Editing Nuclear fusion (section)

===Criteria and candidates for terrestrial reactions===
{{main article|Fusion power#Fuels}}
In artificial fusion, the primary fuel is not constrained to be protons and higher temperatures can be used, so reactions with larger cross-sections are chosen. Another concern is the production of neutrons, which activate the reactor structure radiologically, but also have the advantages of allowing volumetric extraction of the fusion energy and [[tritium]] breeding. Reactions that release no neutrons are referred to as [[Aneutronic fusion|''aneutronic'']].

To be a useful energy source, a fusion reaction must satisfy several criteria. It must:

;Be [[exothermic]]: This limits the reactants to the low ''Z'' (number of protons) side of the [[Nuclear binding energy#Nuclear binding energy curve|curve of binding energy]]. It also makes helium {{SimpleNuclide|link=yes|Helium|4}} the most common product because of its extraordinarily tight binding, although {{SimpleNuclide|link=yes|Helium|3}} and {{SimpleNuclide|link=yes|Hydrogen|3}} also show up.
;Involve low atomic number (''Z'') nuclei: This is because the electrostatic repulsion that must be overcome before the nuclei are close enough to fuse ([[Coulomb barrier]]) is directly related to the number of protons it contains – its atomic number.
;Have two reactants: At anything less than stellar densities, three-body collisions are too improbable. In inertial confinement, both stellar densities and temperatures are exceeded to compensate for the shortcomings of the third parameter of the Lawson criterion, ICF's very short confinement time.
;Have two or more products: This allows simultaneous conservation of energy and momentum without relying on the electromagnetic force.
;Conserve both protons and neutrons: The cross sections for the weak interaction are too small.

Few reactions meet these criteria. The following are those with the largest cross sections:<ref>{{cite book
 |author1         = M. Kikuchi, K. Lackner
 |author2         = M. Q. Tran
 |name-list-style = amp
 |year            = 2012
 |title           = Fusion Physics
 |url             = http://www-pub.iaea.org/books/IAEABooks/8879/Fusion-Physics
 |page            = 22
 |publisher       = [[International Atomic Energy Agency]]
 |isbn            = 9789201304100
 |access-date     = 8 December 2015
 |archive-date    = 8 December 2015
 |archive-url     = https://web.archive.org/web/20151208122642/http://www-pub.iaea.org/books/IAEABooks/8879/Fusion-Physics
 |url-status      = live
}}</ref><ref>{{cite book
|author1=K. Miyamoto
|year=2005
|title=Plasma Physics and Controlled Nuclear Fusion
|publisher=[[Springer-Verlag]]
|isbn=3-540-24217-1
}}</ref>

<!-- Autogenerated using Phykiformulae 0.10 by [[User:SkyLined]]
(1)     D + T    → He   (3.52 MeV ) + n   (14.06 MeV )
(2i)    D + D    → T    (1.01 MeV) + p    (3.02 MeV ) _ _ _ _       _ _50%
(2ii)   _ _ _    → He-3 (0.82 MeV) + n    (3.27 MeV ) _ _ _ _       _ _50%
(3)     D + He-3 → He   (3.6 MeV ) + p    (14.7 MeV )
(4)     T + T    → He   _ _       _ + 2n   _ _        _ _ _ + 11.3MeV
(5)  He-3 + He-3 → He   _ _       _ + 2p   _ _        _ _ _ + 12.9MeV
(6i) He-3 + T    → He   _ _       _ + p    + n        _ _ _ + 12.1MeV _ _57%
(6ii)   _ _ _    → He   (4.8 MeV ) + D    (9.5 MeV  ) _ _ _ _       _ _43%
(7i)    D + Li-6 → 2He  + 22.3 MeV
(7ii)   _ _ _    → He-3 + He      _ + n    _ _        _ _ _ + 1.8 MeV
(7iii)  _ _ _    → Li-7 (0.625 MeV) + p (4.375 MeV)
(7iv)   _ _ _    → Be-7 (0.425 MeV )+ n (2.975 MeV)
(8)     p + Li-6 → He   (1.7 MeV ) + He-3 (2.3 MeV)
(9)  He-3 + Li-6 → 2He  + p       _ _ _    _ _        _ _ _ + 16.9 MeV
(10)    p + B-11 → 3He  _ _       _ _ _    _ _        _ _ _ + 8.7 MeV

