the following content is provided under a Creative Commons license your support will help MIT OpenCourseWare continue to offer high quality educational resources for free to make a donation or to view additional materials from hundreds of MIT courses visit MIT opencourseware at ocw.mit.edu so today I wanted to give you some context for why we're learning about all the Neutron stuff and go over all the reactor types that until this year the first time you learned about the non light water reactors at MIT was once you left MIT I remember that as an undergrad as well the only exposure we had to non light water reactors is in our design course because we decided to design one so I wanted to show you guys all the different types of reactors are out there how they work and start generating and marinating in all the different variables and nomenclature that we'll use to develop the neutron transport and Neutron diffusion equations the nice part is now until quiz 2 you can pretty much forget about the concept of charge so 802 can go back on the shelf because every interaction we do here is neutral charge neutral there'll be radioactive decays that are not the case but everything Neutron is neutral doesn't mean it's going to be simple it's just gonna be different but in the meantime today is not going to be particularly intense but I do want to show you where we're going and this goes with the pedagogical switch that we made in this department starting this year and you guys are the first trial of this we're switching to context first in theory second I personally find it much more interesting to study the theory of something for which I know the application exists who here would agree just about actually everybody ok yeah that's what I thought too so in the end we had arguments amongst the Faculty of all well you have to learn the theory to understand the application and that works really well when you say it behind the closed office door by yourself but the fact is I'm in it for yeah I'm in it for a maximum subject matter retention so in whatever order that works the best and sounds like for you guys this works the best that's what we're doing with the whole undergrad curriculum not just this class so let's launch into all the different methods of making nuclear power both fission and fusion and to switch gears since we're dealing with neutrons I don't know what happened with the oh there we go the idea here is that neutrons hit things like uranium and plutonium the fizzle isotopes that you guys saw in the exam and caused the release of other neutrons as we come up with these variables I'm gonna start laying them out here it might take more than a board to fill them all and I'll warn you ahead of time this is the only time in this course that we're gonna have V and knew the Greek letter nu on the board at the same time and I'm gonna make it really obvious which one is nu and which one is V so this parameter that describes how many neutrons come out from each fission reaction we refer to as nu or the average number you'll see in the data tables as nu bar and so as we come up with these sorts of things I will start going over them and the idea here is that each uranium-235 or plutonium or whatever nucleus B gets two to three neutrons the exact number for which is still under a hot debate and I don't think it actually matters we'll make a couple of fission products that take away most of the heat of the nuclear reaction and I just want to stop there even though you know there's going to be a chain reaction and that's what makes nuclear power happen and we can go over the timeline of what actually happens in fission and what kind of a nuclear reaction it really is so in this case this is a reaction where a neutron is heading towards this time are actually gonna give it a label a uranium-235 nucleus and it very temporarily like I showed you yesterday forms a compound nucleus some sort of large excited nucleus that lasts for about ten to the minus fourteen seconds so it doesn't instantly fizz apart there's actually a neutron absorption event some sort of nuclear instability at which point your two fission products break off notice you don't have let's call them fission product one and fission product to notice you don't quite have any neutrons yet Neutron production is not instantaneous for the following reason if you remember back to nuclear stability when we plotted let's say n I think that was maybe Z and this was N and I think this was a homework problem and you had to come up with some sort of curve of best fit for the most stable come combination of n and Z for a nucleus it was not a straight line it was something on the order of like N equals like what is it 1.00 5 5 z plus some constant something with a rather small slope well if you have a heavy nucleus like uranium-235 and you split it apart evenly let's just pretend it splits evenly for now you're kind of splitting that nucleus along a rather unstable line and as you saw in the semi empirical mass formula a little bit of instability goes a really long way towards making the nucleus extremely unstable so let's say you'd make a couple of fission products that just cleave that just cleave that nucleus with the same proportion of protons and neutrons how would they decay or how can they decay there's a couple different ways what do you guys think it can emit neutrons if it's really unstable at which point it would just go down a neutron number or how else could it decay alpha decay