 And he was doing the specialities nuclear reactor core physics of existing designs or old fleet like as a condo reactors and research reactors as a Canadian nuclear laboratories and McMaster University, as well as future reactor designs such as advanced condo reactor. The Canadian supercritical water reactor and molten stone reactors. So, today, Adrian will deliver his first lecture on innovative nuclear energy systems, core design and nitronics. Adrian, are you with us here. Yes. Yes, I'm here. Can you hear me. Yes, yes, we can hear please. You can see me. Okay. Yeah, we see you. Thank you very much. So I am. First of all, thank you for inviting me. Again, it is always a pleasure. I'm very sorry that I cannot be there with you. I'm much more, much more rewarding to be to be with the people that I talked to rather than through a little camera and recently at the university where started to do in person lectures again, and the students have told me that they never ever want to go back to this kind of talks but I guess at the moment that is the best we can do. And therefore I will share my screen and start my presentation. So, let me see. There we go. Okay, it's completely about add-ins for some reason. Oh, excuse me. This is something I could not have practiced. Can you see it now, my screen. Yes. Yes. All right. All right. So, I will talk to you about about nuclear system. And I am not going to give you a list of nuclear power plants or designs that I have been working on other people are working on. I would rather take you through the reactor core design. And in the end, maybe the purpose of this is more to give you a sense of what, how to design a reactor, how to, how to make a choice because that was the actually the question from the last experience. How do we choose? Well, I can't tell you that and you can look at the brochures, but I can at least give you an idea of what the nuclear reactor core looks like, and how you can then assess yourself of how it would work. So I'm going to go a little bit into prehistory of things. It's just for fun. Inception, evolution and innovation. So my, my own personal experience relates somewhat more to the heavy water reactors. And there's also molten salt reactors and solid state reactor. I will talk a lot about the molten salt reactor today. And in the next lecture, I would like to go back to, to a solid state reactor. So the, the concepts that I will talk about are relevant to SMRs, and they're based on the on the electronics of the core design. So, the first nuclear reactor was actually in the in Gabon in the Oclo site. I'm not sure if you know that but just a little bit older 1.7 billion years ago, and it was just an open pits where uranium had accumulated and the water, rainwater, made the reactor critical, and therefore it operated for about half an hour. And then the water would evaporate, and then it would condense again and restart and there's a cycle that was going on for hundreds of thousands of years. Now, nowadays that wouldn't happen anymore. And at this point I will, for example, ask the audience, why would it not happen today. Is there any way that any of you can answer that to me. Anybody wants to answer this question. Well, eventually if you have, if nobody else answers then, and then of course should also be the chat actually I can try to look in the chat. You can put your questions in the chat and I may see those two. Due to the half life of the enrichment had decreased before it was like more in 1.7 billion years ago, and now the enrichment has decreased. The amount of your name has decreased in this region. So natural. Change is not possible anymore. Yes, the enrichment has, and well, enrichment is something that we do, but the, the U235 content has decreased so about 3% to 0.7% that it is now. Yes, very good. That's correct. So that is what we do, of course that. Now, in the more recent history, of course, you know, you guys know this but I just want to give you a line to the present. In 1939 you had Otto Hansen Fritz Stassmann who first observed the fishing of a uranium, and Otto Fritz and Lisa Meitner were actually the ones who provided the correct interpretation of that. Interestingly, this is just a little side note here, but Hans received a Nobel Prize for that, and Lisa Meitner, who was actually the one who discovered this, did never really got the acknowledgement for that. Now hopefully nowadays this is not the case anymore that female researchers to work like this that they don't get to recognition. Certainly, my university had a woman researcher gets a Nobel Prize just two years ago. But at the time it was like that. Now, if you look at the date you see this is just before World War II broke out. And at that time, then a race picked up to build a bomb, unfortunately, and in 1942, Enrico Fermi, who is also famous for actually lots and lots of other things. He built a Chicago pile, which was the first pile that went critical. So here, I would like to immediately make a small and second notation to history, because if we look at George Lawrence, for example, who lived there at the same time, he built the world's first large scale fishing experiments in graphite, and he was Canadian and he did this in Ottawa. So his experiments was similar to the Enrico Fermi's, except his pile did not get critical because the graphite was not pure enough to sustain the reaction. Now, you have not heard of him, but you have heard of Enrico Fermi. And that's, that's life. That's how things go. But it also means that things are usually not a single invention. It is usually taken by different people at different times. And some of these are successful and some of them are not. So just a quick slide for it. There might be some of you are actually not that familiar with nuclear. Here is the plot that shows how it works. In the first step, you have Einstein's formula equals equals mc squared that tells you that you make energy matter. And in order to see where that matter comes from, you look at the mass defect per nucleon as a function of atomic mass. On the right, you see uranium, and you see when that fissions into something lower something halfway up the scale, then there is a mass defects per nucleon, which is released as energy. The same plot also shows you the fusion energy on the left