Nuclear Fusion – an ideal energy source Two nuclei combine into one nucleus with the emission of a nucleon is called nuclear fusion

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Chapter 9

According to Niels Bhor's definition, an expert is a person who, through his own bitter experience, has found out all the mistakes that one can commit in a very field.

Edward Teller (1981)

Nuclear Fusion
an ideal energy source

Two nuclei combine into one nucleus with the emission of a nucleon is called nuclear fusion. The most familiar and promising nuclear fusion is the conversion of a deuterium and a tritium into helium with the release of a neutron and a lot of energy. There are many more possibilities and examples* of fusion described in this Chapter.

Nuclear fusion reactions provide energy in the sun, which provides us with almost all the energy. Energy from the sun drives the weather, causing rain, snow, wind, and heat. Solar energy makes plants grow, and energy stored in plants sustains animal lives. The sun is 150 million kilometers far, even light leaving the sun surface takes more than 4 minutes to reach the Earth, yet it plays a dominant role in our lives. Indirectly, nuclear fusion energy is part of our daily live. So, understanding what is going on in the sun is important.

On the other hand, raising living standard also raises energy consumption. Increase in energy demand causes all kinds of problems, some of which are social and political ones. Nuclear fission energy was once thought to be a big help, and solve all the problems, but fission technologies are now not acceptable to the public because of the big risks associated with them. The big hope is now fusion technologies. Therefore, it is important for us to understand the basic science of nuclear fusion.

Nuclear Fusion

The sun is one of the billions of stars out there in the universe. Only a small number of stars are visible to the unaided eyes, and the Sun is one of them. The next nearest star, the Alpha or Proxima Centauri is 4.3 light years from the Sun, whereas the Sirius and the Procyon are 8.6 and 11.4 light years from the Sun respectively. Stars generally occur in pairs and multiple systems (clusters), but the Sun and a few others exist singly.

The mean distance between the Sun and the Earth is usually called an Astronomical Unit (AU), which is 149,597,870.7 km (one hundred fifty million kilometers), 4.3 light minutes. The mass of the Sun is 333,000 times that of the Earth, whereas its radius is 109 times that of the Earth. The sun is a big nuclear fusion reactor, which lasts a long time, unlike a fusion bomb.

From Stars to Hydrogen Bombs

A bright sunny day makes everybody happy. The Sun dominates our lives in more than one way, but most people do not know the basic facts about the sun or about stars in general.

  • How do stars produce energy?
    What is the power output of the Sun?
    What is the solar power received on Earth?
    Is it possible to produce a small Sun on Earth?

The Sun emits 3.861026 watts of power, almost 8 kwatt/cm2 at the surface. Just outside the atmosphere, the planet Earth receives 0.14 watt/cm2, and this value is known as the solar constant, a value important for the design of solar energy supply for spaceships. Solar power reaching the sea level varies with weather conditions.

Thermonuclear reactions (another term for nuclear fusion) provide energy in the Sun, proposed Atkinson and Houtermans in 1929. George Gamow, a young physicist, learned the proposal. At a meeting in Leningrad, he reported that if hydrogen a gas were heated to very high temperatures, nuclear fusion would take place, releasing energy like a sun. He was immediately offered the privilege of research for making a sun for the Communist party, but he did not accept. He is very well known for having written extensively on many aspects of science. He also worked in the Manhattan project.

The theory on the energy production of the Sun continued to develop, but difficulties in heating and holding the hot hydrogen gas are the barriers for creating another sun on Earth. Fortunately, particle accelerators have been available for the investigation of fusion reactions. Using accelerated protons and deuterons, exothermic nuclear fusion has been confirmed. The fusion of 1H, deuterium, tritium, helium, carbon etc. releases a large amount of energy.

In 1939, Hans A. Bethe (1906 ) proposed that stars derive their energy from fusion reactions. During World War II, the idea emerged that a fission explosion could heat up and compress light nuclides to initiate a chain of nuclear fusion (Teller, 1981). Soon after the war Teller, Bethe and others directed the Manhattan project, and they utilized fission explosions to heat and to compress mixtures of deuterium and tritium. They made hydrogen bombs (or thermonuclear bombs) and the first one was tested on November 1, 1952 (code name "Mike") on a Pacific coral atoll. Thereafter, USSR, Britain, China, and France have tested similar bombs. A single bomb can completely destroy a large city. Nearly all scientists who have worked on these weapons campaign for the banning of further nuclear tests.

Skill Developing Questions

  1. The fusion of what type of nuclides will release large amounts of energy?
    What are the applications of nuclear fusion?

  2. What reactions are responsible for generating the energy in stars?
    What evidences support the your claim?

Nuclear Fusion

Nuclear fusion is a special nuclear reaction, opposite to fission. Like all nuclear reactions, the reactants are converted to different elements.

  • What is nuclear fusion?
    How can fusion reactions be studied?
    What are the best fusion materials?
    What fusion reaction is the most promising for a fusion reactor to supply energy for the future?

In nuclear fusion, two light nuclei combine into one, but some nucleons may also be released. For fusion to take place, two bare nuclei must approach each other within a short distance of 10–15 m so that the strong force becomes sufficiently effective to hold the nucleons together. Both nuclei are positively charged, and the nuclei must move at high speed to overcome the Coulomb barrier before fusion takes place. In other words, fusion reactions requires very high temperatures.

