Nuclear fusion

Figure 1.1: Binding energy per nucleon versus atomic mass number (courtesy of J.V. Hofmann, IPP Garching)

Figure 1.1 of the binding energy per nucleon versus atomic mass number shows that just as mass can be converted into energy by splitting apart heavy nuclei in fission, it also occurs when light nuclei fuse together. In both cases the mass of the reactants exceeds that of the products, thus yielding energy $E$ according to Einstein's relation, $E = \Delta m \, c^2$, where $\Delta m$ is the mass difference and $c$ the speed of light in vacuo. The direct conversion of mass to energy via fusion is the most fundamental source of energy in the universe; it is the process that fuels the stars. We concentrate on the reactions which convert hydrogen and its isotopes to helium, since the energy gain is clearly greatest for these.

Figure 1.2: Plot of the reaction probability for the 3 of the accessible fusion reactions (courtesy of J.V. Hofmann, IPP Garching)

Many fusion reactions (e.g., proton-proton fusion) require prohibitively large particle energies to occur for the rate of the process to be appreciable. However, examples of fusion reactions which could potentially be used as the basis for a terrestrial energy source are:

$$\mathrm{D}_1^2 + \mathrm{D}_1^2 \rightarrow \mathrm{T}_1^3 + \mathrm{H}_1^1 + 4.0 \mathrm{MeV}$$ (1.1)

$$\mathrm{D}_1^2 + \mathrm{D}_1^2 \rightarrow \mathrm{He}_2^3 + \mathrm{n}_0^1 + 3.25 \mathrm{MeV}$$ (1.2)

$$\mathrm{D}_1^2 + \mathrm{D}_1^2 \rightarrow \mathrm{He}_2^4 + 23.0 \mathrm{MeV}$$ (1.3)

$$\mathrm{D}_1^2 + \mathrm{T}_1^3 \rightarrow \mathrm{He}_2^4 + \mathrm{n}_0^1 + 17.6\mathrm{MeV}.$$ (1.4)

Of these, the D-T fusion reaction (1.4) has by far the largest cross-section at low energies (see figure 1.2) and is therefore amongst the most promising of the candidates. Both deuterium and tritium are hydrogen isotopes and exist in gaseous form above roughly 20 Kelvin.

As a potential source of energy, D-T fusion is attractive for a number of reasons. Firstly, the fuels are naturally abundant. Vast quantities of deuterium are present in sea-water, and tritium can be bred by neutron bombardment of lithium, a common element in the earth's crust. It is estimated that, based on D-T fusion, there is enough lithium on earth to provide energy for many tens of thousands of years.

The reaction is also safe in that it does not generate hazardous waste; indeed the sole by-product is helium, a chemically inert gas that poses no threat to the environment. The large neutron flux from the reaction will naturally result in some activation of the surrounding materials (e.g. the containment vessel and support structure), though with proper choice these should be relatively short-lived. Moreover, whilst the nuclear fission process is a finely controlled chain reaction, fusion is not, meaning that any containment failure in a hypothetical fusion reactor would merely lead to spontaneous extinction of the reaction rather than a dangerous reactor meltdown. The fuel inventory in a reactor would be extremely small (typically just a few grammes of D-T mixture), further inhibiting the scope of accidents. It is also impossible to produce material suitable for use in nuclear weapons via fusion reactions, since the by-products (helium ``ash'') are non-fissile.

Since fusion relies on the strong nuclear force which is effective only at ranges of the order of the nuclear dimensions, the reacting nuclei must come into direct contact. Since the nuclei are positively charged, they must possess considerable amounts of kinetic energy in order to overcome the repulsive Coulomb force between them. However, directly imparting atoms with large energies and colliding them with a cooler target, such as using an accelerator to bombard a tritium target with deuterium, will not produce net fusion power. This is because Coulomb collisions, which slow down the projectile particles, have a far larger probability of occurring over fusion events. A better solution is to confine the reactants at very high temperatures such that the particles' thermal velocity is sufficient to overcome their mutual Coulomb repulsion. Only at temperatures of roughly 10 keV ($10^8$ Kelvin)^1.1 will fusion occur due to random thermal collisions. This far exceeds the ionization energies of hydrogen and the lighter atoms, meaning that the gaseous reactants are further separated into electrons and ions whilst maintaining global electrical neutrality. This is known as the plasma state, the so-called fourth state of matter. The requisite temperatures must also be coupled with high fuel densities to yield a substantial rate of fusion. These ambient conditions occur naturally only in extreme environments, such as those in the centre of a star, and the challenge of re-creating them on earth is formidable. Predictably, any material in contact with the hot plasma will be instantly vaporized, necessitating the isolation of the plasma from its containment vessel. Various schemes for achieving this have been proposed, including the use of inertial confinement and heavy ion beams, however magnetic confinement is generally regarded as the best prospect for near-term fusion reactors.