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Muon catalyzed fusion is currently little more than a lab curiosity today in part because of how many hydrogen nuclei can be fused before the muon is carried away by an alpha particle. Deuterium+deuterium reactions are ten times more likely than deuterium tritium reactions to result in a muon sticking to a helium ion. I am wondering if some one can calculate the ionization energy needed to prevent that from happening and to speculate if a laser can be built to do it.

If it is possible, it may help pave the way to clean low-temperature fusion energy that produces more power than is used to make it.

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2 Answers 2

Muon mean lifetime is 2.2 µs. There's your problem. Muons mass 105.7 MeV/c2, about 200 times that of the electron. If you wanted to ionize a hydrogen atom, you would need 13.6 eV. If you wanted to ionize a muonic hydrogen atom, you would need about 2813 eV or about a 0.441 nm photon. Start building your laser.

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Certainly the muon's mean lifetime is major contributing factor. If 0.441nm is close, then you are talking about mid to high range Xrays. That doesn't seem feasible to build a laser for. –  Keith Reynolds Apr 3 at 23:41
    
Odd that someone refers to X-rays using wavelengths, usually one uses keV. –  Kyle Kanos Apr 4 at 2:54
    
If 2813 eV is personally inconvenient, feel free to divide by 1000 for 2.813 keV. Chemistry and crystallography find distances to be defining. –  Uncle Al Apr 4 at 17:18

For what it's worth (I cannot verify the claims): http://www.j.sinap.ac.cn/nst/EN/article/downloadArticleFile.do?attachType=PDF&id=448 (NUCLEAR SCIENCE AND TECHNIQUES 25, 020201 (2014) - I guess this is a Chinese journal). Abstract: "Considering the mixture after muon-catalyzed fusion ($\mu$CF) reaction as overdense plasma, we analyze muon motion in the plasma induced by a linearly polarized two-colour laser, particularly, the effect of laser parameters on the muon momentum and trajectory. The results show that muon drift along the propagation of laser and oscillation perpendicular to the propagation remain after the end of the laser pulse. Under appropriate parameters, muon can go from the skin layer into field-free matter in a time period of much less than the pulse duration. The electric-field strength ratio or frequency ratio of the fundamental to the harmonic has more influence on muon oscillation. The laser affects little on other particles in the plasma. Hence, in theory, this work can avoid muon sticking to $\alpha$ effectively and reduce muon-loss probability in $\mu$CF."

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