EXTRACTION OF ELECTRONS FROM A BETATRON BY AN ELECTROSTATIC METHOD

Part II

SELECTION OF THE TYPE OF VOLTAGE ON THE PLATES OF THE DEFLECTING CAPACITOR

B. A. Kononov

(Presented by Professor, Doctor A. A. Vorob’ev)

At the end of the accelerating cycle there must be a voltage on the deflecting capacitor that ensures the extraction of electrons from the betatron chamber. In the literature there is no information as to what voltage—direct, alternating, or pulsed—is applied to the plates of the deflecting capacitor. It is more convenient to use a direct voltage, in view of two important advantages over a pulsed one. First, the simplicity of obtaining a constant high voltage of the order of 30–50 kV in comparison with a pulsed voltage, and the convenience in operation, since at whatever moment the electrons are dumped onto the capacitor (in the case where the electron energy is set by changing the phase of expansion of the electron orbit), the required voltage is always present on it. With pulsed feeding of the deflecting capacitor, it is necessary to adjust the phase of the voltage on the plates to the phase of the electron dump. Second, pulsed feeding of the capacitor will require synchronization of the voltage pulse on the plates and the pulse of electron dumping, which also complicates the electrical circuits of the betatron. However, feeding with a direct voltage has a substantial drawback, namely that at the moment of injection of electrons into the accelerating chamber there will be a strong electric fringe field of the capacitor, which must affect the motion of electrons with energy 20–30 keV, all the more since the injector and the capacitor are located at almost identical radii. \(R_{\text{inj}} = 157\text{–}159\ \text{mm}\), \(R_{\text{cond}} = 160\text{–}163\ \text{mm}\). It is therefore necessary to determine how strong the influence of the voltage on the capacitor is at the moment of injection.

Figure 1 presents the scheme of experiments for studying the influence of the electric field of the capacitor on the injection process. The accelerated electrons are dumped at the end of the cycle onto the capacitor and partly onto the injector; the X-ray radiation is monitored by a thimble ionization chamber installed at the maximum of the radiation lobe.

Figure 2 presents the dependence of the radiation intensity on the voltage on the deflecting capacitor (curve 1). The radiation decreases sharply with increasing voltage and disappears completely, although the working value of the voltage, \(\sim 30\ \text{kV}\), is still far away. The cause of the sharp decrease in radiation is the dumping of electrons emerging from the injector by the strong electric fringe field of the capacitor, located near the injector. Indeed, after some operating time, a blurred dark spot 40 mm in diameter appeared on the silver layer of the accelerating chamber, located behind the capacitor and caused by bombardment by unaccelerated electrons.

Increasing the emission current \(J_e\) of the injector (see the table and Fig. 2),

the magnitude of the radiation can be raised somewhat (Fig. 2, curve 2); evidently, despite the sweeping-out of electrons by the capacitor field, a larger number of electrons is captured into acceleration, since a larger number is also emitted. But this effect occurs only at low voltage. At voltages above 10 kV the radiation is barely noticeable and is of practically no interest.

The influence of the electric field of the capacitor on the radiation intensity is somewhat weaker when it is placed behind the injector. The dependence of the betatron X-radiation intensity on the voltage on the capacitor is shown in Fig. 3. The curves correspond to different positions of the capacitor along the radius: 1—the inner edge of the capacitor is located at \(R=162\) mm; 2—\(R=160\) mm; 3—\(R=158\) mm; 4—\(R=156\) mm. As the capacitor is moved toward the equilibrium orbit, the steepness of the decline of the curves increases, i.e., the capacitor field has a stronger effect on the injection process. At \(R=156\) mm the capacitor interferes with the emitted electrons not only by its electric field but also directly by its electrodes; the total radiation intensity begins to fall.

Fig. 1. Investigation of the effect of voltage on the capacitor on the injection process (experimental setup).

1—injector; 2—deflecting capacitor; 3—betatron electromagnet; 4—vacuum pump; 5—spot from the swept-out electrons;
\(IK\)—ionization chamber; \(\gamma\)—direction of the X-radiation; \(VN\)—high-voltage unit.

At a voltage on the capacitor of about 1.5 kV, a slight increase in the radiation intensity is observed. Evidently, the weak stray electric field of the capacitor improves the injection conditions, creating a certain focusing electric field and clearing the volume in the vacuum chamber of excess charged particles.

With a negative voltage on the deflecting capacitor this effect is not observed; the radiation rapidly falls to zero (Fig. 3, curve 5, \(R=162\) mm).

Thus, the presence of voltage on the deflecting capacitor at the moment of injection worsens the conditions for electron capture into acceleration. The radiation intensity of the accelerator decreases, and at the voltage needed for extracting electrons, \(U \approx 30\) kV, the radiation disappears. Consequently, supplying the deflecting capacitor with a constant voltage cannot be used for a betatron—

Fig. 2. Dependence of the radiation intensity \(J\) on the constant voltage on the capacitor.

