The fusion energy gain factor, usually expressed with the symbol Q, is the ratio of fusion power produced in a nuclear fusion reactor to the power required to maintain the plasma in steady state. The Sun is a natural fusion reactor. ... The deuterium-tritium fusion reaction is considered the most promising for producing fusion power. ... This article is about plasma in the sense of an ionized gas. ... For alternative meanings see steady state (disambiguation). ...

In a fusion power reactor a plasma must be maintained at a high temperature in order that nuclear fusion can occur. Some of this power comes from the fraction of the fusion power contained in charged products which remain in the plasma. This power may be designated f_chP_fus. The rest, designated P_heat comes from external sources required for heating, some of which may also serve additional purposes like current drive and profile control. This power is lost through various processes to the walls of the plasma chamber. In most reactor designs, various constraints result in this heat leaving the reactor chamber at a relatively low temperature, so that little or none of it can be recovered as electrical power. In these reactors, electrical power is produced from the fraction of the fusion power contained in neutrons, (1-f_ch)P_fus. The neutrons are not held back by the magnetic fields (in magnetic confinement fusion) or the dense plasma (in inertial confinement fusion) but are absorbed in a surrounding "blanket". Due to various exothermic and endothermic reactions, the blanket may have a power gain factor a few percent higher or lower than 100%, but that will be neglected here. The neutron power heats a working medium such as helium gas or liquid lithium to a high temperature, and the working medium is used to produce electricity at some efficiency η_elec, so that P_elec = η_elec(1-f_ch)P_fus. A fraction f_recirc of the electrical power is recirculated to run the reactor systems. Power is needed for lighting, pumping, producing magnetic fields, etc., but most is required for plasma heating so we can write P_heat = η_heatP_elec, where η_heat is substantially the efficiency with which electrical power is converted to the form of power needed to heat the plasma. The magnetic fusion energy (MFE) program seeks to establish the conditions to sustain a nuclear fusion reaction in a plasma that is contained by magnetic fields. ... In inertial confinement fusion (ICF), nuclear fusion reactions are initiated by heating and compressing a target – a pellet that most often contains deuterium and tritium – by the use of intense laser or ion beams. ... Exothermic has several meanings, including: In biology, an exothermic or poikilothermic animal is one that requires external sources of heat (usually sunlight) to maintain its internal temperature: for example, reptiles. ... Endothermic can mean: in chemistry, a type of process that absorbs heat from its surroundings. ...

The heating power can thus be related to the fusion power by the following equation:

P_heat = η_heatf_recircη_elec(1-f_ch)P_fus

The fusion energy gain factor is then

Q = P_fus/P_heat = (η_heatf_recircη_elec(1-f_ch))^-1

For the D-T reaction, f_ch = 0.2. Efficiency values depend on design details but may be in the range of η_heat = 0.7 and η_elec = 0.4. The purpose of a fusion reactor is to sell power, not to recirculate it, so a practical reactor must have f_recirc = 0.2 approximately. Lower would be better but will be hard to achieve. Using these values we find for a practical reactor Q = 22. Of course, Q = 15 might be enough and Q = 30 might be achievable, but this simple calculation shows the magnitude of fusion energy gain required.

The goal of ignition, a plasma which heats itself by fusion energy without any external input, corresponds to infinite Q. Note that ignition is not a necessary condition for a practical reactor. On the other hand, achieving Q = 20 requires quality of confinement almost as good as that required to achieve ignition, so the Lawson criterion is still a useful figure of merit. The condition of Q = 1 is referred to as breakeven. It is somewhat arbitrary, but it does mean that a significant fraction (20%) of the heating power comes from fusion, so that fusion heating can be studied. Above Q = 5 the fusion heating power is greater than the external heating power. 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 one channel of energy loss that is independent of the confinement scheme and practically impossible to avoid is Bremsstrahlung radiation. Like the fusion power density, the Bremsstrahlung power density depends on the square of the plasma density, but it does not increase as rapidly with temperature. By equating the two power densities, one can determine the lowest temperature for which the fusion power can overcome the Bremsstrahlung power. This ignition temperature is about 4 keV for the D-T reaction and about 35 keV for the D-D reaction. Bremsstrahlung, German for braking radiation, is electromagnetic radiation produced by the acceleration of a charged particle, such as an electron, when deflected by another charged particle, such as an atomic nucleus. ...