Nuclear Fusion

Nuclear fusion is the source of energy that powers the stars.

Fusion occurs when atomic nuclei combine to produce a larger nucleus. Fusion reactions that result in the creation of a nucleus with an atomic mass lower than that of iron will generally result in a net release of energy. This is because iron is the most tightly bound atomic nucleus and, therefore, the overall binding energy after the reaction will be lower (more negative) than the total binding energy before the nuclei fused together. This results in a release of energy equivalent to the difference between the total binding energy before and after the reaction. The energy is usually released through the emission of a photon (electromagnetic radiation), a beta particle (an electron or a positron) or an alpha particle (a helium-4 nucleus).

Atomic nuclei can fuse together when they come close enough to be attracted to each other through the powerful, but short-range, strong nuclear force. However, extremely high energies, and hence high temperatures, are necessary to first overcome the repulsive force from the nuclei’s less powerful, but longer-range, electromagnetic fields.

The potential for energy generation from nuclear fusion vastly exceeds that which can be produced through chemical reactions. This is because chemical reactions only involve the electromagnetic interactions of the electrons that orbit the nuclei of atoms, rather than the much more powerful strong nuclear force.

The energy from fusion reactions can also exceed that which can be produced through nuclear fission – where atomic nuclei, more massive than that of iron, are split into smaller atomic nuclei to release energy.

Nuclear fusion is also the means by which a large proportion of the energy is produced by a thermonuclear hydrogen bomb, the most destructive weapon yet to be devised. This should not be confused with a nuclear fission bomb (which the term “atomic” bomb usually refers to), powered exclusively by nuclear fission reactions. Note that nuclear fission is also used in a thermonuclear bomb to initiate the hydrogen fusion reactions.

Nuclear Fusion Power Stations

Despite its potential for mass destruction, nuclear fusion could, one day, provide us with a virtually unlimited, safe and clean source of energy, if we are able to develop the technology to sustain controlled nuclear fusion reactions here on Earth.

Unlike with nuclear fission, in a nuclear fusion reactor there would be no possibility of a runaway chain reaction, causing a reactor meltdown or an explosion. There would also be no possibility of a release of large quantities of radioactive material from a fusion reactor, hence nuclear fusion is considered to be an extremely safe form of energy production. This is mainly because fusion reactors would only require very small amounts of radioactive material to operate, and the conditions necessary to sustain the reaction are extremely fine-tuned, so any disruption to the process would simply cause the fusion reaction to cease.

Nuclear fusion is also considered to be environmentally friendly because, unlike burning fossil fuels, nuclear fusion does not produce carbon dioxide, or other atmospheric pollutants, and would not contribute to anthropogenic climate change. Fusion power stations would also produces no high-level radioactive waste.

ITER, an experimental fusion power plant, currently being constructed in southern France, aims to demonstrate that nuclear fusion could be a commercially-viable source of energy. However, it is not scheduled to become operational before 2027, and even if successful, it’s unlikely that we’ll have fully-operational fusion power stations producing electricity before the mid-2030s. (Note that, originally, ITER stood for International Thermonuclear Experimental Reactor, although this somewhat alarming sounding acronym, considering the connotations of the word thermonuclear in connection with the hydrogen bomb, has now been dropped, and officially the name ITER is Latin for “the way”.)

The Joint European Torus (JET), in Oxfordshire in England, and the JT-60 (Japan Torus), in Japan, are currently the most advanced experimental fusion reactors we have. Like the design for ITER, both of these machines are magnetic confinement reactors, containing plasma at extremely high temperatures, using magnetic fields, in a torus-shaped (doughnut-shaped) reaction chamber, known as a “tokamak”. This word comes from a Russian acronym that can be closely translated as toroidal chamber with magnetic coils.

Another promising technology is inertial confinement fusion, which uses laser beams to heat and compress pellets of nuclear fuel. However, problems with uneven compression of the fuel pellets, as well as the high cost of manufacturing the pellets, which need to be perfectly spherical to a high level of precision, are yet to be overcome.

