# Prompt neutrons, delayed neutrons, chain reaction control

Hello, I am reading about this and I have a question , so let me explain how I understood this and please correct where I am wrong. I will ask about nuclear reactors because obviously in bombs only prompt neutrons matter since there is no need for any control only an exponential increase in reaction rate.
So I'll start from ground up , one assembles a fresh new nuclear reactor core , the fuel is loaded and the reactor is kickstarted by an external neutron source like a radium rod or whatever.In the first few seconds I assume there are only prompt neutrons , the ones that start the chain reaction and split the U235 nucleus creating the first isotopes of U235(or should I say nuclides? since they haven't yet decayed to isotopes?) , seconds to minutes later (depending on the radionuclide) secondary fission starts correct? the main U235 nucleus has been split into many isotopes which are now decaying , some with beta decay and some with direct neutron release if they are energetic enough to brake the bond?
I assume that once this beta decay is over for a given element it then releases a neutron which is the delayed neutron that can then go on and if not absorbed create a new split of U235?

This is the part that I don't understand , a nuclear reactor has neutron moderators usually of two kind , one is water or heavy water which also acts as coolant , the others are boron etc used in control rods which are inserted or taken out to compensate reactivity and control the reactor but then how do the neutron absorbers decide to catch the Prompt or fast neutrons and leave out or let the delayed ones do the work , how come the delayed ones aren't absorbed too and the chain reaction killed altogether?
Is it because the prompt neutrons have higher energies (fast neutrons) than the delayed ones, so the neutron absorber catches more high energy neutrons than lower energy delayed ones allowing them to do the main deal of splitting new nucleus?
I don't quite get this because the water acts as a moderator for the fast neutrons making them thermal neutrons , so if the delayed neutrons are weaker than the fast prompt ones how come the water doesn't slow them down so much so that they can't initiate a fission anymore?

Also in that case do fast reactors like a fast molten salt breeder for example have delayed neutrons at all and if yes then do they play any role? do the fast ones catch into the breeder substance like thorium more and the delayed ones fission the primary fissile core due to the difference in neutron absorbtion between nuclear fuels like U235 and Th232? In other words the fast ones make the throium232 into fissile U233, while the delayed ones split the U235 in the core and also the added U233?

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mfb
Mentor
Uranium nuclei can also fission without absorbing a neutron first. That is rare, but in a reactor it still happens many times per second, leading to a very low fission rate if the reactor is subcritical. There is no need to introduce an external neutron source.
(or should I say nuclides? since they haven't yet decayed to isotopes?)
That doesn't make sense. U-235 is an isotope of uranium. A nuclide is more specific: It also fixes the energy level, not just proton and neutron numbers.

The fission directly releases some neutrons. Sometimes the decay products release a neutron quickly afterwards, sometimes something like seconds later. The decay products often take days or even decades to reach a stable nucleus, that happens on a much longer timescale.

Prompt and delayed neutrons have the same probability to get absorbed, and all other probabilities are the same as well. The chain reaction is not killed simply because every fission reaction triggers on average (prompt plus delayed neutrons) one more fission reaction. The value can go slightly below or above 1 for short periods of time, in that case the power decreases/increases. You need some self-regulation: If the power goes up, you want the criticality to go down. That has to happen fast enough to prevent a nuclear explosion. Delayed neutrons are helpful here: They make the power go up/down slower. Fast reactors use delayed neutrons as well.