let's see yeah a lot of those will the heavier ones tend to do alpha decays what would it do at alpha decay for alpha you guys have we go in that direction right yeah you know what I'm not gonna rule that out yet so let's let's go with that how else could they decay yeah through beta decay let's say in that direction pretty much all these happen just not necessarily in this order when you have a really really asymmetric nucleus a lot of these fission products will emit neutrons almost instantaneously in the realm of like 10 to the minus 17 seconds some incredibly short time line you'll start to decay downwards a little bit but you're not quite at the stability line which is why a lot of the fission products then go on and they deposit their kinetic energy by bouncing around the different atoms and material creating heat but a lot of them will also send off betas or gammas and it may take you know ten to the minus thirteen seconds for them to whatever the half-life of that particular isotope is and after around like ten to the let's say 10 to the minus 10 to 10 to the minus six seconds depending on the isotope in the medium those two fission products will stop and let's just say that they stop there so the whole process of fission it's actually quite a compound process first the neutron is absorbed forming a compound nucleus then it splits apart then those individual fission products undergo what ever decays suit them best and that's the source of the neutrons in fission sometimes one of those fission products might be particularly unstable and it might send off two neutrons in other cases that I don't know of it one off the top of my head it might be none but this is the whole timeline of events in fission and the justification for why this happens straight from the first month to 2201 and I wanted to pull up some of the nuclear data so you can see what these values tend to look like and also where to find them I've got to do that screen cloning thing again hey there we go so I've already pre pulled up the Janus library I've already clicked on uranium-235 thanks to you guys I have all the data now on my shirt but so you can see a little better I also have it on the screen so let's look at this value right here a new bar total neutron production and I'll make it bigger so it's easier to see did I click on the right one yeah so take a look at that then total number of neutrons produced during u-235 it's for most energies it's hovering around the 2.4 or so there's been arguments about whether it's two point four three or two point four four and that's a linear scale that's not very helpful let's go to a logarithmic scale that's more like what I'm used to seeing most of the fission happens for u-235 in the thermal region in the region where the neutrons are at values let's say the cutoff usually about one electron volt or lower in average energy and noubar is fantastically constant at that level then as you go up and up in energy you start to make more and more neutrons why do you guys think that would be the case what are you doing to that compound nucleus as you increase the incoming Neutron energy it's gonna have more energy itself you might excite other nuclear states that can then lead to other sorts of decays or other neutron emission so to me that's the reason why once you hit about 1 MeV you can start to see a lot more neutrons being given off the reason we usually treat this as a constant notice I haven't given it an energy dependence is because most of the fission that happens is at thermal energies for that I want to show you the fission cross-section there's a lot of cross-sections and it's probably gonna be in a different graph because it's in different units and this gives you a rough measure per atom what's the probability of fission happening as a function of incoming Neutron energy at those high energies you have relatively low cross sections or low probabilities of fission happening then there's this crazy resonance region that looks like a sideways mustache but then as you get down to the lower energy levels it gets much more in fact exponentially more likely that fission will happen so almost all the fissioning in a light water reactor or any sort of other thermal reactor happens at thermal energies and that's why we take nu bar as a constant you don't have to especially if you're analyzing what's called a fast reactor or a reactor whose Neutron population remains fast on purpose and so with that I want to launch into some of the different types of reactors that you might see you guys already did those calculations in problem set 1 so I don't have to repeat them for you let's get right into the acronym so if you haven't figured this out already nuclear is a pretty acronym dense field does anyone can anyone say they know all the acronyms on this slide you're gonna know about 90% of them in about 90 minutes so it's okay or you'll have seen them at least and you look completely unfamiliar most of them well let's knock them off so KN last Thursday already showed you the basic layout of a boiling water reactor one of the types of light water reactors and the reason that this is a thermal reactor is because it's full of water water as we saw in our old Q equation argument is very good at stopping neutrons because if you guys remember this the maximum change in energy that a neutron can get is related to alpha times its incoming energy where this alpha is just a minus 1 over a plus 1 squared and I think this should actually