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Muon-catalyzed fusion

Muon-catalyzed fusion (μCF) is a process allowing nuclear fusion to take place at temperatures significantly lower than the temperatures required for thermonuclear fusion, even at room temperature or lower. Although it can be produced reliably with the right equipment and has been much studied, it is believed that the poor energy balance will prevent it from ever becoming a practical power source. However, if muons (μ−) could be produced more efficiently, or if they could be used as catalysts more efficiently, the energy balance might improve enough for muon-catalyzed fusion to become a practical power source.

A brief history

Andrei Sakharov and F.C. Frank [1] predicted the phenomenon of muon-catalyzed fusion on theoretical grounds before 1950. Yakov Borisovich Zel'dovich[2] also wrote about the phenomenon of muon-catalyzed fusion in 1954. Luis W. Alvarez et al.,[3] 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.[4] 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 way of producing the catalyzing muons.[4] This assessment has, so far, stood the test of time.

Potential benefits

If muon-catalyzed d-t nuclear fusion were able to be realized practically, it would be a much cheaper 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, and hardly any greenhouse gases. Practical and economically sensible muon-catalyzed d-t nuclear fusion would go a long way toward reducing the production of greenhouse gases, such as carbon dioxide (CO2), by reducing or even eliminating the need to burn fossil fuels and biomass that contain carbon, for example.

Some people have proposed a hybrid fusion/fission schemes to use the large amount of neutrons produced in muon-catalyzed d-t nuclear fusions to breed fissile fuels, from fertile material - for example, thorium-232 could breed uranium-233 in this way.[note 1] The fissile fuels that have been bred can then be "burned," either in a conventional supercritical nuclear fission reactor or in an unconventional subcritical fission pile. One example of an unconventional subcritical fission pile is an Accelerator-Driven System (ADS) that has been proposed for, and in some places is currently being developed for, the Accelerator Transmutation of Waste (ATW)—for example, using neutrons to transmute large quantities of highly radioactive and extremely long-lived nuclear wastes, such as those produced (mainly) by conventional nuclear fission reactors, into less harmful, less radioactive, less toxic, and much less long-lived transmuted elements. Another example of the creative use of an unconventional subcritical fission pile is the energy amplifier devised by Physics Nobel Laureate Carlo Rubbia, among others.

Some conclusions

Except for refinements such as these, little has changed in the half-century since Jackson's assessment of the feasibility of muon-catalyzed fusion, other than Vesman's 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 among those who continue to be fascinated and intrigued (and frustrated) by this tantalizing approach to controllable nuclear fusion that almost works. Clearly, as Jackson observed in his 1957 paper, muon-catalyzed fusion is "unlikely" to provide "useful power production… unless an energetically cheaper way of producing μ−-mesons[note 2] can be found."[4]


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 kelvins (−270 degrees Celsius) 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 resistance 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 kick in and 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 (see nuclear fusion to understand how this energy is released). 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, there is a major drawback with muon-catalyzed fusion: not all of the muons are recycled, and too many 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 and ultimately chokes off the reactions, as there are fewer and fewer muons with which the nuclei may bond. The highest success rate achieved in the lab has been on the order of about 100 reactions or so per muon.

Some problems facing practical exploitation

One practical problem with the muon-catalyzed fusion process is that muons are unstable, decaying in about 2.2 µs (in their rest frame).[5] 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 notorious "alpha-sticking" problem mentioned in the previous section, which was recognized by Jackson in his seminal 1957 paper.[4][note 3] 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 1957 estimate.[4]

More recent measurements seem to point to more encouraging values for the α-sticking probability, finding the α-sticking probability to be about 0.5% (or perhaps even about 0.4% or 0.3%), which could mean as many as about 200 (or perhaps even about 250 or about 333) muon-catalyzed d-t fusions per muon.[6][note 4] Indeed, the team led by Steven E. Jones achieved 150 d-t fusions per muon (average) at the Los Alamos Meson Physics Facility.[7] Unfortunately, 200 (or 250 or even 333) muon-catalyzed d-t fusions per muon is still not enough to reach 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 estimated guess of the electrical "energy cost" per muon[note 5] is about 6 GeV with accelerators that are (coincidentally) about 40% efficient at taking electrical energy from the alternating current (AC) mains (the plugs in the wall) and accelerating the deuterons using this electrical energy.