Edit: Missing word

Uranium nuclei can also fission without absorbing a neutron first. That is rare, but in a reactor it still happens many times per second, leading to a very low fission rate if the reactor is subcritical. There is no need to introduce an external neutron source.
1 kg of U-235 has on average 1 fission per 6 seconds.
The fission directly releases some neutrons. Sometimes the decay products release a neutron quickly afterwards, something like seconds later.
Longest lived delayed neutron emitters (that are fission products) have halflives of a bit over 50 seconds. Some bromine isotopes IIRC.
The decay products often take days or even decades to reach a stable nucleus, that happens on a much longer timescale.
Or tens of millions of years.
Isotopes which decay to emit just an electron can be very unstable/short-lived, or only slightly unstable/long-lived. Isotopes whose beta decay is energetic enough to knock out a neutron are short-lived - as mentioned, these bromine isotopes are most stable.
Prompt and delayed neutrons have the same probability to get absorbed, and all other probabilities are the same as well.
No. They have different energy distributions.
The chain reaction is not killed simply because every fission reaction triggers on average (prompt plus delayed neutrons) one more fission reaction. The value can go slightly below or above 1 for short periods of time, in that case the power decreases/increases.
Indeed, it has to. You cannot start a reactor unless the value goes over 1.

mfb
Mentor
No. They have different energy distributions.
Fine, not identical, but the difference does not matter to understand nuclear reactors. They would work with identical distributions as well.

Fine, not identical, but the difference does not matter to understand nuclear reactors. They would work with identical distributions as well.
One condition for a nuclear reactor to work is that delayed neutrons are capable of causing fission. A condition not always met.

Astronuc
Staff Emeritus
Delayed neutrons represent less than 1% (0.01) of the neutrons born in the core, yet they are important for the control of a reactor, since the delay allows movement (withdrawal) of control rods followed by a relatively slow (and controlled) response by the core. The fraction of delayed neutrons is about 0.0065 for U-235, 0.0157 for U-238, but only 0.002 for Pu-239.

Code:
Group Half-Life (sec) Uranium-235 Uranium-238 Plutonium-239
1      55.6            0.00021     0.0002      0.000076
2      22.7            0.00141     0.0022      0.00056
3      6.22            0.00127     0.0025      0.00043
4      2.30            0.00255     0.0061      0.00066
5      0.61            0.00074     0.0035      0.00021
6      0.23            0.00027     0.0012      0.00007
TOTAL      -             0.00650     0.0157      0.0020
There are 6 main groups, although some might split some of the larger groups and the half-life is an average for the group.

"Delayed neutrons do not have the same properties as prompt neutrons released directly from fission. The average energy of prompt neutrons is about 2 MeV. This is much greater than the average energy of delayed neutrons (about 0.5 MeV). The fact that delayed neutrons are born at lower energies has two significant impacts on the way they proceed through the neutron life cycle. First, delayed neutrons have a much lower probability of causing fast fissions than prompt neutrons because their average energy is less than the minimum required for fast fission to occur. Second, delayed neutrons have a lower probability of leaking out of the core while they are at fast energies, because they are born at lower energies and subsequently travel a shorter distance as fast neutrons."
Reference: DOE-HDBK-1019/2-93, Nuclear Physics and Reactor Theory

Prompt neutrons may cause fissions in U-235, U-238 and Pu-239, Pu-240, Pu-241. The Pu-isotopes (and other transuranic isotopes) are formed by successive neutron captures and beta-decays in U-238. Fast fission accounts for about 7 to 10% of fissions in a thermal reactor, while thermal fissions are the majority.

When the reactor is critical, k = 1, there is no noticeable effect of the delayed neutrons. It would take two or more collisions for the average fast neutron to approach 0.5 MeV.

Fission produces two new nuclei, although in rare circumstances three nuclei (ternary fission). The delayed neutron precursors are minority of fission products that emit neutrons instead of beta decay. Br-87 is one such nuclide with a half-live of 54.5 sec (Group 1). Group 2 consists of I-137 (t1/2 = 24.4 sec) and Br-88 (t1/2 = 16.3 sec). There are other isotopes of Br, I, Rb, and others that are involved. Delayed neutrons also play a role in controlling fast reactors.

For reactor startup, neutron sources are used so that there is enough neutrons to be detected (by neutron detectors) in order to monitor the neutron level, which should decrease as a function of time when k < 1. Primary sources use Cf-252, although in the past, they could be Po-Be, or Ra-Ba, which produce neutrons by (α,n) reaction with Be. Secondary sources use Sb-Be, which produces a high energy gamma ray (when Sb-124 decays to Te-124, and Te-124 releases a 1.69 MeV gamma ray), which produces neutrons by photodissociation of Be.

