Tucker does devote 4 or 5 pages to Doppler broadening, but I don't think it's his strongest section. Overall it is a great book for learning how a PWR works, but when it come to policy, he definitely in the you-cant-be-too-safe club.
Laymen don't understand terms such as "excursion". Why not say, near the end, "the stability guarantees no nuclear meltdown and no release of harmful radiation"?
I also very much like the idea of designing nuclear reactor steam vent structures to look like teacups. Yes, the "handle" is purely decorative and a (small) added cost. But it says, in an unmistakable way to the layman: Look here! This is STEAM. Not nuclear radiation!!
Let's not ever say "no release". There is always some possibility of that. I am confident, however, that we could say "The new designs have no possibility of meltdown." Even ThorCon's reactor, the safest I have seen yet, I could imagine something like a leak from the offgas storage tank, or maybe a used can gets stuck halfway out of the silo as they are trying to pull it out. I'm still looking for a good number on the exposure rate of a worker 10 meters away from that. I expect it is negligible.
The stability guarantees NEITHER no meltdown nor no release. There was no reactivity excursion at Three Mile Island. There was no reactivity excursion at Fukushima. To my knowledge, there was no reactivity excursion at the handful of other partial meltdown s we have had.
If a reactor loses cooling, you have to not only get the reactor shut down, but you also have to handle the decay heat among other things.
I dont know what I have to do to get it thru your thick heads: if nuclear power is truly successful, we will not only have releases, we will have a release at least every few years.
These releases are not only tolerable in return for the benefits but socially optimal. Put it another way, if our future is a planet with no releases, it's a future in which I don't want my grandkids to live because it's a future in which there is no nuclear power.
Are there any new designs where meltdown is possible? I don't mean the fuel melting in a controlled and intended way, like IFR, but "meltdown" in the sense that the public understands - Jane Fonda scary. I don't even mean the kind of meltdown that could occur in an MSR with a melt plug jammed by sediment, where the pipe connection melts and the fuel flows out safely - costly but not dangerous.
Should we allow any design that has a possibility of meltdown?
Why this fixation with meltdowns? A portion of the core overheating to melting point is a symptom not a cause. You don't go after symptoms, you go after causes. And a meltdown is just one of the many possible casualties that can happen, one that need not lead to a release.
What we are interested in is providing on demand, pollution free electricity as cheaply as possible while maintaining a tolerable level of nuclear power harm. If a meltdown prone reactor is the way to do that, that's the way we should go.
So the answer to your question is: no. We should let the underwriters evaluate each design and figure out how large the premium for each should be.
I agree with everything you say, even allowing for a "meltdown prone" design, if the underwriters will approve it. Still, it would be nice if we could have a short response to the idiot in the elevator yapping about "Chernobyl". Until I learn otherwise I will say "The new designs have no possibility of meltdown."
If there is a little more time for conversation, I might start with a question - What caused that disaster? Yes, I know the meltdown was not the root cause, but that is what most people will think of. Then I might have a follow-on question - Did you know they have designs now that cannot have a meltdown? Give me a call if you have time to discuss it.
Excellent. Excellent. Excellent. I have long been confused as to how this "resonance" works. This is worthy of a new article in Citizendium. I will get to work now.
I would just add one paragraph, for the benefit of us physicists. The resonance integral is the same in all the curves you have shown. The incoming neutron spectrum is flat over that small range. That kind of implies the total absorption is the same, regardless of the width of the resonance.
The answer must be that the resonance is so strong that there is saturation of the absorption spectrum over a small range near the peak. So the cross-section can show a sharp peak, but the absorption spectrum has a flat top with a width that varies in proportion to temperature. If this doesn't make sense, I need to work on it some more. Maybe add a line to the graph with a different color.
Correct. For narrow, high peaks, we very quickly run out of neutrons in that frequency range. The rest of the cross-section integral is "wasted".
I think the produc t of the neutron flux and the resonance cross-section is more complicated than simply a flat top whose width is proportional to temperature. You'd have to work it out.
OK, I make a plot and in the process clarified my thinking. In spite of my PhD in physics, I am still a student when it comes to fission. I didn't need to calculate the "resonance integral". It is clear from the plot that the line with more Doppler broadening has more absorption (i.e. punches a bigger hole in the neutron spectrum).
