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  • MICHAEL SHORT: 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

  • that 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 two,

  • you can pretty much forget about the concept of charge.

  • So 8.02 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.

  • It doesn't mean it's going to be simple.

  • It's just going to 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 and 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 about,

  • 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 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 fissile

  • isotopes that you guys saw on the exam,

  • and caused the release of other neutrons.

  • And as we come up with these variables,

  • I'm going to 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

  • going to have V and nu, the Greek letter nu,

  • on the board at the same time.

  • And I'm going to 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 begets two to three neutrons,

  • the exact number for which is still under a hot debate,

  • and I don't think it actually matters,

  • will 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 we're actually going to 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 10

  • to the minus 14 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 two.

  • 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, 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 combination of NZ

  • for a nucleus.

  • It was not a straight line.

  • It was something on the order of like N equals--

  • what is it?

  • --1.0055Z 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 cleaved 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?

  • AUDIENCE: It can emit neutrons.

  • MICHAEL SHORT: 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?

  • AUDIENCE: Alpha decay.

  • MICHAEL SHORT: Alpha decay.

  • Let's see, yeah, a lot of those will--

  • the heavier ones tend to do alpha decay.

  • What would it do at alpha decay?

  • For alpha, I guess it will be going that direction, right?

  • You know what?

  • I'm not going to rule that out yet.

  • So let's go with that.

  • How else could they decay?

  • AUDIENCE: Through beta decay.

  • MICHAEL SHORT: 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 timeline.

  • You will 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 in material

  • creating heat.

  • But a lot of them will also send off betas or gammas.

  • And it may take 10 to the minus 13 seconds for them

  • to whatever the half-life of that particular isotope is.

  • And after around, let's say, 10 to the minus 10 to 10

  • to the minus 6 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 whatever 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, though I don't know of one

  • off the top 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 of 22.01.

  • 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'm going to do that screen cloning thing again.

  • There we go.

  • So I've already pre-pulled up the JANIS library.

  • I've already clicked on uranium-235.

  • Thanks to you guys, I have all the data now on my shirt

  • so you can see a little better.

  • I also have it on the screen.

  • So let's look at this value right

  • here, nu 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.

  • The total number of neutrons produced during U-235,

  • for most energies it's hovering around the 2.4 or so.

  • There's been arguments about whether it's 2.43 or 2.44.

  • 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 is usually about one electron volt or lower

  • in average energy.

  • And nu bar 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?

  • AUDIENCE: It's going to have more energy.

  • MICHAEL SHORT: It's going to 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 are a lot of cross sections.

  • And it's probably going to be on 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.

  • And you guys already did those calculations

  • in problem set one, so I don't have to repeat them for you.

  • Let's get right into the acronyms.

  • So if you haven't figured this out already,

  • nuclear is a pretty acronym dense field.

  • Can anyone say they know all the acronyms on this slide?

  • You're going to know about 90% of them in about 90 minutes.

  • So it's OK.

  • Or you'll have seen them at least.

  • Any look completely unfamiliar?

  • AUDIENCE: Most of them.

  • MICHAEL SHORT: Most of them?

  • [LAUGHTER]

  • Well, let's knock them off.

  • So [INAUDIBLE],, 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.

  • Or this alpha is just A minus 1 over A plus 1 squared.

  • And I think this would 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 for kinematics that we looked at.

  • When I said let's do the general form,

  • then OK, let's take the simplest form,

  • neutron elastic scattering.

  • Here's where it comes back.

  • If a neutron hits water, which is made mostly of hydrogen,

  • and A is 1, then it can transfer a maximum of all of its energy,

  • let's say, to that hydrogen atom, therefore,

  • giving the neutron no energy and thermalizing 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.

  • Did [INAUDIBLE] show you this before?

  • OK.

  • So you've already seen what this generally looks like.

  • What about the turbine?

  • Has anyone actually seen a turbine this size close up,

  • a gigawatt electric turbine?

  • I'm trying to see which one of those pixels is a person.

  • I don't see anything person-sized.

  • There's a ladder that looks to be about 6 feet tall,

  • so to 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 that simple .

  • These things take up entire hallways,

  • or kind of airport hangar sized buildings.

  • I've never seen one in the US, but I've seen one in Japan.

  • It 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 transfers some of its energy to get the turbine rotating.

  • And there's going to be a generator, kind

  • of like an alternator, to generate the electricity there,

  • which looks to be roughly 100 feet away.

  • Just to give you a sense of scale for this stuff.

  • As [INAUDIBLE] showed you, a pressurized water reactor

  • is 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 introduce this stuff way

  • 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.

  • We'll 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 JANIS 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, and 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.

  • 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 use.

  • I prefer Cartesian, because it makes sense.

