General Problems of Controlled Thermonuclear Reaction*

E. Teller

Almost all the energy available to us ultimately comes from the Sun. The Sun, in turn, produces energy by means of thermonuclear reactions that proceed at the extremely high temperatures prevailing within it, analogous to the way this occurs in laboratory thermochemical processes at much lower temperatures. If we were able to bring about the controlled release of thermonuclear energy, we could reproduce something similar to the processes occurring on the Sun. At the same time, the energy needs of our industry would be satisfied not merely for the next few years, but for as long as one can possibly imagine.

The already achieved uncontrolled release of thermonuclear energy gives grounds for hoping that we stand on the threshold of these accomplishments. And this is indeed so, if only one measures time in decades or even centuries. Impatient people, asking what will happen next year, and skeptics, wishing to know what we have already achieved, must be satisfied with the fact that part of the road has been traveled. We have gone far enough to encounter real difficulties, but at the same time far enough that we nourish some hope of success. Let us attempt, in broad outline, to consider the range of questions with which we are now confronted.

Production of Energy in Stars

It has been known for about 30 years that nuclear reactions may be regarded as the source of the greater part of the energy produced by almost all stars. These reactions are of interest not only as sources of energy; in them, at least the lightest elements are also produced. There is no need for us to consider each reaction separately, since they have little bearing on the processes that will occur in a terrestrial thermonuclear installation.

Common to these reactions—both inside a star and in any machine that can be made by human hands—is their dependence on density and, especially, on temperature. Most intrastellar and all laboratory reactions proposed so far are based on collisions between two particles. Therefore the energy released per unit volume must be proportional to the square of the density of the nuclei participating in the reaction.

All reactions of interest proceed at temperatures at which the average energy of the colliding particles is insufficient to overcome the Coulomb repulsion between them. However, nuclei can come into

* Lecture delivered at the 2nd conference of the American Nuclear Society on June 8, 1956. Nuclear Science and Engineering 1, 313 (1956). Translation by A. P. Grishin.

come into contact and react for two reasons. First, even if there exists a potential barrier preventing the particles from coming into contact, contact is nevertheless possible (though unlikely) owing to the quantum-mechanical “tunnel effect.” The probability of contact and of the reaction following it is proportional to the Gamow transmission coefficient of the barrier:

\[ \exp\{-2\pi Z_1 Z_2 e^2/\hbar v\}, \tag{1} \]

where \(Z_1 e\) and \(Z_2 e\) are the charges of the colliding particles, \(v\) is their relative velocity, and \(\hbar\) is Planck’s constant divided by \(2\pi\). Second, if the particles have a Maxwellian distribution of velocities, then the probability of encountering a particle with an extremely high velocity is proportional to

\[ \exp\{-Mv^2/2kT\}, \tag{2} \]

where \(M\) is the reduced mass of the colliding particles, \(M=M_1M_2/(M_1+M_2)\), \(T\) is the absolute temperature, and \(k\) is Boltzmann’s constant. In expressions (1) and (2) we have restricted ourselves to the most important, exponential factors.

The probability of a reaction between two nuclei will be proportional to the product of these two factors. The expression obtained should be integrated over all possible values of the relative velocity \(v\). The result may be estimated by substituting into the product of (1) and (2) that value of \(v\) for which the absolute magnitude of the exponent has a minimum, since the greatest contribution to the integral is given by values of \(v\) close to this value. The minimum is attained at

\[ v=\left(\frac{2\pi Z_1 Z_2 e^2 kT}{M\hbar}\right)^{1/3}. \tag{3} \]

Let us note that the corresponding kinetic energy is

\[ \frac{Mv^2}{2}=\overline{E}^{1/3}(kT)^{2/3}, \tag{4} \]

where

\[ \overline{E}=\frac{\pi^2 Z_1^2 Z_2^2 M e^4}{2\hbar^2}\simeq \frac{1}{4} Z_1 Z_2 \frac{M}{M_p}\ \text{MeV}, \]

and \(M_p\) is the proton mass.