Particle accelerators invented for the study of nuclear reactions are also wonderful machines for the study of fusion. Accelerated H, D, T, 3He, 4He particles are used to bombard targets of these nuclides. These experiments enable us to learn the nature of fusion. Probabilities of fusion reactions are quantitatively defined as the cross sections. Cross sections for various fusion reactions at various temperatures are different and their variations with temperatures are also different.

Well known plots of these cross sections have been given by Post (1970), and an approximate sketch is illustrated here. The higher the effective fusion cross section, the higher the probability of fusion. In general, the probability increases with kinetic energy of the nuclei. Kinetic energies of nuclei are proportional to their temperatures in K. Note that the vertical axis (effective fusion cross section) is a log scale, and the divisions increase by a factor of 10, whereas the horizontal (kinetic energy or temperature) scale is a linear scale. All things considered, the most favorable reaction is

2D + 3T  4He + n.

The D + T fusion has the highest cross section at any temperature, and the cross section is high even at moderate temperatures. Thus, thermal nuclear fusion of deuterium and tritium is the reaction of choice for fusion research and thermonuclear bombs. Neutrons are also products of the nuclear fusion reactions.

At the temperature corresponding to a kinetic energy of 40 keV, the cross sections for D-3He, D-D, and D-T fusions are 0.3, 3, and 700 mb respectively. Thus, the probability of D-T fusion is 230 times that of the D-D fusion reaction, and 2300 times that of the D-3He fusion reaction.

Review Question

  1. How can fusion reactions be studied?

  2. In general, how does fusion cross section of a reaction vary with temperature?
    Which fusion reaction requires the lowest temperature to have the same probability of fusion?

Fusion Energy

In the earlier discussion of binding energy, it has been pointed out that fusion of light nuclei into nuclides with a combined mass will release energy.

  • How can fusion energy be estimated?
    How much energy is released in a fusion reaction?
    Which reaction releases the most energy?
    All things considered, which is the most promising reaction for application?

IMass excess (MeV) of some light nuclides and particles.













The energy released from nuclear fusion reactions is at the expense of the mass. The mass differences before and after the fusion reactions are converted to energy. Thus, the energy of fusion Q can be treated as part of the reaction equation. For example, the equation of D-T fusion is,

D + T  4He + n + Q

and if the mass excess (in MeV) is available, the equation based on mass and energy conservation is

13.136 + 14.950 = 2.425 + 8.071 + Q

Therefore, Q = 17.6 MeV

The actual masses rather than mass excesses can also be used, and the calculation is just as easy. The four commonly studied fusion reactions and their Q values are:

D + T  4He + n + 17.6 MeV

D + 3He  4He + p + 18.4 MeV

D + D  3He + n + 3.3 MeV

D + D  3T + p + 4.0 MeV

Reactions D + T and D + 3He releases similar amounts of energy, but the D + T reaction takes place at much lower temperatures and is particularly interesting from an engineering point of view.

The release of (Q) 17.6 MeV per 4He nuclide formed is impressive when this quantity is translated to 1.7x1012 J per mole (or 1.7x109 kJ or 4.1x108 kcal for about 4 g) of He formed. This is a very large amount of energy! However, due to the fact that both the reactants and products are at very high temperature, a considerable amount of fusion energy is released as short-wave X- or -ray radiation.

It is interesting to note that products (3He and 3T) of the D-D fusion reactions are fuels in the D + T and D + 3He reactions. Thus, 3He and 3T are intermediates of 2D fusion, and protons are also products of these reactions. Taking all the reactions into consideration, no radioactive ash or waste is produced. For this reason, fusion is considered to be clean and environmental friendly for energy generation. However, the product neutrons will cause the structural material to be radioactive due to neutron capture reactions.

The fusion of hydrogen only takes place at very high temperatures, and the energy released is 1.44 MeV, not counting the decay energy of the neutron,

H + H  D + + +  + 1.44 MeV

Another hypothetical reaction has not been observed, but it releases 23.85 MeV per 4He formed.

D + D  4He + 23.85 MeV.

Can this hypothetical reaction take place under peculiar conditions? Although speculative in nature, the fusion of deuterium to form a 4He nucleus would be an attractive reaction to have.

Although deuterium contains much more energy than helium, the fusion rate is so slow that natural nuclear fusion has been observed at ordinary temperatures and pressures on the planet Earth. Furthermore, electrostatic repulsion of atomic electrons keeps the nuclei more than 10 10 m apart. Recall that nuclei have to approach each other at 10–15 m in order to from a compound nucleus before a fusion is possible. Even when electrons are stripped, the bare nuclei have to overcome the Coulomb repulsive force before a compound nucleus can be formed.

Skill Developing Questions

  1. The star Sun emits 3.861026 watts of power. If all the energy is released from the D + T fusion, what is the rate of 4He nuclei formation?

  2. How much energy is released in a hydrogen bomb if 4 kg of 4He is formed in an explosion?

  3. How much energy would be released per mole of 4He formed by the hypothetical reaction 2DHe?

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