Muon-catalyzed fusion
Encyclopedia
Muon-catalyzed fusion is a process allowing nuclear fusion
to take place at temperature
s 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 might prevent it from becoming a practical power source. However, if muon
s 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.
Muon
s are unstable subatomic particles. They are similar to electrons, but are about 207 times more massive. If a muon replaces one of the electrons in a hydrogen molecule, the nuclei are consequently drawn 207 times closer together than they would be in a normal molecule. When the nuclei are this close together, the probability of nuclear fusion is greatly enhanced, to the point where a significant number of fusion events can happen at room temperature. Unfortunately, it is difficult to create large numbers of muons efficiently; moreover, the existence of processes that remove muons from the catalytic cycle mean that each muon can only catalyze a few hundred nuclear fusion reactions before it decays away. These two factors limit muon-catalyzed fusion to a laboratory curiosity, although there is some speculation that an efficient muon source could lead to a useful room-temperature fusion reactor.
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 of utilizing the catalyzing muons. This assessment has, so far, stood the test of time.
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 fuel
s 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.The breeding takes place due to certain neutron-capture nuclear reactions, followed by beta decay
s, 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 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 extremely long-lived nuclear wastes, such as those produced (mainly) by conventional nuclear fission
reactors, into 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.
s are not meson
s, they are lepton
s. 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. can be found."
s, 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 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, not all of the muons are recycled: some bond with other debris emitted following the fusion of the nuclei (such as alpha particle
s and helions
), removing the muons from the catalytic process. This gradually 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.
). 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.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 1957 estimate.
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.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. Indeed, the team led by Steven E. Jones
achieved 150 d-t fusions per muon (average) at the Los Alamos Meson Physics Facility. 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 muonOne 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 pion
s . 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
. 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 2011, no practical method of producing energy through this means has been published, although some discoveries using "hall effect" show promise.
(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, 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),According to , 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.) so the average separation between the triton and the deuteron in the muonic molecular ion is about 207 times smaller than that.In other words, the separation in the muonic case is about 500 femtometersThe 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
. 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.
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. Each catalyzing muon thus spends most of its ephemeral existence of about 2.2 microseconds, 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.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. 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),This somewhat clumsy notation attempts to convey the information that the neutral deuterium molecule has a covalent bond
provided by the two electron
s binding the two deuterons together. 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. 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.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."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 moderator
s, cooling down to "room temperature
" and having a thermalized kinetic energy
of about 0.025 eV, corresponding to an average "temperature" of about 300 kelvin
s or so.
(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.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 never been even one p-d electron-catalyzed fusion (eCF) in Earth's oceans.
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 radioactiveExcept, of course, for the ever-so-slight chance of proton-decay predicted in most Grand Unified Theories (or GUTs).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). (Tritium rarely occurs naturally, and is radioactive with a half-life of about 12.5 years.ref name="NIST"/>)
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.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. 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. 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.
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
to take place at temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
s significantly lower than the temperatures required for thermonuclear fusion, even at room temperature
Room temperature
-Comfort levels:The American Society of Heating, Refrigerating and Air-Conditioning Engineers has listings for suggested temperatures and air flow rates in different types of buildings and different environmental circumstances. For example, a single office in a building has an occupancy ratio per...
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 might prevent it from becoming a practical power source. However, if muon
Muon
The muon |mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...
s could be produced more efficiently, or if they could be used as catalysts more efficiently, the energy balance
First law of thermodynamics
The first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...
might improve enough for muon-catalyzed fusion to become a practical power source.
