Chapter 14. Fusion Reactors

A device that permits the controlled release of fusion energy is designated as a fusion reactor in contrast with one yielding fission energy, the fission reactor. As discussed in Chapter 7, the potentially available energy from the fusion process is enormous. The possibility of achieving controlled thermonuclear power on a practical basis has not yet been demonstrated, but progress in recent years gives encouragement that fusion reactors can be in operation in the 21st century. In this chapter we will review the choices of nuclear reaction, study the requirements for feasibility and practicality, and describe the physical features of machines that have been tested. Suggestions on this chapter by John G. Gilligan are recognized with appreciation.

14.1. Comparison of Fusion Reactions

The main nuclear reactions that combine light isotopes to release energy, as described in Section 7.1, are the D-D, D-T, and D-³He. There are advantages and disadvantages of each. The reaction involving only deuterium uses an abundant natural fuel available from water by isotope separation. However, the energy yields from the two equally likely reactions are low (4.03 and 3.27 MeV). Also the reaction rate as a function of particle energy is lower for the D-D case than for the D-T case, as shown in Figure 14.1. The quantity , dependent on cross section and particle speed, is a more meaningful variable than the cross section alone.

Figure 14.1. Reaction rates for fusion reactions. The quantity , the average over a Maxwellian distribution of cross section times speed, when multiplied by particle densities gives the fusion rate per unit volume.

The D-T reaction yields a helium ion and a neutron with energies as indicated:

The cross section is large and the energy yield is favorable. The ideal ignition temperature (Section 7.3) for the D-T reaction is only 4.4 keV in contrast with 48 keV for the D-D reaction, making the achievement of practical fusion with the former far easier. One drawback, however, is that the artificial isotope tritium is required. Tritium can be generated by neutron absorption in lithium, according to the two reactions

The neutron can come from the D-T fusion process itself in a breeding cycle similar to that in fission reactors. Liquid lithium can thus be used as a coolant and a breeding blanket.

The fact that the D-T reaction gives a neutron as a byproduct is a partial disadvantage in a fusion machine. Wall materials are readily damaged by bombardment by 14.1 MeV neutrons, requiring frequent wall replacement. Also, materials of construction become radioactive as the result of neutron capture. These are engineering and operating difficulties, whereas the achievement of the high enough energy to use neutron-free reactions would be a major scientific challenge.

In the long run, use of the D-T reaction is limited by the availability of lithium, which is not as abundant as deuterium. All things considered, the D-T fusion reactor is the most likely to be operated first, and its success might lead to the development of a D-D reactor.

14.2. Requirements for Practical Fusion Reactors

The development of fusion as a new energy source involves several levels of accomplishment. The first is the performance of laboratory experiments to show that the process works on the scale of individual particles and to make measurements of cross sections and yields. The second is to test various devices and systems intended to achieve an energy output that is at least as large as the input and to understand the scientific basis of the processes. The third is to build and operate a machine that will produce net power of the order of megawatts. The fourth is to refine the design and construction to make the power source economically competitive. The first of these levels has been reached for some time, and the second is in progress with considerable promise of success. The third and fourth steps remain for achievement in the 21st century.

The hydrogen bomb was the first application of fusion energy, and it is conceivable that deep underground thermonuclear explosions could provide heat sources for the generation of electricity, but environmental concerns and international political aspects rule out that approach. Two methods involving machines have evolved. One consists of heating to ignition a plasma that is held together by electric and magnetic forces, the magnetic confinement fusion (MCF) method. The other consists of bombarding pellets of fuel with laser beams or charged-particle beams to compress and heat the material to ignition, the inertial confinement fusion (ICF) method. Certain conditions must be met for each of these approaches to be considered successful.

The first condition is achievement of the ideal ignition temperature of 4.4 keV for the D-T reaction. A second condition involves the fusion fuel particle number density n and a confinement time for the reaction, τ. It is called the Lawson criterion and is usually expressed as:

A formula of this type can be derived for MCF by looking at energy and power in the plasma. Suppose that the numbers of particles per cm³ are n^D deuterons, n^T tritons, and n^e electrons. Furthermore, let the total number of heavy particles be n = n^D + n^T with equal numbers of the reacting nuclei, n^D = n^T, and n^e = n for electrical neutrality. The reaction rate of the fusion fuel particles is written with Section 4.3 as n^Dn^Tσ υ, and if E is the energy yield per reaction, the fusion power density isproportional to the square of the ion number density.

