Electron-Beam Generators of Ultrahigh-Frequency Oscillations

E. M. Studenkov, Moscow

Introduction

Undamped electromagnetic oscillations of ultrahigh frequency, i.e., oscillations whose wavelength lies in the decimeter and centimeter range, have in the last 10–15 years been the subject of especially intensive study. This is explained by the fact that decimeter waves, and still more centimeter waves, in addition to their scientific significance, are also of great practical interest. The possibility of concentrating such waves into rather narrow beams and thereby achieving directed transmission of signals makes them very convenient for various practical applications (directional radio communication, radio beacons, blind-landing devices for aircraft, devices for determining the absolute altitude of an aircraft above the terrain, etc.).

The principal problem to whose solution most of the work of recent years has been devoted, and on which work is still being conducted, is to find a reliable and effective source of ultrahigh-frequency oscillations of sufficiently large power.

In the region of long waves the problem of generating oscillations is solved simply. An ordinary electronic triode tube in a feedback circuit makes it possible to obtain oscillations of almost any power and over very wide frequency ranges (beginning with the lowest and up to 200–300 MHz). It would seem that the same principle of a tube generator with feedback could also be used to excite ultrahigh-frequency oscillations, by suitably selecting the oscillatory system and the tube. In practice, however, it turned out that advancement toward ever shorter waves with the ordinary tube circuit is connected with a whole series of difficulties, which make it impossible to use this very simple and convenient method in the ultrahigh-frequency range. These difficulties are mainly of two kinds: 1) with the oscillatory system and 2) with the electronic tube.

Oscillatory systems, consisting of so-called circuits with lumped inductance \(L\) and capacitance \(C\), are entirely suitable and work well in the region of low frequencies,

but they become completely unsuitable when one passes to ultrahigh frequencies for a number of reasons.

First, in order to raise the natural frequency of a circuit, its electrical parameters \(L\) and \(C\) must be decreased, which is achieved by reducing the geometrical dimensions of the circuit; the reduction of dimensions, however, besides mechanical inconvenience, leads to the fact that, owing to the increasing role of the capacitance \(C\), the characteristic impedance of the circuit rapidly decreases,

\[ \rho = \sqrt{\frac{L}{C}}, \]

and, consequently, so does its resonance impedance

\[ Z_r = \frac{\rho^2}{R} \simeq \frac{L}{RC}. \]

A decrease of \(Z_r\), on the one hand, worsens the self-excitation conditions of the generator, and, on the other hand, reduces the power that can be developed in the circuit.

Second, with the decrease of \(\rho\), another very important quantity characterizing the circuit also decreases—the so-called “quality factor” of the circuit \(Q\), proportional to the ratio of the total energy of the system at resonance to the energy expended per period as Joule heat:

\[ Q = \frac{\omega E}{W}, \]

or

\[ Q = \frac{\omega L I^2}{R I^2} = \frac{\omega L}{R} = \frac{\sqrt{\frac{L}{C}}}{R} = \frac{\rho}{R}. \]

Since, on the other hand,

\[ \pi R \sqrt{\frac{C}{L}} = d \]

is the decrement of damping of the system, it is clear from this what the significance of \(Q\) is: it is the quantity inverse to the damping of the system. In ordinary circuits, for frequencies up to \(1.5\) MHz, \(Q\) is of the order of several hundreds and then, as the frequency increases, it decreases.

Finally, at high frequencies a circuit with lumped constants cannot be realized at all. It must already be regarded as an oscillatory system with distributed constants. The electric and magnetic fields are not concentrated in certain sections of the circuit, as at low frequencies, but are distributed over the whole circuit. This leads to the presence of large leakage fluxes of the electric and magnetic fields (radiation), to the existence of various undesirable couplings, etc.

All these shortcomings of the ordinary oscillatory circuit make it completely unsuitable for an ultrahigh-frequency generator.

Meanwhile, there exist such types of oscillatory systems that are, to a considerable degree, free of all the indicated shortcomings and, moreover, prove to be the more perfect and convenient the shorter the wavelength used. Such oscillatory systems are volumes filled with a dielectric (air)

and bounded by closed or nearly closed conducting surfaces.

Such hollow oscillatory systems have so far not found wide application. This is explained partly by the difficulty of using them in ordinary tube generators, and, on the other hand, by the fact that their properties had not been studied in sufficient detail. Recently, intensive research has been carried out on the properties of hollow conductors. The conditions for the propagation of electromagnetic waves in metallic tubes of various shapes are being studied\(^{1,2}\). It turns out that such tubes can be successfully used for the transmission of electromagnetic energy when operating at ultrahigh frequencies. The properties of such hollow transmission systems are considered in detail in the article by N. N. Malov\(^{2a}\).

Studies by a number of authors\(^{3,4,5}\), who investigated the resonant properties of closed conducting surfaces of various shapes, showed that hollow resonators make it possible to obtain large oscillation powers, since even at very high frequencies their resonant resistance is quite large. Likewise, the quality factor \(Q\) of these oscillatory systems can reach an enormous value—of the order of \(5 \cdot 10^4\). To this must be added a number of other advantages, such as the absence of external fields, high frequency stability, etc.

Thus, overcoming the difficulties associated with the oscillatory system and, consequently, the path to obtaining large powers at ultrahigh frequencies undoubtedly lies in making maximum use of all the merits of hollow resonators.

Turning now to the difficulties associated with the electron tube, we encounter first of all the circumstance that at ultrahigh frequencies the tube is no longer merely a device for controlling the anode current, but also an essential component of the oscillatory circuit, since its interelectrode capacitances become comparable with the capacitance of the circuit \(C\) and may even replace the latter entirely. This means that, in order to increase the frequency of the generator, the dimensions of the tube and of its electrodes must be reduced, which inevitably leads to a reduction in the power that the generator can deliver. But an even more serious drawback of an ordinary electron tube at ultrahigh frequencies is that, under these conditions, it can no longer be regarded as a device that quite reliably supplies energy periodically from the source to the oscillatory circuit. Here the inertia of the electrons already begins to make itself felt. The transit time of the electrons between the electrodes of the tube becomes comparable with the period of oscillation. As a result, the phase difference between the voltage on the grid and on the anode, necessary for exciting oscillations, is disrupted. The supply of energy to the circuit takes place “out of step” with the oscillations of the circuit, and excitation does not occur.

