Nuclear reactions are actually very similar to exothermic chemical
reactions. In exothermic reactions, the reactants are combined through
burning, and thermal energy released. The reactants started in a higher
energy state, and through the burning process, they came into a lower
energy state. The difference in energy between these states is what is
released in an exothermic reaction. Nuclear fusion works by essentially
the same principle: releasing the energy difference between the initial
and final states of a reaction.
Fusion can be self-sustaining for the same reasons a fire is self-sustaining. When you make a fire the reactants (some fuel with carbon and the oxygen in the air) are initially in a higher energy state. They are also repelled by one another. However, get them going fast enough (e.g. by applying heat) and they will snap together (forming mostly carbon dioxide), releasing the energy difference I mentioned earlier. The released thermal energy allows more of the reactants to get close enough and snap together, releasing more energy until there is no more fuel to burn.
Nuclear fusion is a bit more extreme than normal exothermic reactions, and in order to understand what's going on we need to understand nuclear binding energy.
Nuclear fusion works through releasing the binding energy of a system of nuclei. We will consider the case that the ITER
research project is investigating: deuterium-tritium reactions.
Deuterium is a hydrogen atom with one neutron in its nuclei. This makes it about twice as heavy as hydrogen. Deuterium is useful for man-made fusion reactions because it is stable and can be extracted from sea water fairly easily.
Tritium (as you may have guessed from the name) is a hydrogen atom with two neutrons. This makes it about three times as heavy as hydrogen. Tritium is radioactive and not as easy to come by as deuterium, but it's significantly easier to fuse with deuterium than other deuterium atoms.
An atom that has the same number of protons as a particular element but a different number of neutrons is called an "isotope" of that element. Deuterium and tritium are therefore isotopes of hydrogen.
As you said in your question, fusion of deuterium and tritium requires temperatures of about 100 million Kelvin.
That's all nice to say, but why do we need such ridiculous energies to fuse these them together, and how does their fusing even release any energy?
To understand why fusion releases energy, let's explore binding energy a bit more. Suppose we have a system that is made up of our deuterium and tritium pre-fusion; that is, they are sitting around by themselves. If we measured the energy of the system in this state, and then measured it after the two fuse to become a helium isotope, what would you expect the difference to be? It turns out that if you measure the energy after you'll find that the system has less of it! The difference is what we call the binding energy or the mass defect. Both terms are appropriate since mass and energy are equivalent. The system started in a higher energy state, and through the fusion process, ended up in a lower energy state. The difference in those two energies is what we are trying to harness in a fusion reactor.
The reason fusion doesn't happen spontaneously in most scenarios is a result of the electric or "Coulomb" repulsion between the deuterium and tritium. As both of them are hydrogen isotopes, they both have one proton. These protons have a positive electric charge, and thus repel one another. The result is a kind of energy barrier keeping the deuterium and tritium from getting close to one another. In order to overcome this barrier, we need to give them monumental amounts of thermal energy. When they're going fast enough, they can overcome the energy barrier. Once this happens, another force called the strong force takes over. The nuclei now become attracted to one another, and fuse together.
This diagram roughly plots the energy versus the separation for the deuterium and tritium:
The bottom of the dip on the left is the state they obtain after fusing together (forming a helium-4 nucleus). The rightmost would be the energy they have at rest. This energy is also represented by the dashed line on the diagram. The hill in the center is the energy barrier that needs to be overcome for the two to fuse together. Once enough energy is gained to overcome the barrier, it goes down into the left dip and the net energy released is the binding energy.
This is the deuterium-tritium fusion reaction with the reactants on the left and the products on the right:
Fusion processes are theoretically self-sustaining, since the energy released provides energy for more nuclei to overcome the barrier. In deuterium-tritium reactions, most of the energy is released as a high energy neutron. As more nuclei gain this thermal energy and overcome the energy barrier, they release their binding energy and the process can go on as long as there is more fuel to fuse. This is often referred to as a "chain reaction" since the number of nuclei that fuse together increases exponentially with time.
(published on 02/28/12)