 vectors, some of the innovative designs I'm going to show you and I'm going to show you how calculations can be done. So a couple of things first, the first thing is that sometimes I give an opinion and when I give an opinion it is my own opinion, not the opinion of anybody I work for, that's a good thing because professors can just have random opinions and still keep their jobs. So that's a bit important, when I say something it may not even be true and it may be my opinion and then that's just me. The second thing is that you have heard the presentation from Konstantin yesterday and he stepped you through all the Gen 4 designs starting with one and then the next one and each time at the end he said okay so this one has a problem and the problem is solved in the next one, right? After a while all of you figured out that actually the list was in the corner there so you could have easily figured out which one was the next one. But the thing is that the molten salt reactor was at the end, that was the last one, all problems solved. That's the thing that's the design to go with and yeah there is something to be said for that and let's see whether I can get that idea across. So yeah the way I'm going to present it also is I'm not going to put lots and lots of information in front of you because I haven't collected lots and lots of information but I will go through some of the things that I think are important in somewhat more detail. So in an audience like this there's two kinds of you, there's those of you who know all of this anyway and you know what can I tell them and there are those who are maybe in a slightly different field and who don't know these things and I would really for those people explain some of the things in a little bit more detail. So here we go. The outline is that first I will talk to you about the idea of the molten salt reactors, then give some history, history is nice, it's an interesting history, then comes the real work which is the introduction to relevant neutronics. So it won't be just any neutronics but the neutronics that's relevant for molten salt reactor. The turn out is mostly the same as the others but okay it doesn't matter. Then in my world we always have a break after 45 minutes because students tend to fall off their chairs after 45 minutes but I guess we just barrel through. As a matter of fact we know that students only learn what is said in the first two minutes and in the last two minutes. So if you have one stretch of three hours then that's only four minutes. If you have two stretches of 45 it makes eight minutes but okay. Then I will go to the neutronics of molten salt reactors. If you want to have that break then please make the sound of falling off your chair then we can have a little break. So then we go to the neutronics of molten salt reactors and then I'll show some designs. So to begin with you all know this graph but I thought I showed it anyway. This is the World Nuclear Energy Production. It comes from the WNA which is actually a great source of information so you can go find lots of stuff there and it shows up to 2016 who has produced how much electricity and obviously Western Central Europe and the North America. There's a very small line there that's only South America. It's not that much and then Asia is up here. You know that curve? It's an interesting curve actually because when you start here in 1970 so now we're going to get an exponential growth right? Exponential growth. But then what happens? Why is there no exponential growth? Yes, before that, which was at 1979. So here is where you get the first hiccup and then it doesn't grow that well but then it still grows and then indeed Chernobyl happens here at 1986 and then it really sort of flattens off. The exponential growth is not really happening that much. Then for quite a while nothing happens until here in 2011 something really unfortunate happened again. Of course there's Fukushima and that was a real bummer but yeah. We all think that the future is still nuclear so we have good hopes for it. Now the real reason that I put this up is that for the most part these things are pressurized water reactors or boiling water reactors. And whatever they are they were always designs of solid fuels. And also the new designs that are being made these days are solid fuels. So solid fuel, this is what solid fuel looks like. Of course we have just listened for 15 hours to solid fuel. So that's you know that now. But from the neutronics point of view if you look at something like this. Here, what is the flux shape? So if I make a drawing of that, if you have your fuel rods or pins or whatever your design looks like this and then we have along this axis we put the flux. What is the, what shape does it have? Is the Z coordinate? Cosine, well, yeah, sure, yeah, cosine shape. That's what you always say, that is correct. Depends on where you start with your Z. If you make your Z here is zero, then it is cosine. If you make your Z here is zero it will be a sine, but it's a cosine shape, right? So, and radially, what would it be? So if we have the flux in this direction and then in this direction we have R. Well, so we have R on one side here. What does it look like? Yes, the genre, or you want to approximate that to the cosine too? Okay, anyway, this is something that looks like this. Okay, and of course on the other side you have the same, well this is R. So we have it only in one direction. What does it mean? Well, it means that for example up here, the flux is always lower. And also in the, not in the edges in the radial direction, but top and bottom you have just a lower flux, no matter what you do. And you can make, you can adjust that flux by all kinds of methods, by having graded enrichment, which will help you in the radial direction. You can have control devices and try to, what's called flatten the flux. You can put burnable absorbers. And you can also start to do fuel shuffling between the reloads, right? So you can do it radially in BWRs and PWRs. You do that, you move these elements around. And you can do it axially, which is what the PHWR does, the Kandu reactor. Kandu reactor you fuel, there's a guy standing there putting bundles in everywhere where the, where the burn up has been high. You put in a new bundle, so that works, but it doesn't really work very well. It's, you always lose burn up and it's always unfortunate. Just imagine that you could use a liquid fuel, right? And it would flow through the core. And then the power shape that I drew there is of course still the same. Because if this is the core and there's fuel here flowing through, then the neutronics makes that you get this flux shape, this power shape. But now, since the fuel is moving slowly through, then things that get a lot of neutrons here will also pass through an area where there's less fuel and everybody gets the same thing. So that's really good, that's really, that's really a great thing to do. The burn up would be completely uniform, assuming that there's perfect mixing of course. If you screw that up somehow, then that's not very good. And there are other immediate advantages that you have. The one is the first one that was mentioned already is a bit semantics. You don't have a core melt down because the core is already molten. But it doesn't mean that anything, that nothing can go wrong. You cannot have fuel failure. Fuel failures, we didn't talk much about fuel failures this week. Fuel failures is this thing where the cladding breaks up and then all the efficient products come out and foul your coolant and all nasty things happen. We don't have that because the fuel is just the coolant anyway. Another good thing that you can do that people realized very soon is that you can get rid of the fission gases. They will just bubble to the surface and you just vent them out. Maybe not to the outside, but in any case you can get rid of them. And you don't need coolant, at least not in the primary circuit, because the fuel is the coolant. Now, right away I have to tell you that there are different designs. There are designs where the liquid is really the fuel and the coolant. But there are others where the salt, which we will talk about, is used to cool solid fuel. So we'll talk about that later, okay? So choice of liquid, the fluid fuel, salt. And this is salt. And when I drew that first there was a space there on the one that's on the internet. It says not this salt, but actually it turns out that there's a reactor design that uses this salt as well, so I took