Is Muon Catalyzed Fusion a Viable Source of Energy?

[VernonNemitz]

Let me start with some statements that I think are fairly accurate. That way errors can more easily be corrected later, when I use those statements to ask some questions and maybe speculate a bit.

The muon is a subatomic particle that greatly resembles an electron, except it is about 206 times as massive, and is unstable, with a lifespan of about 2 microseconds. Therefore, anyone who wants to use one in an experiment needs to invest considerable energy into making it.

In the 1950s, when a number of experiments were using liquid hydrogen "bubble tanks" to observe various particle-interaction events, it was discovered that a muon could cause some nuclear fusions to occur, in that liquid hydrogen. The discovery was quickly analyzed to determine whether or not the process could become a useful source of energy, but unfortunately, even though one muon might catalyze quite a few fusions during its short lifespan, the total amount of energy produced was inadequate to "pay" for making the muon, by a factor of at least five or six.

Finally, it is known that after it catalyzes a fusion reaction, sometimes the muon leaves the scene with considerable energy, and sometimes it doesn't leave the scene at all; it is trapped in "orbit" until it dies. That's a major reason why a muon can't reliably catalyze a larger number of fusions.

Assuming the preceding is accurate, I now need to mention that I once ran across an equation (long since forgot where, and I haven't seen it since) that related the probability of a reaction's occurrence to the energy of the particles, after the reaction (the more energy, the less likely the reaction). I knew that the very rare reaction between two deuterons, which might produce a helium-4 nucleus, yielded a quite-large energy of about 24Mev, and I wondered about the ability of a muon to carry enough of it away to increase the probability of that reaction's occurrence.

(Never mind that the notion pays no attention to HOW a muon might be a recipient of any of the fusion energy released; see above about "sometimes it leaves the scene with considerable energy".) Anyway, if I used the equation correctly all those years ago, and accurately remember the result, then the conclusion was that D+D-->⁴He might be possible as often as 25% of the time.

Obviously I'd like to know what experimental data is available, about muon catalyzed fusion. Is there any evidence that the process ever directly produces ⁴He from two deuterons more frequently than the natural 1-in-a-million-odds? What is the maximum energy observed for a muon leaving the scene of a just-catalyzed reaction?

And as for speculation, has anyone besides me considered shooting muons into the middle of an inertially-confined implosion event? After all, if a pellet can be squeezed down by a factor of 50 to make nuclear fusion happen from sheer temperature and pressure, then think about adding muons when the pellet has been compressed by a factor of only 7 or 8... With the nuclei closer together, each muon would encounter 7 or 8 times more of them and could cause 7 or 8 times more fusions to happen, in its normal short lifetime.

Thanks in advance; if I haven't skirted the guidelines so closely as to cause this post to be deleted, then I await some interesting replies.

 

[PAllen]

If you actually want to read about it, the following appears to be a major review:

http://www.annualreviews.org/doi/abs/10.1146/annurev.ns.39.120189.001523?journalCode=nucl

If you can find this in a library (or have it shipped to yours):

https://www.amazon.com/dp/9810215371/?tag=pfamazon01-20

there is a big chapter on muon catalyzed fusion.

 

[the_wolfman]

And as for speculation, has anyone besides me considered shooting muons into the middle of an inertially-confined implosion event? After all, if a pellet can be squeezed down by a factor of 50 to make nuclear fusion happen from sheer temperature and pressure, then think about adding muons when the pellet has been compressed by a factor of only 7 or 8... With the nuclei closer together, each muon would encounter 7 or 8 times more of them and could cause 7 or 8 times more fusions to happen, in its normal short lifetime.

Recall that Muon catalysed fusion works because the muon is closely bound to the reactant nuclei. This allows it shield the Coulomb potential. However in an imploding pellet the temperatures are hot enough to ionize the fuel. Here is the muons are not bound to the reactants, and thus cannot effectively shield the Coulomb potential.

 

[VernonNemitz]

To PAllen: Thank you, and WOW! That book is expensive!

Recall that Muon catalysed fusion works because the muon is closely bound to the reactant nuclei. This allows it shield the Coulomb potential. However in an imploding pellet the temperatures are hot enough to ionize the fuel. Here is the muons are not bound to the reactants, and thus cannot effectively shield the Coulomb potential.

Ah, the fun begins! While I didn't mention this in the first message, it is known that because a muon is 206 times as massive as an electron, when it goes into orbit around a nucleus it orbits 206 times closer than an electron. The the associated energy is much greater -- photons from orbital-changes are in the X-ray region. This means that there is a range of temperatures in which ordinary atoms will be ionized, but muonic atoms will not be ionized. That's part of the reason why I suggested an implosion/compression of only 7 or 8 times normal pellet-density, not the 50+ sought in most inertial-confinement experiments. I can't say that I know that even 7 or 8 times pellet-density is not too hot for muonic atoms, but if I pretend that the Temperature-Pressure-Volume Gas Law applies (which it should when dealing with a low-temperature plasma), then the conclusion is that the temperature would not be too hot.