Now the power loss rate can be expressed as the quotient of the energy content (n^D + n^T) (3kT/2) and the confinement time τ, i.e.,

Equating the powers and solving,

Insert the ideal ignition energy of kT = 4.4 keV, the fusion energy E = 17.6 MeV, and let be equal to the value of from Figure 14.1 of approximately 10⁻¹⁷. The result is 3 × 10¹⁴, of the correct order of magnitude. The Lawson criterion, however, is only a rough rule of thumb to indicate fusion progress through research and development. Detailed analysis and experimental testing are needed to evaluate any actual system.

Similar conditions must be met for ICF. An adequate ion temperature must be attained. The Lawson criterion takes on a little different form, relating the density ρ and the radius r of the compressed fuel pellet,

The numerical value is set in part by the need for the radius to be larger than the range of α particles to take advantage of their heating effect. For example, suppose that 1 mm radius spheres of a mixture of D and T in liquid form, density 0.18 g/cm³, are compressed by a factor of 2500. The radius is reduced by a factor of (2500)^1/3 = 13.6, and the density is increased to (2500) (0.18) = 450 g/cm³. Then ρr = 3.3, which meets the objective.

It is interesting to note that the factors that go into the products nτ are very different for the two types of fusion. For MCF typically n = 10¹⁴/cm³ and τ = 1 s, whereas for ICF n = 10²⁴/cm³ and τ = 10⁻¹⁰ s.

The analysis of fusion reactors involves many other parameters of physics and engineering. A useful collection of formulas and methods of calculating are discussed in Computer Exercise 14.A.

Progress toward practical fusion can be measured by the parameter Q, which is the ratio of energy output to energy input. Four stages of plasma can be identified. In the first, more energy must be supplied than is produced, Q < 1. In the second, the breakeven case, fusion power equals input power, Q = 1. In the third, for an operating fusion power plant, Q is considerably larger than 1 (e.g., 10). In the fourth, the burning plasma, which results from ignition, heats itself without external input, and Q is infinity.

14.3. Magnetic Confinement Machines

A number of complex MCF machines have been devised to generate a plasma and to provide the necessary electric and magnetic fields to achieve confinement of the discharge. We will examine a few of these to illustrate the variety of possible approaches.

First, however, consider a simple discharge tube consisting of a gas-filled glass cylinder with two electrodes as in Figure 14.2(A). This is similar to the familiar fluorescent light bulb. Electrons accelerated by the potential difference cause excitation and ionization of atoms. The ion density and temperature of the plasma that is established are many orders of magnitude below that needed for fusion. To reduce the tendency for charges to diffuse to the walls and be lost, a current-carrying coil can be wrapped around the tube, as sketched in Figure 14.2(B). This produces a magnetic field directed along the axis of the tube, and charges move in paths described by a helix, the shape of a stretched coil spring. The motion is quite similar to that of ions in the cyclotron (Section 8.4) or the mass spectrograph (Section 9.1). The radii in typical magnetic fields and plasma temperatures are the order of 0.1 mm for electrons and near 1 cm for heavy ions (see Exercise 14.1). To further improve charge density and stability, the current along the tube is increased to take advantage of the pinch effect, a phenomenon related to the electromagnetic attraction of two wires that carry current in the same direction. Each of the charges that move along the length of the tube constitutes a tiny current, and the mutual attractions provide a constriction in the discharge.

Figure 14.2. Electrical discharges.

Neither of the preceding magnetic effects prevent charges from moving freely along the discharge tube, and losses of both ions and electrons are experienced at the ends. Two solutions of this problem have been tried. One is to wrap extra current-carrying coils around the tube near the ends, increasing the magnetic field there. This causes charges to be forced back into the region of weak field (i.e., to be reflected). This “mirror machine” is not perfectly reflecting. Another approach is to create endless magnetic field lines by bending the vacuum chamber and the coils surrounding it into the shape of a figure eight. An early version of this arrangement, called a “stellarator,” is still being considered as a favorable system because it does not depend on internal currents for plasma confinement. It could operate continuously rather than in pulses.

A completely different solution to the problem of charge losses is to produce the discharge in a doughnut-shaped tube, a torus, as shown in Figure 14.3. The first successful ring-shaped fusion machine was developed by scientists in the U.S.S.R. around 1960. They called it tokamak, an acronym in Russian for toroid–chamber–magnet–coil. Because the tube has no ends, the magnetic field lines produced by the coils are continuous. The free motion of charges along the circular lines does not result in losses. However, there is a variation in this toroidal magnetic field over the cross section of the tube that causes a small particle migration toward the wall. To prevent such migration, a current is passed through the plasma, generating a poloidal magnetic field. The field lines are circles around the current and tend to cancel electric fields that cause migration. Vertical magnetic fields are also used to stabilize the plasma.