be a 1 minus right there a is that mass number of whatever the neutrons are hitting and that one comes directly from the neutron mass number if you remember this was the simplest reduction of the Q equation the generalized Q equation or kinematics that we looked at when I said let's do the general form and okay let's take the simplest form Neutron elastic scattering here's where it comes back if a neutron hits water which is made mostly a hydrogen and a is one then it can transfer a maximum of all of its energy to the let's say to that hydrogen atom therefore given the neutron no energy and thermal izing it or slowing it down very quickly to show you what one of these things actually looks like that's the underside of a BWR I don't know if K did K and show you this before okay you've already seen what this generally looks like what about the turbine does anyone actually seen a turbine this size close up gigawatt electric turbine trying to see which one of those pixels is a person so I'm person-sized I don't see anything persons oh there's a ladder that looks to be about 6 feet tall so give you guys a sense of scale of the sort of turbines that we say oh yeah we draw a turbine on our diagram well it's not actually not simple these things take up entire hallways they're kind of airport hangar size buildings never seen one of the you but I've seen one in Japan there was a lot cleaner than this but otherwise it looked pretty much the same and the way this actually works for those who haven't taken any thermo classes yet is this turbine is full of different sets of blades that are curved at an angle so that when steam shoots in it transfer some of its energy to get the turbine rotating and there's going to be a generator found of an eye like an alternator to generate the electricity there which looks to be roughly a hundred feet away just to give you a sense of scale for this stuff as Kayne showed you a pressurized water reactor it's another kind of light water reactor with what's called an indirect cycle so this water stays pressurized it also stays liquid which is good for Neutron moderation or slowing down because in addition to the probability of any interaction some probability Sigma if you want to get the total reaction probability you have to multiply by its number density to get a macroscopic cross-section this is why I introduced this stuff Y at the beginning of class so you'd have time to marinate in it and then bring it back and remember what it was all about and so every single reaction that goes on in a nuclear reactor has got its own cross section will probably need half the board for this one you can say you have a total microscopic cross-section these are all going to be as a function of neutron energy what's the probability of anything happening at all and these are actually tabulated up on the janice website so let's unclick that get rid of neutron production and go all the way to the top n comma total so all this stuff is written in nuclear reaction parlance where if you have let's say n comma total that means a neutron comes in and that's the reaction that you're looking at so this data file here once I open it up will give you the probability that anything at all will happen you can see as the neutron energy gets higher the probability of anything happening at all gets less and less less and it follows the shape of most of the other cross-sections and I'm going to leave this up right there you've also got a few different kinds of reactions like you can have a scatter let's call that scatter which we've already said can either be elastic or inelastic it may not matter to us from the point of view of neutron physics whether the collision is elastic or inelastic all that matters is the neutron goes in and a slower Neutron comes out because what we're really concerned with here is tracking the full population of neutrons at any point in the reactor so we'll give this a position vector R which has just got x y and z in it or whatever other coordinate system you might happen to you is I prefer Cartesian because it makes sense at every energy going in any direction so we now have a solid angle vector that's got both theta and Phi in it at any given time and the whole goal of what we're going to be doing today and all of next week is to find out how do you solve for and simplify this population of neutrons let's see make sure to fill that in as velocity yes and so a lot of let's see let me get back to the cross sections and stuff if we want to know how many neutrons are in a certain little volume element in some D volume in some certain little increment of energy de traveling in some very small solid angle D Omega supposedly if you have this function then you know the direction and location and speed of every single Neutron everywhere in the reactor and this is eventually what the goal of things like Ben and cords group does the computational reactor physics group is solve for this or a simplified version of it over and over and over again for different sorts of geometries and in order to do so you need to know the rates of reactions of every kind of possible reaction that could take a neutron out of its current position like if it happens to be moving which most of them are out of its current energy group which pretty much any reaction will cause the neutron to lose energy what's the only reaction we've talked about where the neutron loses absolutely no energy it's a type of scattering yep exactly forward scattering