side. On the left side you go from left to right, that means that you add two particles, and you also gain energy. So this plot shows how both fission and fusion create energy. It is misleading, because it seems to imply that the fusion energy is larger than the fission energy, which it is not. It is because it is per nucleon. So this is a uranium 235 has a lot more nuclear than deuterium. This is the same plot, but gives you the actual data and it is inverted. It is the binding energy per nuclear. So this is just the physics that behind it that will give us the energy but that's not quite enough yet. You also need the quantum mechanics. You also need a neutron that comes by and that causes the fission, just like you need some physics mechanism that will cause the fusion, you will need to create the fission as well. And that is shown in this plot here, which is derived from the nuclear data center in Brookhaven, which is only available. Let's say the only good source of nuclear data. This is an aside here, and it shows something that people in my field often show it shows the cross section as a function of energy. The energy here is the energy of the neutron. And it is in, in what's called an mega electron volt. An electron volt is the energy that particle gets single charge gets when it is accelerated over one volt and a barn. Does anyone know what the barn is? Can I ask that question? I should ask questions for the microphone. Yeah. A unit. Okay. And how big is it? Unit of cross section 10 to the bar minus 24 centimeters square. Very good. Actually, it buys a place where they keep farm animals, but it is also used as a unit and it is 10 to the minus 24 square centimeter, which is really, really small. And the concept of a cross section is, of course, that it is like something that you shoot at. So you take a neutron, you shoot it at a barn, and it hits the barn. And instead of calling it a bar, you call it 10 to the minus 24 centimeter square. And the thing to notice here, and there's of course no scale for you to understand that, that 10 to the fifth barn is large, 10 to the fifth is a large number, but 10 to the minus 24 is a very small number. But in any case, the, the, the cross section for fission of uranium 235 increases tremendously, and you go to very low energies and these low energies. If you go to about less than one electron volt, they are called thermal energies and they're called thermal, because they are. They have the same temperature, the energy as what you have in your room, or in your, in your reactor if it is not too hot. So, it's always a good idea to go to these very low energies, except if you look at the tail of the green one, which is the U238 that has a high higher cross section than the part at the left. And that is the fast area, the one MVV. And if you manage to have your neutrons there and they happen to be there, you might use that too. And that gives you the concept of the fast reactor. And it's just for those of you who have never seen this before. Now, you have all seen this of course and we will get back to that this as well later. See what happens you have a uranium atom that receives a neutron and then splits into two and three neutrons come out and they each make a uranium atom split into two, and then one, two or three come out and so on so on that is the, this is the multiplication, which is a bit more than a chain reaction in this case. If we just do a little bit of math, just on this graph here, you can see that in the in the drawing, it doubles every generation to every dotted line is a generation. And the, the change of the number of neutrons that is the little n, which is actually the neutron density, the change of the neutron density is in this case equal to the number of neutrons that are there per generation. So this formula here describes that picture each time. Everyone gives you each one of those gives you one more neutron, one more efficient than you had before. One more neutral that you had before. So the solution to this is something that is exponential we know that. And that's quite a bomb. So we don't quite want that. What we really want is there's a change of the neutron population is approximately zero. Now those are you do more in math, you know that equilibria are always given by a change being zero. So the parameter row there to the Greek letter row. That's called reactivity. And we have if it is zero critical, super critical, and subcritical. And the solution of the equation that turns into what we, what we see on the left there, but we see at the bottom there. Now, there's a little picture that I have drawn next to it, which will tell you what happens if your reactor goes super critical or subcritical, we will get to that later. Let me do one thing I could do this. So I know I can show, I can show you the picture here, but we will not look at this picture now, you will look at that later. Now that we have made the, we've made a physics we know that we understand the physics behind it at the fundamental level. We understand that you have a spectrum. We also understand that you have a fuel, and we understand that you need a moderator, if you want to use thermal neutrons. So now you have to go and start to make choices. And interestingly, we saw that the, the original choices by Lawrence and then they go for me, you're pretty much the same using uranium oxide, and then graphite. And then, that's the way they got there. But we don't have to do that today we can make our choices we can have a fast neutrons without moderation so neutrons, and then we can use graphite for moderation, light water, heavy water, brilliant, all kinds of other stuff. As long as it's light for fuel we have the options that we can use enriched uranium or natural uranium. In first instance, we can also use plutonium, because we have plutonium. Why do we have plutonium. Don't ask. We have. If you want to use natural uranium, you either need heavy water or graphite to run your reactor. So these are choices that you can make, and you can make more complicated choices, but we will go through through one particular chain of choices that has been made. And walk you through that a little bit. And, by the way, I do not have a clock. I have no idea what time it is. So I need to be interrupted when, when I go over my