# Nuclear fusion

Fusion of deuterium and tritium to form a helium nucleus
Binding energy per nucleon as a function of the mass number

When nuclear fusion are nuclear reactions refer to operations where two atomic nuclei fuse into a new core. Nuclear fusion reactions are the reason why the sun and all shining stars radiate energy .

The cross-section , the measure of the probability that colliding nuclei react with one another, is of decisive importance for the creation of a fusion . The cross-section is usually only sufficiently large when the two cores collide with one another with high energy. This is necessary to overcome the Coulomb barrier , the electrical repulsion between the positively charged nuclei, or to tunnel through its narrow maximum . Beyond the barrier, at a distance of only about 10 −15  m, the attraction predominates through the strong interaction and the nuclei fuse with one another.

Fusion reactions can be exothermic (releasing energy) or endothermic (absorbing energy). Exothermic fusion reactions can maintain the high temperatures necessary for the thermal energy to lead to further fusion reactions. Such thermonuclear processes take place in stars and fusion bombs under extreme pressure. In contrast to nuclear fission , a chain reaction with fusion reactions is not possible.

The fusion reaction shown above as a thermonuclear process is intended to be used in future to generate electricity in nuclear fusion reactors : The nuclei of deuterium ( 2 H) and tritium ( 3 H) fuse to form a helium nucleus ( 4 He), releasing a neutron (n) and energy (3, 5  MeV + 14.1 MeV).

The figure below shows the binding energy per nucleon of the nuclides . Energy is released with reactions in the upward direction of the curve or is required in the downward direction. The fusion of hydrogen (H) to helium-4 releases a lot of energy.

## Nuclear fusion research

The first nuclear reaction observed was an (endothermic) fusion reaction. It was discovered - long before nuclear fission - by Ernest Rutherford in 1917 during experiments with alpha particles . Protons of relatively high energy were found, which only appeared when the irradiated gas contained nitrogen. This nuclear reaction is called in today's notation 14 N (α, p) 17 O or, written in detail:

${\ displaystyle {} ^ {14} \ mathrm {N} + {} ^ {4} \ mathrm {He} \, \ rightarrow \, {} ^ {17} \ mathrm {O} + {} ^ {1} \ mathrm {H} -1,2 \, \ mathrm {MeV}}$

This conversion of nitrogen into oxygen , like the alpha decay itself, contradicted the classical theory, according to which the Coulomb barrier can only be overcome with sufficient energy. It was not until 1928 that George Gamow was able to explain such processes on the basis of the new quantum mechanics with the tunnel effect .

As early as 1920 Arthur Eddington had suggested fusion reactions as a possible energy source of stars based on the precise measurements of isotope masses by Francis William Aston (1919) . Since it was known from spectroscopic observations that stars largely consist of hydrogen , its fusion to form helium was considered here. In 1939, Hans Bethe published various mechanisms for how this reaction could take place in stars.

The first fusion reaction specifically carried out in the laboratory was the bombardment of deuterium with deuterium nuclei in 1934 by Mark Oliphant , Rutherford's assistant, and Paul Harteck . The fusion of this hydrogen isotope, which is rare in stars, branches into two product channels:

${\ displaystyle {} ^ {2} \ mathrm {H} + {} ^ {2} \ mathrm {H} \, \ rightarrow \, {} ^ {3} \ mathrm {He} + {} ^ {1} \ mathrm {n} +3 {,} 3 \, \ mathrm {MeV}}$
${\ displaystyle {} ^ {2} \ mathrm {H} + {} ^ {2} \ mathrm {H} \, \ rightarrow \, {} ^ {3} \ mathrm {H} + {} ^ {1} \ mathrm {p} +4 {,} 0 \, \ mathrm {MeV}}$

The technical use of thermonuclear nuclear fusion was first pursued with the aim of developing military weapons. Hence, this research took place in secret for the first decades after World War II . The USA had been in possession of the fission- based atomic bomb since 1945 and the Soviet Union since 1949 . In the period that followed, Edward Teller and Stanislaw Ulam developed a concept for building a hydrogen bomb in the USA , which is based on nuclear fusion and promised a significantly higher explosive power. On November 1, 1952, the first hydrogen bomb called Ivy Mike was detonated in Eniwetok Atoll in the Pacific. This provided proof that large amounts of energy can also be released on earth through nuclear fusion.