so for forward scattering for that case where theta scattering equals zero again that's you missed the neutron didn't actually change direction at all and therefore it didn't transfer any energy but for everything else for every other possible reaction there's gonna be an energy change associated with it and probably some corresponding change in angle because a neutron can't just be moving and hit something and continue moving more slowly there's got to be some change in momentum to balance along with that change of energy and it might slightly move in some different direction and all this is happening as a function of time as you can see this gets pretty hairy pretty quick and that's why we put the full equation for this on our department t-shirts but no one ever solves the full thing what we're gonna be going over is how do you simplify it into something you can solve with like pen and paper or possibly a gigantic computer but it's not impossible so inside this Sigma total we talked about different scattering and then you could have absorption in all its different forms what sort of reactions with a neutron would cause it to be absorbed yes vision thank you so there's going to be some Sigma fission cross-section as a function of energy and if it doesn't fizz but it is absorbed we'll call that capture but capture can mean a whole bunch of different things to right there could be also a whole bunch of other nuclear reactions like there could be a reaction where one Neutron comes in two no neutrons go out like we looked at with beryllium in the Chadwick paper from the first day we're like what actually does exist for this stuff so Janice doesn't like multi-touch so have to bear with me on the small print on the screen but there should be up here it is cross-section number 16 there is a probability that one Neutron goes in that Z right there is whatever your incoming particle happens to be and in this case we know it's a neutron because we picked incident Neutron data and two n means two neutrons come out let's plot that cross-section you can see that the value is zero until you hit about four or five oh it's actually five point two nine seven seven eight one MeV so that's the Q value at which this particular reaction happens to turn on might be responsible for a little bit of the blip in the total cross-section so technically if we were to turn on every single cross-section in this database it should add up to that red line right there so you can start to get an idea for how much of all the reactions of uranium-235 are due to fission that's the one we want to exploit so let's find fission right down there oh wow there's a 3n reaction I want to see that that doesn't happen until 12 MeV yeah so neutrons don't typically tend to hit 12 MeV in a fission reactor so this is a flute and the perfect flimsy pretext to bring in another variable it's called the Chi spectrum or what's called the fission birth spectrum yeah we've already talked about the neutrons being born and how many there were but we're didn't say at what energy they're born in fusion reactors this is pretty simple you've already looked at this case what is it fourteen point seven MeV that's a lot simpler that's the fusion for fission it's not so simple for the case of fission if you draw energy versus this Chi spectrum it takes an interesting looking curve from about one MeV to about ten MeV with the most likely energy being around to anything so you aren't really going to get neutrons at the energy required for a three n reaction in a regular fission reactor just not gonna happen but it's good that you know that that exists so let's go and answer my original question how much of the total cross-section is due to fission most of it especially at low energies so let me get rid of those two n and 3n ones because they're kind of ruining our data it's making it harder to see that's better so you can see at energies below around let's say a KETV or so almost all of the reactions happening with neutrons in uranium-235 are fission this is part of what makes it such a particularly good isotope to use in reactors the other one is you can find it in the ground unlike most the other fissile isotopes unlike I think any of the other fissile isotopes thorium you got to breed and turn it into uranium 233 have to think about that one but then you can start to look at what are the other components of this cross-section like ZN prime in elastic scattering which doesn't turn on until about 0.002 MeV but later on is one of the major contributors and actually is responsible for and I've brought this for a reason is responsible for that little bump in the total cross-section so eventually all these things do matter but let's think about which ones we actually care about at all because what we eventually want to do is develop some sort of Neutron balance equation if we can measure the change in the number of neutrons as a function of position energy angle and time as a function of time and that would probably be a partial derivative because there's like seven variables here before I write any equations it's just going to be a measure of the gains minus the losses and while every particular reaction has its own cross section there's only going to be a few that we care about like they'll only be one or two types of reactions that can result in a gain of the neutron population into a certain volume with a certain energy with a certain angle and for losses there's only one we really care about total