As an example, consider the collision of two protons. Such collisions occur inside the Sun and can lead to \(\beta\)-emission and the formation of a deuteron. In this case \(M/M_p=1/2\) and \(\overline{E}=125\ \text{keV}\). The thermal energy \(kT\) at the center of the Sun is approximately \(2\ \text{keV}\). The mean energy at which the reaction occurs, according to (4), should be \(8\ \text{keV}\), which is appreciably higher than the energy of thermal motion.

After substituting into the product of (1) and (2) the most probable particle velocity (3), at which the reaction proceeds, the expression for the rate of the thermonuclear reaction takes the following form:

\[ \exp\left\{-\frac{3}{2}\left(4\pi^2 Z_1^2 Z_2^2 e^4/M\hbar^2 kT\right)^{1/3}\right\}. \tag{5} \]

This formula expresses only the strongest, exponential dependence of the reaction rate on temperature, or, more precisely, on \((kT)^{-1/3}\). It is not difficult to estimate the true reaction rate if one recalls that at very high temperatures, when (5) approaches unity, the thermal velocities must be multiplied by the effective cross sections characteristic of the considered

...of a controllable nuclear reaction. More exact formulas are available in the literature\(^{2,3}\), but for general orientation the statements given above are sufficient.

Inside the Sun and the stars, matter has a temperature of several thousand eV and a very varied density, often quite high. At the center of the Sun the density of matter is approximately one hundred times greater than the density of water. Under such extreme conditions matter in stars can exist only because of their great mass. The whole secret of cosmic thermonuclear installations lies in the presence of a powerful and heavy shell. Under laboratory conditions we have at our disposal the same kinds of fuel as in the stars, and even better ones; only we are not able to tamp it down properly without getting burned.

ENERGY OUTPUT AND LOSSES AT HIGH TEMPERATURE

From expression (5) it is clear that we cannot count on obtaining useful thermonuclear energy until a temperature of at least several keV has been reached. At such a temperature all materials emit light very intensely. In installations made by human hands, at the pressures and volumes that may be in question, the radiation will instantly leave the system, having no chance of being absorbed again. In designing a thermonuclear installation, one of the main considerations is the balance between the energy produced in the nuclear reaction and the energy expended on radiation.

The energy balance is further affected by the fact that almost exclusively electrons radiate, whereas the energy released in the nuclear reaction first appears in the form of the kinetic energy of nuclear fragments. The transfer of energy from heavy particles to light ones takes place rather slowly. If this energy is carried by a neutron, then it leaves the region where the reaction is occurring altogether, without having time to give up its energy.

In what follows we shall consider, in simplified form, both the process of radiation and the process of energy transfer from nuclei to electrons.

Let us first note that any process of interest to us is carried out by the collision of two particles. Nuclear reactions occur when two nuclei collide. Radiation is possible if an electron is deflected near a nucleus. Finally, for energy exchange between nuclei and electrons, their collision is, of course, necessary. Therefore all relevant processes depend in the same way on the density of the reacting gas. Thus it is possible to use a highly rarefied gas, in which the need to maintain a high temperature will not require excessively high pressures. The relative contribution of the various processes will be the same for all pressures.

The energy radiated by an electron per unit time is approximately equal to:

\[ \frac{e^{2}}{c^{3}} \ddot{x}^{2}, \tag{6} \]

where \(c\) is the speed of light, and \(\ddot{x}\) is the acceleration of the electron.

The factor \(2/3\) in (6) has been omitted. It would be difficult in our qualitative discussion to retain all numerical coefficients. Indeed, neglecting them leads to a result that differs little from the exact expression\(^{3}\).

The acceleration of an electron located at a distance \(r\) from a nucleus with charge \(Ze\) is equal to \(Ze^{2}/mr^{2}\) (\(m\) is the electron mass), and for the radiated energy one obtains the expression

\[ \frac{Z^{2} e^{6}}{m^{2} c^{3} r^{4}} . \tag{7} \]

One can integrate over space by multiplying (7) by \(r^2\,dr\) and taking the integral

\[ \frac{Z^2 e^6}{m^2 c^3}\int \frac{dr}{r^2}. \tag{8} \]

This expression is proportional to the difference of \(r^{-1}\) taken at the limits of integration. As \(r\to\infty\) the integral is zero; as \(r\to 0\) it diverges. Thus, practically all the radiation occurs when the electron is very close to the nucleus.

