HIGH-VOLTAGE INJECTION SYSTEM FOR A COMPACT HIGH-CURRENT BETATRON

V. A. Moskalev, Yu. M. Skvortsov

The high density of the accelerated electron beam in a high-current betatron \[1, 2, 3\] is achieved both by increasing the region of focusing forces and creating a “capacitive” field, and by introducing no fewer than \(10^{13}\) electrons into acceleration in each pulse. The use of an increased injection voltage leaves its own distinctive imprint on the form and design features of the high-voltage injector device \[4\], as well as on its power-supply circuit. Below are presented the results of the development of a high-voltage injection system for a compact high-current betatron (BCK).

It is known that, in order to ensure a proportional change in the number of accelerated particles with an increase in the injection voltage \[5, 6\], the pulse generator feeding the electron gun must have a power providing a current of not less than

\[ I_{\max}=1.8(\beta\gamma)^3 \frac{x_i^2-b}{\beta \ln x_i^2}, \tag{1} \]

where \(\beta\) and \(\gamma\) are relativistic factors taking into account the velocity and energy of the injected particles; \(x_i=\frac{\rho_i}{\rho_0}\) is the ratio, reduced to a circular cross section, of the radii of the region of focusing forces and the aperture of the injection device; \(b=1+2\tg^2\alpha\left(\frac{R_0}{\rho_0}\right)^2\) is a parameter taking into account the divergence of the beam injected into the inter-pole space at an angle \(\alpha\); \(R_0\) is the equilibrium radius, and 1.8 is a coefficient taking into account the physical constants when the quantities are substituted in the MKS system. It is precisely this current that determines the pulse power of the generator of the BCK injection circuit, in whose modulator (Fig. 1) a combined storage unit is provided \[7\].

Since in such a betatron all units and elements, including the pulse systems, are calculated for optimal parameters, in designing the pulse modulator the experience of using high-voltage injection in the first high-current betatrons was taken into account. For this purpose, in the linear modulator the storage unit, whose principal parameters are determined from the expressions:

\[ C_0 = 2\frac{I_{\mathrm{i}}}{U_{\mathrm{i}}} g^2 \tau_{\mathrm{i}}, \]

\[ C'_{\mathrm{cor}} = 0.5\frac{I_{\mathrm{i}}}{U_{\mathrm{i}}} g^2 \sigma \tau_{\mathrm{i}}, \tag{2} \]

\[ L'_{\mathrm{cor}} = 0.25\frac{U_{\mathrm{i}}}{I_{\mathrm{i}} g^2}\sigma \tau_{\mathrm{i}}, \]

consists of a limited number of capacitors of the IM or KV type, and, for the sake of economy and to increase the efficiency, their charging is carried out through a choke with inductance:

Fig. 1. Schematic diagram of a pulse modulator with a combined storage unit

\[ L_{\mathrm{ch,opt}} = \frac{1}{C_{\Lambda} f^2 \chi^2}\cdot 10^{-2}. \tag{3} \]

In (2) and (3), \(C_0\), \(C'_{\mathrm{cor}}\), \(L'_{\mathrm{cor}}\) are the parameters of the storage unit and of the correcting line (CFL); \(U_{\mathrm{i}}\), \(I_{\mathrm{i}}\), and \(\tau_{\mathrm{i}}\) are the amplitude values and the magnitude of the voltage, current, and duration of the generated pulse; \(\sigma\) is the selected moment of pulse correction (front, top, or cutoff) \((\sigma = 0.1 \div 0.9)\); \(C_{\Lambda} = C_0 + \sum C'_{\mathrm{cor}}\) is the total capacitance of the storage unit; \(f\) and \(\chi\) are the frequency of the supply voltage and the relative period of the storage-unit charging process. The use of the indicated modulator in the injection system of a compact high-current betatron makes it possible not only to apply to the injector device a voltage of specified power, but also, within certain limits, to correct the pulse shape in order to optimize the capture conditions [8].

