Laboratory Method for Obtaining High Potentials

L. V. Mysovskii, Leningrad

Various Methods of Obtaining a High Potential

Recently, technical transformers for voltages up to one million volts and more are no longer a particular rarity. Such transformers exist not only abroad, but also here in the USSR. It must be said, however, that these transformers are too bulky, require a large amount of energy for their supply, and therefore can hardly be used in delicate laboratory work. For most scientific and scientific-technical work with high potential, great power is not at all necessary. On the contrary, the enormous sparks produced by powerful transformers do not even allow physical instruments to be brought near them, and the role of these transformers in engineering is limited chiefly to the testing of insulators. In addition to the magnitude and power of the sparks, the very dimensions of technical transformers also constitute a considerable hindrance in laboratory work. For high-voltage installations it is necessary to allocate special halls, many times larger than an ordinary room for scientific work. Often such installations are even placed in separate, specially adapted buildings.

Meanwhile, in nature we have examples—the nuclei of atoms—where potentials of several million volts are concentrated in an extremely small volume. It is therefore not surprising that physicists have sought, by various methods, to-

to obtain a high voltage from a small and low-power source. To build an ordinary transformer, with a coupling coefficient close to unity, of small dimensions but giving a high voltage is not possible, because the individual turns of the transformer must be very well insulated from one another and from the transformer case so that a voltage of one or two million volts will not cause a discharge inside the transformer itself.

Attempts were made to avoid this difficulty, or at least to reduce it, by means of the series (cascade) connection of several separate transformers. But even with a cascade connection the dimensions of the high-voltage installation remain enormous. Moreover, the high voltages at the transformer terminals during discharges produce such strong currents even in the secondary winding of the transformer that the power supplied to the primary winding must be very considerable. For this reason one has to use wire of larger cross-section for the primary winding. All this taken together compelled physicists to seek other ways of obtaining high potentials. The aim of these searches is to create a low-power source of a potential of several million volts and then to apply it to the artificial splitting of elements. Of course, obtaining a potential of several million volts is of interest from other points of view as well. Obtaining merely a potential gradient of a million volts has already enabled Millikan to observe the so-called cold emission of electrons by metals. Undoubtedly, a high potential, when it is mastered, will make it possible to carry out a whole series of interesting observations in the most varied fields of physics.

What paths, then, are being outlined at the present time for obtaining a high potential suitable for laboratory purposes? One of these paths is the switching of capacitors from parallel to series connection. This method has not received practical application in its pure form, although with it voltages of up to one million volts have been attained. Only in combination with transformers

and kenotrons, this method makes it possible to increase the limiting voltage of the transformer by two or three times. As an example of such a device, which has become widely used in practice, one may point to the stabilivolt of Siemens and Halske, based on a circuit first proposed by Greinacher. Another method of obtaining a high potential, requiring comparatively little power, was proposed by Tesla. The Tesla transformer is so well known that there is no need to describe its construction. For a long time this transformer was used only as an effective apparatus for demonstrating the resonance of high-frequency electrical oscillations. The long and powerful sparks that could be drawn from Tesla’s secondary coil had long attracted the attention of physicists and raised the question: what potentials arise here? Drude, and then a number of other investigators, worked on the theory of the Tesla transformer. However, we still do not have a complete theory of this transformer even at the present time. The question of the magnitude of the potential also remained open until very recently. Only recently has it been possible to determine experimentally the magnitude of this potential and thus to verify certain theoretical conclusions. In what follows we shall dwell mainly on an account of two works concerning the Tesla transformer. One of these works was carried out at the State Radio Institute in Leningrad by a postgraduate student of the Physics Department, electrical engineer V. N. Rukavishnikov. The other work was carried out at the Carnegie Institution in Washington.^1 Although this work was published in full only in January 1930, the substance of this work and the potentials that were obtained were already known earlier from a preliminary communication in Nature, published in 1928. This preliminary communication already aroused great interest in scientific circles and was cited repeatedly in the scientific literature.

^1 G. Breit, M. A. Tuve and O. Dahl. Phys. Rev. 35, 51 (1930).

L. V. MYSOVSKY

ELEMENTARY THEORY OF THE TESLA TRANSFORMER WITH DAMPED OSCILLATIONS

The complete theory of the Tesla transformer, as has already been indicated above, is too complicated, and therefore we shall not dwell on it. As for the elementary theory, it is usually presented under the assumption that the ohmic resistances of both circuits may be neglected, and therefore these resistances are taken to be equal to zero. In reality, however, the ohmic resistance has a very strong effect on the operation of the Tesla transformer. Here we shall give the derivation of the fundamental equations of the Tesla transformer, taken from the work: “The Role of Ohmic Resistance in the Tesla Transformer” by V. N. Rukavishnikov.

