Experimental Study of the Mechanism of Formation of Nonstationary Current in a Betatron

O. V. Sokolov, B. L. Chastokolenko

(Submitted by the scientific seminar of the Research Institute of Electrical Engineering)

Introduction

During injection into the accelerating chamber of a betatron, a so-called nonstationary current is formed. The nonstationary current exists for a very short interval of time (0.1–1.0 μsec); however, in magnitude it may exceed by a factor of 10 or more the current captured into the acceleration regime [1–3]. In a fairly large number of experimental works [3–6], the magnitude of the nonstationary current and its dependence on the emission current were determined for various divergence angles of the electron beam upon leaving the injector; also determined were the average number of revolutions of the electrons forming the nonstationary current and the form of the signal from the nonstationary current obtained with the aid of some kind of detector. The question of the mechanism of formation of the nonstationary current has not been investigated, with the exception of work [7], in which the authors proceeded from a simplified picture of the motion of a narrow electron beam in the magnetic field of a betatron. Investigation of the mechanism of formation of the nonstationary current is of interest for the purpose of clarifying the possibility of its capture into the acceleration regime, and should also contribute to a deeper understanding of the process of electron capture into acceleration.

It follows from the theoretical work [8] that the most essential factor affecting the capture of electrons into acceleration is the resonance damping of the amplitudes of oscillations of circulating electrons as they pass through an inhomogeneity in the azimuthal distribution of the density of the space charge created by the electron beam emerging from the injector as a result of its divergence under the action of its own space charge. In studying the mechanism of formation of the nonstationary current, we proceeded from the fact that the electron beam emerging from the injector throughout the entire injection time must exert an influence on the motion of the circulating electrons. In this connection, we calculated the trajectories of electron motion during injection. In the calculation, the azimuthal variation of the radial focusing forces of the betatron magnetic field was taken into account, caused by the presence of the electron beam emerging from the injector and by its divergence under the action of its own space charge. Figure 1 gives calculated data on the character of the change in the amplitudes of radial oscillations of electrons ($\rho$) as a function of the number of revolutions of the electrons in the accelerating chamber for various angles of their departure from the injector (the signs “+” and “−” correspond to the departure of electrons toward the outer and inner walls of the accelerating chamber, respectively—

Fig. 1

…ingly). It is evident that, for electrons emitted from the injector in an interval of certain angles, the amplitude of the oscillations after several revolutions has a minimum value and then increases again; i.e., the formation of nonstationary current has a resonant character. This means that, under certain conditions, when the oscillation amplitudes of most electrons decrease, a compression in the radial direction of the entire beam of electrons forming the nonstationary current must occur. Such a phenomenon should occur during the formation of nonstationary current on the fronts of the injection pulse, when a single formation of nonstationary current takes place. During the formation of nonstationary current on the flat top of the injection pulse, compression of the electron beam in the radial direction should not be observed. In this case, repeated formation of nonstationary current will occur, since over a long interval of time the electron energy will correspond to the magnetic-field strength of the betatron, and the nonstationary current is formed by electrons having the entire set of oscillation amplitudes from the minimum to the maximum. It is interesting to note that the most effective capture of electrons into acceleration is observed on the fronts of the injection pulse, i.e., where a single formation of nonstationary current should occur.

An experimental investigation of the transverse dimensions of the circulating electron beam during injection should serve as one of the criteria for the correctness of the judgment concerning the mechanism of formation of nonstationary current.

Experimental results

The experimental investigation of the behavior of the nonstationary current in time was carried out on a 15 MeV betatron with the aid of electrostatic electrodes located in the accelerating chamber, as shown in Fig. 2, a. The electrodes were placed at an azimuth of 180° relative to the injector. The magnitude of the signal arising on each of the electrodes (2, 3) will depend primarily on the magnitude of the current circulating in the chamber, on the distance between the electrode and the center of the beam, and also on the size of the transverse cross section of the electron beam. In this case it was necessary to take into account the possibility of distortion of the signal, formed—

Fig. 2. 1 — accelerating chamber; 2—3 — electrostatic electrodes; \(r_0 = 130\) mm; \(\alpha = 80\) mm; \(\beta = 45\) mm.

Fig. 3

by a nonstationary current, as a result of electrons directly striking the electrostatic electrodes. Observation of the character of the signals from the electrodes at different emission currents from the injector, using screens installed in front of the measuring electrodes to prevent direct incidence on the latter of electrons from the injector [9], and also the insertion of electrodes into the chamber at various distances from the median plane, showed that distortions of the signal associated with direct incidence of electrons on them are very small and become noticeable only at large emission currents exceeding by a factor of 2–3 the optimum emission current corresponding to the radiation maximum. The complete identity of the signals taken from electrodes 2 and 3 (Fig. 2), arranged symmetrically with respect to the median plane of the accelerator, as is seen from oscillograms б and в (Fig. 3), indicates that during the existence of the nonstationary current there is no displacement of the beam center relative to the electrodes in the vertical direction.