that away. So salt is an ionic compound that can be formed by the neutralization reaction of an acid and a base. Salts are composed of related numbers of cations and anions, negative ions, so that the product is electrically neutral. Yeah, of course, of course it's neutral. And yeah, and this comes from Wikipedia. I use Wikipedia a lot because it has a lot of good information. And it's, as long as you're not talking about politics or circumcision, it's probably correct information. So one of the things is that salts have characteristically very high melting points, and that's why they are good. But there's a whole long list of requirements for these salts. So let me write them down, you have seen them before. And the ones that are indicated as an asterisk here are the ones that involve neutronics. So you need a low capture cross-section for neutrons. Why? Well, because, well, they say that, but of course, if your fuel is in the salt, then you want to have a high capture cross-section because the fuel has to capture the neutrons. Has to be stable against radiation, so you don't want your salt to fall apart if you're irradiated. And it needs to, and this is actually a big one here, it needs to be able to dissolve enough fissile fertile material to achieve criticality. So that has an asterisk because the criticality is of course a neutronics thing. But this other thing about being able to dissolve enough material that is not a neutronics, that is a chemical thing. It needs to be thermally stable, and in particular, they always talk about eutectic. Does everyone know what eutectic is? You know what eutectic. Approximately. OK, well, that was, then I'll explain what eutectic is. It's actually very simple. Can I wipe this up? So if you have a mixture of two things, and you draw a diagram where you have a mixture of A and B, and at this point it is 100% A, and at this point it's 100% B. So halfway it would be A slash B, 50, 50, right? And then here you plot the melting point, melting point. Then A may have a melting point here, and B may have a melting point here. Now if you start to mix them, then the melting point changes, the melting point of the mixture changes when you start to add B into it, goes down like that. And then if you go further, you do more of B, you may get something like this. So you may get a curve like this. You start to produce a mixture of these two components. Now this is the eutectic point. So this brings me to one of my important statements of this talk, and make it right away, that most of the things that have to do with molten salt reactors is chemistry. And this is chemistry, of course. Some sort of chemistry that tells you the interaction between those two that changes the crystal structure or the molecular structure of the thing that you have. And if you change the molecular structure, you change the temperature behavior. So the eutectic point is this point here, and it's very important that you go and sit there if you make your salt. And why is it important? Well, Christian yesterday explained, if you put your sugar in your coffee, when it's hot, and you want to get your sugar out of it, you let the coffee cool down, and then your sugar goes to the bottom of your coffee cup. That's a very good analogy, and it's very nice. Maybe if you work with sodium. But if you work with a liquid that has uranium in it, you don't want that. You do not want to have that when this stuff cools down, that uranium says, oh, OK, I'm going to solidify now, and then boing drops to the bottom of your reactor. Because then all kinds of terrible things may happen. So it's very important that your liquid stays at this point here, where the temperature, where the two components melt at the same time. There's no precipitation of anything. And again, this is chemistry. And to make the story complete about this, the problem is not just that you should come up with a salt that has this property, and then start up your reactor and then walk away. No, because the chemistry of your salt will change because of the efficient products. Everything will change. You have to make sure you never get away too far from this, because otherwise halfway through you may discover that something really bad happens. OK, it has to have low vapor pressure, the fuel, a good heat transfer, and it has to be non-aggressive to structural components, of course. Now, again, that is a chemical thing. And again, that is something where, in my opinion, maybe I should put something that indicates that I am giving my opinion now, that is where most of the work with molten salt reactors is going. It's in the chemistry of the salt and the interaction with the structural materials. So then you get to the choice of the liquid fuel. Well, for neutronic reasons, you can only have the low Z materials, like beryllium, bismuth, boron 11. Why can't you have boron 10? Why do I put boron 11? OK, so that's an easy one. That's a slam dunk. OK, I'll show it to you. Carbon, deuterium, fluorine, lithium, lithium-7, nitrogen 15, and oxygen. So note that I put these numbers there with some of them, also noted I don't do it in the official notation, but that's OK. So let's have a look. Maybe we can see that in here. Do you know this chart? Chart of new clients. OK? Now, I have always said that Wikipedia is a totally acceptable source for all kinds of information. But if you are really going to build a nuclear reactor, you cannot go and look for cross-sections there, because sometimes they are just wrong. Whereas this place, everything is always correct. If it's not correct, it's not your fault anyway. So the thing is that here you can, this is the chart of new clients, it is on the National Nuclear Data Center from Brookhaven. Of course, this is not an American thing, but this is an IAEA, but it's very much connected with IAEA, same data, and so on. You have the same stuff on IAEA. And the nice thing about it is that you can actually click on this one, and then you say, cannot download the information you requested. OK, that is very sad. Let me just give it one more try. I was promised that it was connected to the internet. But let's go there directly then. National, eh, what? Was that the one I just typed? No, no, no, no. It can't be, right? Oh, maybe it is orc. Orc, must be orc, sorry. Otherwise, we could buy this one and then eat. Oh, dot gov, maybe? I'm so sorry. What? Just Google it. This was not supposed to be a big thing. What was it? Oh, dot gov. Oh, it's a bit more complicated. Yes, and now it doesn't let me run Adobe Flash. OK, so this should have been prepared a little bit better by yours truly. Maybe it'll work. Yeah, it works. So you get this page here, and it has everything on it. So for one thing, it has this chart of the nuclides, and you can click on that. You can then go down here, click on it. Get the whole chart. This is like that. So in this particular case, the number of neutrons is in the x direction, and the number of protons in the y direction, which means the curve goes like this. Otherwise, it would go like that. So it depends on what you are used to. But now you can then, oh, by the way, does anyone know what those lines mean? They're magic numbers. What does magic number mean, Sofia? No, that's correct. It is stable. So the shells are full. That is the whole idea. But it's not necessarily the same number as no neutrons and protons, because it goes up all the way there. But yeah, so they're more stable. So they don't want to accept neutrons. And if you don't want to accept neutrons, then your cross-section is small. And where the lines cross, that's what's called, in some cases, you may have double magic. Which one is a double magic one? Yes? OK, let's go a bit higher, a bit higher. We were talking about it for a lot today and yesterday. Lead. Lead is a double magic nucleus. So that explains why, for example, all the decay chains, they all end up in lead. Everything always ends up in lead. And also, it explains why it is such a good coolant for a nuclear reactor, because it doesn't absorb neutrons. And that is so funny, sometimes, when you talk to people, they say, oh, well, we have to put more lead around this. So wait a minute, you want to shield neutrons with lead? Hello? There's a certain company in Canada that tried to do that in their fusion project. Let's not get into that. OK, so but then you can click on this, for example. Here, you can click on one of these, whatever it is. And then you can zoom in. It's supposed to be able to do that. OK, so this was a bit risky, I