Muon-catalyzed fusion: Difference between revisions

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Revision as of 01:36, 9 September 2006 editRandyfurlong (talk \| contribs)60 edits A major edit, so a review would be welcomed--nothing really dispute-worthy, in my opinion--just fleshing out and, hopefully, improving an article to which I've contributed in the past. Thanks!← Previous edit		Revision as of 07:44, 9 September 2006 edit undoRandyfurlong (talk \| contribs)60 editsm Minor edit of my earlier major edit.Next edit →
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	'''Muon-catalyzed fusion''' is a process allowing ] to take place at ]. 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. It used to be known as ]; however, this term is now avoided as it can create confusion with other suggested forms of room-temperature fusion that are rejected by ].		'''Muon-catalyzed fusion''' is a process allowing ] to take place at ]. 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. It used to be known as ]; however, this term is now avoided as it can create confusion with other suggested forms of room-temperature fusion that are rejected by ].

	In the muon-catalyzed fusion of most interest, a positively charged ] nucleus (a ], d), a positively charged ] nucleus (a ], t), and a negatively charged ] (μ), which is basically a "heavy" ], essentially form a positively charged muonic molecular "heavy" ] '']'' (d-μ-t)^+. The negative muon (μ), with a ] about 200 times greater than the rest mass of an electron, is able to drag the more massive triton (t) and deuteron (d) about 200 times closer together to each other than can an electron in the corresponding positively charged electronic molecular "heavy" Hydrogen ion (d-e-t)^+. The average separation between the triton (t) and the deuteron (d) in the ''electronic'' molecular heavy Hydrogen ion (d-e-t)^+ is about one ] (a tenth of a ] or one ten-billionth of a ]), so the average separation between the triton (t) and the deuteron (d) in the ''muonic'' molecular heavy Hydrogen ion (d-μ-t)^+ is about 200 times smaller than that, or about 500 ] (] or million-billionths of a meter), which is about 354 times the ] of a ]. (The pion's Compton wavelength is characteristic of the range of the ] between ] (such as ] and ]) in atomic nuclei, at least the ones that are more complicated than a single proton, the nucleus of ], otherwise known as ]).		In the muon-catalyzed fusion of most interest, a positively charged ] nucleus (a ], d), a positively charged ] nucleus (a ], t), and a negatively charged ] (μ), which is basically a "heavy" ], essentially form a positively charged muonic molecular "heavy" ] '']'' (d-μ-t)^+. The negative muon (μ), with a ] about 200 times greater than the rest mass of an electron, is able to drag the more massive triton (t) and deuteron (d) about 200 times closer together to each other than can an electron in the corresponding positively charged electronic molecular "heavy" Hydrogen ion (d-e-t)^+. The average separation between the triton (t) and the deuteron (d) in the ''electronic'' molecular heavy Hydrogen ion (d-e-t)^+ is about one ] (a tenth of a ] or one ten-billionth of a ]), so the average separation between the triton (t) and the deuteron (d) in the ''muonic'' molecular heavy Hydrogen ion (d-μ-t)^+ is about 200 times smaller than that, or about 500 ] (] or million-billionths of a meter), which is about 354 times the ] of a ]. (The pion's Compton wavelength is characteristic of the range of the ] between ] (such as ] and ]) in atomic nuclei, at least the ones that are more complicated than a single proton, the nucleus of ], otherwise known as ]).

	Consequently, whenever the triton (t) and the deuteron (d) in the muonic molecular heavy Hydrogen ion (d-μ-t)^+ happen to get even closer to each other during their periodic vibrational motions, the probability is very greatly increased that the positively charged triton (t) and the positively charged deuteron (d) would ] through the repulsive ] that acts to keep them apart. Indeed, the quantum mechanical tunnelling probability depends roughly ] on the average separation between the triton (t) and the deuteron (d), allowing a single muon (μ) to catalyze the d-t nuclear fusion in less than about half a ] (a trillionth of a second), once the muonic molecular heavy Hydrogen ion (d-μ-t)^+ is formed. The muonic molecular heavy Hydrogen ion (d-μ-t)^+ formation time 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 d-t mixture, for example. Each catalyzing muon (μ) thus spends most of its ephemeral existence of about 2.2 microseconds (millionths of a second, measured in its ]) wandering around looking for suitable deuterons (d) or tritons (t) with which to bind.		Consequently, whenever the triton (t) and the deuteron (d) in the muonic molecular heavy Hydrogen ion (d-μ-t)^+ happen to get even closer to each other during their periodic vibrational motions, the probability is very greatly increased that the positively charged triton (t) and the positively charged deuteron (d) would undergo ] through the repulsive ] that acts to keep them apart. Indeed, the quantum mechanical tunnelling probability depends roughly ] on the average separation between the triton (t) and the deuteron (d), allowing a single muon (μ) to catalyze the d-t nuclear fusion in less than about half a ] (a trillionth of a second), once the muonic molecular heavy Hydrogen ion (d-μ-t)^+ is formed. The muonic molecular heavy Hydrogen ion (d-μ-t)^+ formation time 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 d-t mixture, for example. Each catalyzing muon (μ) thus spends most of its ephemeral existence of about 2.2 microseconds (millionths of a second, measured in its ]) wandering around looking for suitable deuterons (d) or tritons (t) with which to bind.

