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
Best Answer
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.