Editing Nuclear fusion (section)

===Bremsstrahlung losses in quasineutral, isotropic plasmas===
{{unreferenced section|date=August 2023}}
The ions undergoing fusion in many systems will essentially never occur alone but will be mixed with [[electron]]s that in aggregate neutralize the ions' bulk [[electrical charge]] and form a [[Plasma (physics)|plasma]]. The electrons will generally have a temperature comparable to or greater than that of the ions, so they will collide with the ions and emit [[x-ray]] radiation of 10–30 keV energy, a process known as [[Bremsstrahlung]].

The huge size of the Sun and stars means that the x-rays produced in this process will not escape and will deposit their energy back into the plasma. They are said to be [[Opacity (optics)|opaque]] to x-rays. But any terrestrial fusion reactor will be [[Optical depth|optically thin]] for x-rays of this energy range. X-rays are difficult to reflect but they are effectively absorbed (and converted into heat) in less than mm thickness of stainless steel (which is part of a reactor's shield). This means the bremsstrahlung process is carrying energy out of the plasma, cooling it.
 
The ratio of fusion power produced to x-ray radiation lost to walls is an important figure of merit. This ratio is generally maximized at a much higher temperature than that which maximizes the power density (see the previous subsection). The following table shows estimates of the optimum temperature and the power ratio at that temperature for several reactions:

{| class="wikitable" style="margin:auto;"
|-
!fuel                                        !!''T''<sub>i</sub> [keV]!!''P''<sub>fusion</sub>/''P''<sub>Bremsstrahlung</sub>
|-
|{{nuclide|deuterium}}–{{nuclide|tritium}}   ||   50 || 140
|-
|{{nuclide|deuterium}}–{{nuclide|deuterium}} ||  500 ||   2.9
|-
|{{nuclide|deuterium}}–{{nuclide|helium|3}}  ||  100 ||   5.3
|-
|{{nuclide|helium|3}}–{{nuclide|helium|3}}   || 1000 ||   0.72
|-
|p<sup>+</sup>–{{nuclide|lithium|6}}         ||  800 ||   0.21
|-
|p<sup>+</sup>–{{nuclide|boron|11}}          ||  300 ||   0.57
|}

The actual ratios of fusion to Bremsstrahlung power will likely be significantly lower for several reasons. For one, the calculation assumes that the energy of the fusion products is transmitted completely to the fuel ions, which then lose energy to the electrons by collisions, which in turn lose energy by Bremsstrahlung. However, because the fusion products move much faster than the fuel ions, they will give up a significant fraction of their energy directly to the electrons. Secondly, the ions in the plasma are assumed to be purely fuel ions. In practice, there will be a significant proportion of impurity ions, which will then lower the ratio. In particular, the fusion products themselves ''must'' remain in the plasma until they have given up their energy, and ''will'' remain for some time after that in any proposed confinement scheme. Finally, all channels of energy loss other than Bremsstrahlung have been neglected. The last two factors are related. On theoretical and experimental grounds, particle and energy confinement seem to be closely related. In a confinement scheme that does a good job of retaining energy, fusion products will build up. If the fusion products are efficiently ejected, then energy confinement will be poor, too.

The temperatures maximizing the fusion power compared to the Bremsstrahlung are in every case higher than the temperature that maximizes the power density and minimizes the required value of the [[Lawson criterion|fusion triple product]]. This will not change the optimum operating point for {{nuclide|link=yes|deuterium}}–{{nuclide|link=yes|tritium}} very much because the Bremsstrahlung fraction is low, but it will push the other fuels into regimes where the power density relative to {{nuclide|link=yes|deuterium}}–{{nuclide|link=yes|tritium}} is even lower and the required confinement even more difficult to achieve. For {{nuclide|link=yes|deuterium}}–{{nuclide|link=yes|deuterium}} and {{nuclide|link=yes|deuterium}}–{{nuclide|link=yes|helium|3}}, Bremsstrahlung losses will be a serious, possibly prohibitive problem. For {{nuclide|link=yes|helium|3}}–{{nuclide|link=yes|helium|3}}, [[Proton|p<sup>+</sup>]]–{{nuclide|link=yes|lithium|6}} and [[Proton|p<sup>+</sup>]]–{{nuclide|link=yes|boron|11}} the Bremsstrahlung losses appear to make a fusion reactor using these fuels with a quasineutral, isotropic plasma impossible. Some ways out of this dilemma have been considered but rejected.<ref>{{cite journal|title=Fundamental Limitations on Plasma Fusion Systems not in Thermodynamic Equilibrium|journal=Dissertation Abstracts International|volume= 56-07 |issue=Section B|page= 3820|author=Rider, Todd Harrison|bibcode=1995PhDT........45R|year=1995}}</ref><ref>Rostoker, Norman; Binderbauer, Michl and Qerushi,
Artan. [https://web.archive.org/web/20051223133818/http://fusion.ps.uci.edu/artan/Posters/aps_poster_2.pdf Fundamental limitations on plasma fusion systems not in thermodynamic equilibrium]. fusion.ps.uci.edu</ref> This limitation does not apply to [[Non-neutral plasmas|non-neutral and anisotropic plasmas]]; however, these have their own challenges to contend with.