## Energy balance

Is the mass of the nuclei or particles formed in the fusion less than the sum of the mass of the starting nuclei, the mass difference is , as with any nuclear reaction to that of Einstein derived mass-energy equivalent formula liberated in the form of energy (as kinetic energy of the reaction products and possibly as electromagnetic radiation). Exothermic, i.e. energy-releasing fusion reactions only occur when light nuclei fuse together, since the binding energy per nucleon only increases with increasing mass number up to the element iron (isotope 58 Fe). However, it is very large in reactions that generate helium-4: The conversion of one gram of deuterium-tritium mixture in a nuclear fusion reactor would produce thermal energy of around 100 megawatt hours (MWh) or 12.3  tonnes of TCE . ${\ displaystyle \ Delta m}$ ${\ displaystyle E = \ Delta mc ^ {2}}$

The previous experiments on controlled thermonuclear fusion do not yet show a positive energy balance. The most successful so far has been the British JET ( Joint European Torus ), which was able to achieve a peak output of 16 MW for less than a second. 65 percent of the energy put in could be recovered as fusion energy.

## Stellar nuclear fusion

Proton-proton reaction and continuation until the formation of He-4

In many stars, like our sun, a long phase of hydrogen burning is at the beginning of development. During this period as a main sequence star, protons , the atomic nuclei of hydrogen , fuse to form helium , releasing energy . In moderately large stars, this occurs mainly through a chain of reactions known as the proton-proton reaction; at higher temperatures the Bethe-Weizsäcker cycle becomes more important. In these reaction chains, neutrinos with characteristic energy distributions are formed, the measurement of which provides information about the interior of the sun.

When hydrogen has become scarce in the core of a main sequence star, the fusion of helium begins . Due to their mass , larger stars also generate greater gravitational pressure, which means that density and temperature reach higher values ​​and, in the end, heavier elements are also created through fusion. This process leads to nuclei in the range of the maximum of the binding energy per nucleon (mass numbers around 60, with extensions up to about 70). Elements with even larger mass numbers, however, can no longer be created in this way, since such fusions are increasingly endothermic , i.e. H. provide less energy than they need for their own maintenance. They are formed by neutron ( s and r process ) and proton accumulation ( p process ) (see supernova, core collapse ).

Fusion reactions with different starting materials require different temperatures. Different reactions take place one after the other in stars. When the fuel is used up for a reaction, the star contracts, which increases its central temperature. A new reaction that requires this higher temperature can then start.

## Nuclear fusion reactions for technical energy generation

### Possible input materials and reactions

The pp reaction is far too slow for technical thermonuclear use. Even in the core of the sun , the mean lifespan of a proton before it reacts is on the order of ten billion years. But all fusion reactions that come into question for technical use also take place between very light atomic nuclei, and their energy gain is explained by the generation of helium-4 nuclei with their high binding energy per nucleon. One of the reactions considered, the proton-boron-11 reaction (last line of the following table), is not a fusion at all in the sense of the above definition - no nucleus arises that is heavier than the starting nucleus - but it produces the same for each reacting nucleus pair three helium-4 nuclei. Usually this reaction is counted as part of “nuclear fusion”.

The concepts for nuclear fusion reactors are based on the fusion of deuterium and tritium, hereinafter referred to as DT. Other fusion reactions would have advantages over DT, in particular with regard to radioactivity resulting from activation of the wall materials or easier utilization of the reaction energy. However, due to the smaller energy gain per individual reaction, the need for significantly higher plasma temperatures or the lack of availability of the starting materials, they are only theoretical possibilities for energy generation for the time being.

