Lawson criterion
In nuclear fusion research, the Lawson criterion, first derived on fusion reactors (initially classified) by John D. Lawson in 1955 and published in 1957, is an important general measure of a system that defines the conditions needed for a fusion reactor to reach ignition, that is, that the heating of the plasma by the products of the fusion reactions is sufficient to maintain the temperature of the plasma against all losses without external power input. As originally formulated the Lawson criterion gives a minimum required value for the product of the plasma (electron) density ne and the "energy confinement time" .
Later analysis suggested that a more useful figure of merit is the "triple product" of density, confinement time, and plasma temperature T. The triple product also has a minimum required value, and the name "Lawson criterion" often refers to this inequality.
The central concept of the Lawson criterion is the energy balance for any fusion power plant, using a hot plasma. This is shown below:
Net Power = Efficiency × (Fusion − Radiation Loss − Conduction Loss)
Lawson calculates the fusion rate by assuming that any fusion reactor contains a hot plasma cloud which has a Gaussian curve of energy. Based on that assumption, he estimates the first term, the fusion energy coming from a hot cloud using the volumetric fusion equation.
Fusion = Number Density of Fuel A × Number Density of Fuel B × Cross Section(Temperature) × Energy Per Reaction
This equation is typically averaged over a population of ions which has a normal distribution. For his analysis, Lawson ignores conduction losses. In reality this is nearly impossible, practically all systems lose energy through mass leaving. Lawson then estimated the radiation losses using the equation below.
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