Muon-catalyzed fusion

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., 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 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−-mesons can be found." 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. 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, 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), so the average separation between the triton and the deuteron in the muonic molecular ion is 207 times smaller than that. Due to the strong nuclear force, whenever the triton and the deuteron in the muonic molecular ion happen to get even closer to each other during their periodic vibrational motions, the probability is very greatly enhanced that the positively charged triton and the positively charged deuteron would undergo quantum tunnelling through the repulsive Coulomb barrier that acts to keep them apart. Indeed, the quantum mechanical tunnelling probability depends roughly exponentially on the average separation between the triton and the deuteron, allowing a single muon to catalyze the d–t nuclear fusion in less than about half a picosecond, once the muonic molecular ion is formed. Once the muonic molecular ion state is formed, the shielding by the muon of the positive charges of the proton of the triton and the proton of the deuteron from each other allows the triton and the deuteron to tunnel through the Coulomb barrier in time span of order of a nanosecond The muon survives the d–t muon-catalyzed nuclear fusion reaction and remains available (usually) to catalyze further d–t muon-catalyzed nuclear fusions. Each exothermic d–t nuclear fusion releases about 17.6 MeV of energy in the form of a "very fast" neutron having a kinetic energy of about 14.1 MeV and an alpha particle α (a helium-4 nucleus) with a kinetic energy of about 3.5 MeV. == Deuterium–deuterium and other types ==

The first kind of muon–catalyzed fusion to be observed experimentally, by L.W. Alvarez et al., was protium (H or 1H1) and deuterium (D or 1H2) muon-catalyzed fusion. The fusion rate for p–d (or pd) muon-catalyzed fusion has been estimated to be about a million times slower than the fusion rate for d–t muon-catalyzed fusion. Of more practical interest, deuterium–deuterium muon-catalyzed fusion has been frequently observed and extensively studied experimentally, in large part because deuterium already exists in relative abundance and, like protium, deuterium is not at all radioactive. Tritium rarely occurs naturally, and is radioactive with a half-life of about 12.5 years. The fusion rate for d–d muon-catalyzed fusion has been estimated to be only about 1% of the fusion rate for d–t muon-catalyzed fusion, but this still gives about one d–d nuclear fusion every 10 to 100 picoseconds or so. However, the energy released with every d–d muon-catalyzed fusion reaction is only about 20% or so of the energy released with every d–t muon-catalyzed fusion reaction. Moreover, the catalyzing muon has a probability of sticking to at least one of the d–d muon-catalyzed fusion reaction products that Jackson in this 1957 paper estimated to be at least 10 times greater than the corresponding probability of the catalyzing muon sticking to at least one of the d–t muon-catalyzed fusion reaction products, thereby preventing the muon from catalyzing any more nuclear fusions. Effectively, this means that each muon catalyzing d–d muon-catalyzed fusion reactions in pure deuterium is only able to catalyze about one-tenth of the number of d–t muon-catalyzed fusion reactions that each muon is able to catalyze in a mixture of equal amounts of deuterium and tritium, and each d–d fusion only yields about one-fifth of the yield of each d–t fusion, thereby making the prospects for useful energy release from d–d muon-catalyzed fusion at least 50 times worse than the already dim prospects for useful energy release from d–t muon-catalyzed fusion. Potential "aneutronic" (or substantially aneutronic) nuclear fusion possibilities, which result in essentially no neutrons among the nuclear fusion products, are almost certainly not very amenable to muon-catalyzed fusion. One such essentially aneutronic nuclear fusion reaction involves a deuteron from deuterium fusing with a helion (He+2) from helium-3, which yields an energetic alpha particle and a much more energetic proton, both positively charged (with a few neutrons coming from inevitable d–d nuclear fusion side reactions). However, one muon with only one negative electric charge is incapable of shielding both positive charges of a helion from the one positive charge of a deuteron. The chances of the requisite two muons being present simultaneously are exceptionally remote. == In culture ==

The term "cold fusion" was coined to refer to muon-catalyzed fusion in a 1956 New York Times article about Luis W. Alvarez's paper. In 1957 Theodore Sturgeon wrote a novelette, "The Pod in the Barrier", in which humanity has ubiquitous cold fusion reactors that work with muons. The reaction is "When hydrogen one and hydrogen two are in the presence of Mu mesons, they fuse into helium three, with an energy yield in electron volts of 5.4 times ten to the fifth power". Unlike the thermonuclear bomb contained in the Pod (which is used to destroy the Barrier) they can become temporarily disabled by "concentrated disbelief" that muon fusion works. In Sir Arthur C. Clarke's third novel in the Space Odyssey series, 2061: Odyssey Three, muon-catalyzed fusion is the technology that allows mankind to achieve easy interplanetary travel. The main character, Heywood Floyd, compares Luis Alvarez to Lord Rutherford for underestimating the future potential of their discoveries. == See also ==