I think the way to present this to students is - acknowledge the confusion, then show the plot. I was confused, because I was thinking - What difference does it make if the line is narrow or broad. The total absorption should be the same. That may be true for very weak absorption lines, but when the absorption is strong, the neutron spectrum can't drop any lower than zero. Only the width matters.
Nice graph. Much better than mine. I'll use it in the future. Choice of colors could be better. Maybe 4 colors. Maybe one color for both narrow peak lines, and the otehr color for both wide peak lines.
Done. If you haven't used Google's chart editor, I highly recommend it. With Excel, I always get lost trying to find the setting I want. This one is really well organized.
That analysis is for broadening of lines in optical spectra. Assuming the same applies to neutrons, then yes, the line width is proportional to absolute temperature. A 1% increase in temperature should result in 1% more absorption by one line. If the resonant lines account for 10% of the total absorption (just guessing) then there would be only 0.1% more total absorption. We need a nuclear engineer.
I started a draft of a Citizendium article on Doppler Broadening, then realized this is too deep for our journalist readers. What we really need is a good article on Reactor Safety, with a section on Doppler, and link to Jack's article for those who are interested. Here is a start on that article in my sandbox:
If anyone wants to jump in and finish it, your help is welcome. My day job is keeping me from spending the time I would like on this project. Use whatever tools you like. I can do the formatting for Citizendium.
Natural circulation BWRs are even more self compensating because of flow effect on void reactivity.
How To Drive A Nuclear Reactor is a pretty fabulous book if anyone wants a book length of this post
I don't remember if there's a section on the doppler effect guaranteeing no excursion... that is sweet
Tucker does devote 4 or 5 pages to Doppler broadening, but I don't think it's his strongest section. Overall it is a great book for learning how a PWR works, but when it come to policy, he definitely in the you-cant-be-too-safe club.
or causing a fission by hitting a fissionable nucleus such as U-238 really hard.
Laymen don't understand terms such as "excursion". Why not say, near the end, "the stability guarantees no nuclear meltdown and no release of harmful radiation"?
I also very much like the idea of designing nuclear reactor steam vent structures to look like teacups. Yes, the "handle" is purely decorative and a (small) added cost. But it says, in an unmistakable way to the layman: Look here! This is STEAM. Not nuclear radiation!!
Let's not ever say "no release". There is always some possibility of that. I am confident, however, that we could say "The new designs have no possibility of meltdown." Even ThorCon's reactor, the safest I have seen yet, I could imagine something like a leak from the offgas storage tank, or maybe a used can gets stuck halfway out of the silo as they are trying to pull it out. I'm still looking for a good number on the exposure rate of a worker 10 meters away from that. I expect it is negligible.
The stability guarantees NEITHER no meltdown nor no release. There was no reactivity excursion at Three Mile Island. There was no reactivity excursion at Fukushima. To my knowledge, there was no reactivity excursion at the handful of other partial meltdown s we have had.
If a reactor loses cooling, you have to not only get the reactor shut down, but you also have to handle the decay heat among other things.
I dont know what I have to do to get it thru your thick heads: if nuclear power is truly successful, we will not only have releases, we will have a release at least every few years.
These releases are not only tolerable in return for the benefits but socially optimal. Put it another way, if our future is a planet with no releases, it's a future in which I don't want my grandkids to live because it's a future in which there is no nuclear power.
Are there any new designs where meltdown is possible? I don't mean the fuel melting in a controlled and intended way, like IFR, but "meltdown" in the sense that the public understands - Jane Fonda scary. I don't even mean the kind of meltdown that could occur in an MSR with a melt plug jammed by sediment, where the pipe connection melts and the fuel flows out safely - costly but not dangerous.
Should we allow any design that has a possibility of meltdown?
David, David, David,
Just when I thought you were starting to get it.
Why this fixation with meltdowns? A portion of the core overheating to melting point is a symptom not a cause. You don't go after symptoms, you go after causes. And a meltdown is just one of the many possible casualties that can happen, one that need not lead to a release.
What we are interested in is providing on demand, pollution free electricity as cheaply as possible while maintaining a tolerable level of nuclear power harm. If a meltdown prone reactor is the way to do that, that's the way we should go.
