CURRENT STATE OF THE THEORY AND PRACTICE OF ELECTROSTATIC MACHINES AND PROSPECTS FOR THEIR DEVELOPMENT

A. A. VOROB’EV, A. F. KALGANOV, V. V. PASHCHEVICH

(Presented by the scientific seminar of the Research Institute of High Voltages)

The rapid development of science and technology in the present period is characterized not only by swift progress in their newest fields, but also by the revival, at a higher level, of discoveries, phenomena, and processes that had appeared earlier and then were rejected or forgotten.

One example of this latter tendency is the revival of interest in electrostatic machines (ESM).

The weaker development of electrostatic machines, which appeared almost two centuries before electromagnetic ones, was explained by the lack of a solution to their basic problem as converters of one form of energy into another—the problem of obtaining high specific electromechanical power per unit volume or weight of the machine. This was mainly connected with the absence, until recently, of the scientific and technical foundations for solving problems of the maximum concentration of electric-field energy in moving systems, and with the lack of the necessary materials, such, for example, as electrically and mechanically high-quality dielectrics.

The progress achieved to the present time in the creation of new solid dielectrics with high electrical and mechanical properties, and progress in the study of the electrical properties of gaseous, liquid, and solid dielectrics and of their behavior in strong electric fields, have contributed substantially to the solution of the questions indicated above. A great influence on the development of electrostatic machines was exerted by establishing a broad analogy between electrostatic and electromagnetic machines. This analogy, on the one hand, is a reflection of the unity of the electromagnetic field; on the other hand, it reflects specific phenomena connected with different aspects of the single electromagnetic field.

The establishment of an analogy between electrostatic and electromagnetic machines made it possible, from scientific positions, to assess the place of electrostatic machines among other converters of mechanical energy into electrical energy, and also to determine the conditions and paths for improving the energy characteristics of electrostatic machines. An ESM is an electrical machine in which, instead of electromagnetic induction, magneto-electric induction is used.

The basic condition for high energy efficiency of electrostatic machines reduces to obtaining high specific power, comparable with the specific power of electromagnetic machines. In compari-

conditions. In this case, if the specific energy of the magnetic field of an electromagnetic machine depends mainly on the magnitude of the magnetic induction, i.e., on the magnetic permeability of the magnetic circuit, then the specific energy of the electric field of an electrostatic machine is determined by the magnitude of the field strength.

The need to provide high electric-field strengths and to concentrate its energy also determined the scientific principles for designing electrostatic machines, such as: a rigid rotor system and a stator made of semiconducting material, ensuring a uniform field distribution; the use of compressed gases or vacuum and small but strictly defined gaps, which help increase the electric strength of the medium; and so forth.

It must be noted that the works of Soviet scientists (Acad. A. F. Ioffe and others) had an exceptionally great influence on the development of electrostatic machines.

The heightened interest currently being shown in electrostatic machines is not accidental. The point is that such machines possess a number of properties and advantages that are peculiar only to them and that in many cases make it necessary to give them preference.

First, electrostatic machines can directly generate or consume high-voltage current at hundreds of thousands and millions of volts. When they are used as power installations, the need for step-up or step-down transformers is therefore eliminated.

Second, electrostatic machines, by their nature, are best adapted to generating or consuming high-voltage direct current. In this case there is no need for rectifier devices.

Third, it is theoretically possible to create electrostatic machines for the same powers as electromagnetic machines, but with greater specific power per unit volume and weight. This is explained by the fact that the field in the gap of an ESM, owing to its discontinuity, does not require a flux conductor and can be concentrated in the greater part of the volume occupied by the machine in its disk-type design.

It follows from the foregoing that the use of electrostatic machines can make it possible to facilitate significantly the solution of the problem of long-distance transmission of electrical energy, the electrification of railway transport, and other tasks with an enormous economic effect. In practice, thanks to the expenditures of scientific thought and the contribution of industry that have been realized, electrostatic machines of small power have at present achieved a certain development, mainly as electrostatic generators (ESG). The possibility of obtaining high constant voltage with a small ripple, reaching tenths and hundredths of a percent, makes the ESG indispensable for accelerator technology, electronics, radiation chemistry, laboratory and control-measuring apparatus, etc.

