue. 365 00:40:01.240 --> 00:40:07.089 Mark Kushner: You can see they're both in reasonable agreement with the data here. Here, we're getting a little bit of a difference showing up. 366 00:40:07.430 --> 00:40:08.790 Mark Kushner: or too high. 367 00:40:09.460 --> 00:40:13.439 Mark Kushner: That… Harry's over here, where Tartus is way too high. 368 00:40:13.950 --> 00:40:20.959 Mark Kushner: And But Typhon picks out very nicely this peak, this 1s to 5p. 369 00:40:21.240 --> 00:40:25.909 Mark Kushner: Similar story for 1S to 4P. Now Tartarus is in the wrong place. 370 00:40:26.650 --> 00:40:29.880 Mark Kushner: And Typhon is in the right place, that's again. 371 00:40:30.780 --> 00:40:34.389 Mark Kushner: I'll explain that in a second. Again, we get a better 372 00:40:34.570 --> 00:40:37.430 Mark Kushner: agreement here. Iphone is very good agreement. 373 00:40:37.730 --> 00:40:42.670 Mark Kushner: Target is slightly off. And here for this 1S to 2P. 374 00:40:43.140 --> 00:40:48.029 Mark Kushner: Typhon, again, is much better qualitative agreement, as well as quantitative. 375 00:40:48.630 --> 00:40:50.529 Mark Kushner: But there are some differences, right? 376 00:40:50.750 --> 00:41:05.750 Mark Kushner: So I think the big picture is we're doing a lot better than DFT. And we're doing that because we have this configurational broadening, but also we have relaxation effects in the excitation energy. 377 00:41:05.810 --> 00:41:12.179 Mark Kushner: It's a little bit unfair to Dft here, because we haven't got. We should be compared to time dependent Dft. But I'm not. 378 00:41:13.390 --> 00:41:24.820 Mark Kushner: There's also some broadening effects which we have in Typhon, which are not in the DFT models. So it's a little bit unfair, but I think, you know, the line positions, this difference would not improve. 379 00:41:25.660 --> 00:41:27.800 Mark Kushner: Dramatically. 380 00:41:28.460 --> 00:41:34.580 Mark Kushner: I have got TDDFT calculations, and they do not change things. They change them very little. 381 00:41:35.200 --> 00:41:41.580 Mark Kushner: But you can see down here, this is one of the most dramatic differences here. So in the experiment, there's these three peaks. 382 00:41:42.560 --> 00:41:47.749 Mark Kushner: And… iPhone picks out all 3, whereas Tartarus just gives you this one big blob. 383 00:41:48.310 --> 00:41:51.609 Mark Kushner: That is because this is. 384 00:41:52.190 --> 00:42:00.859 Mark Kushner: configurational broadening and action. This is 1s to 2p in the central peak here, where there's only one bound electron, and there's no other bound electrons. 385 00:42:01.320 --> 00:42:10.830 Mark Kushner: But these satellite peaks here are where you have one bound electron and other bound electrons. So there might be one like in the 1s as well. So it's helium-like. 386 00:42:11.170 --> 00:42:13.830 Mark Kushner: So one of these is helium like, I think it's this one here. 387 00:42:15.170 --> 00:42:25.789 Mark Kushner: Well, I can't remember. I've labeled them both helium-like, but I don't think… I don't know if that's true. Anyway, there's… there's two electrons in your plasma now, but you're still looking at the same 1S to 2P transition. 388 00:42:25.970 --> 00:42:34.210 Mark Kushner: So you get the splitting into three lines, it does not show up in DFT, and it can't show up in DFT unless you've got it in your exchange correlation potential. 389 00:42:35.790 --> 00:42:37.340 Mark Kushner: And and so 390 00:42:37.770 --> 00:42:46.510 Mark Kushner: That's a dramatic difference. So we're really, really encouraged by this. It seems to be making a 8. 391 00:42:47.130 --> 00:42:50.149 Mark Kushner: begging people. What time am I supposed to finish? Let's go to Sono. 392 00:42:50.330 --> 00:42:52.210 Mark Kushner: 5 min. 5 min. Okay. 393 00:42:53.110 --> 00:43:00.940 Mark Kushner: Okay, so this seems to be working for Apache now. We've rescued Average Adam by making it less averaged. 