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In nuclear fusion research, the Lawson Criterion is an important general measure of a system that defines the conditions needed for a fusion reactor to generate net output energy -- that is, produce more energy in the fusion reactions than is lost in thermal and other radiation out of the fuel. The Lawson Criterion combines three important factors, the temperature of the fuel (which defines the reaction rate), the density of the fuel (how many reactions per unit volume), and the time that the energy of the reactions remains inside the reaction, the so-called "confinement time".
In order to undergo fusion, atoms must be given enough energy to overcome the Coulomb barrier between them. Since this number is easily defined, it would seem that a fusion fuel would have to be at that temperature in order for the fuel to fuse. However this is not the case, due to the Maxwellian distribution of energies, some of the fuel will be at significantly higher temperatures than the rest. This fuel can then undergo a fusion reaction, releasing significant energy, which can then heat the surrounding nuclei up to the point where they will undergo fusion as well. This "lower temperature" is known as the fusion ignition temperature. For the easiest reaction, a 50-50 mix of deuterium and tritium, ignition temperature is about 4.5 x 107 K.
Reaching ignition temperature does not automatically define a system in which net power is produced, however. Heat is lost to the surroundings through a variety of methods, which may more than make up for the energy gained in the reactions. The energy must be retained in the system, at least to some degree, for the reaction to become self-sustaining. Likewise the amount of energy being generated is also defined by the number of particles involved, simply increasing the density of the fuel will increase the overall rate. These three factors are key, the density and temperature define the rate of energy addition, which is balanced by the rate of energy loss. Together they create the Lawson criterion.
For the D-T fusion reaction the Lawson criterion requires about 1021 keV m3 sec. This number has not yet been achieved in any reactor, although the latest generations of machines have come close. For instance, the TFTR has achieved the densities and energy lifetimes needed to achieved Lawson at the temperatures it can create, but it cannot create the temperatures at the same time. ITER aims to do both.
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