In thermal reactors, U-235 and Pu-239/-241 have a higher probability (cross-section) of fission from neutrons in the thermal range (0.01 to 0.1 eV) as compared to fast (MeV) energies.

The neutron-absorbing materials in control elements are considered absorbers, not moderators.

Edit note: Corrected data for Pu fractions in above table

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The fraction of delayed neutrons is about 0.0065 for U-235, 0.0157 for U-238, but only 0.002 for Pu-239.
That´s one important factor, yes...
"Delayed neutrons do not have the same properties as prompt neutrons released directly from fission. The average energy of prompt neutrons is about 2 MeV. This is much greater than the average energy of delayed neutrons (about 0.5 MeV).
Another relevant factor is that delayed neutrons have maximum energies...
The fact that delayed neutrons are born at lower energies has two significant impacts on the way they proceed through the neutron life cycle. First, delayed neutrons have a much lower probability of causing fast fissions than prompt neutrons because their average energy is less than the minimum required for fast fission to occur.

Prompt neutrons may cause fissions in U-235, U-238 and Pu-239, Pu-240, Pu-241.
And Pu-238, Pu-242...
Pu-238 does not undergo fission with thermal neutrons. Yet its cross-section for fast neutron is so big that its critical mass is even slightly smaller than that of Pu-239.
Pu-242 definitely has a finite critical mass. It appears not to be well ascertained whether Pu-244 has a critical mass.
And since these isotopes have energy thresholds for fast fission, a question is what fraction, if any, of delayed neutrons meets that threshold.

Astronuc
Staff Emeritus
And since these isotopes have energy thresholds for fast fission, a question is what fraction, if any, of delayed neutrons meets that threshold.
Essentially, none. As mentioned, the energies of delayed neutrons are below 1 MeV.

Since the subject is nuclear reactors, we don't need to be concerned with critical masses of pure transuranic isotopes. A critical mass of Pu-238 would be rather impractical given the high alpha-decay activity, which is why Pu-238 is used as a source of thermal energy in radioisotopic thermal generators (RTGs). BTW, Pu-238 can undergo fission by thermal neutrons, but the fission cross-section is more than an order of magnitude less than the fission cross-sections of Pu-239 and Pu-241.

In a reactor, one has to look at the entire neutron energy spectrum, and consider the absorption rates besides fission rates. The conversion of U-238 to transuranic isotopes is an important aspect of fuel cycle economy.

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Essentially, none. As mentioned, the energes of delayed neutrons are below 1 MeV.
Not quite mentioned.
Since the subject is nuclear reactors, we don't need to be concerned with critical masses of pure transuranic isotopes. A critical mass of Pu-238 would be rather impractical given the high alpha-decay activity, which is why Pu-238 is used as a source of thermal energy in radioisotopic thermal generators (RTGs).
Yes, but a critical mass of Pu-240 is much less hot. And a critical mass of Pu-242 is much less hot than a critical mass of Pu-239.
Which already has a much smaller delayed fraction than U-235.

mfb
Mentor
@Astronuc: I don't understand Pu-239 in your table. For the uranium isotopes, "total" is the sum of the groups, for plutonium, it is much smaller than the sum. Where does that come from?

Ok so as I was writing my response I saw new answers but since my text is still relevant I will post it anyway.

Correct uranium has 6 known isotopes from U233 to 238 ,thanks for clarification.

