Editing Fusion power (section)

== Background ==
{{main|Nuclear fusion}}
[[File:Sun in X-Ray.png|thumb|upright=1|The [[Sun]], like other [[star]]s, is a natural fusion reactor, where [[stellar nucleosynthesis]] transforms lighter elements into heavier elements with the release of energy.]]
[[File:Binding energy curve - common isotopes.svg|thumb|upright=2|[[Binding energy]] for different [[atomic nucleus|atomic nuclei]]. Iron-56 has the highest, making it the most stable. Nuclei to the left are likely to release energy when they fuse ([[nuclear fusion|fusion]]); those to the far right are likely to be unstable and release energy when they split ([[nuclear fission|fission]]).]]

=== Mechanism ===
Fusion reactions occur when two or more atomic nuclei come close enough for long enough that the [[nuclear force]] pulling them together exceeds the [[electrostatic force]] pushing them apart, fusing them into heavier nuclei. For nuclei heavier than [[iron-56]], the reaction is [[endothermic]], requiring an input of energy.<ref>{{cite web|url=http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/nucbin.html#c2|title=Fission and fusion can yield energy|publisher=Hyperphysics.phy-astr.gsu.edu|access-date=October 30, 2014}}</ref> The heavy nuclei bigger than iron have many more protons resulting in a greater repulsive force. For nuclei lighter than iron-56, the reaction is [[exothermic]], releasing energy when they fuse. Since hydrogen has a single [[proton]] in its nucleus, it requires the least effort to attain fusion, and yields the most net energy output. Also since it has one electron, hydrogen is the easiest fuel to fully ionize.

The repulsive electrostatic interaction between nuclei operates across larger distances than the strong force, which has a range of roughly one [[femtometer]]—the diameter of a proton or neutron. The fuel atoms must be supplied enough kinetic energy to approach one another closely enough for the strong force to overcome the electrostatic repulsion in order to initiate fusion. The "[[Coulomb barrier]]" is the quantity of [[kinetic energy]] required to move the fuel atoms near enough. Atoms can be heated to extremely high temperatures or accelerated in a particle accelerator to produce this energy.

An atom loses its electrons once it is heated past its [[ionization energy]]. The resultant bare nucleus is a type of [[ion]]. The result of this ionization is plasma, which is a heated cloud of bare nuclei and free electrons that were formerly bound to them. Plasmas are [[electrically conducting]] and magnetically controlled because the charges are separated. This is used by several fusion devices to confine the hot particles.

=== 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.

=== Lawson criterion ===
The [[Lawson criterion]] considers the energy balance between the energy produced in fusion reactions to the energy being lost to the environment. In order to generate usable energy, a system would have to produce more energy than it loses. Lawson assumed an [[First law of thermodynamics|energy balance]], shown below.<ref name="Lawson"/>

:<math>P_\text{out} = \eta_\text{capture}\left(P_\text{fusion} - P_\text{conduction} - P_\text{radiation}\right)</math>
where:
* <math>P_\text{out}</math> is the net power from fusion
* <math>\eta_\text{capture}</math> is the efficiency of capturing the output of the fusion
* <math>P_\text{fusion}</math> is the rate of energy generated by the fusion reactions
* <math>P_\text{conduction}</math> is the conduction losses as energetic mass leaves the plasma
* <math>P_\text{radiation}</math> is the radiation losses as energy leaves as light and neutron flux.

The rate of fusion, and thus P<sub>fusion</sub>, depends on the temperature and density of the plasma. The plasma loses energy through [[Thermal conduction|conduction]] and [[radiation]].<ref name="Lawson"/> Conduction occurs when [[ion]]s, [[electron]]s, or [[neutral particle|neutrals]] impact other substances, typically a surface of the device, and transfer a portion of their kinetic energy to the other atoms. The rate of conduction is also based on the temperature and density. Radiation is energy that leaves the cloud as light. Radiation also increases with temperature as well as the mass of the ions. Fusion power systems must operate in a region where the rate of fusion is higher than the losses.

