RESEARCH AND DEVELOPMENT OF INDUCTION ELECTRON ACCELERATORS—BETATRONS AT TOMSK POLYTECHNIC INSTITUTE

L. M. ANAN’EV, V. A. MOSKALEV

A betatron is an electron accelerator based on the use of a vortex electric field induced by an alternating magnetic flux.

In the USSR, work on the theory of the induction method of electron acceleration and on developing the fundamentals of betatron design began as early as the beginning of the 1930s, i.e., practically simultaneously with Wideröe (1928) and Steenbeck (1935), who were working in Germany.

In 1935 V. V. Yasinskii published the results of theoretical studies of the motion of electrons in a quasi-stationary and alternating electromagnetic field with axial symmetry in the presence of an additional radial electric field. Under appropriately chosen conditions, stable orbits of electron motion exist. In this connection, V. V. Yasinskii proposed, when accelerating electrons in a vortex electric field, to use a radial electric field acting for a short time, \(10^{-7}\)—\(10^{-8}\) sec, in order to bring them onto the equilibrium orbit.

The possibility of such acceleration in outer space was also pointed out by Ya. P. Terletskii. Similar studies in the 1930s at the Siberian Physico-Technical Institute (Tomsk) were carried out by A. K. Krasin and A. A. Vorob’ev. However, the indicated works did not at that time receive proper practical development.

For the first time, stable induction acceleration on the basis of the developed one-electron theory was achieved by D. Kerst in his accelerator, which included all the principal components of the modern betatron.

In 1943–1944, among other scientific investigations in the Soviet Union, work was begun on the induction method of acceleration. The work began practically simultaneously at the Institute of Physics of the USSR Academy of Sciences in Moscow, at the Ukrainian Physico-Technical Institute in Kharkov, at the Ural Branch of the Academy of Sciences under the direction of A. P. Komar and S. K. Sidorov, at the Special Design Bureau of the Moscow Electric Lamp Plant under the direction of B. B. Gel’perin, and at Moscow University in the group of Prof. A. A. Sokolov and D. D. Ivanenko, among others. Work at Tomsk Polytechnic Institute began in 1944–1945. The considerable efforts expended in this large collective undertaking yielded positive results.

At the present time about three hundred betatrons are operating in the USSR; of these, about two hundred were manufactured at TPI. The parameters of these installations

in general no worse than known betatrons developed in other countries. Betatrons of the Tomsk Polytechnic Institute are manufactured in various types, suited to the practice of their use for the purposes of flaw detection, therapy, biological and physical scientific research, geophysics, etc. The basic data on the TPI betatrons are presented in Table 1.

At the Tomsk Polytechnic Institute, development and research in the field of the induction electron accelerator—the betatron—carried out under the direction of A. A. Vorob'ev, proceeded along three lines: the creation of a theory of accelerator operation, including the dynamics of electrons in the chamber and the capture of electrons into acceleration; the development of practical engineering methods for calculating betatrons as electrotechnical installations, which made it possible to create a methodology for calculating individual accelerator units satisfying the conclusions of the theory of its operation; and, finally, research in the area of practical applications. Although by the beginning of the development of work at TPI several theories of betatron operation were known (Kerst, Kerst and Serber, etc.), they did not make it possible to study the totality of all questions associated with the induction acceleration of electrons. The principal shortcoming of the existing theories and hypotheses was the attempt to explain betatron operation by analyzing the acceleration of a single electron.

At the Tomsk Polytechnic Institute, theoretical research immediately followed the path of creating a many-electron theory of the betatron, which was developed in the works of V. S. Melikhov and A. A. Vorob'ev, B. N. Rodimov, P. A. Cherdantsev, O. V. Sokolov, and A. G. Vlasov, and others.

As a result of these studies, a theory of the betatron was created which explains the capture of electrons into acceleration primarily by the electrostatic interaction of electrons that have already made one or several revolutions with electrons emerging at that moment from the injector. In this process the radial oscillations of some electrons are damped, which allows them to bypass the injector. This mechanism is inefficient, since it captures into acceleration an insignificant fraction of that charge which the focusing forces of the betatron magnetic field can retain.

