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A nuclear fusion reaction which occurs between various nuclei of the light elements when they are constituents of a gas at very high temperatures. Thermonuclear reactions, the source of energy generation in the Sun and the stable stars, are utilized in the fusion bomb. See Nuclear fusion
Thermonuclear reactions occur most readily between isotopes of hydrogen (deuterium and tritium) and less readily among a few other nuclei of higher atomic number. At the temperatures and densities required to produce an appreciable rate of thermonuclear reactions, all matter is completely ionized; that is, it exists only in the plasma state. Thermonuclearer fusion reactions may then occur within such an ionized gas when the agitation energy of the stripped nuclei is sufficient to overcome their mutual electrostatic repulsions, allowing the colliding nuclei to approach each other closely enough to react. For this reason, reactions tend to occur much more readily between energy-rich nuclei of low atomic number (small charge) and particularly between those nuclei of the hot gas which have the greatest relative kinetic energy. This latter fact leads to the result that, at the lower fringe of temperatures where thermonuclear reactions may take place, the rate of reactions varies exceedingly rapidly with temperature. See Kinetic theory of matter, Magnetohydrodynamics, Nuclear reaction, Pinch effect
thermonuclear reaction() See nuclear fusion.
a nuclear reaction that occurs between light atomic nuclei at very high temperatures (of the order of 107°K or higher). Sufficiently high temperatures—that is, sufficiently high relative energies of colliding nuclei—are necessary in order to overcome the electrostatic barrier created by the mutual repulsion of the nuclei, which are particles of like charge. In the absence of such high temperatures, the nuclei cannot approach each other to a distance of the order of the range of nuclear forces, and, consequently, the alteration of nuclei that occurs in thermonuclear reactions is impossible. Thermonuclear reactions therefore occur under natural conditions only in the interiors of stars. In order to achieve such reactions on earth, a substance must be subjected to extreme heating through a nuclear explosion, a powerful gas discharge, a tremendous pulse of laser radiation, or bombardment with an intense beam of particles.
Thermonuclear reactions are generally processes of the formation of tightly bound nuclei from more loosely bound nuclei and are therefore accompanied by the release of energy. More precisely, such reactions are accompanied by the release in the reaction products of the excess kinetic energy equal to the increase in
|Table 1. Energy release, σmax, and corresponding energy of incident particle for a number of thermonuclear reactions|
|Reaction*||Energy release (MeV)||σmax† (bams)||Energy of incident particle corresponding to σmax (MeV)|
|*Symbols used include the following: (p) proton, (D) deuteron (nucleus of deuterium, or 2H, atom). (T) triton (nucleus of tritium, or 3H, atom), (n) neutron, (e+) positron, (v) neutrino, (γ) photon †Unless otherwise stated, figures are for the region of energies ≤ 1 MeV|
|(1) p + p → D + e+ + v||2.2||10–23||—|
|(2) p + D → 3He + γ||5.5||10–6||—|
|(3) p + T → 4He + γ||19.7||10–6||—|
|(4) D + D → T + p||4.0||0.1 6 (at 2 MeV)||2.0|
|(5) D + D → 3He + n||3.3||0.09||1.0|
|(6) D + D → 4He + γ||24.0||—||—|
|(7) D + T → 4He + n||17.6||5.0||0.13|
|(8) T + D → 4He + n||17.6||5.0||0.195|
|(9) T + T → 4He + 2n||11.3||0.10||1.0|
|(10) D + 3He + 4He + p||18.4||0.71||0.47|
|(11) 3He + 3He → 4He + 2p||12.8||—||—|
|(12) n + 6Li → 4He + T||4.8||2.6||0.26|
|(13) p + 6Li → 4He + 3He||4.0||10–4||0.3|
|(14) p + 7Li → 24He + γ||17.3||6 × 10–3||0.44|
|(15) D + 6Li → 7Li + p||5.0||0.01||1.0|
|(16) D + 6Li → 24He||22.4||0.026||0.60|
|(17) D + 7Li → 24 He + n||15.0||10–3||0.2|
|(18) p + 9Be → 24He + n||0.56||0.46||0.33|
|(19) p + 9Be → 6Li + 4He||2.1||0.35||0.33|
|(20) p + 11B → 34He||8.6||0.6||0.675|
|(21) p + 15N → 12C + 4He||5.0||0.69 (at 1.2 MeV)||1.2|
binding energy. These formation processes may be said to represent an exoergic shift toward the central part of the periodic table of the elements. The mechanism of the shift is opposite to the mechanism of the shift that occurs in the fission of heavy nuclei; that is, nearly all thermonuclear reactions of practical interest are reactions involving the fusion of light nuclei to form heavier nuclei. There are, however, exceptions: because the 4He nucleus (an alpha particle) is especially tightly bound, exoergic fission reactions are possible for some light nuclei. In particular, the “clean” reaction 11B + p → 34He + 8.6 million electron volts (MeV) has attracted interest of late.
Because of the great energy release in a number of thermonuclear reactions, the study of such reactions is of considerable importance for astrophysics, applied nuclear physics, and nuclear power engineering. Another interesting problem is the role of thermonuclear reactions in prestellar and stellar processes of the synthesis of the atomic nuclei of chemical elements—that is, in nucleogenesis.