Figure 14.3. Plasma confinement in torus.

Plasmas of MCF machines must be heated to reach the necessary high temperature. Various methods have been devised to supply the thermal energy. The first method, used by the tokamak, is resistance (ohmic) heating. A changing current in the coils surrounding the torus induces a current in the plasma. The power associated with a current through a resistance is I²R. The resistivity of a “clean” hydrogen plasma, one with no impurity atoms, is comparable to that of copper. Impurities increase the resistivity by a factor of four or more. There is a limit set by stability on the amount of ohmic heating possible.

The second method of heating is neutral particle injection. The sequence of events is as follows: (a) a gas composed of hydrogen isotopes is ionized by an electron stream; (b) the ions of hydrogen and deuterium produced in the source are accelerated to high speed through a vacuum chamber by a voltage of approximately 100 kV; (c) the ions pass through deuterium gas and by charge exchange are converted into directed neutral atoms; (d) the residual slow ions are drawn off magnetically, whereas the neutral ions cross the magnetic field lines freely to deliver energy to the plasma.

The third method uses microwaves in a manner similar to their application to cooking. The energy supply is a radiofrequency (RF) generator. It is connected by a transmission line to an antenna next to the plasma chamber. The waves enter the chamber and die out there, delivering energy to the charges. If the frequency is right, resonant coupling to natural circular motions of electrons or ions can be achieved. The phrase electron (or ion) cyclotron radiofrequency, ECRF (or ICRF), comes from the angular frequency of a charge q with mass m in a magnetic field B, proportional to qB/m as discussed in Section 8.1.

Because the fusion reactions burn the deuterium-tritium fuel, new fuel must be introduced to the plasma as a puff of gas, as a stream of ions, or as particles of liquid or solid. The latter method seems best, despite the tendency for the hot plasma to destroy the pellet before it gets far into the discharge. It seems that particles that come off the pellet surface form a protective cloud. Compressed liquid hydrogen pellets of approximately 10²⁰ atoms moving at 80 m/s are injected at a rate of 40 per second.

The mathematical theory of electromagnetism is used to deduce the magnetic field shape that gives a stable arrangement of electric charges. However, any disturbance can change the fields and in turn affect the charge motion, resulting in an instability that may disrupt the field configuration. The analysis of such behavior is more complicated than that of ordinary fluid flow because of the presence of charges. In a liquid or gas, the onset of turbulence occurs at a certain value of the Reynolds number. In a plasma with its electric and magnetic fields, many additional dimensionless numbers are needed, such as the ratio of plasma pressure to magnetic pressure (β) and ratios to the plasma size of the mean free path, the ion orbits, and the Debye length (a measure of electric field penetration into a cloud of charges). Several of the instabilities such as the “kink” and the “sausage” are well understood and can be corrected by assuring certain conditions.

Stability of the plasma is not sufficient to assure a practical fusion reactor because of various materials engineering problems. The lining of the vacuum chamber containing the plasma is subjected to radiation damage by the 14-MeV neutrons from the D-T reaction. Also, when the plasma is disrupted, the electric forces cause “runaway electrons” to bombard the chamber wall, generating large amounts of heat. Materials will be selected to minimize the effects on what are called plasma-facing components and reduce the frequency of need for replacement. An example is a graphite fiber composite similar to those used to protect the surface of the space shuttle on reentry. Other possible wall materials are silicon carbide, beryllium, tungsten, and zirconium, with the latter metals possibly enriched in an isotope that does not absorb neutrons. Some self-protection of the chamber lining is provided by vaporization of materials, with energy absorbed by a “vapor shield.”

The eventual practical fusion reactor will require a system to generate tritium. As an alternative to the use of liquid lithium in a breeding blanket, consideration is given to a molten salt composed of fluorine, lithium, and beryllium (Li²BeF⁴ called “flibe”). The (n,2n) reaction in Be would enhance the breeding of tritium. Another possibility is the use of the ceramic lithium oxide (Li²O).

A number of tokamaks have been built at research facilities around the world. Prominent examples are:

• The Tokamak Fusion Test Reactor (TFTR) at Princeton, now shut down, that achieved very high plasma temperatures.
• The Joint European Torus (JET) at Abingdon, England, a cooperative venture of several countries, which has used the D-T reaction. Figure 14.4 shows the interior of JET with a person inside to provide scale.