-->:{| border="0"
|- style="height:2em;"
|(1)&nbsp;||{{nuclide|link=yes|deuterium}}&nbsp;||+&nbsp;||{{nuclide|link=yes|tritium}}&nbsp;||→&nbsp;||{{nuclide|link=yes|helium|4}}&nbsp;||(&nbsp;||style="text-align:right;"|{{val|3.52|u=MeV}}||)&nbsp;||+&nbsp;||[[Neutron|n<sup>0</sup>]]&nbsp;||(&nbsp;||style="text-align:right;"|{{val|14.06|u=MeV}}||)
|- style="height:2em;"
|(2i)&nbsp;||{{nuclide|link=yes|deuterium}}&nbsp;||+&nbsp;||{{nuclide|link=yes|deuterium}}&nbsp;||→&nbsp;||{{nuclide|link=yes|tritium}}&nbsp;||(&nbsp;||style="text-align:right;"|{{val|1.01|u=MeV}}||)&nbsp;||+&nbsp;||[[Proton|p<sup>+</sup>]]&nbsp;||(&nbsp;||style="text-align:right;"|{{val|3.02|u=MeV}}||)&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;|| 50%
|- style="height:2em;"
|(2ii)&nbsp;||&nbsp;||&nbsp;||&nbsp;||→&nbsp;||{{nuclide|link=yes|helium|3}}&nbsp;||(&nbsp;||style="text-align:right;"|{{val|0.82|u=MeV}}||)&nbsp;||+&nbsp;||[[Neutron|n<sup>0</sup>]]&nbsp;||(&nbsp;||style="text-align:right;"|{{val|2.45|u=MeV}}||)&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;|| 50%
|- style="height:2em;"
|(3)&nbsp;||{{nuclide|link=yes|deuterium}}&nbsp;||+&nbsp;||{{nuclide|link=yes|helium|3}}&nbsp;||→&nbsp;||{{nuclide|link=yes|helium|4}}&nbsp;||(&nbsp;||style="text-align:right;"|{{val|3.6|u=MeV}}||)&nbsp;||+&nbsp;||[[Proton|p<sup>+</sup>]]&nbsp;||(&nbsp;||style="text-align:right;"|{{val|14.7|u=MeV}}||)
|- style="height:2em;"
|(4)&nbsp;||{{nuclide|link=yes|tritium}}&nbsp;||+&nbsp;||{{nuclide|link=yes|tritium}}&nbsp;||→&nbsp;||{{nuclide|link=yes|helium|4}}&nbsp;||&nbsp;||&nbsp;||&nbsp;||+&nbsp;||2&nbsp;[[Neutron|n<sup>0</sup>]]&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||+&nbsp;||style="text-align:right;"|{{val|11.3|u=MeV}}
|- style="height:2em;"
|(5)&nbsp;||{{nuclide|link=yes|helium|3}}&nbsp;||+&nbsp;||{{nuclide|link=yes|helium|3}}&nbsp;||→&nbsp;||{{nuclide|link=yes|helium|4}}&nbsp;||&nbsp;||&nbsp;||&nbsp;||+&nbsp;||2&nbsp;[[Proton|p<sup>+</sup>]]&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||+&nbsp;||style="text-align:right;"|{{val|12.9|u=MeV}}
|- style="height:2em;"
|(6i)&nbsp;||{{nuclide|link=yes|helium|3}}&nbsp;||+&nbsp;||{{nuclide|link=yes|tritium}}&nbsp;||→&nbsp;||{{nuclide|link=yes|helium|4}}&nbsp;||&nbsp;||&nbsp;||&nbsp;||+&nbsp;||[[Proton|p<sup>+</sup>]]&nbsp;||+&nbsp;||[[Neutron|n<sup>0</sup>]]&nbsp;||&nbsp;||&nbsp;||&nbsp;||+&nbsp;||style="text-align:right;"|{{val|12.1|u=MeV}}||&nbsp;|| 57%