admit. Why can't you do that? All right, so OK, a little bit of the effect goes away. But yeah, so up here, there are all the things that you can plot. And the things you can plot is, for example, the neutron, the n gamma reaction. So this is the, what should I do? Oh, new dot, oh, dot what? Dot com? Gives me the same thing? Oh, it gives me something Google. It works for you right now, yeah. The other one, yeah. So there is a German word for that. It's called the Vorfuhr effect. When you try to demonstrate something, then it doesn't work. That's OK. We just missed the educational experience, but that's OK. We are two. Oh, that looks the same. It directed us to the same page. Oh, yeah, it goes to the same page. It's not working. Just one more time, just like this. Just to try, maybe. Oh, it did work. Now it works. So I clicked on the n gamma cross-section, right? So the little thing in yellow there that says that now you plot in color-coded, oops, no. In color-coded, you plot the cross-section for absorbing a neutron. And if a nucleus absorbs a neutron, it feels it has to emit a gamma. Why is that? Yeah, no, that's correct. Yes? No, it's fine. The nucleus is fine. It gets excited, and then it falls to the ground state and emits a photon. But it has to do that anyway, because if an object is standing still, another object hits it, then you have to conserve momentum and energy at the same time. So you need to emit something. But the point here is now that if you go and look, so green is good, right? Green doesn't absorb neutrons. Red, not so good. Up here, lots of stuff is red and yellow. It's only down here when you get into the green. And this is where I hoped maybe now it works, that if I zoom into that a little bit, click. Oops, get that one back. OK, if this doesn't work, then we give up on it. It doesn't matter. Yeah, that's what I did. Well, let's take this one, Boron 10. That was the one that we were talking about, right? OK, so let's abandon this project and go back to our thing here. So that shows it here already. And you see that these down here are green. And the only one that is a bit of a problem here is when you get to this one here that is the Boron 10, which has a considerable neutron absorption. And that is actually the one that's being used to poison reactors, right? So when you start up a reactor, you put a lot of boron in the moderator and then that absorbs neutrons. So that's not a good one to use. But Boron 11 is OK. So that's one of the reasons why we go to take the Boron. Lithium. Why do we take Lithium 7 and not 6? Well, that is because of this. And by the way, I was also going to demonstrate how you get these curves from that same web page. If you click on NFB, you can get any cross-section. But let's make sure that we understand what this is because I don't want to put up pictures. And then people don't know what they are looking at. Unless everybody really understands these graphs. How are regulators? Do they understand these graphs? Important, OK? You have to remember. So what we have here is energy. Incident energy of the neutron. Starting at 1 MeV going down to 10 to the minus 10 MeV. And the thermal energy that we usually talk about is around here. And here we have the cross-section barns. Why do we call cross-section barn? That's a story. We'll tell that some other time. It's a true story as opposed to the scram story, which is not a true story. And you can find both of them in Wikipedia. So this is the cross-section for lithium-6 absorbing a neutron, emitting a triton, and then the lithium-6 turns into helium-4. This is the nuclear way of describing, the old-fashioned way of describing nuclear reactions. And it comes from NFB 8 already. Wow, this way ahead. And the cross-section goes up to 10 to the fourth barn, which is rather large. And you produce this triton here, which has a 12 years beta decay. Why is that bad? You have heard it already before this week. It's bad because lithium is bad. It gives you misforn babies if you give it to women. At least that's what they always say, what the anti-nuclear people say. Of course, nobody plans to do that, but OK. So tritium is bad. You don't want to have tritium in your stuff. And anyway, it absorbs neutrons like crazy. So you don't want to have anything that A absorbs neutrons like crazy, and B produces tritium. At least I don't want that. Who would want that? Yes? Say it loud? Eater. I love that. Get the tritium for free. Helium, helium is very innocent. So this is why lithium-6 is out. Lithium-7 is in. Why the speed? I'm going to be here for four hours. So that's the lithium story. Then beryllium is another one, which I come back to in a moment. So then there's chemistry. Chemistry rejects bismuth. Moron-11, carbon, luterium, nitrogen-15. Why would we only talk about nitrogen-15? By now you know that, right? It's obvious. Because nitrogen-14 would absorb neutrons again. You don't want that. And oxygen. Oxygen is something you don't want to have in there. And this is all chemistry. And it's really important. And I really have no idea about it. So we are left with fluorine, which is really good. And you will see that all the molten salts is always fluorites. Lithium-7, which is really good. And beryllium, which is so-so. And it's commonly referred to this combination as flyb. Call that flyb. Now beryllium is interesting because it acts as a neutron doubler. So you take beryllium, shoot a neutron on it. You get two helium. Must be helium-4. Mistake. This has to be a 4, of course. And then you get two neutrons. So you shoot with a neutron, and you get two neutrons out, which is nice. It's actually very nice to have a beryllium neutron multiplier. But the problem is that that was shown in the next graph here on this one. This is the neutron multiplier. So again, I got from the same source that same cross-section. So here we have the energies again, but now look at the scale. And here we have the cross-section, which is not that high. And here we have that same process of beryllium-9, neutron, two neutrons come out in a beryllium-8, which then decays to two helium-4. And that is the neutron multiplier effect. But it starts only at basically two MEV. We have two MEV neutrons in a nuclear reactor. Where do they come from? On the fission. And right after the fission, they may have that energy. What is the average energy of a fission neutron? So you have to be a little louder. Six? I think one is better, yes. But it is a distribution. And it covers two, not six. I mean, it still covers six, because distributions go infinitely. But one is the more correct number. Yes. Sorry, I should not have reacted to your six so much. That was not a, what you are confused with maybe is the gamma energy from the N gamma reactions. That's typically six. As we have seen in the poster from one of you. All right, so we have looked at the salt now. We know what the salt is like. OK, yeah, beryllium has a good elastic cross-section, makes a good moderator. But the problem with beryllium is its poisonous. Beryllium is one of these things that people get very nervous about, just like asbestos. Everybody gets worried about asbestos, which is OK. Now, sometimes you find other things like zirconium, sodium, potassium, they're added, and they're added for different purposes. OK, so we go through all of the things that we just saw. And then we get to the salt itself. So the fuel that we're going to put in that salt is, of course, either uranium or plutonium of some sort, or thorium, which either fissile, fissionable, or fertile, depending on whether you want to breed or not. And these are included in those salts as fluorides. So we have, for example, UF4. That is typically what goes into a fuel salt. Not to be confused with UF6, which is what you use when you enrich uranium. The other thing is that the thing that goes into the fuel salt is usually enriched. And typically it is 20% LEU. And sometimes they tell you that, yeah, it's not 20%, but there are some question marks with that. Then typically you could use thorium fluoride as a breeding material. And then there are two ways of doing that. There are probably more ways, but you can either just put it in the fuel itself, or you can have a separate blanket outside the fuel where it gets irradiated, but it doesn't produce any heat. And then lastly, you have the plutonium, which also has only three floors instead of four here. And so a typical salt, and this is not just typical, but it is the salt of the molten salt experiment, reactor experiment, would be 