time. So, in, in a way, we, this happens by natural selection and evolution. And certainly the case of Canada is very interesting because it has a very interesting history in nuclear power. The upshot of its history is that it had heavy water. Just had heavy water. That's it had heavy water. So if you have heavy water, you can use natural uranium to fuel your reactors. That was part of the war effort in Canada. But later it was also used for the civilian program. And that's why all the Canadian reactors at this moment are can do reactors that have natural uranium and the theory and moderation, heavy water Now others have gone to light water moderated, which requires you to enrich your fuel. So either you enrich your moderator or you enrich your fuel. And I just mentioned Soviet Union here because it makes the completes the picture of the graphite moderated reactor which uses low enriched uranium fuel with the RBM case. Now, all of these are, and there are other designs, of course, we have been talking, you're talking a lot about the past reactors and other things that are out there. I don't want to mention that because it's a part of my line of thought. But one thing is that all of these have have solid fuel, and they're cool cooled by a liquid or a gas as the case may be. Now, what if in nature you have something evolution and evolution is brought about by mutations. I think sometimes an animal appears that has wings and can fly, not quite just like that. That's how it goes. So what if we think out of the box what if the fuel is actually the liquid and water is solid and the fuel also then becomes the coolant. Okay, so what would be an advantage of that. Now, if you look at the traditional design here, just to point out an advantage right away. If you look at burn up. So burn up means that just like in the ochre reactor in Gabon, your, your, your your radium, your U235 disappears. It gets replaced by plutonium 239 for a while, but then that doesn't work anymore either. Also it poisons out because it accumulates the efficient products that absorb neutrons. So the burn up distribution. And the burn up distribution is caused by a flux shape, which has some actual distribution, which is along the rods, and the radio distribution in the other direction. Now if you want to optimize your burnout, you need to shape the flux. So you can use graded enrichment or enrichment that centered as at the top. You can control devices, burnable absorbers, you can shuffle the fuel between reloads, radially, like it's done in live water reactors and boiling water reactors, pressurized water reactors and boiling water reactors. You can do it axially, as it is done it can do reactors can do reactors the fuel is shifted along the fuel channel, whatever you do. It's always uneven and uneven is inefficient. So imagine you could use a liquid fuel, which will flow through the core. Now the flux shape you have to realize is still the same. In the axial distribution you would have something that looks like a sine distribution, sort of a shape like that assigned distribution, H is the height of the cylinder. And radially, you would have some vessel function, which looks like half of a bell curve. That makes the distribution go to zero at the radius of your cylinder. Now your burn up would be completely uniform. If you have perfect mixing every uranium atom in the fuel gets its chance to be efficient. And there are some other immediate advantages there too. You have no core meltdown, which is semantics of course because it's molten already. You have no fuel failure. You can say that the fuel has already failed, and fishing gases will be your bubble to the top and can be vented off. The fuel is also the coolant you don't need any separate coolant. From just these simple perspectives, you can already see that the liquid fuel would be a good thing to do. So what do you choose as a, as a liquid. Well, salt. Salt is going to Wikipedia. I only compound. Number of cat yarns and onions. Electrically noodle. They have high melting points high melting points is good because you want to work at high temperatures. And it will somebody solidify if you go no more. Now, that sounds great. Now, but there's a long list of requirements now. There's things that become a bit more complicated. Our mutation, the wings on our animal really need a few requirements. And some of them are that it has to have a low capture cross section for neutrons. So this is that barn thing again has to be low as to be stable against radiation because it's not a radiation. You need to actually dissolve the material the fissile or fertile material to achieve criticality. It has to be stirred thermally stable eutectic eutectic is a thing that you often hear. And Well, I mean, that was your I didn't know what it was. So what it means is that when assault which is a combination of different elements if it cools down, that all of these start to solidify at the same temperature. It would be really, really problematic if some of them solidified earlier than others, because then they separate the ones that would solidify earlier, would then just sort of sink to the bottom or flow to the top. And they would separate, and that may have very, very nasty consequences for your for your reactor. So vapor pressure, good heat transfer. And another one that's really important is that it is not aggressive to structural components shouldn't have something that then eats up your device and sold certainly eats up my car where I live. Okay. So the things that are indicated is a star here are actually the ones that are important for electronics. So, for the new tonic reasons here, the only the lowest that materials remain so you have brilliant basement or on. Carbon, deuterium fluorine lithium nitrogen and oxygen. And the absorption of these you find in the nuclear database and other normal circumstances I would link you to it now, but I can't doesn't really work here. So the chemistry, which I don't know anything about tells you additional requirements and it's rejects the basement more on 11 carbon, deuterium nitrogen and oxygen so you're left basically is fluorine lithium seven brilliant. And these are commonly called referred to as fly in this field. Now the nice thing about brilliant and I'll get back to that in a second is that it