  Figure 14.4. Interior of tokamak fusion reactor Joint European Torus at Culham, U.K.

  

  (Courtesy Joint European Torus).
• The Japanese Atomic Energy Research Institute Tokamak-60 (JT-60 Upgrade) used to study plasma physics. The National Institute for Fusion Sciences also operates the Large Helical Device, a modern stellarator.
• The DIII-D of General Atomic in San Diego is a modification of Doublet III. It involves science studies of turbulence, stability, and interactions, along with the role of the diverter, a magnetic method of removing debris from a fusion reaction.
• The Alcator-C-Mod of MIT, a compact machine with high general performance.

Concepts other than the tokamak have been studied. Princeton Plasma Physics Laboratory operates the National Spherical Torus Experiment, in which a hole passes through a spherical plasma (see References). The National Compact Stellarator Experiment, in which the chamber is in the shape of the figure eight (see References) was cancelled in 2008 by the Department of Energy.

14.4. Inertial Confinement Machines

Another approach to practical fusion is ICF, which uses very small pellets of a deuterium and tritium mixture as high-density gas or as ice. The pellets are heated by laser light or by high-speed particles. They act as miniature hydrogen bombs, exploding and delivering their energy to a wall and cooling medium. Figure 14.5 shows a quarter coin with some of the spheres. Their diameter is approximately 0.3 millimeters. To cause the thermonuclear reaction, a large number of beams of laser light or ions are trained on a pellet from different directions. A pulse of energy of the order of a nanosecond is delivered by what is called the “driver.” The mechanism is believed to be as follows: the initial energy evaporates some material from the surface of the microsphere in a manner similar to the ablation of the surface of a spacecraft entering the earth's atmosphere. The particles that are driven off form a plasma around the sphere that can absorb further energy. Electrons are conducted through the sphere to heat it and cause more ablation. As particles leave the surface, they impart a reaction momentum to the material inside the sphere, just as a space rocket is propelled by escaping gases. A shock wave moves inward, compressing the D-T mixture to many thousands of times normal density and temperature. At the center, a spark of energy approximately 1 keV sets off the thermonuclear reaction. A burn front involving alpha particles moves outward, consuming the D-T fuel as it goes. Energy is shared by the neutrons, charged particles, and electromagnetic radiation, all of which will eventually be recovered as thermal energy. Consistent numbers are: 1 milligram of D-T per pellet, 5 million joules driver energy, an energy gain (fusion to driver) of approximately 60, and a frequency of 10 bursts per second.

Figure 14.5. Gold microshells containing high-pressure D-T gas for use in laser fusion

(Courtesy Los Alamos National Laboratory, No. CN 76-6442).

In an alternate indirect method of heating, laser light or ions bombard the walls of a pellet cavity called a hohlraum, producing X-rays that drive the pellet target. One advantage besides high-energy efficiency is insensitivity to focus of the illuminating radiation.

The energy released in the series of microexplosions is expected to be deposited in a layer of liquid such as lithium that is continuously circulated over the surface of the container and out to a heat exchanger. This isolation of the reaction from metal walls is expected to reduce the amount of material damage. Other candidate wall protectors are liquid lead and flibe. It may not be necessary to replace the walls frequently or to install special resistant coatings. Figure 14.6 shows a schematic arrangement of a laser-fusion reactor.

Figure 14.6. Laser-fusion reactor.

Research on ICF is carried out at several locations in the United States:

• Lawrence Livermore National Laboratory (LLNL) operated Nova from 1985 to 1999. It used a neodymium-glass laser, with 10 separate beams. Nova could deliver 40 kJ of 351-nm light in a 1-ns pulse. It was the first ICF machine to exceed the Lawson criterion. Experiments are discussed in a comprehensive Web site (see References). LLNL is also the site of the National Ignition Facility (NIF), which has a dual purpose. The first is to provide information on target physics for the United States research program in ICF. The second is to simulate conditions in thermonuclear weapons as an alternative to underground testing actual devices (also see Chapter 26). NIF will have 192 beam lines focused on a target fuel capsule. The design permits either direct or indirect heating. One beam line called Beamlet was tested successfully, then transferred to Sandia National Laboratories. See References for additional information.
• The University of Rochester's Laboratory for Laser Energetics (LLE) operates the facility OMEGA, which has had impressive success, see Figure 14.7(B). Also, the effect on ICF of magnetic fields is being studied.