65% of lithium-7 fluoride, 29.1% beryllium fluoride, 5% zirconium fluoride, and 0.9% enriched with 35% UF4. So here it is 35% enriched, not 20%. But 35% is a bit much these days. I don't like that so much anymore. Now you look at this and you say, gee, it's interesting. Why is this here? That's actually an interesting thing. The reason for the zirconium here, you don't need this at all. Why do you need that? You don't need that. I just suppose that there would be oxygen coming into this system. And the oxygen would combine with the uranium here to form U02, which is all of a sudden not part of the salt anymore. So it would fall to the bottom of the reactor and it would get very hot because all of a sudden you don't have a fuel salt anymore, doesn't flow anymore, and just all kinds of nasty things happen. So in order to avoid that, you put the zirconium in there because if there is oxygen, now it would go to the zirconium for the most part. And if the zirconium just drops out at the bottom, well, who cares? That's OK. It's smart. It's really smart to think of something like this. So here are some fuel properties. We compare water, sodium, lithium, and then the same eutectic mixture here. And then the melting point of water, well, we know that it's 0 degrees for sodium 98 for lithium 181. And this is much higher. So you have about 400, 500 degrees for a salt like this. That's very good. And then the boiling point, well, for water we know that it's 100. That's actually how you define the boiling point. Sodium 880, lithium 1342. And for this fuel here, it's very high as well. So it is much higher than the U02. And then the density, at this point you should say, wait a minute, that's not right. The density of water is defined to be 1,000 kilograms per cubic meter. But this is under reactor conditions. So this is actually the density when it is very hot. So it is a little bit, pulling a bit of a fast one. So all of these numbers are under reactor conditions. And you see that the density, of course, here is much higher than the densities here. Thermal conductivity is so-so. Specific heat capacity is similar to the other ones. Of course, the water is a very good one for specific heat capacity. That's why it is so bad to burn yourself with water. And the viscosity is, of course, enormous. So these are the salt properties that you have to deal with when you build a reactor like that. This is what it looks like. This is what fly looks like. I got this from Wikipedia. So I think it is not copyrighted. And you see the liquid come out here. It is sort of greenish because of the uranium. That's in there. Of course, it has to be heated here. Otherwise it would solidify at this point. It's just a liquid. I wouldn't want to touch it just like that, though. So the strong point of the MSR is the inherent safety. No meltdown. Then one of the neutronics things is here negative power coefficient. That's a good one. Did anyone calculate it for the exercise? No? OK, that's all right. And the other thing is that it's so easy to have a dump tank with a freeze plug. We have seen that already. If your system runs away, you just open the dump tank. All stuff goes out. And then the reaction stops. But if you put your safety hat on, and you look at some of these designs, I'm just saying it right away now. Well, let me say it later. The efficient products can be removed easily. Yeah, right. Because you have a liquid. You could flow it through something that extracts the efficient products. They form stable fluorides, if you say so. Operation is at low pressure. That's a good one. That's a nice one. We heard the other day, I guess it was Christian, who proudly announced that his sodium-cooled reactor had walls this thick. Well, you don't need that here. There's no pressure. Just make sure it doesn't melt. Then you're OK. The xenon can be skimmed off. I noticed that. That's a reactivity effect. Because xenon is, of course, a strong absorber. And fuel can be added at will, or as needed. It's maybe a better thing to say. And that's also a neutronic effect. There's no water or sodium present, which makes that you have a smaller risk of steam explosions or hydrogen production. In traditional candle reactors, if you have zirconium, for example, and Fukushima, you have these fuel rods. They have zirconium. You get water. And that produces hydrogen. And then slowly, the whole fills up with hydrogen. And one thing about hydrogen, hydrogen will always explode. And that's what happened. You saw it on TV. People were just sitting there waiting until it goes boom. Because that's what hydrogen does. So if you can avoid to have hydrogen in your system, so water, then you're good. And also sodium, although we hear how safe it is, would be nice if we don't need to have to use that. So now we're going to look a bit at history. So the molten-salt reactors were, most people maybe know, they were pioneered at Oak Ridge National Labs in Tennessee in the 1940s. Oak Ridge was one of the labs that was built to build the nuclear bomb of the Americans. So it is in the middle of nowhere, more or less, and has all these facilities. But then after the war, they went on and started to build aircraft reactor experiments. And these are two aircraft reactor experiments that are standing around in Massimo Salvatore's backyard, namely at the Idaho Labs. And they're just standing there in the middle of nowhere. You see, there's nothing there. When you turn around, there's still nothing. They didn't. So they were built in Oak Ridge, but they transported them. But since this is a conference on small modular reactor technology, this is what they are, small modular reactors. And the purpose, of course, was to put them in an airplane. That's why they're called aircraft reactors. And to have these airplanes fly so they could fly forever and just keep the atomic bombs above everybody's head forever without having to land. Program was canceled because they found other ways of doing that. But there you are. And here is the first experiment, the real aircraft reactor experiment, which operated for nine days in 1954 in Oak Ridge. It had this salt. And here you see there's now sodium in there and against the conium. And this is really highly enriched, okay? The moderator was beryllium oxide. Temperature was at 860 degrees C. And the power was two and a half megawatt thermal. So this is what the core looked like. Actually you see a nice diagram here and the photograph. So the channels, the liquid fuel channels are here. And these are the beryllium oxide reflector blocks. And it operated very well. The other thing, then the second thing after that came the real molten salt reactor experiment, which operated much longer, actually, from 1965 to 1969. And it had this salt. This is the same one that I mentioned before. So the lithium fluoride, beryllium fluoride, zirconium fluoride, uranium fluoride. And these proportions here, 33, oh, this is now, I say 33%, the previous one was 35. They also did experiments with uranium 233 and plutonium 239. They had a secondary circuit with lithium fluoride and beryllium fluoride in this relationship here. Went to eight megawatt thermal at a temperature of 650 degrees and operated for 9,000 full power hours with uranium 235 and 4,157 full powers with uranium 233. And it was a successful proof of concept. And the documents, the records, the reports are all on the internet. You can find them if you just look for them. They have been declassified at the time. It was, of course, all classified work. But when you read these reports, there's a couple of things that jump out. But one of them is that the design just sort of worked. This is what it looked like. So they built a special house for it. That's another thing that's special. At that time, if somebody said, oh, let's go build a reactor, then four years later, the reactor was there. And now, if somebody says, let's go and build the reactor and humming and humming for five years and 25 years later, there's nothing there still. Okay, it has its pros and its cons, I guess. So the reactor vessel is here. And then you get the little thing here. It's a heat exchanger, fuel pump. These are the three things that you can easily see. There's a freeze flange here of which I don't quite understand what it does. It isolates the circuit, but okay. Thermal shield, coolant pump, which is number six, that is up here. So there's a primary circuit here in red. And then the secondary circuit is in green. And the secondary circuit here has a radiator and there's just