In connection with this, B. N. Rodimov proposed the so-called oscillation-free capture, in which, by means of a contractor circuit, the orbit is displaced beyond the injector and, by reducing the injection current according to a specially calculated law, oscillation-free, spiral introduction of electrons into acceleration is achieved.

In the studies of P. A. Cherdantsev, the theory of the betatron proposed by B. N. Rodimov was detailed and developed. A number of relationships were found between practically determined quantities, for example, between the magnitude of the injection voltage and the current of accelerated electrons in the orbit. The radiation intensity is determined by a relation of the form $\sim I \cdot U^{-3/2}$, where $I$ is the injector current and $U$ is the injection voltage. The experiments of O. V. Sokolov confirmed the correctness of the theoretically obtained conclusions and, consequently, the correctness of the theory of electron capture into acceleration under certain conditions.

In the course of acceleration, electrons are lost as a result of an increase in the amplitude of radial or axial oscillations caused by inhomogeneities of the magnetic field. Certain special cases of this problem had been described earlier, for example, by Bardeen, Kerst, and others. At TPI this problem was investigated theoretically and experimentally by L. S. Sokolov, O. V. Sokolov, and K. S. Grishin.

In order to increase the efficiency of the accelerator, works were presented on studying the influence of various concentrated and distributed

…of certain defects of the control magnetic fields on the dynamics of the electron and the suppression of the buildup of electron oscillations. These studies yielded several conclusions of practical interest. In particular, it was investigated what is achieved in an induction accelerator by the use of alternating-gradient rigid magnetic (G. I. Dimov) or electrostatic focusing, by the use of several electron injectors, and by several accelerated beams to improve the damping of oscillations (O. V. Sokolov).

As a result of theoretical and experimental studies, it proved possible to develop a methodology for designing and constructing betatrons for various applications.

First of all, practical engineering methods were developed for calculating betatron electromagnets. The methods proposed at TPI by M. F. Filippov make it possible, with accuracy sufficient for practice, to select the main parameters of the electromagnet and calculate all its dimensions.

On the basis of calculations and experimental studies of the first experimental betatrons, M. F. Filippov found the interdependence of the principal dimensions and parameters of the electromagnet when the betatron condition is satisfied; this was then used in developing calculation methods. Subsequently these calculations were developed in the works of L. M. Anan’ev, who, on the basis of the relations found by M. F. Filippov, obtained similarity laws for betatron electromagnets and proposed criteria of compactness, which formed the basis for the design of small-sized and portable betatrons.

The relatively low radiation intensity of ordinary betatrons restrains further expansion of the field of application of these accelerators. Therefore one of the basic requirements imposed on betatrons, as on other types of accelerators, is to increase the current of accelerated particles. This problem is successfully solved in the works of A. A. Vorob’ev and V. A. Moskalev, which culminated in the creation of a high-current betatron accelerating a charge hundreds of times greater than the charge accelerated in ordinary betatrons.

The increase in the current of accelerated particles in a high-current betatron was obtained by a substantial change mainly in two accelerator parameters, namely:

a) an order-of-magnitude increase in the region of action of the focusing forces of the betatron control magnetic field;

b) a considerable increase in the initial energy of the electrons (to several hundred kilovolts) at which they are introduced into acceleration.

The increase in the volume of the magnetic field in high-current betatrons, in turn, is achieved by increasing the geometric dimensions of the inter-pole space (by a relative increase of $\delta_0$; in a high-current betatron $\frac{\delta_0}{z_0} \approx 1$). Since this is accompanied by an increase in the dimensions and weight of the accelerator and by an increase in the consumed electrical energy, the enlargement of the inter-pole space is limited by certain reasonable bounds.

In the course of constructing high-current betatrons, various designs of accelerator poles were investigated, in particular poles without correcting “visors” but with an increased radial dimension, which provide the closest approximation to the theoretically specified configuration of the magnetic field; and also variants of pole profiles with variable and, within certain limits along the pole radius, constant indices of decrease $n$ of the magnetic field.

