# cosmic radiation muons as a source for muon-catalyzed fusion

taking rough numbers from here and here, it seems that with natural cosmic radiation sources, we could sustain $10^6$ muon-catalyzed fusion reactions per square-meter per minute. This would be $14 \times 10^6$ MeV of neutron energy (for D-T reactions, assuming 14 MeV per event) per square-meter per minute. In Watts-hour this would be $4 \times 10^{-12}$ KWh

I think this is the right estimate, but wanted to check if someone spots a problem with my estimate

cheers

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Muon catalyzed fusion needs the muons to be low enough energy to replace an electron and stay in a stable orbit. Since the reason the catalysis happens is because the atom is much smaller and two protons can get close together enhancing the probability of overlap and fusion, one needs a large number of low energy muons so that the probability of two muonic hydrogens to be in contact would be high. Fusion has been observed in molecules that have an orbital electron replaced by a muon, binding the atoms of the molecule into closer distances, so that the nuclear force can have a probability of fusing the two nuclei, of H2 for example, and releasing the muon for a next round.

The 10.000 muons per minute per square meter are mainly above GeV energies whereas for atomic sizes one needs keV at best, so your calculations cannot be correct. In addition the muon decays in 10^-6 seconds, so it cannot accumulate in a volume to keep on catalyzing.

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Moun catalyzed fusion requires very specific kinematics, but cosmic muons come in all energies from stopped to tens of GeV at any particular spot.

Care to work out the cross-section for having the right kinematics? If you're having trouble I know a graduate student who is familiar with several of the common cosmic muon Monte Carlo generators.

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This has absolutely got to be the key consideration. I'm pretty sure that muon-catalyzed fusion wants very low-energy muons, orders of magnitude lower than most cosmic rays. –  Ted Bunn Apr 13 '11 at 18:53
One muon catalyses maximal some thousand D ot T fusions before it decays. (After deceleration to interact "chemically" with the D²or DT) –  Georg Apr 13 '11 at 19:29

"The 10.000 muons per minute per square meter are mainly above GeV energies whereas for atomic sizes one needs keV at best,"

Perhaps there is a certain depth in the ocean or underground where the surviving muons have been slowed to average keV energies?

If so, is there possibly a "slow muon layer" in the ocean where a tiny amount of natural deuterium and protium is being naturally muon-fused? Would this layer be helium-enriched in a detectable way?

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i don't think muons will survive long after slowing down, but the big thing here is that even assumming optimal thermal spectra, still the numbers are sufficiently small to discard it as a viable option –  lurscher Apr 22 '11 at 23:12
Actually it is well known in the neutrino community that as you go deeper the median muon energy increases (at least for reasonable depths, i.e. up to a few thousand meters water equivalent) because the more common lower energy cosmic rays have been effective filtered above you. –  dmckee May 16 '12 at 14:44