Hydraulic Model of Klystron-Type Electron-Beam Devices

E. M. Studenkov

This article gives a brief description of a hydraulic model of electron-beam devices operating on the principle of velocity modulation of an electron beam (of the klystron type), developed by the author and tested experimentally.

Fig. 1.

The model gives a visual representation of the principles of operation of these devices and can be successfully used in lecture demonstrations, and can also provide some practical data for the design of electron-beam devices.

1. Construction of the model. In the model, the role of the electron beam is played by a jet of liquid (see Fig. 1) flowing out of tube \(T\) at a definite velocity under the pressure of liquid contained in reservoir \(K\) at a certain height.

Before leaving the tube, the liquid passes through the velocity modulator \(M\), which is a small hollow cylinder (Fig. 1, top), one base of which is connected to the outlet tube \(T\), while the opposite—

...is made in the form of a flexible rubber membrane, through which, by means of the disk \(D\) and the lever \(R\), an additional variable pressure can be transmitted to the liquid, changing the velocity of the jet.

A rapid decrease or increase in the volume of the modulator, under the action of an external variable force acting on the lever \(R\), causes, respectively, an increase or decrease in the velocity of the liquid particles flowing out of the tube \(T\). Under the presence of the simplest case of a harmonic force acting on the lever \(R\), the jet will take the form shown for a definite instant of time in the same Fig. 1, where the fastest parts of the jet move along the upper parabola \(P_1\), the parts that have undergone no change in velocity along the middle parabola \(P_0\), and the slowest parts along the lower parabola \(P_2\). As is seen from the figure, the modulated jet, in the course of its motion, is deformed and at some distance from the outlet, ruptures occur in some places, while in others there are accumulations or coalescences of liquid, i.e. the phenomenon of phase focusing sets in, analogous to the same phenomenon in electron-beam devices. Here there is a slight difference caused by the presence of the force of gravity constantly acting on the jet. The latter, however, has no essential influence on the operation of the model.

The place \(F\), in which the parts of the deformed jet are arranged approximately in the vertical direction, may be regarded as the phase focus of the modulated jet. The distance \(MF\), as is known, depends on the frequency and amplitude of the modulating force, as well as on the initial velocity of the jet.

2. Model of an oscillation amplifier. The modulated jet passes through the phase focus \(F\) in the form of individual successive slugs, whose kinetic energy can be used to excite oscillations more powerful than the oscillations required to modulate the velocity of the jet.

In the amplifier model, for modulating the velocity of the jet, oscillations of a somewhat weighted armature of an electric buzzer, rigidly connected with the modulator lever \(R\), were used. The armature oscillated with a frequency of about \(20\)—\(25\) Hz.

At the phase focus of the jet there was placed a vibrator (Fig. 2, \(a\)), consisting of a small elastic plate, one end of which was fixed to a stand, while at the other end there was a weight \(G\) and a light metal disk \(S\), which received the impacts of the successively falling slugs of the modulated jet.

The length of the vibrating part of the spring could be regulated by means of the screw and the movable sleeve \(E\), which moved along the spring. This made it possible to “tune” the vibrator to the frequency of the primary oscillations arriving at the modulator from the electric interrupter.

When the oscillation frequencies of the modulator and vibrator coincided, and with a suitable choice of the distance between them, the vibrator began to oscillate intensely. The amplitude of the oscillations increased when the liquid head was increased; at the same time it was necessary to increase the distance \(MF\).

With slight detuning, beats occurred in the oscillations of the vibrator, while with complete mismatch of the frequency of the primary oscillations and the oscillations of the vibrator, the latter almost did not oscillate at all.

3. Model of an auto-oscillation generator. The generator model was obtained by establishing feedback between the vibrator and the modulator. For this purpose the vibrator was made in the form of a small pendulum with a weight and the same kind of flat disk at the end for receiving the action of the jet, as in the preceding case (Fig. 2, \(b\)). By changing the length of the spring \(N\) and the position of the weight, it was possible to change the oscillation frequency of the vibrator. To the axis of the pendulum was attached a small lever \(r\), from which a thin wire went to the lever of the modulator \(R\) (feedback). The lever \(r\) could be rotated about the screw \(z\) securing it, owing to which it was possible to change

its arm and, consequently, to vary the magnitude of the feedback from a certain maximum down to zero, or even to change the phase of the action of the feedback to the opposite one, by turning the lever \(r\) through \(180^\circ\).

The operation of the model was tested as follows: the load of the vibrator pendulum was set to a certain definite frequency, which was measured by means of an oscillation counter, the description of which is not given here. The vibrator was then placed at a certain distance from the origin of the jet, feedback was established by tensioning the connecting wire, the jet was started, and, by moving the reservoir with the liquid in height, its optimum position was selected, i.e. that jet velocity at which

Fig. 2.

self-excitation of the generator occurred most easily and the oscillations took place with maximum intensity.

Below are several numerical data for the optimum oscillation conditions obtained in the experiment:

In the model, it would undoubtedly have been possible to verify and confirm quantitatively many theoretical propositions relating to electron-beam amplifiers and generators. Various modifications of the model could also have been tested, such as: a model of an anti-transit-time generator with two modulators and two liquid jets directed toward one another, a model of a generator with a retarding field (a jet directed vertically upward), etc.; however, the working conditions did not allow the author to carry out experiments with the described model in full.