fans blowing air through so that it gets cooled. So the heat is not used for anything. And here you have your freeze plug. And then down here are the dump tanks. Coolant drain, the fuel drain tank. And here's a coolant drain tank. Now what I wanted to say, and I can say it on this picture, about this nice feature of the coolant of the fuel drain tank, it's really nice. Gravity helps you, takes your fuel from the reactor and just flushes it away. And you don't have to worry about it, right? Until it starts raining. And then the rainwater starts to run into here. Glue, glue, glue, glue, glue, glue, glue, glue, glue, fills up this area here. And what do you have then? Well, maybe it will go critical or maybe it will not. But you better make sure it doesn't go critical. So that is something that you worry about. In Canada we would worry about snow. It's not a joke, actually. Because snow is water with a lower density, right? And sometimes you can prove that, okay, with water you don't get criticality, but if you reduce the density of the water by 50%, you would get criticality. When does that happen? Well, it happens if a truck with fuel drives on the road, somewhere in Canada, slips off the road in the snow and hop and all the fuel falls into the snow. I've done that, I've calculated that. So this is what it looks like from above. This is the same thing as in the previous one. So here we are now looking at this from above here, so. And you see the vessel core. This is the heat exchanger sitting there and the pump. And this gives you about indication of the size, right? This is a manhole. That's what it looked like. The summary here, this is more or less what I said already. This is the years that it operated, the power, the low power temperatures, the moderators, this molten salt reactor was operated with graphite. The fuel salts, they were slightly different. This is the standard one. And the secondary loop had just sodium, sodium cooled and the other one was just standard fly. Okay, are we all still there? Now we're going to look at some of the neutronics. And now these are the equations that, those of you who have seen the equations, they know these equations. Those of you who have not seen them, I'm going to try to explain them to you. Who has not seen these? You have not seen them? Nobody raises their hand and maybe I go away, is that what you're hoping? No, we're going to explain them anyway. So we want to look at how neutrons behave in a reactor. And we look at one group only and you have done that because you have done Constantine's exercise. Constantine's exercise in MATLAB, he explained to you three groups. You wanted three groups, right? But you can also put it all in one group and then just not worry about it. So the first thing on the left here, this is what we always write. And actually even this morning we saw that in the thermal hydraulics presentation, because the same thing is true for heat, that the change of something is always here. So the change of the number of neutrons, or the density of neutrons, at a given point in the reactor, at a given time, as a function of time. So this is the change. The DDT is always a change. It's given by, now here are three terms. The first term is just a regular diffusion term. So by itself if you just take this and that, then you describe the same thing that you could describe when you put your young baby in a bathtub and you see how slowly the bathtub becomes yellow. That's diffusion, okay? There is no force driving that. It is just neutrons flowing by themselves. They're just having a good time. How long would they do that anyway if it was just that? What's the lifetime of a neutron? 14 minutes? 15 minutes? 10 to the 12th? 10 to the 12th minutes, yeah. Yeah, that's okay, that's about right. My number would have been 12 minutes, but 14, 10, yes. So according to this formula, they would float around for 10 minutes, which of course, since they go with 2200 meters per second, they will be pretty far. But there are not just these two terms. There is this one here and there's that one. This one has a plus sign, which means that it adds neutrons. This one has a minus sign, which means it subtracts neutrons. Makes sense, right? Now the terms are, here we have the, what's called the fission cross section. You have seen that in your exercise, which is because of the uranium. And then this little thing, new in front of it, tells you how many new neutrons you get each time a fission happens. How much is that? You have to speak up, I can't hear so well here. 2.35. 2.35. That's good enough for government work, yes. I would have said 2.4. Does it depend on the nucleus? Yes, it depends on the energy as well. So it's not totally constant. This one is not totally constant either, of course. And of course it is proportional to the flux. There are more neutrons flying around, you get more fissions, you get more new neutrons, right? And this term here, the minus sign, is just the absorption. The neutrons hit the wall and get absorbed. They'll take care of them. So this is what's called a neutron balance equation. And this, this is it. If you can solve this, you're good to go. Now there's just one small thing that the diffusion coefficient here is supposed to be, is assumed to be constant here. It may not be a constant. If it's not a constant, then you have to split up this thing here, and yeah, this is a derivative, right? Derivative x, y, and z. But other than that, this equation, whenever they show you flux distributions, that's what you calculate. You can do it with diffusion code, or you can do it with Monte Carlo, more or less that. Now the next thing people always do is while we make our life easy, we make this zero, which means it doesn't change. dn dt is equal to zero means no change. It's like your bank account. dn dt, the d euros dt in your bank account is zero. That's it. You earn as much as you spend. And then you just have to this part here, which is zero, and then that's this. It's the same thing. So you have this term here. It's the diffusion term, absorption term, and the fission term. Now in equilibrium, that means that we are looking at the reactor that would be humming along happily, which means that it has a k-effective of one. It means that it produces as many neutrons as it loses. And that's what this equation here implies. In reality, when we want to study a nuclear reactor, we may have cases where that's not the case. So we introduce this thing here called k-effective. If k-effective is equal to one, you get this back. If it's not equal to one, then you either, if it's bigger than one, it means that you produce more neutrons than you lose. And if it's smaller than one, then you lose more than you produce. Okay, so these equations, I hope that I have sort of, you will see them, you always see them. If you have never seen them before, now next time you see them, you say, oh yeah, yeah, I saw those. I know what they mean. And actually, if you then calculate it, you get an example like this. Rage is, of course, exactly what I do on the blackboard, except switched. And this one here is for the aircraft reactor experiment. They did this measurement here. And there are three curves here. And these are measurements. So they do measurements, and they do measurements by activation. So they take indium, put it in the reactor, then they run the reactor, take it out, and then they do counting. And with the counting, you get an activation. You can see that the different places, the indium has been activated differently, and it follows nicely this cosine shape that we had here. But now, if you're smart, and they are smart, you want to know a little bit about the energy spectrum. And it so happens that cadmium has a very sharp cutoff at around one electron volt. So if you take indium and you cover it with cadmium, then you get rid of the thermal spectrum. And what you're left over is something which we would then reflect the fast spectrum. So if you then want to know what the, if you take the difference then between the two, you get the separation into the, this is this one here, this is the bear minus the cadmium covered. So this would be the thermal, and then this would be the fast flux. That's what they did. That's neutronics for you. That's the only thing we do the whole day. And if you, so that was in this direction, in this direction, you get the same picture. It's just a bit more complicated because now you have again the same measurements up here. All right, but now the structure has the tubes