 

[PAllen]

To PAllen: Thank you, and WOW! That book is expensive!

That's why I did NOT suggest buying it. A useful suggestion IF you can get a uni-library to get it via some sharing arrangement (if they don't have it). If you do searching in book on the web, you can access some of the chapter on muon catalyzed fusion.

Generally (and I am no expert at all in this field) it appears to me that most active research in this area was 1990s or earlier, with only a smattering of new results since then. Thus thorough reviews from that era are probably still up to date.

(For example:

http://books.google.com/books?id=3GoM3D4I_dYC&printsec=frontcover#v=onepage&q&f=false

From this link, you should be able to page to the TOC, follow link to chapter, and see the majority of the chapter.
)

 

[mfb]

I don't think a compression will help to improve the fusion rate per muon significantly - travel time between atoms is not the limiting factor for fusion, and sticking will occur at a higher density, too.

 

[the_wolfman]

Ah, the fun begins! While I didn't mention this in the first message, it is known that because a muon is 206 times as massive as an electron, when it goes into orbit around a nucleus it orbits 206 times closer than an electron. The the associated energy is much greater ...

I thought about that after I posted. I think the ionization energy for a muon orbiting a hydrogen nucleus is around 2-3keV. You're right that there is a huge range of temperatures where electrons are stripped but muons are not.

There are still problems with an inertial approach to muon fusion.

The burn times of fusion capsules are much shorter than the muon life time. A typical ICF shot lasts ~20 ns, and the burn time is a tiny fraction of this. This means that each muon has significantly less time to catalyse the nessicary number of fusion reactions. Also the number of fusion reactions each muon has to catalyze to break even increases to account for the energy from the drive (the lasers or heavy ion beams). Finally once your target begins to burn, it will heat up. I'd expect that it would quicky reach temperatures hot enough to completely ionize fuel. When this happens the muon catalyzed fusion will stop.


You might be able to use a muon beam to "spark" a capsule burn similar to fast ignition. Here you would compress a target normally, and then zap it with a muon beam. The beam would initate fusion is the core of the pellet. It's not obvious to me if there are any advantages to this over using a second laser to spark the burn.

 

[VernonNemitz]

I'm seeing something in my first post that may have been misinterpreted. "think about adding muons when the pellet has been compressed by a factor of only 7 or 8" --I forgot to indicate that that was supposed to be something like the maximum amount of compression. I did not mean to imply that this experiment should be done when the goal is a 50-fold compression (or more) of the pellet.

So, consider a rather-larger-than-normal pellet which is, as now indicated, only compressed by a factor of 8 times, and no farther. My assumption was that this might allow a muon to "reach" a greater number of deuterium nuclei in its short lifespan, than when a deuterium pellet is normal-density. I was not aware that the sticking problem was the main reason why a muon couldn't reach more deuterons in its lifespan; I just assumed it died too soon. Well, the experiment would at least verify whether or not sticking actually is the main problem.

Even if verified, there may be a possible solution to that problem! Let us pretend that if the pellet is compressed by a factor of 12 (correct number to be computed, of course!), the temperature of the plasma is almost --but not quite!-- hot enough to make the muonic atoms ionize. Logically, muonic atoms could still form, but sticking should be reduced. That book PAllen pointed out, has this to say regarding muon-catalyzed fusion between Deuterium and Tritium nuclei:

"The resulting charged [alpha] particle is so fast that the sticking probability is fairly small (<1%) and even if it occurs the muon may be stripped by subsequent collisions."

That last thing is the factor we want to enhance, even for the product of fusion between two deuterons, by having a just-hot-enough plasma. And, of course, the factor-of-12 compression gives the muons even more opportunities to catalyze fusions.

 

[mfb]

The binding energy at a helium nucleus (where you do not want bound muons) is 4 times the binding energy at a hydrogen nucleus (where you need bound muons). Even worse, it is not sufficient to have muonic hydrogen atoms - you want muonic hydrogen molecules for the best fusion rate.
If the concentration of helium is low enough and the temperature is high enough, there might be some beneficial effect, but I think this requires really special conditions.

 

[VernonNemitz]

The binding energy at a helium nucleus (where you do not want bound muons) is 4 times the binding energy at a hydrogen nucleus (where you need bound muons). Even worse, it is not sufficient to have muonic hydrogen atoms - you want muonic hydrogen molecules for the best fusion rate.
If the concentration of helium is low enough and the temperature is high enough, there might be some beneficial effect, but I think this requires really special conditions.

