# Could atmospheric muons be used to catalyze nuclear fusion?

https://en.wikipedia.org/wiki/Muon-catalyzed_fusion

I read above that some work as been done investigating whether muons could be used to catalyze fusion of deuterium and tritium. Apparently they can draw the particles closer together so that the electric repulsive force between the nuclei can be overcome at much lower temperatures than required for thermonuclear fusion. One of the issues faced with actually producing net positive energy from the reaction seems to be coming up with an efficient muon source.

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/muonatm.html

According to the above link, muons arrive "at sea level, with a flux of about 1 muon per square centimeter per minute."

Could these atmospheric muons be used as a catalyst source? With only one per minute, you wouldn't get a whole lot. But could you get at least get some usable electricity out of the setup?

• Run some numbers. Assume you had a setup where every single muon actually catalyzed a D-T fusion event (note - that won't happen by a large factor). The energy released in D-T fusion is about 18MeV, of 2.88fJ (yes, femtoJoules). Across a 1km by 1km array, that would yield 28.8 mJ per minute, or 0.5 mW of power. In to a one square kilometer array. And that assumes that the cross section is essentially infinite (every muon catalyzes a reaction). Compare with a 1km$^{2}$ solar array averaging 100W/m$^{2}$ = 100MW. Which would you invest in? – Jon Custer Dec 8 '15 at 17:28
• @JonCuster That's what I thought. You can just make your comment an answer and I'll accept it. I wasn't saying I thought it should work, I was asking if it could. It's OK if the answer is "No" lol – John Dec 8 '15 at 17:47

## 1 Answer

OK, lets run some numbers. Assume you had a setup where every single muon actually catalyzed a D-T fusion event (note - that won't happen by a large factor). The energy released in D-T fusion is about 18MeV, of 2.88fJ (yes, femtoJoules). Across a 1km by 1km array, that would yield 28.8 mJ per minute, or 0.5 mW of power. In to a one square kilometer array. And that assumes that the cross section is essentially infinite (i.e. every muon catalyzes a reaction). Compare with a 1km2 solar array averaging 100W/m2 = 100MW. Which would you invest in?

• This doesn't account for the energy present in the muons already (in the form of their kinetic energy). What if that were harnessed and captured somehow? Would that change the calculation? – DJG Jul 11 '18 at 7:34
• @DJG - From various sources I get that the mean energy of muons at the ground is ~4GeV. So, that is about 20x the energy of a catalyzed D-T fusion reaction, so if you could capture it all (really hard!) you would get 10mW across the 1km x 1km array. Still 4 orders of magnitude less than a solar cell (which should make sense - otherwise we might have evolved to sense muons rather than photons). – Jon Custer Jul 11 '18 at 12:54
• What about stratospheric muons? The intensity there is about 20x what it is at sea level. What if some of their energy was captured, and they were used to catalyze fusion reactions? – DJG Jul 11 '18 at 20:17
• Furthermore -- perhaps muon utilization and photon utilization are not mutually exclusive. – DJG Apr 18 at 16:36