The higher the oscillation frequency on the control grid, the more strongly the inertia of the electrons is manifested, and, finally, at a very high frequency of the control voltage one may reach the point where

electrons will not produce current pulses at the anode at all, i.e., as the frequency increases the tube becomes, as it were, less and less sensitive to the signals arriving at the grid, and in the end ceases entirely to act as a control element for the anode current.

Thus, an ordinary electronic triode tube in a feedback circuit sets a limit to the possibility of generating short waves. Attempts to push this limit as far as possible toward short waves by designing tubes with very small distances between the electrodes have not led to great success. Experience has shown that for generators operating with the smallest “acorn” tubes in feedback circuits, the limiting wave is about 30 cm. Moreover, the power of such generators reaches only a few tenths of a watt and, of course, cannot be sufficient for any practical purposes.

From all that has been said it is clear that the difficulties associated with the electronic tube, i.e., ultimately with the inertia of the electrons, make it impossible to use the ordinary methods of generating oscillations in the ultrahigh-frequency range, since by this method we can obtain neither practically useful powers nor sufficiently short waves.

A partial overcoming of these difficulties was achieved in fundamentally new generator circuits, in which the inertia of the electrons is used precisely to excite oscillations. Such circuits are the retarding-field circuit, found in 1920 by Barkhausen and Kurz, and the magnetron generator.

The main factor determining the operation of the Barkhausen–Kurz generator is the oscillatory motion of electrons about a grid that has a high positive potential relative to the anode. The period of the generated oscillations is directly dependent on the period of oscillation of the electrons and, within known limits, does not depend on the external oscillatory system. We have the same thing in the magnetron generator, in the case of the so-called first-order oscillations, when the period of the oscillations obtained is determined by the time of revolution of the electrons along their orbits inside the cylindrical anode and also does not depend on the external oscillatory system. But, in addition, in magnetrons with split anodes there may arise the so-called “dynatron” oscillations, or oscillations of higher order. The mechanism of their occurrence is quite different and is due to the fact that such magnetrons under certain conditions have a static falling characteristic. The presence of the latter makes it possible to generate oscillations whose period is determined mainly by the external circuit and can be very large and even incomparable with the time of revolution of the electrons.

The Barkhausen–Kurz circuit and the magnetron opened a new page in the technique of generating ultrahigh-frequency oscillations. They made it possible to move still farther toward short waves. It became possible to generate not only decimeter and centimeter waves, but even waves measured by only a few milli-

meters. Thus, for example, waves with a length of 4.9 mm have already been obtained with the aid of a magnetron.

Nevertheless, all these methods of generation do not completely solve the problem of a reliable, technically usable source of ultrahigh-frequency oscillations. The Barkhausen circuit has proved in practice to be of little use because of its very low power, which is usually no more than 0.5—1 W, and its very low efficiency, reaching only 5% under the best conditions. Magnetron generators, on the other hand, turn out to be very convenient only in the case when operation is carried out on higher-order oscillations, i.e., when the generated waves lie in the upper and middle part of the decimeter range. Under these conditions, with the aid of a magnetron, it is possible to obtain powers of several hundred watts at an efficiency of 30—50%. At shorter wavelengths the power and efficiency decrease markedly, and on fundamental oscillations, i.e., such oscillations at which it is possible to generate the shortest waves, the power becomes of the same order as in the Barkhausen circuit, only with a somewhat better efficiency (10—15%). This is why the reports that have appeared recently in the press that a new principle of generating ultrahigh-frequency oscillations has been found, making it possible to obtain powers considerably exceeding those obtained up to now, are of unusually great interest.

The most interesting news was the report by workers at Stanford University (California)^6,7 on a generator of a new type constructed in their laboratory, which received the name “klystron” (Klystron). According to a number of sources^8,9, this generator makes it possible to obtain up to 1 kW of power at a wavelength of 20—30 cm and about 500 W at a wavelength of 10 cm, with an efficiency of 30—40%.

The new generator—the klystron—is now at the center of attention of all the literature on high-frequency engineering. It is reported^10 that the Sperry Gyroscope aeronautical company has tested the klystron for use as a source of directional waves for blind landing of aircraft (the Metcalf system). The test results proved good, after which a contract was immediately concluded with Stanford University for the production of klystrons for the specified purposes.

Almost simultaneously with the first report on the klystron, papers by other authors^11,12 appeared in print, describing generators and amplifiers of a type similar to the klystron and with equally good data with respect to the power developed and efficiency. What is fundamentally new in all these designs is that, for the excitation of oscillations in one system or another, an electron beam is used, i.e., a beam of rapidly flying electrons. In this case the kinetic energy of the electrons, imparted to them by a constant field, is converted into the oscillatory energy of the system.

It should be noted that although the designers of these new electron-beam generators and amplifiers do not cite any previous works relating to this question, theoretical indications of the possibility of generating oscillations with the aid of an electron

of the beam had been published several years earlier. Thus, for example, in 1935 there appeared a paper by Arsen’eva-Heil and Heil^13, in which a method was described for generating oscillations by means of an electron beam passing through a system of electrodes consisting of two diaphragms and a cylinder between them. The arrangement of these electrodes and the distribution of the potential in the system are shown in Fig. 1 (the negative potential is plotted upward). The diaphragms \(A_1A_2\) have a high potential relative to the cathode and serve to accelerate the electrons. The cylinder \(C\) is connected to the oscillatory circuit \(K\), and therefore, when oscillations are present in the circuit, the potential of the cylinder changes, taking values from \(U'_c\) to \(U''_c\), which is shown in the figure by dashed lines.