For now, the centre of a star is one of the few places where the necessary conditions exist for self-sustaining nuclear fusion reactions to occur.

Atomic Nuclei

Most of the mass of an atom is concentrated at a tiny point in its centre, called the nucleus. Atomic nuclei consist of particles known as protons and neutrons, and collectively as nucleons. These are not fundamental particles, but are members of the family of particles known as baryons, which consist of three quarks held together by the strong nuclear force. Each proton consists of two up quarks and a down quarks, while each neutron consists of two down quarks and an up quark. Protons and neutrons, therefore, have similar masses but are nearly two thousand times more massive than the electrons that orbit the atomic nucleus.

The strong nuclear force acts over very short distances between quarks; however, some of this force extends beyond the boundaries of the individual protons and neutrons. Protons are positively charged, so will normally repel each other via the longer-range electromagnetic force. However, if protons come close enough together, this repulsion can be overcome by the more powerful, but short range, strong nuclear force, which can bind them together to form the nuclei of atoms. Stable atomic nuclei also require the presence of neutrons, however, to stop the repulsive electromagnetic force from dominating.

As its name suggests, the neutron is an electrically neutral particle, which helps to reduce the effect of the repulsive electric field between the positively-charged protons. However, neutrons cannot be held together by the strong nuclear force on their own. If a nucleus contains too many neutrons, some of them will spontaneously decay into protons through the emission of an electron. This is known as radioactive beta decay and is due to a third fundamental force known as the weak nuclear force. This means that the most stable forms of atomic nuclei usually consist of a roughly equal number of protons and neutrons.

For example, the nucleus of a helium atom usually consists of two protons and two neutrons, although helium nuclei containing just one neutron are also stable. Unstable forms of helium can also exist, briefly, with up to eight neutrons, although they are highly radioactive, with extremely short half-lives (the half-life being the time taken for half of the atoms in a sample to undergo radioactive decay).

It is the number of protons in the nucleus of an atom that determines its chemical properties, which is why all atoms with two protons in their nucleus are considered to be helium atoms and all of the alternative forms, with differing numbers of neutrons, are known as isotopes of helium.

Note, however, that the force between nucleons becomes repulsive again at even smaller separations because of the Pauli exclusion principle. Note also that neutrons can be held together without decaying to protons by the extreme gravitational field of a neutron star.

Binding Energy

The binding energy of the nucleus is the potential energy of its constituent protons and neutrons. In other words this is a measure of the energy that would be needed to completely separate the individual nucleons. Conversely, this is also a measure of the energy that is released if the individual nucleons are combined together.

Hydrogen is the simplest atomic nucleus, requiring just one proton, although three different isotopes of hydrogen exist. The vast majority of hydrogen atoms have no neutrons and are composed of just a proton surrounded by one orbiting electron (which has the opposite electric charge, creating an electrically neutral atom). The two other isotopes of hydrogen are known as deuterium and tritium. Deuterium gets its name because it consists of two nucleons – one proton and one neutron – while tritium contains three nucleons – one proton and two neutrons. The most common form of hydrogen, consisting of just one proton, is also known as protium, to distinguish it from deuterium and tritium. Protium and deuterium are stable isotopes of hydrogen, while tritium has a half-life of about 12.3 years.

Two protons (i.e. two typical hydrogen nuclei) can be fused together so that they produce deuterium. If this occurs, energy is released, equivalent to the binding energy of the deuterium nucleus.

This is actually a two-stage process. First, the two protons fuse together releasing a high-energy photon in the gamma-ray region of the electromagnetic spectrum. Almost immediately after this, one of the protons emits a positron (the positively charged antiparticle of the electron), as well as a neutrino, turning this proton into a neutron.

Most of the energy released, in the second stage of the reaction, goes towards the creation of this positron, although some energy is also carried away by the neutrino, which is necessary in order to conserve the total lepton number before and after the reaction. A positron is a particle of antimatter and has a lepton number of -1, while the neutrino has a lepton number of +1, making a total lepton number of zero, both before and after the reaction (see Particle Physics).

