Fusion energy gain factor

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 condition of Q = 1 is referred to as breakeven.

In a fusion power reactor, a plasma must be maintained at a high temperature in order for nuclear fusion to occur. Some of this power comes from the fraction f_ch of the fusion power P_fus 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 contained by the magnetic fields (in magnetic confinement fusion) nor the dense plasma (in inertial confinement fusion) but are absorbed in a surrounding walls (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 would be used to heat a working medium such as helium gas or liquid lithium to a high temperature, and the working medium is then 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_heat f_recircP_elec, where η_heat is substantially the efficiency with which electrical power is converted to the form of power needed to heat the plasma.

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