Proceedings of the Tomsk Order of the October Revolution and Order of the Red Banner of Labor Polytechnic Institute named after S. M. Kirov

Vol. 244　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1972

STUDY OF THE OPERATION OF A SMALL-SIZED ELECTROSTATIC GENERATOR

A. P. Kononov, V. A. Lukutin, L. M. Leus, A. I. Naletov

(Presented by the scientific seminar of the Department of Theoretical Foundations of Electrical Engineering and by the RESG Department of the Research Institute of Nuclear Physics)

A large number of works published in recent years have been devoted to the study of the operation of electrostatic generators with disk- and cylindrical-type conductor carriers [1, 2]. All these studies were carried out on generators with a rotating rotor either in air or in a compressed-gas medium.

This article presents the results of a study of an electrostatic generator in which rotating parts are absent. These conditions make it possible to dispense with bearings, lubrication of rubbing elements, and a cooling device. The developed and constructed small-sized generator without rotating parts is placed in a glass cylinder 7.5 cm in diameter and 15 cm long; it has two plates, one of which can move, while the other is fixed immovably. The area of one plate is 15 cm²; the minimum gap between the plates was set at 0.05 cm, and the fixed plate was coated with fluoroplastic with \(\varepsilon_r = 2\).

The magnitude of the charge deposited on the moving plate can be determined by the formula

\[ q = C_1 U_{\mathrm{v}}, \tag{1} \]

where

\[ \begin{aligned} q &\text{ — magnitude of the deposited charge, in coulombs;}\\ C_1 &\text{ — charging capacitance, in farads;}\\ U_{\mathrm{v}} &\text{ — excitation voltage, in kV.} \end{aligned} \]

The charging capacitance can be determined by the formula for a plane capacitor, taking into account the edge effect [3]:

\[ C_1 = \frac{1.2 \varepsilon_0 \varepsilon_{\mathrm{r}} S}{d}, \tag{2} \]

where

\[ \begin{aligned} S &\text{ — plate area, in m}^2,\\ d &\text{ — distance between the plates, in m.} \end{aligned} \]

Assuming that the deposited charge is transferred completely to the load, and first determining the discharge capacitance \(C_2\) by formula (2), one can calculate the load voltage by a formula analogous to equation (1):

\[ q = C_2 U_{\mathrm{n}}, \]

where

$C_2$ — discharge capacitance in pF,
$U_{\mathrm{n}}$ — load voltage in kV.

Preliminary calculations showed that the developed generator is capable of producing a load voltage $U_{\mathrm{n}} = 50$ kV at a current $I_{\mathrm{k}} = 10$ μA and at an excitation voltage $U_{\mathrm{v}} = 2$ kV.

A number of experimental studies were carried out on a prototype of the ESG made at the Department of TOE of TPI. Thus, for example, the short-circuit current characteristics and the load characteristics were taken both in air and in vacuum. The influence of the vacuum depth on the above-mentioned characteristics of the generator was investigated.

When taking the characteristic of the short-circuit current as a function of the excitation voltage in air, it was observed that saturation occurs at low excitation voltages (0.6 kV).

A further increase in the excitation voltage (above 0.6 kV) leads to breakdown between the generator electrodes. The characteristic $I_{\mathrm{kz}} = f(U_{\mathrm{v}})$ for air is presented in Fig. 1 by curve 1. Similar characteristics were obtained when the generator operated in vacuum. The experimental characteristic $I_{\mathrm{kz}} = f(U_{\mathrm{v}})$ at a vacuum of $1 \cdot 10^{-5}$ mm Hg is shown in Fig. 1 by curve 2. The calculated dependence is also presented in the same figure by curve 3.

Fig. 1. Dependences $I_{\mathrm{kz}} = f(U_{\mathrm{v}})$: 1 — experimental, taken in air; 2 — experimental, taken at a vacuum of $1 \cdot 10^{-5}$ mm Hg; 3 — calculated.

When comparing the obtained dependences, it can be noted that the dependence $I_{\mathrm{kz}} = f(U_{\mathrm{v}})$ taken in vacuum is similar to the calculated one, whereas the dependence of the short-circuit current on the excitation voltage taken in air differs very strongly from the calculated one. This difference is explained by the insufficient electrical strength of air. This once again indicates that a high vacuum is the medium in which very high voltages can be obtained without reaching breakdown between the generator plates.

The load characteristics $U_{\mathrm{n}} = f(I_{\mathrm{n}})$ taken on this same generator are shown in Fig. 2. Curve 1 was taken in air at $U_{\mathrm{v}} = 0.6$ kV, curve 2 is the calculated curve at $U_{\mathrm{v}} = 1$ kV, and curve 3 is for various excitation voltages. The indicated characteristics were taken at a vacuum of the order of $1 \cdot 10^{-5}$ mm Hg.

In addition, on the experimental generator a study was carried out of the influence of the vacuum depth on the electric strength of the medium. As the studies showed, the lowest electric strength of the medium, significantly worse than in air, is observed at a vacuum on the order of \(1 \cdot 10^{-1}\) mm Hg.

Fig. 2. Dependences \(U_{\mathrm{n}} = f(I_{\mathrm{n}})\):
1—experimental, taken in air; 2—calculated; 3—experimental, taken under vacuum at various excitation voltages.

Further deepening of the vacuum leads to an increase in the electric strength of the medium. Therefore, a high vacuum is the medium in which high voltages can be obtained without breakdown between the electrodes.

REFERENCES

1. Izv. TPI, vol. 149, 1966.
2. Izv. TPI, vol. 191, 1960.
3. A. P. Kononov. Izv. vuzov, “Elektromekhanika,” No. 3, 1966.