In fact, there is no need to consider arbitrarily small distances. If we are dealing with electrons having velocity \(v_{\rm el}\), then for them the uncertainty principle forbids localization with accuracy greater than \(\hbar/mv_{\rm el}\). This distance may be used as the smallest effective distance, and (8) may be rewritten in the form

\[ \frac{Z^2 e^6 v_{\rm el}}{mc^3\hbar}. \tag{9} \]

Finally, expressing the electron velocity in terms of the thermal energy, \(v_{\rm el}\sim \sqrt{kT/m}\), we obtain:

\[ \frac{Z^2 e^6 (kT)^{1/2}}{m^{3/2}c^3\hbar}. \tag{10} \]

This is the energy radiated by an electron in the field of one nucleus with charge \(Ze\). If there are \(n\) electrons and \(N\) nuclei per \(1\ \mathrm{cm}^3\), then the energy radiated by a unit volume per unit time is obtained from (10) by multiplying by \(nN\). The latter can be written in a form that clearly shows the dimensions and order of magnitude. Let us introduce the electron rest energy \(E_0=mc^2=0.5\ \mathrm{MeV}\) and the classical electron radius \(r_0=e^2/E_0\). Then the expression for the energy radiated by unit volume per unit time takes the form

\[ nNZ^2 r_0^3 (E_0^3 kT)^{1/2}/\hbar. \tag{11} \]

In a successfully operating thermonuclear installation, the energy released in nuclear reactions and imparted to the reacting gas must be at least equal to the radiated energy, which is approximately given by expression (11). If this condition is not fulfilled, the gas temperature will fall and the reaction will quickly cease.

When comparing the released energy, proportional to (5), with the losses to radiation, approximately equal to (11), special attention should be paid to the temperature \(T\) appearing in both formulas. In (5) one must substitute the temperature of the reacting nuclei, and in (11) the temperature of the electrons. Under the conditions of a highly rarefied gas in which a thermonuclear installation must operate, a Maxwell distribution need not be fully established between the individual types of particles. Energy exchange between nuclei and electrons proceeds extremely slowly, and the electron temperature may differ noticeably from the temperature of the nuclei.

We saw earlier that nuclear fragments carry away the energy released in the nuclear reaction and then transfer it to the electrons. In reality, in all practical cases the electrons move faster than the nuclear fragments. Consequently, the question arises of the transfer of energy from a slowly moving body to a rapidly moving one. It turns out that this process is improbable and proceeds slowly. Let us try to find a rough approximation for this process in two stages. First we shall calculate the amount of energy transferred from electrons to nuclei at rest, and then consider how this affects the

the motion of the nuclei into transition. Finally, let us assume that in the state of thermodynamic equilibrium there is no transfer of energy in either direction. From this one can obtain the magnitude of the energy transferred from the nuclei to the electrons.

The energy losses of the electrons can be calculated by the method which Bohr used in calculating the braking of α-particles. Consider the motion of an electron with velocity \(v_{\mathrm{el}}\) near a nucleus having charge \(Ze\) and mass \(M_1\). Let us denote by \(r\) the smallest distance to which the electron approaches the nucleus. An approximate value of the momentum given by the electron to the nucleus can be obtained by multiplying the greatest interaction force \(Ze^2/r^2\) by the interaction time \(r/v_{\mathrm{el}}\). The magnitude of the kinetic energy transferred to the nucleus as a result of the collision can be estimated if the momentum is squared and divided by the mass of the nucleus \(M_1\). The value of this kinetic energy is

\[ \frac{Z^2 e^4}{M_1 r^2 v_{\mathrm{el}}^2}. \tag{12} \]