Thus, in the geometry shown in Fig. 2, а, at constant circulating current the magnitude of the signal from the electrodes must depend on the transverse size of the electron beam forming the nonstationary current.

For calibrating the signals from the sensors, metal cylinders of elliptical cross section were used, through which a current pulse was passed corresponding in magnitude and duration to the pulse produced by the nonstationary current. The centers of the cross sections of the cylinders were located at the same distance from the electrodes. In our case, with radial injection, it was necessary to establish the relation between the magnitude of the signal arising on the electrodes and the radial size of the cylinder. Therefore changes in the cross section of the cylinders were made only along the major axis, as shown in Fig. 2, а (I, II). The shape of the cross section was established beforehand from observation of the electron beam on a fluorescent screen placed in the accelerating chamber on the azi-

minute arrangement of the electrodes. Figure 2,b presents the dependence of the magnitude of the signal from one of the electrodes on the radial size of the cylinders. It is seen that as the radial size of the cylinder increases, the magnitude of the signal from the electrodes increases. This dependence was used in studying the pulses produced by the nonstationary current at the electrodes (Fig. 3,b,c).

Figure 3,a shows such a matching of the injection pulse with the region of the required voltage at which a single formation of the nonstationary current should occur on the leading and trailing edges of the injection pulse. The oscillograms of the signals (Fig. 3,b,c) were taken at an injection voltage of 20 kV, an emission current from the injector of 200 mA, and a bell-shaped injection-pulse duration of 2.8 μsec. To take the oscillograms (Fig. 3,b,c), a high-speed two-beam oscilloscope SI-7 was used. From oscillograms b,c (Fig. 3) it is seen that at the peaks of the pulses corresponding to the formation of the nonstationary current, both on the leading and on the trailing edge of the injection pulse, there are dips. Comparison of the oscillograms with the calibration curve (Fig. 2,b) leads to the conclusion that the dimensions of the electron beam forming the nonstationary current decrease after several revolutions and then increase.

Figure 3,d presents the signals created by the nonstationary current in a magnetic-induction pickup made in the form of turns laid on the surface of the accelerating chamber along the electron orbits [9]. The positive part of the pulse corresponds to an increase of the current in the chamber, and the negative part to a decrease. From comparison of signals d and b,c it is seen that the dips in oscillograms b,c correspond to the maximum value of the nonstationary current (after integration of signal d). Consequently, the dips observed in oscillograms b and c (Fig. 3) indicate compression of the electron beam, and are not associated with a change in the magnitude of the circulating current.

When the emission current from the injector is increased, a more rapid decrease in the amplitudes of the electron oscillations occurs, and an equally rapid increase in them occurs because a larger emission current from the injector also corresponds to a larger azimuthal variation of the focusing forces of the betatron magnetic field. This leads to a substantial decrease in the average number of revolutions of the electrons forming the nonstationary current. In this case, repeated formation of the nonstationary current occurs. Comparison of oscillograms d and e (Fig. 3), the first of which was taken at the optimum emission current from the injector, and the second at an emission current three times greater than the optimum (injection voltage 8 kV), shows that the dips at the high emission current are absent. The distortions of the signals arising on the leading edge of the pulses are associated with the presence of interference from the injection circuit.

Thus, the resonance mechanism of formation of the nonstationary current is confirmed experimentally. Since the capture of electrons into acceleration is always accompanied by the formation of a circular nonstationary current of sufficiently large magnitude, its role in the capture process is unquestionable.

Conclusions

1. An experimental study of the behavior of the nonstationary current in time has shown that, in the mechanism of its formation, an essential role is played by resonant damping of the amplitudes of electron oscillations at the inhomogeneity in the azimuthal distribution of the density of the space charge produced by the emission current.

2. A fraction of the electrons forming the nonstationary current is captured--

... into the acceleration regime owing to the emergence of conditions for an irreversible change in their oscillation amplitudes after damping.

1. To capture a nonstationary current into acceleration, it is necessary to create conditions for an irreversible change in the oscillation amplitudes after damping.

REFERENCES

1. Yu. S. Korobochko. ZhTF, 27, 745, 1957.

2. D. P. Ivanov, A. P. Komar, Yu. S. Korobochko. ZhTF, 29, 978, 1959.

3. D. P. Ivanov, A. P. Komar, Yu. S. Korobochko. ZhTF, 29, 1235, 1959.

4. O. E. Zhukov, D. P. Ivanov, Yu. S. Korobochko. ZhTF, 38, 1067, 1968.

5. V. N. Logunov, E. P. Ovchinnikov et al. ZhTF, 27, 1143, 1957.

6. I. P. Chuchalin. Izv. TPI, 87, 275, 1957.

7. Yu. N. Lobanov, N. I. Tulinova. ZhTF, 31, 194, 1961.

8. P. A. Cherdantsev. Dissertation. TPI, Tomsk, 1961.

9. O. V. Sokolov, B. L. Chastokolenko. Izv. vuzov SSSR, “Fizika”, 9, 106, 1970.