...of an accelerator having the injector on the outer side of the equilibrium orbit. The possibility of operating the capacitor at a constant voltage with the injector located inside the circle of the equilibrium orbit was not investigated, owing to the absence of injectors of such a design.

The influence of the electric field of the capacitor on the injection process can be reduced by choosing the positions of the injector and the capacitor. From comparison of Figs. 2 and 3 it is seen that in the first case the electric field of the capacitor affects the injection process much more strongly than in the second, when the capacitor is located behind the injector. Consequently, the capacitor must be installed behind the injector. However, the distance between the injector and the capacitor must not be large. For example, they cannot be placed diametrically opposite, since then at the moment of injection two different obstacles must be bypassed, the capture of electrons into acceleration becomes worse, and the radiation intensity of the installation decreases.

A constant voltage on the deflecting capacitor interferes with the injection of electrons. It is necessary to remove the voltage from the capacitor at the moment when the electrons are admitted into acceleration, i.e., it is necessary to create pulsed feeding of the capacitor. The ideal form of the voltage pulse on the deflecting capacitor would be rectangular, and the pulse should be applied at the end of the acceleration cycle. Then at the moment of injection the voltage on the capacitor is zero, while at the moment of expansion of the electron orbit there will be a constant voltage on the capacitor. This pulse must be capable of shifting synchronously with the expansion pulse. The pulse amplitude must be adjustable; the maximum voltage should be of the order of 30–50 kV. The pulse duration is determined by the duration of the dumping of accelerated electrons onto the capacitor. In our experiments, when using a symmetrical expanding winding that increases the flux in the central core of the betatron electromagnet, the duration of the x-ray radiation pulse, equal to the time of dumping the electrons onto the target from which the radiation is recorded, is about 20 μsec.

Fig. 3. Effect of the voltage on a capacitor located behind the injector on the radiation intensity.

It is rather difficult to obtain a rectangular pulse with an amplitude of 50 kV and a duration of more than 20 μsec. Because of the absence of gas-discharge devices with the necessary characteristic at such a voltage, the pulse has to be transformed. In this case distortion of the rectangular pulse is inevitable—it becomes trapezoidal or even sinusoidal. The flat portion at the top of the pulse—the working portion—will decrease; consequently, it is necessary deliberately to increase the duration of the voltage pulse in comparison with the duration of the radiation pulse, which in turn will require high-current gas-discharge devices and a bulky pulse transformer.

To investigate the possibility of operating the deflecting capacitor at a pulsed voltage, a pulsed circuit was used (Fig. 4), in which the forming line is discharged through a pulse transformer. The valve is a thyratron of type TG 8/3000, the ignition of wh...

which is produced by a pulse transformer fed from a phase-shifting bridge, making it possible to vary the firing instant of the thyratron so as to obtain a voltage pulse on the capacitor at any moment of the accelerating cycle. The experimental arrangement for investigating the influence of a pulsed voltage on the injection process is similar to the analogous experiments with a constant voltage (Fig. 1).

If the voltage pulse is applied to the deflecting capacitor at a time far from the instant of electron injection, then, naturally, the conditions for capturing the electrons into acceleration are not disturbed. This remains true until the pulse is brought close to the injection pulse by 5–10° (250–500 μsec). With further convergence of the pulses, the intensity of the betatron X-radiation at first decreases slowly, then ever more rapidly, and disappears completely when they coincide. The character of the dependence of the radiation intensity on the magnitude of the voltage on the capacitor when the pulses coincide is similar to the dependence for a constant voltage. This fact once again confirms that the voltage on the capacitor precisely at the instant of injection disturbs the conditions for stable motion of the electrons in a circular orbit. If the voltage is applied to the capacitor after the electron beam has become focused on the equilibrium orbit and the electrons have acquired some velocity (500–1,000 keV), the stray electric field of the capacitor is not capable of disturbing the motion of the electrons.

Fig. 4. Schematic circuit of the pulsed voltage.

Thus, a pulsed voltage can be used to feed the deflecting capacitor. The possibility of extracting the electron beam from the accelerator chamber when feeding the deflecting capacitor with a pulsed voltage was investigated by us. The pulsed voltage was obtained from the circuit assembled according to Fig. 4. The accelerated electrons were dumped onto the wall of the vacuum chamber (the chamber had no tube for extracting the electron beam into the atmosphere). The dumping of electrons was very unstable because of poor synchronization of the displacement pulses and the voltage on the deflecting capacitor. In particular, the instability was caused by the imprecise triggering of the thyratrons in both circuits, which were fired by voltage pulses from two different pulse transformers whose cores were assembled from ordinary transformer steel. The leading edge of the firing pulses was not sufficiently steep, and this caused a spread in the firing time of the thyratrons. In order to make the firing of the tritrons precise, we abandoned the triggering pulse transformers. They were replaced by two locked multivibrators triggered from a single peaker with a per-

with a permalloy core, installed in the magnetic field of the accelerator [1]. This makes it possible to make the firing of the thyratrons more precise. By changing the pulse-delay time in each of the multivibrators, one can align the moment of triggering of the thyratrons or give either of the pulses a lead or lag with respect to the other. This is necessary because the discharge of electrons onto the deflecting capacitor begins not immediately after the thyratron in the bias circuit is triggered, but after 10–15 μsec, when the current in the expanding winding rises to a certain value.