  • At every energy going in any direction,

  • so we now have a solid angled vector

  • that's got both theta and phi in it 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?

  • Make sure to fill that in as velocity.

  • 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 Kord's 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.

  • AUDIENCE: Forward scattering?

  • MICHAEL SHORT: Yep, exactly, forward scattering.

  • So for forward scattering for that case

  • where theta scattering equals 0.

  • Again, 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 going to 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.

  • 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 going to be going over is,

  • how do you simplify it into something

  • you can solve with a 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?

  • AUDIENCE: Fission.

  • MICHAEL SHORT: Yes, fission.

  • 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

  • too, right?

  • There could be also a whole bunch

  • of other nuclear reactions.

  • There could be a reaction where one neutron comes in,

  • two neutrons go out, like we looked at with beryllium

  • in the Chadwick paper from the first day

  • or like what actually does exist for this stuff.

  • So JANIS doesn't like multi-touch,

  • so you have to bear with me on the small print on the screen.

  • But there should be-- yep, 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 2n means two neutrons come out.

  • Let's plot that cross section.

  • You can see that the value is 0 until you hit about 4 or 5.

  • Oh, it's actually 5.297781 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 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 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?

  • 14.7 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 1 MeV to about 10 MeV with the most likely energy

  • being around 2 MeV.

  • So you aren't really going to get neutrons

  • at the energy required for a 3n reaction in a regular fission

  • reactor, just not going to 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 2n 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 keV 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 of the other fissile isotopes, unlike,

  • I think, any of the other fissile isotopes.

  • Thorium you got to breed and turn it into uranium-233.

  • I'll have to think about that one.

  • But then you start to look at, what

  • are the other components of this cross section,

  • like zn prime, inelastic 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--

  • wait, 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 are 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.

  • There will 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?

  • AUDIENCE: Yeah.

  • MICHAEL SHORT: Awesome.

  • OK.

  • Yeah.

  • Yeah, so Sarah and Jared are doing that.

  • Anyone else training or trained?

  • No.

  • I'd say folks are 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.

  • AUDIENCE: Yeah.

  • MICHAEL SHORT: What they don't realize

  • is there's been basically no problems since 1954.

  • The only one I know of is someone

  • fell asleep at the controls once and forgot

  • to push the Don't Call Fox News button,

  • and it called Fox News or something.

  • So there was a big story about, asleep at the helm,

  • ignoring all of the 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?

  • AUDIENCE: No.

  • It's on console, but it beeps at you.

  • MICHAEL SHORT: Ah.

  • AUDIENCE: Yeah, it's pretty tiring.

  • MICHAEL SHORT: So you want to hit it before it beeps at you.

  • AUDIENCE: It's reminding you to take hourly logs.

  • MICHAEL SHORT: OK.

  • AUDIENCE: It does go off every half hour.

  • AUDIENCE: It is half hour, but you we don't do [INAUDIBLE]..

  • MICHAEL SHORT: Ah, OK, yeah.

  • I'd heard the button's every half hour.

  • Gotcha.

  • Cool.

  • Yeah, so for all of you watching on camera or 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 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 you don't have to do that in every case.

  • And you'll also see these acronyms, LEU, MEU, or HEU,

  • 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 19.99% 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 19.75% given as the LEU limit,

  • because there's always some processing error,

  • inhomogeneities, measurement error.

  • Hedge 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 and 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 the 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 O2.

  • And O2 plus graphite yields CO2 gas.

  • Graphite was solid.

  • In 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 years or so due

  • to this natural recombination with whatever little bit of O2

  • is in 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.

  • AUDIENCE: [INAUDIBLE]

  • MICHAEL SHORT: Mm-hm.

  • AUDIENCE: [INAUDIBLE]

  • MICHAEL SHORT: Absolutely.

  • So well, let's say, you need the same cooling capacity,

  • but you're right.

  • CO2, even if pressurized, is not as good a heat transfer medium

  • as water.

  • Water is 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,

  • then 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 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.

  • Let me think.

  • When did Windscale happen?

  • Windscale was also the source of an interesting fire

  • that you guys might want to know about.

  • It's one of those only nuclear disasters

  • that hit 7 on the arbitrary unit scale.

  • I don't quite know how they determine what's a seven.

  • But there was a fire at the Windscale plant

  • 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 asks me to explain,

  • what do you do for a living?

  • And I can only think, well, they don't know radiation damage.

  • They've watched Harry Potter.

  • I'd like to say, radiation, like dark magic, leaves traces.

  • Well, it leaves traces in the graphite

  • in the form of atomic defects, 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.

  • 11 tons of uranium ended up burning,

  • because all of a sudden, the temperature in the graphite

  • 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 tons of uranium out

  • in the countryside.