	Another way of looking at muon-catalyzed fusion is to try to visualize the ground state orbit of a negative muon (μ) around either a deuteron (d) or a triton (t). The negative muon (μ), if given a choice, would actually prefer to orbit a triton (t) rather than a deuteron (d), since the triton (t) is about half again as massive as the deuteron (d). Suppose the negative muon (μ) happens to have fallen into an orbit around a deuteron (d) initially, which it has about a 50% chance of doing if there are approximately equal numbers of deuterons (d) and tritons (t) present, forming an electrically neutral muonic Deuterium atom (d-μ) that acts somewhat like a "fat neutron" due both to its relatively small size (again, about 200 times smaller than a neutral electronic Deuterium atom, d-e) and to the very effective shielding by the negative muon (μ) of the positive charge of the deuteron's (d's) proton (p). Even so, the negative muon (μ) still has a much greater chance of being ''transferred'' to any triton (t) that comes near enough to the muonic Deuterium (d-μ) than it does of forming a muonic molecular heavy Hydrogen ion (d-μ-t)^+. The muonic Tritium atom (t-μ) thus formed will act somewhat like an even "fatter neutron," but it will most likely hang on to its negative muon (μ), eventually forming a muonic molecular heavy Hydrogen ion (d-μ-t)^+, most likely due to the resonant formation of a hyperfine molecular state within an entire Deuterium molecule (d-d), as predicted by Vesman, an Estonian graduate student, in 1967.		Another way of looking at muon-catalyzed fusion is to try to visualize the ground state orbit of a negative muon (μ) around either a deuteron (d) or a triton (t). The negative muon (μ), if given a choice, would actually prefer to orbit a triton (t) rather than a deuteron (d), since the triton (t) is about half again as massive as the deuteron (d). Suppose the negative muon (μ) happens to have fallen into an orbit around a deuteron (d) initially, which it has about a 50% chance of doing if there are approximately equal numbers of deuterons (d) and tritons (t) present, forming an electrically neutral muonic Deuterium atom (d-μ) that acts somewhat like a "fat neutron" due both to its relatively small size (again, about 200 times smaller than a neutral electronic Deuterium atom, d-e) and to the very effective shielding by the negative muon (μ) of the positive charge of the deuteron's (d's) proton (p). Even so, the negative muon (μ) still has a much greater chance of being ''transferred'' to any triton (t) that comes near enough to the muonic Deuterium (d-μ) than it does of forming a muonic molecular heavy Hydrogen ion (d-μ-t)^+. The muonic Tritium atom (t-μ) thus formed will act somewhat like an even "fatter neutron," but it will most likely hang on to its negative muon (μ), eventually forming a muonic molecular heavy Hydrogen ion (d-μ-t)^+, most likely due to the resonant formation of a ] molecular state within an entire Deuterium ] (d-d), as predicted by Vesman, an Estonian graduate student, in 1967.

