4.5.4: Nuclear Fusion
- Page ID
- 85095
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)In Fig. \(4.3\) one can see that the binding energy for \({ }^{4} \mathrm{He}\) is unusually high. If we look at the binding energies of several nuclei from this \(\mathrm{Z}\) region \(\left({ }_{1}^{2} \mathrm{H}\right.\) is also known as "Deuterium", \(\operatorname{and}_{1}{ }_{1}^{3} \mathrm{H}\) as "Tritium"):
| Nucleus | E_{\text {Bind |
| \({ }_{1}^{1} \mathrm{H}\) | 0 |
| \({ }_{1}^{2} \mathrm{H}\) | 2.2245 |
| \({ }_{1}^{3} \mathrm{H}\) | 8.4820 |
| \({ }_{2}^{4} \mathrm{He}\) | 28.2970 |
| \({ }_{5}^{11} \mathrm{~B}\) | 76.2060 |
In contrast to fission reactions, in which energy is released due to the split of a heavy nucleus into two lighter nuclei, energy can also be released in fusion reactions, in which two light nuclei merge into a single heavier one.
Consider the reaction:
\[ { }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \rightarrow{ }_{2}^{4} \mathrm{He}+\text { Energy } \]
Using the data from the table provided above and the same method as is used in the preceding section for calculating the energy released in U-235 fission, it can be readily found that the energy released in a single reaction is \(28.297 \mathrm{MeV}-2 \chi 2.2245 \mathrm{MeV}=23.848 \mathrm{MeV}\). It's about 10 times less from a single fission event, but the mass of the "fuel" is about 60 times less, so by the fusion of one pound of Deuterium one should obtain about 6 times more energy than from the fission of all nuclei in one pound of U-235. And Deuterium is available commercially for \(\$ 138\) per \(20 \mathrm{~g}\) (in \(100 \mathrm{~g}\) of "heavy water" \(\mathrm{D}_{2} \mathrm{O}\) ), while \(\mathrm{U}-235\) is offered for \(\$ 1500\) per o.1g, or \(\$ 300,000\) per 20 \(\mathrm{g}\), over two thousand times more expensive than Deuterium.
So, a fusion reaction might be a much, much cheaper way for generating power than the currently used methods based on Uranium fission. The fuel for generating \(1 \mathrm{~kW}\) power might be even much, much cheaper than the oil or natural gas needed for generating \(1 \mathrm{~kW}\) in a conventional power plant. The picture would be really glamorous, if not the fact that currently there exists no technology making it possible to conduct such reaction in a controlled manner. The only time humans succeeded to initiate a Deuterium-Deuterium (D-D)fusion reaction was during the test of the very first American thermonuclear charge "Ivy-Mike", detonated on Nov. 1, 1952. It was definitely not a deliverable bomb, but a device of a total weight of nearly 75 metric tons.
A much easier to ignite than the D-D fusion is the Deutrium-Tritium (D-T)reaction:
\[ { }_{1}^{2} \mathrm{H}+{ }_{1}^{3} \mathrm{H} \rightarrow{ }_{2}^{4} \mathrm{He}+{ }_{0}^{1} n+17.59 \mathrm{MeV} \]
This reaction is used in all currently existing deliverable "hydrogen bombs". Many of them have been successfully tested - the largest one was the Soviet test of a monster, which later became known in the West as the "Tsar Bomb", which was detonated in October 1961, with a yield about 5000 times more powerful than that of the bomb which on August 6, 1945 had wiped out the city of Hiroshima.
Until now, however, all attempts to realize a controlled D-T fusion process lasting for a prolonged time have failed. But countless experiments carried out so far (since the 1950-ties) have offered much hint of how to design a giant machine promising a good chance for achieving a "breakthrough" the construction of such machine, a huge effort code-named ITER jointly sponsored by 35 countries, is currently under way in France. The latest schedule revision foresees the first plasma runs in 2025 . The schedule was revised several times before the last revision - but let's hope there will be no more revisions...
It is perhaps worth mentioning about other possible fusion schemes that are now being researched. A big inconvenience of the D-T "fuel cycle" is the fact that this reaction fast neutrons are created. Prolonged exposure to them may make the parts of "fusion reactors" highly radioactive. The plans for ITER are that it will only be a research facility. But dealing with intense high-energy neutron radiation may become a major challenge for the designers of future power generators utilizing the D-T reaction. In view of that, much interest is currently focused on the so-called "aneutronic fusion" - i.e., reaction, in which no neutrons are produced. One such reaction is the "Hydrogen-Boron" fusion:
\[ { }_{1}^{1} p+{ }_{5}^{11} \mathrm{~B} \rightarrow 3{ }_{2}^{4} \mathrm{He}+8.7 \mathrm{MeV} \]
Another advantage of this "cycle" is that both fuel components, hydrogen and boron, are inexpensive and easily available. A new interesting idea of using powerful laser beams for achieving a sustained fusion process in the H-B fuel mix has recently emerged. It is certainly worth paying attention to any new developments in this research project.