  • This was 1957.

  • So again, a 7 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 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, where

  • 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 in to make steam

  • and goes into the turbine like I showed you before.

  • So this is what the fuel actually looks like.

  • Inside each one of these tennis ball

  • 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 nonradioactive.

  • 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 going to run this at 1100 Celsius.

  • Then I started studying material science.

  • And I was like, yeah, nothing wants to be 1100 Celsius.

  • By that time, they downgraded it to 1000.

  • Now they've asymptoted it at around 800 or 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 superalloys,

  • like Alloy 230, they can slightly

  • carburize or decarburize depending

  • on the amount of carbon in 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, we haven't really seen one of these yet.

  • Then onto water cooled reactors.

  • Has anyone here heard of the reactors

  • they have in Canada, the CANDU reactors?

  • That's my favorite acronym.

  • I hope that was intentional.

  • It what?

  • AUDIENCE: It's convenient.

  • MICHAEL SHORT: Yeah.

  • [LAUGHS] 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 moderator

  • is 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-- where did my alpha thing-- oh,

  • it was right here all along.

  • Even though A is 2 instead of 1 for deuterium,

  • it's absorption cross section, or specifically-- yeah,

  • because it doesn't fission.

  • Its absorption cross section is way lower than that of water.

  • 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 D2O as your moderator.

  • The problem with that is D2O is expensive.

  • Anyone priced out deuterium oxide before?

  • Probably have at the reactor, because I

  • know you have drums of it.

  • AUDIENCE: It's like a couple thousand per kilogram.

  • MICHAEL SHORT: 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 it,

  • even if it's crystal clear, filtered

  • D2O, a lot of what the cellular machinery depends

  • on the diffusion coefficients of various things in water,

  • those solutes in water.

  • And if you change the mass of the water,

  • then 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 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 I'm getting into material science.

  • 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 Chernobyl-- one

  • of the many problems that 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.

  • 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 in a light water reactor,

  • 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 were supposed to shut down the reaction, made of things

  • like boron 4 carbide, or hafnium, or something

  • with a really high capture cross section

  • were 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.

  • In the actual reactor hall you can go and stand

  • on one of these things.

  • It's a 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'd probably get a little too much

  • radiation.

  • But this is actually what an RBMK reactor

  • hall 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 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.

  • AUDIENCE: So supercritical refers to the coolant

  • not the neutrons?

  • MICHAEL SHORT: Good question.

  • For a supercritical water reactor,

  • it most definitely refers to the coolant.

  • It's the phase of the coolant where

  • it's beyond the liquid gas 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 have 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 melts at 123.5 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 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 is already molten to begin with.

  • Sodium melts at like 90 Celsius.

  • 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.

  • 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

  • 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 can 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 fission.

  • 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 that 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 on 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 fissions even better than it

  • thermal fissions.

  • 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 populations 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 eV.

  • If your neutrons don't need to slow down and travel anywhere,

  • and 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.

  • And 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.

  • Their BN-300 and BN-600 reactors are 300 and 600 megawatt sodium

  • cooled reactors.

  • One of them in the Chelyabinsk region

  • they use pretty 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 noticed 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's the bathroom?

  • And they started laughing at me.

  • And 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, the moisture out, wick away the moisture

  • or whatever else sand does.

  • I don't know.

  • But you can't use normal fire extinguishers

  • to put out a sodium fire.

  • AUDIENCE: When you said sand, I thought of kitty litter.

  • MICHAEL SHORT: Ah.

  • I don't know if that would work.

  • [LAUGHTER]

  • I guess it's worth a shot.

  • [LAUGHTER]

  • 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 lead or lead-bismuth fast reactor.

  • This one does not have the disadvantages

  • 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 ultimate temperature

  • is medium, but higher soon.

  • Hopefully, someone picks up our work

  • and is like, yeah, that was a good idea, because we think

  • it can raise the outlet temperature

  • of a lead-bismuth reactor by like 100 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 Alfa 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 person A leaves

  • Pittsburgh at 40 miles an hour and person

  • B leaves Boston at 30 miles an hour,

  • where do 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 Alfa 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,

  • a fellow by the name of Georgy Toshinsky, when he came here

  • to talk about his experience with these 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're underwater in a 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.

  • It doesn't have as many of the corrosion problems as lead

  • or the exploding problems as sodium.

  • It does have 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,

  • where in each of these pipes once in a while 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 neat safety features.

  • Like if something goes wrong, just break open a pipe.

  • All the salt spills out, becoming subcritical,

  • 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.

  • It's zero of five of.

  • I'll stop here.

  • On 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.

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20.核能如何運作 (20. How Nuclear Energy Works)

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    林宜悉 發佈於 2021 年 01 月 14 日
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