Controlled Fusion

the fusion of light atomic nuclei that occurs at high temperatures under controlled conditions and is accompanied by an energy release. Thermonuclear reactions proceed slowly because of the Coulomb repulsion of positively charged nuclei (seeCOULOMB’S LAW). Therefore, fusion occurs with an appreciable intensity only between light nuclei that have a small positive charge and only at high temperatures, where the kinetic energy of colliding nuclei is sufficient to overcome the Coulomb potential barrier.

Under natural conditions, thermonuclear reactions between hydrogen nuclei, or protons, occur deep inside stars, particularly in the interior regions of the sun, and thus serve as a constant energy source that governs the radiation of stars. The burning of hydrogen in stars occurs at a low rate, but the huge dimensions and densities of the stars ensure the continuous emission of tremendous energy fluxes for billions of years (seeTHERMONUCLEAR REACTIONS). Reactions between the heavy isotopes of hydrogen, deuterium ²H and tritium ³H, occur at an incomparably higher rate and result in the formation of strongly bound helium nuclei:

These reactions are of the greatest interest in controlled fusion. The second reaction, which is accompanied by a large energy release and occurs at a significant rate, is particularly interesting. Tritium is radioactive, with a half-life of 12.5 years, and is not found in nature. Consequently, to ensure the operation of a proposed fusion reactor that uses tritium as the fuel, the tritium must be bred. For this purpose, the reaction zone of the proposed system may be surrounded by a blanket of a light isotope of lithium, and the following breeding process would occur in that blanket:

⁶Li + n → ³H + ⁴He

The probability or effective cross section of thermonuclear reactions increases rapidly with temperature but, even under optimum conditions, remains incomparably smaller than the probability or effective cross section of atomic collisions. For this reason, fusion reactions must occur in a completely ionized plasma heated to a high temperature. In such a plasma, the ionization and excitation of atoms do not occur and, sooner or later, deuteron-deuteron or deuteron-triton collisions culminate in nuclear fusion.

Figure 1

The specific power output of a fusion reactor is obtained by multiplying the number of nuclear reactions that occur each second per unit volume of the reaction zone of the reactor by the energy released in each reaction event.

The Lawson criterion. The use of the laws of conservation of energy and particle number makes it possible to elucidate some general requirements imposed on a fusion reactor, requirements that are independent of any particular engineering or design characteristics of the system in question. A schematic diagram of the operation of a reactor is provided in Figure 1. A device of arbitrary design contains a pure hydrogen plasma with a density n and a temperature T. Fuel, such as a mixture of equal parts of deuterium and tritium already heated to the required temperature, is injected into the reactor. Inside the reactor the injected particles collide with one another from time to time, and nuclear interactions occur. This is a useful process. At the same time, however, energy escapes from the reactor as a result of the electromagnetic radiation of the plasma, and some “hot,” that is, high-energy, particles that have not undergone nuclear interactions escape from the reaction zone.

Let τ be the mean particle confinement time in the reactor; the meaning of the quantity τ is that, on the average, n/τ particles of each sign escape from 1 cm³ of the plasma in 1 sec. In steady-state operation the same number of particles (calculated per unit volume) must be injected into the reactor each second. To cover the energy losses, the fuel supplied must be fed into the reaction zone with an energy exceeding the energy of the flux of escaping particles. This additional energy must be compensated for by the fusion energy released in the reaction zone and by the partial recovery of electromagnetic radiation and corpuscular fluxes in the reactor walls and blanket.

Let us assume, for simplicity’s sake, that the ratio of conversion into electrical energy is identical for the nuclear reaction products, electromagnetic radiation, and thermal particles and is equal to η. The quantity η is often called the efficiency. When the system operates in the steady state and the effective power output is zero, the energy balance equation for the reactor has the form

(1) η(P₀ + P_r + P_t) = P_r + P_t

where P₀ is the energy released as nuclear power, P_r is the power of the radiation flux, and P_t is the power of the escaping particle flux. When the left-hand side of the equation is made greater than the right-hand side, the reactor stops expending energy and begins operating as a thermonuclear electric power plant. In writing equation (1), it is assumed that all the recovered energy is returned without losses to the reactor through the injector, together with the flow of the heated fuel that is supplied. Since the quantities P₀, P_r, and P_t depend in a known way on the plasma temperature, we can easily calculate from the balance equation the product

(2) nτ = f(T)

Here, f(T) for a given value of the efficiency η and the type of fuel selected is a well-defined function of temperature. Plots of f(T) are given in Figure 2 for two values of η and for both deuteron-deuteron (d, d) and deuteron-triton (d, t) reactions. If the values of nτ attained in a given device lie above the curve of f(T), the system will operate as an energy generator. When η = ⅓, the operation of the reactor in producing useful power corresponds under optimum conditions (the minimum of the curves in Figure 2) to the following condition, which is called the Lawson criterion: for (d, d) reactions, nτ ≥ 10¹⁵ cm^–3 · sec, and T ~ 10⁹⁰K; for (d, t) reactions, nτ ≥ 0.5 × 10¹⁴ cm^–3 · sec, and T ~ 2 × 10⁸⁰K.