A reduction in the geometrical dimensions of a high-current betatron without changing its electrophysical parameters at a specified injection energy is achieved by combining the electron source—the gun—and the pulsed-voltage source—the high-voltage injection transformer—into a single unit, similarly to [9]. Until recently, in all betatrons (with the exception of the PMB-6 [10] and the betatron manufactured by FRI for 42 MeV [11]) the electron gun and the pulse transformer (IT) were separated by a distance which, on the one hand, ensured the electrical strength of parts under high pulsed voltage, but, on the other hand, substantially increased the dimensions of the accelerator, limiting its mobility, since the transmission of voltage pulses to the injector device was carried out along cable or rigidly fixed wire lines at voltages of 25–300 kV.

Let us consider some aspects that make it possible to solve the problem of creating a pulsed source of accelerated electrons (PSAE). First of all, it is necessary to accept the condition that such a PSAE must not degrade the pulse and energy characteristics of the previous system, when an end-type high-voltage injector with inflector injection of electrons into the capture region was powered from separate generators by pulses of different polarity.

In the BSK, the injector device and the pulse power transformer are made as a combined structure (Fig. 2), allowing

Fig. 2. Sketch of the structural integration of an end-type electron gun and a pulse transformer

the injection of an electron beam with parameters that ensure attainment of the required magnitude of the accelerated charge. The PSAE is based on a pulse transformer consisting of eight separate steel cores 1, which are wound from strip cold-rolled steel grade E310A and fastened in a star-shaped arrangement around injector 5. Using air-frame insulation 2 with the use of organic glass and polyethylene-terephthalate film, and parts of rounded shape that help to equalize the electrostatic field [12], it was possible, for the specified injection voltage, to design a PSAE that fits within the established dimensions. The evaluation carried out of the efficiency of transforming pulses of a specified shape (duration, front, decay at the top, etc.) showed that deteriora-

Fig. 3. Schematic circuit of the combined power supply of the gun and inflector using two pulse transformers

the transient characteristic [13] of such a PT led to some increase in the rise time, but within permissible limits. In the indicated system it is possible to preserve an important advantage of the pulse transformer for high-voltage injection [14]—the slight dependence of the energy parameters on the degree of loading.

However, even when using an IIEA it is necessary to feed the gun and the inflector separately with pulses of different polarity, and their amplitude and phase relationships must be in a definite relation.

In the BSK injection system, the supply of an IIEA equipped with an electrostatic inflector will be provided from a single modulator. This will make it possible [15] to simplify the tuning process of an accelerator with a high-voltage injection system.

As the final stage of the pulse generator, it is proposed to use one of the two circuits considered below, employing for the purpose of matching pulses in phase the so-called “quasi-low-frequency” or “quasi-high-frequency” filters [16]. In one of the circuits (Fig. 3), two pulse transformers are used. The transformer for feeding the inflector is connected directly to the output terminals of the modulator, while the pulse transformer feeding the electron gun is connected to the modulator through a “quasi-low-frequency” filter \(L_{\phi}' C_{\phi}' — L_{\phi}'' C_{\phi}''\). By regulating the voltage on the secondary side of \(\mathrm{PT}_2\), it is possible to obtain the required ratio between the inflector voltage and the gun voltage, which subsequently, as the voltage at the modulator output changes (\(T'1—1\), Fig. 1), will remain unchanged, i.e.

\[ \frac{U_{\mathrm{vy}}}{U_{\mathrm{i}}} = \mathrm{const}. \]

The “filter” will make it possible to ensure the necessary phase matching of the pulses \(U_{\mathrm{i}}\) and \(U_{\mathrm{vy}}\); moreover, for the case (Fig. 4), when

Fig. 4. Wave diagram of the pulses: \(U_{\mathrm{vy}}\)—inflector pulse, \(U_{\mathrm{i}}\)—electron-gun pulse, \(\varphi_{\mathrm{vy}}\) and \(\varphi_{\mathrm{i}}\)—delays (phases) of the corresponding pulses

Fig. 5. Schematic circuit of combined feeding of the gun and inflector from a single pulse transformer

\[ \Delta \varphi = \varphi_n - \varphi_{vu} > 0, \tag{4} \]

the condition of maximum “transmission” of the electron beam through the inflector can be achieved.