Fig. 1

If we are given two oscillatory circuits I and II, see Fig. 1, then, going around both circuits on the basis of Kirchhoff’s law, we obtain:

\[ \begin{aligned} w_1 i_1 + L_1 \frac{d i_1}{d t} + M \frac{d i_2}{d t} &= V_1,\\ w_2 i_2 + L_2 \frac{d i_2}{d t} + M \frac{d i_1}{d t} &= V_2. \end{aligned} \tag{1} \]

Here \(w_1\) and \(w_2\) are the ohmic resistances of the circuits, \(i_1\) and \(i_2\) are the current intensities, \(L_1\) and \(L_2\) are the coefficients of self-induction, \(M\) is the coefficient of mutual induction, and \(t\) is time. \(V_1\) and \(V_2\) are the potentials on the plates of the capacitors. Using the equality

\[ i = C \frac{dV}{dt} \]

we transform the linear equations (1) into a system of linear equations of the second order with respect to the potentials. After the indicated transformation this system will have the following form:

\[ \begin{aligned} L_1 C_1 \frac{d^2 V_1}{d t^2} + w_1 C_1 \frac{d V_1}{d t} + V_1 + M C_2 \frac{d^2 V_2}{d t^2} &= 0,\\ L_2 C_2 \frac{d^2 V_2}{d t^2} + w_2 C_2 \frac{d V_2}{d t} + V_2 + M C_2 \frac{d^2 V_1}{d t^2} &= 0. \end{aligned} \tag{2} \]

In order to find the characteristic equation for this system as well, let us substitute into it particular solutions of the form

\[ V_1=a_1 e^{\rho t} \]

\[ V_2=a_2 e^{\rho t}. \]

As a result of the substitution we obtain:

\[ L_1C_1a_1\rho^2e^{\rho t}+w_1C_1a_1\rho e^{\rho t}+a_1e^{\rho t} +MC_2a_2\rho^2e^{\rho t}=0 \]

\[ L_2C_2a_2\rho^2e^{\rho t}+w_2C_2a_2\rho e^{\rho t}+a_2e^{\rho t} +MC_1a_1\rho^2e^{\rho t}=0. \]

After transformations and cancellation by \(e^{\rho t}\) we have:

\[ a_1(L_1C_1\rho^2+w_1C_1\rho+1)=-a_2MC_2\rho^2 \]

\[ a_1MC_1\rho^2=-a_2(L_1C_1\rho^2+w_2C_2\rho+1). \]

Dividing these equations term by term one by the other and writing the equality of the products of the extreme and middle terms, we obtain the characteristic equation in the following symmetric form:

\[ (L_1C_1\rho^2+w_1C_1\rho+1)(L_2C_2\rho^2+w_2C_2\rho+1)-M^2C_1C_2\rho^4=0 \tag{3} \]

This is an equation of the fourth degree with respect to \(\rho\), and the general solution could lead to a complete theory of the Tesla transformer. We shall not do this here for two reasons. First, as a result of the general solution of an equation of the fourth degree, we would arrive at expressions that are too complicated, which would be difficult to investigate, and therefore it would be difficult to clarify the role of the separate factors \(L\), \(C\), \(M\), and \(w\) in the operation of the Tesla transformer. Second, what interests us here is not the general case of operation of the Tesla transformer, but only the case of resonance of the circuits. Equation (3) is greatly simplified if we assume that

\[ L_1C_1=L_2C_2 \quad \text{and} \quad w_1C_1=w_2C_2. \]

These conditions may be written in another, still more symmetric form:

\[ \frac{w_1}{w_2}=\frac{L_1}{L_2}=\frac{C_2}{C_1} \tag{4} \]

As is not difficult to see, under condition (4), equation (3) splits into two quadratics:

\[ (L_1C\rho^2+wC\rho+1)-M\sqrt{C_1C_2}\rho^2=0 \]

\[ (LC_2\rho^2+wC\rho+1)+M\sqrt{C_1C_2}\rho^2=0 \tag{5} \]

Here, for the products \(LC\) and \(wC\) the indices have been omitted, since, on the basis of condition (4), these products have one and the same value regardless of which circuit they belong to.