To obtain the differential cross section for collisions with a minimum distance of approach lying in the interval between \(r\) and \(r+dr\), one must multiply (12) by \(r\,dr\). Integration with respect to \(r\) gives \(\ln r\), which slowly tends to \(+\infty\) as \(r\to\infty\) and to \(-\infty\) as \(r\to 0\). In fact, one must integrate from some \(r_{\min}\), determined by the uncertainty relation, to \(r_{\max}\), determined by the screening action which other charges exert on the interaction of the two colliding particles. Thus, for the energy loss one obtains the expression

\[ \frac{Z^2 e^4}{M_1 v_{\mathrm{el}}^2}\ln\left(\frac{r_{\max}}{r_{\min}}\right). \tag{13} \]

The ratio \(r_{\max}/r_{\min}\) is very large, and in practical cases the logarithm is approximately equal to 20. Multiplying (13) by the number of nuclei and the number of electrons in a cubic centimeter, and by \(v_{\mathrm{el}}\), one can obtain the amount of energy transferred from the electrons to the nuclei at rest per unit time and per unit volume:

\[ \frac{nNZ^2 e^4}{M_1 v_{\mathrm{el}}}\ln\frac{r_{\max}}{r_{\min}}. \tag{14} \]

Let us now suppose that the nuclei are not at rest, but move slowly with velocity \(v\ll v_{\mathrm{el}}\). If the energy transferred from the electrons to the nuclei is now expanded in a series in powers of \(v/v_{\mathrm{el}}\), then (14) will be the constant term of this series. Among the following terms of the series the term with the first power \(v/v_{\mathrm{el}}\) will be absent, since the direction of motion of the nuclei cannot affect the exchange of energy. Thus, for small velocities of the nuclei, an essential role will be played only by the term quadratic in \(v/v_{\mathrm{el}}\). The amount of transferred energy can now be written in the form

\[ \left[ \frac{nNZ^2 e^4}{M_1 v_{\mathrm{el}}} \ln\left(\frac{r_{\max}}{r_{\min}}\right) \right] \left[ 1-\mathrm{const}\left(\frac{v}{v_{\mathrm{el}}}\right)^2 \right]. \tag{15} \]

The minus sign in the square brackets reflects the circumstance that the faster the nuclei move, the less energy is transferred to them. When the temperatures of the electrons and nuclei are equal, no energy should be transferred at all. Under these conditions \(mv_{\mathrm{el}}^2=M_1v^2\). It follows from this that the constant in formula (15) must have the value \(M_1/m\). Thus, for the amount of energy transferred from the nuclei to the electrons in \(1\ \mathrm{sec}\) in \(1\ \mathrm{cm}^3\), the following is obtained

approximate expression:

\[ \frac{nNZ^2 e^4}{M_1}\cdot \frac{M_1v^2-mv_{\mathrm{el}}^2}{mv_{\mathrm{el}}^3}\cdot \ln\left(\frac{r_{\max}}{r_{\min}}\right). \tag{16} \]

In order, as above, to ascertain the dimensions and order of magnitude, let us introduce, besides \(E_0=mc^2=0.5\ \mathrm{Mev}\) and \(r_0=e^2/E_0=2.8\cdot 10^{-13}\ \mathrm{cm}\), also the quantity reciprocal to the fine-structure constant, \(\hbar c/e^2=137\), the temperature of the nuclei \(kT_{\mathrm{n}}=M_1v^2\), and the temperature of the electrons \(kT_{\mathrm{el}}=mv_{\mathrm{el}}^2\). Hence, for the amount of energy transferred from electrons to nuclei per second per unit volume, we obtain the formula

\[ \frac{nNZ^2 r_0^3 E_0^{5/2}}{\hbar}\cdot \frac{(kT_{\mathrm{n}}-kT_{\mathrm{el}})}{(kT_{\mathrm{el}})^{3/2}}\cdot \frac{m}{M_1}\cdot \frac{\hbar c}{e^2}\ln\frac{r_{\max}}{r_{\min}}. \tag{17} \]

Similar, but more exact, expressions have been derived in astrophysics \(^{4,5}\).