The binding energy between helium and a muon is only about twice that of the binding energy between hydrogen and a muon. Only two protons in a helium nucleus are doing the attracting, and the muon's electric charge is unchanged.

Yes, the book that PAllen recommended clearly explains how muon catalyzed fusion involves a whole molecule, not just an atom, of hydrogen. It might still be interesting to see what muons might be able to do inside a hot plasma. For example, consider two deuterons on a collision course in the plasma. The point that is halfway between them is a point of greatest attraction for an electron or a muon. Well, if a muon happens to get into that spot, does this allow the deuterons to approach each other more closely than they otherwise might? Note that even though the muon isn't part of an atom or molecule in this case, it still has only a fraction of the mass of the two approaching deuterons. That means its "location cloud" is considerably larger than the location clouds of either deuteron. So, could that still suffice to shield the deuterons' charges from each other, until they got close enough to fuse, in spite of the temperature of the plasma? I'd really like to see some experiments done!

With respect to my last post, here is some relevant data:
Energy of an alpha particle produced by the D+T reaction: 3.54Mev
Energy of a helium-3 nucleus produced by the D+D reaction: 0.82Mev

It is apparent that the alpha particle has more than four times the energy of the ³He nucleus. If that suffices to lead to a low sticking rate, and can even dislodge the muon in a collision with a molecule of, say, liquid hydrogen, then I'd like to see an overall average plasma temperature such that when a 0.82Mev ³He nucleus has a muon sticking with it, a collision with one of the other particles in the plasma could knock the muon loose. It is not my intention to imagine a plasma so hot that muonic atoms can't persist; it is just that when a rather energetic nucleus appears, we want it to bleed off any sticking muon, while it also bleeds off energy in collisions with other particles in the plasma.

Finally, your last point about helium seems somewhat irrelevant when we have no intention of adding helium to a pellet of frozen deuterium. Any helium nucleus that begins to exist in that pellet would be a product of a fusion reaction. There would have to be a lot of fusions to produce a quantity of helium such that your problematic scenario becomes realized. I would think that if that many heliums got produced, then the experiment would have been a success, and we could start building fusion power plants.

 

[mfb]

The binding energy between helium and a muon is only about twice that of the binding energy between hydrogen and a muon. Only two protons in a helium nucleus are doing the attracting, and the muon's electric charge is unchanged.

Binding energy scales with the squared charge of the nucleus, and 2²=4

For example, consider two deuterons on a collision course in the plasma. The point that is halfway between them is a point of greatest attraction for an electron or a muon. Well, if a muon happens to get into that spot, does this allow the deuterons to approach each other more closely than they otherwise might?

I would not hope for 3-particle interactions. Muonic deuterium and another deuterium nucleus can come closer before they feel their electrostatic repulsion, however.

Finally, your last point about helium seems somewhat irrelevant when we have no intention of adding helium to a pellet of frozen deuterium. Any helium nucleus that begins to exist in that pellet would be a product of a fusion reaction. There would have to be a lot of fusions to produce a quantity of helium such that your problematic scenario becomes realized. I would think that if that many heliums got produced, then the experiment would have been a success, and we could start building fusion power plants.

I am not so sure in that respect. I do not know how much fuel you have to burn to get a reasonable fusion output relative to the energy required to ignite it. Current machines are orders of magnitude away from a net gain anyway.

 

[VernonNemitz]

Binding energy scales with the squared charge of the nucleus, and 2²=4

OK, I did not know that; I was confusing the force of attraction with the binding energy. Thank you.


Let me now get back to something mentioned in the original post here. I asked about the possibility of the D+D->⁴He, with the muon acquiring considerable energy. Well, the book that PAllen recommended does have something about it (if not quite what I wanted to know). There is an "overview table" in which this is stated:

"Muon-catalyzed fusion occurs for all of the following reactions (experimentally observed except as noted), where the kinetic energies (in Mev) are given in parentheses after the product particles and the branching fractions are given to the right:

⁴He (0.08) + μ + γ(23.77) (~10^-7%)
⁴He (0.73) + μ(23.12)"

The second one was tagged as being theoretical, and no percentage was given. Meanwhile, the results a different catalyzed reaction, between Protium and Deuterium, was also listed in the table:

"³He (0.005) + μ + γ(5.49) (85%)
³He (0.2) + μ(5.29) (15%)"

This is encouraging since the observations show that the muon really can, somehow, acquire energy from the fusion reaction. Finally, the table also includes these theoretical results for a catalyzed reaction between Protium and Tritium:

"⁴He (0.05) + μ + γ(19.76) (~90%)
⁴He (0.59) + μ(19.22) (~10%)"

But in addition to those theoretical results, there is a footnote:

"Preliminary experimental results for ptμ indicate yields of 30% γ and 70% conversion μ"

That's wildly different from the theory, and may indicate that my own figurings, all those years ago, might have some relevance... The key thing is simply that if ⁴He can be produced from two deuterons more frequently than the one-in-ten-million listed in the table (to just about any decent whole-number percentage value), then significantly more energy will be produced, overall, in any fusion reactor that can take advantage of muon-catalyzed deuterium fusion. Which again is why I really want to see more experiments done!