It is necessary to note certain advantages of ESGs over other high-voltage sources. At present, in many cases, cascade-valve installations, or so-called cascade generators, are used to obtain high voltage. And they have proved successful, being constructed for voltages up to several million volts and currents up to several milliamperes, in a number of cases having better specific characteristics than ESGs. However, as soon as large currents are involved, cascade generators are forced to yield their place to electrostatic generators. There-

...for example, in radiation chemistry, which requires high-voltage installations with powers of tens of kilowatts, see the path of development specifically through electrostatic generators. To this it must also be added that electrostatic generators prove unsurpassed in the stability of high voltage, estimated, as already noted, in hundredths of a percent. As a low-power source of constant high voltage with small ripples, an electrostatic generator at the same time has low energy capacity, which ensures almost complete safety of its use where frequent short circuits are inevitable or possible.

Of the various types of electrostatic generators, capacitive generators are at present receiving preferential development; they are divided into two main classes: electrostatic generators with conductor carriers (ESGP) and electrostatic generators with a dielectric carrier (ESGD). In structural terms, capacitive electrostatic generators in most cases are rotating machines of disk or cylindrical design. In this case the conducting carriers have the form of disk sectors, cylinder segments, or rods. Figure 1 shows the circuit of an ESGP in cascade connection.

Fig. 1. Circuit of an electrostatic generator with cascade connection of conductor carriers.

In electrostatic generators with a dielectric carrier, cylinders have replaced the belt. The circuit of a cylindrical ESGD is shown in Fig. 2.

Although the operation of capacitive electrostatic generators is based on one and the same principle of changing the capacitance of a system of charged solid bodies, each class has its own specific features, determined mainly by the character of the switching devices. They also differ in their energy capabilities. Thus, an electrostatic generator with conductor carriers with a limited number of carriers has a maximum power one-half the maximum power of a generator with a dielectric rotor, all other conditions being equal.

Theoretical studies carried out by us to determine the rational design of an electrostatic generator have shown that the power of an electrostatic generator with conductor carriers increases by a factor of two, i.e., becomes equal to the power of an electrostatic generator with a dielectric rotor, if the number of conductor carriers is increased to infinity [1]. It was shown that, all other conditions being equal (overall dimensions, form of construction, etc.), an electrostatic generator with a dielectric carrier develops the greatest specific power in comparison with other types of electrostatic generators. This is explained by the fact that in an ESGD the electric field is most uniform, and the forces of the electric field are used with the greatest efficiency in time and in space.

The conditions characteristic of an ESGD are approached by those attained in electrostatic generators with conductor carriers embedded in a dielectric.

From the practical point of view, the preferred type of electrostatic generator is determined by the possibilities of its realization, its purpose, and other external or internal factors.

At the present time, the best practical development has been achieved by electrostatic generators with a cylindrical dielectric rotor (Fig. 2). For example, the French firm “Sames” has for several years been producing in series about two dozen types of rotary electrostatic generators for voltages from 80 to 600 kV and currents from 0.3 to 40 mA, characterized by high voltage stability, a relatively long service life (about 10 thousand hours), and simplicity and safety of maintenance.

Fig. 2. Electrostatic generator with a cylindrical-type dielectric transporter.
1—rotor, 2—cylindrical stator, 3—inductor, 4—stator body, 5—dielectric frame, 6—dielectric shield, 7, 17—flanges, 8—metal casing, 9—drive shaft, 10—coupling, 11, 13, 15, 16—bearings, 12—rotor shaft, 14—ionizer (blade tape).

The cylindrical design of rotary electrostatic generators with dielectric transporters does not, however, make it possible to count on obtaining large specific and absolute powers, owing to the small ratio of the area of the working surfaces to the total volume occupied by the generator, and owing to limitations on overall dimensions.