Energy is equivalent to mass, through Einstein’s famous equation E = mc2 (where E represents energy, m represents mass and c is the speed of light in a vacuum – see Relativity Theory). This equation can be used to calculate the energy required to make up the rest masses of the positron and the neutrino. However, the rest mass of the neutrino is tiny in comparison to that of the positron (and possibly even zero, as some theories of particle physics predict that the neutrino is a massless particle). The remainder of the energy released goes towards the kinetic energy of the positron and the neutrino – as they are expelled at high velocities from the deuterium nucleus – as well as the recoil kinetic energy of the deuterium nucleus. In total, along with the energy from the gamma ray, emitted in the first stage of the reaction, the total energy released is around 26.2 megaelectronvolts (MeV).

The overall mass of the nuclei before a fusion reaction will be greater than the mass of the resulting nucleus, by an amount equivalent to the energy that has been radiated away (via E = mc2). This difference is known as the ‘mass defect’. (Note, that mass defects are not peculiar to nuclear reactions. A chemical reaction will also have an associated mass defect, equivalent to the difference in energy of the reacting particles before and after the reaction. However, chemical reactions generally produce much less energy than nuclear reactions, so the associated mass defect is much smaller.)

However, in order for two protons to fuse, they must first be brought close enough together to overcome the electromagnetic repulsion between them. The energy required for this is known as the activation energy of the reaction. In this type of reaction, the activation energy is much less than the binding energy released when the deuterium nucleus is formed, leading to an overall release of energy.

The Proton-Proton Chain Reaction

This fusing of two protons, to form deuterium, is the first step of the proton-proton chain reaction, which is the dominant fusion process in the majority of stars of a similar size or smaller than our Sun.

The material in the centre of a star exists in the form of a plasma. This is a state of matter where some of the electrons have enough thermal energy to be considered to be free of the atomic nuclei they normally orbit. A plasma is, therefore, a “soup” of electrons and ionised atomic nuclei.

The positron, produced when one of the two fused protons turns into a neutron, will annihilate almost immediately with an electron, producing two more gamma ray photons.

Once a deuterium nucleus is formed from two protons in this way, it will exist for only a matter of seconds before it fuses with a further proton to produce a helium nucleus. Since this new nucleus contains two protons and one neutron, it has an atomic mass of three, and hence is known as Helium-3 (also written as He-3 or 3He.

This second fusion process also releases energy, again in the form of a gamma ray.

After this, the reaction can proceed in any of four ways, although in the dominant reaction that occurs at stellar temperatures between around 10 million to 14 million Kelvin, two He-3 nuclei will combine, and almost immediately split, to form a He-4 nucleus (two protons and two neutrons) as well as two separate protons. The total net energy released in this form of the proton-proton chain reaction is 26.22 MeV.

Above around 14 million Kelvin, the dominant process is the combination of a He-3 nucleus with a pre-existing He-4 nucleus, to produce a beryllium nucleus containing four protons and seven neutrons. This nucleus then undergoes the process of electron capture – the reverse of beta decay – turning one of the neutrons into a proton and hence creating a lithium nucleus, with the release of a further neutrino. This lithium nucleus will then combine with another proton and then split into two He-4 nuclei.

Alternatively, the beryllium nucleus can combine with a proton, rather than capturing an electron, to produce boron, which then decays, emitting a positron and a neutrino, to produce Be-8. This will then splits in half to produce two He-4 nuclei.

In the fourth possible process, the He-3 nucleus simply reacts directly with a proton to create He-4 with the emission of an electron and a neutrino, to change one of the protons into a neutron.

The CNO Cycle

In stars that are more than around 1.3 solar masses, the Carbon-Nitrogen-Oxygen (CNO) process is the dominant means of energy production.

A carbon nucleus containing six protons and six neutrons (i.e. carbon-12) can absorb a proton to become a nitrogen nucleus, emitting a gamma ray. One of the protons in this nitrogen nucleus then decays, via positron emission, to become a neutron (also releasing a neutrino), producing carbon-13. this carbon nucleus can then absorb another proton, to become nitrogen-14, which then absorbs a further proton to become oxygen-15, containing eight protons and seven neutrons. Both these transitions release energy as gamma ray photons. The oxygen nucleus then decays, via positron emission, to nitrogen-15. Finally, this nitrogen nucleus absorbs a further proton and then splits to produce a carbon-12 nucleus and a helium-4 nucleus.