For $n(z)=\mathrm{const}$ (a concave profile), the efficiency of using the betatron aperture is somewhat higher.

The high-current betatrons developed and built provide a high radiation intensity. The electron charge accelerated in them has been brought up to \((1 \div 3)10^{12}\) particles per acceleration cycle.

At present, a design has been developed for a compact high-current betatron in which, through the use of new magnetic materials, as well as corresponding design modifications, a fourfold reduction in the weight of the electromagnet of a high-current betatron has been achieved.

As a result of theoretical and techno-economic studies, as well as experimental design developments, scientists at Tomsk Polytechnic Institute have created highly advanced designs of betatron electromagnets for various purposes. These include electromagnets with magnetic cores having special laminations that improve the structure of the guiding magnetic field; with windings on the posts and yokes, appropriate for betatrons with a small cross section; multi-post and shielded types, promoting the best use of active materials and shielding of stray radiation; two-chamber betatrons possessing a number of specific features; and so on. Simultaneously with the electromagnets, their power-supply circuits were also being developed intensively.

In creating a betatron for mass application, for many techno-economic reasons work began on the development of an installation powered from an industrial-frequency alternating-current network. Experience showed that the choice of industrial frequency was successful. This greatly simplified the installation and increased its reliability, and reduced the area of the required working premises. The use of an increased frequency to power the windings of betatron electromagnets can justify itself only when creating an installation for a special purpose.

In the laboratories of TPI, studies were also carried out on mixed powering of the electromagnet by direct and alternating currents. It was established that the use of biasing for the purpose of increasing the final energy of the electrons is economically advantageous beginning with energies of \(25 \div 35\) MeV; at the same time, the use of simple mixed powering to reduce reactive power and losses in the electromagnet in some cases proves expedient also in installations for considerably lower energies, especially when they are powered by current of increased frequency. Recently, at TPI, a simpler and more reliable system for feeding the electromagnet with direct current was developed, consisting of an additional low-voltage winding on the electromagnet, a semiconductor rectifier, and a compensating transformer.

For powering the electromagnet with currents of increased frequency, simple and reliable converters using semiconductor devices were developed for operation; with pulsed input of energy into the circuit, with recharging of the capacitance, as well as pulsed generators with a high repetition frequency of current pulses.

The purpose of the indicated studies was to develop an economical electromagnetic system for an accelerator, making it possible to obtain the specified radiation parameters with the least expenditure of materials. This was also facilitated by proposals for using the winding’s own capacitance to compensate reactive power and for compensating the compression of the equilibrium orbit at the end of acceleration by shifting, in phase, the accelerating flux of saturation of the outer pole regions.

In addition to advanced electromagnets and devices for their power supply, the creation of a highly reliable and effective betatron presupposes the development of all its other systems as well, with proper characteristics and parameters. This led to the need for careful

studying the dynamics of accelerated electrons not only during the period of beam formation, but also throughout the entire acceleration cycle.

A. G. Vlasov presented a method for calculating electron losses in the residual gas, which is expedient to use for engineering calculations in the design and operation of accelerators. Studies of the variation of electron losses with the chemical composition of the residual gas in the chamber showed that when the chamber is filled with light gases—helium and hydrogen—the losses decrease by an order of magnitude. Therefore, the operating vacuum in the chamber can be reduced by an order of magnitude, which is important in the manufacture of sealed accelerator chambers.

A method has been developed for observing the beam during its acceleration by means of a scintillation counter installed in the immediate vicinity of the accelerating chamber. The method makes it possible to observe, on an oscilloscope screen, the process of electron loss during the acceleration cycle by the luminescence they produce when they strike the chamber wall, and also to carry out quantitative measurements of these losses. The decrease in the number of electrons over the entire acceleration cycle has been studied, and methods have been indicated for increasing the lifetime of electrons in the betatron chamber.

Having obtained this conclusion about the required operating pressure in betatron chambers, designs and technology were developed for semi-sealed betatron chambers with a titanium pump. V. P. Ponomarev created interesting designs of titanium pumps of the necessary capacity and chambers with such pumps for betatrons of various energies.