because any interaction with a neutron is going to cause that Neutron to leave this little group of perfect position energy and angle so that's where we're going we'll probably start down that route on Tuesday because I promised you guys context today you've all been to the MIT research reactor a couple of you are you running it yet awesome okay yeah say that Bo so yeah so Sarah and Jared's doing that anyone else training or trained no I'd say the folks usually pretty scared when they find out mit has a reactor and they're even more scared when they find out you guys run it what they don't realize is there's been basically no problem since 1954 the only one I know of as someone fell asleep at the controls once and forgot to push the don't call FoxNews button and it called Fox News or something so there was a big story about asleep at the helm Nora knew alarms and passive safety systems and backup operators and everything else that actually made sure that nothing happened but nowadays correct me if I'm wrong you actually have to get up every half hour reach around a panel and hit a button right so you want to hit it before it beeps at you it's reminding you okay okay yeah I'd heard the buttons every half-hour gotcha cool yeah so for all use watching on camera whatever just know that these guys got it under control so onto some gas cooled reactors and to explain some of these acronyms there are some that use natural uranium though all the ones pretty much all the ones in this country you need to enrich the uranium to get enough u-235 to turn the reaction on but that's not actually you don't have to do that in every case and you'll also see these acronyms Leu meu or h EU standing for low medium or high enrichment the accepted standard for what's low enriched uranium is 20% or below an interesting fact though you can't have something at 19 what at 19 point 99 percent enriched uranium and expect it to be low enriched uranium because every measurement technique has some error and what really determines if it's Leu is when an inspector comes and takes a sample it better be below 20% including their error so you'll usually see 19 point 75% given as the Leu limit because there's always some processing error in homogeneities measurement error head your bets pretty much like in england or the UK the advanced gas reactors have been churning along for decades they actually use co2 as the coolant which is relatively inert and they use graphite as the moderator so in this case the coolant in the moderator are separate unlike the light water reactors we have so this way the graphite right here just sits in solid form and slows down those neutrons not quite as good as water but pretty good there is an issue though that co2 just like anything has a natural decomposition reaction where co2 naturally is in equilibrium with CO and O 2 and O 2 plus graphite yields co2 gas graphite was solid and talking with a couple folks from the National Nuclear Laboratory they said that 40 years later when they took the caps off these reactors a lot of that graphite was just gone with a good explanation it vaporized very very very slowly over 40 earth years or so due to this natural recombination with whatever little bit of o2 is an equilibrium with co2 and possibly some other leaks I'm sure I wouldn't have been told that if there was a leak so I'd say the feasibility is high because they've been running for almost half a century the power density is very low why do you guys think that's the case yeah mm-hmm absolutely so well let's say you need the same cooling capacity but you're right co2 even if pressurized is not a good at heat transfer medium as water water's dense it's also got one of the highest heat capacities of anything we've ever seen the other reason is right here if you want enough reaction density it not only matters what the per atom density is but what the number density is and if you're using gaseous co2 coolant even if it's pressurized there are fewer reactions happening per unit volume because there are a few co2 molecules per unit volume than water would have so that's why we pressurize our light water reactors to keep water in its liquid state where it's a great heat absorber takes a lot of energy to boil it and it's really dense so it's a very effective dense moderator these have been around forever I think when did Windscale happen when scale was also the source of an interesting fire that's you guys might want to know about it's one of those only nuclear disasters that hit seven on the arbitrary unit scale I don't quite know how they determine what's a seven but there was a fire at the wind scale plan due to the build-up of what's called Wigner energy it turns out that when neutrons go slamming around in the graphite they leave behind radiation damage and when my family always explained what do you do for a living and I just can only think well they don't know radiation damage they've watched Harry Potter I like to say radiation like dark magic leaves traces well it leaves traces in the graphite in the form of atomic defense which took energy to create so by causing damage to the graphite you store energy in it which is known as Wigner energy and you can store so much that it just catches fire and explodes sometimes that's what happened here at Windscale eleven tons of uranium ended up burning because all of a sudden the temperature in the graph I just started going up for no reason no reason that they understood at the time it turns out