Muon
Muon
The muon |mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...
s are unstable subatomic particles. They are similar to electrons, but are about 207 times more massive. If a muon replaces one of the electrons in a hydrogen molecule, the nuclei are consequently drawn 207 times closer together than they would be in a normal molecule. When the nuclei are this close together, the probability of nuclear fusion is greatly enhanced, to the point where a significant number of fusion events can happen at room temperature. Unfortunately, it is difficult to create large numbers of muons efficiently; moreover, the existence of processes that remove muons from the catalytic cycle mean that each muon can only catalyze a few hundred nuclear fusion reactions before it decays away. These two factors limit muon-catalyzed fusion to a laboratory curiosity, although there is some speculation that an efficient muon source could lead to a useful room-temperature fusion reactor.
A brief history
Andrei SakharovAndrei Sakharov
Andrei Dmitrievich Sakharov was a Soviet nuclear physicist, dissident and human rights activist. He earned renown as the designer of the Soviet Union's Third Idea, a codename for Soviet development of thermonuclear weapons. Sakharov was an advocate of civil liberties and civil reforms in the...
and F.C. Frank predicted the phenomenon of muon-catalyzed fusion on theoretical grounds before 1950. Yakov Borisovich Zel'dovich
Yakov Borisovich Zel'dovich
Yakov Borisovich Zel'dovich was a prolific Soviet physicist born in Belarus. He played an important role in the development of Soviet nuclear and thermonuclear weapons, and made important contributions to the fields of adsorption and catalysis, shock waves, nuclear physics, particle physics,...
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
Bubble chamber
A bubble chamber is a vessel filled with a superheated transparent liquid used to detect electrically charged particles moving through it. It was invented in 1952 by Donald A. Glaser, for which he was awarded the 1960 Nobel Prize in Physics...
at Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
in 1956, observed muon-catalysis of exothermic p-d, proton and deuteron, nuclear fusion
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
, which results in a helion
Helion (chemistry)
A helion is a short name for the naked nucleus of helium, a doubly positively charged helium ion. In practice, helion refers to the stable helium-3 nucleus, in opposition to the other stable nucleus helium-4, which is usually referred to as an alpha particle...
, a gamma ray
Gamma ray
Gamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency . Gamma rays are usually naturally produced on Earth by decay of high energy states in atomic nuclei...
, and a release of about 5.5 MeV of energy. The Alvarez experimental results, in particular, spurred John David Jackson
J. D. Jackson
John David Jackson is a Canadian–American physics professor emeritus at the University of California, Berkeley and a faculty senior scientist emeritus at Lawrence Berkeley National Laboratory...
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 of utilizing the catalyzing muons. 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 fissionNuclear fission
In nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts , often producing free neutrons and photons , and releasing a tremendous amount of energy...
reactors because muon-catalyzed d-t nuclear fusion (like most other types of nuclear fusion
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
), 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
Carbon dioxide
Carbon dioxide is a naturally occurring chemical compound composed of two oxygen atoms covalently bonded to a single carbon atom...
(CO2), by reducing or even eliminating the need to burn fossil fuel
Fossil fuel
Fossil fuels are fuels formed by natural processes such as anaerobic decomposition of buried dead organisms. The age of the organisms and their resulting fossil fuels is typically millions of years, and sometimes exceeds 650 million years...
s and biomass that contain carbon
Carbon
Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...
, 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
Fissile
In nuclear engineering, a fissile material is one that is capable of sustaining a chain reaction of nuclear fission. By definition, fissile materials can sustain a chain reaction with neutrons of any energy. The predominant neutron energy may be typified by either slow neutrons or fast neutrons...
fuels, from fertile material
Fertile material
Fertile material is a term used to describe nuclides which generally themselves do not undergo induced fission but from which fissile material is generated by neutron absorption and subsequent nuclei conversions...
- for example, thorium
Thorium
Thorium is a natural radioactive chemical element with the symbol Th and atomic number 90. It was discovered in 1828 and named after Thor, the Norse god of thunder....
-232 could breed uranium
Uranium
Uranium is a silvery-white metallic chemical element in the actinide series of the periodic table, with atomic number 92. It is assigned the chemical symbol U. A uranium atom has 92 protons and 92 electrons, of which 6 are valence electrons...