Thus, even under optimum conditions and with very optimistic assumptions concerning the value of η temperatures of about 2 × 10⁸⁰K must be attained for the case of greatest interest, namely, a reactor fueled by a mixture of equal parts of deuterium and tritium. In this case, confinement times of the order of seconds must be achieved for a plasma with a density of about 10¹⁴ cm^–3. The reactor, of course, may produce useful energy at lower temperatures, but the energy must be “paid for” by higher values of nτ.

In short, the construction of a fusion reactor presupposes (1) the creation of a plasma heated to temperatures of hundreds of millions of degrees and (2) the maintenance of a plasma configuration for the time required for nuclear reactions to occur. Research in controlled fusion is following two paths—the development of quasi-steady-state systems, on the one hand, and the development of extremely high-speed devices, on the other.

Figure 2

Controlled fusion with magnetic confinement. Let us first consider quasi-steady-state systems. An energy yield at the level of 10⁵ kilowatts per cubic meter (kW/m³) is achieved for (d, t) reactions when the plasma density is about 10¹⁵ cm^–3 and the temperature is about 10⁸⁰K. This means that the size of a reactor with an output of 10⁶–10⁷ kW—the typical output of large present-day electric power plants—should be in the range 10–100 m³, which is entirely acceptable. The main problem is how to confine the hot plasma in the reaction zone. The diffusive particle and heat fluxes at the cited values of n and T ate huge, and no material walls are suitable. A ground-breaking idea advanced in 1950 in the Soviet Union and the USA consists in the use of the principle of magnetic confinement of the plasma. When the charged particles that form the plasma are located in a magnetic field, they cannot move freely perpendicular to the field’s lines of force. As a result, the coefficients of diffusion and thermal conductivity across the magnetic field decrease very rapidly with increasing field strength in the case of a stable plasma; for example, with fields of ~ 10⁵gauss the coefficients are reduced by 14–15 orders of magnitude as opposed to their “unmagnetized” value for a plasma with the density and temperature indicated above. Thus, in principle, the use of a sufficiently strong magnetic field opens the way to the design of a fusion reactor.

There are three areas of research in the field of controlled fusion with magnetic confinement: (1) open, or mirror-type, magnetic traps, (2) closed magnetic systems, and (3) pulsed machines.

In open traps, particles cannot easily escape, across the lines of force, from the reaction zone to the walls of the device. The particles escape either during “magnetized” diffusion—that is, very slowly—or by means of charge exchange with the molecules of the residual, that is, un-ionized gas. The escape of the plasma along the lines of force is likewise inhibited by regions of intensified magnetic field located at the open ends of the trap; such regions are called magnetic mirrors, or end plugs. The traps are usually filled with plasma by injecting plasmoids or individual high-energy particles. Additional plasma heating can be accomplished with the aid of adiabatic compression in a rising magnetic field (seeMAGNETIC TRAPS).

In closed systems, such as Tokamaks and stellarators, the escape of particles to the walls of a toroidal device across a longitudinal magnetic field is also difficult and occurs as a result of magnetized diffusion and charge exchange. The plasma column in a Tokamak is heated in the initial stages by a ring current that flows through the column. As the temperature rises, however, Joule heating becomes increasingly less effective, since the resistance of the plasma decreases rapidly with increasing temperature. Methods of heating by a high-frequency electromagnetic field and by the injection of energy with the aid of fluxes of fast neutral particles are used to heat the plasma above 10⁷⁰K.

In pulsed machines, such as the Z pinch and 8 pinch, plasma heating and plasma confinement are accomplished by strong short-period currents that flow through the plasma. As the current and magnetic pressure increase simultaneously, the plasma is squeezed away from the walls of the containment vessel. This effect ensures that the plasma is confined. The temperature increases as a result of Joule heating, adiabatic compression of the plasma column, and, apparently, turbulent processes associated with the development of a plasma instability (seePINCH EFFECT).

The study of hot plasmas in high-frequency (HF) fields is an independent area of research. As the experiments of P. L. Kapitsa have shown, in hydrogen and helium a freely hovering plasma column with an electron temperature of about 10⁶⁰K can be produced in HF fields at sufficiently high pressure. Such a system allows for the closing of the column into a ring and the superposition of an additional longitudinal magnetic field.

The successful operation of any of the devices listed above is possible only if the initial plasma structure is macroscopically stable and maintains a specified shape for the entire period of time necessary for the reaction to occur. Furthermore, microscopic instabilities must be suppressed in the plasma. When such instabilities arise and develop, the energy distribution of the particles ceases to be an equilibrium distribution, and the particle and heat fluxes across the lines of force increase sharply in comparison with their theoretical values. Since 1950 most research in magnetic systems has been directed at the stabilization of plasma configurations; this work still cannot be regarded as completed.