	As described above, once the d-μ-t state is formed, the shielding by the negative muon (μ) of the positive charges of the protons (p's) of the triton (t) and the deuteron (d) from each other allows the triton (t) and the deuteron (d) to move close enough together to fuse with alacrity. The negative muon (μ) survives the d-t nuclear fusion reaction and remains available (usually) to ] further d-t nuclear fusions. Each ] d-t ] releases about 17.6 ] of energy in the form of a "very fast" neutron having a kinetic energy of about 14.1 ] and an ] α (a ]-4 nucleus) with a kinetic energy of about 3.5 MeV, an MeV being a million ] (eVs) or about 1.6 millionths of an ]. An additional 4.8 MeV can be gleaned by having the neutrons moderated in a suitable "blanket" surrounding the reaction chamber, with the blanket containing ]-6, which readily and exothermically absorbs ], the Lithium-6 ~~transmuting~~ thereby into an alpha particle (α) and a triton (t). 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, 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 or so.		As described above, once the d-μ-t state is formed, the shielding by the negative muon (μ) of the positive charges of the protons (p's) of the triton (t) and the deuteron (d) from each other allows the triton (t) and the deuteron (d) to move close enough together to fuse with alacrity. The negative muon (μ) survives the d-t nuclear fusion reaction and remains available (usually) to ] further d-t nuclear fusions. Each ] d-t ] releases about 17.6 ] of energy in the form of a "very fast" neutron having a kinetic energy of about 14.1 ] and an ] α (a ]-4 nucleus) with a kinetic energy of about 3.5 MeV, an MeV being a million ] (]) or about 1.6 millionths of an ]. An additional 4.8 MeV can be gleaned by having the neutrons moderated in a suitable "blanket" surrounding the reaction chamber, with the blanket containing ]-6, which readily and exothermically absorbs ], the Lithium-6 being transmuted thereby into an alpha particle (α) and a triton (t). 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, 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 or so.

	] and F.C. Frank (see reference below) predicted the phenomenon of muon-catalyzed fusion on theoretical grounds before ]. Ya.B. Zel'dovitch (see reference below) also wrote about the phenomenon of muon-catalyzed fusion in 1954. L.W. Alvarez ''et al.'', (see reference below) when analyzing the outcome of some experiments with negative muons (μ's) incident on a Hydrogen ] at Berkeley in 1956, observed muon-catalysis of exothermic p-d, proton (p) and deuteron (d), ], which results in a ] (a ]-3 nucleus) and a release of 5.5 MeV of energy.		] and F.C. Frank (see reference below) predicted the phenomenon of muon-catalyzed fusion on theoretical grounds before ]. Ya.B. Zel'dovitch (see reference below) also wrote about the phenomenon of muon-catalyzed fusion in 1954. L.W. Alvarez ''et al.'' (see reference below), when analyzing the outcome of some experiments with negative muons (μ's) incident on a Hydrogen ] at ] in 1956, observed muon-catalysis of exothermic p-d, proton (p) and deuteron (d), ], which results in a ] (a ]-3 nucleus) and a release of 5.5 MeV of energy.

	One practical problem with the muon-catalyzed fusion process is that muons (μ's) are unstable, decaying in about 2.2 microseconds (in their rest frame). Hence, there needs to be some cheap means of producing muons (μ's), and the muons (μ's) must be arranged to catalyze as many nuclear fusion reactions as possible before decaying.		One practical problem with the muon-catalyzed fusion process is that muons (μ's) are unstable, decaying in about 2.2 microseconds (in their rest frame). Hence, there needs to be some cheap means of producing muons (μ's), and the muons (μ's) must be arranged to catalyze as many nuclear fusion reactions as possible before decaying.
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	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%), which could mean as many as about 200 (or perhaps even about 250) muon-catalyzed d-t fusions per muon (μ). (Interestingly, very detailed and involved 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 0.5% (or perhaps even about 0.4%) to be somewhat mysterious.) Unfortunately, even 200 (or perhaps even 250) d-t nuclear fusions are still not quite enough even to reach break-even, much less have enough to convert the ''thermal'' energy released into more useful ''electrical'' energy and have any left over to sell to the commercial electrical power "grid." The conversion efficiency from ''thermal'' energy to ''electrical'' energy is only about 40% and some of that ''electrical'' energy will have to be recycled to make more negative muons (μ's) to keep the d-t nuclear fusion fires burning.		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%), which could mean as many as about 200 (or perhaps even about 250) muon-catalyzed d-t fusions per muon (μ). (Interestingly, very detailed and involved 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 0.5% (or perhaps even about 0.4%) to be somewhat mysterious.) Unfortunately, even 200 (or perhaps even 250) d-t nuclear fusions are still not quite enough even to reach break-even, much less have enough to convert the ''thermal'' energy released into more useful ''electrical'' energy and have any left over to sell to the commercial electrical power "grid." The conversion efficiency from ''thermal'' energy to ''electrical'' energy is only about 40% and some of that ''electrical'' energy will have to be recycled to make more negative muons (μ's) to keep the d-t nuclear fusion fires burning.