 

[Kidphysics]

Vernon is the idea just to shoot a beam of muons into the ICF haloraum during the ~20ns it is fusing and hope to get some economy off of each? Do you have any other ideas for this muon catalyzation? Generally curious undergrad.

 

[VernonNemitz]

Not quite. First, we want a larger-than usual pellet, and second, we don't want to implode it so much that that alone would cause fusions. We want the beam of muons to cause the fusions. So, with a larger pellet and a lesser compression, the time it is compressed should be a lot longer than 20ns, giving the muons time to do their thing.

 

[Kidphysics]

Not quite. First, we want a larger-than usual pellet, and second, we don't want to implode it so much that that alone would cause fusions. We want the beam of muons to cause the fusions. So, with a larger pellet and a lesser compression, the time it is compressed should be a lot longer than 20ns, giving the muons time to do their thing.

Ah, less money on the lasers and more use of the catalyst

 

[PAllen]

I think the bottom line on why research has really fallen down on this is the alpha sticking problem. Virtually all other parameters have been pushed (e.g. with some resonance research at TRIUMPH circa 2000) into a range interesting for practical use. However, even at .5% rate, alpha sticking is more than sufficient to kill any possibility of net energy gain. All experiments and theory (so far) converged on the finding that alpha sticking of this amount was impervious to improvement. Without some idea on this specific problem, everything else, I surmise, became uninteresting - especially because all the physical processes were mostly understood by 1990.

 

[VernonNemitz]

I think the bottom line on why research has really fallen down on this is the alpha sticking problem. Virtually all other parameters have been pushed (e.g. with some resonance research at TRIUMPH circa 2000) into a range interesting for practical use. However, even at .5% rate, alpha sticking is more than sufficient to kill any possibility of net energy gain. All experiments and theory (so far) converged on the finding that alpha sticking of this amount was impervious to improvement. Without some idea on this specific problem, everything else, I surmise, became uninteresting - especially because all the physical processes were mostly understood by 1990.

Well, I did have one idea, described in messages #8 and #10 of this Thread. So long as I don't know that others have already studied the notion and shown it to be inadequate, I remain hopeful.

 

[Jess H. Brewer]

... I was not aware that the sticking problem was the main reason why a muon couldn't reach more deuterons in its lifespan; I just assumed it died too soon. Well, the experiment would at least verify whether or not sticking actually is the main problem.

Even if verified, there may be a possible solution to that problem! Let us pretend that if the pellet is compressed by a factor of 12 (correct number to be computed, of course!), the temperature of the plasma is almost --but not quite!-- hot enough to make the muonic atoms ionize. Logically, muonic atoms could still form, but sticking should be reduced. That book PAllen pointed out, has this to say regarding muon-catalyzed fusion between Deuterium and Tritium nuclei:

"The resulting charged [alpha] particle is so fast that the sticking probability is fairly small (<1%) and even if it occurs the muon may be stripped by subsequent collisions."

That last thing is the factor we want to enhance, even for the product of fusion between two deuterons, by having a just-hot-enough plasma. And, of course, the factor-of-12 compression gives the muons even more opportunities to catalyze fusions.

Yes, experiments all confirm that sticking is THE problem. Best so far is 200 or so fusions before the muon sticks to an alpha.

Temperature is largely irrelevant. The alpha has kinetic energy far in excess of anything you will produce thermally at any compression; that's why the muon doesn't ALWAYS stick to it. In any case, the muon is 207 times more tightly bound than electrons, so muonic helium remains bound long after all electronic atoms are fully ionized.

Density is also irrelevant; even in gases the muon has plenty of time to catalyze lots of fusions, and it generally sticks before it decays.

I believe people have talked about adding muons to the pellet mix just to get ignition started; but timing and focusing a muon beam to that small a spot is 'way beyond any existing or proposed technology. You'd have to inject the muons BEFORE zapping with lasers, and even then we have no such muon beam capability.

 

[Dale]

It might be better to start a new thread, this one is more than two years old.