L. M. Ananyev and the group he headed worked out the design and manufacturing technology of sealed chambers for small betatrons. These chambers are characterized by simplicity of design and sufficient reliability in operation. Recently, the parameters of sealed small-sized chambers have been improved through the use of an external injector with an inflector, which, as studies have shown, makes it possible, even in chambers of small cross section, to increase the injection voltage, longevity, and effective volume. This made it possible to substantially increase the charge accelerated in the betatron.

Extensive work on the design of accelerating chambers was carried out under the direction of V. A. Moskalev in the development of high-current betatrons. The considerable volume of these chambers made it necessary to revise the entire electrovacuum system in a fundamental way. Above all, this affected the design features of the vacuum accelerating chamber itself. The chamber for a high-current 25 MeV betatron has a radial cross-sectional area of more than 500 cm² and a volume exceeding 100 liters, which did not permit the use of the technology for manufacturing cast (one-piece) chambers, as is done for ordinary betatrons, and led to the use of a sector-type design.

The chamber is made of glazed porcelain and consists of six sectors bonded with an epoxy compound. The inner surface of the chamber is coated with a conducting layer of tin dioxide. Electrical connection of the layer of the individual sectors is accomplished through copper foils along the outer perimeter of the chamber. The chamber has 12 branch pipes for accommodating the high-voltage injector, inflector, final-dump windings, induction electrode, targets, etc. Pumping of the chamber is carried out by a powerful multistage pump of the VA-1M type with a capacity of 1000 l/s. The operating vacuum is \(5 \cdot 10^{-6}—1 \cdot 10^{-5}\) torr.

The desire to increase the intensity of the radiation and its quality compelled close attention to be paid to the injection, displacement, and control systems of the betatron. Numerous theoretical and experimental studies to determine the parameters of injection into the operation of the betatron made it possible to create highly sophisticated high-pulse-voltage sources with pulse characteristics and system designs optimal for each case. The developed designs of injection generators for medium-energy betatrons are distinguished by their simplicity, small dimensions, and ability to create injection voltages of up to 80–100 kV. The specific features of small-sized betatrons led to the creation of compact pulse generators based on semiconductor devices with pulse transformers having a solid dielectric. The volume of such injection-voltage sources does not exceed 500 cm³.

For the complete extraction of the accelerated equilibrium electron charge onto the orbit, contractors of various designs were proposed. Yu. M. Akimov investigated the focusing action of contractors and concluded that the use of a contractor increases the radiation intensity severalfold if the betatron is not tuned for maximum radiation. When the installation is well adjusted and provides the maximum radiation possible in the given cases, the use of a contractor can increase the output only by 40–60%. Ferromagnetic and electronic contractors were also proposed.

A wide range of research was carried out in developing systems for displacing electrons from the equilibrium orbit and extracting them from the betatron chamber. The displacement systems created are distinguished by originality and high efficiency. Thus, displacement systems with an extra-orbital winding, with short-circuiting windings, and rapid-discharge systems were proposed. They are powered by similar generators based on gas-discharge and semiconductor devices.

For extracting electrons from the betatron chamber, detailed studies were carried out on the behavior of electrons at the final stage of the acceleration process. Original variants of three methods for extracting the electron beam from the chamber of the ring accelerator were developed and implemented:

1. By deflecting the beam with an electrostatic field and various types of deflectors developed by B. A. Kononov.

2. By means of magnetic shunts and nonmagnetic tunnels for electron extraction, developed by L. S. Sokolov and Yu. M. Akimov.

3. By means of magnetic coils or methods of magnetic-field fluctuations, developed by L. S. Sokolov.

More than 10 betatrons with extracted electron beams are in operation. The magnitude of the average current in the extracted beam reaches \(10^{-8}\) A, and the dose rate reaches 10,000 roentgens/min.

Studies on beam extraction, continued recently by V. P. Anokhin, led to the development of parametric extraction systems that possess high efficiency, especially in accelerators with a large air gap.

Numerous theoretical and experimental studies were carried out to improve the quality of the radiation generated by the betatron through the development and use of effective systems for controlling and stabilizing the dose rate and radiation energy.

