Nuclear fusion

In physics, nuclear fusion is the process by which two nuclei join together to form a heavier nucleus. It is accompanied by the release or absorbtion of energy depending on the masses of the nuclei involved. The iron nucleus has the largest binding energy of all nuclei and so is the most stable. The fusion of two nuclei to produce a nucleus lighter than iron generally gives off energy while the fusion of nuclei heavier than iron absorbs energy. Nuclear fusion of light elements is the energy source which causes stars to shine and hydrogen bombs to explode. Nuclear fusion of heavy elements occurs in the extreme conditions of a supernova explosion. Nuclear fusion in stars and supernovae is the primary process by which new natural elements are created.

Important fusion reactions

Astrophysical reaction chains

The most important fusion process in nature is that which powers the stars. The net result is the fusion of four protons into one alpha particle, with the release of two positrons, two neutrinos, and energy, but several individual reactions are involved, depending on the mass of the star. For stars the size of the sun or smaller, the proton-proton chain dominates. In heavier stars, the CNO cycle is more important. See stellar nucleosynthesis.

Related Topics:
Proton - Alpha particle - Positrons - Neutrino - Proton-proton chain - CNO cycle - Stellar nucleosynthesis

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Criteria and candidates for terrestrial reactions

In man-made fusion, the primary fuel is not constrained to be protons and higher temperatures can be used, so reactions with larger cross-sections are chosen. This implies a lower Lawson criterion, and therefore less startup effort. Another concern is the production of neutrons, which activate the reactor structure radiologically, but also have the advantages of allowing volumetric extraction of the fusion energy and tritium breeding. Reactions that release no neutrons are referred to as aneutronic.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

In order to be useful as a source of energy, a fusion reaction must satisfy several criteria. It must:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

• ... be exothermic. This one is obvious, but it limits the reactants to the low Z side of the curve of binding energy. It also makes helium He-4 the most common product because of its extraordinarily tight binding, although He3 and T also show up.
• ... involve low Z nuclei. This is because the electrostatic repulsion must be overcome before the nuclei are close enough to fuse.
• ... have two reactants. At anything less than stellar densities, three body collisions are too improbable.
• ... have two or more products. This allows simultaneous conservation of energy and momentum without relying on the (weak!) electromagnetic force.
• ... and conserve both protons and neutrons. The cross sections for the weak interaction are too small.

Not many reactions meet these criteria. The most interesting reactions are the following.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

p (proton), D (deuterium), and T (tritium) are shorthand notation for the first three isotopes of hydrogen. For reactions with two products, the energy is divided between them in inverse proportion to their masses, as shown. In most reactions with three products, the distribution of energy varies. For reactions that can result in more than one set of products, the branching ratios are given.

Related Topics:
Proton - Deuterium - Tritium

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Some reaction candidates can be eliminated at once.http://theses.mit.edu/Dienst/UI/2.0/Page/0018.mit.theses/1995-130/30?npages=306 The D-6Li reaction has no advantage compared to p-11B because it is roughly as difficult to burn but produces substantially more neutrons. There is also a p-7Li reaction, but the cross section is far too low except possible for Ti > 1 MeV, but at such high temperatures an endothermic, direct neutron-producing reaction also becomes very significant. Finally there is also a p-9Be reaction, which is not only difficult to burn, but 9Be can be easily induced to split into two alphas and a neutron.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

In addition to the fusion reactions, the following reactions with neutrons are important in order to "breed" tritium in "dry" fusion bombs and some proposed fusion reactors:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:n + 6Li ? T + 4He

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:n + 7Li ? T + 4He + n

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

To evaluate the usefulness of these reactions, in addition to the reactants, the products, and the energy released, one needs to know something about the cross section. Any given fusion device will have a maximum plasma pressure that it can sustain, and an economical device will always operate near this maximum. Given this pressure, the largest fusion output is obtained when the temperature is chosen so that

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Note that many of the reactions form chains. For instance, a reactor fueled with T and 3He will create some D, which is then possible to use in the D + 3He reaction if the energies are "right". An elegant idea is to combine the reactions (11) and (12). The 3He from reaction (11) can react with 6Li in reaction (12) before completely thermalizing. This produces an energetic proton which in turn undergoes reaction (11) before thermalizing. A detailed analysis shows that this idea will not really work well, but it is a good example of a case where the usual assumption of a Maxwellian plasma is not appropriate.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Neutronicity, confinement requirement, and power density