The following table lists the possible fuels, the reaction products and the energy released. In the case of reactions with various possible end products, the percentages of the reaction channels are given.

If there are only two product particles, they have the specified, well-defined kinetic energies according to the kinematics (if the impact energy in the input channel is neglected) . In the case of reactions with more than two product particles, on the other hand, only the total energy released can be stated.

No. Raw materials Products
(1) 2 D  3 T  4 He  (3.5  MeV ) + n 0  (14.1 MeV)
(2a) 2 + 2 3 T (1.01 MeV) + p +  (3.02 MeV) (to 50%)
(2 B) 2 + 2 3 He (0.82 MeV) + n 0  (2.45 MeV) (to 50%)
(3) 2 + 3 He 4 He (3.6 MeV) + p +  (14.7 MeV)
(4) 3 T + 3 T 4 He + 2 n + 11.3 MeV
(5) 3 He + 3 He 4 He + 2 p + 12.9 MeV
(6a) 3 He + 3 T 4 He + p + n + 12.1 MeV (to 57%)
(6b) 3 He + 3 T 4 He (4.8 MeV) + 2 D (9.5 MeV) (to 43%)
(7a) 2 D + 6 li 4 He (11.2 MeV each)
(7b) 3 He + 4 He + n + 1.8 MeV
(7c) 7 Li (0.6 MeV) + p (4.4 MeV)
(7d) 7 Be  (0.4 MeV) + n (3.0 MeV)
(8th) p + 6 li 4 He (1.7 MeV) + 3 He (2.3 MeV)
(9) 3 He + 6 li 4 He + p + 16.9 MeV
(10) p + 11 B 4 He 8.7 MeV

### Deuterium / tritium

For nuclear fusion reactors on earth, a mixture of equal parts of the hydrogen isotopes deuterium (D) and tritium (T) is by far the most promising fuel. In order for this fusion reaction - reaction (1) in the table above - to take place independently, the Lawson criterion (a minimum value for the product of temperature, particle density and energy inclusion time ) must be met. This results in a required temperature of approx. 150 million K (ten times higher than in the core of the sun) and a pressure of a few bar (several orders of magnitude lower than in the core of the sun). With these technically achievable values, the cross-section of the DT reaction is much larger than that for the first step of the proton-proton reaction.

In order to use the DT reaction as an energy source on earth, fusion reactors with magnetic confinement of the plasma are being developed in international cooperation , whereby the main aim to date (2020) is to generate a stable plasma. Hydrogen, deuterium or mixtures thereof are used almost exclusively for this purpose, and radioactive tritium is only used in rare cases. Most plasma-physical and technical problems related to heating, stabilization and diagnostics can be investigated with hydrogen and deuterium. The energy containment time required to meet the Lawson criterion has not yet been reached; the previous (as of 2016) test facilities are too small for this. The DT fusion has been demonstrated with JET for a short time. A physical energy gain, i. H. an energy release that exceeds the energy used for plasma heating is to be achieved with ITER . The first electricity production is planned with DEMO .

### Deuterium / Deuterium

Two reaction channels are about equally frequent:

${\ displaystyle \ mathrm {D} + \ mathrm {D} \ \ rightarrow \ \ mathrm {p} + \ mathrm {T} +4 {,} 0 \; \ mathrm {MeV}}$
${\ displaystyle \ mathrm {D} + \ mathrm {D} \ \ rightarrow \ \ mathrm {n} + {} ^ {3} \! \, \ mathrm {He} +3 {,} 3 \; \ mathrm { MeV}}$

For a power plant, the disadvantages compared to DT are the much smaller energy gain and the much smaller effective cross section , which increases the required containment time. If the conversion of the DD reaction is significant (especially in bombs), the DT reaction occurs as a subsequent reaction, as well as the following reactions:

