INVESTIGATION OF THE PROPERTIES OF BETATRON INJECTORS

N. M. GOLOSHCHAPOV

(Presented by the scientific seminar of the Faculty of Physics and Technology)

The design, electron-optical, emission, and other properties of an injector to some extent determine the magnitude of the radiation output of a betatron. However, judging from the periodical literature, little attention has been paid to the question of investigating the properties of injectors and improving their design. The literature \[1, 2, 3\] mentions new injectors, but, as far as we know, these injectors apparently have not found wide application and development, since in most cases the ordinary Kerst-type injector is still used. And there is almost no information at all on investigations of the properties of injectors.

In investigating the properties of injectors and improving their geometry, it is necessary to proceed from the requirements imposed on them:

1. The service life of the injector cathode must in any case be no less than the service life of the conducting layer of the chamber and of the chamber itself. This is especially important for the sealed betatron chamber. At present, in most cases, the durability of the cathode is very low.

2. The beam of electrons from the injector must emerge parallel, or nearly parallel, since the amplitude of oscillations will be smallest for those electrons that are injected tangentially to the orbit of the injector, and the conditions for capture into acceleration of these electrons will be the best in comparison with other electrons emitted at an angle to this tangent.

3. The injector must be simple in design and accessible for manufacture and repair under the conditions of any laboratory.

4. The injector must provide sufficient emission and have high electrical strength.

We used the method of comparison, i.e., different variants of injectors were investigated under identical conditions, since calculations based on the optics of a single electron do not yield positive results. The investigation was carried out in an electrolytic bath of the usual type, on an experimental setup that made it possible to observe the motion of the beam on the first turn in the betatron and on an electron-optical bench.

For the Kerst-type injector used in all betatrons of the faculty laboratories, the electric field recorded in an electrolytic bath is shown in Fig. 1. The angle of divergence of the electron trajectories is found to be \(\varphi \simeq 40 \div 45^\circ\). The resultant action of such an optical system is sharp defocusing of the beam.

The part of the cathode surface participating in the formation of the beam from the injector turns out to be very small (angle \(\gamma \simeq 20^\circ\)). Such injectors

because, owing to their poor optics and the small useful surface of the cathode, they operate in an overload regime and therefore are short-lived.

After testing several variants of other injectors, we settled on a long-focus injector used in electron microscopes [4]. Such an injector was manufactured and its electric field was investigated (Fig. 1). It is seen from the figure that the angle of divergence of the trajectories here is \(\varphi \approx 15 \div 20^\circ\), the beam is focused considerably better, and the useful surface of the cathode is approximately 8–9 times larger than in the old injector. Thus, in order to create the required initial charge density of the beam, this injector can operate under considerably easier filament-heating conditions than the old one, i.e., its lifetime can be increased.

Fig. 1. Electric field and electron trajectories for betatron injectors. Top—Kerst injector. Bottom—the selected injector.

Since the electrolytic bath does not give us an idea of the shape of the beam emerging from the injector, we investigated the injectors on an experimental setup for observing the first turn. The scheme of this setup is given in Fig. 2. A magnetic field similar to the guiding field of a \(15\ \mathrm{MeV}\) betatron is produced by magnetizing coils and continuous profiled pole cores. The curves of the potential function (for the plane \(z = 0\) and \(R_0 = 12.75\ \mathrm{cm}\)) and \(n\) are shown in Fig. 4. The well-known method of constructing the potential function [5] was used. We see,

that the focusing properties of the magnetic field of the installation are even better than in operating betatrons. In addition to the injector and pumping ports, the chamber has six more ports (Fig. 3), into which a current receiver is placed in turn, in the form of a system of Faraday cylinders over the entire cross-section of the chamber. In front of the Faraday cylinders there is a brass screen with holes opposite the brass cylinders, which are fastened in a Plexiglas plate.

By measuring the current from each cylinder, we can thus determine the distribution of the beam current density over the cross-section of the chamber. This method of investigation brings us considerably closer to the actual conditions that occur in a betatron, and the beam shape is obtained as it is on the first turn.

Fig. 2. Schematic of the electromagnet of the experimental installation for observing the electron beam on the first turn. I — profiled pole cores, II — magnetizing coils, III — current receiver.

During one turn, for example the first, the magnetic field may practically be regarded as constant, and the electron velocity likewise as constant (for a 15 MeV betatron with \(U_i = 30 \div 40\) kV, the energy acquired by the electrons during the first turn amounts to about 0.0005 of the initial energy). Therefore we feed the electromagnet of the installation with direct current, and apply a constant voltage to the injector. This considerably facilitates measurement of the distribution of the beam density over the cross-section.