The disk design of an electrostatic generator makes it possible to increase the ratio of area to volume, but for electrostatic generators with dielectric transporters the effect is considerably weakened by the need to provide each disk with commutating devices. For the disk design, electrostatic generators with conductor transporters are better suited. It is apparently precisely this fact that explains why some American firms are designing, or have already built, disk electrostatic generators for voltages of more than one million volts and powers of several tens of kilowatts, intended primarily for radiation chemistry [2].

On the other hand, the development of electrostatic generators with conductor transporters encounters difficulties of a new order. First, experience in operating electrostatic generators with conductor transporters shows that the brush-commutator commutation system, inevitably used in direct-current generators, does not meet the requirements of long-term operation. The sparking that occurs causes separation of the contacts, which leads to contamination of the working medium with metallic dust and, consequently, to deterioration of the generator’s energy characteristics. Second, many important issues have still not been solved.

theoretical questions concerning methods for calculating ESPGs, the conditions of natural recharging in them, etc.

In ESGs, as in electromagnetic machines, an armature reaction is observed, causing the generator voltage to decrease as its current increases. This question was first investigated in sufficient detail for its time by Academician A. F. Ioffe and his colleagues [3]. It was shown that the cause of this is the so-called parasitic capacitances. Later, the influence of parasitic capacitances was studied in more detail by the French [4]. In this work, A. F. Ioffe and his colleagues took into account only the parasitic capacitance to ground, while the French considered only an ESG with a minimal number of transporters, equal to two. Therefore, in practice, in most cases the electrical calculation of an ESG was carried out on the basis of the most general relationships, when the generator current was calculated by the formula

\[ I_0 = 2mn C_1 U_1 = g_0 U_1, \tag{1} \]

while the voltage was estimated approximately and served only as a guide for comparison with the actually obtained value. In the above equation \(C_1\) is the useful capacitance of one transporter, \(m\) is half the number of transporters, \(n\) is the number of rotor revolutions per second, and \(U_1\) is the excitation voltage. At the present time, when corona in ESGs is eliminated by giving the transporters appropriate dimensions and shape, the voltage of an ESG is determined with sufficient accuracy from the dielectric strength of the medium used and the principal dimensions of the generator. But the calculation problem, generally speaking, has never been and is not reducible to the determination of voltage. Since voltage is a quantity fixed at its maximum for a given ESG, the calculation of an ESG reduces to determining its maximum operating current, or to determining its dimensions for a prescribed operating current.

On the basis of a development of Academician A. F. Ioffe’s ideas, we have obtained a refined formula for the current of an ESPG, which can also be extended to an ESGD:

\[ I = \delta g_0 (U_1 - \alpha U_{\mathrm{н}}). \tag{2} \]

Here \(\delta\) is a coefficient accounting for the phenomenon of recharging or undercharging,

\[ \alpha \]

is a coefficient accounting for armature reaction,

\[ U_{\mathrm{н}} \]

is the load voltage of the ESG.

There are several possible ways to use equation (2). The first way is practical. Estimating, from previous experiments, the values of the coefficients \(\delta\) and \(\alpha\) for individual types of ESGs, as is practiced in machine building, one can calculate the corresponding type of ESG for the required power. The accuracy of the calculation is greatly increased.

The second way is analytical, but it also leads to practically important results. By evaluating the essence of what the coefficients \(\delta\) and \(\alpha\) represent, one can find means of controlling them in order to increase the energy efficiency of an ESG. From (2) it is evident that, in order to increase the current, it is necessary to have as large a value of \(\delta\) as possible and as small a value of \(\alpha\) as possible. As theoretical investigations of the generator circuits in Fig. 1 have shown, the values of the coefficients \(\delta\) and \(\alpha\) depend in a complex manner on the ratio of the individual partial capacitances of the ESG, i.e., ultimately, on the dimensions, shape, and mutual arrangement of the rotor and stator elements, as well as on the number of these elements [5]. It has been shown, in particular, that recharging in an ESPG with a large number of elements is due to the presence of capacitance between adjacent rotor elements and that, for example, when this capacitance is equal to the useful capacitance (between rotor and stator elements), the coefficient \(\delta\) is approximately equal to 2. Further—

...a further increase in the ratio of these capacitances causes only an insignificant increase in \(\delta\). It has also been shown that additionally taking into account the stray capacitances of the transporters to ground “causes” a decrease in the coefficient \(\delta\).