Reaction rates. Table 1 (on page 621) gives for a number of thermonuclear reactions the values of three characteristic quantities: the energy release; the maximum effective cross section σmax, which is a measure of the probability of the reaction; and the corresponding energy of the incident particle, which is the first particle on the left in the reaction formulas in the table.
The principal reason for the very large spread in reaction cross sections is the marked difference in the probabilities of nuclear transformations in the strict sense. Thus, the cross section is large for most reactions accompanied by the formation of the very tightly bound nucleus 4He but is extremely small for reactions due to the weak interaction—for example, p + p → D + e ++ v.
Thermonuclear reactions occur as a result of binary collisions between nuclei. The number of events per unit volume per unit time is therefore n1n2<vσ(v)>. Here, n1 and n2 are the concentrations of nuclei of the first and second species (if the nuclei are of the same species, then n1n2 must be replaced by n2/2), v is the relative velocity of the colliding nuclei, and the quantity <vσ(v)> indicates an average of the product of the mutual reaction cross section σ and relative velocity v of the nuclei over the velocity distribution of the nuclei, which is here assumed to be Maxwellian.
The temperature dependence of the reaction rate is determined by the factor <vσ(v)>. Of practical importance is the case where the temperature T < 107°–108°K. Here, the temperature dependence may be approximately expressed in a form that is identical for all thermonuclear reactions. In this case the relative energies E of the colliding nuclei are generally much less than the height of the Coulomb barrier. (Even for a combination of nuclei with the lowest charge Z = 1, this height is ~200 kiloelectron volts, which corresponds, in accordance with the equation E = kT, to T ~ 2 × 109°K.) Consequently the form of the function σ(v) in this temperature region is determined principally by the probability of tunneling through the barrier and not by a nuclear interaction in the strict sense. In many cases nuclear interactions in the strict sense account for the “resonance” character of the function σ(v). Indeed, such a resonance character of the function is reflected in the largest of the values of σmax in Table 1.
The following expression can be given for <vσ(v)>:
where const is a constant characteristic of the given reaction, Z1 and Z2 are the charges of the colliding nuclei, μ = m1m2/(m1 + m2) is their reduced mass, e is the charge of the electron, h is Planck’s constant, and k is the Boltzmann constant.
Thermonuclear reactions in the universe. Thermonuclear reactions play a dual role in the universe: they are the principal source of the energy of the stars, and they constitute the mechanism of nucleogenesis. For normal main sequence stars, including the sun, the main process of exoergic fusion is the burning of H to form He, or, more precisely, the conversion of four protons into a 4He nucleus and two positrons. According to notions advanced by H. Bethe and others in 1938 and 1939, this result can be obtained in two ways: through the proton-proton chain, which is also known as the deuterium cycle, and through the carbon-nitrogen, or carbon, cycle (Tables 2 and 3).
|Table 2. Proton-proton chain|
|Reaction||Energy release (MeV)||Average reaction time|
|p + p→D + e+ + v||2 × 0.164 + (2 × 0.257)||1.4 × 1010 yr|
|e+ + e– →2γ||2 × 1 .02||—|
|p + D→3He + γ||2 × 5.49||5.7 sec|
|3He + 3He → 4He + 2p||12.85||106yr|
|Overall, 4p → 4He + 2e+||26.21 + (0.514)|
In both cycles the first three reactions are found twice in the overall cycle. For both the proton-proton chain and carbon-nitrogen cycle, the reaction times were calculated for conditions at the center of the sun, with T = 13 × 106°K(16 × 106°K according to other data) and a concentration of H nuclei of 100 g/cm3. The energy release figures in parentheses represent the energy that irreversibly escapes with neutrinos.
In the carbon-nitrogen cycle the 12C nucleus plays the role of a catalyst. For the sun and less luminous stars, the proton-proton cycle predominates in the total energy release. For more luminous stars, on the other hand, the carbon-nitrogen cycle is the main source of energy.
The proton-proton chain can follow three different paths. At sufficiently large concentrations of 4He and at T > (10–15) × 106°K, there begins to predominate a path that differs from the one given in Table 2 in the replacement of the 3He + 3He reaction by the following chain:
3He + 4He → 7Be + γ
7Be + e– → 7Li + γ
p + 7Li → 24He
At still higher temperatures a third path begins playing an important role:
3He + 4He → 7Be + γ
p + 7Be → 8B + γ
8B → 8Be + e+ + v
8Be → 24He
For giant stars with dense cores depleted of H, helium burning and the neon cycle are important. They occur at much higher temperatures and densities than do the proton-proton chain and the carbon-nitrogen cycle.