Expression (17) should be compared with the amount of energy radiated by the electrons [formula (11), into which the electron temperature \(kT_{\mathrm{el}}\) is substituted]. The ratio of the energy transferred from nuclei to electrons to the radiated energy is expressed by the dimensionless quantity

\[ \frac{E_0(kT_{\mathrm{n}}-kT_{\mathrm{el}})}{(kT_{\mathrm{el}})^2}\, \frac{m}{M_1}\, \frac{\hbar c}{e^2}\, \ln\frac{r_{\max}}{r_{\min}} \approx 1.5\,\frac{M_p}{M_1}\cdot \frac{E_0(kT_{\mathrm{n}}-kT_{\mathrm{el}})}{(kT_{\mathrm{el}})^2}. \tag{18} \]

It is not necessary to retain the factor 1.5, since the approximation is of a rough character. Its magnitude follows from the numerical constants given above.

In the stationary state the electrons must receive as much energy as they radiate, although energy is imparted to the electrons not only by those nuclei whose state can be described by a thermal distribution corresponding to a definite temperature. If one adheres to the idea of some mean temperature of the nuclei, then it is clear that (18) must be equal to unity. It may be noted that, since \(E_0=0.5\ \mathrm{Mev}\), for an electron temperature of the order of several \(\mathrm{kev}\) the temperature difference between nuclei and electrons must be small. However, at higher electron temperatures the temperature difference in the stationary state may turn out to be appreciable.

All these statements are given here only for orientation. In a real thermonuclear device, attainment of the stationary state is not obligatory.

THERMONUCLEAR FUEL

From the considerations set forth it follows that, as thermonuclear fuel, one should choose materials in which energy is released at the lowest possible temperature and which, at the same time, radiate as little as possible. The appearance of the nuclear charges in expression (5) indicates that it will be most expedient to stop our choice at hydrogen isotopes. At the same time, from expression (11) for the amount of radiated energy it is also seen that the energy losses are minimal at \(Z=1\). In practice this means that, in the reaction zone, nuclei of higher atomic numbers should, as far as possible, be completely excluded.

As regards the hydrogen isotopes, it will be necessary to consider two reactions involving them. One of them, somewhat slower, is the reaction between deuterons:

\[ \mathrm{H}^2+\mathrm{H}^2\to \mathrm{He}^3+\mathrm{n}, \tag{19a} \]

\[ \mathrm{H}^2+\mathrm{H}^2\to \mathrm{H}^3+\mathrm{H}^1. \tag{19б} \]

Another is the very rapid reaction between deuterium and artificially produced tritium:

\[ \mathrm{H}^{2}+\mathrm{H}^{3}\to \mathrm{He}^{4}+\mathrm{n}. \tag{20} \]

If the latter reaction is chosen, then for the thermonuclear process a temperature of several kev will prove sufficient. In the case of pure deuterium, however, temperatures approximately 10 times higher are necessary.

In any case, in order to maintain a sufficiently high level of energy production (several watts per cubic centimeter or more) and at the same time to keep the pressure within reasonable limits, a rarefied and, of course, completely ionized gas with a density of \(10^{15}\)—\(10^{16}\) particles per \(1\ \mathrm{cm}^{3}\) will be required.

THE PROBLEM OF ISOLATION

The gas in a thermonuclear installation, as has already been said, must have a high temperature and a high rarefaction; the main technical difficulty consists in finding a way to maintain these conditions so that the gas does not immediately give up its energy to the walls of the vessel. One of the possible methods that have been proposed consists in isolating the fuel from the walls of the vessel by a magnetic field. In fact, the gas is completely ionized; consequently, its electrically charged ions will move along the lines of force of any magnetic field that appears in the system. If it is possible to maintain such a distribution of the field in which the lines of force do not allow the ions to reach the vessel walls, then the problem will thereby be solved.

This path leads us to the study of the behavior of a highly ionized gas, or plasma, in a magnetic field. At first glance the theoretical formulation of the problem seems uncomplicated. In fact, all that is required is to construct a hermetic “magnetic vessel.” But upon more detailed examination the question proves to be very intricate. At present one can describe only the general properties of such a system and indicate the character of the difficulties that arise.