Fig. 1

The explanation of the operation of such a generator given by the authors is not entirely clear or convincing. In essence it amounts to the following: the accelerating potential on the diaphragms \(A_1A_2\), the length of the cylinder \(C\), and the oscillation frequency of the circuit \(K\) can be chosen in such a way that in the cylinder \(C\), owing to the somewhat different velocities of motion of the electrons, during negative half-periods there will be a larger number of electrons than during positive ones. In short, because of the different residence time of the electrons inside the cylinder, a pulsating space charge is, as it were, produced there, which maintains the oscillations of the circuit. Later we shall see that the process by which oscillations arise in such a system occurs somewhat differently and has another explanation; nevertheless the idea of the generator of Arsen’eva and Heil is in the main correct and valuable as the first indication of an entirely new method of exciting oscillations.

At the end of 1938 there appeared a paper by Brüche and Recknagel^14, which is of great importance for understanding the operation of electron-beam generators. In it the conditions for the occurrence of the so-called “phase focusing” of electrons were clarified. The theoretical conclusions of this work were later confirmed experimentally by Meyer^15.

1. PHASE FOCUSING OF ELECTRONS

In a theoretical discussion of the processes taking place in a Barkhausen generator or in a magnetron, one usually proceeds as follows: 1) first the motion of one individual electron is considered, and it is determined under what conditions the desired effect occurs, i.e. what the relations must be between the oscillation frequency, the velocity of the electron’s motion, the phase of its departure from the cathode, and so on, in order that the oscillations be maintained for a long time; 2) then the question is investigated of what happens to those electrons which move somewhat differently

from the already considered first electron, i.e., they have a somewhat different velocity, leave at a different time, etc., or, in short, have a somewhat different phase with respect to the first electron. It is clear that, for very large differences in phase, these latter electrons not only contribute nothing to the desired effect, but may even act counter to what we wish to achieve.

Thus there arises the necessity, on the one hand, somehow to eliminate the electrons moving with an incorrect phase, and, on the other hand, to increase the number of electrons moving with the correct phase. Only after such “sorting” of the electrons can the desired effect occur.

In all devices whose action is based on a more or less ordered motion of electrons, “sorting” obviously has fundamental importance and in many cases occurs there spontaneously. Thus, for example, in the Barkhausen–Kurz generator it may be assumed approximately that sorting occurs because electrons possessing an excessively high velocity and, consequently, running ahead with respect to the others are periodically absorbed by the anode, while those that are too slow are absorbed by the grid, so that only electrons moving with the required phase remain; these may to some extent be regarded as an oscillating electron cloud.

Fig. 2

It is clear that it would be highly desirable not only to know how the sorting of electrons occurs in one case or another, but also to try consciously to influence this process or even to control it. It is quite possible that this would provide a means for improving the operation of generators and increasing their efficiency.

An attempt at such a conscious approach to clarifying the conditions under which a group of electrons of different phases can be equalized in phase is represented by the already mentioned work of Brüche and Recknagel.

The chief interest of this work consists in the following: the authors found an analogy between the focusing of light rays by an ordinary lens and what they call the “focusing of phases” of electrons. This analogy is so great that, to questions of phase focusing, almost all the conclusions of geometrical optics are applicable, and only in some cases are there substantial discrepancies.

Let us consider the most essential part of the arguments of Brüche and Recknagel.

Figure 2,a shows the well-known path of rays in optical focusing. A parallel bundle of rays, bounded by the diaphragm \(D\), encounters on its path the lens \(L\). At some distance from the lens, at the point \(F\), the rays of the bundle are gathered into one point—the focus. To this picture the authors compare the following (Fig. 2,b): from left to right there moves a sequence of electrons with equal velocities. From this sequence the diaphragm \(D\) (which in this case is rather like a photographic shutter) cuts out a series of portions of electrons of equal length. The time during which this portion moves past the observer is equivalent to the width of the bundle in the optical case.

This series of portions then enters the time-varying field \(L\). This field must act on the portion of electrons in such a way that after passing through it all the electrons are gathered simultaneously on a certain plane \(F\). “Phase focusing” will occur.

This process proceeds as follows: at the moment when the first electrons of some portion enter the field \(L\), the latter has such a direction that these electrons are decelerated, and consequently on leaving the field their velocity will be somewhat less than the initial one. Conversely, the electrons of the last part of the portion enter a field which accelerates them, and consequently on leaving the field they will have velocities somewhat greater than the initial one. The middle electrons of each portion pass through the field at the moment when it is equal to zero, i.e., they undergo no change in velocity. It is clear that a portion of electrons with velocities altered in this way, in its subsequent motion over some distance, must become compressed, since the electrons flying behind will catch up with the front ones.

This process is seen more clearly in the space-time diagram of the motion of the electrons (Fig. 2,c). The electrons entering the field correspond to a bundle of parallel straight lines, whose inclination to the \(t\)-axis is determined by the initial velocity of the electrons. Owing to the action of the alternating field \(L\), the inclination of the straight lines (i.e., the velocity of the electrons) changes so that they all meet at the point \(F\).

By analogy with optics, the distance \(LF=f\) may be called the phase focal distance, and the alternating field \(L\)—the phase lens.

Let us determine how the field in the phase lens must vary with time for the focusing to occur in the best possible way. A simple calculation shows that, in the case where we have sufficiently short portions of electrons, for focusing them it is enough for the field to vary according to a linear law.

Let \(v\) be the initial velocity of the electrons. The middle electron passes through the field at the moment \(t=0\), without changing this velocity, since we assume that the potential of the field \(U\) at this moment is equal to zero. An electron that entered the phase lens later by a time \(\Delta t\),

ELECTRON-BEAM GENERATORS

enters a field with potential

\[ \Delta U=\frac{dU}{dt}\Delta t. \]

Let us determine by how much the velocity of this electron changes. If its new velocity is denoted by \(w\), then from the law of conservation of energy we obtain

\[ \frac{mw^2}{2}=\frac{mv^2}{2}+\frac{dU}{dt}e\Delta t, \]

or

\[ w^2=v^2+\frac{dU}{dt}\frac{2e}{m}\Delta t =v^2+2D\Delta t, \]

where

\[ mD=\frac{d}{dt}\left(\frac{mv^2}{2}\right) =\frac{d}{dt}(eU) \tag{1} \]

is the change in kinetic energy per unit time. Neglecting terms of second order, we have

\[ w=v\left(1+\frac{2D\Delta t}{v^2}\right)^{\frac12} \simeq v\left(1+\frac{D\Delta t}{v^2}\right). \tag{2} \]