  Figure 14.7. (A) Progress towards a practial MCF reactor. (Courtesy Japan Atomic Energy Research Institue. Thanks are due Robert Heeter). (B) Progress towards a practial ICF reactor.

  

  

  (Courtesy Lawrence Livermore National Laboratory. Thanks are due to John Soures and Alan Wootton.)
• Sandia National Laboratories first demonstrated with its Particle Beam Fusion Accelerator (PBFA) that targets could be heated with a proton beam. The equipment was converted into the Z-accelerator, which uses a pulse of current to create a powerful pinch effect (see Section 14.3). The energy from the electrical discharge goes into accelerating electrons that create X-rays that heat the DT capsules. Power levels of near 300 trillion watts have been achieved (see References).
• Lawrence Berkeley National Laboratory tests methods of accelerating heavy ions such as potassium to serve as driver for ICF.
• General Atomics provides inertial fusion targets—spheres and hohlraums—for other laboratories.
• Los Alamos National Laboratory had an excimer (excited molecular) laser facility Aurora. It was followed by Mercury, which produced energy of approximately 50 J.

A number of conceptual inertial fusion reactor designs have been developed by national laboratories, universities, and companies to highlight the needs for research and development. These designs are intended to achieve power outputs comparable to those of fission reactors. They include both laser-driven and ion-driven devices. Examples are HIBALL-II (University of Wisconsin), HYLIFE-II and Cascade (Lawrence Livermore), Prometheus (McDonnell Douglas), and OSIRIS and SOMBRERO (W. J. Shafer). A considerable gap remains between performance required in these designs and that obtained in the laboratory to date.

14.5. Other Fusion Concepts

Over the years since 1950 when research on fusion was begun in earnest, there have been many ideas for processes and systems. One was the “hybrid” reactor with a fusion core producing 14-MeV neutrons that would be absorbed in a uranium or thorium blanket, producing new fissile material. It was proposed as a stepping-stone to pure fusion, but seems unlikely to be considered.

Of the approximately 100 fusion reactions with light isotopes, some do not involve neutrons. If a “neutron-free” reaction could be harnessed, the problems of maintenance of activated equipment and disposal of radioactive waste could be eliminated. One example is proton bombardment of the abundant boron isotope, according to

Because Z = 5 for boron, the electrostatic repulsion of the reactants is five times as great as the for D-T reaction, resulting in a much lower cross section. The temperature of the medium would have to be quite high. On the other hand, the elements are abundant and the boron-11 isotope is the dominant one in boron.

Another neutron-free reaction uses the rare isotope helium-3,

The D-³He electrostatic force is twice as great as the D-T force, but because the products of the reaction are both charged, energy recovery would be more favorable. The process might be operated in such a way that neutrons from the D-D reaction could be minimized. This would reduce neutron bombardment to the vacuum chamber walls. A D-³He fusion reactor thus could use a permanent first wall, avoiding the need for frequent replacement and at the same time reducing greatly the radioactive waste production by neutron activation.

The principal difficulty with use of the reaction is the scarcity of ³He. One source is the atmosphere, but helium is present only to 5 ppm by volume of air and the helium-3 content is only 1.4 atoms per million of helium. Neutron bombardment of deuterium in a reactor is a preferable source. The decay of tritium in nuclear weapons could be a source of a few kilograms a year, but not enough to sustain an electrical power grid. Extraterrestrial sources are especially abundant but of course difficult to tap. Studies of moon rocks indicate that the lunar surface has a high ³He content as the result of eons of bombardment by solar wind. Its ³He concentration is 140 ppm in helium. It has been proposed that mining, refining, and isotope separation processes could be set up on the moon, with space shuttle transfer of equipment and product. The energy payback is estimated to be 250, the fuel cost for fusion would be 14 mills/kWh, and the total energy available is approximately 10⁷ GWe-y. If space travel is further perfected, helium from the atmospheres of Jupiter and Saturn could be recovered in almost inexhaustible amounts.

A fusion process that is exotic physically but might be simple technically involves muons, negatively charged particles with mass 210 times that of the electron, and half-life 2.2 m/s. Muons can substitute for electrons in the atoms of hydrogen but with orbits that are 210 times smaller than the normal 0.53 × 10⁻¹⁰ m (see Exercise 14.5). They can be produced by an accelerator and directed to a target consisting of a deuterium-tritium compound such as lithium hydride. The beam of muons interacts with deuterons and tritons, forming DT molecules, with the muon playing the same role as an electron. However, the nuclei are now close enough together that some of them will fuse, releasing energy and allowing the muon to proceed to another molecule. Several hundred fusion events can take place before the muon decays. The system would appear not to need complicated electric and magnetic fields or large vacuum equipment. However, the concept has not been tested sufficiently to be able to draw conclusions about its feasibility or practicality.