Solving equations (5), we obtain:

\[ \rho_{1,2}= \frac{-wC\pm\sqrt{wC-4LC(1-\chi)}}{2LC(1-\chi)} = \]

\[ = \frac{1}{2(1-\chi)}\cdot\frac{wC}{LC} \pm \sqrt{ \frac{1}{4(1-\chi)^2}\cdot\left(\frac{wC}{LC}\right)^2 -\frac{1}{LC(1-\chi)} } = \]

\[ = \alpha_1\pm\sqrt{\alpha_1^2-\frac{1}{LC(1-\chi)}} = -\alpha_1\pm j\omega_1, \]

\[ \rho_{3,4}= \frac{-wC\pm\sqrt{wC-4LC(1-\chi)}}{2LC(1-\chi)} = \]

\[ = \frac{1}{2(1-\chi)}\cdot\frac{wC}{LC} \pm \sqrt{ \frac{1}{4(1-\chi)^2}\cdot\left(\frac{wC}{LC}\right)^2 -\frac{1}{LC(1-\chi)} } = \]

\[ = \alpha_2\pm\sqrt{\alpha_2^2-\frac{1}{LC(1-\chi)}} = -\alpha_2\pm j\omega_2 . \]

The expressions written by us for the roots require some explanation. First of all, the coupling coefficient \(\chi\) has been introduced into them on the basis of the equality defining its magnitude, \(M^2=\chi^2L_1L_2\). Next, it must be pointed out that we assume in advance that the expressions under the radical are less than unity, since we are interested only in the oscillatory regime of the transformer. The conditions for the existence of oscillations in our case will be expressed as follows:

\[ \frac{1}{4(1\pm\chi)^2}\left(\frac{wC}{LC}\right)^2 -\frac{1}{LC(1\pm\chi)}<0 \quad\text{or}\quad w<2\sqrt{\frac{L}{C}(1\pm\chi)}. \]

As we see, this condition differs from the analogous condition relating to a single circuit only by the presence of the coupling coefficient.

Writing, according to the generally known rules, the solution of the system of differential equations (2), and replacing in them the factors with imaginary exponents by their expression in terms of trigonometric functions, we obtain for \(V_1\) and \(V_2\):

\[ \begin{aligned} V_1={}&[A_{11}\cos\omega_1 t+A_{12}\sin\omega_1 t]e^{-\alpha_1 t} +[B_{11}\cos\omega_2 t \\ &\qquad +B_{12}\sin\omega_2 t]e^{-\alpha_2 t},\\ V_2={}&[A_{21}\cos\omega_1 t+A_{22}\sin\omega_1 t]e^{-\alpha_1 t} +[B_{21}\cos\omega_2 t \\ &\qquad +B_{22}\sin\omega_2 t]e^{-\alpha_2 t}. \end{aligned} \tag{6} \]

Let us now return to the basic condition (4), which made it possible to simplify the solution of the characteristic equation, and try to elucidate its physical meaning. From the expressions (6) we see that, even with so considerable a simplification of the problem as is afforded us by condition (4), in each circuit two oscillations will nevertheless occur simultaneously, and moreover with different frequencies \(\omega_1\) and \(\omega_2\). Condition (4) says only that the damping of these oscillations will occur identically in both the first and the second circuit. Indeed,

\[ \alpha_1=\frac{1}{2(1-\chi)}\cdot\frac{wC}{LC} \quad \text{and} \quad \alpha_2=\frac{1}{2(1+\chi)}\cdot\frac{wC}{LC}. \]

Consequently \(\alpha_1\) and \(\alpha_2\) depend not on the separate values \(L_1, C_1, w_1\) and \(L_2, C_2, w_2\), but on the products \(wC\) and \(LC\), which by condition (4) have the same values for both circuits. Using (4), one can obtain the transformation coefficient directly from the basic differential equations (2). In fact, let us denote the transformation coefficient by \(S=\dfrac{V_2}{V_1}\) and replace, in the first of equations (2), \(V_1\) by \(V_2/S\) and \(V_2\) by \(V_1S\); we obtain:

\[ L_1 C_1 \frac{d^2 V_2}{dt^2} + w_1 C_1 \frac{dV}{dt} + V_2 + MS^2 C_2 \frac{d^2 V_1}{dt^2} =0. \]

Comparing this equation with the second of (2) and taking into account condition (4), we see that \(S^2 C_2=C_1\), whence

\[ S=\sqrt{\frac{C_1}{C_2}}. \]

We shall confine ourselves here to this investigation, since it turns out that even the simplest case considered by us would be too complicated in practice. To be convinced of this, it is enough to recall that the expressions (6) indicate the simultaneous existence of two oscillations in the circuits with frequencies \(\omega_1\) and \(\omega_2\). As a result of their simultaneous existence we must obtain beats. In order to avoid this unpleasant phenomenon, one usually uses so-called impact excitation. With such excitation, the primary circuit, after oscillations have been excited in it, is automatically opened and thus switched out of the system. This is achieved by a corresponding *

device of the spark gaps. When the primary circuit is switched off, then \(x=0\), and consequently \(\omega_1=\omega_2\) (see the expressions for \(\rho\)), and in the secondary circuit we shall have only one oscillation. In this case the secondary circuit will have oscillations with frequency

\[ \omega=\sqrt{\frac{1}{4}\left(\frac{w}{L}\right)^2-\frac{1}{LC}}. \]