So the answer to your question is: no. We should let the underwriters evaluate each design and figure out how large the premium for each should be.
I agree with everything you say, even allowing for a "meltdown prone" design, if the underwriters will approve it. Still, it would be nice if we could have a short response to the idiot in the elevator yapping about "Chernobyl". Until I learn otherwise I will say "The new designs have no possibility of meltdown."
If there is a little more time for conversation, I might start with a question - What caused that disaster? Yes, I know the meltdown was not the root cause, but that is what most people will think of. Then I might have a follow-on question - Did you know they have designs now that cannot have a meltdown? Give me a call if you have time to discuss it.
Excellent. Excellent. Excellent. I have long been confused as to how this "resonance" works. This is worthy of a new article in Citizendium. I will get to work now.
I would just add one paragraph, for the benefit of us physicists. The resonance integral is the same in all the curves you have shown. The incoming neutron spectrum is flat over that small range. That kind of implies the total absorption is the same, regardless of the width of the resonance.
The answer must be that the resonance is so strong that there is saturation of the absorption spectrum over a small range near the peak. So the cross-section can show a sharp peak, but the absorption spectrum has a flat top with a width that varies in proportion to temperature. If this doesn't make sense, I need to work on it some more. Maybe add a line to the graph with a different color.
David,
Correct. For narrow, high peaks, we very quickly run out of neutrons in that frequency range. The rest of the cross-section integral is "wasted".
I think the produc t of the neutron flux and the resonance cross-section is more complicated than simply a flat top whose width is proportional to temperature. You'd have to work it out.
OK, I make a plot and in the process clarified my thinking. In spite of my PhD in physics, I am still a student when it comes to fission. I didn't need to calculate the "resonance integral". It is clear from the plot that the line with more Doppler broadening has more absorption (i.e. punches a bigger hole in the neutron spectrum).
https://docs.google.com/spreadsheets/d/1Zg6oSowPP5HtRITqSkQw7GhVjKzcsaaChlSYJ1P6SRI/edit?usp=sharing
I think the way to present this to students is - acknowledge the confusion, then show the plot. I was confused, because I was thinking - What difference does it make if the line is narrow or broad. The total absorption should be the same. That may be true for very weak absorption lines, but when the absorption is strong, the neutron spectrum can't drop any lower than zero. Only the width matters.
Nice graph. Much better than mine. I'll use it in the future. Choice of colors could be better. Maybe 4 colors. Maybe one color for both narrow peak lines, and the otehr color for both wide peak lines.
Done. Blue is cold. Red is hot.
Here is an editable copy, if you want to make the scales more realistic or play with the formulas. https://docs.google.com/spreadsheets/d/1VPZqvGUMBacStIHsoZdGjYF3Lnyl1ZHJyRROJthP9C0/edit?usp=sharing
Nice.
One final thought to make the explanatory text easier, how about solid lines for the cross-sections, and dashed lines for the neutron fluxes.
Done. If you haven't used Google's chart editor, I highly recommend it. With Excel, I always get lost trying to find the setting I want. This one is really well organized.
Thank you. I made my own copy so I can play with it a bit.
BTW, how does Line Width scale with temperature?
I just eyeballed Jack's diagram, but if you would like more accuracy, maybe put a question on Quora.com.
I'm not sure how I could even frame the question. Perhaps the answer could be obtained from https://en.wikipedia.org/wiki/Doppler_broadening?
That analysis is for broadening of lines in optical spectra. Assuming the same applies to neutrons, then yes, the line width is proportional to absolute temperature. A 1% increase in temperature should result in 1% more absorption by one line. If the resonant lines account for 10% of the total absorption (just guessing) then there would be only 0.1% more total absorption. We need a nuclear engineer.
I started a draft of a Citizendium article on Doppler Broadening, then realized this is too deep for our journalist readers. What we really need is a good article on Reactor Safety, with a section on Doppler, and link to Jack's article for those who are interested. Here is a start on that article in my sandbox:
https://citizendium.org/wiki/User:David_MacQuigg/Sandbox/Reactor_Safety
If anyone wants to jump in and finish it, your help is welcome. My day job is keeping me from spending the time I would like on this project. Use whatever tools you like. I can do the formatting for Citizendium.
Great explainer.