Muon Fusion?

[Betruger]

It is. You can see the quote formatting was broken.

[D Tibbets]

In a plasma the muons would be free flying. Do to their semirandom motions in the plasma (free ions, electrons, and muons) occasionally they will pass very close to the nucleus of an ion( maby even completing half an orbit before departing if the plasma is cool enough). Compared to a muonic atom, the time spent in this neighborhood would be much less, but the temperature dependant fusion crossection would be much greater. ...

Are you talking about a three-body reaction?! You can wait forever for that to happen.

Good point, three body reaction probabilities are very low. I understand P-P fusion in the Sun overcomes this low probability through extreamly high densities and huge volumes. I understand the effective P-P cross section in the Sun's core is ~ 10^-45. But, the crossection boost given by muons is tremendous. Again, this link shows a crossection gain of ~ 10^80 , compared to D-D fusion with electrons only at, I presume, eqivalent temperatures. That is why significant reactions can occur, even at liquid hydrogen temperatures (at least when the muon is confined to tight atomic orbitals).

http://www.muonfusion.com/

Compitition between very low probabilities, and very high probabilities. With density (and presumed confluence estimates in a Polywell type reactor), and temperature differences factored in, what would the final rates be? I can only speculate. Someone with much more math skills, and relavent knowledge would have try to calculate the answer.

I've heard estimates that in the Polywell the average ion density may be ~ 10^20 to 10^22 ions / M^3. If significant confluence occurs, the core density might be even higher. What type of density are FRC's expected to obtain? What is the lifetime of the fusing ball of plasma in the center of the FRC. If the high density plasma lifetime is similar to the muon lifetime, it could be a good match for a pulsating fusion approach.

For that matter, how high of a temperature, and pressure could you maintain in a neutral deuterium gas that is loaded with muons? Would the increased crossection at say 1000 degrees C overcome the greater density of liquid hydrogen (also concidering how much time it takes the mouns to transfer from one molecule to another in the different enviorments)? How high of a temperature could you go to without ionizing to much of the deuterium gas, 100,000 degrees C (~ 9 eV)?

Any concerns about fusion heat changing the deuterium enviorment would, I'm guessing, need to be addressed weather you are opperating at frigid liquid hydrogen temperatures, or warm gas temperatures.

Dan Tibbets

[Art Carlson]

Good point, three body reaction probabilities are very low. I understand P-P fusion in the Sun overcomes this low probability through extreamly high densities and huge volumes.

The p-p chain is actually a series of binary reactions with stable products. A better anology is the triple-alpha process, which looks like a three-body process (e.g. the power per volume is proportional to the density squared), but it really it binary reactions with an unstable intermediate Be-8. And even then it only works (in some stars) because of resonances in the energy levels of Be-8 and C-12.

[jmc]

Thinking about 5 GeV per muon, theoretically with the rest energy of the moun being a mere 100MeV or so I would have thought there should be plenty of scope for improvement. It seems you need to collide 5GeV electrons with carbon to make a muon.

I wonder whether MTF could improve things. Instead of starting with a high density, FRC at 300eV, start with a low density FRC at 10MeV, or so, then compress it to make a carbon- electron plasma at 5GeV for a few microseconds by passing it throung a metal bottleneck, this produces the muons, then slam your plasmoid filled with mouns into a solid DT target. Solid DT is an insulator so the flux lines should penetrate it quickly causing all the efficiently manufactured muons to go flowing into the solid DT ice.

Probably won't work, just a wack idea.

[D Tibbets]

Good point, three body reaction probabilities are very low. I understand P-P fusion in the Sun overcomes this low probability through extreamly high densities and huge volumes.

The p-p chain is actually a series of binary reactions with stable products. A better anology is the triple-alpha process, which looks like a three-body process (e.g. the power per volume is proportional to the density squared), but it really it binary reactions with an unstable intermediate Be-8. And even then it only works (in some stars) because of resonances in the energy levels of Be-8 and C-12.

True, I was thinking in the wrong direction.
There is a side reaction of P + electron + P yields D. This is a three body reaction as I understand it, but it makes up less than 1% of the total.

http://www.sns.ias.edu/~jnb/Papers/Prep ... usion.html

So, if the total crossection in the Sun's core for P-P fusion is ~10^-45 (for this rate limiting first step), the three body side reaction would be ~10^-47. What would the crossection be in these conditions if a mon replaces the free electron? Could the results be extrapolated for relative crossections in D-D and D-T reactions?


Of course if 5 Giga eV is required to produce a muon, and only a few hundred fusions can be catalyzed per muon, I don't see how breakeven could ever be possible.


Dan Tibbets

[chrismb]

True, I was thinking in the wrong direction.
There is a side reaction of P + electron + P yields D. This is a three body reaction as I understand it, but it makes up less than 1% of the total.

I think you are misunderstanding that. P+P gives you a 2He which is highly unstable and just fissions back into protons. But very very infrequently, whilst it exists, it decays by the weak force into D+(e+). It doesn't need an electron, it generates a positron (to the same effect, once annihilated with an electron).

[Art Carlson]

True, I was thinking in the wrong direction.
There is a side reaction of P + electron + P yields D. This is a three body reaction as I understand it, but it makes up less than 1% of the total.

I think you are misunderstanding that. P+P gives you a 2He which is highly unstable and just fissions back into protons. But very very infrequently, whilst it exists, it decays by the weak force into D+(e+). It doesn't need an electron, it generates a positron (to the same effect, once annihilated with an electron).

The reaction Dan is talking about also exists. See http://en.wikipedia.org/wiki/Proton-pro ... p_reaction I couldn't find a lot of detailed information, but it seems to be a true three-body reaction. You can see this reaction as a separate peak ("pep", as opposed to "pp") in the solar neutrino spectrum.

[D Tibbets]

True, I was thinking in the wrong direction.
There is a side reaction of P + electron + P yields D. This is a three body reaction as I understand it, but it makes up less than 1% of the total.

I think you are misunderstanding that. P+P gives you a 2He which is highly unstable and just fissions back into protons. But very very infrequently, whilst it exists, it decays by the weak force into D+(e+). It doesn't need an electron, it generates a positron (to the same effect, once annihilated with an electron).

The reaction Dan is talking about also exists. See http://en.wikipedia.org/wiki/Proton-pro ... p_reaction I couldn't find a lot of detailed information, but it seems to be a true three-body reaction. You can see this reaction as a separate peak ("pep", as opposed to "pp") in the solar neutrino spectrum.

In my first claim of a three body reaction in the P-P chain I was thinking of the:
11H + 11H → 21D + e+ + νe + 0.42 MeV .
The problem was that I was confused and was stupidly thinking of this reaction in reverse (lots of luck trying to get a neutrino to react). With AC's correction, I actually looked it up, and saw the PEP side reaction. So, I was right in claiming there was an example of a three body reaction with known probabilities, but with a wrong example in my mind.
In this case there is enough complexity in nuclear physics that you can be right, even when you are wrong!

Dan Tibbets