This frequency, as is known, is the frequency of the natural free oscillations of a circuit consisting of capacitance, self-inductance, and ohmic resistance. There is still one reason, of which we shall speak below, and thanks to which in practice one has to restrict oneself to impulse excitation, if the matter concerns a laboratory method of obtaining high potential. If this is so, then almost the whole theory of a Tesla transformer suitable for laboratory work reduces to the consideration of energy oscillations in a closed circuit. This question has been sufficiently developed, and here we shall dwell only on the most essential point, which has a direct bearing on the construction of the Tesla transformer.

Joule Heat in the Secondary Spiral of a Tesla Transformer with Impulse Excitation

In ordinary work with Tesla transformers it is almost entirely unnecessary to take into account the expenditure of energy on heating the wires. However, this is observed only for a small number of sparks that jump across the spark gap in the primary circuit under impulse excitation. In this case the ohmic resistance can indeed be neglected, and the current strength can be calculated only on the basis of the so-called wave resistance. If the maximum voltage at the ends of the secondary spiral is \(E_0\), and \(L\) and \(C\) are its self-inductance and capacitance, then the maximum current strength is expressed as follows:

\[ J_0=\frac{E_0}{\sqrt{\frac{L}{C}}}, \]

where \(\sqrt{\frac{L}{C}}\) is the above-mentioned wave resistance. The situation is different with undamped oscillations. Below we shall present

experiments and calculations with a Tesla transformer on undamped oscillations. From these experiments, carried out by Rukavishnikov, it follows that a Tesla transformer operating on undamped oscillations consumes an enormous amount of energy. Since this energy is spent chiefly on Joule heat, the heating of the spiral proves to be very strong. Thus a Tesla transformer with undamped oscillations, or with a very large number of sparks per second, in its properties already begins to acquire the shortcomings of which we spoke at the beginning when mentioning high-voltage technical transformers. In order to construct a Tesla transformer with undamped oscillations, one has to consume a large power and use thick wires capable of withstanding strong heating. This is the second reason why, for obtaining high voltages in the laboratory, one has to make use of impulse excitation. Here we have a complete analogy with the production of enormous magnetic fields by the Kapitza method. To obtain such fields, as is known, a current of great strength is passed through a solenoid for a very short interval of time. The period during which the solenoid cools (so to speak, rests) is many times greater than the interval during which the magnetic field is created. Essentially the same thing occurs with impulse excitation. Although the sparks from the secondary coil of the transformer seem to issue continuously, in reality the transformer rests for much more time than it operates. This result, of course, cannot be called especially consoling, but nevertheless one may hope to obtain a whole series of interesting results even with short-lived strong electric fields, provided only that it proves possible to introduce them into a vacuum tube.

Methods of measuring superpotentials

Even the inventor of the Tesla transformer himself drew enormous and powerful sparks from it, but to measure the poten-

to obtain them experimentally only quite recently. The first attempt in this direction is found in Wolff in 1923.1 Wolff attached to the secondary coil of a Tesla transformer a large cathode tube, from which the gas released from the electrodes was continuously pumped out. By observing the deflection of the cathode beam in a given magnetic field, it was possible to determine the maximum velocity of the electrons and consequently the maximum potential. Wolff determined the potential of his Tesla transformer to be 600,000 volts. Such a method cannot be considered especially convenient, since connecting the tube increases the capacitance of the secondary coil and thus worsens the transformation coefficient \(S\) (see above). Moreover, as Wolff himself also points out, the cathode tube cannot be used for measuring potentials higher than 600,000 volts, since with a further increase discharges from the coil begin to occur into the surrounding air. Nevertheless, Wolff succeeded in verifying experimentally and demonstrating the possibility of obtaining high potentials with the aid of a Tesla transformer. Rukavishnikov at first also used, for measuring potential, a cathode tube similar to that described by Wolff. Subsequently, however, Rukavishnikov, at my suggestion, used for this purpose a cathode oscillographic tube of the Western Electric Company. A feature of this tube is its low cathode voltage—only 300–400 volts—and consequently the low velocity of the electrons in the cathode beam. The general appearance of the tube and of the installation used by Rukavishnikov is shown in Fig. 2.