Two researchers in 1989 reported the startling news that they had achieved fusion at room temperature, a process called “cold fusion.” The experiments received a great deal of media attention because if the phenomenon were real, practical fusion would be imminent. Their equipment consisted of a heavy water electrolytic cell with cathode of metal palladium, which can absorb large amounts of hydrogen. They claimed that application of a voltage resulted in an enormous energy release. Attempts by others to confirm the experiments failed, and cold fusion is not believed to exist. Under certain conditions, there may be a release of large amounts of stored chemical energy, and research is continuing.

A scientific breakthrough whose effect is not yet determined is the discovery of materials that exhibit electrical superconductivity at relatively high temperatures, well above that of liquid helium. Fusion machines that use superconducting magnets will, at a minimum, be more energy efficient.

14.6. Prospects for Fusion

Research on controlled thermonuclear processes has been underway for more than 50 years at several national laboratories, universities, and commercial organizations. The results of the studies include an improved understanding of the processes, the ability to calculate complex magnetic fields, the invention and testing of many devices and machines, and the collection of much experimental data. Over that period, there has been an approach to breakeven conditions, but progress has been painfully slow, involving decades rather than years. Various reasons have been suggested for this. First, and probably most important, is the fact that fusion is an extremely complex process from both the scientific and engineering standpoints. Second are policy decisions (e.g., emphasis on fundamental plasma physics rather than building large machines to reveal the true dimensions of the problem). In the case of ICF, the United States security classification related to weapons inhibited free international exchange of research information. Finally, there have been inconsistencies in funding allocations.

Figure 14.7(A) shows accomplishments of the MCF machines being tested. The plots give the Lawson criterion product of number density n and confinement time τ as a function of ion temperature T expressed as an energy in keV. Also noted on the diagram are the goals of breakeven and ignition. Although breakeven has been achieved, there still is a considerable way to go to approach ignition.

Figure 14.7(B) shows the progress by ICF machines. The plot relates the ion temperature to the product of density and radius as discussed in Section 14.2. OMEGA is expected to come near ignition and NIF to exceed it.

Predictions have repeatedly been made that practical fusion was only 20 y away. Two events provide some encouragement that the elusive 20-y figure might be met. The first is the discovery of a new tokamak current. As noted earlier, current flow in the plasma is induced by the changing external magnetic field. Because that field cannot increase indefinitely, it would be necessary to shut down and start over. In 1971 it had been predicted that there was an additional current in a plasma, but not until 1989 was that verified in several tokamaks. That “bootstrap” current amounts to up to 80% of the total, such that its contribution would allow essentially continuous operation.

The second event was a breakthrough in late 1997 in fusion energy release. Most fusion research had been conducted with the D-D reaction rather than the D-T reaction, to avoid the complication of contamination of equipment by radioactive tritium. At the JET in England, tritium was injected as a neutral beam into a plasma. A series of records was set, ultimately giving 21 MJ of fusion energy, a peak power of 16 MW, and a ratio of fusion power to input power of 0.65. These results greatly exceeded those from D-D reactions.

In 1985, progress in tokamak performance over the years prompted planning for a large machine with the acronym ITER. Its objective is to demonstrate that fusion can be used to generate electrical power. Scientists will study conditions expected in a fusion power plant.

Participants in the project are the European Union, Japan, China, India, South Korea, Russia, and the United States (which withdrew in 1999 but reentered in 2001). ITER will be built at Cadarache in the South of France, with leadership provided by Japan. On November 21, 2006, an agreement was signed that established the ITER International Organization.

The tokamak is expected to produce more power than it consumes, with a Q value greater than 1. Technologies used include superconducting magnets, heat-resistant materials, remote handling systems for radioactive components, and breeding of tritium from lithium. The design was completed in 2001. Some of the features are a large plasma volume of roughly elliptical shape, a blanket to absorb neutron energy, and a diverter to extract the energy of charged particles and the helium ash. Selected parameters are:

 

Plasma major radius	6.2 m
Plasma minor radius	2.0 m
Magnetic field	5.3 T
Plasma current	15 MA
Fusion power	500 MW
Burn time	>400 s
Power amplification	>10
Temperature	107 °C

The schedule calls for the first plasma by 2016 and an operating period for approximately 20 y. The construction cost is estimated to be 5 billion Euros (1 EUR ≅ 1.45 USD), with another 5 billion over the 20 y. ITER maintains a comprehensive Web site (see References).

