Muon-Catalyzed Fusion in the Upper Atmosphere

[loseyourname]

All right, you're going to have to really humor me here.

As far as I know, the only kind of 'cold' fusion that has ever been demonstrated to work is muon-catalyzed. The reason it isn't viable is that is takes so much energy in the first place to create muons and they have a very short half-life. There is, however, a neverending supply of free muons continually being produced in the upper atmosphere above the ozone layer by cosmic rays interacting with the atmospheric gases. If (I know it isn't possible, but this is where you have to humor me) we could float a reactor platform in low orbit just above the ozone layer, what kind of yield would such a reactor give?

If I'm wrong about anything I said above, please correct me. My knowledge of this subject is limited to what I learned just reading through books for fun over ten years ago. It's out of date and I've forgotten most of it besides. I'm considering using an orbiting reactor platform like this in a science fiction story, and I just have to know if it's even theoretically possible.

 

[ohwilleke]

The issue would be how dense the supply of muons would be. The upper atomosphere is very low pressure, which means that there are very few atoms per square meter. Unless the flux of muons through your reactor was very high, you have a problem. Wikipedia has a nice article on muon fusion by the way.

 

[loseyourname]

Yeah, I know. According to my preliminary designs, they keep the needed gases in pressurized containers that are transparent to cosmic rays, not relying on low-density atmospheric gases. The problem is that I don't have any clue how many pions (and hence muons) are produced per unit of gas due to cosmic rays. I've read the wikipedia article and it doesn't say. That and of course I don't know what the energy yield of muon catalyzed fusion is besides.

 

[Astronuc]

Muons are produced from the decay of pions, which in turn are products of the annihilation of anti-protons, which themselves are produced when high energy protons (from cosmic radiation or solar wind) collide with protons/nuclei in the upper atmosphere. The atmosphere is very thin, so the production of anti-protons (and hence pions -> muons) may likewise be too low to be feasible for muon-catalyzed fusion.

One cannot change the cosmic sources of high energy protons, however, one can influence the 'target' with which high energy protons interact. One way would be to put a volume of liquid hydrogen (with higher atomic density of H) in the vicinity of the fusion reactor. But the density of liquid hydrogen is still fairly low. Another way to improve the atomic density of hydrogen would be the use of metal hydrides - e.g. LiH, ZrH2, TiH2 - or other system with the optimal atomic density of H.

 

[dfarr]

I immediately thought of cosmic rays when I (just now) heard of muon-induced fusion.

1. In the 70s I worked briefly at a cosmic ray observatory in Antarctica run by theBartol Research Foundation. I believe they are still in business and can provide data on muon densities. http://www.bartol.udel.edu/

2. The muons (some) survive to sea level due to relativistic lengthening of their lifetimes. So the reactor would not necessarily have to be floating in the ionosphere. A high mountain near the magnetic poles might be a good spot.

3. On the moon it should be possible to take a lemon (intense radiation) and make lemonade (cheap fusion) using muons from cosmic rays striking a target that could double as radiation shielding. I find this a lot less detestable than a nuclear reactor on the moon.

4. Bartol had neutron monitors and meson telescopes near both magnetic poles and probably still does. I remember the neutron detectors were surrounded by blocks of polyehtylene, which apparently has a pretty good density of protons at room temperaturre

 

[Astronuc]

The lifetime of muons is spent over km's of distance. A fusion reactor characteristic length is on the order of 1 meter.

The plasma density in a fusion reactor is on the order of 10¹⁴ nuclei/cm³, as opposed to the atmosphere near sea level, with a density on the order of 10¹⁸ molecules/cm³.

It is important to realize the natural constraints one faces with energy producing techniques.


With respect to neutrons, they slow down best in hydrogenous material, and polyethylene is a pretty good shield for neutrons. In addition, the (n,p) collisions allow detection of the neutrons by virtue of the p energies. From the website, it appears that neutron detection is via n-capture in He3.

Neutrons would be produced by spallation reactions between the cosmic rays (p, d, α particles) and structural materials (e.g. Al, Li and other light nuclei). Spallation reactions are problematic for spacecraft and aircraft since they produce secondary particles (nuclei) which are quite damaging to tissue (astronauts and flight crew).

Nice overview of cosmic rays - http://neutronm.bartol.udel.edu/catch/cr2.html

 

[Bob S]

Here is a serious technical review of muon catalysis by J D Jackson in Phys ReV (1957)
http://prola.aps.org/abstract/PR/v106/i2/p330_1
This is pay per view, but is the most complete analysis of events first seen in the Alvarex bubble chamber. Here is abstract

The mechanism by which negative μ mesons catalyze nuclear reactions between hydrogen isotopes is studied in detail. The reaction rate for the process (p+d+μ-→He3+μ-+5.5 Mev), observed recently by Alvarez et al., is calculated and found to be in accord with the available data. The μ- meson binds two hydrogen nuclei together in the μ-mesonic analog of the ordinary H2+ molecular ion. In their vibrational motion the nuclei have a finite, although small, probability of penetrating the Coulomb barrier to zero separation where they may undergo a nuclear reaction. The intrinsic reaction rates for other, more probable, reactions are also estimated. The results are ∼0.3×106 sec-1 for the observed p-d reaction, ∼0.7×1011 sec-1 for the d-d reaction, and ∼0.4×1013 sec-1 for the d-t reaction. For the reaction observed by Alvarez rough estimates are made of the partial widths for nonradiative and radiative decay of the excited He3 nucleus. The ejection of the μ- meson by "internal conversion" seems somewhat less likely. Speculations are made on the release of useful amounts of nuclear energy by these catalyzed reactions. The governing factors are not the intrinsic reaction rate once the molecule is formed, but rather the time spent (∼10-8 sec) by the μ- meson between the breakup of one molecule and the formation of another and the loss of μ- mesons in "dead-end" processes. These factors are such that practical power production is unlikely. In liquid deuterium, each μ- meson will catalyze only ∼10 reactions in its lifetime, while for the d-t process it will induce ∼100 disintegrations. A longer lived particle will not be able to catalyze appreciably more reactions.

I think muons are pretty sparce in the upper atmosphere because as already pointed out, a primary cosmic ray has to produce a pionic (hadronic) shower, and then the relativistic negative charged pions (1/3 of all pions) have to decay to negative muons, and the negative muons then have to stop in the reactor before decaying. I have counted muons in cosmic rays with a muon scintillator telescope, and they pass through (rarely stop) a few times per minute. I think the rate of pass-thru muons (half are negative) at sea level is about 30 per m² per second per sterad.
Bob S