394 00:43:01.210 --> 00:43:08.749 Mark Kushner: Instead of averaging over all the occupations like you do in DFT, we now have broken out that average into different configurations. 395 00:43:09.840 --> 00:43:16.140 Mark Kushner: And it remains to be seen, okay, I'm gonna have to skip over this, so… 396 00:43:16.390 --> 00:43:19.130 Mark Kushner: I told you we're not doing so well here. 397 00:43:19.250 --> 00:43:28.530 Mark Kushner: And we think that's because of the average atom approximation in the sense that you need at least one atom in a sphere. We're still doing that here in this Type I model. 398 00:43:28.750 --> 00:43:40.270 Mark Kushner: But we think if we did a better multicenter picture, we would get that better, because it's those electrons that are near zero energy, this bind-free transition region, that would be sensitive to that. 399 00:43:41.310 --> 00:43:47.910 Mark Kushner: And I have a staff member working with me, Bao Tran, who's working on that. 400 00:43:48.270 --> 00:43:51.330 Mark Kushner: Unfortunately, I don't have to go and have time to go into details. 401 00:43:52.290 --> 00:43:58.270 Mark Kushner: We also have a postdoc, Jackson White, who is. 402 00:43:58.920 --> 00:44:01.480 Mark Kushner: He's working on something very interesting. 403 00:44:02.070 --> 00:44:12.409 Mark Kushner: We made this model, and one of the ways they broaden these lines is you use something called a microfield. So you have this atom. 404 00:44:12.530 --> 00:44:27.690 Mark Kushner: But all the other atoms around it are moving around it, and they're sort of… they're changing the field, the electrons' fields subtly, and each atom will feel it slightly differently. So you get these so-called microfield fluctuations, and they lead to broadening in themselves. 405 00:44:28.180 --> 00:44:42.089 Mark Kushner: So that's sensitive to the positions of the atoms themselves in the plasma. Jackson realised that it seems obvious now, but he realised that the standard models get those ion positions by assuming 406 00:44:42.130 --> 00:44:52.530 Mark Kushner: the ions don't change their character. So if something's one times ionized, it remains one time ionized forever. Or two times ionized, it always remains two times ionized. 407 00:44:52.590 --> 00:45:00.010 Mark Kushner: Well, that's that's you put those potentials in your molecular dynamics, and you get out the positions of the ions. That's not really what's happening. 408 00:45:00.230 --> 00:45:05.339 Mark Kushner: What happens is you might be one times ionised and then another photon comes in and you get excited. 409 00:45:06.010 --> 00:45:11.489 Mark Kushner: or you get ionized. So it changes its character, and that character changes the interatomic forces. 410 00:45:11.840 --> 00:45:17.849 Mark Kushner: And it turns out that changes the line shape too. So Jackson developed this very nice paper. 411 00:45:18.330 --> 00:45:25.620 Mark Kushner: quantum fluctuations in dense plasma, and it was recently published, so I encourage you to go look at it if you're interested. 412 00:45:26.720 --> 00:45:32.369 Mark Kushner: Okay, so I want… got, like, 4 minutes left. 413 00:45:32.500 --> 00:45:39.559 Mark Kushner: I just want to thank you for listening and I want to thank the people that work with me in this, the staff members. 414 00:45:40.140 --> 00:45:53.990 Mark Kushner: And if you're interested in our work, you can feel free to reach out to us. There's my email. We have a lot of summer students, and postdocs, so if you're interested in working with us, please feel free to reach out. 415 00:45:54.110 --> 00:45:58.420 Mark Kushner: I haven't talked a lot about the summer student work. 416 00:45:58.690 --> 00:46:14.709 Mark Kushner: But we've had postbacks, postmasters who stay for years, you know, one or two years. We get summer students, sometimes from academic collaborators, sometimes through this program, which is the Landlord Computational Physics Workshop. 