Ok lets touch upon the reactor startup condition which you mentioned here , I also am reading a book about reactor physics and it says that to start a reactor or in other words to go critical one needs to make k (the multiplying coefficient) larger than one. So I assume at first the reactor needs to see a small and allowed power excursion in terms of neutron flux increasing and then when a certain threshold is reached the control rods are lowered to achieve a stable condition which then become k=1 correct?
So for a 3000MW (thermal) reactor they allow the power to rise until they reach say the full 100% and then insert the rods and maintain that level?
I also suppose that once starting up a new or idle reactor whose metal and material structure is at room temperature they have to rise the power very gradually in order to let the materials and pipe welds to gradually accumulate to the heat , because I get that as far as the nuclear reaction is concerned the reactor heat capacity could be made from zero to full allowed power in a matter of seconds to minutes right?
But if they have to increase the heat capacity/neutron flux so gradually then how do they make the reactor critical in the first place because a chain reaction is non existing until the moment of criticality so they need to first reach that moment when the neutron flux begins to increase at all but then they somehow need to keep it increasing rather slowly instead of exponentally as it would when a critical mass is achieved like in a bomb , so I guess that this is the part where the delayed neutrons come into play , if there would be no delayed neutrons they couldn't increase the neutron flux gradually but instead would reach criticality and after that the reaction would fly out of control ad into a bomb or wouldn't start at all if not enough neutrons would be present and so no criticality correct?
Can anyone tell me in terms of a real reactor how would the control rod sequence look like in terms of first startup and reaching criticality and then reaching stable thermal power output at maximum design parameters.?

Also i read that a reactor has two states , the controllable state in which the fast neutrons together with the delayed ones are below a certain margin and then the uncontrollable chain reaction when these numbers exceed a certain margin , why is this so ? Does it mean that operating below this margin enough fast neutrons are absorbed/moderated each second that the chain reaction is basically working on split conditions like most of it is done by slowed down fast neutrons and rest is done by delayed ones but above this margin there are too many fast neutrons that they take over the job and simply start splitting all the U235 nucleus so fast that control is impossible due to their fast timing and the control mechanism being of mechanical nature?
I assume this is what happened at Chernobyl block N.4 when they disregarded security protocol and withdrew too many control rods in order to compensate for neutron poisoning of the reactor running at low power output and when the reactor suddenly had burned up all its neutron poison and with no neutron absorbtion in the way the flux increased so rapidly that the crew was unable to put the rods back in fast enough leading to a rapid exponential increase in thermal power output?

thanks.

I also suppose that once starting up a new or idle reactor whose metal and material structure is at room temperature they have to rise the power very gradually in order to let the materials and pipe welds to gradually accumulate to the heat , because I get that as far as the nuclear reaction is concerned the reactor heat capacity could be made from zero to full allowed power in a matter of seconds to minutes right?
In real power reactors the plant is heated to normal operating temperature and pressure before the core is made critical. In PWRs this is around 550F and 2250 psi. The heat up is accomplished by running the reactor coolant pumps. The friction of the water circulating around the system heats it up.

Correct uranium has 6 known isotopes from U233 to 238 ,thanks for clarification.
In that range by definition. But there are other known isotopes.
Ok lets touch upon the reactor startup condition which you mentioned here , I also am reading a book about reactor physics and it says that to start a reactor or in other words to go critical one needs to make k (the multiplying coefficient) larger than one.
By definition, a reactor would be "critical" as soon as k is exactly one... but at that value, the power would be constant (or increase at a steady but very slow rate?).
So I assume at first the reactor needs to see a small and allowed power excursion in terms of neutron flux increasing and then when a certain threshold is reached the control rods are lowered to achieve a stable condition which then become k=1 correct?
So for a 3000MW (thermal) reactor they allow the power to rise until they reach say the full 100% and then insert the rods and maintain that level?
I also suppose that once starting up a new or idle reactor whose metal and material structure is at room temperature they have to rise the power very gradually in order to let the materials and pipe welds to gradually accumulate to the heat , because I get that as far as the nuclear reaction is concerned the reactor heat capacity could be made from zero to full allowed power in a matter of seconds to minutes right?
But if they have to increase the heat capacity/neutron flux so gradually then how do they make the reactor critical in the first place because a chain reaction is non existing until the moment of criticality
No. Actually chain reactions exist under subcritical conditions.
After all, if k is above zero but below one then a spontaneous fission event or a neutron emitted by a neutron source can and usually does start a long chain reaction before all neutrons are absorbed. k=0,9 means that 1 spontaneous fission creates about 9 induced fissions.