here. So this is where the fuel is really. There's the fuel tubes. And then here you get the sector. So they have a few more activation measurements out here. And then here again, the bear, the cadmium covered. And then they take the difference between them. So the bear is actually like that. But you average it out like this more or less. Where do you expect thermal neutrons to be? The fuel or in the moderator? Moderator, because they get absorbed in the fuel, right? That's the whole point. Where do you expect the fast neutrons to be? In the fuel, why? Because that's where they're born. Well, and then they move out and they get moderated. They are everywhere, sure, in the end. But yeah, and actually you can see that from this plot as well. Okay, so I think the next one shows the cadmium absorption just in case you had never seen that. So again, we have the energy here. So around here, this is about 10 to the minus six MEV. 10 to the minus six MEV is one electron volt. So this is at one electron volt. And here we have a cross-section that's 10 to the fifth and then it drops to one. That's a really very sharp cutoff there. I think I'm going very slow, am I right? Get up a bit. I started at speed of a little bit. So that was, okay, so that was the, these are the flux distributions, which is nice. If you have a nice reactor running and it is like that, so the flux has been great. But sometimes things happen to reactors and the flux goes up and down. So in order to calculate that, we use something that's called point kinetics. And the point kinetics, we make the assumption that the flux distribution by itself, so this distribution here doesn't change. It just gets bigger or smaller, amplitude changes. And in order to analyze that, we need a few parameters. There's one that is the very important one. That is the generation time. The generation time is the neutron population divided by the production rate. So that means since this is a number and that is one over a second, so this has the dimension of seconds. And this means basically how long it takes to reproduce all the neutrons that you had. If that's short, then, well, that means that your reactor is acting fast. And the other thing that has been mentioned over and over again, and you may not have seen that before, is the word reactivity. Reactivity, it's only a word that exists in nuclear reactors. And that is the production rate minus the loss rate divided by the production rate in a nuclear reactor. So that's, by definition, equal to one minus one over k effective. And that k effective was the one that we introduced in the other equation, remember that? Okay, so that is rho and lambda. Now the point kinetics equations say now that the change of the neutron population, the average neutron population, no, there's no R here anymore. So this is the average neutron population, is now rho over lambda times N. Dimensionally, this is okay. And that means that the change is proportional to how many there are times the reactivity. So the obvious solution to this equation, and most of you should be able to know that, is an exponential, right? If you take this exponential and you plug it in there, then it is satisfied. And this here is the number of neutrons at the beginning, at the steady state, and then you have this exponential here. Ooh, exponential. So the exponential has a rho. If rho is zero, so if the reactivity is zero, then there's a Nt is N zero, constant, no problem. If rho is negative, then dies out. If rho is positive, then we get into bomb territory, because lambda is actually very small, the order of milliseconds. So this is of the order of milliseconds, and even if this is, you know, 1%, then fraction of a second, you have gone up by a huge number. That's not good. But this is only considering neutron sufficient. Fortunately, we have delayed neutrons, okay? And the delayed neutrons come from the following. If you have these fission products, they're always radioactive. They're always south of the line of stability. If the curve is like that, otherwise it would be north. And they decay towards the line of stability by beta decay, followed possibly by emission of a neutron. Now beta decay is slow. 20 seconds, seconds, minutes, even longer, which is both a blessing and a curse. Why is it a curse? Well, it means that you spend fuel, stays radioactive for a long time, right? For those of us who want to put it under the ground, it's a nuisance. Why is beta decay slow? Weak interaction, yes! It's a totally different interaction. What interactions exist? The electromagnetic, weak, strong, and gravitational. Which one is actually the weakest of those? Gravitational, otherwise you would all be so short if it was much stronger. So the emitted neutrons are called the delayed neutrons and the emitters are called precursors. The delayed neutron precursors and the delayed neutrons. Much more important. And now you, from what I just said, since they come from the fission products, you know that there's tons of fission products, so there's tons of different delayed neutron precursors and tons of delayed neutrons with their own times. But what one conventionally does is separate them in six groups. There's six groups and they have six decay constants. The decay constant is log of two divided by the half-life or something like that. So these ones here have a very long half-life. These ones have a very short. So here you have 2.8 decays per second. This one has 0.01 decays per second. All right, so these are the different groups. And here is how much you have of that. Delayed yield. This is how they are distributed. And the delayed fraction tells you now of all the neutrons that fly around in the nuclear reactor, how many of those are from delayed neutrons from these groups. So if you add them up, you get this number here. 0.006 or seven. That is a famous number. It's called beta, beta, some of these things. Mucho important. Actually it's the most important number in the nuclear reactor because without that you wouldn't be able to use it. Now, so remember that number. Is that the same for all fuels? It's different. For plutonium, is it higher or lower? Lower, yes. I don't know exactly how it's lower. So that's a bummer if you want to run with plutonium because your beta is lower. Another thing you have seen already is the expression row over beta. What is row over beta? What is the unit of row over beta? Is that it? Dollar, yes. It's the worth. The row over beta is $1. What happens above $1? You get prompt criticality. Bad thing. Don't want to be there. That's why some of you in the posters they tried to convince me that they have a 90 cents worth in their reactor and that's a save. So now we get the point kinetics with delayed neutrons and the thing that changes is that in this equation becomes like that now. So earlier we had only the dndt is row over lambda times n. Now the row is row minus beta. So we can afford to have fewer, we can afford to have a slightly, even a slightly positive row will lead us to a stable situation. But the other thing that produces neutrons is this one here. And these ones here are the, it's the concentration of the neutron precursors. So this here is now the equation that describes the number of neutrons. But how do we know C? Well, for C, we know that the change in the number of those is proportional to the number of neutrons that fly around and that is beta over lambda minus the decay of them, right? Because every time one of them decays, you have one less. Whereas here, every time one of them decays, you get one more neutron. So it's the plus sign here, canceled by the minus sign here. And now we have six precursor groups so we have six of these equations, one, two, three, four, five, six. And you have the previous equation which now has the sum here. Okay, so this was that one that was up here, no, in the previous slide. And then these six equations here. So this thing here are the point kinetics equations. And they're not that hard to solve, actually. I mean, it's just, yeah, you can do that in your MATLAB but you should do that just for fun. Actually, I once asked a student of mine to make an electronic circuit that would simulate that and he did. So now a Doppler broadening, maybe I don't need to go into Doppler broadening. Doppler broadening is just the effect that if a resonance you have here at the low temperature may be sharp but then if the temperature gets higher, it broadens and that means that neutrons that were here originally, they now see a higher cross-section. So