|- style="height:2em;"
|(6ii)&nbsp;||&nbsp;||&nbsp;||&nbsp;||→&nbsp;||{{nuclide|link=yes|helium|4}}&nbsp;||(&nbsp;||style="text-align:right;"|{{val|4.8|u=MeV}}||)&nbsp;||+&nbsp;||{{nuclide|link=yes|deuterium}}&nbsp;||(&nbsp;||style="text-align:right;"|{{val|9.5|u=MeV}}||)&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;|| 43%
|- style="height:2em;"
|(7i)&nbsp;||{{nuclide|link=yes|deuterium}}&nbsp;||+&nbsp;||{{nuclide|link=yes|lithium|6}}&nbsp;||→&nbsp;||2&nbsp;{{nuclide|link=yes|helium|4}}&nbsp;||+&nbsp;||style="text-align:right;"|{{val|22.4|u=MeV}}
|- style="height:2em;"
|(7ii)&nbsp;||&nbsp;||&nbsp;||&nbsp;||→&nbsp;||{{nuclide|link=yes|helium|3}}&nbsp;||+&nbsp;||{{nuclide|link=yes|helium|4}}&nbsp;||&nbsp;||+&nbsp;||[[Neutron|n<sup>0</sup>]]&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||+&nbsp;||style="text-align:right;"|{{val|2.56|u=MeV}}
|- style="height:2em;"
|(7iii)&nbsp;||&nbsp;||&nbsp;||&nbsp;||→&nbsp;||{{nuclide|link=yes|lithium|7}}&nbsp;||+&nbsp;||[[Proton|p<sup>+</sup>]]&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||+&nbsp;||style="text-align:right;"|{{val|5.0|u=MeV}}
|- style="height:2em;"
|(7iv)&nbsp;||&nbsp;||&nbsp;||&nbsp;||→&nbsp;||{{nuclide|link=yes|beryllium|7}}&nbsp;||+&nbsp;||[[Neutron|n<sup>0</sup>]]&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||+&nbsp;||style="text-align:right;"|{{val|3.4|u=MeV}}
|- style="height:2em;"
|(8)&nbsp;||[[Proton|p<sup>+</sup>]]&nbsp;||+&nbsp;||{{nuclide|link=yes|lithium|6}}&nbsp;||→&nbsp;||{{nuclide|link=yes|helium|4}}&nbsp;||(&nbsp;||style="text-align:right;"|{{val|1.7|u=MeV}}||)&nbsp;||+&nbsp;||{{nuclide|link=yes|helium|3}}&nbsp;||(&nbsp;||style="text-align:right;"|{{val|2.3|u=MeV}}||)
|- style="height:2em;"
|(9)&nbsp;||{{nuclide|link=yes|helium|3}}&nbsp;||+&nbsp;||{{nuclide|link=yes|lithium|6}}&nbsp;||→&nbsp;||2&nbsp;{{nuclide|link=yes|helium|4}}&nbsp;||+&nbsp;||[[Proton|p<sup>+</sup>]]&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||+&nbsp;||style="text-align:right;"|{{val|16.9|u=MeV}}
|- style="height:2em;"
|(10)&nbsp;||[[Proton|p<sup>+</sup>]]&nbsp;||+&nbsp;||{{nuclide|link=yes|boron|11}}&nbsp;||→&nbsp;||3&nbsp;{{nuclide|link=yes|helium|4}}&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||+&nbsp;||style="text-align:right;"|{{val|8.7|u=MeV}}
|}
{{Nucleosynthesis}}

