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visit MIT OpenCourseWare at ocw.mit.edu. 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.