As of 2010, no practical method of producing energy through this means has been discovered, although new discoveries show promise.[8]

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 about 207 times greater than the rest mass of an electron,[5] is able to drag the more massive triton and deuteron about 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),[4][note 6] so the average separation between the triton and the deuteron in the muonic molecular ion is about 207 times smaller than that.[note 7][note 8] 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.[4]

The formation time of the muonic molecular ion is one of the "rate-limiting steps" in muon-catalyzed fusion that can easily take up to ten thousand or more picoseconds in a liquid molecular deuterium and tritium mixture (D2, DT, T2), for example.[4] Each catalyzing muon thus spends most of its ephemeral existence of about 2.2 microseconds,[5] as measured in its rest frame wandering around looking for suitable deuterons and tritons with which to bind.

Another way of looking at muon-catalyzed fusion is to try to visualize the ground state orbit of a muon around either a deuteron or a triton.[note 9] Suppose the muon happens to have fallen into an orbit around a deuteron initially, which it has about a 50% chance of doing if there are approximately equal numbers of deuterons and tritons present, forming an electrically neutral muonic deuterium atom (d-μ)0 that acts somewhat like a "fat, heavy neutron" due both to its relatively small size (again, about 207 times smaller than an electrically neutral electronic deuterium atom (d-e)0) and to the very effective "shielding" by the muon of the positive charge of the proton in the deuteron. Even so, the muon still has a much greater chance of being transferred to any triton that comes near enough to the muonic deuterium than it does of forming a muonic molecular ion. The electrically neutral muonic tritium atom (t-μ)0 thus formed will act somewhat like an even "fatter, heavier neutron," but it will most likely hang on to its muon, eventually forming a muonic molecular ion, most likely due to the resonant formation of a hyperfine molecular state within an entire deuterium molecule D2 (d=e2=d),[note 10] with the muonic molecular ion acting as a "fatter, heavier nucleus" of the "fatter, heavier" neutral "muonic/electronic" deuterium molecule ([d-μ-t]=e2=d), as predicted by Vesman, an Estonian graduate student, in 1967.

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 move close enough together to fuse with alacrity. 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.[4] An additional 4.8 MeV can be gleaned by having the fast neutrons moderated in a suitable "blanket" surrounding the reaction chamber, with the blanket containing lithium-6, whose nuclei, known by some as "lithions," readily and exothermically absorb thermal neutrons, the lithium-6 being transmuted thereby into an alpha particle and a triton.[note 11][note 12]

Deuterium-deuterium (d-d or dd) and other types

The first kind of muon-catalyzed fusion to be observed experimentally, by L.W. Alvarez et al.,[3] was actually 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.[4][note 13]

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 hydrogen, deuterium is not at all radioactive[note 14][note 15] By way of contrast, tritium, with a half-life of about 12.5 years,[5] must be painstakingly made atom by atom, most often in a nuclear fission reactor, using the lithion (lithium-6) thermal neutron absorption nuclear reaction described in the previous section. In addition, tritium is still radioactive enough to be inconvenient to work with, requiring both protective shielding and special handling.

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.[4] 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.[4] 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[4] 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.[note 16] 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.[4] This is somewhat disappointing because aneutronic nuclear fusion reactions typically produce substantially only energetic charged particles whose energy could potentially be converted to more useful electrical energy with a much higher efficiency than is the case with the conversion of thermal energy. One such essentially aneutronic nuclear fusion reaction involves a deuteron from deuterium fusing with a helion (h+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.