Thanks to the low velocity of the electrons in this tube, the cathode beam and the spot on the phosphorescent screen can respond to oscillations of very high frequency. An enormous advantage of measuring potential with the aid of such a tube is the circumstance that it is placed at a great distance from the transformer, and by

by its dimensions so small that it had no noticeable influence even on the operation of small Tesla-transformer models. The actual measurement of the potential was carried out as follows. First the tube was placed between two plates of a plane capacitor, to the plates of which a known potential difference was connected. By varying the field between the plates of the capacitor, it was possible to calibrate the tube for the required values of the potential.

Fig. 2

After calibration, the tube was placed at a certain distance from the operating Tesla transformer. The spot on the phosphorescent screen, under the influence of the alternating high-frequency field, was drawn out into a line. The length of this line made it possible to determine the field strength at the given point. By bringing the tube nearer and moving it farther away, it was possible to find the law of variation of the field strength with distance. The potential at the end of the secondary spiral of the transformer was determined by interpolation. In order to make finally certain that the cathode beam was deflected exclusively under the influence of the electric field alone, in control experiments the tube was shielded with a copper sheet, after which co-

the oscillations of the spot on the screen ceased. In this way Rukavishnikov succeeded in measuring the voltage on a Tesla transformer operating under impulse excitation, and in checking some of the calculations he had made. It is interesting to note that the same idea of using a cathode oscillograph for potential measurements, quite independently of the work at the Radium Institute (V. N. Rukavishnikov’s work has not yet been published), occurred to Breit, Tuve, and Dahl.* Although the American physicists mentioned made use of the method just described, the highest potential was measured by them by another method. They indicate several reasons that compelled them to turn to another method of measurement. First of all, the method with the tube proved unsuitable for measuring the potential of a transformer located in oil under high pressure, since the vessel in which the transformer was placed was made of metal. For the purposes of the measurement it would have been necessary to replace the metal vessel by a wooden one, but then the pressure under which the oil was kept would have had to be reduced, which in turn would have led to a decrease in the potential obtained. Moreover, since the Tesla transformer operated under impulse excitation, the oscillations of the spot did not occur all the time, and therefore the brightness of the line on the fluorescent screen was too small to measure its length accurately. All this taken together forced the authors mentioned to use another method of measurement, to the description of which we now turn. In Fig. 3, which schematically depicts their apparatus, it is seen that, besides the transformer itself, there is a small spherical electrode in the vessel with oil. This electrode is connected, through an insulating lead-in, with a spark gap located outside the vessel. During operation of the Tesla transformer, a potential difference appeared across the spherical gap which could be measured. In order to find the potential on the transformer, it is necessary to determine how many times this potential is greater than the potential on the auxiliary arrester. Relat—

* Phys. Rev. 35, 51, 1930.

tion of the potentials was determined by means of a special and complicated calibration. The main drawback of this method is undoubtedly the circumstance that the entire installation has to be calibrated at potentials much lower than the one being measured, and then extrapolated. Nevertheless, with the aid of this, albeit imperfect, method the Americans succeeded in changing potentials up to 5,000,000 volts with an accuracy, as they believe, of up to 10%.

Fig. 3

The Tesla Transformer with Undamped Oscillations

We have already established the advantage of a Tesla transformer operating under impulse excitation. In order finally to convince ourselves of the correctness of such a conclusion and at the same time to study in greater detail the properties of the Tesla transformer, several models operating with undamped oscillations were built at the Radio Institute by Rukavishnikov. The source of oscillations for these models was a generator tube with a power of 250 watts. The theory of the Tesla transformer, including the elements and operating regime of the generator tube, is too complicated, and therefore we shall not dwell on it at all. Instead, let us simply assume that some source of oscillations creates in the primary-

variable electromotive force \(K\) in the secondary circuit. Then equations (1) may be written as follows:

\[ \begin{aligned} K &= W_1 i_1 + L_1 \frac{di_1}{dt} + V_1 + M \frac{di_2}{dt},\\ 0 &= W_2 i_2 + L_2 \frac{di_2}{dt} + V_2 + M \frac{di_2}{dt}. \end{aligned} \tag{10} \]

The general integral of these differential equations, as is known, differs from the general integral of equations (2) only by the presence of an additional term containing a periodic function. This latter is a particular solution of the system of equations (10). It is not difficult to understand the physical meaning of such a solution. When the current is switched on, oscillations arise in the transformer, similar to those which we analyzed in the transformer with damped oscillations; but since thereafter the transformer is fed without any interruptions, these oscillations, after damping out, are not renewed. Consequently there remain only the oscillations corresponding to the periodic function, which contains no damping factor. Thus the problem reduces to finding a particular solution of the system of equations (10). In the present case this particular solution can be found and the problem is solved completely. Since the Tesla transformer with undamped oscillations is not of special interest, we shall present only some results of the theoretical derivations and compare them with experimental data. First of all, we point out that experiment indeed confirms the presence of only one oscillation in the Tesla transformer with undamped oscillations. This can be judged from the intensity and uniform brightness of the line obtained on the screen of a cathode oscillograph. In addition, the very character of the discharge in air also changes. Instead of separate serpentine sparks we obtain a “torch,” burning with remarkable constancy and stability. The potential on such a transformer can be measured with great accuracy by means of a cathode tube, since the line into which the spot is drawn out also has a constant length and is quite stable. By measuring the potential, one can verify the correct—