Since, in this instance, the reaction started with a carbon-12 nucleus, the cycle can recommence, producing a helium-4 nucleus each time, with the overall release of 26.7 MeV.

In this reaction, carbon, nitrogen and oxygen nuclei act as catalysts, i.e. depending on where you define the start and end point of the reaction to be, they will facilitate the creation of He-4 from four protons, and be unchanged from their original form at the end of each cycle.

There are three more variations of the CNO cycle; however, the process described above is by far the dominant CNO process in most stars.

Stella Nucleosynthesis of Heavier Elements

Following the big bang, the only chemical elements that existed were hydrogen, helium and lithium – with roughly three quarters of the mass of this baryonic matter in the form of hydrogen, around a quarter in the form of helium and less than two per cent as lithium. This primordial abundance of hydrogen is why young stars are mostly made up of hydrogen, which is fused to form helium. However, stars also produce heavier atomic nuclei via nuclear fusion. In fact all of the chemical elements we find on Earth, heavier than lithium, were created by stars. This process is known as stellar nucleosynthesis.

The Triple-Alpha Process

Besides burning hydrogen, stars can produce energy via fusion of helium nuclei. The main process by which this occurs is known as the triple alpha process, since it involves the creation of a carbon nucleus by the fusion of three alpha particles. The term alpha particle is another name for a helium-4 nucleus, since they are the particles emitted in radioactive alpha decay.

Generally, the heavier the nucleus, the lower the difference in binding energy per nucleon between successive elements in the periodic table. This means that, mass-for-mass, the fusion of hydrogen to form deuterium or helium releases more energy than the fusion of, say, two carbon atoms. The difference in binding energy per nucleon between heavier atoms, closer to iron in the periodic table, is much smaller still.

However, the nucleons in a helium-4 nucleus are particularly tightly bound. This means that fusion of just two helium-4 nuclei to produce Beryllium-8 actually consumes energy rather than releasing it. The same is true for the creation of a lithium-5 nucleus, which would be formed from the fusion of helium-4 with a proton. This is why two helium-4 nuclei or helium and hydrogen, do not readily fuse together in stars, and why the fusion of helium requires the combination of three helium-4 nuclei to proceed.

The triple-alpha process is a two-stage process, starting with the creation of a beryllium-8 nucleus from two alpha particles. This then combines with a third alpha particle to form carbon-12. To create the beryllium-8 nucleus, requires 93.7 keV of energy to be put in, however, the second stage releases +7.367 MeV, so the reaction releases much more energy than it absorbs, overall.

However,  beryllium-8 is extremely unstable and will decay quickly back into helium nuclei. Only at temperatures above 100 million Kelvin will the second stage of the reaction proceed faster than the beryllium-8 nucleus can decay.  It is possible that this temperature will be reached in the cores of the most massive of stars; however, in most main sequence stars this will not happen until they have exhausted nearly all of their hydrogen supply.

When the proton-proton or CNO reactions have burnt most of the hydrogen in the core of a star, the temperature will start to fall and the core will start to collapse under its own gravity. This marks the beginning of the red giant phase, where hydrogen is still being burnt in a layer surrounding the core that mostly consists of helium.

For stars between around 0.8 and 2.0 solar masses, eventually the core of the star will reach a point where only the electron degeneracy pressure – the outward pressure due to the Pauli exclusion principle – is keeping the core from collapsing further. When the proportion of degenerate electrons has reached a certain level (depending on the mass of the star), the required temperature for the triple-alpha processes will be reached. When this happens, the star’s core temperature increases extremely rapidly in a runaway reaction, as energy is released from the fusion of helium nuclei. This process lasts only a few seconds but consumes between 60 and 80 percent of the helium in the star’s core. This is known as the helium flash.  The star’s rate of energy production can briefly be higher than that of an entire galaxy during this stage and the star’s core will quickly become hot enough for the thermal energy to again expand the core of the star and for stable helium burning to proceed. However, during the helium flash, the star does not increase in brightness, as the energy is absorbed by the star and does not immediately escape as radiation.

