Nuclear fusion occurs when two atomic nuclei come close enough for the attraction governed by the strong nuclear force to overcome the electromagnetic repulsion of the positive charges of the individual nuclei. Usually, this requires temperatures and pressures normally found in the cores of stars (i.e. ≈ 15,000,000°K, 15,000 kg/m3). In this scenario, atoms as we know them cease to exist, replaced by a plasma, that is to say a soup of delocalised electrons and nuclei. Here, when two nuclei collide with enough velocity, the two nuclei fuse, releasing a large quantity of energy, because 3He, resulting from the fusion of 2H (deuterium) with 1H (hydrogen), is slightly less massive than the two reactants. By e=mc2, this small change in mass results in a large output of energy, thus making fusion a very desirable source of energy, since this process releases far more than other methods, like nuclear fission, because splitting atoms releases much less energy than fusing them.
In theory, it is possible for regular molecules to fuse at standard temperatures and pressures: covalent bonding keeps the nuclei relatively close together, and their vibrations (caused by the internal energy resulting from their temperature being above absolute zero), on very rare occasions bring the nuclei close enough together to fuse. Recreating and maintaining conditions such as those described before still requires more energy than is gained from the fusions, so this is not yet viable commercially, thus we want another way for the nuclei to come close enough to fuse. So, instead of trying to accelerate the nuclei to extremely high speeds, we can instead replace the electrons in the reactant molecules with muons.
Muons form orbitals in almost exactly the same way as electrons, but muons have a mass ≈200x larger than an electron, so, given the same energy and angular momentum, muons’ orbital radii will be ≈200x closer to the nucleus than in ‘regular’ molecules. (Other characteristics of the atoms would change if they were stable too, like the transition energy (energy required to change the energy level of a given atom) becoming higher, which would shift all the spectral lines of the original atom to higher frequencies. Most things that normally burn with a visible flame would produce ultraviolet light instead, for example.) Now, the same vibrations that were present in the old molecules bring the two nuclei much closer to the point at which the strong force can overcome the electromagnetic repulsion, thereby facilitating fusion much more often. This fact also means that fusion can happen at much lower temperatures, since the nuclei do not need to vibrate much at this proximity to fuse, so such fusion has been observed even close to absolute zero.
This begs an obvious question: why aren’t we using muon-catalysed fusion to power modern civilisation? To begin with, muons are not at all abundant naturally, so the only way to generate a reliable supply of muons is by using a particle accelerator. However, this again requires a lot of energy, about -5GeV/muon. Muons are also easily distracted, that is to say they decay in 2×10-6 seconds (by μ–→e–+νμ+νe). Luckily, we don’t need a muon for every single reaction, since after one fusion takes place, the muon can move onto another atom, replacing electrons there (in the short time in which it has not decayed). However, muons can sometimes become stuck to a fused atom, and therefore cannot facilitate any further fusions. So, most muons facilitate ≈150 fusion reactions before they either become ‘stuck’, or decay as above, and each fusion reaction described above releases around 18MeV. This gives us:
150×18 MeV=2.7 GeV
This is, in fact, a maximum value, as 1H+1H, 2H+2H, etc. release less energy than this. So even in a best-case scenario, we are only just over half-way to breaking even, since we make a net loss of 2.3GeV overall. This doesn’t even begin to consider that in order to make this commercially viable, we would need a surplus in the region of 10-20GeV…
Is there any hope for cold fusion? For the moment, the limiting factors on net production of energy by this method are the cost of making the muons in the first place, coupled with the relative inefficiency of the muons as they become stuck to fused atoms. So, we either need a method to make muons at a lower cost of energy, ideally somewhere closer to -3GeV or -2GeV, to figure out how to stop as many muons getting stuck to the 4He atoms, or, indeed, how to ‘unstick’ them once they’re stuck. The first might be a little more of an engineering issue, although all three stray very close to theoretical limits, so are, in fact, rather challenging ‘engineering issues’. In short, cold fusion exists, but won’t be powering the world anytime soon.