But chain reactions may not be going on at all times nor most of time.
As mentioned, 1 kg of U-235 has one fission per 6 seconds. And critical mass of U-235, with suitable moderator, is under 800 g.
If you take U-235 to high subcritical conditions then at for example k=0,9, 1 spontaneous fission causes a total of 10 fissions. But this does not mean there is a fission each 0,6 seconds. Rather, when a spontaneous fission happens, the chain reaction of 9 prompt induced fissions is over in milliseconds, and then there are no neutrons present in reactor for another 6 seconds.
In which time the geometry of reactor may change. You might have a neutron at k=0,9, a chain reaction ends after 10 fissions, and in the next 6 seconds the value of k increases to 1,1. Nothing happens until a neutron comes across or another fission happens, and then the reactor is prompt critical which it has been for several seconds, and explodes.
so they need to first reach that moment when the neutron flux begins to increase at all but then they somehow need to keep it increasing rather slowly instead of exponentally
It is increasing exponentially. But it is increasing slowly because the base of the exponent is small.
as it would when a critical mass is achieved like in a bomb , so I guess that this is the part where the delayed neutrons come into play , if there would be no delayed neutrons they couldn't increase the neutron flux gradually but instead would reach criticality and after that the reaction would fly out of control ad into a bomb or wouldn't start at all if not enough neutrons would be present and so no criticality correct?
Yes. If there would be no delayed neutrons, or if they exist but have no effect because nuclei undergo fission with high energy prompt neutrons but not with low energy delayed neutrons.

mfb
Mentor
so I guess that this is the part where the delayed neutrons come into play , if there would be no delayed neutrons they couldn't increase the neutron flux gradually but instead would reach criticality and after that the reaction would fly out of control ad into a bomb or wouldn't start at all if not enough neutrons would be present and so no criticality correct?
There are some passive control mechanisms, but without delayed neutrons it would be extremely challenging to operate a power plant.
With delayed neutrons: You can have an exponentially increasing power - as long as the characteristic time is long enough (k just a bit above 1). Once the desired power level is reached, the control rods are inserted a bit more than before (or more rods are inserted) to reduce the criticality to a value much closer than 1.
Also i read that a reactor has two states , the controllable state in which the fast neutrons together with the delayed ones are below a certain margin and then the uncontrollable chain reaction when these numbers exceed a certain margin , why is this so ?
You answered your own question in the previous paragraph. If the reactor is in k>1 with prompt neutrons only, it can explode.

Astronuc
Staff Emeritus
@Astronuc: I don't understand Pu-239 in your table. For the uranium isotopes, "total" is the sum of the groups, for plutonium, it is much smaller than the sum. Where does that come from?
I corrected the data for Pu. The source table was incorrect, mixing yields and fractions. The data for U-235 and Pu-239 are for a thermal neutron spectrum, while the data for U-238 for fast spectrum, since U-238 does not fission by thermal neutrons.

mfb
Astronuc
Staff Emeritus
Ok lets touch upon the reactor startup condition which you mentioned here , I also am reading a book about reactor physics and it says that to start a reactor or in other words to go critical one needs to make k (the multiplying coefficient) larger than one. So I assume at first the reactor needs to see a small and allowed power excursion in terms of neutron flux increasing and then when a certain threshold is reached the control rods are lowered to achieve a stable condition which then become k=1 correct?
So for a 3000MW (thermal) reactor they allow the power to rise until they reach say the full 100% and then insert the rods and maintain that level?
In pressurized water reactors, control rods are generally withdrawn during full power operation, and most are withdrawn during startup. One bank is partially withdrawn, although in some reactor designs, there are so-called gray rods, which are used during operation for adjusting the axial shape of the neutron flux and power.