In a star that is greater than around twice the mass of the Sun, the required temperature for helium burning will be reached before the electrons in the core of the star become degenerate, so no helium flash occurs.

The triple alpha process is responsible for the current abundance of carbon in the universe, and therefore for the existence of life on Earth, which depends upon it.

The Alpha Process

Once carbon has been created in a star’s interior, it can then continue to fuse with further helium nuclei (protons), to produce progressively heavier elements.  The first stage produces oxygen, followed by neon, magnesium, silicon, sulfur, argon, calcium, titanium, chromium and iron. This is known as  the ‘alpha ladder’, with energy released as a photon at each stage.

The nucleus of an iron atom has a higher binding energy than the nucleus of any other element. Since an iron nucleus is the most tightly bound, it is impossible to release energy by further fusion reactions to produce heavier elements.

The more massive the star, the hotter its core temperature and the higher up the alpha ladder the process can go. In very massive stars, the process can continue to convert iron into nickle and then nickle into zinc, but these reactions consume energy and the star’s core will cool and eventually collapse again.

Prior to exploding as a supernova, a massive red giant star will eventually come to consist of concentric ‘onion-like’ layers, burning different elements via the alpha process.  lighter elements will be produced in the outer layers, moving progressively through the alpha ladder towards the interior of the star, with iron and nickle at the core.

Lower mass stars, will not explode as supernovae, as the electron degeneracy pressure will balance the star’s gravitation. The star will evolve into a white dwarf. This type of star produces no further energy from nuclear fusion but continues to cool as it radiates its energy, eventually fading, over billions of years, to become a black dwarf. The majority of white dwarfs will be composed of carbon and oxygen, however, white dwarfs composed of heavier elements such as neon and magnesium can be formed.

It is though that white dwarfs consisting of carbon could crystallise to diamond as they cool – literally becoming a ‘diamond in the sky’.

Fusion of Heavier Elements

Stars of around eight times the mass of the Sun or greater can fuse the elements created via the alpha and triple-alpha processes, to produce yet heavier atomic nuclei. For example, two carbon-14 nuclei can be combined to produce neon, sodium or magnesium, emitting an alpha particle, a proton or a gamma ray, respectively. These reactions release energy, whereas two other possible carbon fusion reactions – producing magnesium via neutron emission and oxygen via the emission of two alpha particles – both consume energy.

Neon, and oxygen nuclei can also be fused together, with some reaction modes producing  energy and other modes consuming energy.

The S-Process

The s-process, or slow-neutron-capture-process, is similar to the alpha-process, except that a neutron, instead of a proton, is captured at each stage. A neutron can then emit an electron (beta-minus decay) to create a proton, which moves the nucleus up the periodic table of elements.

This process can occur in stars that are in the asymptotic-giant branch of the Hertzsprung-Russell diagram. This is part of the red-giant stage late in the lives of stars with masses between around 0.6 to 10 times the mass of the Sun.

The s-process can produce elements up to bismuth-209 and polonium-210.

Supernovae and the R-Process

The r-process is a ‘rapid’ version of the s-process, occurring in supernova core collapse and possibly when a neutron star merges with a black hole in a binary system.

The r-process can synthesise atomic nuclei up to plutonium-244.

When a star explodes as a supernova, much of its mass and, hence, the atomic nuclei produced throughout its lifetime, are ejected into space.  The only chemical elements that were left over from the big bang are hydrogen, helium and lithium. The rest of the elements found on Earth were produced in the interiors of stars. Our Sun and its protoplanetary disk, from which the Earth was created, formed from the debris of generations of stars that existed before the birth of our Sun.

As Carl Sagan put it: “The cosmos is within us. We are made of star-stuff. We are a way for the universe to know itself.”

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Astronomy, Cosmology, Space and Astrophysics