The results of the current measurements, recalculated as current density, are shown in Fig. 5 (\(U_i = 2000\) V, \(U_k = 2.84\) V). The change in current density over its cross-section, projected onto the axis of the chamber cross-section¹, is given. The cathodes of the injectors are identical.

It turned out that the total beam current for the new injector is 3.5–4 times greater than for the old injector¹. It is not difficult to see that, for the old injector, it generally makes no sense to speak of a beam. Rather, it is an electron cloud in the volume of the chamber, whereas the new injector gives a clearly defined beam that exists throughout the entire first revolution (up to tube 7). True, its current density decreases considerably toward the end of the revolution, but the beam is preserved.

Fig. 3. Chamber used in the experiment. 1–7—tubes, 8—injector, 9—current collector.

Finally, we observed the divergence of the electron beam from the injectors under study on an electron-optical bench: the beam falls on a fluorescent screen, and from the dimensions of the luminous spot at different distances from the injector one can determine the angle of beam divergence. The results (Fig. 6) also proved to be in favor of the selected injector. In these experiments the beam divergence angle is greater by 30–35% than the angle obtained in the electrolytic bath. Clearly, such a difference is due primarily to the electrostatic interaction of the electrons in the beam, while the magnitude of this difference remains approximately the same for other variants of the injector geometry as well.

In studying the effect of the potential of the focusing electrode on beam divergence, it turned out that when a negative potential relative to the cathode is applied to the focusing electrode, up to 1% of \(U_i\), the beam divergence angle decreases by approximately a factor of two. The total emission current also decreases somewhat. With a further increase of the negative potential on the focusing electrode, the injector is almost completely cut off. When a positive potential is applied to the focusing

electrode, the beam divergence angle increases and the total emission current from the cathode increases significantly.

The use of pulsed power for the injector does not lead to substantial changes in the beam divergence, except that the boundaries of the luminous spot become blurred and indistinct, and the shape of the spot (i.e., the beam cross section) changes somewhat. These phenomena are evidently caused by the presence in the beam of electrons with different velocities.

Fig. 4. Characteristics of the control magnetic field of the electromagnet of the experimental setup.

Top—curves of the potential function \(V_m\) and \(n\) for \(z=0\); bottom—equipotential curves of the potential function over the chamber cross section.

Finally, the following was found in the experiments. For a Kersht-type injector, the greatest electron current from the cathode to the anode is from the cathode to the edge of the anode aperture. Owing to electron bombardment of the anode, a reverse ion current arises here [6], which very strongly reduces the electric strength of this gap. Breakdown in most cases occurs first precisely here. It is impossible to avoid this ion current in the design of the Kersht injector. In the selected injector such an ion current takes place from the cathode into the ver—

vertical direction, i.e., along the cathode axis upward and downward. At the edge of the anode aperture there is no current, which is due to the shape of the focusing electrode. In this case the ion current can be eliminated by installing shutters or by making the focusing electrode in the form of a special box. An injector with such a box-type focusing electrode was tested by us and gave good results. It may also be noted that ion currents lead not only to a decrease in the electric strength, but also to rapid destruction of the cathode because of its bombardment by ions.

Fig. 5. Change in the beam-current density over the beam cross section. a — beams from a Kerst-type injector, b — beams from an injector of the new design, dashed line — current receiver in the third tube, solid line — current receiver in the fifth tube.

From electron optics it is known that the equations of motion of an electron moving under the action of an axially symmetric field \(E\) have the form [4]

\[ \ddot z = -\frac{e}{m}\frac{\partial V}{\partial z}, \]

\[ \ddot r = -\frac{e}{m}\frac{\partial V}{\partial r}. \]

And the ray equation is written [7]

\[ \frac{d^{2}r}{dz^{2}}+\frac{V'_o(z)}{2V_o(z)}\frac{dr}{dz}+\frac{V''_o(z)}{4V_o(z)}\,r=0. \]

These are the basic equations of electron optics, which make it possible to determine the cardinal points and planes of an electric lens and the trajectories of electrons in it.

To find the solution of these equations, one must know the dependence of the electric potential \(V\) on the coordinates.

Fig. 6. Dependence of the beam divergence angle on the injector filament current (at \(U_i=\mathrm{const}\)) and the injection voltage (at \(I_n=\mathrm{const}\))

It turns out that, both in the case where space charge is taken into account and in the case where it is neglected, in order to find the solution of these equations one must know the distribution of the potential along the axis of symmetry as a function of the coordinate \(z\) (along this axis of symmetry), i.e. \(V_o(z)\), and the even derivatives of it.