The interaction of hydrostatic equilibrium and hydrodynamic motion with a magnetic field forms a new and interesting domain of hydromagnetism. This domain is of great interest not only with respect to controlled thermonuclear reactions, but also in questions connected with terrestrial magnetism\(^6\), astrophysics\(^7,8\), and cosmic rays\(^9\).

With regard to hydromagnetic systems, two simple assertions may be made. In the first of these, the Maxwell stresses and the density of magnetic energy \(H^{2}/8\pi\) are compared with the pressure and kinetic energy per unit volume of the plasma. If these latter hydrostatic and hydrodynamic quantities are larger, then the behavior of the whole system is determined, in first approximation, by the laws of ordinary hydrostatics and hydrodynamics. On the other hand, if the Maxwell stresses are larger, then in first approximation the system is described by the laws of the electromagnetic field. Finally, if both types of quantities are comparable with one another, then a close interaction takes place between magnetism and hydrodynamics. In thermonuclear installations it is precisely these conditions that one attempts to realize. If the hydrodynamic forces predominate, it will not be possible to isolate the system with the aid of a magnetic field. On the other hand, if everywhere the hydrodynamic forces and pressures prove small in comparison with the magnetic stresses, this will mean that we have applied an excessively strong magnetic field and have expended an unjustifiably large amount of magnetic energy on the isolation.

The second assertion concerns the mechanism by means of which changes in the magnetic field and the motion of the plasma influence one another. In all

In cases of interest, the conductivity of the plasma is large, while the lifetime of the magnetic insulation is relatively short. Under these conditions the magnetic lines of force are rigidly connected with the plasma in the following sense. The plasma can move without hindrance along the magnetic lines of force, but any motion of it in a direction perpendicular to the lines of force will cause the lines of force to be displaced together with the plasma. Conversely, any displacement of a magnetic line of force will draw along with it ions that wind around this line of force as they move. The statements just made require refinement for many reasons, but the superficial exposition of hydromagnetism is best begun precisely with this simple connection between the plasma and the magnetic field.

As a result of collisions between ions, their spiral motion is interrupted, and diffusion arises which can carry the reacting gas to the walls of the vessel. This process proceeds rather slowly and—if only simple calculations may be trusted—should not lead to any appreciable leakage in a magnetic vessel.

Apparently more dangerous are statistical phenomena in the ionic cloud. An example of such phenomena is hydromagnetic instability, the nature of which has been understood to some extent.^10

Let us consider a magnetic line of force bent in such a way that inside it the plasma pressure is greater than outside. In fact, it is difficult to make a magnetic vessel without curvatures of this kind. The following question now arises. Is it not possible to attain a state of lower energy if this line of force is straightened? For the magnetic line of force behaves in many respects like a rubber cord. The plasma can flow around the lines of force and partly leave the space bounded by them. By such a change in configuration one could attain a lower energy state. The difference in energies would appear in the form of kinetic energy, and the change, once it had arisen, would develop with increasing speed.

To deal with such situations, one can develop a theory of virtual displacements of the magnetic field and the plasma. The equilibrium condition for a hydromagnetic system requires that an infinitesimally small virtual displacement should not cause a change of energy linear in this displacement. The stability condition is stronger: it requires that every change of energy accompanying a small virtual displacement be positive. To test instability it is not enough to show that there exists a lower energy state. It is necessary, in addition, that the lower state be attainable by descent along a continuous sequence of small steps.

The examination of these stability criteria is very complicated. They inspire apprehension, indicating a path by which leakage may arise, but thus far we have not succeeded in showing that true stability is impossible. We have not yet reached the state of those specialists in hydrodynamics who, in the last century, proved the impossibility of flight. Unfortunately, we cannot point to any simple model. The people who built the airplane could say that birds fly in any case. We, however, in developing thermonuclear reactors, cannot refer to even a single simple example.