=== Triple product: density, temperature, time ===
[[File:Fusion Triples 2021.png|thumb|upright=2|alt=Fusion trapping (left) against temperature (bottom) for various fusion approaches as of 2021, assuming DT fuel. |Fusion trapping (left) against temperature (bottom) for various fusion approaches as of 2021, assuming DT fuel<ref>Wurzel, Samuel E., and Scott C. Hsu. "Progress toward fusion energy breakeven and gain as measured against the Lawson criterion." arXiv preprint arXiv:2105.10954 (2021).</ref> Solid line corresponds to Q = ∞ for IFC (inertial confinement fusion). Dashed line corresponds to Q = 0.01 for IFC. Colored contours correspond to Q factors for MFC (magnetic confinement fusion): Q = ∞ (brown), Q = 10 (red), Q = 2 (yellow), Q = 1 (green), Q = 0.1 (strong blue), Q = 0.01 (lighter blue), Q = 0.001 (even lighter blue), Q = 0.0001 (faint blue).{{clarify|date=March 2025}}]]
The [[Lawson criterion]] argues that a machine holding a thermalized and quasi-[[Neutral particle|neutral]] plasma has to generate enough energy to overcome its energy losses. The amount of energy released in a given volume is a function of the temperature, and thus the reaction rate on a per-particle basis, the density of particles within that volume, and finally the confinement time, the length of time that energy stays within the volume.<ref name="Lawson"/><ref>{{cite web |url=http://www.efda.org/2013/02/triple-product/ |title=Lawson's three criteria |publisher=EFDA |date=February 25, 2013 |access-date=August 24, 2014 |archive-url=https://web.archive.org/web/20140911210243/http://www.efda.org/2013/02/triple-product/ |archive-date=September 11, 2014 |url-status=dead }}</ref> This is known as the "triple product": the plasma density, temperature, and confinement time.<ref>{{cite web |url=http://www.efda.org/glossary/triple-product/ |title=Triple product |publisher=EFDA |date=June 20, 2014 |access-date=August 24, 2014 |archive-url=https://web.archive.org/web/20140911205015/http://www.efda.org/glossary/triple-product/ |archive-date=September 11, 2014 |url-status=dead }}</ref>

In magnetic confinement, the density is low, on the order of a "good vacuum". For instance, in the [[ITER]] device the fuel density is about {{nowrap|1.0 × 10<sup>19</sup> m<sup>−3</sup>}}, which is about one-millionth atmospheric density.<ref>{{cite web |url=https://accelconf.web.cern.ch/e06/TALKS/FRYCPA01_TALK.PDF |title=ITER and the International ITER and the International Scientific Collaboration |first=Stefano |last=Chiocchio}}</ref> This means that the temperature and/or confinement time must increase. Fusion-relevant temperatures have been achieved using a variety of heating methods that were developed in the early 1970s. In modern machines, {{as of|2019|lc=yes}}, the major remaining issue was the confinement time. Plasmas in strong magnetic fields are subject to a number of inherent instabilities, which must be suppressed to reach useful durations. One way to do this is to simply make the reactor volume larger, which reduces the rate of leakage due to [[classical diffusion]]. This is why ITER is so large.

In contrast, inertial confinement systems approach useful triple product values via higher density, and have short confinement intervals. In [[National Ignition Facility|NIF]], the initial frozen hydrogen fuel load has a density less than water that is increased to about 100 times the density of lead. In these conditions, the rate of fusion is so high that the fuel fuses in the microseconds it takes for the heat generated by the reactions to blow the fuel apart. Although NIF is also large, this is a function of its "driver" design, not inherent to the fusion process.

=== Energy capture ===
Multiple approaches have been proposed to capture the energy that fusion produces. The simplest is to heat a fluid. The commonly targeted D-T reaction releases much of its energy as fast-moving neutrons. Electrically neutral, the neutron is unaffected by the confinement scheme. In most designs, it is captured in a thick "blanket" of [[lithium]] surrounding the reactor core. When struck by a high-energy neutron, the blanket heats up. It is then actively cooled with a working fluid that drives a turbine to produce power.

Another design proposed to use the neutrons to breed fission fuel in a blanket of [[nuclear waste]], a concept known as a [[fission-fusion hybrid]]. In these systems, the power output is enhanced by the fission events, and power is extracted using systems like those in conventional fission reactors.<ref>{{cite web|url=https://life.llnl.gov/ |title=Laser Inertial Fusion Energy |publisher=Life.llnl.gov |access-date=August 24, 2014 |url-status=dead |archive-url=https://web.archive.org/web/20140915170021/https://life.llnl.gov/ |archive-date=September 15, 2014 }}</ref>

Designs that use other fuels, notably the proton-boron [[aneutronic fusion]] reaction, release much more of their energy in the form of charged particles. In these cases, power extraction systems based on the movement of these charges are possible. [[Direct energy conversion]] was developed at [[Lawrence Livermore National Laboratory]] (LLNL) in the 1980s as a method to maintain a voltage directly using fusion reaction products. This has demonstrated energy capture efficiency of 48 percent.<ref name="ReferenceA">{{cite journal | last1=Barr | first1=W. L. | last2=Moir | first2=R. W. | last3=Hamilton | first3=G. W. | title=Experimental results from a beam direct converter at 100 kV | journal=Journal of Fusion Energy | publisher=Springer Science and Business Media LLC | volume=2 | issue=2 | year=1982 | issn=0164-0313 | doi=10.1007/bf01054580 | pages=131–143| bibcode=1982JFuE....2..131B | s2cid=120604056 }}</ref>