energy produced by the plasma Number density is the density in particles per unit volume of the respective fuels (or just one fuel, in some cases) Cross section is a measure of the probability of a fusion event, which is based on the plasma temperature Energy per reaction is the energy released in each fusion reaction This equation is typically averaged over a population of ions which has a normal distribution. The result is the amount of energy being created by the plasma at any instant in time. Lawson then estimated the radiation losses using the following equation: where N is the number density of the cloud and T is the temperature. For his analysis, Lawson ignores conduction losses. In reality this is nearly impossible; practically all systems lose energy through mass leaving the plasma and carrying away its energy. By equating radiation losses and the volumetric fusion rates, Lawson estimated the minimum temperature for the fusion for the deuterium–tritium (D-T) reaction to be 30 million degrees (2.6 keV), and for the deuterium–deuterium (D-D) reaction to be 150 million degrees (12.9 keV). Extensions into nτE The confinement time measures the rate at which a system loses energy to its environment. The faster the rate of loss of energy, , the shorter the energy confinement time. It is the energy density (energy content per unit volume) divided by the power loss density (rate of energy loss per unit volume): For a fusion reactor to operate in steady state, the fusion plasma must be maintained at a constant temperature. Thermal energy must therefore be added at the same rate the plasma loses energy in order to maintain the fusion conditions. This energy can be supplied by the fusion reactions themselves, depending on the reaction type, or by supplying additional heating through a variety of methods. For illustration, the Lawson criterion for the D-T reaction will be derived here, but the same principle can be applied to other fusion fuels. It will also be assumed that all species have the same temperature, that there are no ions present other than fuel ions (no impurities and no helium ash), and that D and T are present in the optimal 50-50 mixture. Ion density then equals electron density and the energy density of both electrons and ions together is given by where is the temperature in electronvolt (eV) and is the particle density. The volume