SOME ISSUES IN THE STUDY OF AUTOMATIC REGULATION AND CONTROL IN BETATRON INSTALLATIONS

V. M. Razin

A betatron installation comprises several separate units, the proper interaction of which ensures sufficiently effective operability of the accelerator as a source of electrons with energies on the order of several tens of MeV. As is known [1], these units are the betatron electromagnet and its power-supply system, the injection and displacement systems, the vacuum system, etc. Here we consider issues associated with the development and study chiefly of the injection and displacement systems and, in part, of the electromagnet power-supply systems, in which the author took direct part in 1954–1968 while working within the Tomsk Order of the Red Banner of Labor Polytechnic Institute named after S. M. Kirov (TPI).

The process of accelerating electrons in an induction accelerator of the betatron type may conventionally be divided into three stages: injection, acceleration, and extraction or dumping of the accelerated electrons onto a target. When the betatron electromagnet is powered from an industrial-frequency electrical network, these stages are synchronized in a definite way with respect to the alternating magnetic field in the betatron inter-pole space by means of automatic control systems.

In some cases, pulsed power supply of the electromagnet is expedient. Since the betatron electromagnet, as a rule, consumes considerable reactive power, it is then necessary to switch current pulses on the order of several tens of kiloamperes at voltages on the order of tens of kilovolts. One method of generating electrical pulses with such parameters consists in using the discharge of a capacitive energy storage unit into the inductance of the electromagnet through switching gas-discharge devices such as ignitrons and thyratrons. When switching large currents, it is necessary to ensure uniform distribution of the load among gas-discharge devices connected in parallel, which can be achieved with the aid of equalizing reactors, anode current dividers, etc. In our work [2] a method was proposed for calculating an equalizing reactor that provides protection against overload of one serviceable gas-discharge device when a second device connected in parallel fails. The reduction of overload in this case is achieved by automatic increase of the inductance in the discharge circuit. The appearance of reverse voltage on the anode of a gas-discharge device after the capacitance has recharged into the inductance of the electromagnet sometimes leads to the appearance of reverse ignitions and distur-

…disturbance of the proper operation of the commutator. In works [3, 4] the solution of the problem of suppressing the reverse voltage at the anode of a gas-discharge device that commutates the pulsed current through the electromagnet winding was considered. In our works [5, 6, 7], together with I. P. Chuchalin, V. A. Kochegurov, and others, questions were considered concerning the investigation, calculation, and modeling of other types of pulse generators with capacitive energy-storage units.

The processes mentioned above—introducing injection and extracting or dumping electrons in a betatron—are provided by electrical pulse circuits for injection and displacement. We developed an engineering method for calculating injection and displacement circuits [8, 9, 10, 11, 12], which was tested experimentally and found practical application in a whole series of betatrons manufactured at TPI.

As a result of theoretical calculations and experimental studies, we showed that, for forming injection-voltage pulses, it is advisable to use methods and circuits employed in radar. In the initial betatron models, the source of high-voltage pulses in the form of an “air-core” transformer was replaced by us with a pulse transformer having an iron core. We suggested that strict “rectangularity” of the voltage, as required in radar pulse generators, is not necessary, and this considerably relaxed the requirements imposed on the magnetic material of the pulse-transformer core. Calculations showed that the core of a pulse transformer could be made of ordinary transformer steel E34A, 0.35 mm thick. Experiments confirmed the validity of these calculations [9]. Several samples of such pulse transformers with a double step-up winding were made, which made it possible to avoid the use of a filament transformer with high-voltage insulation. The pulse transformer with an iron core made it possible to create a pulse generator with low internal resistance, which in turn made it possible, without a substantial reduction in the amplitude of the voltage pulses, to ensure operation at currents in the pulses close to the optimum. The simultaneous increase of the pulse voltage, while making it possible to operate with the optimum emission current of the gun cathode, made it possible to increase the radiation intensity of betatrons by an order of magnitude and more in comparison with an injection circuit based on an “air-core” transformer. Beginning in 1953, on all TPI betatrons without exception, the injection circuits developed by us, based on the use of pulse transformers with an iron core, began to be applied. We made samples of small-size pulse transformers with a voltage amplitude of up to 100 kV at a pulse duration of 5–10 μsec. Later, the calculation methods and manufacturing technology were substantially improved, and under the direction of N. I. Vorob’ev and V. A. Moskalev, pulse transformers for voltages of 400 kV and higher were manufactured at TPI. We also developed an engineering method for calculating the displacement circuit for various methods of dumping accelerated electrons onto the target [9, 10], and calculation formulas were obtained with allowance for radiation braking of electrons in the acceleration process as applied to accelerators for high energies [11, 12]. This method found practical application in the design of displacement circuits for many types of betatrons manufactured at TPI.

In the presence of random changes of considerable magnitude in the voltage of the supply electric network, in a number of cases it is advisable to apply autonomous stabilization of such parameters in the injection system as the amplitude of the pulsed voltage and the emission current of the cathode of the betatron injector. The systems we developed

the stabilization of the indicated injection parameters [13, 14] were studied experimentally, and the stabilization coefficient proved to be sufficiently high.