1. ^ 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.
2. ^ Muons are not mesons, they are leptons. However, this was not clear until 1947, and the name "mu meson" was still used for some time following the identification of the muon as a lepton.
3. ^ Eugene P. Wigner pointed out the α-sticking problem to Jackson.
4. ^ Detailed theoretical calculations of the α-sticking probability in muon-catalyzed d-t fusion appear to yield a higher value of about 0.69%, which is different enough from the experimental measurements that give 0.3–0.5% to be somewhat mysterious.
5. ^ One common way to make muons is to accelerate deuterons to energies of about 800 MeV per nucleon (in the "lab frame", where the suitable target particles are essentially at rest) and to smash the deuterons into an appropriate target, such as a gas of molecular deuterium and molecular tritium. Smashing the deuterons into other neutron-containing nuclei creates a fair number of negative pions (π−). As long as pions are kept away from the nuclei (which would absorb the pions via the strong interaction), they will generally decay into a muon and a muon antineutrino after about 26 ns.
6. ^ According to S. Cohen, D.L. Judd, and R.J. Riddell, Jr. (1960). ""μ-Mesonic Molecules. II. Molecular-Ion Formation and Nuclear Catalysis". Phys. Rev. 119: 397. doi:10.1103/PhysRev.119.397. , footnote 16, Jackson may have been overly optimistic in Appendix D of his 1957 paper in his roughly calculated "guesstimate" of the rate of formation of a muonic (p-μ-p)+ molecular ion by a factor of about a million or so.)
7. ^ In other words, the separation in the muonic case is about 500 femtometers
8. ^ The strong nuclear force is (roughly) about a hundred times stronger in attracting a deuteron to a triton than the electromagnetic force is at repelling them, for example, at a distance between them on the order of the pion's Compton wavelength.
9. ^ The muon, if given a choice, would actually prefer to orbit a triton rather than a deuteron, since the triton is about half again as massive as the deuteron.
10. ^ This somewhat clumsy notation attempts to convey the information that the neutral deuterium molecule has a covalent bond provided by the two electrons binding the two deuterons together.
11. ^ Using the difference between the known rest masses of the n and 3Li6 reactants, on the one hand, and the known rest masses of the α and t products, on the other, along with the conservation of momentum and the conservation of energy, the over-all energy release (the Q-value), as well as the respective non-relativistic or Galilean velocities and non-relativistic or Galilean kinetic energies of the α and t products may be readily calculated directly.
12. ^ "Thermal neutrons" are neutrons that have been "moderated" by giving up most of their kinetic energy in collisions with the nuclei of the "moderating materials" or moderators, cooling down to "room temperature" and having a thermalized kinetic energy of about 0.025 eV, corresponding to an average "temperature" of about 300 kelvins or so.
13. ^ In principle, of course, p-d nuclear fusion could be catalyzed by the electrons present in the odd HDO "heavy-ish" water molecule that naturally occurs at the level of 0.0154% in ordinary water (H2O). However, because the proton and the deuteron would be more than 200 times farther apart in the case of the electronic HDO molecule than in the case of the muonic (p-μ-d)+ molecular ion, there has almost certainly[original research?] never been even one p-d electron-catalyzed fusion (eCF) in all the vast wine-dark seas covering about three-quarters of the face of the Earth during all the long eons that water has existed here.
14. ^ Except, of course, for the ever-so-slight chance of proton-decay predicted in most Grand Unified Theories (or GUTs).
15. ^ Even though the amount of deuterium is only about 1.5% of 1% of the amount of hydrogen, since hydrogen is far and away the most abundant element in the Universe, there is more than enough deuterium in the seven seas to supply the energy and power needs of humankind at least several billion years (assuming humankind can figure out clever ways of making some kind of nuclear fusion work at all).
16. ^ This "alpha-sticking" or "α-sticking" problem is mentioned briefly in the next section and then is discussed in more detail in the section after that.

See also

* Nuclear fusion
* Steven E. Jones (coined the term 'cold fusion')


1. ^ F.C. Frank (1947). "Hypothetical Alternative Energy Sources for the ‘Second Meson’ Events". Nature 160: 525. doi:10.1038/160525a0.
2. ^ Zel'dovitch, Yakov Borisovich (1954). Doklady Akademii Nauk SSSR 95: 493.
3. ^ a b L.W. Alvarez et al., Phys. Rev. 105, 1127 (1957).
4. ^ a b c d e f g h i j k l m n J.D. Jackson (1957). "Catalysis of Nuclear Reactions between hydrogen isotopes by μ−-Mesons". Physical Review 106: 330. doi:10.1103/PhysRev.106.330.
5. ^ a b c d 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.
6. ^ J. Rafelski, S.E. Jones (1987). "Cold Nuclear Fusion"". Scientific American 257: 84. .
7. ^ S.E. Jones (1986). "Muon-Catalysed Fusion Revisited". Nature 321: 127–133. doi:10.1038/321127a0.
8. ^ J. W. Negele, Erich Vogt (1998). Advances in nuclear physics (illustrated ed.). Springer. pp. 194–198. ISBN 0306457571, 9780306457579.

External links

* Articles and presentation on this topic
* Muon-catalyzed fusion diagram

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