	One of the favorite and apparently preferred ways to make negative muons (μ's) is to accelerate deuterons (d's) to have kinetic energies of about 800 MeV (in the Lab frame) using one or more ], such as ] (]) and/or ] (with either ] or non-superconducting ]), and smash the accelerated deuterons (d's) into an appropriate target, such as a gas of molecular Deuterium (d-d) and molecular Tritium (t-t), for example. Smashing the deuterons (d's) having a ] of about 800 MeV into other neutron-containing nuclei creates a fair number of negative ] (π's) among other things. As long as these negative pions (π's) are kept away from nuclei that would strongly absorb the strongly interacting negative pions (π's), ~~they~~ will generally decay after about 26 nanoseconds (in ~~their~~ rest frame) into negative ~~muons~~ (μ's) and ~~muonic~~ ] (ν_μ-bar's). The best recent "guesstimate" of the energy cost per negative muon is about 6 ] (billion electron Volts), using these deuterons (d's) that are accelerated to have kinetic energies of about 800 MeV, with accelerators that are (coincidentally) about 40% efficient at taking ''electrial'' energy from the ] (]) mains (the plugs on the wall) and accelerating the deuterons (d's) using this ''electrical'' energy.		One of the favorite and apparently preferred ways to make negative muons (μ's) is to accelerate deuterons (d's) to have kinetic energies of about 800 MeV (in the Lab frame) using one or more ], such as a ] (]) and/or a ] (with either ] or non-superconducting ]), and smash the accelerated deuterons (d's) into an appropriate target, such as a gas of molecular Deuterium (d-d) and molecular Tritium (t-t), for example. Smashing the deuterons (d's) having a ] of about 800 MeV into other neutron-containing nuclei creates a fair number of negative ] (π's), among other things. As long as these negative pions (π's) are kept away from nuclei that would strongly absorb the strongly-interacting negative pions (π's), each negative pion (π) will generally decay after about 26 nanoseconds (in its rest frame) into a negative muon (μ) and a ] (ν_μ-bar). The best recent "guesstimate" of the ''electrical'' "energy cost" per negative muon (μ) is about 6 ] (billion electron Volts), using these deuterons (d's) that are accelerated to have kinetic energies of about 800 MeV, with accelerators that are (coincidentally) about 40% efficient at taking ''electrial'' energy from the ] (]) mains (the plugs on the wall) and accelerating the deuterons (d's) using this ''electrical'' energy.

	Some have proposed very innovative "hybrid" ]/] schemes to use the copious neutrons produced in muon-catalyzed d-t nuclear fusions to "breed" ], such as ]-233, from "]" materials, such as ]-232, for example. The fissile fuels bred can then be "burned," either in a convential ] ] or, better yet, in an unconventional ] ] not unlike that proposed and currently being developed for ] ].		Some have proposed very innovative "hybrid" ]/] schemes to use the copious neutrons produced in muon-catalyzed d-t nuclear fusions to "breed" ] (]) fuels, such as ]-233, from "]" materials, such as ]-232, for example. The fissile fuels that have been bred can then be "burned," either in a convential ] ] or, better yet, in an unconventional ] ] not unlike the accelerator-driven systems (ADS) that have been proposed for, and in some places are currently being developed for, the accelerator transmutation of waste (ATW), for example, using neutrons to ] large quantities of highly radioactive and extremely long-lived ], such as those produced (mainly) by conventional nuclear fission reactors, into less harmful, less radioactive, less toxic, and much less long-lived transmuted elements, as well as for the ] devised by Physics ] ] among others.

	Except for refinements such as these, not all that much has changed in nearly half a century since Jackson's assessment of the feasibility of muon-catalyzed fusion, other than Vesman's prediction of the ] resonant formation of d-μ-t, 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 can be found."		Except for refinements such as these, not all that much has changed in nearly half a century since Jackson's assessment of the feasibility of muon-catalyzed fusion, other than Vesman's prediction of the ] resonant formation of d-μ-t, 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 can be found."

Revision as of 07:44, 9 September 2006

Muon-catalyzed fusion is a process allowing nuclear fusion to take place at room temperature. 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. It used to be known as cold fusion; however, this term is now avoided as it can create confusion with other suggested forms of room-temperature fusion that are rejected by mainstream science.