also acts as a neutron Doppler. If you have brilliant, brilliant nine shooting neutron on it, higher energy, you get actually two neutrons out. And that's good. That's one of the things that, as I mentioned at the beginning, the difference between Lawrence's pile and Enrico's Fermi's pile was that the new tons got lost in Lawrence's pile is new ton economy was not good as a result of the impurities. So if you find a way to make more neutrons, good for you. So that's one way of doing it. Really most has a high elastic cross section so it's a good moderator. It's always the conservation of misery. It's one of the laws of physics that tells you that Borrelian is poisonous. And sometimes people add elements like zirconium sodium or potassium for different purposes. So, that's how we choose our queue. Yeah, this is a plot that I want to show. I don't know how familiar you are with this. I have, I've looked at your CVs and I've looked at your abstracts of your questions and I've seen that some of you are really hardcore physicists already. So I'm, you know, talking. You know all of that stuff already, but some of you may not be so much familiar with it. For those of you are not familiar with it. The chart of new clients is the source to go to for anything that has to do with new tropics. Now, again, I would normally call up the website of it. And the website looks very different these days they have updated it, not necessarily better, but it looks different now, but it used to look like this. It used to go to place for, for anything that has to do with absorption. So here is plotted, as you can see by the highlight here, the cross section for absorption of neutrons and emission of a gamma. And that is the, that's the important part here, because down here, you see that the green and green means that the absorption here is pretty low. So here's where you want to be, you don't want to be up here, because there you would absorb your neutrons. Interestingly enough, there's also a little black one here, which is the hydrogen, hydrogen likes to absorb neutrons as well. And that's the difference between light water reactor, heavy water reactor, light water reactor absorbs neutrons like crazy, but also moderates very nicely. Heavy water reactor does not absorb neutrons so much, but it moderates a little bit less. And of course, light water comes out of your tap and heavy water is really difficult to make. So, one word about the one of the elements there I mentioned lithium seven, and lithium has actually significant component of lithium six in it as well. And you can see here, from that same database, that lithium six has a tremendous as the same cross section here as uranium. So if you have a little bit of lithium six in your reactor, you start to compete with the U235 for patients. You don't want that. And it is actually interesting in a different concept, because the lithium is something that's going to be produced in or it's going to be used in fusion reactors to produce straight here, which is the fuel for fusion reactors. So that's how things fit together, but not. I don't want to ruin you with that idea here now. In the same cross section I mentioned already that it is a doubler. Right, so you can see that here in the reaction, really nine neutrons in one neutron in two neutrons out gives you brilliant eight, but you get two neutrons. But the energy is high. But it's good enough because this is where the fast neutrons come out. The fuel will be uranium plutonium thorium thorium by itself is of course not fissile, but it will be the uranium 233 and may therefore be included in your in your soul. I will make a comment on that. Hope I will remember to make a comment on that later. It is included in the soldiers of fluoride, you have for which is not to be confused with the US six, which is used in the uranium enrichment process. Now in these molten salt reactors in the molten in this concept you typically have to enrich the uranium. For days, we don't go over 20% so 20% is sort of our limit. And for some reasons we actually would like to go even lower than 20% these days, but 20% is still acceptable. So the thorium fluoride would be a reading material that you can either put in the fuel itself, or in a blanket outside. It would be plutonium in which case it would be a few F3 typical salt would be this one, 65% lithium fluoride, 79% brilliant 5% zirconium and 0.9% uranium. And in this case, the MSRE I'll get back to that later is 35% and it's to radio. The, the comment I should make state away here is that I have taken a typical soul, because that's the one that's in the literature, and my friends at terrestrial energy who are building one of these things or trying to build one of these things. They, they don't tell me well they do but that's not it's not public, but their soul looks like that is their proprietary thing. They don't tell the public what that is. And otherwise other people will do it too and there will be no fun. So the properties of these are. If you look at these these fuels on the right there you see that the melting point is high. The melting point of water is around zero boiling point also high density is much higher than water sodium or lithium thermal conductivity is okay, sort of better than water, but not as good as the sodium or lithium specific heat same story. The velocity of course is very, very high. This is under typical reactor conditions that's why the density of water is listed as 712 and not as 1000. Obviously, this is what it looks like looks like liquid if you eat it up enough. Just becomes like a liquid, transparent as well. So the strong points here is actually it's inherently safe there's no meltdown, then there's this thing called the negative power coefficient. They always tell you that they always tell you about the negative power coefficients, and the US reactors are required to have negative power coefficients. If the power goes up, the activity goes down. This is a feedback mechanism to make sure that the reactor will not run away from you it will not. Well, let's say overeat let's not use bad words here, but get too hot to terminate its own excursions power excursions. But is it problem with that a little bit. And I will get to that later. In my second lecture probably the they also have dump tanks with