${\ displaystyle \ mathrm {p} + \ mathrm {T} \ \ rightarrow \ {} ^ {4} \! \, \ mathrm {He} + \ gamma +19 {,} 8 \; \ mathrm {MeV}}$
${\ displaystyle \ mathrm {D} + \! ^ {3} \ mathrm {He} \ \ rightarrow \ \ mathrm {p} + {} ^ {4} \! \, \ mathrm {He} +18 {,} 3 \; \ mathrm {MeV}}$
${\ displaystyle \ mathrm {T} + \ mathrm {T} \ \ rightarrow \ 2 \, \ mathrm {n} + {} ^ {4} \! \, \ mathrm {He} +11 {,} 3 \; \ mathrm {MeV}}$

### Deuterium / Helium-3 and Helium-3 / Helium-3

The helium- 3 nucleus is the mirror nucleus to the tritium nucleus: it contains 2 protons and 1 neutron instead of 1 proton and 2 neutrons. The D- 3 He reaction (No. (3) of the table), already listed above as a subsequent reaction to the deuterium-deuterium fusion, accordingly provides a helium-4 nucleus and a proton of 15 MeV energy. However, the higher repulsion of the doubly charged helium-3 nucleus must be overcome. The conversion of the kinetic energy of the proton into usable form would be easier than with the neutron. At the same time, deuterium ions would also react with one another to form protons and tritium or to form neutrons and helium-3. This would also produce neutrons. If the tritium is not removed from the reaction gas, DT reactions also lead to the release of neutrons.

In a fusion reactor operated solely with 3 He (reaction (5)) there would be much less radioactivity, since only a He-4 nucleus and protons are produced. However, you would need for the response

${\ displaystyle \ mathrm {^ {3} He + \! ^ {3} He \ \ rightarrow \ ^ {4} He + \ 2 \ p + 12.9 \; MeV}}$

even greater repulsive forces are overcome. At the high temperatures of the plasma, tritium would be formed from He-3 and electrons with a certain reaction rate through inverse beta decay .

A fundamental difficulty lies in the availability of He-3, which is only available in small quantities on earth. Larger amounts of He-3 have been detected in lunar rocks. For a possible extraction on the moon and transport to earth, the technical feasibility would have to be proven and the cost-benefit ratio weighed.

### Other possible fuels

Compared to its neighboring nuclides, the He-4 atomic nucleus has a particularly high binding energy per nucleon; This explains the large energy gain of the DT reaction (see above), and therefore other reactions with lighter nuclides, as far as they produce He-4, are also conceivable as an energy source. However, creating the necessary conditions is even more difficult because the repulsion between the multiply charged atomic nuclei is stronger than that between the hydrogen nuclei. An example is the boron-proton reaction (No. (10))

${\ displaystyle \ mathrm {^ {11} B + \! p \ \ rightarrow \ 3 \ ^ {4} He + 8.7 \; MeV}}$.

Like the 3 He- 3 He reaction, it would have the advantage of not releasing any neutrons. For them, compared to the DT reaction, the temperature would have to be about ten times higher and the containment time 500 times longer. Due to the high temperatures required and the nuclear charge of the boron, the energy losses of the fusion plasma through bremsstrahlung represent a physical limit that has so far been insurmountable.

### Nuclear fusion with polarized particles

The reaction rates of the fusion reactions are dependent on a possible spin polarization of the ions involved. For example, the cross-section of the DT or the D- 3 He fusion reaction could be increased by a factor of up to 1.5 if the spins of the particles involved are aligned in parallel. In addition, the preferred directions of emission of the reaction products could be influenced. In principle, this would simplify the energy extraction somewhat and increase the service life of the blank parts. However, it is unclear how the quantities of polarized fuel required for reactor operation can be produced, brought into the plasma vessel and protected there against depolarization effects.

## Technical applications

### Power generation

In international cooperation, research is being carried out into whether and how fusion energy can be used to generate electricity . From today's perspective, the first economically viable reactor is not expected before 2050 if the technological obstacles can be overcome and the political decision in favor of the new technology should be made. Provided that fossil fuels are pushed back due to their harmful effects on the climate and that nuclear fusion is therefore economically competitive, the new technology could, according to current knowledge, be used on a large scale in the last quarter of the 21st century.