The main reaction in helium burning comes into play at T ≈ 2 × 108°K. Sometimes called the Salpeter process, the reaction has the following formula:
34He → 12C + γ1 + γ2 + 7.3 MeV
Strictly speaking, the reaction does not simply involve the collision of three He nuclei but is a two-stage process that proceeds through the compound nucleus 8Be. There may follow the reactions
12C + 4He → 16O + γ
16O + 4He → 20Ne + γ
These reactions constitute one of the mechanisms of nucleogenesis. The existence of an appropriate discrete energy level in the 8Be nucleus is responsible for the great “sharpness” of the resonance in the reaction 34He → 12C. It is interesting that such a chance circumstance makes possible the Salpeter process and, consequently, the nucleogenesis of most elements, which is a prerequisite for the rise of all forms of life.
The neon cycle can occur when the reaction products of helium burning come into contact with H. In this cycle a 20Ne nucleus acts as a catalyst for the conversion of H into He. The sequence of reactions here is analogous to that of the carbon-nitrogen cycle (Table 3), with the 12C, 13N, 13C, 14N, lsO, and 15N nuclei being replaced by 20Ne, 21Na, 21Ne, 22Na, 23Na, and “Mg nuclei, respectively. The neon cycle is not an important energy source. It apparently, however, is of great significance for nucleogenesis, since 21Ne, which is one of the nuclei formed in the cycle, can serve as a source of neutrons:
21Ne + 4He → 24Mg + n
It should be noted that a similar role can be played by the C nucleus, which participates in the carbon-nitrogen cycle. The consequent neutron-capture chain, along with β-decay processes, is the mechanism for the building of increasingly heavy nuclei.
The average rate of energy release e in typical stellar thermonuclear reactions is negligible by terrestrial standards. In the case of the sun, for example, the average rate of energy release per gram of solar mass is ε = 2 ergs/sec-g. This figure is much less than, say, the rate of energy release in the metabolic processes of a living organism. The sun, however, has the very large mass of 2 × 1033 g. Consequently, the total power radiated by the sun is extremely great: 4 × 1026 watts, which corresponds to a decrease of ~4 × 106 tons/sec in the sun’s mass. Even a negligible fraction of this energy output is enough to have a decisive influence on the energy balance of, for example, the earth’s surface and life.
Because of the huge size and mass of the sun and other stars, the problem of the confinement and thermal insulation of a plasma is solved in an ideal manner. Confinement is gravitational in nature. The thermonuclear reactions occur in the hot core of the star, and heat transfer from the star occurs at the distant and much cooler surface. It is for this reason alone that stars can efficiently generate energy through such slow processes as the proton-proton chain and the carbon-nitrogen cycle (Tables 2 and 3). Under terrestrial conditions these processes are practically unrealizable. For example, the fundamental reaction p + p — D + e+ + v has not yet been directly observed.
Thermonuclear reactions under terrestrial conditions. On the earth only the most efficient thermonuclear reactions—those involving the isotopes D and T of H—are practicable. Such thermonuclear reactions have thus far been achieved on a comparatively large scale only in test explosions of hydrogen bombs. The energy released by the explosion of such a bomb amounts to 1023–1024 ergs, which exceeds the weekly electric power production on the entire earth and is comparable to the energy of earthquakes and hurricanes. The probable mechanism of the action of the bomb includes reactions (12), (7), (4), and (5) of Table 1. Other thermonuclear reactions, such as (16), (14), and (3), have also been discussed in connection with thermonuclear explosions.
|Table 3. Carbon-nitrogen cycle|
|Reaction||Energy release (MeV)||Average reaction time|
|p + 12C → 13N + γ||1.95||1.3 × 107yr|
|13N→13C + e+ + v||1.50 + (0.72)||7.0 min|
|p + 13C→14N + γ||7.54||2.7 × 106yr|
|p + 14N→15O + γ||7.35||3.3 × 106yr|
|15O→ 15N + e+ + v||1.73 + (0.98)||82 sec|
|P + 15N → 12C + 4He||4.96||1.1 × 105yr|
|Overall, 4p → 4He + 2e +||25.03 + (1.70)|
Controlled fusion may provide a way of using thermonuclear reactions for peaceful purposes. Hopes have been raised that mankind’s energy problems can be solved through controlled fusion, since the deuterium contained in the water of the oceans is a practically inexhaustible source of inexpensive fuel for controlled thermonuclear reactions. The greatest progress in controlled-fusion research has been achieved within the framework of the Soviet Tokamak program. In the mid–1970’s, intensive work was underway in similar programs in a number of other countries. The most important reactions in Table 1 for controlled fusion are (5), (7), and (4); in addition, reaction (12) provides a means of breeding costly T. Besides the production of energy, a thermonuclear reactor could be used as a powerful source of fast neutrons. “Clean” reactions that do not produce neutrons, such as (10) and (20) in Table 1, have also attracted considerable attention.
REFERENCESArtsimovich, L. A. Upravliaemye termoiadernye reaktsii, 2nd ed. Moscow, 1963.
Frank-Kamenetskii, D. A. Fizicheskie protsessy vnutri zvezd. Moscow, 1959.
“Termoiadernye reaktsii.” In Problemy sovremennoi fiziki, fasc. 1. Moscow, 1954.
Fowler, W. A., G. R. Caughlan, and B. A. Zimmerman. Annual Review of Astronomy and Astrophysics, vol. 5, 1967, p. 525.
V. I. KOGAN