In the muon-catalyzed fusion of most interest, a positively charged deuterium nucleus (a deuteron, d), a positively charged tritium nucleus (a triton, t), and a negatively charged muon (μ), which is basically a "heavy" electron, essentially form a positively charged muonic molecular "heavy" Hydrogen ion (d-μ-t)^+. The negative muon (μ), with a rest mass about 200 times greater than the rest mass of an electron, is able to drag the more massive triton (t) and deuteron (d) about 200 times closer together to each other than can an electron in the corresponding positively charged electronic molecular "heavy" Hydrogen ion (d-e-t)^+. The average separation between the triton (t) and the deuteron (d) in the electronic molecular heavy Hydrogen ion (d-e-t)^+ is about one Angstrom (a tenth of a nanometer or one ten-billionth of a meter), so the average separation between the triton (t) and the deuteron (d) in the muonic molecular heavy Hydrogen ion (d-μ-t)^+ is about 200 times smaller than that, or about 500 Fermis (femtometers or million-billionths of a meter), which is about 354 times the Compton wavelength of a pion. (The pion's Compton wavelength is characteristic of the range of the strong nuclear force between nucleons (such as protons and neutrons) in atomic nuclei, at least the ones that are more complicated than a single proton, the nucleus of Protium, otherwise known as Hydrogen).

Consequently, whenever the triton (t) and the deuteron (d) in the muonic molecular heavy Hydrogen ion (d-μ-t)^+ happen to get even closer to each other during their periodic vibrational motions, the probability is very greatly increased that the positively charged triton (t) and the positively charged deuteron (d) 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 (t) and the deuteron (d), allowing a single muon (μ) to catalyze the d-t nuclear fusion in less than about half a picosecond (a trillionth of a second), once the muonic molecular heavy Hydrogen ion (d-μ-t)^+ is formed. The muonic molecular heavy Hydrogen ion (d-μ-t)^+ formation time 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 d-t mixture, for example. Each catalyzing muon (μ) thus spends most of its ephemeral existence of about 2.2 microseconds (millionths of a second, measured in its rest frame) wandering around looking for suitable deuterons (d) or tritons (t) with which to bind.

Another way of looking at muon-catalyzed fusion is to try to visualize the ground state orbit of a negative muon (μ) around either a deuteron (d) or a triton (t). The negative muon (μ), if given a choice, would actually prefer to orbit a triton (t) rather than a deuteron (d), since the triton (t) is about half again as massive as the deuteron (d). Suppose the negative muon (μ) happens to have fallen into an orbit around a deuteron (d) initially, which it has about a 50% chance of doing if there are approximately equal numbers of deuterons (d) and tritons (t) present, forming an electrically neutral muonic Deuterium atom (d-μ) that acts somewhat like a "fat neutron" due both to its relatively small size (again, about 200 times smaller than a neutral electronic Deuterium atom, d-e) and to the very effective shielding by the negative muon (μ) of the positive charge of the deuteron's (d's) proton (p). Even so, the negative muon (μ) still has a much greater chance of being transferred to any triton (t) that comes near enough to the muonic Deuterium (d-μ) than it does of forming a muonic molecular heavy Hydrogen ion (d-μ-t)^+. The muonic Tritium atom (t-μ) thus formed will act somewhat like an even "fatter neutron," but it will most likely hang on to its negative muon (μ), eventually forming a muonic molecular heavy Hydrogen ion (d-μ-t)^+, most likely due to the resonant formation of a hyperfine molecular state within an entire Deuterium molecule (d-d), as predicted by Vesman, an Estonian graduate student, in 1967.

As described above, once the d-μ-t state is formed, the shielding by the negative muon (μ) of the positive charges of the protons (p's) of the triton (t) and the deuteron (d) from each other allows the triton (t) and the deuteron (d) to move close enough together to fuse with alacrity. The negative muon (μ) survives the d-t nuclear fusion reaction and remains available (usually) to catalyze further d-t 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 MeV being a million electron volts (eVs) or about 1.6 millionths of an erg. An additional 4.8 MeV can be gleaned by having the neutrons moderated in a suitable "blanket" surrounding the reaction chamber, with the blanket containing Lithium-6, which readily and exothermically absorbs thermal neutrons, the Lithium-6 being transmuted thereby into an alpha particle (α) and a triton (t). 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, 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 or so.

Andrei Sakharov and F.C. Frank (see reference below) predicted the phenomenon of muon-catalyzed fusion on theoretical grounds before 1950. Ya.B. Zel'dovitch (see reference below) also wrote about the phenomenon of muon-catalyzed fusion in 1954. L.W. Alvarez et al. (see reference below), when analyzing the outcome of some experiments with negative muons (μ's) incident on a Hydrogen bubble chamber at Berkeley in 1956, observed muon-catalysis of exothermic p-d, proton (p) and deuteron (d), nuclear fusion, which results in a helion (a Helium-3 nucleus) and a release of 5.5 MeV of energy.