### Physical research, neutron sources

Like other nuclear reactions, fusion reactions can be carried out using particle accelerators in the laboratory for physical research purposes. The above-mentioned deuterium-tritium reaction is used to generate fast free neutrons. The Farnsworth-Hirsch Fusor is also a source of free neutrons for research and technical purposes.

### weapons

In hydrogen bombs , the deuterium-tritium reaction takes place in an uncontrolled manner, with the tritium usually only being extracted from lithium during the explosion. The largest hydrogen bomb ever tested, the Tsar bomb , achieved an explosive force of 57 megatons of TNT. But many atom bombs also contain a few grams of a deuterium-tritium mixture inside the hollow sphere made of nuclear explosives. Once the chain reaction has started, it is heated up sufficiently to start the nuclear fusion. The neutrons released in large numbers intensify the chain reaction in the nuclear explosive.

Since the cessation of the nuclear weapons test explosions, questions of functional safety and the further development of fusion weapons have been investigated using computer simulations, among other things. The exact material parameters required for this are determined, among other things, through experiments on laser-driven inertial fusion .

Cold fusion is the name given to nuclear fusion reactions without hot plasma. This should keep the effort involved in generating energy by means of nuclear fusion manageable. Most of the processes (except e.g. pyrofusion , which works in principle, but can only be used as a neutron source, but not for energy generation) turned out to be pseudoscientific self-importance of the researchers involved with no actual function, even during the brief hype of the 1980s or practical use.

## literature

• Alexander M. Bradshaw , Thomas Hamacher: Nuclear Fusion - A Sustainable Energy Source of the Future . Naturwissenschaftliche Rundschau 58 (12), pp. 629-637 (2005),

Commons : Nuclear fusion  - collection of images, videos and audio files
Wiktionary: Nuclear fusion  - explanations of meanings, word origins, synonyms, translations

## Individual evidence

1. Ernest Rutherford: Collision of α particles with light atoms. IV. An abnormal effect in nitrogen , Philosophical Magazine 37, 1919, pp. 581-587. ( Publication text )
2. Hans Bethe: Energy Production in Stars , Phys. Rev. 55, 1939, pp. 434-456.
3. Rutherford, Oliphant, Paul Harteck: Transmutation effects observed with heavy hydrogen, Proc. Roy. Soc. A, Vol. 144, 1934, pp. 692-703, and under the same title, Nature, Vol. 133, 1934, p. 413
4. ^ The discovery of DD fusion , EuroFusion, 2010
5. M. Keilhacker, JET Deuterium-Tritium Results and their Implications, website of EUROfusion. Retrieved August 16, 2016.
6. Michael Schirber, APS : Synopsis: Rare Fusion Reactions Probed with Solar Neutrinos , 2012.
7. ^ Weston M. Stacey: Fusion. An Introduction to the Physics and Technology of Magnetic Confinement Fusion. 2010, p. 1.
8. H. Paetz gen. Schieck: The status of Polarized Fusion , Eur. Phys. J. 44 A, 2010, pp. 321-354
9. Armin Grunwald, Reinhard Grünwald, Dagmar Oertel, Herbert Paschen: Sachstandsbericht Kernfusion. Office for Technology Assessment at the German Bundestag, March 2002, accessed on October 9, 2014 .
10. ^ ITER and beyond. On to DEMO http://www.iter.org/proj/iterandbeyond ( Memento from September 22, 2012 in the Internet Archive ) . ITER organization website. Retrieved July 4, 2013.
11. Why fusion research? - Cost archive link ( memento from April 9, 2015 in the Internet Archive ). EURO fusion website . Retrieved November 1, 2014.
12. A roadmap to the realization of fusion energy . EFDA roadmap
13. ^ How Nuclear Weapons Work by Phillip R. Hays PhD LT USNR-R, Nuclear / Special Weapons Officer, USS Oklahoma City CLG-5 1970–1972