The discharge of accelerated electrons by the capacitor onto the chamber wall was considerably improved, as could be observed from the glow of the chamber at the point where the electron beam fell (the inner surface of the chamber was dusted with ZnS powder, which glows under electron bombardment). The glow disappeared if the voltage pulse on the capacitor led in time the electron-bias pulse, or if the voltage amplitude decreased below the value at which the electrons were discharged. The discharge of the accelerated-electron beam is also observed from the strong X-ray radiation in the direction of the glowing spot. However, the “extraction” of electrons (the beam was not released into the atmosphere) could not be satisfactory for two reasons. First, the duration of the voltage pulse on the deflecting capacitor is less than the duration of the pulse of discharge of accelerated electrons onto the capacitor; consequently, there must inevitably be losses of electrons. Second, the ignitron fired very indistinctly, although the firing voltage was 800–1000 V. The beginning of the radiation pulse fluctuated with respect to the moment of firing of the thyratron in the bias circuit. The fluctuations reached 5–10 μsec. This also reduced the extraction of electrons, since the overlap time of the pulses was reduced. It was necessary to replace the ignitron with a powerful hydrogen thyratron or to increase considerably the duration of the voltage pulse on the capacitor. In the latter case the pulse transformer would be very bulky (for a pulse duration \(\tau = 50\) μsec, the weight of the iron alone of the transformer is more than 80 kg). The problem can be solved more simply by replacing the pulse voltage circuit, operating with gas-discharge devices, by one large peak transformer. In this case, at the moment of electron injection, the voltage on the deflecting capacitor is small (Fig. 5), but it will rapidly increase toward the end of electron acceleration. It is precisely such a voltage that we need for extracting the electrons. But feeding the deflecting capacitor from a peak transformer is considerably simpler than a pulse-power supply circuit. The peak transformer is fed from an alternating-current mains (Fig. 6). To regulate the phase of the voltage peak, a phase-shifting bridge is used, but this does not complicate the circuit much.

Fig. 5. Mutual arrangement of the injection pulse 1, the expanding pulse 2, the voltage from the peak transformer \(U\), and the magnetic flux of the betatron \(\Phi\).

The transformer, giving a pulse of up to 50 kV, was calculated as an ordinary low-voltage peak transformer; therefore experimental adjustment of the air gap \(\delta\) and of the thickness of the packet \(S_2\) was required in order to obtain the calculated voltage value and a satisfactory pulse shape. The principal dimensions of the transformer and its data are presented in Fig. 7. It should be noted that, if special measures are not taken, then in the secondary circuit of a peak transformer having a large interturn capacitance (\(W_2 = 60\,000\)) and loaded by cap—

of the deflecting capacitor, the voltage pulse causes an oscillatory process which dies out insufficiently rapidly. The oscillations persist until the next pulse and interfere with electron injection if the moment of injection coincides with the amplitude value of the harmonic. The decay of voltage oscillations in the circuit of the deflecting capacitor can be accelerated by introducing an active resistance into the oscillatory circuit. For damping the oscillations, the voltage divider (Fig. 6), also needed for voltage monitoring, may be used. The value of the divider resistance (5–15 MΩ) is selected

Fig. 6. Schematic diagram of the supply of the deflecting capacitor \(e\) from a peak transformer.

\(1\) — peak transformer; \(2\) — voltage divider.

Fig. 7. Peak transformer.
\(W_1 = 250,\ W_2 = 60\,000,\ S_1 = 40\ \text{cm}^2,\)
\(S_2 = 4\ \text{cm}^2,\ U_1 = 220\ \text{V},\ U_2 = 50\,000\ \text{V}.\)

from the condition of rapid damping of the oscillations, but with an allowable reduction of the voltage that occurs when the active load is connected into the peak-transformer circuit.

To tune the betatron for extraction of electrons of different energies, the voltage peak on the deflecting capacitor must be shifted in time. In our experiments this is achieved by feeding the peak transformer from a phase-shifting bridge (Fig. 6). A coarse stepwise shift of the peak within \(60^\circ\) is carried out by changing the capacitance; smooth adjustment within one step is by a rheostat [2]. With the aid of this supply circuit for the deflecting capacitor, extraction of electrons from the betatron at \(15\ \text{MeV}\) was achieved.

The author expresses gratitude to Professor A. A. Vorob'ev, under whose supervision the present work was carried out.

References

1. N. N. Krylov, Pulse Technique, Tekhteoretizdat, Moscow, 1950.
2. F. V. Mayorov, Electronic Regulators, Tekhteoretizdat, Moscow, 1956.