Lawson Criterion
The amount of energy created in a fusion reaction is determined by the number of particles colliding and fusing (represented by the particle density n), their energy (represented by their temperature T) which must be sufficient to overcome their electrostatic repulsion and the characteristic time over which the particles retain that energy against losses (denoted by the energy confinement time 𝜏E).
In 1955 J.D. Lawson showed that for the rate of energy generated by fusion reactions to exceed the rate of energy loss by electromagnetic radiation (so-called “ignition”) the product of density and confinement time, n𝜏E , must exceed a certain value which is temperature dependent. For D-T fusion the required value of n𝜏E has a minimum at ~ 300 million kelvin (20 times the temperature at the core of the sun) and the requirement for ignition at this temperature is
n𝜏E > 1.5×1020 m-3 s. This is the so-called Lawson Criterion.
A more useful and commonly used figure of merit is the “fusion triple product” nT𝜏E. For D-T fusion, the required value of nT𝜏E for ignition has a minimum at about 150 million kelvin and at this temperature the requirement is
nT𝜏E > 3.5×1028 m-3 K s.
Because of the high values involved, physicists often refer to plasma temperatures by their equivalent energies in electron volts (eV) or kilo-electron volts (keV). One keV corresponds to 11.6 million kelvin and in these units the minimum ignition requirement for D-T fusion becomes nT𝜏E > 3×1021 m-3 keV s.
For magnetic confinement systems that produce output power for durations longer than the energy confinement time, operation at plasma parameters slightly below the Lawson criterion is normally desirable. Extra power is then supplied to the system to maintain the fusion reaction, which allows the plasma to be controlled by varying the amount of externally injected power. In such systems, the ratio of the fusion power to the externally supplied power is usually denoted by the symbol Q. Designs typically aim to achieve Q≥30 to keep the fraction of electricity that is recirculated into the heating and supporting infrastructure systems acceptable. The heating systems may also be used to maintain the plasma current and control its profile.