For reactions with two products, the energy is divided between them in inverse proportion to their masses, as shown. In most reactions with three products, the distribution of energy varies. For reactions that can result in more than one set of products, the branching ratios are given.

Some reaction candidates can be eliminated at once. The D–<sup>6</sup>Li reaction has no advantage compared to [[Proton|p<sup>+</sup>]]–{{nuclide|link=yes|Boron|11}} because it is roughly as difficult to burn but produces substantially more neutrons through {{nuclide|link=yes|Deuterium}}–{{nuclide|link=yes|Deuterium}} side reactions. There is also a [[Proton|p<sup>+</sup>]]–{{nuclide|link=yes|Lithium|7}} reaction, but the cross section is far too low, except possibly when ''T''<sub>''i''</sub> > 1 MeV, but at such high temperatures an endothermic, direct neutron-producing reaction also becomes very significant. Finally there is also a [[Proton|p<sup>+</sup>]]–{{nuclide|link=yes|Beryllium|9}} reaction, which is not only difficult to burn, but {{nuclide|link=yes|Beryllium|9}} can be easily induced to split into two alpha particles and a neutron.

In addition to the fusion reactions, the following reactions with neutrons are important in order to "breed" tritium in "dry" fusion bombs and some proposed fusion reactors:
<!-- Autogenerated using Phykiformulae 0.10 by [[User:SkyLined]]
{{Nuclide2|neutron}} + {{Nuclide2|lithium|6}} -> T + He + 4.784 MeV
n + {{Nuclide2|lithium|7}} -> T + He + n − 2.467 MeV

-->:{| border="0"
|- style="height:2em;"
|[[Neutron|n<sup>0</sup>]]&nbsp;||+&nbsp;||{{nuclide|link=yes|lithium|6}}&nbsp;||→&nbsp;||{{nuclide|link=yes|tritium}}&nbsp;||+&nbsp;||{{nuclide|link=yes|helium|4}} + 4.784 MeV
|- style="height:2em;"
|[[Neutron|n<sup>0</sup>]]&nbsp;||+&nbsp;||{{nuclide|link=yes|lithium|7}}&nbsp;||→&nbsp;||{{nuclide|link=yes|tritium}}&nbsp;||+&nbsp;||{{nuclide|link=yes|helium|4}} + [[Neutron|n<sup>0</sup>]] − 2.467 MeV
|}

The latter of the two equations was unknown when the U.S. conducted the [[Castle Bravo]] fusion bomb test in 1954. Being just the second fusion bomb ever tested (and the first to use lithium), the designers of the Castle Bravo "Shrimp" had understood the usefulness of <sup>6</sup>Li in tritium production, but had failed to recognize that <sup>7</sup>Li fission would greatly increase the yield of the bomb. While <sup>7</sup>Li has a small neutron cross-section for low neutron energies, it has a higher cross section above 5 MeV.<ref name=cross_section>[http://www.kayelaby.npl.co.uk/atomic_and_nuclear_physics/4_7/4_7_4c.html Subsection 4.7.4c] {{Webarchive|url=https://web.archive.org/web/20180816195425/http://www.kayelaby.npl.co.uk/atomic_and_nuclear_physics/4_7/4_7_4c.html |date=16 August 2018 }}. Kayelaby.npl.co.uk. Retrieved 19 December 2012.</ref> The 15 Mt yield was 150% greater than the predicted 6 Mt and caused unexpected exposure to fallout.

To evaluate the usefulness of these reactions, in addition to the reactants, the products, and the energy released, one needs to know something about the [[nuclear cross section]]. Any given fusion device has a maximum plasma pressure it can sustain, and an economical device would always operate near this maximum. Given this pressure, the largest fusion output is obtained when the temperature is chosen so that {{math|{{angbr|''σv''}}/''T''<sup>2</sup>}} is a maximum. This is also the temperature at which the value of the triple product {{mvar|nTτ}} required for [[Fusion energy gain factor#Ignition|ignition]] is a minimum, since that required value is inversely proportional to {{math|{{angbr|''σv''}}/''T''<sup>2</sup>}} (see [[Lawson criterion]]). (A plasma is "ignited" if the fusion reactions produce enough power to maintain the temperature without external heating.) This optimum temperature and the value of {{math|{{angbr|''σv''}}/''T''<sup>2</sup>}} at that temperature is given for a few of these reactions in the following table.

{| class="wikitable" style="margin:auto;"
|-
!fuel                                           !! ''T'' [keV] !! {{math|{{angbr|''σv''}}/''T''<sup>2</sup>}} [m<sup>3</sup>/s/keV<sup>2</sup>]
|-
|{{nuclide|deuterium}}–{{nuclide|tritium}}      || 13.6        || {{val|1.24|e=-24}}
|-
|{{nuclide|deuterium}}–{{nuclide|deuterium}}    || 15          || {{val|1.28|e=-26}}
|-
|{{nuclide|deuterium}}–{{nuclide|helium|3}}     || 58          || {{val|2.24|e=-26}}
|-
|p<sup>+</sup>–{{nuclide|lithium|6}}            || 66          || {{val|1.46|e=-27}}
|-
|p<sup>+</sup>–{{nuclide|boron|11}}             || 123         || {{val|3.01|e=-27}}
|}

Note that many of the reactions form chains. For instance, a reactor fueled with {{nuclide|tritium}} and {{nuclide|helium|3}} creates some {{nuclide|deuterium}}, which is then possible to use in the {{nuclide|deuterium}}–{{nuclide|helium|3}} reaction if the energies are "right". An elegant idea is to combine the reactions (8) and (9). The {{nuclide|helium|3}} from reaction (8) can react with {{nuclide|lithium|6}} in reaction (9) before completely thermalizing. This produces an energetic proton, which in turn undergoes reaction (8) before thermalizing. Detailed analysis shows that this idea would not work well,{{Citation needed|date=April 2010}} but it is a good example of a case where the usual assumption of a [[Maxwell–Boltzmann distribution|Maxwellian]] plasma is not appropriate.