In the previous chapters, we explored radioactive decay and nuclear fission, both of which release energy because the products are more tightly bound than the original nuclei. In this chapter, we examine the complementary process of nuclear fusion, in which two light nuclei combine to form a heavier nucleus. Fusion powers the Sun and other stars and has the potential to provide a nearly limitless source of energy if it can be controlled on Earth.

Imagine relaxing in the warmth of the summer Sun while reading about the latest advances in fusion energy research. You may also remember hearing about the controversial claims of cold fusion. These topics are related because they all involve attempts to harness the same process that powers the Sun. Thermonuclear power refers to the production of energy through controlled nuclear fusion at extremely high temperatures. Although remarkable progress has been made, achieving practical fusion power remains a major scientific and engineering challenge. By contrast, the widely publicized claims of room-temperature "cold fusion" have never been independently verified and are not accepted by the scientific community.

Nuclear Fusion and Binding Energy

Nuclear fusion is a nuclear reaction in which two light atomic nuclei combine, or fuse, to form a heavier nucleus. Like nuclear fission, fusion releases energy because of differences in binding energy. As discussed in the previous chapter, the mass of a nucleus is always less than the combined masses of the protons and neutrons that make it up. This missing mass, called the mass defect, corresponds to the nuclear binding energy through Einstein's relation

The binding energy per nucleon, written as [latex]\mathrm{BE}/A[/latex], measures how tightly nucleons are bound within a nucleus. As shown in Figure 119.2, this quantity increases rapidly for light nuclei, reaches a maximum near iron (Fe), and then slowly decreases for heavier nuclei.

This trend explains why both fusion and fission can release energy. When light nuclei fuse, the resulting nucleus has a larger binding energy per nucleon than the original nuclei. Because the product nucleus is more tightly bound, its total mass is slightly smaller than the combined masses of the reactants. The missing mass is converted into energy according to [latex]E=mc^2[/latex]. Although the exact energy released depends on the particular nuclei involved, the fusion of light elements generally produces substantial amounts of energy.

Overcoming the Coulomb Barrier

The greatest obstacle to nuclear fusion is the Coulomb repulsion between positively charged nuclei. Because like charges repel one another, two nuclei naturally push apart as they approach. In contrast, the strong nuclear force, which binds protons and neutrons together inside nuclei, acts only over extremely short distances. As a result, nuclei must come within about a femtometer ([latex]10^{-15}[/latex] m) of one another before the attractive nuclear force can overcome their electrical repulsion and allow fusion to occur.

Figure 119.3 illustrates how the potential energy between two nuclei changes as the distance between them decreases. At large separations, the Coulomb force dominates, creating a potential energy barrier that prevents the nuclei from approaching each other. Once the nuclei come close enough, however, the attractive nuclear force becomes much stronger than the electrical repulsion, causing the nuclei to bind together and release energy.

A useful analogy is a ball rolling toward a hill. The ball must first climb the hill before it can roll down into a deep valley. Likewise, two nuclei must acquire enough kinetic energy to overcome—or nearly overcome—the Coulomb barrier before they can enter the region where the strong nuclear force pulls them together. One way to increase the nuclei's kinetic energy is to heat the fusion fuel to extremely high temperatures.

Quantum Tunneling Makes Stellar Fusion Possible

At first glance, it might seem that fusion inside the Sun should be impossible. Calculations show that temperatures of approximately [latex]10^8\ \text{K}[/latex] would be needed for hydrogen nuclei to overcome the Coulomb barrier through thermal motion alone. However, the temperature at the Sun's core is only about [latex]1.5\times10^7\ \text{K}[/latex], far below this value.

The solution comes from quantum mechanical tunneling. In quantum mechanics, particles do not always behave like tiny classical objects. Instead, there is a finite probability that a particle can penetrate an energy barrier even when it does not have enough energy to pass over it. This phenomenon, known as quantum tunneling, makes fusion possible in the Sun and plays an essential role in nearly all practical fusion reactions.

The probability of tunneling depends strongly on how close the nuclei come to one another. As temperature increases, the nuclei move faster and can approach each other more closely before being repelled. Although they may still lack enough energy to overcome the Coulomb barrier completely, the remaining barrier becomes thinner, greatly increasing the probability that tunneling will occur. Consequently, even relatively small increases in temperature produce large increases in the fusion rate.

Because temperatures and pressures are highest at the centers of stars, fusion occurs primarily in their cores. Likewise, any practical fusion reactor on Earth must heat its fuel to extremely high temperatures to maximize the probability of fusion reactions.

