Muon catalysed fusion from cosmic muons

Question

If thousands of muons are coming to earth. Why can't we use them for muon catalysed fusion which was proved legitimate

Answer 1

Cosmic-ray muons are produced when energetic particles from space collide with particles in the Earth's upper atmosphere. Muons only have a lifetime of around a few microseconds before they decay, so the only way that they can reach the surface is due to the effects of time dilation (incidentally, this is one of the more accessible pieces of evidence for special relativity). This means that cosmic-ray muons that reach the surface have a lot of kinetic energy.

Muon-catalyzed fusion works by replacing an electron in a hydrogen isotope with a muon, which shrinks the atomic radius to the point where nuclear fusion becomes much more probable. Typically the desired fusion reaction is deuterium-tritium fusion, because this is the easiest to make happen for various nuclear-physics-related reasons. The ground-state orbital of a hydrogen atom is a very low-energy state, and we want the muon to be in that state in order to catalyze fusion. So, somehow, the muon has to lose a ton of energy, in just the right way to get into the right configuration, and this is exceedingly unlikely to happen; it's much more likely that the muon will simply ionize the atom rather than replace the electron. We don't really have a very good way of decelerating cosmic muons in a controlled manner, so there's not a whole lot we can do about that. In short, muon-catalyzed fusion requires slow muons, but cosmic muons are very fast, and it's difficult to interconvert between the two while leaving enough time to do multiple fusion reactions.

Even if we did have a reliable slow-muon source (like S$\mu$S at the Paul Scherrer Institut in Switzerland), muon-catalyzed fusion has another problem, which is that sometimes the muon ends up "sticking" to the fusion product. When it does this, it isn't available for further fusion reactions, which immediately lowers the fusion rate. The probability of this happening is around 1%, which is large enough to be a significant worry - you're essentially depleting your catalyst supply after a few hundred reactions, which doesn't amount to a whole lot of power. To overcome this for practical power generation, we would need an economical high-intensity source of slow muons, which does not exist at the moment.

Answer 2

It is also impractical to capture muons because they are on the verge of decaying. Special relativity called for time dilation but only so much time dilation can happen. Soon the muon will decay into an electron, muon neutrino, and electron antineutrino. It can happen but the chances of it happening are really low.