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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