The Proton–Proton Cycle

The Sun generates its energy through a series of nuclear fusion reactions that convert hydrogen into helium. Because hydrogen nuclei (protons) are by far the most abundant nuclei in the Sun, the dominant energy-producing process is known as the proton–proton (pp) cycle. In this sequence of reactions, four hydrogen nuclei are ultimately transformed into one helium nucleus, releasing energy that powers the Sun and other Sun-like stars.

The proton–proton cycle proceeds through three primary reactions:

In these equations, [latex]e^{+}[/latex] represents a positron, the antimatter counterpart of the electron, and [latex]\nu_e[/latex] represents an electron neutrino. The values shown in parentheses indicate the energy released by each reaction.

Although only three reactions are listed, the complete cycle requires the first two reactions to occur twice before the third can take place. As a result, six hydrogen nuclei are initially consumed, but two are returned in the final step. The two positrons produced during the cycle quickly encounter electrons in the solar plasma. Each positron-electron pair annihilates, producing two gamma rays. Taking these annihilation events into account, the overall proton–proton cycle can be summarized as

Thus, the net result of the proton–proton cycle is the conversion of four hydrogen nuclei into one helium nucleus while releasing approximately 26.7 MeV of energy. This energy is shared among gamma rays, neutrinos, and the kinetic energy of the reaction products.

How Energy Leaves the Sun

Fusion reactions occur deep within the Sun's core, where the temperature and density are highest. Once produced, most of the energy is carried outward by photons. However, photons do not travel directly to the Sun's surface. Instead, they are repeatedly absorbed and re-emitted by the dense solar material, taking on the order of tens of thousands of years to gradually diffuse outward before finally escaping into space as sunlight.

Neutrinos behave very differently. Because they interact only through the weak nuclear force and gravity, they pass through the Sun almost without interacting with matter. Most neutrinos produced in the core escape into space in less than two seconds, carrying away a small fraction of the energy generated by fusion.

The Sun as a Natural Thermostat

The Sun maintains a remarkably stable energy output through a process of negative feedback. If the core temperature increases slightly, fusion reactions occur more rapidly, producing additional energy. This extra energy causes the Sun to expand slightly, lowering the core temperature and slowing the fusion rate.

Conversely, if the core cools slightly, gravity causes the Sun to contract. Compression increases the temperature and density of the core, accelerating fusion reactions until the energy output returns to its previous level. This self-regulating process has allowed the Sun to remain stable for billions of years while gradually converting hydrogen into helium.

Solar Neutrinos and Evidence for Fusion

Our understanding of how the Sun produces energy is based on theoretical models developed during the twentieth century. Beginning in 1938, the German-born American physicist Hans Bethe (1906–2005) developed the theory of the proton–proton cycle and other nuclear reactions that power stars. For this pioneering work, he was awarded the 1967 Nobel Prize in Physics.

One of the strongest pieces of evidence supporting these theories comes from the detection of solar neutrinos. Because neutrinos interact only very weakly with matter, they escape almost immediately from the Sun's core and travel directly to Earth. By detecting these particles, scientists can observe the nuclear reactions taking place deep inside the Sun, providing a unique window into its interior.

Large underground detectors have been built to measure these elusive particles (Figure 119.6). Despite the enormous number of neutrinos passing through Earth every second, only a tiny fraction interact with detector materials, making their detection extremely challenging.

The Solar Neutrino Problem

Early experiments consistently detected fewer solar neutrinos than theoretical models predicted. For many years, scientists debated whether this discrepancy indicated that models of the Sun were incomplete or whether some property of neutrinos had not yet been discovered. This discrepancy became known as the solar neutrino problem.

The puzzle was eventually resolved through a combination of theoretical and experimental advances. Physicists discovered that neutrinos have a small, nonzero mass and exist in three different types, or flavors. As neutrinos travel from the Sun to Earth, they can change from one flavor to another through a process called neutrino oscillation. Early detectors were sensitive to only one flavor of neutrino, explaining why fewer neutrinos were observed than expected. Modern detectors can account for all three flavors, confirming that the Sun's energy is indeed produced by nuclear fusion as predicted.

Neutrinos have also been detected from exploding stars, including Supernova 1987A. These observations provided valuable information about both stellar explosions and the properties of neutrinos.