The use of a separate transformer somewhat complicates the circuit, but does not preclude its possible application. In this connection, for the CBK system it is preferable to use a circuit with one pulse transformer, but with two separate windings for feeding the gun and the inflector (Fig. 5).

To vary the instants at which pulses are applied to the gun and to the inflector from a single modulator—in accordance with (4)—a “quasi-high-frequency filter” is installed at the output of winding \(W_3\), which feeds the inflector, with capacitance \(C_f = 2C'\), where \(C' = \dfrac{1}{2\omega \rho}\) is a nominal capacitance characterizing the transmission of a pulse with frequency \(w = \dfrac{2\pi}{\tau_i}\), and \(L_f = \dfrac{\rho}{2\omega}\) is the inductance of the filter. Here \(\tau_i\) is the duration of the pulse formed in the modulator. The parameters of such filters are determined from the condition of transmitting the pulse in the time \(t = \varphi_{vu} = 2\pi \sqrt{L_f C_f}\), in order to maintain the necessary matching (4).

References

1. V. A. Moskalev, B. V. Okulov, Yu. A. Otrubyanikov, Yu. M. Skvortsov, A. G. Skorikov, V. G. Shestakov. Proceedings of TPI, vol. 2, 122, 1962, 50–58.

2. V. A. Moskalev, Yu. M. Skvortsov, B. N. Okulov, V. G. Shestakov. Electron accelerators. Proceedings of the Fourth Interuniversity Conference, 1964, 204–209.

3. A. A. Vorobev, V. A. Moskalev, Yu. M. Skvortsov, A. M. Slupskii, V. G. Shestakov. Proceedings of Higher Educational Institutions, Physics, No. 4, 1967, 139–140.

4. B. V. Okulov. Dissertation. Nuclear Physics Research Institute, Tomsk, 1969.

5. L. Gonella, Nucl. Instr. a. Meth., 22, 1963, 269–291.

6. B. N. Rodimov. Doctoral dissertation. Nuclear Physics Research Institute, Tomsk, 1966.

7. V. A. Moskalev, B. V. Okulov, Yu. M. Skvortsov, A. M. Slupskii. Electron accelerators. Proceedings of the Fourth Interuniversity Conference, 1968, 273–276.

8. A. A. Vorobev, V. A. Vorobev, L. N. Drozdov, O. V. Sokolov, I. A. Tsekhanovskii. Electron accelerators. Proceedings of the Seventh Interuniversity Conference, issue 2, 1970, 41–43.

9. E. A. Abramyants, S. B. Vasserman, V. M. Dolgushin, A. A. Egorov, I. V. Kazarezov, A. V. Filipchenko, G. I. Yasnov. Electron accelerators. Proceedings of the Seventh Interuniversity Conference, issue 3, 1970, 36–38.

10. L. M. Ananev, M. I. Shtein, V. L. Chakhlov, Yu. P. Yarushkin. Defectoscopy, 1968, No. 6.

11. R. Schittenhelm et al. Strahlentherapie, vol. 127, no. 4, 1965.

12. S. V. Krivonosov. Electron accelerators. Proceedings of the Seventh Interuniversity Conference, issue 3, 1970, 49–51.

13. Ya. S. Itskokh. Pulse Transformers. VI, 1950.

14. Yu. M. Skvortsov, A. M. Slupskii. Electron accelerators. Proceedings of the Seventh Interuniversity Conference, issue 2, 1970, 41–43.

15. B. B. Okulov. Electron accelerators. Proceedings of the Seventh Interuniversity Conference, issue 2, 1970, 25–28.

16. G. V. Zeveke, P. A. Ionkin, S. V. Strakhov. Fundamentals of Circuit Theory. Energiya Publishing House, 1965.