V. M. Razin, V. I. Gorbunov, E. M. Belov, O. I. Nedavin, M. M. Shtein, and others created systems for stabilizing the dose rate, voltage, and injection current. Stabilization systems for radiation by deviation, level, and extremal systems have found wide application in the practice of betatron construction. Recently, V. M. Razin and Ryabukhi

specialized computing devices were developed for optimizing injection conditions.

R. P. Meshcheryakov developed instruments for monitoring the maximum radiation energy of a betatron and stabilizing it, instruments for monitoring the intensity and integral dose, and radiation detectors. In experiments, stabilization accuracy of the maximum energy of 25 MeV ± (10–15) keV was achieved.

A detailed study of the causes affecting radiation stability showed that the determining destabilizing factor is instability of the supply voltage. In this connection, M. M. Shtein and G. S. Vorob’eva developed simple designs of ferromagnetic and semiconductor stabilizers for the supply voltage. Their distinctive feature is that, for voltage stabilization, the nonlinear properties of the betatron electromagnet and the high quality factor of its oscillatory circuit are used.

Most betatrons currently in operation make it possible to accelerate \(10^9 \div 10^{10}\) particles in a single cycle, which in a number of applications proves insufficient. In particular, for pulsed radiography of rapidly occurring processes it is necessary to accelerate, per cycle, a number of particles at least two orders of magnitude greater. Such an increase in the charge accelerated in the pulse can be obtained only with a simultaneous substantial increase in the “capacity” of the stability region, the injection voltage, and the injection current. This problem was solved by a team under the leadership of V. A. Moskalev, and the result of the work carried out was the creation of a special group of betatrons, called high-current betatrons.

The theoretical justification of the possibility of solving the posed problem was carried out by B. N. Rodimov and P. A. Cherdantsev.

B. V. Okulov developed a methodology for engineering calculation of high-voltage injector devices and created several design variants for voltages of 200–300 kV and currents of 10 A and more, ensuring injection and capture into the betatron stability region of up to \(10^{13}\) electrons per pulse.

For powering high-voltage injector devices, Yu. M. Skvortsov developed powerful high-voltage generators of injection voltage of 200–400 kV.

V. G. Shestakov solved the problem of displacing, in a short time, a beam of accelerated electrons from the equilibrium orbit onto a target in a betatron with a large gap between the poles. The radiation-pulse duration achieved in this case is less than 0.2 μs, which makes it possible to photograph rapidly occurring physical or chemical processes and fast-moving parts of machines and mechanisms.

The extraction of an intense electron beam from the accelerating chamber of a high-current betatron into the atmosphere further expanded the field of application of the induction accelerator. V. V. Shashov, for the first time in betatron practice, solved the problem of extracting an electron beam from a betatron by a pulsed single-turn method, which made it possible to obtain current pulses of the extracted beam with a duration of 5–6 ns and a beam power in the pulse of up to 120 MW (electron energy, 25 MeV). The average current in the extracted beam reaches \(10^{-6}\) A, and the dose rate reaches \(10^6\) rad/min. As the extraction device, a pulsed magnetic deflector is used, consisting of two short-circuited lines connected in parallel at the end and matched with the high-voltage nanosecond-pulse generator feeding them. The operation of the generator circuit is based on the discharge of a noninductive capacitance into a forming coaxial

line through a commutating controlled spark gap, with subsequent discharge of the forming line into the transmission line and onto the deflector through a sharpening spark gap. Both spark gaps are under high nitrogen pressure, equal to 15 atm. As the commutating spark gap, a “trigatron”-type spark gap proposed by Johnson (USA) is used. A distinctive feature of such a spark gap is the trigger electrode, made in the form of a toroid located near the cathode. The trigger electrode practically does not burn out, since the working current does not pass through it. When the commutating spark gap is filled with nitrogen, the generator operates stably at a pulse repetition frequency of 25 Hz. The output parameters of the generator in this case are as follows: voltage-pulse amplitude—100 kV, pulse duration 13 nsec, pulse-front duration about 1.5 nsec. The pulse power of the generator is 400 MW.

