INVESTIGATION OF A BETATRON ELECTRON GUN USING AN ELECTROLYTIC TANK

B. N. GULKO

(Presented by the scientific seminar of the Radio Engineering Faculty)

It is known that one of the important questions connected with improving the betatron is the question of developing methods for increasing the intensity of the electron beam. In this connection, much attention is being devoted to the focusing of electrons moving in the accelerating chamber, and to increasing the maximum input energy of the electrons, which leads to a lengthening of the working injection interval. At the same time, a partial increase in the intensity of the electron beam can also be achieved by improving old designs and creating new designs of electron guns that give a strictly parallel or only weakly divergent electron beam.

The betatron electron gun has so far remained a comparatively little-studied element of it. The existing design of the electron gun was first proposed by Kerst for his 20 MeV betatron [1]. In the 14 years that have passed since then, no substantial changes have been made in its design. Only in recent years have several papers [2,3] devoted to the study of such a gun been published in the foreign press. It should be noted that in the works cited no paths are indicated for constructive modification and improvement of its operation.

An electron gun for producing a ribbon electron beam, used in a betatron, is a three-electrode system and represents a cylindrical immersion objective. The design of the gun is rather simple. It is made in the form of a little box bent from tantalum sheet, serving as the anode. Inside is located a control electrode having a trough-like shape. In the latter is placed a filament wound from thin tungsten wire, which is also the cathode of the gun. In the anode, opposite the cathode, a narrow slit is cut through which the electrons leaving the gun emerge. On the rear side of the anode a thin tungsten plate is fastened, serving as a target. Such a gun gives a stream of electrons flying in one direction. Its construction is shown schematically in Fig. 1.

As is known [4], a three-electrode electron-optical system makes it possible to control the electron beam electrically, i.e., its focal distance is a function of the ratio of the grid potential to the anode potential, but often, for the sake of simplifying the circuit

injection, the control electrode (grid) and the cathode are connected together and the same potential is applied to them. Such a simplification leads to the loss of the possibility of focusing the electron beam by changing the potential of the control electrode. The three-electrode electron-optical system is thereby transformed into a two-electrode one. In such a two-electrode system the focusing of the beam can be changed only by changing the position of the cathode inside the control electrode. In practice, however, even this possibility cannot be used, since during assembly of the gun the cathode is fixed in some definite position. It is therefore important to know at what distance from the anode slit the cathode should be installed in order to obtain either a parallel or a weakly diverging flow of electrons.

The displacement of the cathode from this optimum position in either direction along the axis leads to electrons emerging from the anode slit as a diverging fan-shaped beam. The latter is undesirable, since a large number of electrons, not taking part in the acceleration process and contaminating the betatron chamber, enter the accelerating chamber.

The general laws of geometrical electron optics make it possible to determine approximately the focal length of such an electron gun if the potential distribution along its axis is known.

Fig. 1

In Fig. 2 the potential distribution in such a system is shown schematically. The immersion electron objective thus consists of a cylindrical immersion lens and a round cathode situated in the field of the lens.

A cylindrical immersion lens is formed in the gap between the control electrode and the slit diaphragm in the anode. According to the method of equivalent thin lenses, the immersion lens may be regarded as a system consisting of two thin lenses.

The field of the lens to the left of the mean plane \(MN\), i.e., in the region of the control electrode, has a converging action on the electron rays (a converging thin lens), whereas the field to the right of the mean plane, in the region of the anode diaphragm, disperses the electron rays (a diverging thin lens). The diverging action is always smaller than the converging action of the first lens, since the velocity of the electrons in the second field region is always greater.

To estimate the action of these parts of the field, let us estimate their optical powers. The optical power of the immersion objective is equal to the sum of the optical powers of the grid and anode diaphragms. To calculate the latter, one may use the expression for the optical power of a thin cylindrical lens [5]:

\[ \frac{1}{f} = \frac{1}{2\sqrt{\varphi_0}} \int_a^b \frac{1}{\sqrt{\varphi}}\, \frac{d^2\varphi}{dz^2}\cdot dz, \tag{1} \]

where \(\varphi_0\) is the potential to the right and to the left of the lens. This expression gives, for the optical power of the grid lens,

\[ \frac{1}{f_c}=\frac{1}{2\varphi_c}\int_a^b \frac{d}{dz}\left(\frac{d\varphi}{dz}\right)\,dz, \tag{2} \]

where \(\varphi_c\) is the potential on the axis in the plane of the grid diaphragm.

Fig. 2

Integrating (2), we obtain

\[ \frac{1}{f_c} = \frac{\left(\dfrac{d\varphi}{dz}\right)_2-\left(\dfrac{d\varphi}{dz}\right)_1}{2\varphi_c} = \frac{E_1-E_2}{2\varphi_c}, \tag{3} \]

where \(E_1\) and \(E_2\) are the field strengths to the left and to the right of the plane of the diaphragm.

Similarly, the optical power of the anode diaphragm is

\[ \frac{1}{f_a} = -\frac{\left(\dfrac{d\varphi}{dz}\right)_2}{2\varphi_a} = \frac{E_2}{2\varphi_a}, \tag{4} \]

where \(E_2\) is the field strength to the left of the anode diaphragm (it is always negative), \(\varphi_a\) is the potential on the axis in the plane of the anode diaphragm. The field strength to the right of the anode diaphragm is assumed equal to zero.