417 00:46:15.000 --> 00:46:21.449 Mark Kushner: We host this every year. It's a student workshop aimed at undergrads and graduate students. 418 00:46:21.810 --> 00:46:31.739 Mark Kushner: there's a wide range of projects. It's not all just stuff I do. It's, we'll offer a project, but there'll also be stuff on hydrodynamics and numerical methods and 419 00:46:31.990 --> 00:46:49.360 Mark Kushner: all sorts of weird stuff that I don't know anything about. So, if you're interested in trying out Los Alamos but don't have contacts there, this is a good programme you can apply to. It, just search for the programme, and the applications usually open around Thanksgiving time. 420 00:46:49.560 --> 00:46:59.129 Mark Kushner: It's competitive entry, so you get in, you should be very proud of yourself, because it's not easy to get into, but I encourage you to apply if you're interested. 421 00:47:00.120 --> 00:47:04.720 Mark Kushner: Okay, well I finished two minutes early, but thank you very much for your attention. 422 00:47:10.720 --> 00:47:14.330 Mark Kushner: Very much. Questions? 423 00:47:16.060 --> 00:47:23.109 Mark Kushner: Thank you very much for the interesting talk. I'm wondering, how do you deal with the boundaries? 424 00:47:24.000 --> 00:47:27.379 Mark Kushner: The boundaries, you said? Boundaries, yeah, like. 425 00:47:27.710 --> 00:47:37.440 Mark Kushner: 1st of all, in a simulation, do you assume periodic boundary for the simulation of calculations? It's a good question. And it's actually the key to our multicenter method. 426 00:47:37.570 --> 00:47:51.130 Mark Kushner: So in the average atom model, which I didn't originally develop, it was developed back in the 70s by a man named Lieberman at Los Alamos, actually. You determine the sphere size by the density of the plasma. 427 00:47:51.240 --> 00:48:01.530 Mark Kushner: And then you approximate the boundary conditions as being that of free electron. A free electron is applied… boundary condition is applied at the sphere edge. 428 00:48:01.900 --> 00:48:07.590 Mark Kushner: So that's what forces your pressurization gives you physics like pressure ionization. And 429 00:48:07.750 --> 00:48:11.050 Mark Kushner: It doesn't just. It doesn't just look like an atom. It looks like a compressed atom. 430 00:48:11.580 --> 00:48:25.389 Mark Kushner: When you go to these multi-center models, which is what we developed and Bowie's working on, the boundary condition becomes much more complicated. You solve a Dyson equation, which basically says that 431 00:48:26.210 --> 00:48:33.100 Mark Kushner: all the incoming and outgoing waves must match, and then you put the whole thing inside a periodic cell. 432 00:48:33.550 --> 00:48:36.450 Mark Kushner: With, say, 10 or 20 or 30 items in it. 433 00:48:37.590 --> 00:48:39.450 Mark Kushner: So that's the that's the short of it. 434 00:48:48.840 --> 00:48:57.369 Mark Kushner: I have a question. Thank you for your talk. When it comes to running Typhon versus Tartarus, what does the computational complexity change look like? 435 00:48:57.840 --> 00:49:01.709 Mark Kushner: It's, it's, it's… there's two aspects to it, 436 00:49:03.240 --> 00:49:08.940 Mark Kushner: Well, I guess the main one is, you need to know what excited states you want to include in your list, and that's 437 00:49:09.050 --> 00:49:21.030 Mark Kushner: That's hard to know. So we typically run the average annum model, the DFT model, and see what it thinks the excise dates that are important will be. We use that as an initial guess. 438 00:49:21.180 --> 00:49:29.730 Mark Kushner: It's obviously… it's also a lot more expensive, because instead of running one DFT problem, you're running N, where N is the number of excised dates. 439 00:49:30.190 --> 00:49:38.649 Mark Kushner: So that can get astronomical very quickly. So we've borrowed a method called superconfigurations from the atomic physics world. 