Let us compute now the path \(Z\) traversed by the electron after leaving the field during the time \(t\):

\[ Z=w(t-\Delta t)=v\left(1+\frac{D\Delta t}{v^2}\right)\cdot t\left(1-\frac{\Delta t}{t}\right)= \]

\[ =vt\left[1+\Delta t\left(\frac{D}{v^2}-\frac{1}{t}\right)\right]. \tag{3} \]

[[unclear: beginning of line]] it is necessary to determine under what conditions the distance \(Z\), traversed by the electrons, will be independent of \(\Delta t\), i.e. of the moment at which they enter the field. This distance, evidently, will be the focal distance \(f\). If the time of motion to the focus is denoted by \(t_f\), then from equation (3) it is seen that \(Z\) does not depend on \(\Delta t\) if

\[ \frac{1}{t_f}=\frac{D}{v^2}. \]

Since the focal distance \(f\) can be expressed as

\[ f=vt_f, \]

we obtain

\[ \frac{1}{f}=\frac{D}{v^3}. \tag{4} \]

Formula (4) shows that, indeed, with a linear change of the field (\(D=\mathrm{const}\)) one can find such a distance \(f\) at which all electrons, regardless of when they entered the variable field, will come together, i.e. will have the same phase.

More interesting results are obtained when considering the focusing process of “diverging” portions of electrons, i.e.

such in which the electrons have different velocities. In optics this corresponds to the focusing of a divergent beam of rays. In Fig. 3,a and 3,b these two cases are compared. Electrons leaving at a certain instant from the source \(A\) and having different velocities will, in their subsequent motion, diverge in space. The variable field must now act on them in such a way that at the point \(B\) a certain portion of the electrons is again brought together.

Let us call, by analogy with optics, \(A\) the source and \(B\) the image. Let their distances from the field be, respectively, the object distance \(a\) and the image distance \(b\). Denote the corresponding times of motion of the electrons by \(t_a\) and \(t_b\). The mean electron again passes through the field without change of velocity. An electron with a somewhat smaller velocity \(w_a = v - \Delta v\) will enter the field later by \(\Delta t\). Since the object distance \(a\) is the same for both electrons, we may write:

\[ a = vt_a = (v - \Delta v)(t_a + \Delta t), \]

whence, neglecting terms of the second order, we obtain

\[ \Delta t = \frac{a}{v^2}\Delta v . \]

Fig. 3

The velocity of the slow electron after passing through the field can again be determined from the law of conservation of energy

\[ w_b^2 = w_a^2 + 2D\Delta t, \]

whence, neglecting terms of the second order, we find

\[ w_b = v\left[1 - \frac{\Delta v}{v} + \frac{D}{v^2}\frac{a}{v^2}\Delta v + \ldots \right]. \]

Let us find the path \(Z\) which the electron will traverse after passing through the field by the time \(t_b\):

\[ Z = w_b(t_b - \Delta t) = vt_b\left[1 - \frac{\Delta v}{v} a\left(\frac{1}{a} + \frac{1}{vt_b} - \frac{D}{v^3}\right) + \ldots \right]. \]

This path will not depend on \(\Delta v\), i.e., on the velocity with which the electron left the source, in the case where the expression in parentheses is equal to zero. This gives us

\[ \frac{1}{a} + \frac{1}{vt_b} = \frac{D}{v^3}, \]

and since \(vt_b = b\), the last equality takes the form

\[ \frac{1}{a} + \frac{1}{b} = \frac{D}{v^3}, \]

or, taking into account relation (4), we obtain:

\[ \frac{1}{a}+\frac{1}{b}=\frac{1}{f}, \]

i.e. the well-known lens formula.

Thus, an alternating field of the kind indicated above acts on a finite portion of diverging electrons in a focusing manner, and here, as in optics, the lens formula holds. Brüche and Recknagel develop this optical analogy further: they introduce the concept of the “coefficient of refraction,” which, moreover, turns out to depend on the third power of the velocity; they consider the action of a system of lenses, i.e. of several fields arranged one after another, and arrive at the conclusion that here, as in optics, it is possible to describe the system by means of principal planes.

They next consider the case of focusing very long portions of electrons, which in optics corresponds to very large diaphragms, and conclude that in this case, as in optics, a simple lens (i.e. in optics a lens bounded by spheres, and in our case a field varying according to a linear law) does not give good focusing. The lens must be “corrected” by applying a law of variation of the field with time differing from the linear one.

The form of the function \(U(t)\), for the case of focusing long portions, can be determined from equality (4)

\[ \frac{1}{f}=\frac{D}{v^{3}}, \tag{4} \]

by writing it in a somewhat more general form. Namely, here \(v\) appears, i.e. the velocity which, after leaving the field, the mean electron has, not changing, as is known, its initial velocity (i.e. \(v=v_{0}\)). But it can be shown that the same equality is also valid for an electron leaving the field with a changed velocity \(v_{1}\ne v_{0}\), but focusing at the same point \(F\), i.e. that

\[ \frac{1}{f}=\frac{D}{v_{1}^{3}}, \]

and since

\[ v_{1}=\sqrt{v_{0}^{2}+\frac{2e}{m}U} \]

and

\[ D=\frac{e}{m}\frac{dU}{dt}, \]

equality (4) will take the form

\[ \frac{1}{f}= \frac{D}{\left(v_{0}^{2}+\frac{2e}{m}U\right)^{\frac{3}{2}}} = \frac{e}{m}\frac{dU}{dt} \left(v_{0}^{2}+\frac{2e}{m}U\right)^{-\frac{3}{2}}. \tag{5} \]

From this, by integration, one can find the following expression for \(U(t)\):

\[ U=-\frac{mv_0^2}{2e}\left[\frac{1}{\left(1-\frac{v_0t}{f}\right)^2}-1\right], \tag{6} \]

in which the constant of integration is determined from the condition that at the moment \(t=0\) the field also passes through the zero value.