Adding the optical powers of the grid and anode diaphragms, we obtain the optical power of the immersion objective

\[ -\frac{1}{f} = \frac{1}{f_c}+\frac{1}{f_a} = \frac{E_1-E_2}{2\varphi_c} - \frac{E_2}{2\varphi_a}. \tag{5} \]

Hence we find an approximate formula for the focal length of the system

\[ f= \frac{2\varphi_c\varphi_a}{E_1\varphi_a-E_2(\varphi_c+\varphi_a)} . \tag{6} \]

Method of Investigation

The influence of the depth of immersion of the tungsten cathode inside the control electrode on the “focusing” of the electron beams was investigated with the aid of an electrolytic tank.

The electrolytic-tank method is described quite fully in the specialized literature [6] and makes it possible to obtain a picture of the field with high accuracy [7].

In the work a model of the electrodes was used, made of white tinplate and enlarged 100 times in comparison with the original. The electrolytic tank was made of textolite 0.5 cm thick; its dimensions were \(90 \times 77 \times 32\) cm. A probe made of platinum wire 0.2 mm thick was fastened to one arm of a pantograph. On its other arm there was a special holder into which a pencil was inserted, making it possible to make the necessary marks. Ordinary tap water was used as the electrolyte. A voltage with a frequency of 50 cps was applied to the electrodes by means of a laboratory autotransformer. The probe potential was varied by means of a potentiometer consisting of two resistance boxes of 10,000 ohms each.

The probe was immersed in the electrolyte to a depth of 0.5–1.0 mm. An EO-4 oscillograph was used as the zero-current indicator at the probe. The depth of immersion of the cathode was taken to be the distance from the front edge of the cathode (facing the anode) to the edge of the control electrode.

The electron trajectories were constructed by the method of radii of curvature [5].

Fig. 3

Results of the Investigation and Their Discussion

The potential distributions in the gap between the control electrode and the anode were investigated for three positions of the cathode inside the control electrode. The distribution of equipotential lines for immersion depths of 0.25 mm, 1.00 mm, and 1.75 mm is presented

in Figs. 3, 4, and 5. In the middle region of the field, the potentials of the equipotential lines differ by 5% from the potentials of neighboring lines.

Near the cathode and beyond the anode the field was measured with greater accuracy. A cathode immersion depth of 0.25 mm corresponds to the usual position of the cathode in the electron gun. As can be seen in Fig. 3, with this position of the cathode the electron gun gives a strongly diverging electron beam. Comparison of the figures shows that, as the depth of immersion of the cathode inside the control electrode is increased, the width of the electron beam decreases owing to a more intense deflection of the electrons toward the axis of the system.

Fig. 4

Fig. 5

At a certain immersion depth the effect of “refocusing” of the electrons becomes noticeable, when the electron rays, crossing the axis of the system, again form a diverging beam.

The electrostatic-field patterns found make it possible to establish certain limits for the depth of immersion of the cathode, at which one may expect the electron beam emerging from the gun to have minimum dimensions. Figs. 3, 4, and 5 show electron trajectories for electrons leaving the cathode at various angles \(\Theta\).

We assume, in a first approximation, that electrons which leave the last equipotential extending beyond the anode then move rectilinearly. For several electron trajectories with an angle of emission from the cathode of 5° or less, the electron beam at the anode has the smallest cross section.

with values of \(\Theta\) from 5 to 30° the angles \(\varphi\), formed by the straight lines extended backward with the axis of the system, were measured. The values of these angles for four trajectories with the same \(\Theta\) at different immersion depths are given in Table 1.

Table 1

Values of the angles \(\varphi\) for different electron exit angles \(\Theta\) and different cathode immersion depths

Fig. 6

Figure 6 presents the graphical dependence of these angles, for different \(\Theta\), on the cathode immersion depth \(x\). If it is assumed that the angles \(\varphi\) for all trajectories must not exceed \(6^\circ\), then from the graph we find that, for an electron-beam divergence of \(12^\circ\), the cathode immersion depth should lie within the limits from \(1.2\) to \(1.3\) mm.

Here we have taken the minimum divergence of the electron beam, since the “refocusing” effect does not make it possible to obtain a beam with the same cross section along its length. The space charge, which we have not taken into account, should further increase the beam dimensions somewhat. Similar investigations of a betatron electron gun were undertaken by Allen [3] using a rubber membrane. He established that the minimum half-width of the electron spot occurs at a cathode immersion depth of \(0.71\) mm. These results also confirm the existence of a dependence between the dimensions of the electron beam and the cathode immersion depth.

The difference between Allen’s results and ours can be explained by the fact that, in his experiments, a gun of different dimensions was used.

On the basis of the results we have obtained, it may be recommended to increase the cathode immersion depth in the betatron electron gun and to take it equal to \(1.2\)—\(1.3\) mm, and not \(0.25\) mm, as is customary. Improvement in the operation of the betatron at the recommended immersion depth also confirms these conclusions.

REFERENCES

1. D. W. Kerst. A 20 Million Electron-Volt Betatron or Induction Accelerator, Rev. Sci. Instr., vol. 14, 1942.

2. M. M. Zipsicas. The Electrostatic Field of an Electron Gun for a 20 Mev Betatron, Metropolitan Vickers Research Report No. 10522, 1953.

3. Use K. P. Allen.of Rubber Sheet Model for Investigation of Electron Trajectories, Electron Engineering vol. 27, 1955.

4. E. Weinrib, V. Milyutin. Electron Optics, Gosenergoizdat, 1951.

5. A. Rusterholtz. Electron Optics, Foreign Literature Publishing House, 1952.

6. V. V. Lukoshkov. Electrolytic Method for Studying Electrostatic Fields. Izvestiya Elektroprom. Slabogo Toka No. 10, 1939.