freeze plugs because the good thing is you can visit molten salt you can have something that melts at the higher temperature. And if the reactor gets too hot, the plug will melt, and you will lose the fuel and it will disappear. And I will show you that in a picture. Fish and products can be removed easily. That's what they always say and that's absolutely not happening. Fish and products are they form stable fluorides. So they don't, they don't bubble to the surface and that's good at least low pressure operation. That's an important one. No need high pressure. Because xenon can be skimmed off the xenon. Does anyone know why xenon is a problem. Why do you call why do we call xenon a problem. In the chat. Yeah, go ahead. Because xenon is a poison that have a high absorption cross section so it will affect their activity of the actor. That's correct. Yes. It is a pain that is, it is what's called a saturating poison, and it means that it just saturates at a certain level in the operation of the reactor. And if you can remove it, then you save your neutrons again. So again, one of these things. Okay, fuel can be added that will you just open a tap and you pour in new fuel. It's as simple as it sounds but that is actually what people plan to do. And there's no water or sodium presence. So there is not this, not a big risk of steam explosions or hydrogen production. Now, a bit of history. So these molten salt reactors in the 1940s already in Oak Ridge National Labs, and they had these things called aircraft reactor experiments. And I like this picture here. This picture here shows some of these old reactors that they were building at the time. And they just have them out on the parking lot as a demonstration object. These are two test reactors, or at least the vessels of directors that were used for for experiments. And I want to go a little bit into detail of this, because of the, basically the MSR aspect of the whole thing. And the first thing I want to point out here, the aircraft reactor experiment here, the power is 2.5 megawatts thermal. That is a small, and some people will actually say micro modular reactor. And if you if you look at if you look at the thing, you have a picture here. The picture doesn't tell you how big it is. There's no little person next to it. But the scale here tells you in inches. This is eight inches, which is about 20 centimeters. So, this whole thing is about a meter across or so, a little bit more than a meter. It's small, very small. Whether it is modular is a different story. Now it has a salt. composition here, and it's high energy remaining 93%. So nowadays, we don't do that. Moderator is brilliant oxide, which I already told you is a good moderator also because of multiplication. Things, and it runs at a temperature of 860 degrees C, which is sort of a good temperature where we will see other modular reactors run as well. And what you can see here is the fuel channels, and these little these little pipes here are the connections between the fuel channels, so the fuel goes around in an influence, but in a loop goes around in a loop and then exits the core. So they actually operated the thing. And, sorry, this is a different one. There's no, there's no no more information about this one. Actually later on days. So, other experiments with the molten salt reactor experiment, which was much bigger that operators for four years actually with the salt that I just mentioned, 30% enrichment, and there was also salt in the secondary circuit. Now we're talking about eight megawatts thermal and 650 degrees C. So that is pretty, pretty good actually for, you know, small modular reactors in the previous speaker showed these. Yeah, the 300 megawatt reactors that they're going to build in various places to replace cofire plans. And she also asked, yeah, are these are these small modular reactors, or is that just an excuse to call something a small modular reactor which is actually just a normal reactor. Anyway, so here this one would be really small. And it operated for thousands of full power hours with you to 35 and they also used you to 33 and was successful. Now the thing is that it's actually pretty simple the way it worked. You have the vessel here. You have the heat exchanger pump for the heat exchanger. So the green is the secondary loop with the secondary salt, and everything that's read is the primary fuel salt. And important is the safety mechanism that sits down here, the freeze valve, please plug please well. This is one that are the normal circumstances frozen, and the reactor gets too hot, it melts, and all the fuel zooms just goes into these tanks. Since there's no moderation in these tanks, the Now, having said that, can anyone say what, if you if you look at this sort of safety perspective, what is the first thing you say, you see when I say that there is no moderation there. And it is therefore safe. Can anyone tell me something about that. Why does that big red flags go up and you were. You hear that you see this picture. Yes, I don't hear you. I saw your hand but I don't hear you. Oh, there's a question for you in the, in the, in the chat, I will answer it. So first, first my other question, why, why, why, why does this raise a red flag for safety. Just this design. No, no one. Okay. Yeah, so the, it, it's because, you know, what happens if it is flooded down there. You know, something happens that never happens, of course, you get it tsunami. And the whole thing is flooded, and there's water, and then you pump in your highly enriched uranium. Yes. So that's maybe not quite the thing you want to do or, but you know we're talking 1950s here people did a lot of things that you're not supposed to do. So does it have the negative feedback coefficient to the visiting material. No, that it. Well, it's always, it's always more than one. It's always two things, right the negative feedback coefficient is, I will show that later when it comes from, but it's also due to the expansion of the material where it gets very hot. This is what the thing looked like in reality. And what I like about it is that it's actually small, and you can recognize components in the vessel, the heat exchanger, the pump. And here you have the person who is making it all work, cranking it up. Was the freeze valve ever used. Good question. I, I'm