The practical results following from studies of ESMs through partial capacitances consist in the fact that this approach makes it possible to assess realistically the effectiveness of various types of ESM. In this way, in particular, evidence has been obtained of the high energy efficiency of ESMs with embedded rods, as well as a large number of practical recommendations for the design of the latter. It may even be said that at present this is the most fruitful path for further research and development of ESMs.

Fig. 3. Some types of ESMs made at the Tomsk Polytechnic Institute:
a) self-excited ESMP rated at 50 kV, 120 μA; b) rod-type ESMP rated at 100 kV, 100 μA; c) ESMP with a double rotor rated at 120 kV; d) electrostatic ignition generator rated at 21 kV.

Figure 3 shows photographs of a number of small-size ESMPs built by us, which served as models for testing both theoretical and design developments. The most difficult problem proved to be that of contact commutation, which does not ensure a long service life for the ESM. More successful were the experiments with an ESMP using corona commutation. The ESMP used for these experiments is shown in Fig. 4. The generator is of disk construction. Thin U-shaped wires embedded in a dielectric were used as transporters. The charges on the transporters—the wires (in the experimental generator their number was 200)—were applied by means of a corona produced by ionizers in the form of thin plates.

It is not without interest to note the tendency of some researchers to bypass the problems of commutation in ESMs by using alternating-current generators with subsequent rectification [6]. Under the specific conditions of space, when very high voltages are not required and when high rotor speeds can be achieved in a vacuum, this approach...

may prove advisable, but, as it seems to us, it cannot be regarded as universal, determining the direction of development of electrostatic generators and converters (ESGP). Further research is needed on problems of commutation in ESGP.

Until now we have considered electrostatic generators intended for operation in compressed gases or in vacuum. In the search for new possibilities for increasing the specific powers of electrostatic generators (ESG), the literature is increasingly considering the question of using other dielectric media, such as liquid and solid dielectrics with high dielectric permittivity. The use of such media would bring about a revolution in ESG construction, but so far this question has not gone beyond pure ideas or exploratory experiments [7—9].

The prospects for ESG as high-voltage apparatus or as powerful energy sources appear enormous. This can be judged both from the wealth of ideas concerning their future development and from the results already achieved. Their field of application is broad; individual examples of it have already been given above. The immediate prospect of using ESG in electron-ion technology is especially great. As is known, the technology of processing products in an electric field is now becoming most widely disseminated because of its high efficiency and, in a number of cases, its indispensability. Electrostatic machines and apparatus, by their very nature, are, as it were, intended for their use in this field. The task is to place theoretical research and practical development of ESG on a broad and firm foundation.

Fig. 4. Disk ESGP with an increased number of carriers.
1, 7—inductors; 2, 8—brush holders; 3—ionizer; 4—U-shaped wire carriers; 5—semiconducting layer of the stator; 6—rotor.

REFERENCES

1. A. F. Kalganov and V. V. Patsevich. Izvestiya vuzov, “Elektromekhanika,” No. 8, 917, 1963.

2. Engineer 209, No. 5426, 152, 1960.

3. A. F. Ioffe. Zh. T. F. 9, No. 23, 2071, 1939.

4. R. Morel, Contribution à l’étude rationelle des machines électrostatiques, Grenoble, 1948 (dissertation).

5. V. V. Patsevich. Some Questions in the Theory and Calculation of ESG with Wire Carriers, dissertation, Tomsk, 1964.

6. J. G. Trump. Report at the 102nd International Seminar of the National Center for Scientific Research of France, Grenoble, 1960.

7. N. J. Felici. Report at the 102nd International Seminar of the National Center for Scientific Research of France, Grenoble, 1960.

8. L. S. Polotovsky. High-Voltage Direct-Current Capacitive Machines, Gosenergoizdat, 1960.

9. V. L. Lavrovsky. “The problem of a high-power capacitive generator for power-engineering purposes,” report at the IV Inter-Institutional Conference on Electron Accelerators, Tomsk, 1962.