PWRs also use boric acid in the coolant to absorb neutrons. During startup up, the pumps are started to warm up the core and primary system, and that can increase the primary coolant temperature to near core inlet conditions. The control rods are removed and the boric acid concentration reduced so that k is slightly great than one. The heat up of the primary system reduces the coolant (moderator) density in the core, so that is one way the reactor is controlled. As the fuel heats up, the uranium atoms start vibrating in the fuel lattice, and this produces a broadening of absorption resonances, particularly when the power in the fuel increases such that the fuel is hotter than the coolant. The resonance absorption is primarily in U-238 until Pu-240 is produced. The decrease in moderator density and resonance absorption in the fuel help control the reactor, in addition to reducing the boron in the coolant. There are also burnup absorbers, such as gadolinia and boron. In some designs, gadolinia blended with the UO2 in some fuel rods, while for boron, fuel pellets are coated with ZrB2. The burnable absorbers are consumed or 'burned out' during the first cycle of operation.

In Boiling water reactors (BWRs), control rods are used in the core during operation. Most control rods are withdrawn, but usually two groups are used in the core, and they are periodically repositioned in order to distribute the power and burnup. On a longer period, control rods groups in the core are withdrawn while different groups are inserted, for the same reason of distributing the power and burnup. BWRs use the boiling (and production of steam) in the hotter fuel assemblies to reduce moderation. They do not use boron in the coolant, since the boron would deposit in the regions where boiling would take place.

mfb
So the PWR is built such that when the coolant (water) becomes less dense or is lost the reactor power decreases? Why is this, is it because water is also the moderator in the PWR making fast neutrons into thermal ones and the U235 fissions better with thermal than fast neutrons , so loss of coolant means loss of thermal neutrons leaving fast ones which have lower cross section for fission in U235?

Are you saying that simply by applying full power to the main circulation pumps the water flow under pressure makes it to near 270 degrees celsius? Without any other means of preheating like resistance heating or otherwise simply by pure pressure creating by the pumps?

Ok one last time about the delayed neutrons I wanna see if I got it right.
So the reason why a reactor can be controllable due to those neutrons is because if for example we get at first (let's use round numbers for sake of simplicity) 10 fast neutrons which moderated to thermal by water they would split say about 8 U235 atoms (2 getting absorbed or lost) these 8 U235 atoms would now be split and the splitting would release (assuming about 2.4 neutrons per fission) about 19 neutrons and also a bunch of isotopes that undergo decay , so the 19 immediately created neutrons travel through water get to thermal energies , some are lost some absorbed so say some 14 of them survive to hit new nucleus which means this is the fast process that happens on the order of miliseconds ? But we also now have the decay products and since decay takes time some of them will release their neutrons after different time rates from a few secs up to near a minute correct? So instead of multiplying in parts of a second the power multiplies with slowed down exponential increase ? But still I don't get one thing if every U235 nucleus that is hit with a thermal neutron releases on average 2.5 neutrons yet the newly created 2 smaller nucleus release a neutron after decay then I assume that prompt neutrons still dominate in numbers over delayed ones so how come delayed ones get to play such a crucial and important role in allowing the reactor to respond rather slowly that the prompt neutrons still do most of the work but they do it fast.

I understand this analogy is not good because nuclear reactions are not mechanically interconnected like pistons in an engine or horses in a caravan but this feels sort of like having 10 horses in a caravan of which 8 are fast speed runners but two are dying old cripples yet somehow the whole caravan moves slowly even though it could move much faster and technically it should...

Are you saying that simply by applying full power to the main circulation pumps the water flow under pressure makes it to near 270 degrees celsius? Without any other means of preheating like resistance heating or otherwise simply by pure pressure creating by the pumps?
Yes, that's right. Actually more like 290 C. Keep in mind, in a large PWR the coolant pumps are making close to 400,000 gpm (25 m3/sec), circulating around and around the system. The pump heat from the 4 coolant pumps is 10-12 MW, into the reactor coolant which is 450,000 pounds (204,000 kg) of water. It heats up quickly!