Figure 4 presents the graph of the function determined by equation (6). We see that here, as before, an electron passing through the field at the moment \(t=0\) experiences no influence of the field. Electrons entering earlier are decelerated; those entering later are accelerated. The later an electron enters the phase lens, the more strongly the field must act on it so that it can catch up with the electrons that entered earlier. Further, it follows from the graph that an electron entering at the moment \(t=\frac{f}{v_0}\) must undergo an infinitely large increase in velocity, while for still later electrons the reasoning, for the given values of \(f\) and \(v_0\), loses its meaning, since electrons cannot be focused if they pass through the field only when the electrons that entered earlier have already been focused. Obviously, the length of the portion of electrons that can be focused in one operation is the greater, the longer the focal distance and the smaller the electron velocity.

Fig. 4

Without dwelling further on other, less important questions developed in the work of Brüche and Recknagel, let us consider in conclusion the conclusions at which the authors arrive. These conclusions are as follows.

1. At the present time electron optics has become widespread. As lenses it usually uses static fields with axial symmetry. Its task is to investigate the question: where can the trajectories of electrons emitted from a source in different directions intersect? If a high-frequency voltage is applied to such an electron lens, then it will at the same time also be a phase lens. If in the first case we were interested only in the geometry of the electron trajectories, then in the latter case the kinematics of the motion of the electrons is added to this. Here we shall already be interested in the question: where and when will electrons emitted from the source with somewhat different velocities gather?

In this sense one may speak of two parts of electron optics: geometrical and kinematical. When electrons pass through variable fields, both of these parts are, obviously, important for us.

1. The second conclusion, important for practical application, consists in the fact that phase focusing makes it possible to transform

a continuous electron stream of small strength into separate pulses of considerably greater strength. The degree of such an increase in the instantaneous values of the current strength depends on how well the focusing takes place. If the course of the potential on the phase lens were a periodic repetition of the curve defined by equation (6) (Fig. 5), then in this case the electron stream would be almost entirely transformed into separate focused bunches. The current amplification would be greatest. In practice, obtaining such a course of the potential at high frequency does not yet appear possible. The simplest to realize may be a sinusoidal course, but in that case, of course, one cannot expect complete focusing.

1. Finally, the authors also come to the conclusion that periodically consecutive focused bunches of electrons may be used for exciting oscillations, but they do not dwell in detail on the methods by which this can be done.

Fig. 5

The experimental verification of the work of Brüche and Recknagel was carried out by Meyer\(^{15}\), who published the results of his experiments at the beginning of last year.

Meyer used, as a phase lens, a pair of plates with holes through which electrons could fly. A certain constant voltage \(U_0\) was applied to the plates, which served to create the beam, and, in addition, an alternating voltage of high frequency. After passing through the phase lens the beam first entered a constant magnetic field directed transverse to the motion of the electrons, then into a transverse electric field having the same frequency as the field in the phase lens, and finally onto a fluorescent screen, on which the resulting curves could be observed. From the form of these curves one could judge whether focusing was taking place or not.

Since the course of the potential on the phase lens was sinusoidal, complete focusing could not be obtained. Indeed, for a sinusoidal field \(u=-u_0\sin\omega t\), from the general relation (5) the following expression is obtained for the focal distance \(f\):

\[ f=\frac{\sqrt{\frac{2e}{m}u_0\left(\frac{U_0}{u_0}+\sin\omega t_s\right)^{\frac{2}{3}}}}{\omega\cos\omega t_s}, \]

i.e., the dependence of the focal distance on the time of entry \(t_s\) of the electron into the phase lens is obtained. But, as can easily be shown, near the minimum focal distance (\(\omega t_s=0\)) in the phase region extending approximately over \(\pm 30^\circ\), the focal distance is almost constant; consequently, electrons entering the phase lens with a phase difference not exceeding this region will give a more or less focused bunch.

Analysis of the curves obtained on the fluorescent screen shows that, indeed, within the indicated phase region the focusing of electrons occurs quite distinctly. This confirms the principal conclusions of Brüche and Recknagel.

The next task was to use the phenomenon of phase focusing to excite oscillations, and this was realized in the very near future.

2. ELECTRON-BEAM GENERATORS AND AMPLIFIERS

It often happens that in an area where active research work is being carried out, several investigators arrive simultaneously at the solution of one problem or another. This is also true of the problem of the electron-beam generator. At the beginning of last year several descriptions at once appeared in the literature of various designs of generators and amplifiers for ultra-high frequencies, using the electron-beam method of exciting oscillations. The authors of these designs evidently worked independently of one another, and perhaps even independently of the preceding works of Arsen’eva-Heil, Brüche-Recknagel, and Meyer.

The first information on the practical realization of an electron-beam generator appeared in the form of brief communications6,7 stating that at Stanford University a group of workers had constructed an ultrahigh-frequency generator of a new type, which received the name “klystron.” Its description then appeared in print three months later in a paper by the Varian brothers16.

Simultaneously with the first communication on the klystron, two further papers also appeared in print describing devices of a similar type. One of them was a paper by Haeff11, in which a description was given of an ultrahigh-frequency amplifier of a new design, and, following it, a second paper by Hahn and Metcalf12, describing the so-called “velocity-modulating tubes.”

All three devices—the klystron, Haeff’s amplifier, and the velocity-modulating tubes of Hahn and Metcalf—have one and the same principle of operation, although they differ from one another in certain design features.

The klystron of the Varian brothers should be considered the most successful design, since it gives the highest figures with respect to the power developed and the efficiency when operating at the shortest waves. This is explained, apparently, by the fact that in the klystron, first, electron phase focusing in the sense of Brüche-Recknagel is used in the clearest form, and, second, by the fact that here fully closed resonators are used as oscillatory systems, with all their advantages, which were indicated earlier.

In the other designs these two qualities of the klystron are expressed to a lesser degree, but at the same time they have their own positive features, which will be indicated below in a more detailed description of these designs.

ELECTRON-BEAM GENERATORS

It is convenient to begin acquaintance with the klystron generator by describing cavity oscillatory systems, which are its principal components.