Any of the reactions above can in principle be the basis of fusion power production. In addition to the temperature and cross section discussed above, we must consider the total energy of the fusion products Efus, the energy of the charged fusion products Ech, and the atomic number Z of the non-hydrogenic reactant.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Specification of the D-D reaction entails some difficulties, though. To begin with, one must average over the two branches (2) and (3). More difficult is to decide how to treat the T and 3He products. T burns so well in a deuterium plasma that you probably can't get it out even if you want to. The D-3He reaction is optimized at a much higher temperature, so the burnup at the optimum D-D temperature may be low, so it seems reasonable to assume the T but not the 3He gets burned up and adds its energy to the net reaction. Thus we will count the DD fusion energy as Efus = (4.03+17.6+3.27)/2 = 12.5 MeV and the energy in charged particles as Ech = (4.03+3.5+0.82)/2 = 4.2 MeV.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Another unique aspect of the D-D reaction is that there is only one reactant, which must be taken into account when calculating the reaction rate.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

With this choice, we tabulate parameters for four of the most important reactions.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The last column is the neutronicity of the reaction, the fraction of the fusion energy released as neutrons. This is an important indicator of the magnitude of the problems associated with neutrons like radiation damage, biological shielding, remote handling, and safety. For the first two reactions it is calculated as (Efus-Ech)/Efus. For the last two reactions, where this calculation would give zero, the values quoted are rough estimates based on side reactions that produce neutrons in a plasma in thermal equilibrium.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Of course the reactants should also be mixed in the optimal proportions. This is the case when each reactant ion plus its associated electrons accounts for half the pressure. Assuming that the total pressure is fixed, this means that density of the non-hydrogenic ion is smaller than that of the hydrogenic ion by a factor 2/(Z+1). Therefore the rate for these reactions is reduced by the same factor, on top of any differences in the values of

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Thus there is a "penalty" of (2/(Z+1)) for non-hydrogenic fuels arising from the fact that they require more electrons, which take up pressure without participating in the fusion reaction. There is at the same time a "bonus" of a factor 2 for D-D due to the fact that each ion can react with any of the other ions, not just a fraction of them.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

We can now compare these reactions in the following table.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The maximum value of

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Bremsstrahlung losses

The ions undergoing fusion will essentially never occur alone but will be mixed with electrons that neutralize the ions' electrical charge and form a plasma. The electrons will generally have a temperature comparable to or greater than that of the ions, so they will collide with the ions and emit Bremsstrahlung. The Sun and stars are opaque to Bremsstrahlung, but essentially any terrestrial fusion reactor will be optically thin at relevant wavelengths. Bremsstrahlung is also difficult to reflect and difficult to convert directly to electricity, so the ratio of fusion power produced to Bremsstrahlung radiation lost is an important figure of merit. This ratio is generally maximized at a much higher temperature than that which maximizes the power density (see the previous subsection). The following table shows the rough optimum temperature and the power ratio at that temperature for several reactions.http://theses.mit.edu/Dienst/UI/2.0/Page/0018.mit.theses/1995-130/26?npages=306

Related Topics:
Electron - Electrical charge - Plasma - Bremsstrahlung - Opaque - Optically thin

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The actual ratios of fusion to Bremsstrahlung power will likely be significantly lower for several reasons. For one, the calculation assumes that the energy of the fusion products is transmitted completely to the fuel ions, which then lose energy to the electrons by collisions, which in turn lose energy by Bremsstrahlung. However because the fusion products move much faster than the fuel ions, they will give up a significant fraction of their energy directly to the electrons. Secondly, the plasma is assumed to be composed purely of fuel ions. In practice, there will be a significant proportion of impurity ions, which will lower the ratio. In particular, the fusion products themselves must remain in the plasma until they have given up their energy, and will remain some time after that in any proposed confinement scheme. Finally, all channels of energy loss other than Bremsstrahlung have been neglected. The last two factors are related. On theoretical and experimental grounds, particle and energy confinement seem to be closely related. In a confinement scheme that does a good job of retaining energy, fusion products will build up. If the fusion products are efficiently ejected, then energy confinement will be poor, too.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The temperatures maximizing the fusion power compared to the Bremsstrahlung are in every case higher than the temperature that maximizes the power density and minimizes the required value of the fusion triple product. This will not change the optimum operating point for D-T very much because the Bremsstrahlung fraction is low, but it will push the other fuels into regimes where the power density relative to D-T is even lower and the required confinement even more difficult to achieve. For D-D and D-3He, Bremsstrahlung losses will be a serious, possibly prohibitive problem. For 3He-3He, p-6Li and p-11B the Bremsstrahlung losses appear to make a fusion reactor using these fuels impossible. Some ways out of this dilemma are considered — and rejected — in Fundamental limitations on plasma fusion systems not in thermodynamic equilibrium.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~