Ultrahigh-speed controlled fusion systems with inertia! confinement. The difficulties associated with the magnetic confinement of a plasma can be obviated in principle if the nuclear fuel is burned for extremely short periods of time, during which the heated matter cannot disperse from the reaction zone. In accordance with the Lawson criterion, useful energy can be obtained with this method of burning only if the fuel has a very high density. To avoid a high-power thermonuclear explosion, very small amounts of fuel must be used. The initial thermonuclear fuel must be in the form of small pellets, 1–2 mm in diameter, prepared from a mixture of deuterium and tritium and injected into the reactor before each reaction cycle. The main problem consists in supplying the necessary energy to heat the fuel pellets. As of 1976, the solution of this problem lies in the use of laser beams or high-power electron beams. Research in controlled fusion with the use of laser heating was begun in 1964; the use of electron beams is in an early stage of study—thus far, relatively few electron-beam fusion experiments have been performed.

Estimates show that the energy W that must be supplied to sustain the operation of a reactor is expressed as

Here, η is a general expression for the efficiency of the device and α is the coefficient of target compression. As this equation shows, even with very optimistic assumptions regarding the possible value of η the value of W when α = 1 is disproportionately large. Admissible values of Wean therefore be approached only in conjunction with a sharp increase in the density of the target (by a factor of approximately 10⁴) in comparison with the initial density of a solid (d, t) target. Rapid heating of the target is accompanied by the vaporization of its surface layers and the reaction compression of its interior regions. If the power supplied is time-programmed in a specific manner, then, as calculations show, the coefficients of compression indicated can be attained. Another possibility is to program the radial distribution of the target density. In both cases, the energy required is reduced to 10⁶J, which is technically feasible considering the rapid development of laser devices.

Difficulties and prospects. Research in controlled fusion encounters major difficulties that are both purely physical and technical in nature. The physical difficulties include the cited problem of the stability of a hot plasma placed in a magnetic trap. It is true that the use of strong magnetic fields with a special configuration suppresses the particle fluxes escaping from the reaction zone and, in a number of cases, makes it possible to obtain sufficiently stable plasma formations. With n of about 10¹⁵ cm^–3, T of about 10⁸⁰K, and a possible reactor size of 10–100 m³, electromagnetic radiation freely escapes from the plasma. However, for a purely hydrogen plasma, the energy losses are determined solely by electron bremsstrahlung and, in the case of (d, t) reactions, are compensated for by the energy released as nuclear power at temperatures above 4 × 10⁷⁰K.

The second fundamental difficulty is connected with the problem of impurities. Even a small impurity of foreign atoms with a high atomic weight, which are in a highly ionized state at the temperatures considered, leads to a sharp increase in the intensity of the continuous spectrum, to the appearance of a line spectrum, and to an increase in energy losses to a level above the acceptable level. Extraordinary efforts, such as the continuous improvement of evacuation equipment, the use of refractory and nonsputtering metals as the orifice material, and the use of special devices to trap foreign atoms, are required to minimize the amount of impurities in the plasma. More accurately, the “lethal” concentration that makes it impossible for thermonuclear reactions to occur is, for example, a few tenths of 1 percent for a tungsten or molybdenum impurity.

The parameters achieved in various machines as of mid-1976 are shown in Figure 3 in a plot of nτ against T. Tokamaks and laser systems come the closest to the region where the Lawson criterion is met, and a self-sustaining thermonuclear reaction can occur. It would be erroneous, however, to make categorical conclusions, on the basis of the available data, as to the type of device that will be used as a future thermonuclear reactor. The development of this field of technical physics is proceeding too rapidly, and many estimates will change over the next decade.

The tremendous importance attached to research in controlled fusion is explained by a number of factors. The growing pollution of the environment urgently requires the conversion of the planet’s industrial production to a closed cycle with a minimum of waste. However, such a reorganization of industry inevitably entails a sharp increase in energy consumption. Meanwhile, the resources of fossil fuels are limited and, at the current rate of development of power engineering, will be exhausted in the next few decades—as in the case of petroleum and gaseous fuels—or centuries—as in the case of coal. The best alternative, of course, would be the use of solar energy, but the lower power density of incident solar radiation greatly complicates the efficient solution of this problem. The conversion to the use of nuclear fission reactors

Figure 3. Parameters attained by mid-1976 in various machines for studying the problem of controlled fusion: (T-10) a Tokamak machine at the I. V. Kurchatov Institute of Atomic Energy, USSR; (PLT) a Tokamak machine at the Princeton Plasma Physics Laboratory, USA; (Alcator) a Tokamak machine at the Massachusetts Institute of Technology, USA; (TFR) a Tokamak machine at Fontanay-aux-Roses, France; (PR-6) an open trap at the I. V. Kurchatov Institute of Atomic Energy, USSR; (2XIIB) an open trap at the Lawrence Livermore Laboratory, USA; (0 pinch [Scyllac]) a machine at the Los Alamos Scientific Laboratory, USA; (Uragan-1 stellarator) a machine at the Ukrainian Physlcotechnical Institute, USSR; (Laser) pulsed laser-heated systems, USSR and USA

on a global scale raises complex problems of the burial of tremendous amounts of radioactive wastes; the alternative is to eject the radioactive wastes into space. According to available estimates, the radiation danger of controlled fusion installations should be three orders of magnitude less than that of fission reactors. In the future, the best solution would be a combination of solar energy and controlled fusion.