The use of cavity resonators for the klystron was proposed by an employee of the same Stanford University—Hansen, who had previously been studying the properties of resonators of this kind. In the Stanford University laboratory, cavity resonators received the name “rumbatrons,” from the Greek word “rumba,” meaning rhythmic oscillations.

Hansen investigated rumbatrons of several types, determined their resonance properties, the value of the quality factor \(Q\), etc.\(^4\) It turned out that surfaces close to spherical possess the greatest \(Q\) and resonance resistance. For practical purposes, however, surfaces different from spherical ones, whose shape is close to toroidal, proved more convenient (Fig. 6). The choice of such a resonator shape becomes clear after explaining how the excitation of undamped oscillations in this resonator is accomplished.

If there are even slight natural oscillations of the resonator, maximum field values are obtained in its middle part, between the planes \(A\) and \(B\). To excite oscillations with constant amplitude, the planes \(A\) and \(B\) are made in the form of grids, and an electron beam consisting of separate bunches of electrons is passed through them. These bunches must be distributed in time so that they pass through the space between the grids precisely at the moment when the field is retarding them, i.e., is taking away their energy. When the field between the grids has the opposite direction, the electrons must not enter there. Under these conditions, the energy necessary to maintain the oscillations will be periodically pumped into the system, and the oscillations will be undamped.

Fig. 6

It is clear from this why, for example, the spherical shape of a resonator is inconvenient for exciting oscillations. It is necessary that a group of electrons which has entered the field at the moment when it becomes retarding should have time to leave the field before it changes to an accelerating one. Since in a spherical resonator the natural wavelength is approximately \(1.30\) times the diameter of the sphere, it follows that even if a group of electrons has a velocity equal to the velocity of light, it will not be able to pass along the diameter of the sphere before the field changes to the opposite one. In short, the path of the electrons in the resonator must not be longer than

\[ \frac{v}{c}\frac{\lambda}{2}, \]

where \(v\) is the velocity of the electrons, and \(\lambda\) is the natural wavelength of the resonator.

Thus, to excite oscillations in a resonator of the above kind, it is necessary to have periodically successive bunches of electrons. In order to obtain such bunches from the continuous stream of electrons emitted by the cathode, exactly the same resonator-rumbatron is used, to which an external alternating voltage is applied and which in this case acts

as a phase lens. As a result of connecting two such resonators for joint operation, the construction shown in Fig. 7 is obtained.

The first resonator I, serving as a phase lens, has an additional grid G, which acts as an accelerating electrode for obtaining a rapid stream of electrons. From the side E, an alternating voltage is supplied along a coaxial line. At some definite distance beyond the phase lens I there is placed resonator II, which is set into oscillation by the action of electron bunches periodically entering it. After leaving resonator II, the electrons are caught by electrode C.

Fig. 7                Fig. 8

Part I is called by the authors the buncher, while part II, in which the electron bunches are slowed down and, as it were, “broken up,” is called the catcher, and the entire device is called a klystron, from the Greek word “klyzo,” meaning the breaking of waves or bunches.

The klystron in the form shown in Fig. 7, where the “buncher” I is controlled by an independent voltage source, for example, an antenna, is obviously an amplifier. To convert it into a generator, it is necessary to use some part of the oscillatory power of resonator II to control the phase lens I, i.e., to establish feedback. The construction shown in Fig. 8 is obtained. Tube E, connecting resonators I and II, is introduced chiefly for mechanical reasons. Feedback is effected by means of coaxial line F; the same kind of line also serves to take the useful power out of catcher II.

When two methods of controlling the phase lens I are present simultaneously, i.e., feedback and an external signal source, the device will operate as a regenerative amplifier.

In Fig. 9 a photograph of some parts of the klystron is given, and in Fig. 10—the general appearance of the generator.

Generators built in this way at Stanford University gave very good results in tests. As has already been indicated, with the aid of the klystron it proved possible to obtain powers from 300–500 W to 1 kW, at wavelengths from 10 cm to 40 cm with an efficiency of 30–40%.

Fig. 9

A somewhat different construction, as compared with the klystron, is represented by Geff’s amplifier. The author set himself the task of constructing an amplifier for ultrahigh frequencies which would be free from certain shortcomings of ordinary amplifiers, manifested especially sharply at high frequencies. The task consisted in eliminating the effect of the finite transit time of the electrons, eliminating too strong a coupling between the output and the input of the amplifier, and, finally, reducing losses in the oscillatory circuit. In the amplifier constructed by him, essentially all this is achieved.

In Geff’s device an oscillatory circuit is used in the form of a hollow, almost closed system having the shape of a short coaxial line (Fig. 11), the so-called “tank circuit.” To excite it, in exactly the same way an electron beam is used, directed along the inner tube. This beam is modulated in its density. The mechanism of excitation is exactly the same as in the klystron.

Fig. 10

The field during even slight oscillations in the circuit will have the form shown in Fig. 11. We see that almost throughout the entire cavity of the resonator the field is directed radially, while in the aperture \(ab\) there is also an axial component of the field, penetrating to a small extent also into the inner tube.

When charges move along the inner tube, the field will do no work until the charges reach the aperture \(ab\). If the charges pass through the aperture \(ab\) at the moment when the electric field is directed from \(a\) to \(b\), they will be retarded, i.e. their energy will be given to the circuit; conversely, charges which pass through

the aperture during the opposite half-period, when the field has the reverse direction, will be accelerated, absorbing energy from the circuit.

Thus, the oscillatory system will be excited when there passes along the inner tube an electron stream consisting of separate groups of electrons, which must fly past the aperture with the proper frequency and in such a phase that the electrons always enter the retarding field. The conditions for this can always be created by suitably choosing either the dimensions of the circuit or the modulation frequency of the electron beam.

Fig. 11 shows the schematic arrangement of the entire device. An interesting feature of this design is that the oscillatory circuit is located entirely on the outside of the glass tube. This makes it possible to move it to a suitable place, or else to remove it altogether for replacement by another.