In our case the potential distribution along the \(z\)-axis in the cathode–anode region (Fig. 7) was found in the form of the following expressions:

\[ V_o(z)=100\sin\frac{\pi z}{240}\quad \text{— for the Kerst-type injector,} \]

\[ V_o(z)=50\left(1-\cos\frac{\pi z}{364}\right)\quad \text{— for the selected injector.} \]

On the basis of an analysis of the electric fields in the cathode–anode gap for injectors of different geometry (the potential of the focusing electrode is equal to the cathode potential), it may be said that if, for \(V_o(z)\), the second der-

greater than zero, then there will be a focusing region here. If for \(V_0(z)\) the second derivative is less than zero, then this is a defocusing region. The position of the inflection point of the curve \(V_0(z)\) (the point of maximum of the first derivative) determines the degree of focusing of the entire electron-optical system. If there is no inflection point, then the system will be either focusing or defocusing (according to the rule stated above).

Fig. 7. Potential distribution in the injector:
1 — for the Kerst type, 2 — for the selected injector.

It may be assumed that for each definite cathode–anode distance there must exist an optimal potential distribution giving the smallest beam divergence angle. Such an optimal potential distribution can be obtained by an appropriate shape of the focusing electrode and by the shape and dimensions of the anode aperture.

The results of the work carried out, of course, cannot serve as final initial data in the design and calculation of injectors, and the injector selected by us apparently still cannot be called sufficiently perfect. In addition, we did not investigate the emission properties of various cathodes, the electric strength under different conditions, etc.

However, on the basis of the work carried out, the following preliminary conclusions may be drawn.

1. The shape and potential of the focusing electrode determine the shape of the beam from the injector; therefore it is advisable to make the focusing electrode in the manner indicated in Fig. 1 and to apply to it a small negative potential relative to the cathode.

2. The beam emerging from an injector with a cathode in the form of a spiral, generally speaking, has a nonuniform distribution of charge density from the electrons emerging from the inner surface of the spiral and from the side surfaces of the turns. A spiral cathode also gives a large beam divergence.

in the vertical direction and is easily deformed during operation. Therefore one may propose, for example, an oxidized indirectly heated cathode in the form of a cylinder or half-cylinder, which is possible for a sealed-off chamber, or an ordinary heated one; in this case it is better to carry out the heating by pulses, since a large heater current will be required.

To increase the electric strength of the injector it is necessary, in addition to choosing the required interelectrode distances and carefully treating the electrode surfaces, also to eliminate ionic currents between the anode and the cathode. This requirement is very important for increasing the electric strength of the injector.

1. In order to make the calculation or selection of the injector geometry possible, correct, and theoretically justified, it is first necessary to solve the problem of determining the dependence of the beam-divergence angle on the distribution of the potential along the cathode–anode axis of symmetry and on the position of the inflection point of the curve of distribution of this potential. For this, of course, additional experimental data will be required.

We also consider it advisable, in the investigation of betatron injectors, to use the method, first proposed and applied by us, of studying the beam from the injector in a magnetic field of the betatron type.

In studying the motion of the beam on the first revolution in a magnetic field of the betatron type under various conditions, we also found the following facts.

The shape and trajectories of the beam are very critical with respect to the initial charge density of the beam, \(\rho_{\text{init}}\). It turned out that if

\[ \rho_{\text{init}} \simeq (0.5 \div 1.0)\rho_{\text{eq}}, \]

then the beam is well focused and its charge density decreases more slowly during the revolution.

Here

\[ \rho_{\text{eq}} \]

is the density of the equilibrium beam¹.

It was observed that at large initial charge densities, of the order

\[ \rho_{\text{init}} \simeq (5 \div 10)\rho_{\text{eq}}, \]

the beam is strongly scattered and in fact does not even complete the first revolution; moreover, the beam is scattered onto the outer wall of the chamber.

LITERATURE

1. W. F. Westendorf, F. R. Elder—Phys. Rev. 76, 445, 1949.
2. б/а—Nucleonics—6, 72, 1950.
3. K. Gund—Stahl und Eisen—Jg. 73, 706, 1953.
4. Electron Microscopy, edited by A. A. Lebedev. State Publishing House of Technical-Theoretical Literature, Moscow, 1954.
5. Noskov L. A. Candidate dissertation. Tomsk Polytechnic Institute, 1954.
6. Vorob'ev A. A. Superhigh Electric Voltages. GEI, Moscow, 1955.
7. Kaptsov N. A. Electronics. State Publishing House of Technical-Theoretical Literature, Moscow, 1954.

1. The concept and method of determining the “equilibrium beam” are given in the article by Rodimov B. N., Izvestiya TPI, vol. 87, 1957. ↩↩↩