sure they tried it. But I'm not sure if it was used in emergency. No, I don't know I couldn't answer that. The difference here is the data of operation power, temperature moderators are the moderators interesting here the difference between the brilliant oxide. And then again, the graphite that comes back to us the graphite in the molten salt reactor fuel salt composition it doesn't tell us anything. The secondary loop, which was sodium for the aircraft reactor, and the molten salt reactor had this even brilliant. So, to our rights. Why would they want to put those on airplanes. Well, that's what people at the time and thought would be a good idea. And I'm supposed to talk about neutronics so I will talk a little bit about, I'm going to throw this at you, and I hope that there will be another core on the reactor physics, another talk. And I trust that that speaker will also talk about these things. And for some of you this is obvious and for some of you, you may not want to know about this but I'm going to sort of try to run it by you in any way. The, this becomes back comes back later and it's somewhat important. And the way calculations are done is using what's called a neutron balance equation. And I say in one group, which doesn't really mean anything to you. But we only consider one energy basically. So normally you would have in a neutron distribution here, you would have the energy as a variable as well. We don't do that we only have time and space. So this tells you how the neutron population changes as a function of space and time. There are a number of components here. The first idea is basically from the diffusion equation it has a diffusion coefficient. And then it has the two things here, which relate to the efficient cross section with a plus. And there is the absorption cross section with a minus. And the flux that is given here is actually the density of neutrons times the velocity. And the flux distribution. And the other sort of neutral distribution flux distribution are related to each other, and the new year tells you how many neutrons are being produced in each efficient reaction. So this tells you everything. And then we go back to the equilibrium situation. We make the derivative zero so in equilibrium we have that the diffusion is balanced by absorption and efficient. But in order to balance it. It's not always quite balanced we can have cases where the population grows over the case. And that's why we introduce the multiplication factor, the K factor, one over K factor. This is the equation that people always stare at to first order. When they look at nuclear reactors. So. And, first of all, how am I doing my time. How am I doing in time. How many. What is the time situation. Just, I think we can delay like 15 minutes. Am I already at the end of the hour is that it. Sorry. How much time do I still have. Like 15 minutes, including questions. Okay. Yeah, okay. That's good. Now, the, the thing is you can build a core and then operate it. But maybe you do want to know how it works but but what's happening inside that core and, you know, there's some interesting. And that's where the catmium absorption comes in. There are two in many in the electronics analysis and experiments. You talk about the cut me and cut me a message very funny absorption here. It's very high cross section. So again it's competing with the uranium itself. And then at some point here. But it is still just a bit beyond thermal. This is. This is going to be a few electron volts, it drops to zero. So if you put cut me around something. It will basically absorb all the thermal neutrons. And that's being used actually in control rods, and we can use it also when you want to find out what the flux distribution is in a reactor. What we did is they looked at that reactor and looked at the axial flux distribution. And here you see the shape here, which is obtained at some point by looking at the activity that an Indian wire obtains after some time. And you see that if you hang the wire in the flux distribution at the top is the highest. But now if you reduce it by covering, take another one that's covered by cut me and you remove the thermal component on it. So what's left over is the fast component so you know that this is the fast component. That's what the difference between the two is the thermal and the ratio between the two is the ratio of fast thermal flux. I'm just showing this to you because I want to give you the taste of how people measure actually what the flux in the reactor looks like and how they used to do that in the past. And in fact, in the back home, where my, our own reactors, we still do this. We still do this to find out what is the plug distribution inside our own nuclear reactor. You can do that in the longitudinal this distribution, and you can do the same thing in the in the axial distribution. Sorry in the radio distribution. So this will be the center of the core. And here you go really really out. You see that now there are dips. And the dips occur where you have the reactivity devices. So what kind of measurements people do to make to show what the flux looks like in the reactor. Okay, that's just why I'm showing that. So, yeah, let me finish this point, my face this point. Now let me see if I want to go through this. Yeah, let me go through this. So, to come back to the to this reactivity thing. I always talk about point kinetics and that is an important part of a reactor that will determine to a large extent if you don't have the computational power to do a lot of stuff. How reactor will react and for that you need a generation time, which is the neutron population divided by the production rate. So the generation time is actually the same as the generation time you know for your population in your country the population time generation time is 30 years or in the world it's about 30 years. It takes 30 years for people to reproduce. And it's the same for neutrons. The activity we have already mentioned it is actually the production rate, minus the most rate divided by the production comes out to be one minus this one over the care. Now, we, we saw the equations, the diffusion equation, but you can also write them in this form here that the change of the neutral population is now the, the reactivity divided by the