The Sun is forced, as it were, to make do with protons as its nuclear fuel. On Earth, we have available a variety of other nuclei, some of which react with higher probability and at lower temperatures than do protons. Actually, the Sun’s proton-proton cycle proceeds at a very leisurely pace. There is no possibility to use the same reaction as an energy source on earth.1 More reactive are the heavier isotopes of hydrogen, deuterium and tritium. Especially favorable is the reaction between a deuteron and a triton, known as the DT reaction. It can proceed explosively at a temperature of about 60 million degrees:
1H1 +1H3 →2He4 +n ,
or, in simpler notation,
d + t → α + n .
This reaction releases 17.6 MeV, or about 3.5 MeV per nucleon. Most of this energy—14 MeV—appears as kinetic energy of the neutron. The DT reaction is one of the key reactions in thermonuclear weapons.
Except for trace amounts produced by cosmic rays, tritium does not occur in nature. It must be manufactured at great expense in nuclear reactors,2 and once manufactured, it decays into He3 with a half life of 12.3 years. If fusion is to be practical as a controlled power source in the future, it must rely on plentiful deuterium for fuel. The DD reaction proceeds with approximately equal probability in two ways:
(1) d +d →He3 +n (energy release = 3.3 MeV)
(2) d +d →t +p (energy release = 4.0 MeV)
In conditions that can be visualized on Earth (even in a thermonuclear explosion), the helium-3 produced does not significantly react further. The tritium, however, is consumed by the DT reaction, adding a large increment of energy. The net reaction in the burning of pure deuterium is approximately,
5d → He3 + He4 + 2n + p (energy release = 25 MeV).
The high-temperature requirement for thermonuclear reactions can be understood quite simply in terms of the small size of nuclei and the electrical repulsive force between them. In order for a pair of deuterons, or a deuteron and a triton, to “touch”—that is, to be close enough together so that their wave amplitudes overlap significantly—their centers must be separated by not more than about 10–14 m. At this separation, the electric potential energy associated with their relative position can readily be calculated (P. E. = ke2/d). It turns out to be 144 keV.
Although small compared with energies available even in the puniest accelerators, this energy is enormous compared with ordinary thermal energy. Normally the electric repulsion between hydrogen nuclei, or any other nuclei, very effectively keeps them apart, even if their atomic electrons are stripped away. Even at a temperature of 10,000 K, capable of vaporizing all matter, the mean kinetic energy of thermal motion is only 1.3 eV per particle, more than 100,000 times smaller than the potential barrier of 144 keV cited above. What temperature would be required in order that an average pair of deuterons, in a head-on collision, could climb the potential barrier and come within 10–14 m of each other? To answer this question, let us suppose that each deuteron has an energy 1⁄2kT equal to half of the total required, or
1⁄2kT = 72 KeV = 1.15 × 10–14 J .
Using k = 1.38 × 10–23 J/K, we find
T = 560 million K .
In energy units, kT = 48 keV. The actual temperature requirement to ignite deuterium is not this extreme, for two reasons. First, some nuclei have considerably more kinetic energy than the average. They can more easily overcome the force of electric repulsion. Second, barrier penetration can be significant. The nuclei need not all surmount the potential-energy barrier in order to react. In practice, thermonuclear explosions proceed at temperatures of about 60 million K (kT = 5 keV). A fission bomb can provide ignition at this temperature.
Deuterium is a satisfactory thermonuclear fuel in principle, and is the only fuel contemplated for possible future fusion power reactors. But as a major component of a bomb, it has a serious disadvantage. In order to be stored compactly at high density, it must be cooled to its liquefaction temperature of 20 K (– 253 °C). This requires elaborate refrigeration techniques. A common fusion fuel actually used in the “H bomb” is a particular isotopic form of lithium hydride, called lithium 6 deuteride (3Li6 1H2), which is a solid at normal temperature. The lithium plays two important roles as a constituent of the thermonuclear fuel. First, through its chemical combination with deuterium, it holds the deuterons close together, thereby helping to make possible the DD reactions. Second, the lithium itself participates in a key reaction that “manufactures” tritium to stoke the DT reaction.
The significant nuclear reactions in lithium 6 deuteride are these:
(1) 1H2 + 1H2 → 2He3 + n (energy release = 3.3 MeV),
(2) 1H2 + 1H2 → 1H3 + p (energy release = 4.0 MeV),
(3) 1H2 + 1H3 → 2He4 + n (energy release = 17.6 MeV),
(4) 3Li6 + n → 1H3 + 2He4 (energy release = 4.9 MeV).
The first two are the branches of the DD reaction. The third is the DT reaction. The fourth reaction, like the second branch of the DD reaction, is a supplier of tritium for the DT reaction. This neutron-induced reaction is not itself a thermonuclear reaction, since the neutron has no energy barrier to overcome to reach the Li6 nucleus. It is in fact a fission reaction (although the word “fission” is usually reserved to describe the splitting of heavy nuclei). The Li6 nucleus absorbs a neutron to become temporarily a Li7 nucleus that splits into a triton and an alpha particle. Note that in these four interlocked reactions both tritons and neutrons play important roles, although neither is initially present in the fuel. Reactions 1 and 3 produce neutrons to stimulate the Li6 reaction; reactions 2 and 4 produce tritium to burn in the DT reaction.
One way to increase both the rate of burning and the energy release of a thermonuclear weapon is to encase its lithium 6 deuteride fuel in U238. The 14-MeV neutrons produced by the DT reaction, many of which escape from the combustion zone, are energetic enough to induce fission in U238. From the fission event emerge several lower energy neutrons that can stimulate the tritium-producing reaction in Li6. Through this sequence of fission-fusion-fission-fusion, the energy of the atomic bomb trigger can be multiplied a thousand-fold,3 using only cheap and readily available materials—lithium 6, deuterium, and uranium 238. In such a uranium-encased weapon, about half of the energy and almost all of the hazardous fallout result from uranium fission. In so-called “clean” bombs (if such exist), most of the energy comes from fusion.
1 Even in the Sun, the proton-proton cycle is a significant energy source only in the hottest and densest central core of the Sun. Outside this relatively small core, there is very little thermonuclear energy production.
2 The tritium-producing reactor in Savannah River, South Carolina, was the site of the first identification of the neutrino.
3 Public reports suggest that nuclear weapons are actually getting smaller, not larger, so that they can be more easily mounted on “delivery vehicles,” and because these vehicles now have a pinpoint accuracy that was lacking in the early days of nuclear weapons. Reportedly, even “small” weapons use thermonuclear burning.