Doppler broadening leads to an increase in Newton absorption. So increase in temperature leads to higher absorption. That's the whole idea of the, and we have plenty of these resonances around. Actually, we have so many here that when you get to here, it just gives up. There's just too many. This is the U238 capture cross-section and that's the one that saves your butt when the thing gets too hot because then all these resonances become a little bit wider, more neutrons gets absorbed, your reactor shuts down. That is what the negative power coefficient does for you or fuel coefficient. But we haven't defined reactivity coefficients yet. So reactivity coefficient is just a change of row with whatever parameter, temperature. And the unit of this is one over the unit of that one. So this is that. You have lots of these coefficients. You have the temperature coefficient of the fuel, the coolant, the moderator. Of course, in a multi-salt reactor, they're all the same, it doesn't matter. You have density coefficients, you have poison coefficients and some of them provide feedback which may be positive or negative. For example, in a Kandu reactor, the density coefficient is, well, the void coefficient, which is the opposite, it's a density coefficient. The void coefficient is positive. So in a Kandu reactor, just like in the sodium reactors, sodium cooled reactors, if you lose the coolant, you might be in trouble, okay? Now another thing is the word about breeding. We're still working our way towards the molten salt reactor, okay? Now a good thing about the breeding, so it happens according to this scheme here. We start with thorium 232, which catches a neutron with this cross-section here, turns into thorium 233, which decays after 21 minutes into protactinium 233. Now protactinium can do two things. It just sits there. It can either happily decay to U233, which is good because we want that as a fissile, right? You want to run a reactor with it, but it can also absorb another neutron in 24, it's with 24 barns, which is a rather high cross-section and then turn it to protactinium 234, which decays to uranium 234, which is not fissile. And it stays around for 27 days, so there's a significant fraction of this that goes that way instead of that way. We would like to avoid that. How do you avoid that? You turn it off and then wait. Yes, but if you turn it off, you get no power, and also you get no new protactinium. How can you do it without turning it off? Of course you have to think molten salt reactor, right? That's why I'm standing here. That's why I'm talking about that. What you do is you take the molten salt, which is the fuel, comes out of the core, you take the protactinium out and you store it, and then you just keep re-circling. The fuel, at each time, you take the protactinium out and let it happily decay to U233, and then you take your bucket of U233 and pour it back into the reactor. You don't have to turn it off for that. The only thing you have to do is to separate to let the salt come out and to take out the protactinium. That's chemistry, so it should be really easy. Now we're going to apply all of this to the molten salt reactors. So the first thing that I just mentioned already here is this chemical processing plant. This is how you draw a plant with little windows. Usually they put a smokestack on it, but recently they haven't done that anymore. So the fuel salt goes like this, goes through. This is the purification part, and most of it goes this way into the secondary, into the heat exchanger, to the secondary circuit, which also has, you would rather not have water there because if something happens here, then you get water in there, maybe not. But you can have a salt here, or sodium, and then you have your usual balance of plant here. Freeze plug, emergency dump tanks, this is the whole thing. So the chemical processing plant, that's where that would happen. That's where you would put the protructinium. You can also remove the fission products there, and that is one of the main design features of the original Oak Ridge design. So as I said, in thorium operation, you would remove the protructinium 233 to let it decay to U233, avoiding the neutron capture. And you can also use it to top up the fuel and to compensate for burnout. Then we have this thing up here. That is the vessel head. And since we have low pressure operation, you can vent off the fission gases from there, krypton, xenon, xenon is a strong neutron absorber. And if you can get rid of that, you get no more poisoning out after shutdown. Now that I'm saying that, is that actually true? People say that, but it's not true, actually. Because the xenon from the poisoning out after the shutdown comes from the iodine, and iodine doesn't disappear. All right. Then we have the dump tank. We don't have to say any much about that. So you have to be careful about the flooding, I said that. And the heat exchanger. But now comes, and this is the last part of the neutronics, something that's really different in molten salt reactors. You really have to wrap your brain around that. That part of the primary circuit is outside the core now. Which is good to let the protequinium decay. And you can make a ratio R, which is the time in core over the time out of core for a given sample of fuel salt. So here we have two buckets which are connected with pipes. And how much time is spent inside the core or inside the other volume? That depends how big they are. And actually, that's the only thing it depends on. If they are the same size, then they spend the same time in and out. If the size out is twice as big, then it spends twice as much time out as in. So that's very simple. We get that ratio, which is just a ratio of V in over V out. And the small R is good for the protequinium decay, but it's bad for the delayed neutrons. Now, what is the time in the core? Well, the time in the core is, of course, the weight of the core divided by the velocity of the liquid, which is about 20 centimeters per second or so. So we go back to the point kinetics in the molten salt reactor. So they were like that. But now we have to change that equation. So let's take this first one. Remember that one? This is how the precursors change with time, has to do with neutrons, and how many there are. But now, this term here is moving. So if we now write the derivative, the derivative now gets two components. There is the time derivative and the derivative with respect to Z. And this morning, you just put a cross through that second one here when you were doing your heat calculation. But here we don't do that. And I have to hurry up. Let me finish this and then I speed up a bit. No, no, it's OK. Calabiniary. Do you want me to finish by what? 330? 330 would be OK. I started at 2. Oh, I'm going to skip the coffee break. OK. Let me just finish this one, because I do this and then I do one other thing. Yeah, sorry, I started too slow. So you get this equation now instead of the regular point kinetics equation. And that one is a real problem, because what does it mean? It means that these delayed neutrons, which were saving you from your reactor exploding, they're being produced in the core and then they move out of the core. They're gone. And then they go through the second circuit where they decay, but they don't do anything good there except make people radioactive. And then they come back into the core and there's no more of them. That is a real thing with molten salt reactors. So that's really bad news. But really what happens is that the concentration, this is what decays outside of the volume. So it reduces your beta, it affects the controllability of the reactor and activates the outer circuit. Now, if you look at the MSRE experience, and this diagram has two features that I would like to say, they have actually calculated that. Reactivity lost due to circulation of delayed neutron precursors. And they have a measured value of 0.2 in percent delta K over K. So that means that your 0.006 goes to 0.004, which is quite a bit. But the amazing thing is that the calculation agrees so well with their measurement. Already in the 60s, they were able to take these complicated equations that people get their PhDs on today and they just calculate it. Yeah, well, that's it. I find that really impressive. And the same actually for the other things, there's the temperature coefficient of reactivity. It's minus eight and minus seven for the fuel and for the total. They were already able to calculate these things with computers