Two cylindrical electrodes \(A\) and \(B\) serve to accelerate the electrons. To obtain a very sharp electron beam, a focusing magnetic field is used (solenoid \(C\)); electrode \(K\) serves as the collector and, finally, to obtain the electron bunches and rarefactions needed to excite the circuit, the usual combination of grid and cathode \(GF\) is introduced. If a high-frequency voltage is applied between the grid and the cathode, the electron beam will vary periodically in its intensity. The separate groups of electrons, then passing through the aperture \(ab\), will excite the circuit, as indicated above.

As we see, nothing is said here about phase focusing of the electrons; it is assumed that the electron beam will be sufficiently density-modulated immediately after leaving the grid. As is known, at very high frequencies, owing to the inertia of the electrons, such direct density modulation ...

of the electron beam becomes almost impossible. Nevertheless, in spite of this, when operating at not very high frequencies the Heff amplifier, even in such a not yet fully perfected form, showed good results. Thus, for example, at a frequency of 450 MHz ($\lambda \simeq 60\ \text{cm}$) and with a control power of about 10 W, an output power of 110 W could be obtained. The overall efficiency was approximately $35\%$. In this case the accelerating voltage was about 6000 V, and the voltage on the catching electrode about 2000 V.

Exactly the same principle of operation also underlies the velocity-modulating tubes of Hahn and Metcalf. There are only minor modifications.

The device that modulates the velocity of electrons moving in a homogeneous beam is nothing other than a shortened phase lens. The electron beam passes through two pairs of grids (Fig. 13,a). The control alternating voltage is applied between the grids connected in pairs, as shown in the figure. If at a given instant there is a positive potential on the upper terminal, and a negative potential on the lower one, then the first pair of grids, $AB$, acts on the electrons in an accelerating manner, and the second pair, $CD$, in a retarding manner. Between the inner grids $B$ and $C$ there is no field, since they are connected to each other. If the transit time of the electrons between grids $B$ and $C$ is equal to an odd number of half-periods of the alternating control voltage, then the actions of the grids $AB$ and $CD$ on the beam are added. In this case the change in the velocity of the electrons upon leaving grid $D$ will be twice as large as it was after the action of the first pair of grids $AB$. To obtain the greatest modulation of the electron velocities, one must always strive for such a superposition of the actions of the first and second pairs of grids.

Fig. 13

The electron beam with electron velocities modulated in this way is then subjected to sorting. The authors propose three methods for this.

1. Simple separation of slow electrons from fast ones by deflection in a magnetic or electric field. In this case a portion of the electrons may be extracted from the beam, so that separate groups of electrons having more or less identical velocities remain. This method is not rational, since it does not make use of the entire electron stream.

2. The “drift” method, which, as it turns out, is no different from focusing electrons according to Brüche–Rechnagel. After leaving the grids, the electrons are allowed to move freely, to “drift,” until they arrive at the phase focus. In this way it is achieved that a beam modulated in velocity becomes modulated in its density.

1. The third, most interesting method consists in making the velocity-modulated electrons move in a retarding field. In this case the slowest electrons, after flying some distance, will turn back, while the faster ones may reach the retarding electrode and will be absorbed by it. Thus sorting occurs, analogous to that considered in the first case. But it is possible to create such a retarding field that no electron at all will be able to reach the retarding electrode; then “reflection” will occur of electrons not yet focused, and focusing will take place during their return motion somewhere not far from the modulating grids.

The electron beam density-modulated in one way or another is then directed into the same two pairs of grids connected to an oscillatory circuit, and excites oscillations in exactly the same manner as has already been described in the case of the klystron and the Geff amplifier. The difference here consists only in the fact that the electron bunch can give up its energy to the circuit twice: once in the first pair of grids, and then in the second.

In the case where the control voltage is applied to the first group of grids from some external signal source, the whole arrangement will operate as an amplifier. If, however, the control voltage is applied to the first group of grids by means of feedback from the second, i.e., excited group of grids, the installation will operate as a generator. A regenerative receiver can be made in the same way. In this respect we encounter nothing new here in comparison with the klystron.

However, an entirely different picture will be observed if we make use of phase focusing of the electrons, occurring after their reflection in the retarding field. Obviously, conditions can be chosen such that the focused electron bunches will again fall into the same group of grids which produced the velocity modulation, and excite oscillations in it. In this case there is no need to make two groups of grids and to establish feedback between them.

Such a generator with a retarding field is more compact and simpler; at the same time it is of interest in that it somewhat resembles the Barkhausen circuit with a retarding field.

Hahn and Metcalf constructed velocity-modulating tubes of several types, intended for various purposes. In almost all tube designs the group of four grids ABCD has the form of two diaphragms, between which a cylinder is placed (Fig. 13, b), i.e., the electrode construction proposed by Arsen’eva and Heil is used.

Figure 14 gives the circuits of similar tubes. Those among them which operate as generators of ultra-high-frequency oscillations, as a rule, have only one group of grids and operate according to the principle just considered, of reflection of electrons in a retarding field. Fig. 14, a represents the circuit of a generator for waves from 10 to 14 cm.

Electron-Beam Generators

Tubes intended for amplification have two groups of grids. One such tube is shown in Fig. 14, b. At a frequency of 300 MHz this tube delivered an output power of about 50 W, with an efficiency of 20–30%.

Finally, the tube shown in Fig. 14, c, is intended for heterodyne reception and, accordingly, has two groups of grids: one for receiving signals and the other for superposing the auxiliary frequency from the local oscillator.

Labels in Fig. 14: “−30 V”; “+350 V”; “+500 V”; “output”; “+4 V”; “25 mm”; “anode”; “output +10, +30 V”; “screen to diaphragm +300 V”; “amplifier electrodes”; “input +10, +30 V”; “grid II”; “400 V”; “grid I”.

Fig. 14

Some data concerning the dimensions of the tubes and the voltages used are indicated in the figures.

Conclusion

The types of generators and amplifiers considered, operating on the electron-beam principle, are still the first and far from perfected designs. Nevertheless, the results they give sharply advance them to first place in comparison

with all other known methods of generation and amplification of ultrahigh-frequency oscillations.

Summarizing all the theoretical and experimental work carried out in the search for new methods of generating ultrahigh-frequency oscillations, one may arrive at the following conclusions.

