Muon-catalyzed fusion (abbreviated μCF or MCF) is a process that allows nuclear fusion to occur at temperatures significantly lower than those needed for thermonuclear fusion, even at room temperature or lower. It is one of the few known ways to catalyze nuclear fusion reactions.
Muons are unstable subatomic particles that are similar to electrons but 207 times more massive. If a muon replaces one of the electrons in a hydrogen molecule, the nuclei are consequently drawn 186 times closer than in a normal molecule, due to the reduced mass being 186 times the mass of an electron. When the nuclei move closer together, the fusion probability increases, to the point where a significant number of fusion events can occur at room temperature.
Methods for obtaining muons, however, require far more energy than can be produced by the resulting fusion reactions. Muons have a mean lifetime of , much longer than that of many other subatomic particles but nevertheless far too brief to allow their useful storage.
To create useful room-temperature muon-catalyzed fusion, reactors would need a cheap, efficient muon source and/or a way for each individual muon to catalyze many more fusion reactions.
History
Andrei Sakharov and F. C. Frank predicted the phenomenon of muon-catalyzed fusion on theoretical grounds before 1950. Yakov Borisovich Zel'dovich also wrote about the phenomenon of muon-catalyzed fusion in 1954. Luis W. Alvarez et al., when analyzing the outcome of some experiments with muons incident on a hydrogen bubble chamber at Berkeley in 1956, observed muon-catalysis of exothermic p–d, proton and deuteron, nuclear fusion, which results in a helion, a gamma ray, and a release of about 5.5 MeV of energy. The Alvarez experimental results, in particular, spurred John David Jackson to publish one of the first comprehensive theoretical studies of muon-catalyzed fusion in his ground-breaking 1957 paper. This paper contained the first serious speculations on useful energy release from muon-catalyzed fusion. Jackson concluded that it would be impractical as an energy source, unless the "alpha-sticking problem" (see below) could be solved, leading potentially to an energetically cheaper and more efficient way to use catalyzing muons.
, at least two companies are pursuing muon-catalyzed fusion reactors, both fueled by deuterium–tritium reactions: Acceleron Fusion, in the United States, founded in 2008 as part of NK Labs, LLC, then spun-off in 2022, and Norrønt AS, in Norway, founded in 2016 as Ultrafusion Nuclear Power, then merged with Norrønt in 2017.
Potential benefits
If muon-catalyzed d–t nuclear fusion is realized practically, it will be a much more attractive way of generating power than conventional nuclear fission reactors because muon-catalyzed d–t nuclear fusion (like most other types of nuclear fusion), produces far fewer harmful (and far less long-lived) radioactive wastes.
The large number of neutrons produced in muon-catalyzed d–t nuclear fusions may be used to breed fissile fuels from fertile material – for example, thorium-232 could breed uranium-233 in this way.The breeding takes place due to certain neutron-capture nuclear reactions, followed by beta decays, the ejection of electrons and neutrinos from nuclei as neutrons within the nuclei decay into protons as a result of weak nuclear forces. The fissile fuels that have been bred can then be "burned," either in a conventional critical nuclear fission reactor or in an unconventional subcritical fission reactor, for example, a reactor using nuclear transmutation to process nuclear waste, or a reactor using the energy amplifier concept devised by Carlo Rubbia and others.
Another benefit of muon-catalyzed fusion is that the fusion process can start with pure deuterium gas without tritium. Plasma fusion reactors like ITER or Wendelstein X7 need tritium to initiate and also need a tritium factory. Muon-catalyzed fusion generates tritium under operation and increases operating efficiency up to an optimum point when the deuterium–tritium ratio reaches about 1:1. Muon-catalyzed fusion can operate as a tritium factory and deliver tritium for material and plasma fusion research.
Viability as a power source
Problems facing practical exploitation
Except for some refinements, little has changed since Jackson's 1957 assessment of the feasibility of muon-catalyzed fusion other than Vesman's 1967 prediction of the hyperfine resonant formation of the muonic (d–μ–t)+ molecular ion which was subsequently experimentally observed. This helped spark renewed interest in the whole field of muon-catalyzed fusion, which remains an active area of research worldwide. However, as Jackson observed in his paper, muon-catalyzed fusion is "unlikely" to provide "useful power production ... unless an energetically cheaper way of producing μ−-mesonsMuons are not mesons; they are leptons. However, this was unclear until 1947, and the name "mu meson" persisted for some time following the identification of the muon as a lepton. can be found."
One practical problem with the muon-catalyzed fusion process is that muons are unstable, decaying in (in their rest frame). Hence, there needs to be some cheap means of producing muons, and the muons must be arranged to catalyze as many nuclear fusion reactions as possible before decaying.