440 00:49:38.780 --> 00:49:42.339 Mark Kushner: To… to make… to do some sort of averaging. 441 00:49:42.610 --> 00:49:51.129 Mark Kushner: But that increases the computational complexity, because you have to need… you have to have some sort of intuition as to know what averaging you should do. 442 00:49:51.620 --> 00:50:07.620 Mark Kushner: So that's the two aspects of it. If it's something like, you know, hydrogen or helium, you can probably put all the excited states you care about in. But if you're doing something like uranium, you have no hope, and you need to do a lot of excited states. So you need to do a lot of averaging. 443 00:50:08.540 --> 00:50:09.629 Mark Kushner: Great, thank you. 444 00:50:10.690 --> 00:50:11.580 Mark Kushner: Get in. 445 00:50:12.130 --> 00:50:14.200 Mark Kushner: talked about going from 446 00:50:15.130 --> 00:50:32.370 Mark Kushner: time-independent average atom model to calculating the passage of time-dependent DFT. I was wondering what type of time-dependent DFT are you using? So, there are types that, like, where the… 447 00:50:32.370 --> 00:50:50.569 Mark Kushner: response of the surrounding electrons is a linear response, and there are types like real-time TFT that's not. And if you're using linear response, do you expect that using, like, real-time TDFT would actually make a big difference, or… That's a good question, Julian. 448 00:50:50.750 --> 00:50:54.050 Mark Kushner: So we use linear response, PDDFT. 449 00:50:54.290 --> 00:51:02.050 Mark Kushner: So that is linear in the sense that there's one excitation by one photon at a time. 450 00:51:02.280 --> 00:51:22.099 Mark Kushner: So, if there's multiple photon excitations, say, an electron absorbs two photons at a time, then it'll be wrong. So, actually, there was a researcher named Richard Moore who suggested multi-photon excitation could be important to these experiments, and that's where this extra opacity is coming from. 451 00:51:22.530 --> 00:51:27.199 Mark Kushner: And so if you were doing real-time DDT, that would pick it up. 452 00:51:28.050 --> 00:51:33.599 Mark Kushner: But it turns out the intensity is too low. So you can look at the intensity of the light as too low. 453 00:51:33.780 --> 00:51:42.379 Mark Kushner: And working with Richard Moore, a researcher named Veronica Cruz at Livermore has done extensive calculations of two photons. 454 00:51:42.540 --> 00:51:45.260 Mark Kushner: Cross sections, and find that they're… 455 00:51:46.280 --> 00:51:53.280 Mark Kushner: they're negligible, I think, is the conclusion. There's still some work to be done there, but it looks like it's not a major effect here. 456 00:51:53.960 --> 00:52:02.079 Mark Kushner: We have tried to write a real-time code for work that's in progress, but we haven't completed it yet. 457 00:52:07.030 --> 00:52:09.270 Mark Kushner: Question? Yeah. 458 00:52:09.490 --> 00:52:20.140 Mark Kushner: So… See? So you're the new model, the more sophisticated model for the qualification instead of the average. 459 00:52:20.390 --> 00:52:25.780 Mark Kushner: I intend to, like, resolve what would otherwise be an overbroad line. 460 00:52:26.100 --> 00:52:32.750 Mark Kushner: right? Yeah. So They're like a… the conclusion for radiation. 461 00:52:32.950 --> 00:52:38.670 Mark Kushner: transport, like, hydrodynamics? If you compare the two models, would you, like, generally 462 00:52:40.020 --> 00:52:45.079 Mark Kushner: Like lower opacities on the average so that you would lower like. 463 00:52:45.530 --> 00:53:02.200 Mark Kushner: Yeah, that's right. So these big gaps here are called windows. We call these radiation windows. So if you have these wrong, then all the radiation energy just tends to flow through these. So the opacity is lowered if these windows are too large. 