Fusion Reactions for Energy Production on Earth

Although the proton–proton cycle powers the Sun, it is not a practical source of energy on Earth. The first reaction in the cycle,

has an extremely low probability of occurring. This slow reaction is actually beneficial for stars because it allows the Sun to produce energy steadily over a lifetime of about 10 billion years. For a fusion power plant, however, the reaction rate is far too low to generate useful amounts of energy.

Instead, researchers focus on fusion reactions involving the hydrogen isotopes deuterium ([latex]{}^{2}\text{H}[/latex]) and tritium ([latex]{}^{3}\text{H}[/latex]), which occur much more readily at achievable plasma temperatures. Some of the most important reactions are

Deuterium makes up approximately 0.015% of naturally occurring hydrogen, meaning that Earth's oceans contain an enormous supply of potential fusion fuel. Tritium is radioactive and occurs only in very small quantities naturally, but it can be produced in nuclear reactors or generated within future fusion reactors. Together, these fuels offer the possibility of producing large amounts of energy with much less long-lived radioactive waste than conventional nuclear fission.

The deuterium–tritium (D–T) reaction is currently the leading candidate for practical fusion power because it has the highest reaction probability at attainable temperatures. Most of the released energy appears as the kinetic energy of the helium nucleus and neutron.

Some fusion reactions also produce neutrons that can participate in additional nuclear reactions, helping to generate new fuel or release additional energy. For example, neutron capture by hydrogen produces deuterium and a gamma ray:

Reactions such as this, together with reactions that emit energetic gamma rays directly, release much of their energy as high-energy electromagnetic radiation. Although gamma rays carry substantial energy, converting that energy efficiently into electricity is considerably more challenging than harnessing the kinetic energy of charged particles.

Requirements for Practical Fusion

Producing useful amounts of fusion energy requires satisfying three key conditions:

• High temperature, so that nuclei have enough kinetic energy to approach closely enough for fusion.
• High fuel density, increasing the likelihood that nuclei will collide.
• Sufficient confinement time, allowing the hot plasma to remain together long enough for a large number of fusion reactions to occur.

These three quantities—temperature, density, and confinement time—are closely related. Improving one can partially compensate for limitations in another, a relationship commonly known as the Lawson criterion.

Two important milestones are used to evaluate fusion experiments:

• Break-even occurs when a fusion plasma produces as much fusion power as the external heating power supplied to it.
• Ignition occurs when the fusion reactions generate enough energy to sustain the plasma without requiring continued external heating.

Although remarkable progress has been made, producing continuous, economically practical fusion power remains one of the major engineering challenges of modern science.

Approaches to Controlled Fusion

Two complementary approaches dominate current fusion research: magnetic confinement and inertial confinement. Both seek to keep extremely hot plasma together long enough for significant numbers of fusion reactions to occur.

Magnetic Confinement

Magnetic confinement uses strong magnetic fields to trap the electrically charged particles that make up a plasma. Because charged particles spiral around magnetic field lines, carefully designed magnetic fields can keep the plasma away from the reactor walls, preventing both excessive heat loss and damage to the containment vessel.

The most widely studied magnetic confinement device is the tokamak, shown in Figure 119.8. A tokamak uses powerful toroidal and poloidal magnetic fields to confine plasma in a doughnut-shaped chamber. Decades of research have demonstrated that this design can produce the temperatures and confinement times required for fusion research.

The largest current international fusion project is ITER, being constructed in southern France. Rather than serving as a commercial power plant, ITER is an experimental reactor designed to demonstrate that controlled fusion can produce far more energy than is required to heat the plasma. The knowledge gained from ITER is expected to guide the development of future fusion power plants.

Inertial Confinement

A second major approach is inertial confinement fusion. In this technique, powerful laser beams are focused simultaneously onto a tiny fuel pellet containing deuterium and tritium. The outer layer of the pellet rapidly vaporizes, and the resulting outward explosion compresses the remaining fuel inward to extremely high density and temperature.

Because the compressed fuel remains together only for a tiny fraction of a second, fusion must occur before the plasma has time to expand. The fuel's own inertia provides this brief period of confinement, giving the technique its name.

The best-known inertial confinement facility is the National Ignition Facility (NIF) at Lawrence Livermore National Laboratory in California (Figure 119.9). NIF uses 192 high-powered laser beams to compress a small fuel capsule. In recent years, NIF achieved important milestones by demonstrating fusion ignition in laboratory experiments, representing a significant scientific achievement. However, substantial engineering advances are still required before inertial confinement fusion can become a practical source of commercial electricity.