One practical problem with the muon-catalyzed fusion process is that muons (μ's) are unstable, decaying in about 2.2 microseconds (in their rest frame). Hence, there needs to be some cheap means of producing muons (μ's), and the muons (μ's) must be arranged to catalyze as many nuclear fusion reactions as possible before decaying.

Another, and in many ways more serious, problem is the "alpha-sticking" (α-sticking) problem, which was recognized by J.D. Jackson in his seminal 1957 paper (referenced below), where he gives due credit to E.P. Wigner for pointing the α-sticking problem out to him. The α-sticking problem is the approximately 1% probability of the negative muon (μ) "sticking" to the doubly positively charged alpha particle (α) that results from the deuteron-triton (d-t) nuclear fusion, thereby effectively removing the negative muon (μ) from the muon-catalysis process altogether. Even if muons (μ's) were absolutely stable, each negative muon (μ) could catalyze, on average, only about 100 d-t nuclear fusions before sticking to an alpha particle (α), which is only about one-fifth the number of d-t fusions needed to produce "break-even," where more thermal energy is generated than the electrical energy that is consumed to produce the muons (μ's) in the first place, according to Jackson's rough 1957 "guesstimate."

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%), which could mean as many as about 200 (or perhaps even about 250) muon-catalyzed d-t fusions per muon (μ). (Interestingly, very detailed and involved 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 0.5% (or perhaps even about 0.4%) to be somewhat mysterious.) Unfortunately, even 200 (or perhaps even 250) d-t nuclear fusions are still not quite enough even to reach break-even, much less have enough to convert the thermal energy released into more useful electrical energy and have any left over to sell to the commercial electrical power "grid." The conversion efficiency from thermal energy to electrical energy is only about 40% and some of that electrical energy will have to be recycled to make more negative muons (μ's) to keep the d-t nuclear fusion fires burning.

One of the favorite and apparently preferred ways to make negative muons (μ's) is to accelerate deuterons (d's) to have kinetic energies of about 800 MeV (in the Lab frame) using one or more particle accelerators, such as a linear accelerator (LINAC) and/or a cyclotron (with either superconducting or non-superconducting magnets), and smash the accelerated deuterons (d's) into an appropriate target, such as a gas of molecular Deuterium (d-d) and molecular Tritium (t-t), for example. Smashing the deuterons (d's) having a kinetic energy of about 800 MeV into other neutron-containing nuclei creates a fair number of negative pions (π's), among other things. As long as these negative pions (π's) are kept away from nuclei that would strongly absorb the strongly-interacting negative pions (π's), each negative pion (π) will generally decay after about 26 nanoseconds (in its rest frame) into a negative muon (μ) and a muon antineutrino (ν_μ-bar). The best recent "guesstimate" of the electrical "energy cost" per negative muon (μ) is about 6 GeV (billion electron Volts), using these deuterons (d's) that are accelerated to have kinetic energies of about 800 MeV, with accelerators that are (coincidentally) about 40% efficient at taking electrial energy from the Alternating Current (AC) mains (the plugs on the wall) and accelerating the deuterons (d's) using this electrical energy.

Some have proposed very innovative "hybrid" fusion/fission schemes to use the copious neutrons produced in muon-catalyzed d-t nuclear fusions to "breed" fissile (fissionable) fuels, such as Uranium-233, from "fertile" materials, such as Thorium-232, for example. The fissile fuels that have been bred can then be "burned," either in a convential super-critical nuclear fission reactor or, better yet, in an unconventional sub-critical fission "pile," not unlike the accelerator-driven systems (ADS) that have been proposed for, and in some places are 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, as well as for the Energy Amplifier devised by Physics Nobel Laureate Carlo Rubbia among others.

Except for refinements such as these, not all that much has changed in nearly half a century since Jackson's assessment of the feasibility of muon-catalyzed fusion, other than Vesman's prediction of the hyperfine resonant formation of d-μ-t, 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 can be found."

References

F.C. Frank, Nature 160, 525 (1947).
Ya.B. Zel'dovitch, Doklady Akad. Nauk U.S.S.R. 95, 493 (1954).
L.W. Alvarez et al., Phys. Rev. 105, 1127 (1957).
J.D. Jackson, "Catalysis of Nuclear Reactions between Hydrogen Isotopes by μ-Mesons," Phys. Rev., 106, 330, April 15, 1957.
Rafelski, Johann and Steven E. Jones (1987). "Cold Nuclear Fusion". Scientific American, v. 257 #1, pp. 84–89.

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