DEMO is a proposed fusion power plant that follows ITER's expected success. It is intended to be comparable in output to current fission power plants, being able to make the tritium it needs. There is a possibility that some magnetic confinement concept other than the tokamak will be used.

Most of the R&D on magnetic fusion has been focused on the tokamak mode. There is a possibility that some magnetic confinement concept other than the tokamak will be used. The United States participates in and supports the ITER program but continues to explore other concepts. The Department of Energy's Office of Fusion Energy Sciences provides research funds and receives recommendations from the Fusion Energy Sciences Advisory Committee (FESAC). In the Innovative Concepts Conferences (ICC), alternatives are discussed. Inspection of a typical meeting program reveals the diversity of fusion science and technology (see References).

It seems that practical fusion reactors still will not be available soon unless there is an unanticipated breakthrough or a completely new idea arises that changes the prospects dramatically. There is yet much to understand about plasma processes and a great deal of time is required to carry out research, development, and testing of a system that will provide competitive electric power.

From time to time, the wisdom of pursuing a vigorous and expensive research program in controlled fusion has been questioned in light of the uncertainty of success in achieving affordable fusion power. An excellent answer is the statement attributed by Robin Herman (see References) to the fusion pioneer Lyman Spitzer, “A fifty percent probability of getting a power source that would last a billion years is worth a great deal of enthusiasm.”

14.7. Summary

A fusion reactor, yet to be developed, would provide power that uses a controlled fusion reaction. Of the many possible nuclear reactions, the one that will probably be used first involves deuterium and tritium (produced by neutron absorption in lithium). A D-T reactor that yields net energy must exceed the ignition temperature of approximately 4.4 keV and have a product nτ above approximately 10¹⁴, where n is the fuel particle number density and τ is the confinement time. Several experimental machines have been tested, involving an electrical discharge (plasma) that is constrained by electric and magnetic fields. One promising fusion machine, the tokamak, achieves magnetic confinement in a doughnut-shaped structure. ITER is a large fusion facility being built in France by an international consortium. Research is also underway on inertial confinement in which laser beams or charged particle beams cause the explosion of miniature D-T pellets. A neutron-free reaction involving deuterium and helium-3 would be practical if the moon could be mined for helium.

14.8. Exercises

1. Noting that the radius of motion R of a particle of charge q and mass m in a magnetic field B is R = mυ/qB and that the kinetic energy of rotation in the x-y plane is (1/2)mυ² = kT, find the radii of motion of electrons and deuterons if B is 10 Wb/m² and kT is 100 keV.
2. Show that the effective nuclear reaction for a fusion reactor that uses deuterium, tritium, and lithium-6 is
3. Verify the statement that in the D-T reaction the particle will have 1/5 of the energy.

4. • Assuming that in the D-D fusion reaction the fuel consumption is 0.151 g/MWd (Exercise 7.3), find the energy release in J/kg. By how large a factor is the value larger or smaller than that for fission?
   • If heavy water costs $100/kg, what is the cost of deuterium per kilogram?
   • Noting 1 kWh = 3.6 × 10⁶ J, find from (a) and (b) the energy cost in mills/kWh.

5. • With the formula for the radius of the smallest electron orbit in hydrogen,where and the basic constants in the Appendix, verify that R is 0.529 × 10⁻¹⁰ m.
   • Show that the rest energy of the muon, 105.66 MeV, is approximately 207 times the rest energy of the electron.
   • What is the radius of the orbit of the muon about hydrogen in the muonium atom?
   • The lengths of the chemical bonds in H² and in other compounds formed from hydrogen isotopes are all approximately 0.74 × 10⁻¹⁰ m. Estimate the bond in molecules where the muon replaces the electron.
   • How does the distance in (d) compare with the radii of the nuclei of D and T (see Section 2.6)?

Computer Exercise

1. Computer program FUSION describes a collection of small modules that calculate certain parameters and functions required in the analysis of a plasma and a fusion reactor. Among the properties considered are the theoretical fusion reaction cross sections, the Maxwellian distribution and characteristic velocities, the impact parameter for 90 ° ion scattering, the Debye length, cyclotron and plasma frequencies, magnetic field parameters, and electrical and thermal conductivities. The filenames of the modules are MAXWELL, VELOCITY, DEBYE, IMPACT, RADIUS, MEANPATH, TRANSIT, and CROSECT. Explore the modules with the menus provided and the sample input numbers.