that they had built up enough radiation damage energy that it started releasing more heat and releasing more heat caused more of that energy to be released and it was self-perpetuating until it just caught fire and burned 11 tonnes of uranium out in the countryside this was 1957 so again a seven on the scale with no units of nuclear disasters argue it's probably not as bad as Chernobyl so they might want a little bit of sort of resolution in that scale there's another type of gas cool reactor called the pebble bed modular reactor a much more up-and-coming one or each fuel element you don't have fuel rods you've actually got little pebbles full of tiny kernels of fuel so you've got a built in graphite moderator tennis ball sized thing with lots of little grains of sand of uo2 cooled by a bed of flowing helium or something like that and then that helium or the other gas transfers heat to water which goes into make steam and goes into the turbine like I showed you before so this is what's the fuel actually looks like inside each one of these tennis balls spheres of mostly graphite there's these little kernels of uranium dioxide about a half a millimeter across covered in layers of silicon carbide a really strong and dense material that keeps the fission products in because the biggest danger from nuclear fuel is the highly radioactive fission products that due to their instability are giving off all sorts of awful for anywhere from milliseconds to mega years after reactor operation and so if you keep those out of the coolant then the coolant stays relatively non radioactive and it's safe to do things like maintain the plant then there's the very high temperature reactor the ultimate in acronym creativity it operates at a very high temperature which has been steadily decreasing over time as reality has caught up to expectations when I first got into this field they were saying we're gonna run this at 1,100 Celsius then I started studying material science and I was like yeah nothing wants to be at 1,100 Celsius by that time they downgraded it to a thousand now they've asked some toda at around 800 850 due to some actual problems in operating things in helium it's not the helium itself but the impurities in the helium that could really mess you up and the sorts of alloys that they need to get this working these nickel super alloys like alloy 230 they can slightly carburized ich arbor eyes depending on the amount of carbon and the helium coolant either way you go you lose the strength that you need so I'll say feasibility is low to medium because well I haven't really seen one of these yet then onto water-cooled reactors has anyone heard hear heard of the reactors they have in Canada the CANDU reactors that's my favorite acronym hope that was intentional is what yeah it's not like the well they're not sorry about anything but whatever at any rate one of the nice features about this is you can actually use natural uranium because the moderators heavy water you have to look into what the sort of cross-sections are even though deuterium won't slow down neutrons as much as hydrogen will or my alpha thing oh it was right here all along even though a is two instead of one for deuterium its absorption cross-section or specifically yeah because it doesn't fish in its absorption cross-section is way lower than that of water so you actually it actually functions as a better moderator because fewer of those collisions are absorption and because you have a better Neutron population and less absorption you don't need to enrich your uranium you also don't need to pressurize your moderator so you can flow some other coolant through these pressure tubes and just have a big tank of close to something room temperature unpressurized e2o as your moderator problem with that is d2 is expensive anyone priced out deuterium oxide before probably have it the reactor because I know you have drums of it a couple thousand a kilo it's an expensive bottle of water it'll also mess you up if you drink it because a lot of that even if it's you know crystal-clear filtered d2o a lot of what if sell your machinery depends on the diffusion coefficients of various things in water those solutes in water and if you change the mass of the water than the diffusion coefficients of the water itself as well as the things in it will change and if you depend on let's say exact sodium and potassium concentrations for your nerves to function a little change in that can go a long way towards giving you a bad day and there's actually we have a little piece of one of these pressure tubes upstairs if anyone wants to take a look there's all these sealed fuel bundles inside what they call a calandria tube just a pressurized tube that's horizontal the problem with some of these is if these spacers get knocked out of place which they do all the time those tubes can start to creep downward and get a little harder to cool or touch the sides and change thermal and now getting into material signs it's it's a mess then there's the old RBMK the reactor that caused chernobyl you can also use natural uranium or low enriched uranium here the problem though that led to turn out one of the many problems led to Chernobyl was you've got all this moderator right here so if you lose your coolant let's say you had a light water reactor and your coolant goes away your moderator also goes away which means your neutrons don't slow down anymore oh that one reaction is messing up there we go which means your neutrons