Ok one last time about the delayed neutrons I wanna see if I got it right.
So the reason why a reactor can be controllable due to those neutrons is because if for example we get at first (let's use round numbers for sake of simplicity) 10 fast neutrons which moderated to thermal by water they would split say about 8 U235 atoms (2 getting absorbed or lost) these 8 U235 atoms would now be split and the splitting would release (assuming about 2.4 neutrons per fission) about 19 neutrons and also a bunch of isotopes that undergo decay , so the 19 immediately created neutrons travel through water get to thermal energies , some are lost some absorbed so say some 14 of them survive to hit new nucleus which means this is the fast process that happens on the order of miliseconds ? But we also now have the decay products and since decay takes time some of them will release their neutrons after different time rates from a few secs up to near a minute correct? So instead of multiplying in parts of a second the power multiplies with slowed down exponential increase ? But still I don't get one thing if every U235 nucleus that is hit with a thermal neutron releases on average 2.5 neutrons yet the newly created 2 smaller nucleus release a neutron after decay then I assume that prompt neutrons still dominate in numbers over delayed ones so how come delayed ones get to play such a crucial and important role in allowing the reactor to respond rather slowly that the prompt neutrons still do most of the work but they do it fast.

I understand this analogy is not good because nuclear reactions are not mechanically interconnected like pistons in an engine or horses in a caravan but this feels sort of like having 10 horses in a caravan of which 8 are fast speed runners but two are dying old cripples yet somehow the whole caravan moves slowly even though it could move much faster and technically it should...
Imagine that a reactor has prompt multiplication factor k=0,999.
In that case, 1 fission event will set off a chain reaction that causes fission of, on average, 1000 nuclei.
But since the prompt k is below 1, the chain reaction eventually dies out after these 1000 fissions - the chain reaction is over in milliseconds or so. Leaving just the fission fragments of 1000 fissions, and no free neutrons.
But if you add the delayed neutron fraction - which is 0,0065 - the total multiplication factor is 1,0055.
Meaning the pieces of 1000 fission effects of one avalanche contain on average 6,5 fission fragments that will emit delayed neutrons. Just 1 of them would be enough to keep the chain reaction going on indefinitely. But the other 5,5 delayed neutrons would, from timescales 2,3 to 55 seconds, initiate 5 new avalanches... and those 25 et cetera.

In the italicized part, I am not quite sure of the exact place where the delayed neutron fraction goes. Perhaps somewhere else. But that delayed neutron fraction is what allows the nuclear chain reaction to expand slowly rather than rapidly.

mfb
Mentor
So the reason why a reactor can be controllable due to those neutrons is because if for example we get at first (let's use round numbers for sake of simplicity) 10 fast neutrons which moderated to thermal by water they would split say about 8 U235 atoms (2 getting absorbed or lost) these 8 U235 atoms would now be split and the splitting would release (assuming about 2.4 neutrons per fission) about 19 neutrons and also a bunch of isotopes that undergo decay , so the 19 immediately created neutrons travel through water get to thermal energies , some are lost some absorbed so say some 14 of them survive to hit new nucleus which means this is the fast process that happens on the order of miliseconds ?
The scenario you describe is prompt criticality (at nuclear weapon levels I think). Without the delayed neutrons, the fission reaction always has to die out in a reactor.

To raise the power level, you need k<1 with just prompt neutrons but k>1 including delayed neutrons.

In real power reactors the plant is heated to normal operating temperature and pressure before the core is made critical. In PWRs this is around 550F and 2250 psi. The heat up is accomplished by running the reactor coolant pumps. The friction of the water circulating around the system heats it up.
BWR reactors generally start up while they are cold, and perform a nuclear heatup. We have the option for a non-nuclear heatup using decay heat and recirculation pumps, but we would rather be steaming at low power to get the steam plant started up and warmed up with the reactor's heatup rate.

We have to maintain < 100 degF per hour per ASME code and the operating license. This can be done one of three ways. The first is to open up the steamlines and the main steam drains as a small heat sink and then move control rods to adjust power. The power adjustments then affect heatup rate. When reactor pressure reaches rated no-load pressure, the steam dumps will auto open to control pressure and temperature. The second way is to lower the steam dump regulator to minimum, and then slowly walk up pressure on the regulator. This is the preferred way to heat up, as it allows for fine control, and also allows you to raise power to higher levels to support putting steam loads in service. The third way is an "isolated" heatup. This is non-preferred and almost never performed anymore. You have the main steamlines shut and heat up to near rated, then begin the process of warming and equalizing the steam lines. Back when steam condensing mode was a thing some plants did this. It can also be done after a scram with isolation when you are in hot-standby, and you can use HPCI/RCIC as steam dumps to the suppression pool while you wait for the steamlines to equalize pressure so you can recover the condenser as a heat sink.

