Muon Catalyzed Fusion

Franklin Huang
January 26, 2018

Submitted as coursework for PH241, Stanford University, Winter 2017


Fig. 1: Muons decay into an electron and two neutrinos. (Source: Wikimedia Commons.)

Muons are one of six types of leptons and leptons are one of several categories of fundamental particles of physics, quarks being another. Muons are similar to electrons (which are also leptons), but 207 times heavier. [1] Most muons that have been detected derive from high energy protons from stars and our sun interacting with the Earth's atmosphere, also known as cosmic rays. These protons fall to the Earth and ionize the atmosphere; this process produces particles that quickly decay into various leptons, including the muon. [2] With a half-life of 2.2 microseconds, the muon is an unstable particle, but due to the near-light speed velocities these particles travel at, the muon takes much longer to decay and thus can travel thousands of meters below the Earth's surface. The muon decays into an electron and two neutrinos (see Fig. 1). [1]

Muons in the Context of Fusion

Muon Catalyzed Fusion is a type of cold fusion, meaning it can occur at temperatures (room temperature or lower) much lower than thermonuclear fusion. [3] The process occurs when a muon replaces an electron in a hydrogen molecule, and because the muon is 207 times more massive than an electron, the nuclei of the molecule is drawn 207 times closer together. [4] This greatly increases the probability of fusion. Pions, which decay into muons, are typically injected into a fuel composed of deuterium and tritium. As stated before, the muon replaces an electron which decreases the size of the nuclei, which in turn reduces the repulsive electric force between different nuclei, making collisions between nuclei more prevalent. When nuclei collide, alpha particles (helium nuclei), neutrons, and energy are released. [3]

Viable Energy Source?

Muon Catalyzed Fusion can produce immense amounts of energy with very few of the harmful byproducts that nuclear fission produces. [5] However, current technology yields a smaller energy output than required energy input. Producing a muon requires an estimate of 10 GeV (Giga-electron-volt) of energy and that muon, on average, induces 100 deuterium to tritium fusions (around 2 GeV of energy). This is because around 1% of muons will stick to the alpha particle after fusion, which prevents that muon from inducing further fusion. Two solutions that could increase efficiency of Muon Catalyzed Fusion are increasing the density of the deuterium-tritium fuel and increasing the temperature of the fuel. The increased density further increases the probability of fusion and also strips helium atoms of muons, which would increase the number of fusions per muon. [4]

© Franklin Huang. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] K. Nagamine, Introductory Muon Science (Cambridge University Press, 2007).

[2] D. J. X. Montgomery, Cosmic Ray Physics (Princeton University Press, 1949).

[3] K. Ishida et al., "Muon Catalyzed Fusion," J. Phys. G 29, 2043 (2003).

[4] J. Yoon, "The Curious Story of the Muon-Catalyzed Fusion Reaction." Physics 241, Stanford University, Winter 2016.

[5] S. E. Jones, "Muon-Catalysed Fusion Revisited," Nature 321, 127 (1986).