don't slow down anymore which means the probability of fission happening could be like 10,000 times lower so losing coolant and a light water reactor might temperature might go up but it's not going to give you a nuclear bad day in the RBMK reactor it will and it did and in addition the control rods which was supposed to shut down the reaction made of things like boron for carbide or hafnium or something with a really high capture cross-section we're tipped with graphite to help them ease in so you've got moderator tipped rods which induce additional moderation which helps slow down the neutrons even more to where they fission even better and that's what led to what's called a positive feedback coefficient so the more you tried to insert the control rods and the more you tried to fix things the worse things got in the nuclear sense and in something like a quarter of a second the reactor power went up by like 35,000 times and we'll do a millisecond by millisecond rundown of what happened in Chernobyl after we do all this Neutron physics stuff when you'll be better equipped to understand it but suffice to say there were some positive coefficients here that are to be avoided at all costs in all nuclear reactor design and the actual reactor Hall you can go and stand on one of these things very different design from what you're used to I don't think anyone would let you stand on top of a pressure vessel first your shoes would melt because they're usually at like 300 Celsius or so and second of all you probably get this a little too much radiation but this is actually what an RBMK reactors all looks like for one of the units that didn't blow up there were multiple units at that site then there's the supercritical water reactor let's say you want to run at higher temperatures than regular water will allow you to you can pressurize it so much that water goes beyond the supercritical point in the phase sense and starts to behave not like a slick wicked liquid not like a gas but somewhere in between something that's really really dense so getting towards the density of water not quite which means it's still a great moderator but still can cool the materials quite well to extract heat to make power and so on and so on yeah ah good question for a supercritical water reactor it most definitely refers to the coolant it's the phase of the coolant words beyond the liquid gas sort of separation line and it's just something in between any of these reactors can go supercritical where you're producing more neutrons than you're consuming and that is a nuclear bad day but the supercritical water reactor does not refer to neutron population just a coolant good question it's never come up before but it's like should've thought of that and so then my favorite liquid metal reactors like LBE or lead bismuth eutectic it's a low melting point alloy of lead and bismuth lead melts at around 330 Celsius bismuth 200-something put them together and it's like a low temperature solder it melted 123 point 5 Celsius you can melt it in a frying pan this is nice because you don't want your coolant to freeze when you're trying to cool your reactor because imagine that you something happens you lose power the coolant freezes somewhere outside the core you can't get the core cool again that's called a loss of flow accident that can lead to a really bad day and the lower your melting point is the better sodium potassium it's already molten to begin with sodium melts at like 90 C and when you add two different metals together you almost always lower the melting point of the combination in this case forming what's called the eutectic or a lowest possible melting point alloy so the sodium fast reactor has a number of advantages like you don't really need any pressure as long as you have a cover gas keeping the sodium width from reacting with anything like the moisture in the air or any errant water in the room you can just circulate it through the core and liquid metals are awesome heat conductors they might not have the best heat capacity as in how much energy per gram they could store like water but they're really good conductors with very high thermal conductivity they also are really good at not slowing down neutrons so these tend to be what's called fast reactors that rely on the ability of other isotopes of uranium like uranium 238 to undergo what's called fast vision and I want to show you what that looks like let's pull up u-238 and look at its fission cross-section and you might find it should look a fair bit different so we'll go down to number 18 to fission cross-section very very different so u-238 is pretty terrible at fission at low energies it's pretty good at capturing neutrons this is where we get plutonium 239 like you guys saw in the exam but then you go to really high energies and all of a sudden it gets pretty good at undergoing fission on its own and so the basis behind a lot of fast reactors is a combination of making their own fuel and the fact that uranium 238 fast visions even better than at thermal visions so something good for you to know even though it's not a fissile fuel that's light water reactor people talking you can get it to fission if the neutron population is higher now there's some problems with this it takes some time for neutrons to slow down from 1 to 10 MeV to about 0.025 Evie if your neutrons don't need to slow down and travel anywhere it pretty much all they have to do is be born and absorbed by a nearby uranium atom the feedback