The only time we do a non-nuclear heatup now-a-days in a BWR is if your core design has positive temperature coefficients at low temperature conditions. In this case, you can end up with short reactor periods (less than 50 seconds) and be forced to push a rod to subcriticality, and heat up to adjust rod worth.

Astronuc
Astronuc
Staff Emeritus
So the PWR is built such that when the coolant (water) becomes less dense or is lost the reactor power decreases? Why is this, is it because water is also the moderator in the PWR making fast neutrons into thermal ones and the U235 fissions better with thermal than fast neutrons , so loss of coolant means loss of thermal neutrons leaving fast ones which have lower cross section for fission in U235?
Density of water (pressurized, sub-cooled liquid, i.e., water is a liquid below the saturation temperature for the given pressure) decreases with temperature, and that mean a reduction in the number of water molecules, which contain hydrogen, which mean less moderation in relation to the fuel. The water is not lost, but rather some of it expands in the pressurizer, which behaves as an accumulator for the coolant as well as maintaining a pressure on the primary coolant system, there is a chemical and volume control system (see Letdown and Volume Control Tank). There is still plenty of moderation to moderate fast neutrons.

https://www.nrc.gov/docs/ML1122/ML11223A214.pdf

One can find the fission cross-section for U-235 in various tables, or data files. At cold conditions (about room temperature), the neutron energy is about 0.0253 eV (multiply by 11605 K/eV) or ~293 K, or 20°C. The coolant heats up to about 290°C (or 563 K), and the neutron thermal energy is then about 0.0485 eV. As the average thermal neutron energy increases, the cross-section decreases. As the coolant is heated in the core, the temperature increases from about 290°C to about 327°C (actually PWRs have a range of inlet and exit temperatures, but the number given are in their respective ranges). Also, in addition to the moderator temperature increase, the fuel gets much hotter, since that is the primary source of heat in the core, and the neutrons have a different thermal equilibrium temperature, than when the reactor is cold, or at hot zero power.

Boiling water reactors exploit the boiling in the core to reduce moderation, and their systems are a bit more complicated since the steam from the core goes directly to the turbines, while liquid is separated and returned to the core.
https://www.nrc.gov/docs/ML1125/ML11258A313.pdf

BWR reactors generally start up while they are cold, and perform a nuclear heatup ...
Thanks Hiddencamper, I like to learn new stuff everyday!

The PWRs have limits on the number of operating reactor coolant pumps at low temps and pressures (the coolant density is a lot higher, among other things) - so generally a four-pump plant runs less than 4 pumps below ~500F. The plant Tech Specs also impose a lower limit on temperature for criticality in the same neighborhood.

The heatup rate limit (also 100F/hr for PWR) means the operators will need to dump steam to the condenser during the heatup; mostly because they do not want to approach that rate. And as mentioned, if the shutdown has been brief, the decay heat also can contribute a lot to the heatup.

mheslep
Gold Member
We have to maintain < 100 degF per hour per ASME code and
Could you elaborate? Is that some nuclear operations aspect of ASME, or simple ASME prohibitions on temperture change rates on metal structures, steam boilers and such? I'm curious as to what rate would apply to molten salt vessels.

The ASME code requires a stress analysis and a fatigue analysis; those analyses need to assume a heatup rate; every one I have seen uses 100F/hour. This is for the normal heatup/cooldown cycles, not the accident conditions.

The heatup rate limit for a molten salt vessel would depend on the value assumed in its analyses. I don't know anything about those. They run at low pressure, right? The stress analysis for them might look a lot different than the analyses for BWR / PWR vessels, where the pressures are medium/high (1000 / 2500 psia).