WHAT ARE THE ADVANTAGES OF THERMONUCLEAR INSTALLATIONS?

Suppose that a thermonuclear installation can be built. One should ask oneself in what respect such a reactor might prove better than a reactor operating on nuclear fission.

One of the advantages was already clarified in the introduction. The quantity of thermonuclear fuel available to us is, in practice, completely inexhaustible. However, this advantage is not as great as it might at first appear—

be used. Although the amount of fissile materials is limited, it is nevertheless also sufficiently large. A good deal of time will pass before the fissile materials available to us are used up—especially if it proves possible to solve the problem of extended reproduction of fuel. I think that for the next two hundred years the reserves of uranium and thorium at our disposal will suffice, even if we assume that the whole world will soon be industrialized and that population growth will continue at its present rate.

A clear advantage of the thermonuclear system is revealed in the fact that the use of deuterium as fuel will hardly require any further regeneration at all. Thus it is possible to avoid at least one of the truly troublesome stages in the processing of fissile materials.

An advantage whose significance, in my view, has been exaggerated concerns the problem of reactor safety. It is unlikely that the thermonuclear reactors being designed would be subject to accidents during which radioactive substances are released in large quantities. Therefore the real danger associated with the operation of fission reactors disappears. However, the danger of fission reactors, in my opinion, is already considerably less than it was several years ago, and I hope that we shall find a way to create a truly safe system based on fission.

Finally, one should take an interest in the question of the direct conversion of nuclear energy into electrical energy, bypassing the use of heat. As for fission reactors, there is apparently little hope of solving this problem in the near future. Looking at the question from the standpoint of the possible creation of a thermonuclear installation, I recall the old method of catching birds, which says: to catch a bird, one must sprinkle salt on its tail. When we learn to keep plasma in a magnetic field under considerable pressure, it will probably no longer be difficult, by changing the magnetic field, to extract the energy contained in it. But first we must learn to catch and hold the plasma.

Having mentioned the possible advantages of thermonuclear systems, we must also say something about the probable difficulties. We compare thermonuclear systems with systems operating on fission. The first fission reactor was built with astonishing ease—astonishing, if one bears in mind the problems that apparently arise now. In fact, the only obvious difficulty in constructing fission reactors was the circumstance that radioactive substances are formed in them, and energy has to be obtained under conditions of high activity. As a result, reactor control and fuel processing become greatly complicated.

In a thermonuclear reactor, as compared with a fission reactor of the same power, neutrons will be produced in even greater quantity. Therefore the system will again become radioactive, and we shall encounter the same control problems as in fission reactors. Only in this case the machine itself will probably be more complex, and it will contain more unusual structural elements than a fission reactor.

In conclusion, I should like to satisfy your curiosity about certain important questions, although I do not know precise answers to them. I am confident that controlled thermonuclear reactors will someday be built. But I do not think that at first such reactors will be able to compete with ordinary sources of energy or even with reactors operating on fission. Nevertheless, in the process of creating a thermonuclear installation, it seems to me, much information will be obtained in the field of plasma physics that may prove very important both for industry and for understanding the world around us.

References

1. G. Gamow and C. L. Critchfield, Theory of Atomic Nuclei and Nuclear Energy Sources, Oxford U. P., New York, 1949, Ch. X.
2. G. Gamow and E. Teller, Phys. Rev. 55, 791 (1939).
3. H. Bethe, Phys. Rev. 55, 434 (1939).
4. S. Chandrasekhar, Rev. Mod. Phys. 21, 383 (1949).
5. L. Spitzer, The Physics of Fully Ionized Gases, Interscience, New York, 1956.
6. W. Elsasser, Rev. Mod. Phys. 22, 1 (1950); ibid. 28, 135 (1956).
7. H. Alfven, Zeits. Phys. 107, 579 (1937).
8. H. Alfven, Cosmical Electrodynamics, Oxford U. P., New York, 1950.
9. E. Fermi, Phys. Rev. 75, 1169 (1949).
10. M. Kruskal and M. Schwarzschild, Proc. Roy. Soc. A223, 348 (1954).