Editing Fusion power (section)

=== Cross section ===
[[File:Fusion rxnrate.svg|upright=1.5|thumb|The fusion reaction rate peaks with temperature within the [[Gamow window]]. Modern tokamaks achieve ~8 keV (100 million kelvin). At these temperatures the D-T reaction is ~100 times more favourable than others.]]

A reaction's [[cross section (physics)|cross section]], denoted σ, measures the probability that a fusion reaction will happen. This depends on the relative velocity of the two nuclei. Higher relative velocities generally increase the probability, but the probability begins to decrease again at very high energies.<ref name="osti.gov">{{cite report |url=https://digital.library.unt.edu/ark:/67531/metadc872035/ |title=Fusion cross sections and reactivities |last1=Miley |first1=G. H. |last2=Towner |first2=H. |date=June 17, 1974 |doi=10.2172/4014032 |osti=4014032 |last3=Ivich |first3=N. |type=Technical Report |via=Osti.gov|doi-access=free }}</ref>

In a plasma, particle velocity can be characterized using a [[probability distribution]]. If the plasma is [[Thermalisation|thermalized]], the distribution looks like a [[Gaussian curve]], or [[Maxwell–Boltzmann distribution]]. In this case, it is useful to use the average particle cross section over the velocity distribution. This is entered into the volumetric fusion rate:<ref name="Lawson">{{cite journal |last=Lawson |first=J. D. |date=December 1, 1956 |title=Some Criteria for a Power Producing Thermonuclear Reactor |journal=Proceedings of the Physical Society. Section B |publisher=IOP Publishing |volume=70 |issue=1 |pages=6–10 |doi=10.1088/0370-1301/70/1/303 |bibcode=1957PPSB...70....6L |issn=0370-1301}}</ref>

:<math>P_\text{fusion} = n_A n_B \langle \sigma v_{A,B} \rangle E_\text{fusion}</math>

where:

* <math>P_\text{fusion}</math> is the energy made by fusion, per time and volume
* ''n'' is the number density of species A or B, of the particles in the volume
* <math>\langle \sigma v_{A,B} \rangle</math> is the cross section of that reaction, average over all the velocities of the two species ''v''
* <math>E_\text{fusion}</math> is the energy released by that fusion reaction.