464 00:53:02.690 --> 00:53:08.600 Mark Kushner: But I just want to be clear. The atomic physics models get this pretty much right. 465 00:53:08.760 --> 00:53:12.660 Mark Kushner: And they don't have these problems. It's just the average animal has this problem. 466 00:53:13.180 --> 00:53:23.759 Mark Kushner: The atomic physics models are fantastic. However, they do break down as you get denser, as you expect, because atomic physics is not really all that's going on. 467 00:53:23.910 --> 00:53:26.790 Mark Kushner: They tend to treat the plasma physics perturbatively. 468 00:53:27.330 --> 00:53:31.439 Mark Kushner: So, so they work at low densities, but not high density. 469 00:53:31.790 --> 00:53:34.330 Mark Kushner: But from a radiation transport point of view. 470 00:53:34.620 --> 00:53:42.089 Mark Kushner: If you used an average atom model without this broadening, the opacity would be far too low. 471 00:53:42.220 --> 00:53:48.969 Mark Kushner: So just think of frame my question in terms of like the Bailey experiments were pretty famous, right? They got a lot of 472 00:53:49.630 --> 00:54:02.079 Mark Kushner: press and stuff, because the I think there's a conclusion that you might they might influence radiation transport rates in some right? Do you have any? 473 00:54:02.280 --> 00:54:09.500 Mark Kushner: Now, with this conclusion, when you 474 00:54:12.890 --> 00:54:24.570 Mark Kushner: Well, I would say that I don't… I wouldn't believe the average atom model as a radiation transport model. I wouldn't use it ever. It's too crude. It's too far wrong. Is that what you're asking? 475 00:54:25.600 --> 00:54:38.500 Mark Kushner: Like, the daily experiments are always like, oh, we're under-predicting the opacity, so if we raise the opacity, then there's something about the experiments of red-gray hydro in the sun that… 476 00:54:38.780 --> 00:54:40.570 Mark Kushner: Yeah, better. 477 00:54:40.940 --> 00:54:49.580 Mark Kushner: modeled something else called the stellar evolutions. And so I'm asking, like, how do you compare your 2 models for RadHydro problems that you study? 478 00:54:49.790 --> 00:54:57.179 Mark Kushner: There's some similar conclusion like how I'm reducing my opacity generally. Right. 479 00:54:58.070 --> 00:55:00.570 Mark Kushner: I mean, I guess what I'm saying is. 480 00:55:01.710 --> 00:55:04.580 Mark Kushner: Nobody was using the average out of model for a PASI. 481 00:55:04.880 --> 00:55:10.929 Mark Kushner: to start with, so we wouldn't have that conclusion, but what I would say is that broadening would generally 482 00:55:11.160 --> 00:55:12.919 Mark Kushner: Increase the opacity. 483 00:55:13.260 --> 00:55:29.690 Mark Kushner: because it fills in these windows. However, it sort of has a ceiling, and the ceiling is such that you could never get this opacity that you're seeing with iron, because there's only so many electrons in iron for opacity. 484 00:55:29.830 --> 00:55:42.319 Mark Kushner: And a researcher named Carlos Iglesias showed that if you put all the electrons in that you can possibly fit in, you know, whatever the quantum physics is, you just put all the electrons in, that should be your maximum capacity. 485 00:55:42.530 --> 00:55:47.370 Mark Kushner: And it's the that experimental data is well above that line. 486 00:55:47.630 --> 00:55:54.899 Mark Kushner: So there has to be, there will have to be some other mechanism for opacity, like two futon or something we don't know about. 487 00:55:55.430 --> 00:56:02.959 Mark Kushner: So that's… but as I said, this data seems to have come down. I mean, they've presented at a couple of conferences now, and it seems they've come down. 488 00:56:05.210 --> 00:56:07.130 Mark Kushner: Okay, any other questions? 489 00:56:07.270 --> 00:56:10.449 Mark Kushner: All right. Let's thank Professor Stark again. 490 00:56:25.010 --> 00:56:26.059 Mark Kushner: better than 491 00:56:31.900 --> 00:56:44.880 Mark Kushner: I haven't looked at you.