-233 in this way.The breeding takes place due to certain neutron-capture nuclear reactions, followed by beta decay
Beta decay
In nuclear physics, beta decay is a type of radioactive decay in which a beta particle is emitted from an atom. There are two types of beta decay: beta minus and beta plus. In the case of beta decay that produces an electron emission, it is referred to as beta minus , while in the case of a...
s, 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 supercritical
Supercritical water reactor
The supercritical water reactor is a Generation IV reactor concept that uses supercritical water as the working fluid...
nuclear fission reactor
Nuclear reactor
A nuclear reactor is a device to initiate and control a sustained nuclear chain reaction. Most commonly they are used for generating electricity and for the propulsion of ships. Usually heat from nuclear fission is passed to a working fluid , which runs through turbines that power either ship's...
or in an unconventional subcritical
Subcritical reactor
A subcritical reactor is a nuclear fission reactor that produces fission without achieving criticality. Instead of a sustaining chain reaction, a subcritical reactor uses additional neutrons from an outside source...
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
Nuclear transmutation
Nuclear transmutation is the conversion of one chemical element or isotope into another. In other words, atoms of one element can be changed into atoms of other element by 'transmutation'...
large quantities of extremely long-lived nuclear wastes, such as those produced (mainly) by conventional nuclear fission
Nuclear fission
In nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts , often producing free neutrons and photons , and releasing a tremendous amount of energy...
reactors, into much less long-lived transmuted elements. Another example of the creative use of an unconventional subcritical fission pile is the energy amplifier
Energy amplifier
In nuclear physics, an energy amplifier is a novel type of nuclear power reactor, a subcritical reactor, in which an energetic particle beam is used to stimulate a reaction, which in turn releases enough energy to power the particle accelerator and leave an energy profit for power generation...
devised by Physics Nobel Laureate Carlo Rubbia
Carlo Rubbia
Carlo Rubbia Knight Grand Cross is an Italian particle physicist and inventor who shared the Nobel Prize in Physics in 1984 with Simon van der Meer for work leading to the discovery of the W and Z particles at CERN.-Biography:...
, 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−-mesonsMuonMuon
The muon |mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...
s are not meson
Meson
In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
s, they are lepton
Lepton
A lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...
s. 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. can be found."
Process
To create this effect, a stream of negative muons, most often created by decaying pionPion
In particle physics, a pion is any of three subatomic particles: , , and . Pions are the lightest mesons and they play an important role in explaining the low-energy properties of the strong nuclear force....
s, 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 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
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
(see nuclear fusion
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
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, not all of the muons are recycled: some bond with other debris emitted following the fusion of the nuclei (such as alpha particle
Alpha particle
Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus, which is classically produced in the process of alpha decay, but may be produced also in other ways and given the same name...
s and helions
Helion (chemistry)
A helion is a short name for the naked nucleus of helium, a doubly positively charged helium ion. In practice, helion refers to the stable helium-3 nucleus, in opposition to the other stable nucleus helium-4, which is usually referred to as an alpha particle...
), removing the muons from the catalytic process. This gradually 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 (in their rest frameRest frame
In special relativity the rest frame of a particle is the coordinate system in which the particle is at rest.The rest frame of compound objects is taken to be the frame of reference in which the average momentum of the particles which make up the substance is zero In special relativity the rest...
). Hence, there needs to be some cheap means of producing muons, and the muons must be arranged to catalyze as many nuclear fusion
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
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.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
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
, 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
Break-even
Break-even is a point where any difference between plus or minus or equivalent changes side.-In economics:A technique for which identifying the point where the total revenue is just sufficient to cover the total cost...
, where as much thermal energy
Thermal energy
Thermal energy is the part of the total internal energy of a thermodynamic system or sample of matter that results in the system's temperature....
is generated as electrical energy is consumed to produce the muons in the first place, according to Jackson's rough 1957 estimate.
