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Physics/Nuclear Fusion Reaction Data


I am currently researching for an Extended Project Qualification in Sixth Form and am doing it on Nuclear fusion, specifically “Which method of nuclear fusion is the most likely to become viable?”.
The three methods I am considering are the usual Magnetic Confinement and Inertial Confinement Fusion but also possibly ‘cold fusion’ catalysed by Muons, which is currently being research by Star Scientific in Austrailia.
The problem I am finding is that although I can collate a lot of information about the various methods and problems, it is difficult to find any reliable sources of data regarding the input and output energies of each separate fusion reaction (so that I would be able to compare the efficiencies of each) since I can find some claims of statistics but they do not have any calculation to show where they came to that conclusion.
Therefore I am writing to ask whether you know of anywhere I could find such data which would also have the calculations to reinforce it, if so I would be very grateful for your assistance.
Thanks very much,
Tom Wagg

ANSWER: Ahhh, well the output energies are quite simple.  You take the energies of various types of fusion reactions and multiply by the mass of fuel burned.  Hyperphysics can help you there, after some unit conversions, or any number of astrophysics websites.

The problem you run into is how to calculate the power inputs so that you can satisfy the Lawson criterion, etc...I'll again point to the fine previous work of the folks who maintain hyperphysics:  (experts)

The problem is that the approaches are so radically different, and the energy loss mechanisms in such extreme environments are almost impossible to estimate.  In theory, if I had a perfect absorber that I could heat to fusion temperatures without it leaking away energy, I could start a fusion reaction with very little power.  It's confinement that confounds us in these matters, and that's a deep subject far beyond the focus of this forum.  Sorry, I can help you with a specific question about the nuclear parts of these processes and their energy outputs, but the ridiculous technical details of the plasma parts related to confinement I can only help you out in broad strokes or in evaluating specific claims they make.

I can say that muon-catalyzed fusion, as proposed, is impossible.  The required energy to generate a single negative pion (the kind that generates a negative muon), as this "company" in Australia claims is 139 MeV.  A d-d fusion reaction like their website mentions will produce 2.4 MeV of energy, meaning that the muons would have to catalyze massive numbers of fusion reactions per input muon, with no mention of how they're generating them with any efficiency.  I mean, I had a student concentrate them from cosmic rays in an experiment when I was a professor, but the source is so weak that you'd never get anything out of it.  You notice that their website VERY CAREFULLY avoids the question of how they generate their muons, only saying that past research discounted this type of fusion as an energy generating mechanism over this concern.  The same basic concern still exists, and they don't address it at all.

---------- FOLLOW-UP ----------

QUESTION: Hi again,
I've looked through all of the Hyperphysics information and it has been immensely helpful so thanks very much for that! The only thing that confuses me is that since there are four different possible reactions going on, how can you see which one will occur. Since, you say that I should multiply by the masses, but the only two fuels added are Deuterium and Tritium yet how can you see whether a D-D reaction will form Tritium or He-3. Moreover although if the only fuel was Deuterium I realise you could use the combined equation of the four constituents of the cycle but since additional tritium is also being added how would I go about calculating this? Is there a way to know how much of each reaction will be completed?
Also regarding the Lawson Criterion, I've looking at it on both Hyperphysics, "" and " (page 15) and they each give different values: for example for D-D Reactions they give, respectively;
nt>10^16 s/cm^3
nt>1.5*10^20 s/m^3
nt>6*10^22 s/m^3
And so I was just curious as to why it seems everywhere I look there are different values quoted and which I should trust or whether I'm just missing some factor which is affecting each to give a different number?
Ah right ok I understand, thanks for your help.
I see, well when I first looked into it because of this company's research I was fascinated by the idea of cold fusion and this drew me in but I was then frustrated by the lack of other research and Star Scientific's quoting of figures on their site without backing them up (such as 99% efficiency!) and I have been searching for the calculations leading to them ever since so thank you very much for that insight! It seems then, that although they have an idea of how they might be able it work, they are far from actually achieving it efficiently (or at least much further than Magnetic or Inertial Confinement)?
Thanks so much for your help, I really appreciate you putting the time in to answer me :)

P.s. Sorry I was late to reply, the email notification went into spam and I didn't realise you would answer so quickly

You can't tell, that process is dominated by quantum mechanics.  Some of the reactions create 3H and some create 3He.  We used one reaction to monitor the number of protons incident on a target when I was in graduate school (target was frozen heavy water, beam was 2H ions), and both neutrons and protons were present.  That's an advanced topic of quantum mechanics, perhaps beyond the scope of this forum, but it was good that you noticed and asked the question.  On rare occasion, the final product is actually 4He and a gamma ray, that's actually the reaction we were studying.  

For the contribution to the fuel from created tritium, that's a secondary effect, but still it will have an effect over time...but for ignition it's most important to try to get as high as possible.  I haven't done the detailed calculation of Lawson's criterion in many years, but I can point out that your units don't agree.  There are other criteria, basic density and confinement time that must be all satisfied.  I think that second value is (order of magnitude wise) for D-T fusion and not D-D fusion.  They must have used slightly different assumptions in their calculations, but hyperphysics is maintained by a university physics department and has pretty stringent standards.  I would stick with them.


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Dr. Stephen O. Nelson


I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.


I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.

Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.

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