time is faster in these sorts of reactors they're inherently more difficult to control and you can't use normal physics like thermal expansion of things that might happen on the order of micro to nanoseconds if it takes less time than that for one Neutron to be born and find another uranium atom you can still use it somewhat but not quite as much so it's something to note backed up by nuclear data that's what one of them actually looks like these things have been built that's a blob of liquid sodium on the Monju reactor in Japan and where I was all last week in Russia they actually have fleets of fast reactors they're bien 300 and bien 600 reactors are 3 and 600 megawatt sodium cool reactors one of them in the Chelyabinsk region they used for much for desalination down in the center of Russia where there's no oceans nearby and probably dirty water they actually use that to make clean water they also use this for power production and for radiation damage studies so when it comes to radiation material science these fast reactors are really where it's at yeah you just notice the bottom I went to Belgium to their National Nuclear labs where they have a slowing sodium test loop it's not a reactor but it's like a thermal hydraulics and materials test loop and I asked a simple question where is the bathroom and they started laughing at me they said we're not putting any plumbing in a sodium loop building you'll have to go to the next building over and that's when I noticed there weren't any sprinkler systems or toilets but every 15 or 20 feet there was a giant barrel of sand that's the fire extinguisher for a liquid metal fire is you just cover it with sand absorb the heat keep the air out of the moisture out wick away the moisture whatever else and does I don't know but you can't use normal fire extinguishers to put out a sodium fire ah I don't know if that would work guess it's worth a shot with glasses and safety and stuff of course and the ones that I spent the most time working on like I showed you in the paper yesterday is the LED or LED bismuth fast reactor this one does not have the disadvantage of exploding like sodium it does have the disadvantage like I showed you yesterday of corroding everything pretty much everything and so the one thing keeping this thing back was corrosion and I say the outlet temperatures medium but hotter soon hopefully someone picks up our work and like yeah that was a good idea because we think it can raise the outlet temperature of a lead bismuth reactor by like a hundred Celsius as long as some other unforeseen problem doesn't pop up and we don't quite know yet these things also already exist in the form of the Alpha class attack submarines from the Soviet Union these are the only subs that can outrun a torpedo so you know that old algebra problem if personated leaves pittsburgh at 40 miles an hour and person B leaves Boston at 30 miles an hour word of the trains collide or I forget how it actually ends well in the end if a torpedo leaves an American sub at whatever speed and the alpha class submarine notices it how close do they have to be before the torpedo runs out of gas so what I was told by the designer of these subs fellow and by the name of George Ito schinsky when he came here to talk about his experience with his lead bismuth reactors is there is a button on the sub that's the forget about safety it's a torpedo button because if you are have a if you're underwater it'll lead bismuth reactor and a torpedo is heading at you you have a choice between maybe dying in a nuclear catastrophe and definitely dying in a torpedo explosion well that button is the I like those odds button and you just give full power to the engines and whatever else happens happens the point is you may be able to outrun the torpedo and quite popular nowadays especially in this department is molten salt cooled reactors that actually use liquid salt not dissolved but molten salt itself as the coolant that doesn't have as many of the corrosion problems as lead the exploding problems is sodium it does have a low a high melting point problem though they tend to melt at around 450 degrees Celsius but there's one pretty cool feature you can dissolve uranium in them so remember how in light water reactors the coolant is also the moderator in molten salt reactors the coolant is also the fuel because you can have principally uranium and lithium fluoride salt Co dissolved in each other and the way you make a reactor is you just flow a bunch of that salt into nearby pipes and then you get less what's called Neutron leakage or in each of these pipes once in awhile uranium will give off a few neutrons most of them will just come out the other ends of the pipes and you won't have a reaction when you put a whole bunch of molten salt together most of those neutrons find other molten salt and the reaction proceeds and it's got some nice AIF tea features like if something goes wrong just break open a pipe all the salt spills out becoming some critical because leakage goes up it freezes pretty quickly and then you must deal with it but it's not a big deal to deal with it if it's already solid and not critical so it's actually five of its 0 of 5 of I'll stop here Tuesday we'll keep developing the many many different variables we'll need to write down the neutron transport equation at which point you'll be qualified to read the t-shirts that this department prints out and then we'll simplify it so you can actually solve the equation you