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.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. Indeed, the team led by Steven E. Jones
Steven E. Jones
Steven Earl Jones is an American physicist. For most of his career, Jones was known mainly for his work on muon-catalyzed fusion. In the fall of 2006, amid controversy surrounding his work on the collapse of the World Trade Center , he was relieved of his teaching duties...
achieved 150 d-t fusions per muon (average) at the Los Alamos Meson Physics Facility. 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 muonOne common way to make muons is to accelerate deuterons to energies of about 800 MeV
MEV
MeV and meV are multiples and submultiples of the electron volt unit referring to 1,000,000 eV and 0.001 eV, respectively.Mev or MEV may refer to:In entertainment:* Musica Elettronica Viva, an Italian musical group...
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 pion
Pion
In particle physics, a pion is any of three subatomic particles: , , and . Pions are the lightest mesons and they play an important role in explaining the low-energy properties of the strong nuclear force....
s . As long as pions are kept away from the nuclei (which would absorb the pions via the strong interaction
Strong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...
), they will generally decay into a muon and a muon antineutrino after about 26 ns
Nanosecond
A nanosecond is one billionth of a second . One nanosecond is to one second as one second is to 31.7 years.The word nanosecond is formed by the prefix nano and the unit second. Its symbol is ns....
. 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 2011, no practical method of producing energy through this means has been published, although some discoveries using "hall effect" show promise.
Deuterium-tritium (d-t or dt)
In the muon-catalyzed fusion of most interest, a positively charged deuteron (d), a positively charged tritonTritium
Tritium is a radioactive isotope of hydrogen. The nucleus of tritium contains one proton and two neutrons, whereas the nucleus of protium contains one proton and no neutrons...
(t), and a muon
Muon
The muon |mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...
essentially form a positively charged muonic molecular heavy hydrogen ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...
(d-μ-t)+. The muon, with a rest mass about 207 times greater than the rest mass of an electron, 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
Ångström
The angstrom or ångström, is a unit of length equal to 1/10,000,000,000 of a meter . Its symbol is the Swedish letter Å....
(100 pm),According to , 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.) so the average separation between the triton and the deuteron in the muonic molecular ion is about 207 times smaller than that.In other words, the separation in the muonic case is about 500 femtometersThe 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
Compton wavelength
The Compton wavelength is a quantum mechanical property of a particle. It was introduced by Arthur Compton in his explanation of the scattering of photons by electrons...
. 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
Quantum tunnelling
Quantum tunnelling refers to the quantum mechanical phenomenon where a particle tunnels through a barrier that it classically could not surmount. This plays an essential role in several physical phenomena, such as the nuclear fusion that occurs in main sequence stars like the sun, and has important...
through the repulsive Coulomb barrier
Coulomb barrier
The Coulomb barrier, named after Coulomb's law, which is named after physicist Charles-Augustin de Coulomb , is the energy barrier due to electrostatic interaction that two nuclei need to overcome so they can get close enough to undergo a nuclear reaction...
that acts to keep them apart. Indeed, the quantum mechanical tunnelling probability depends roughly exponentially
Exponential function
In mathematics, the exponential function is the function ex, where e is the number such that the function ex is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change In mathematics,...
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
Picosecond
A picosecond is 10−12 of a second. That is one trillionth, or one millionth of one millionth of a second, or 0.000 000 000 001 seconds. A picosecond is to one second as one second is to 31,700 years....
, once the muonic molecular ion is formed.
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. Each catalyzing muon thus spends most of its ephemeral existence of about 2.2 microseconds, as measured in its rest frame
Rest frame
In special relativity the rest frame of a particle is the coordinate system in which the particle is at rest.The rest frame of compound objects is taken to be the frame of reference in which the average momentum of the particles which make up the substance is zero In special relativity the rest...