that were half as powerful as your cell phone, if they had computers at all. So you see it actually. You can see in this effect when they start up. When you start up the pump, you have to withdraw the rod. This is what they do. They withdraw the rod up to a certain point because you lose reactivity because the delayed neutrons disappear. And then you have to put them back in when they come back. Some of it. And as I said, people are still working on these things. But now they have more nice displays with colors and so on and three-dimensional. And they get their PhDs on it. And this is exactly what's happening. So here you have the precursor sitting. This is the precursor density. And you see how they move out. After 10 seconds, they're all gone. And then after a while, they come back. But in the meantime, they decayed. So they're not there anymore. That's what causes the reduction in your beta. OK, well, this is about codes. You use the usual codes, MCMP, scale, serpent, drug, for depletion, you can do all of that. That's all not difficult. The difficulty is that you have the very strong feedback with the thermal hydraulics. So you need to have some serious codes here. Abnormal conditions, flow blockage, traveling slugs, higher lower density. Because this thing about the precursor is disappearing. If they all disappear and they don't come back at all, then your reactor will pull out the rod. And then, all of a sudden, a whole flood of them comes back in. And you have inserted too much reactivity. So that is stuff that you have to worry about, OK? Now, this is just one slide that I will just show. There are quite a few modern designs around that are done by private enterprises. These are all private people. And actually, these first ones here are people that I have worked with, that I'm working with. And the others are in different places in the US, in the US, Indonesia, Denmark, UK. And these are all links, actually. So you can click on it, and then you get the information. You will find that there's very nice websites and a bit thin on information sometimes. This is an opinion. Here is a summary of them, but let's not go into that then, a summary of all of those. I just want to say a few words about the first one, because that is actually one that I know a little bit. And that is a modular reactor, a small modular reactor. So it is relevant. And this is the terrestrial energy one. It is based on the experience of MSRE. It has a modular design, two units. One is operational. One will be cooling down. Containment is never opened. It has a seven-year lifecycle. So you put it there. It will run for seven years. Then you put it away and let it cool down. It does phishing gas venting, but no phishing product removal, no online reprocessing. And just top up with 20% uranium. Because you have to realize that you can't have your cake in either, too. You cannot have a reactor and leave the phishing products in and then say, well, I just have to add a little bit of uranium. No, if you leave the phishing products in, you have to add a lot of uranium. If you can take out the phishing products, you don't have to add a lot of uranium. But it's one or the other. And like with all of these companies, the exact fuel salt composition is proprietary. This is what it looks like. It has no dunk tank. It's a joke. It should be dump tank. It has always on passive cooling on the outside. But it's a very simple design. It's a graphite moderator. And the salt is just flowing through and then flowing off to the secondary circuit and the electricity. And the passive cooling is just one big fan here, where the cooling, which is nitrogen, just goes through and gets cooled and goes back. So even if something happens in that reactor, it will shut down automatically because of the feedback. And then it will be cooled because of the natural convection here. Now China is a big player. China has two types, actually. It has the solid fuel and the liquid fuel one. The solid fuel one is actually one with these things that we have seen before as well. It's triso particles. So they go through. But then it is cooled with molten salt. And here are all the coordinates about it. So this one is only molten salt cooled. And all this stuff, it won't work. And then they have the liquid fuel one that looks a bit like they all look like. And that will not have solid fuel. And the parameters are here. The fuel is pretty standard here. Now these people have collaborations with ORL and MIT. And they're actually working very hard on salt properties. As I said, chemistry is the thing here. So they're doing a lot about the chemistry. This one, this is the molten salt fast reactor, which is being developed with CNRS and in the EVOL program before. And now in the Samovar program, it is actually the Gen 4 reference reactor. And it has just one big volume here of fuel salt. It's a fast reactor. So you don't need a moderator. As a matter of fact, you don't want a moderator. And it has a blanket salt on the outside. And the blanket salt is then used for the breathing of the thorium. Whereas the fuel here has heavy metal, which could be either uranium or plutonium. No control rods in here. It just works with temperature feedback. Now that is something that you should realize. If you have a small reactor with a strong negative power coefficient or temperature coefficient, then just by changing the load, you can control the reactor. Because if you take away the load, it means that the temperature difference in the temperature that comes back into the reactor will be higher. So the temperature will go up in the reactor. If the temperature in the reactor goes up, the reactor power goes down. And that means that power goes down, just like the load goes down. So the power in the reactor follows the load. It happens automatically. You don't have to do anything, theoretically. That's what we don't have to show. Yeah, this is the last slide, actually. And the last slide, there's a, it's not the last slide. One more last slide. The last word, the last word is with the regulator. And I'm a bit surprised that we don't talk about that very much because you can make designs as much as you like. You don't talk to the regulator. You don't explain to the regulator what you're doing. It's not going to happen. So each country has its own regulator. And these regulators, of course, work or support it with the IAEA. And I mentioned the Canadian Nuclear Safety Commission, which is our regulator because I know them very well. I mean, they have this logo here. This is the Canadian Maple. And this is a watchdog, of course. The CNSC is the nuclear watchdog. And the one in Canada is actually not prescriptive. I just learned that the one in England is not that descriptive either. But in the US, the regulatory regime is very descriptive. You have to do this. You have to do that. You have to do that. In Canada, the approach is, well, show me that it's safe. And as a result of that, they have a support staff, a big staff of lots of people who do the same kind of calculations that you do to verify that you're not pulling a fast one on them, that you're telling the truth. So they have lots of people. And I mentioned, actually, people here, Romina Velsche, Dumitru Sekyuta, Ramzi Jamal, Parvai Saktar. And actually, there's one person in the audience here. These are people I know from the CNSC. And I mention that because it also shows that the Canadian regulator is very diverse. You may recognize your names there. And it hires people from all over the world. None of these people were born in Canada. So it is a very diverse regulator which is very approachable. And you should consider going and working for a regulator. I'm not saying the Canadian one. But regulator is a perfectly acceptable job. We don't hate these people. We love them. No? You know what? You like know them? No, no, that's OK. These are the same. So the MSRs have a long history. The early design seemed to have been very successful. There is a renewed interest in the technology and interestingly enough by private industry. One of the people in the list was actually one of the companies founded by Bill Gates. The same guy who thought that you never needed more than 640 kilobytes in your PC. It is Gen 4. There's lots of international collaborations. Conservative designs, this is opinion. Conservative designs, in my opinion, are the ones that are likely to succeed. And I think that in general, they are a safe, reliable, and sustainable source of low-carbon electricity. Questions?