14.9 References

Fowler, 1997 T. Kenneth Fowler, The Fusion Quest 1997 Johns Hopkins University Press Baltimore Highly readable, nonmathematical treatment of both MCF and ICF

Dolan, 1982 T.J. Dolan, Fusion Research 1982 Pergamon Press New York

http://www.fusionnow.org/dolan.html http://www.fusionnow.org/dolan.html

Corrected electronic version INIS 2001 Corrected electronic version INIS 2001.

Stacey, 1984 Weston M. Stacey, Fusion: An Introduction to the Physics and Technology of Magnetic Confinement Fusion 1984 John Wiley & Sons New York

Lindl, 1998 John D. Lindl, Inertial Confinement Fusion: The Quest for Ignition and Energy Gain Using Indirect Drive 1998 AIP Press, Springer-Verlag New York

Raeder, 1986 J. Raeder, ... Controlled Nuclear Fusion: Fundamentals of its Utilization for Energy Supply 1986 John Wiley & Sons, Ltd Chichester, England

Niu, 1989 Keishiro Niu, Nuclear Fusion 1989 Cambridge University Press Cambridge, England Treats both magnetic confinement by tokamaks and inertial confinement by lasers and ions

Pfalzner, 2006 S. Pfalzner, An Introduction to Inertial Confinement Fusion 2006 Taylor and Francis and CRC Press New York

Harms et al., 2000 A.A. Harms, K.F. Schoepf, G.H. Miley, D.R. Kingdon, Principles of Fusion Energy 2000 World Scientific Singapore

General Atomics Fusion Energy Research General Atomics Fusion Energy Research

http://fusion.gat.com http://fusion.gat.com

Select various links in Research Select various links in Research, e.g., DIII-D.

ITER (International Tokamak Reactor) ITER (International Tokamak Reactor)

http://www.iter.org http://www.iter.org

Full description of the project and the device Full description of the project and the device.

United States Fusion Energy Sciences Program United States Fusion Energy Sciences Program

http://www.science.doe.gov/ofes http://www.science.doe.gov/ofes

Includes links to fusion research activities around the world Includes links to fusion research activities around the world.

NSTX (National Spherical Torus Experiment) NSTX (National Spherical Torus Experiment)

http://nstx.pppl.gov http://nstx.pppl.gov

Select Overview/NSTX overview Select Overview/NSTX overview.

NCSX (National Compact Stellarator Experiment) NCSX (National Compact Stellarator Experiment)

http://ncsx.pppl.gov http://ncsx.pppl.gov

Select About NCSX Select About NCSX.

JET (Joint European Torus) JET (Joint European Torus)

http://www.jet.efda.org/index.html http://www.jet.efda.org/index.html

Located in the U.K., it serves 20 European countries Located in the U.K., it serves 20 European countries.

Sandia National Laboratories Sandia National Laboratories

http://www.sandia.gov/pulsedpower http://www.sandia.gov/pulsedpower

Select Pulsed Power Facilities Select Pulsed Power Facilities

Nova Laser Experiments and Stockpile Stewardship Nova Laser Experiments and Stockpile Stewardship

https://www.llnl.gov/str/Remington.html https://www.llnl.gov/str/Remington.html

Relationship of NIF to weapons tests Relationship of NIF to weapons tests.

National Ignition Facility Project (LLNL) National Ignition Facility Project (LLNL)

https://lasers.llnl.gov https://lasers.llnl.gov

Photos, videos, and explanations Photos, videos, and explanations

Laboratory for Laser Energetics Laboratory for Laser Energetics

http://www.lle.rochester.edu http://www.lle.rochester.edu

Information on OMEGA and research projects Information on OMEGA and research projects.

Alternative fusion methods Alternative fusion methods

www.iccworkshops.org/icc2007/program/php www.iccworkshops.org/icc2007/program/php

Innovative Confinement Concepts conference at University of Maryland Innovative Confinement Concepts conference at University of Maryland

Fusion Power Associates Fusion Power Associates

http://fusionpower.org http://fusionpower.org

Source of information on latest technical and political developments Source of information on latest technical and political developments. Select Fusion Library.

Herman, 1990 Robin Herman, Fusion: The Search for Endless Energy 1990 Cambridge University Press New York