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.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. 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
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
D2 (d=e2=d),This somewhat clumsy notation attempts to convey the information that the neutral deuterium molecule has a covalent bond
Covalent bond
A covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms. The stable balance of attractive and repulsive forces between atoms when they share electrons is known as covalent bonding....
provided by the two electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s binding the two deuterons together. 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
Exothermic
In thermodynamics, the term exothermic describes a process or reaction that releases energy from the system, usually in the form of heat, but also in the form of light , electricity , or sound...
d-t nuclear fusion
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
releases about 17.6 MeV
MEV
MeV and meV are multiples and submultiples of the electron volt unit referring to 1,000,000 eV and 0.001 eV, respectively.Mev or MEV may refer to:In entertainment:* Musica Elettronica Viva, an Italian musical group...
of energy in the form of a "very fast" neutron having a kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...
of about 14.1 MeV and an alpha particle
Alpha particle
Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus, which is classically produced in the process of alpha decay, but may be produced also in other ways and given the same name...
α (a helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...
-4 nucleus) with a kinetic energy of about 3.5 MeV. 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
Lithium
Lithium is a soft, silver-white metal that belongs to the alkali metal group of chemical elements. It is represented by the symbol Li, and it has the atomic number 3. Under standard conditions it is the lightest metal and the least dense solid element. Like all alkali metals, lithium is highly...
-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.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
Conservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...
, 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."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 moderator
Neutron moderator
In nuclear engineering, a neutron moderator is a medium that reduces the speed of fast neutrons, thereby turning them into thermal neutrons capable of sustaining a nuclear chain reaction involving uranium-235....
s, cooling down to "room temperature
Room temperature
-Comfort levels:The American Society of Heating, Refrigerating and Air-Conditioning Engineers has listings for suggested temperatures and air flow rates in different types of buildings and different environmental circumstances. For example, a single office in a building has an occupancy ratio per...
" and having a thermalized kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...
of about 0.025 eV, corresponding to an average "temperature" of about 300 kelvin
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...
s or so.
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., was actually protium (H or 1H1) and deuteriumDeuterium
Deuterium, also called heavy hydrogen, is one of two stable isotopes of hydrogen. It has a natural abundance in Earth's oceans of about one atom in of hydrogen . Deuterium accounts for approximately 0.0156% of all naturally occurring hydrogen in Earth's oceans, while the most common isotope ...
(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.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 never been even one p-d electron-catalyzed fusion (eCF) in Earth's oceans.
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 radioactiveExcept, of course, for the ever-so-slight chance of proton-decay predicted in most Grand Unified Theories (or GUTs).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
Chemical element
A chemical element is a pure chemical substance consisting of one type of atom distinguished by its atomic number, which is the number of protons in its nucleus. Familiar examples of elements include carbon, oxygen, aluminum, iron, copper, gold, mercury, and lead.As of November 2011, 118 elements...
in the Universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
, 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
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
work at all). (Tritium rarely occurs naturally, and is radioactive with a half-life of about 12.5 years.ref name="NIST"/>)
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.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. 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
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
possibilities, which result in essentially no neutrons among the nuclear fusion products, are almost certainly not very amenable to muon-catalyzed fusion. 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
Helion (chemistry)
A helion is a short name for the naked nucleus of helium, a doubly positively charged helium ion. In practice, helion refers to the stable helium-3 nucleus, in opposition to the other stable nucleus helium-4, which is usually referred to as an alpha particle...
(h+2) from helium-3
Helium-3
Helium-3 is a light, non-radioactive isotope of helium with two protons and one neutron. It is rare on Earth, and is sought for use in nuclear fusion research...
, which yields an energetic alpha particle
Alpha particle
Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus, which is classically produced in the process of alpha decay, but may be produced also in other ways and given the same name...
and a much more energetic proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
, both positively charged (with a few neutrons coming from inevitable d-d nuclear fusion
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
side reactions). However, one muon
Muon
The muon |mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...
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.
