Using Fusion
The product of the fusion reactions suitable for use on a human scale are neutrons or protons, and a heavier nucleus than the incoming nuclei (for instance D+T produces a 4He nucleus, also known as an alpha particle, as shown above, plus 17.6 MeV - 2.75 pJ - of energy). The idea of using these reactions is that if the products of the reaction can be made to slow down in the fusing medium, they can be used to help maintain the reaction temperature, and if neutrons are produced they can escape the medium to heat up the surrounding materials, and their coolants then used at high temperature to generate electricity using a conventional steam or gas turbine.
The energy released is partitioned among the reaction products inversely with their mass, and they carry it away as kinetic energy. About one hundred million billion D+T fusion reactions create enough heat for a cup of hot coffee. The reactions are difficult to achieve, because the nuclei have a positive electrical charge and therefore strongly repel each other. This can be overcome if their kinetic energy is large enough to bring them close enough that the (attractive) strong nuclear force pulls the nuclei together.
The measure of the kinetic energy distribution of a group of particles is its temperature, and the temperatures required for the above close approach, a few million degrees, is so high that electrons become completely separated from the nuclei, forming an ionised gas, or plasma.
Plasma Heating
Heating a plasma requires putting more energy into the plasma than leaks out. In magnetic confinement, energy can be lost from the plasma by conduction and by radiation, convection playing only a very weak role in heat transfer due to the low plasma gas pressure. Radiation inside the plasma comes in two forms - "bremmstrahlung" (braking radiation) due to the deceleration and acceleration of charged particles as they interact with one another, and syncrotron (cyclotron) radiation due to the continuous orbiting of charged particles round the field lines (i.e due to their corresponding acceleration). In addition at the plasma edge "line" radiation occurs as the bound electrons in not fully ionised atoms decay into lower energy states. Conduction is due to the particles leaving the system due to collisions with other particles ejecting them or bringing them into a region where the field lines lead out of the system, such as in the plasma divertor. Usually, the larger the ratio of plasma volume to surface, the lower the overall power loss due to conduction.
(from D.R.Sweetman, Nucl. Fus. 13 (1973) 157-165)
When a current flows in a plasma, it gets hot due to its resistance, which is a manifestation of collisions between electrons and ions. Plasma resistance heating, however, gets increasingly weaker with increasing plasma temperature, and at about 10 million °C, resistive heating alone cannot overcome even radiation power losses (i.e the plasma can get no hotter).
Alpha particle heating is produced when the 4He nuclei resulting from the fusion reactions are trapped by the magnetic field and slow down by colliding with plasma electrons, helping to keep the plasma hot. However there are insufficient of these reactions at 10 million °C to heat the plasma up - about 100 million °C is needed. Bridging the gap requires external heating schemes.
One such method is neutral injection heating. Fuel atoms are accelerated as ions, neutralised by collisions with a gas, then cross the magnetic field, where they are ionized by the plasma and trapped by the magnetic field. They then slow down, transferring their energy to the plasma by collisions (mainly with electrons if the beam particle energy is high enough), thus heating it.
Another method is radio frequency heating, which introduces electromagnetic waves into the plasma. If an electromagnetic wave interacts with particles of various velocities, some will be travelling slower than the wave, and some faster. Usually more particles exist travelling a bit slower than the wave than a bit faster, so electromagnetic waves will preferentially experience drag and be damped by the plasma. This collisionless (or Landau) damping, transfers energy between the waves and the plasma particles. The energy is delivered to the plasma by antennas or wave guides at the plasma edge. The frequencies are tuned so that the energy is absorbed in the appropriate region of the plasma and by the appropriate particles. The plasma has essentially three main "resonant" frequencies where heating is most effective - at the electron and ion cyclotron frequencies, and at the lower hybrid frequency. The first two are the frequencies at ehich the ions and electrons orbit the magnetic field lines as they spiral round the torus. Waves at the lower hybrid frequency propagate well in plasma which has electric fields and magnetic fields perpendicular, typical of the plasma edge.
Both these additional heating systems (beams and radio frequency) can be arranged to also impart momentum preferentialy to the electrons relative to the ions. This allows them to contribute to driving the plasma current, which supplements the current drive provided inductively by transformer action in the tokamak. The pressure profiles within the plasma can also be adjusted by the heating schemes so that the plasma generates a "bootstrap" current, i.e internally drives part of its own plasma current. These features allow the tokamak burn to be stretched well beyond the inductive limit of transformer action, and should allow steady state operation.
The net result of the heating and loss channels in a plasma can be summarised in a single parameter, the energy confinement time of the plasma (t). The energy input to the plasma from fusion reactions scales with the square of the density (n) times the reactivity, which scales with the square of the plasma temperature (T). For this to overcome the losses it must be greater than the net energy leaving the plasma, which is proportional to the quotient of the pressure (nT) and the confinement time. This reduces to the fact that the fusion triple product ntT must be above a certain value for a successful confinement scheme.
Power Amplification, Q
For inertial fusion or magnetic confinement to make an attractive source of electricity, the net electrical energy input into the power plant must be much less than the electrical energy output. As any scheme will need to consume energy to drive internal systems, it will at least be necessary that the integrated thermal power out of the plasma is much greater than the integrated thermal power in. Thus a necessary condition for a fusion power source is that the ratio of these two thermal powers, the "power amplification" (Q), be sufficiently large.
Taking account of the internal system inefficiencies, for example the thermal conversion efficiency of heat into electricity in a turbogenerator system (~35% for steam) and the efficiency of converting electrical power delivered to the heating systems to thermal power to the plasma (~80%), Q>10 is considered a reasonable target for a proof of principle in ITER, whereas Q>30-50 would be desirable for good overall plant efficiency (>25%) in a reactor producing electricity.