The ordinary three-electrode tube, which is a very perfect device at comparatively low frequencies, becomes inapplicable at ultrahigh frequencies, chiefly because under these conditions the method of controlling the electron stream by means of the usual cathode—grid combination proves unsuitable. This combination works well when it is possible to modulate directly the density of the electron stream in the tube, and this is possible only at low frequencies.

At very high frequencies, owing to the inertia of the electrons, which moreover, in order to reduce the transit time, are used at very high velocities, the grid cannot directly affect the density of the electron stream. Consequently, under these conditions, in a tube of ordinary construction, where the anode is located near the grid and the cathode, the controlling action of the grid cannot exert the influence on the anode current required for generation. But this does not mean that in the present case the actions of the grid remain entirely without result. However great the velocity of the electrons may be, and however small and brief the action of the grid may be, it nevertheless manages at least slightly to alter the velocities of the electrons, and this is already sufficient for the necessary changes in the density of the electron stream to occur during their subsequent motion over a certain distance.

Thus, even at high frequency, modulation of the density of the electron stream can be produced, but only not directly, rather through modulation of the velocities of the electrons; and the change in density occurs not immediately after the action of the grid, but after some time.

It is clear that this method of controlling the electron stream is an entirely new one, distinct from the methods used at low frequencies; at ultrahigh frequencies this method of control is at present the only one that leads to the desired results.

The use of the new method of control—this is the chief feature by which the above-considered constructions of generators and some amplifiers are distinguished. Indeed, the generator-klystron is in essence the same circuit with feedback, only with a new method of controlling the electron stream.

What, then, are the possibilities contained in this method of control, and what can it promise for the further development of ultrahigh-frequency technology? One may say with confidence that in the region of waves from 10 to 40 cm, reliable and powerful sources of oscillations will undoubtedly soon appear; as for the possibilities of advancing toward shorter waves, here too, for the time being, there is no

no major obstacles are foreseen, since the difficulties that occurred in the ordinary tube have here been almost completely overcome.

For example, such a phenomenon as the violation of the phase coincidence of the control voltage and the anode current, owing to the finite transit time of the electrons, is completely eliminated. Although here the result of control does not appear immediately, but only after some time, this time can nevertheless always be made equal to an integral number of periods, whereby the phase relation can always be preserved.

It is true that the finite transit time of the electrons may be manifested in the fact that the electrons nevertheless need some time to pass through the controlling (phase lens) and excited (resonator) fields. However, this effect can be reduced by using very short electron paths in these fields and by employing beams of high velocity. Increasing the electron velocity will not substantially affect the effectiveness of control, since focusing of the electrons will still occur, but only at a greater distance.

These, in the main, are the merits of the new method of control. If to this is added such an advantage as the ease of its use with the new method of full resonators, then one cannot but agree with the assertion of some authors^(7,10) that the discovery of the principle of velocity control and the creation of new types of generators is of the same significance for ultrahigh-frequency engineering as the invention of the three-electrode tube and grid control by Lee de Forest in 1906 was in its time for the subsequent development of radio engineering.

Further development of the new method will evidently proceed along the path of creating new, ever more perfect designs of both generators and amplifiers. At the same time, a more or less complete mathematical theory will also be needed, which must make it possible not only to perform technical calculations of generators of the new type, but also to elucidate, as deeply as possible, all those processes that take place there.

In clarifying many questions connected with the character of the oscillations arising in one or another electrical circuit, mechanical analogies are often useful, and these can frequently be chosen in a corresponding way. It is interesting that for the phenomenon of phase focusing there is also a mechanical analogy, which makes it possible even to construct a model of the simplest electron-beam generator, such as, for example, the generator with retarding field of Hahn and Metcalf.

For a visual representation of the motion of a charge in an electric field, in physics one often uses a mechanical analogy, representing the course of the field potential in the form of a certain relief, and the electron as a heavy ball rolling over the surface of this relief. Using the same method, the phenomenon of phase focusing can be represented on such a mechanical model (Fig. 15).

Between two planes \(B\) and \(C\), one of which is inclined to the horizon at a certain angle, there is a horizontal platform \(A\), capable of oscillating up and down while at the same time being connected with \(B\) and \(C\), for example by means of rubber bands \(R\). Balls, emerging uniformly one after another from \(K\), are accelerated when moving along the inclined plane and thus represent an analogy of an unmodulated electron stream. Then, running across the oscillating platform \(A\), they will change their velocities in exactly the same way as the electrons change them in the two pairs of grids in the Hahn–Metcalf tube. With further motion along the horizontal plane \(C\), the balls should group somewhere, forming bunches. Thus we obtain a picture of phase focusing.

If plane \(C\) is now inclined in the same way (position \(C'\)), then the angle of inclination can always be chosen so that bunches are formed, during the return motion of the balls, at the place where platform \(A\) is located (it is only necessary to direct the balls going back past the first ones, in order to avoid collisions). If a bunch runs onto the platform at the moment when it is in its maximum upper position, and runs off when it passes through the equilibrium position, then the energy of the bunch will be given to the oscillatory system and the system will build up its oscillations. Thus we obtain a model of a generator.

Fig. 15

It is quite possible that, using such a visual model, one could establish certain, even if only qualitative, features of the operation of generators of the new type. Nevertheless, the complete picture of the nature of self-excitation and of the establishment of stable amplitudes, the magnitudes of these amplitudes, etc., for generators of the new type can be given by a mathematical theory similar to that which has now been created for ordinary tube generators. At present one can point only to a small number of works devoted to the theoretical analysis of questions connected with the electron-beam method of generating oscillations; these are the works of Hahn\(^{17}\), Ramo\(^{18}\), Geiger\(^{19}\), and Webster\(^{20}\). They all concern, chiefly, only the question of the behavior of an electron beam in longitudinal high-frequency fields. In the first two works\(^{17,18}\), moreover, this question

is solved by a rather interesting method: namely, the electron beam is regarded as a certain medium in which it is possible to excite so-called “electron” waves, i.e., waves of space-charge density propagating with several different velocities along the beam. The superposition of these waves produces, at a certain point, a crest, i.e., the greatest space-charge density, which is quite analogous to Brillouin’s phenomenon of phase focusing.

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