ness of the computed transformation coefficient. However, the most interesting question turns out to be the one connected with losses in the secondary circuit as Joule heat. The power expended on losses in the conductor, as is known, can be expressed by the product \(V_2 J_2 \dfrac{\cos \varphi}{2}\), where \(V_2\) and \(J_2\) are the potential and current strength in the secondary spiral of the transformer; \(\cos \varphi\) in this case has a value equal to \(\dfrac{W_2}{2\omega L}\). By a corresponding choice of the elements of the transformer, \(\cos \varphi\) can be made very small. Then the watt component \(J_2 \cos \varphi\) will also be very small in comparison with the full current strength \(J_2\). Here, just as in a transformer with damped oscillations, the current strength will be regulated chiefly by the wave resistance \(\sqrt{\dfrac{L}{C}}\), so that, neglecting the small \(w\), one may put \(J_2 = -\dfrac{V_2}{\sqrt{\dfrac{L}{C}}}\), but nevertheless, at large \(V_2\), the product of \(V_2\) by \(J_2 \cos \varphi\) assumes a practically colossal magnitude and significance. All this was confirmed experimentally by Rukavishnikov. He tried applying to one and the same model of a Tesla transformer impact excitation and undamped oscillations. It turned out that in the first case it was impossible to detect in the secondary spiral even the slightest traces of heating, whereas in the second case the wire at the grounded end of the spiral, where the current antinode is located, was heated to red heat. “For those models which Rukavishnikov used (their average size is the same as that of the models used in lectures to demonstrate the resonance of electrical oscillations), it was impossible even to use the full power of the 250-watt generator tube, since this would have led to melting of the wire on the secondary spiral. All this shows with particular clarity that there is no point in thinking of using a Tesla transformer with undamped oscillations for laboratory purposes. As an illustration we shall cite one of the approximate calculations made by Rukavishnikov for

Tesla transformer on undamped oscillations. The specified voltage is 7,000,000 volts, the \(\cos \varphi\) is only 0.005, and, despite this, the required power is equal to 11 thousand kilowatts, i.e., one fifth of Volkhovstroi. Obviously, with such power there can be no question of constructing a small laboratory transformer.

Introduction of High Potential into Vacuum Tubes

If one speaks of a laboratory method for obtaining high potential, then one cannot avoid the question of introducing this potential into vacuum tubes. As is known, Coolidge solved this problem for one million volts by taking a cascade connection of several separate tubes. Tuve, Breit, and Hafstad approached this in the same way.1 According to the authors, the main points in the construction of such tubes were: 1) subdivision of the entire tube into sections; 2) uniform distribution of voltage between the individual sections by means of a potentiometer; 3) external electrostatic shielding of the sections. All these devices are visible in the figures provided. Fig. 4 shows a tube of six separate sections.

The internal electrodes of this tube consist of cylindrical copper tubes with rounded edges. The electrodes were connected through leads, the hermeticity of which was achieved by means of ordinary sealing compound. This method of bringing out the electrodes did not permit the entire tube to be heated in an electric furnace in order to free it from gas, but each electrode separately was heated in a quartz tube at a temperature of 950°C. The potentiometer consisted of a glass tube filled with a weak solution of salt in water. The sections of the potentiometer were connected to the corresponding electrodes of the tube. The external appearance of the potentiometer is also given in Fig. 4.

The same figure also shows two shields—one

annular and one bell-shaped. The annular shields were put onto the sections, while the bells served to protect the ends.

Fig. 4

Figure 5 shows a tube of fifteen sections and several shields.

Fig. 5

The following figure shows the assembly of the same tube, already covered with shields around the spirals of the Tesla transformer.

The authors emphasize that electrostatic shielding of the tube proved absolutely necessary. At first glance it might have seemed that, using the principle proposed by Coolidge, one could go arbitrarily far in raising the potential. In practice this turned out not to be quite so. Even to a tube with fifteen sections it was not possible to apply a potential greater than 1,400,000 volts. To a tube of six sections it was possible to apply only 850,000 volts. There are many reasons why this could not be done, and some of them are still unclear.