generation time times the present. Now, we have a new equation, which would have an obvious solution, which either turns into a bomb or in to get immediately goes to zero, because exponents are very, very fast and alumni here is of the order of milliseconds. If you're lucky. Okay, so the point I'm going to make here, and we're going to continue with that later is that this wouldn't work. If you use this you cannot build a reactor based on this principle. Unless you have something that's called delayed neutrons. Now you may not, may or may not have heard of late neutrons in class I would now ask you to raise your hand if you have heard of neutrons delayed neutrons. But I'm going to talk to you about them anyway. The efficient products are always radioactive. And they always have too many neutrons, so they decay, but the decay may be slow in milliseconds, seconds, minutes, much longer. Now the emitters these efficient products are what we call precursors. They are the precursors to the delayed neutrons. So one example of this is just and it is shown here like for example, the cesium here has a one second decay time, again from the, and the case to a neutron. It has a beta and decay, the percent of the cases it will decay to a beta minus and neutral. And this one here as soon as that appears in the fuel, it will give you one second later will give you a neutral. And that neutral helps you to control the nuclear reactor. Okay, the delayed neutrons have a spectrum that looks like this in terms of delay. And there's only a very small fraction of them. And actually there's one zero to many zero point zero zero. Yeah, should be six. This zero shouldn't be there. It's not so good. Sorry about that. And for plutonium it's much less. And that one is the one that provides the feedback stability for the reactor. And the makes it controllable. All right, so this is just the table that shows the previous graphs. Point kinetics that you can now make the equation means that the delayed neutrons show up here. This equation here is a very fundamental equation for the behavior of nuclear reactors. Okay, and it contains the precursors here to delay to show up in this part of the equation with a plus sign, get more neutrons. But of course, since the reactor has to be critical. If you want to make this zero you have to compensate for it by the minus beta again. This is just to make it to make it in equilibrium. You can solve these equations now. I don't want to go through them because different groups of them. But the upshot of it is that the reactor becomes more controllable. You have to delay neutrons. So if you have an upset that would increase the power from where it is supposed to be, let's say P zero, right P zero and take that as one. Then, for without delayed neutrons, you get this exponential here, if the activity goes up, whatever happens, boom, goes up. It goes down very quickly as well, but that's okay. We don't worry about that. We worry about this one. We say that the delayed neutrons. If you this gives you more time to actually take correction, corrective action, if you need to shut down your. So that's the really important part. And I, the reason I show it here is because we will, we will talk about the delayed neutrons in the context of the molten salt reactor, and also in the context of some other reactors in a few in the next lecture. I think this is a good point for me to stop and to take some questions. Okay, thank you very much. I'm also sorry for waking you up that early. Yeah, I'm going to wake up my family very soon. So any questions from from the audience here. First, at the first thank you very much for your attractive presentation. My question is how we include and classify more energy levels in neutral equation. I'm not quite sure I understand the question, but do you mean this equation here. More energy levels. Okay, more energy levels. So, okay, so there's, there's two ways to do that really. The fundamentally what you need to do is to add an energy here. So, by energy, you actually need to include three things you need to have an energy and a direction, because this is part of this formula here also doesn't tell you the direction in which the particular neutrons are moving. So what you would, what you would do is you would, you would include V, for example, as a, as a vector, or what people typically do is include the energy, and then the directional vector. But now if you want don't want to worry about the directional vector but just about the energy. So you have the, you have the possibility to split this one up into different equations. And that's what people usually do. That's what's called the multi group approximation. So you don't take the energy to be a continuous distribution, but you chop it up in certain groups. You say there's the energy thermal group, you can do two groups, you have the thermal group and the fast group. That's the easiest way to do it. Okay, treat them independently. The thermal group, for example, you wouldn't have this expressed, you wouldn't have this term, because the new tons that are generated, go into the fast. You see, so the thermal group would have only the absorption one, which includes the efficient, of course. So, then you have, then you have now two equations, but there might be scattering from do tons from one of the groups into the other group. So the, you would need two turns, two more turns, one that is the scattering into the group, and the other one is the scattering out of the group. So all it does is make this equation a little bit more complicated. It becomes the, it becomes the multi group diffusion equation. It has two more terms for the in scattering and the out scattering, and there are as many equations as there are groups. And all of a sudden it turns into an algebraic problem. Is that what you were asking? Is that okay? Any other questions, please. Also, Iran is asking questions today. Thank you. Thank you. Thank you for your presentation. I have a question about. You say that in one of the presentation slide that fission product can remove easily in a molten soft. I think it's a very challenging because of the, we have a production of gas fission products and many composition changed during the operation of the molten soft reactor. So you, you speak, you tell the two of the