Another, and in many ways more serious, problem is the "alpha-sticking" problem, which was recognized by Jackson in his 1957 paper.Eugene P. Wigner pointed out the α-sticking problem to Jackson. The α-sticking problem is the approximately 1% probability of the muon "sticking" to the alpha particle that results from deuteron–triton nuclear fusion, thereby effectively removing the muon from the muon-catalysis process altogether. Even if muons were absolutely stable, each muon could catalyze, on average, only about 100 d–t fusions before sticking to an alpha particle, which is only about one-fifth the number of muon catalyzed d–t fusions needed for break-even, where as much thermal energy is generated as electrical energy is consumed to produce the muons in the first place, according to Jackson's rough estimate.
More recent measurements seem to point to more encouraging values for the α-sticking probability, finding the α-sticking probability to be around 0.3% to 0.5%, which could mean as many as about 200 (even up to 350) muon-catalyzed d–t fusions per muon. Indeed, the team led by Steven E. Jones achieved 150 d–t fusions per muon (average) at the Los Alamos Meson Physics Facility. The results were promising and almost enough to reach theoretical break-even. Unfortunately, these measurements for the number of muon-catalyzed d–t fusions per muon are still not enough to reach industrial break-even. Even with break-even, the conversion efficiency from thermal energy to electrical energy is only about 40% or so, further limiting viability. The best recent estimates of the electrical "energy cost" per muon is about with accelerators that are (coincidentally) about 40% efficient at transforming electrical energy from the power grid into acceleration of the deuterons.
As of 2012, no practical method of producing energy through this means has been published, although some discoveries using the Hall effect show promise.
Breakeven alternative estimate
According to Gordon Pusch, a physicist at Argonne National Laboratory, various breakeven calculations on muon-catalyzed fusion omit the heat energy the muon beam itself deposits in the target. By taking this factor into account, muon-catalyzed fusion can already exceed breakeven; however, the recirculated power is usually very large compared to power out to the electrical grid (about 3–5 times as large, according to estimates). Despite this rather high recirculated power, the overall cycle efficiency is comparable to conventional fission reactors; however the need for 4–6 MW of electrical generating capacity for each megawatt out to the grid probably represents an unacceptably large capital investment. Pusch suggested using Bogdan Maglich's "migma" self-colliding beam concept to significantly increase the muon production efficiency, by eliminating target losses, and using tritium nuclei as the driver beam, to optimize the number of negative muons.
In 2021, Kelly, Hart, and Rose produced an μCF model whereby the ratio, Q, of thermal energy produced to the kinetic energy of the accelerated deuterons used to create negative pions (and thus negative muons through pion decay) was optimized. In this model, the heat energy of the incoming deuterons as well as that of the particles produced due to the deuteron beam impacting a tungsten target was recaptured to the extent possible, as suggested by Gordon Pusch in the prior paragraph. Further, heat energy due to tritium breeding in a lithium-lead shell was recaptured, as suggested by Jändel, Danos, and Rafelski in 1988. The best Q value was found to be about 130% assuming that 50% of the muons produced catalyze fusion. Further, assuming that an accelerator is 18% efficient at transforming electric energy into deuteron kinetic energy and conversion efficiency of heat energy into electric energy of 60%, they estimate that, currently, the amount of electric energy that could be produced by a μCF reactor would be 14% of the electric energy consumed. For this to improve, they suggest that some combination of increasing a) accelerator efficiency and b) the number of fusion reactions per negative muon above the assumed level of 150, is needed.
Process
To create this effect, a stream of negative muons, most often created by decaying pions, is sent to a block that may be made up of all three hydrogen isotopes (protium, deuterium, and/or tritium), where the block is usually frozen, and the block may be at temperatures of about 3 kelvin (−270 °C) or so. The muon may bump the electron from one of the hydrogen isotopes. The muon, 207 times more massive than the electron, effectively shields and reduces the electromagnetic repulsion between two nuclei and draws them much closer into a covalent bond than an electron can. Because the nuclei are so close, the strong nuclear force is able to bind both nuclei together. They fuse, release the catalytic muon (most of the time), and part of the original mass of both nuclei is released as energetic particles, as with any other type of nuclear fusion. The release of the catalytic muon is critical to continue the reactions. The majority of the muons continue to bond with other hydrogen isotopes and continue fusing nuclei together. However, not all of the muons are recycled: some bond with other debris emitted following the fusion of the nuclei (such as alpha particles and helions), removing the muons from the catalytic process. This gradually reduces the rate of the reactions, as muons with which the nuclei may bond become depleted. The average number of reactions achieved in the lab can be as high as 150 d–t fusions per muon.
Deuterium–tritium (d–t or dt)
In the muon-catalyzed fusion of most interest, a positively charged deuteron (d), a positively charged triton (t), and a muon essentially form a positively charged muonic molecular heavy hydrogen ion (d–μ–t)+. The muon, with a rest mass 207 times greater than the rest mass of an electron,The values of the various physical constants and masses can be found at the National Institute of Standards and Technology website NIST Constants, for example. is able to drag the more massive triton and deuteron 207 times closer together to each other in the muonic (d–μ–t)+ molecular ion than can an electron in the corresponding electronic (d–e–t)+ molecular ion. The average separation between the triton and the deuteron in the electronic molecular ion is about one angstrom (100 pm),According to ,