In any case one may say that it is very difficult to control the discharge at such high potentials. Even if it were possible to pump all the gases completely out of the tube, one still has to take into account the cold emission of electrons and, consequently, the formation of surface charges on the glass. In reality, however, there always remains some amount of gas, participating in the discharge, lowering the potential difference and creating space charges which disturb the proper distribution of the electric field. Mention should also be made of experiments by two of the same authors with an electrodless Pyrex tube. The schematic arrangement of the apparatus is shown in Fig. 6.

Fig. 6

The potential difference between the electrode and the earth was 1,000,000 volts. It is still impossible to say precisely what conditions are necessary for the operation of such a tube. In the authors’ opinion, for the operation of such an electrodless tube it is necessary that there be, on the outer surface of the glass, a layer partially conducting electricity. In the experiments described, this layer may have formed because both the tube and the transformer were immersed in oil saturated with carbon dioxide gas produced by the pressure.

Tesla Transformer with the Secondary Coil Placed in a Vacuum

Another way of solving the problem is to place the secondary coil of the Tesla transformer entirely in a vacuum tube. This method was first applied by me and by Rukavishnikov as early as 1922.^1 One end of the secondary coil is grounded, while, as is known, at the other end a bundle of potential is obtained. The grounded end of the coil is brought out. It is obvious that with such a design the danger from the high potential is completely eliminated, since the lead is at potential 0. With impulse excitation and small models, arranging such a lead presents no difficulty, since, despite the fact that the current antinode is located at the grounded end, the wire at this point is scarcely heated. The situation is otherwise with undamped oscillations or with large coils. As we have already indicated above, in this case the heating of the wire becomes so strong that an entrance directly through the glass will inevitably lead to the formation of a crack. It is comparatively easy to get around this difficulty: it is enough to take a thicker platinum wire and make not one but several lead-ins, with the calculation that the current density falling on each lead-in should not exceed the permissible value. In Fig. 7 one installation of this type, assembled by Rukavishnikov, is shown.

In the upper part of the figure one can see the secondary coil of the transformer, placed in a glass tube connected to a three-stage Gaede diffusion pump. At its other end, the tube with the coil enters inside the self-induction of the primary circuit. On the table is the capacitance of the primary circuit, consisting of a variable-capacitance condenser of the radiotelegraphic type, and a generator tube with the various elements included in its circuit. On the small table at the left is assembled an installation with a cathode oscillograph—

^1 Reports of the Academy of Sciences, 1922.

phon, which served to measure the voltage. Despite all the simplicity of the apparatus described, there are purely technical difficulties which have to be overcome chiefly when placing the spiral in a vacuum. First of all it must be pointed out that up to now Rukavishnikov has managed to place in a vacuum only small spirals, for which tubes with a diameter of no more than

Fig. 7

8–10 cm were needed. Tubes of larger diameter can no longer be worked by glassblowing and would have to be specially cast at a glass factory. But even with such a tube available (one of the specially cast tubes is at the Radium Institute), a new difficulty arises, connected with obtaining a high vacuum. Meanwhile, even in small models, in which there are only glass joints, it is not possible to achieve a sufficiently good vacuum. Despite the continuous operation of powerful pumps (diffu-

zionic Gede or molecular Golbek), a high vacuum is maintained only in the first moments after the current is switched on, and then, as gases are gradually released, an increasingly strong glow is obtained. The causes of the imperfection of the vacuum here are almost the same as when using a cascade connection of tubes. Attempts to insert a tube with a secondary spiral into an electric furnace in order to remove the adsorbed gases by heating were unsuccessful. At high temperature the difference between the coefficient of expansion of the copper wire and that of the glass of the cylinder on which it is wound becomes apparent. As a result, the turns slip and join together, greatly reducing the self-induction. Thus for the time being one had to be satisfied only with moments of good vacuum and then measure the voltage. Obviously, these difficulties will be felt even more in attempts to enclose the secondary spiral in a large glass cylinder, since some of the connections will have to be made with sealing compound. All the difficulties listed here are undoubtedly considerable, but they can in no way be called insurmountable. Therefore it can hardly be doubted that in the future, in constructing vacuum tubes intended to work with a Tesla transformer, the secondary spiral of this transformer itself will be placed in a vacuum and will, as it were, serve as one of the electrodes. The other electrode may then be sealed in at the other end of the tube and may have any form, depending on the purpose for which the tube itself is intended. The discharge in such a tube, at a very high voltage, can also occur without a heated cathode (cold emission of electrons), which further simplifies its construction.