A very important question of the general stabilization of the parameters of a betatron as a source of hard electromagnetic radiation was first considered by us in [15]. There the main causes of instability of such output parameters of a betatron installation as the intensity and energy of the radiation were established, and various methods for stabilizing and optimizing the radiation were outlined and investigated. Later, in these studies, a betatron simulator developed under the author’s direction was used as auxiliary equipment [16].

The problem of general stabilization and optimization of the output parameters of a betatron was considered by us using various approaches. One of the most important static characteristics of a betatron as a controlled object, representing the dependence of radiation intensity on the injection phase, has a clearly pronounced extremum, i.e., the maximum value of the radiation output is reached at a certain, strictly defined under given conditions, phase of the injection-voltage pulse relative to the alternating magnetic field in the interpole space of the betatron. The conditions determining the injection phase optimal in the sense of providing the maximum radiation may change randomly under the action of various kinds of disturbing forces.

In some cases of betatron use, the main factor is the integral action of the radiation, as, for example, in flaw detection of thick-walled products, in medicine, etc. Under these conditions it is desirable to automatically maintain the radiation maximum in the presence of random changes in disturbing influences. The idea of extremal regulation of betatron radiation intensity was first expressed by the author jointly with E. M. Belov in 1959 [17, 18]. Subsequently this idea was widely developed in our works [19, 20, 21, 22, 23, 24, 25, 26, 27] and in the works of other authors. As is known from the field of technical cybernetics, there exist two fundamentally different methods of automatic regulation and control. In open-loop automatic-control systems, compensation of disturbing influences provides high speed of response. Devices of this kind were developed and studied by us in two variants. The analog version of the controlling computing device (CCD) and the theory of its operation are considered in [15, 21, 25]. The analog version of the controlling computing device has a simple design, but the compensation range for disturbing influences from the supply-line voltage proves to be limited to within 5–8%. A somewhat more complex digital-analog version of the CCD [28, 29] is also more advanced.

Long-term tests of the latter device showed that the digital-analog CCD is a reliable and effective means of ensuring optimal injection conditions in a betatron. In the presence of random rapid changes in line voltage within limits up to ±12.5%, this device provides an increase in the average value of the betatron radiation intensity by approximately 25% in comparison with all other known methods of stabilization and optimization. The digital-analog CCD provides compensation in two parameters, in the form of the voltage on the windings of the betatron electromagnet and the amplitude of the injection pulse voltage simultaneously.

In closed-loop systems of automatic regulation and control, the feedback principle is used. Systems of this kind

provide more precise regulation and control; however, owing to their low response speed, the average value of the radiation output cannot be obtained close to the maximum. Optimal solutions can be obtained by using combined methods of automatic regulation and control. In our works [26, 27] the basic principles for constructing such combined control systems were considered as applied to the stabilization and optimization of radiation intensity.

The digital-analog control device considered above also proved applicable to the stabilization of another main parameter of the betatron, namely the maximum energy of the bremsstrahlung radiation [31].

A development of the approaches to solving the problem of stabilizing and optimizing charged-particle accelerators indicated above is the consideration of possibilities for broader use of the ideas, methods, and means of technical cybernetics in accelerator engineering, as set forth in other works [27, 31, 32].

As is known from the field of technical cybernetics, the modeling method is the most effective means for solving problems of analysis and synthesis of automatic regulation and control systems in various areas of technology. Since theoretical calculations of extremal regulation systems in the presence of substantial nonlinearities are very difficult, it proved expedient to carry out these investigations on analog computers. Studies conducted with the author’s participation and under his direction [21, 25, 27, 33, 34, 35] made it possible to establish, in the most economical way and with little expenditure of time, the optimal ratios of the main parameters of extremal regulators for betatron installations. Electronic modeling methods also proved highly effective in solving problems associated with the transport of electron beams in high-energy charged-particle accelerators. The mathematical model we compiled made it possible in these studies to take into account the influence of the beam’s space charge on the trajectories of the outer electrons, which determine the dimensions of the electron beam [36, 37, 38, 39].

The investigations carried out under the author’s direction and with his participation showed that the application of modern methods and means of technical cybernetics to a betatron installation, or to any other type of charged-particle accelerator, yields extremely fruitful results and facilitates the creation of economical, highly reliable, and sufficiently high-quality types of accelerators suitable for practical application in industry, medicine, and other fields of use.

In conclusion, it should be noted that I. P. Chuchalin, V. P. Sherstobitov, E. M. Belov, N. Ya. Makarov, N. V. Trikhanova, V. A. Kochegurov, V. L. Ryabukhin, and many other staff members of the Tomsk Polytechnic Institute took a direct part in solving many of the questions considered above; the author expresses his sincere gratitude to them. The author also sincerely thanks the Honored Worker of Science and Technology of the RSFSR, Doctor of Physical and Mathematical Sciences, Professor A. A. Vorob’ev, who initiated the posing of a number of new approaches to the automation of accelerators and served as a scientific consultant in the field of accelerator engineering, for his constant attention to the work and discussion of the results obtained.

References

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2. V. M. Razin. On the calculation of an equalizing reactor for the parallel operation of ignitrons. Izvestiya TPI, vol. 76, pp. 148–151, 1954.

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