experimental prototype by the Americans, the MSRE and ARE that the American abandoned to develop this technology after 60 decades. Because of the, this challenging issue that the production of the bubble and the many gases, gas production decay during this operation. So, I think that is a very challenge that gas production and processing the fuel during the operation and the corrosion of this type of reactor. What's your opinion. Thank you so much. No, I need to explain about the removed easily. Thank you so much. Thank you so much. The, yeah, so no, well, no, it was a little bit sarcastic when I said removed easily. The original idea was that you would be able to, and to remove the the fission products and the fishing gases, because you but the idea was to have a separate to constantly cycle off part of the fuel, right when it leaves the core, you take separate path of the fuel, and then you would have a chemical processing plant that would use that that that's that liquid fuel, and that would extract the the fission products and the fishing gases. They never did that. And nowadays the designs that still consider molten salt, do not think of ever doing that. It is, first of all, it is, you know, technologically not obvious for all of the reasons that you mentioned. And secondly, it is, of course, a nightmare for safeguarding. And safeguarding is, it's one of the issues it's, you know, the IAEA score, and the idea that you would go and take out your fuel, and then reprocess it while you're running your reactor is absolutely out of the question. So, it's not being considered at the moment, both for technical reasons and for these. Okay, thank you. We have also questions in the chat but now from Christian. Thank you for your very interesting presentation. But my question was very near the question of my colleague. Effectively, the main question is how to reprocess. You know that with a solid fuel generally we transport the fuel towards a reprocessing plant. This is the way we use for example in France. Here, we have done some studies about the extraction of poisons like protakinium or this kind of things by liquid-liquid extraction and so on. So it means we need a near each reactor some kind of reprocessing plant because I think it's not possible to transport this liquid, strange liquid fluid. So, I think this is a weak point of this technology and effectively what is the impact on the safety and the risk of dispersion of these products. And what my question would be also when you have such a system how to keep the right composition of the salt, how to avoid the precipitation in case of for example, hair ingress and so on, because in this case you can have a maybe criticality and so on. So what is your opinions with regard safety because a lot of people advertise the safety but what happens in case of modification of the composition and the risk of precipitation of solid face and so on. Yeah, so I don't know details about that. It is certainly something that you would worry about. Of course, part of it, you have to make sure that the solution is a eutectic solution so it doesn't precipitate in the first place. And the, but the other thing is that you, you can change the composition of the fuel by adding fuel which is what they want to do anyway so it is, in order to operate these reactors you have to constantly add fuel to it. And that allows you to modify the composition if you see that some of the elements are some somehow gets out of balance. But other than that I, I'm sure there is a problem with that, or not a problem but it is an area of concern, and I'm not an expert on that. I'm more into the new tropics of that. Okay, you have one more last question for that. Hello. Thank you for the presentation. Really interesting concept is the good field. I just want to clarify about the concept and the current situation with it maybe I missed something what is the current situation and because you mentioned that last experiment was conducted in 1917 and what is it now and what is the, you know, perspective of the project of the concept. Yeah, so, so my perspective I'm, I'm talking mostly about the, the, the concept that's being developed by a company that is actually here in Canada which is called terrestrial energy. They have taken up that concept and they have developed the reactor for it, and they are still hoping to get it accepted. In terms of history, the, they were hoping to that it would be the design that is adopted by Ontario power generation which has a lot of nuclear power plants in Canada, but the Ontario power generation has last year announced that they're going to go with the boiling water design of the, of the small modular reactor, so that sort of brings it back into the, into the history. Very often the good thing to do or the thing that people want to do is to stick with a concept that they are familiar with. In terms of what is really the future of this design. I cannot, I cannot say really very well. We have, there's still talks ongoing for using it in, in mining operations in northern Canada. Other than that, it is in the design stage. And now to come back to one other, to the question from. Yeah, the other, the other question on the, on the, on the, the, the fuel and how you can transport it. The idea of these reactors is that when the core is done after 20 years, you put it in storage right next to the operating core and let it cool down for a long time. And then you transport it. That's, that's the idea in the design. Now the, the other point, yeah, just let me just the final point to mention in this context as well is that the only small amount of reactors are supposed to operate for 20 years without being without refueling, except these multi salt reactors are topped up. As they call it, they put extra fuel in. So, okay, thank you. Just, just to note that there are several development in this field of the multiple. It wasn't there a power also, but now I know in France now, instead of SFRs, the new development of MSR maybe. There's the fast reactor, of course, yes, I didn't, I will mention them later later on a little bit. Yeah. Okay, again, thank you very much. Okay, I have only one, only I noticed that you put the right title for the workshop is the workshop, which is actually the peer workshop, but the date is wrong.