Extraction of the electron beam from a high-current betatron has also been carried out by the electrostatic method, using an extraction device that is a capacitor with an elongated deflecting plate. This extraction method made it possible to obtain current pulses in the extracted beam with a duration of up to 1 μsec. The average beam current is also about \(10^{-6}\) A.

In high-current betatrons, for the first time in the practice of betatron construction, coherent beam instability during acceleration was detected, caused by the finite conductivity of the surrounding walls and leading to the loss of a considerable part of the charge captured for acceleration. The problem of suppressing this instability is currently being solved.

As a result of an experimental study of the acceleration process in high-current betatrons, it has been established that the greatest “capacity” is possessed by the magnetic field of a betatron whose pole profile ensures a monotonic increase with radius. In this case, all other conditions being equal, the number of particles captured and reaching the end of the acceleration cycle is almost an order of magnitude greater than in a betatron with poles ensuring \(n(r)\approx \mathrm{const}\). These experiments have demonstrated the feasibility and advantages of the so-called optimal field, the theoretical foundations for obtaining which were given by B. N. Rodimov. The use of the most “capacious” field in ordinary and small-sized betatrons (provided that the injection systems are simultaneously improved) can yield a substantial increase in the intensity of the beam delivered by these accelerators.

For stereoscopic radiography, V. A. Moskalev proposed an original design of a two-chamber stereobetatron, which has a number of advantages in comparison with single-chamber two-beam betatrons.

In particular, in a two-chamber stereobetatron two electron beams are accelerated simultaneously, which makes it possible, for example, to perform stereoscopic monitoring of rapidly occurring processes. In addition, in a two-chamber stereobetatron the distance between the radiation sources exceeds the corresponding value in a two-beam betatron. The latter substantially increases the accuracy of stereoscopic monitoring.

The above-mentioned and numerous other studies on the physics and technology of induction acceleration enabled the researchers of the Tomsk Polytechnic Institute to create induction accelerators for various practical applications that are reliable in operation and not inferior to world standards. Thus, for flaw detection of materials under industrial conditions, under the direction of V. I. Gorbunov, betatrons were created for an average energy of:

For radiation inspection of large-sized products and building structures at slipways, airfields, in shops, field conditions, and other nonstationary settings, small-sized portable betatrons of the PMB type have been developed at Tomsk Polytechnic Institute.

The parameters of the radiation generated by these accelerators (energy 3–6 MeV) make it possible to use them to inspect steel products up to 100–200 mm thick and concrete layers up to 600 mm thick.

Structurally, PMB-type betatrons are made as separate units whose weight and dimensions allow them to be transported manually by one or two people without the use of special lifting-and-transport equipment. As an example, Fig. 1 shows a complete PMB-6 betatron set, which generates hard bremsstrahlung radiation with a maximum energy of 6 MeV and a dose rate of 0.6 R/min·m. The installation includes an irradiator containing a multirack-type electromagnet, an accelerating chamber, a radiation detector, electron injection and displacement systems, as well as a fan and protective interlock equipment. The irradiator is mounted on a mobile stand that makes it possible to vary the height and direction of the radiation in the horizontal and vertical planes. The irradiator has dimensions of 400 × 400 × 500 mm³ and a weight of about 60 kg.

The installation set also includes a unit of the compensating capacitor bank and a control panel in which all regulating elements and monitoring instruments are concentrated. The installation is powered from an industrial-frequency mains supply at a voltage of 220 V; the power consumption is 1.2 kVA.

The creation of such an installation became possible thanks to numerous theoretical and experimental studies, some of whose results, protected by inventors’ certificates, have now been patented in England, the GDR, the FRG, Switzerland, the USA, France, and Czechoslovakia.

The PMB-6 installation was exhibited at an international exhibition in Vienna and at the international fair in Leipzig, where it was purchased by a German firm.

At present, in the Soviet Union, about 20 such betatrons are being successfully operated at various industrial enterprises of the aviation, shipbuilding, chemical, and other ministries. The Institute has proposals for the supply of another 100–150 units.