A Tesla Transformer for 5,000,000 Volts in Oil

In order to judge the magnitude of the potential on a Tesla transformer, it is necessary not to allow discharge from the secondary spiral into air. In order to determine how much the potential is lowered when the transformer discharges into air,

Rukavishnikov carried out special experiments with a transformer operating on undamped oscillations. The amplitude of the oscillations of the spot of an oscillographic tube placed near the transformer, which was operating on undamped oscillations, was observed. The current in the primary circuit of the transformer was gradually increased until discharges in air began. When discharges arose, the amplitude of the oscillations of the oscillograph sharply decreased. It is therefore quite understandable that G. Breit, M. Tuve, and O. Dahl, striving to obtain the highest possible potential on the transformer, first of all took care to eliminate discharges. Although the named authors, for their part, also believe that it would have been best to place the secondary spiral of the transformer in vacuum, since the technical difficulties of which we spoke above have not yet been overcome, they settled on immersing the entire transformer in oil under a pressure that reached 500 pounds per square inch. Their installation is shown schematically in Fig. 3.

The current from an ordinary transformer passed through a rectifier at a voltage of 70,000 volts. Since the alternating current had 60 cycles per second, the rectifier charged the capacitor of the primary circuit 120 times per second. Obviously, the number of discharges through the spark gap of the primary circuit was the same. The capacitor used to obtain the highest voltages consisted of mirror-glass plates, each 40 square inches, pasted on both sides with sheets of tinfoil 0.003 inch thick. All the capacitor plates were placed in a wooden frame. The capacitance of the capacitor was equal to 1.6 microfarads.

On a piece of tube only one meter long and 8 cm in diameter, copper wire was wound in a single layer. The entire cylinder contained from 5,000 to 7,000 turns. Covers of spherical shape, approximately 25 cm in diameter, were fitted onto the ends of the spiral. The primary spiral, also shown in Fig. 8, is so simple that it requires no further explanation. The transformer

Tesla was completely immersed in a vessel filled with oil. The vessel itself was made of strong boiler iron and filled with light transformer oil. This oil withstood, without breakdown, a voltage of 46,000 volts per millimeter. The pressure of the vessel was produced by a carbon-dioxide cylinder, likewise shown schematically in Fig. 3. The method of determining the potential used by the authors has already been described by us earlier in considering various methods of measuring the potential on the Tesla transformer. The transformation coefficients obtained under various conditions are given in the following table:

Table 1

As can be seen from this table, the transformation coefficient is rather high and fluctuates around 100. In one case it

L. V. Mysovsky

turned out to be as high as 162. An interesting comparison is that of a Tesla transformer with radium, which the authors make using their data on the magnitude of the potential they attained. Proceeding from the fact that the average current in the secondary coil at 120 sparks per second is \(3 \cdot 10^{-5}\ A\), one can find the number of ions necessary for the transfer of this quantity of electricity.

This number will be

\[ \frac{3 \cdot 10^{-5}}{1.6 \cdot 10^{-19}} = 1.9 \cdot 10^{14}. \]

Since these ions

Fig. 8.

will pass through a field of 5,000,000 volts, their energy will correspond to the energy of \(\alpha\)-particles emitted by radium. If the number of alpha particles that we obtain from one gram of radium in one second is equal to \(3.5 \cdot 10^{10}\), then, taking into account that each \(\alpha\)-particle carries a double charge, we find that a Tesla transformer at 5,000,000 volts is equivalent in its action to \(\frac{1.9 \cdot 10^{14}}{2 \cdot 3.5 \cdot 10^{10}} = 2600\) grams of metallic radium.

Conclusion

The advantages of Tesla transformers are at present appreciated not only by physicists, but also by engineers. In many firms such transformers successfully replace

technical high-voltage transformers with a coupling coefficient close to unity. In America, attempts were even made to use these transformers for artificial rain-making. There is no doubt, however, that the Tesla transformer is of greatest interest to physicists, since they hope, with its aid, to achieve the artificial transformation of elements. On the basis of what has been set forth in this article, it may be said that these hopes are not without foundation. The theory of a transformer operating under impulse excitation is simple and has now been tested experimentally. From the theoretical data it is clear that we can proceed almost without limit along the path of extracting potential. The whole difficulty consists only in not allowing these high potentials to be uselessly spent on the formation of sparks and dielectric breakdown. Undoubtedly, in the future it will be necessary to settle on a transformer in which the secondary spiral is in a vacuum. With some progress in vacuum technique, it may be expected that the final purification of the tube from residual gas will already be carried out by the transformer itself. Under the influence of enormous electric fields, ions will penetrate deeply into the walls of the vessel and will not soon come out from there. By placing a grounded electrode in such a transformer as close as possible to the end of the secondary spiral, we shall almost attain the ideal—an enormous potential difference in a small volume.

1. Phys. Rev. 35, 66, 1930. ↩↩