Some Studies of a Disk ESG

Yu. N. Sivkov

(Presented to the scientific seminars of the Department of Theoretical Foundations of Electrical Engineering and of the rotor ESG sector of the Research Institute of Nuclear Physics)

High-voltage direct current is needed in many fields of science and technology. These include processes of electron-ion technology, X-ray engineering, radiolocation, nuclear physics, radiation chemistry, etc. Sources of high-voltage direct current must be compact, reliable, safe, and in some cases highly voltage-stable.

In the overwhelming majority of cases, electrostatic generators (ESG) with a rigid rotor meet the listed requirements to the greatest degree. Such ESG may have two designs: cylindrical and disk.

Recently, ESG with carrier-conductors located inside a dielectric have become promising with respect to the possibility of increasing the specific power. The most convenient form of these carriers is rod-shaped, in connection with which the generators themselves have received the name rod generators.

As shown theoretically [1], the power of an ESGR approaches the power of an ESGD under equal conditions (per one side of a disk or cylinder of a rotor of identical dimensions), if the rotor carries an infinitely large number of carriers. In practice this power ratio is attained with a comparatively limited number of rods. The advantage of the rod generator consists in the fact that its rotor can be charged from both surfaces. This makes it possible almost to double the power of such generators in comparison with the power of an ESGD of equal dimensions.

The best utilization of the volume occupied by the rotor and stator of a rod generator will occur in the case of a disk design of the latter. The fundamental possibility of creating a disk ESG with a large number of carrier-conductors was shown in [2].

We set ourselves the task of designing and manufacturing a single-disk model of a rod ESG with the aim of further refining its current capabilities.

The generator produced had two pairs of poles. Its schematic section, passing through the low-voltage and high-voltage systems, is shown in Fig. 1. The diameter of the rotor along the outer ends of the carriers was \(D_2 = 228\) mm, and along the inner ones \(D_1 = 138\) mm. The carriers represent

are pieces of copper wire 0.27 mm in diameter, the number of which per row is 597. The depth of the transporters from the surface of the rotor disk is 2 mm. The thickness of the rotor at the location of the transporters is 9 mm. The gas gap between the rotor and stator of the assembled generator was 1 mm. The commutation system provided was gas-discharge. The generator was set into rotation at a speed of \(n = 2860\) rpm \(= 47.6\) rps.

Fig. 1. Schematic cross-section of a disk-type rod ESG:
1—rotor disk; 2—shaft; 3—bearings; 4–5—flanges; 6—two rows of rod transporters; 7—low-voltage grounded brush; 8—excitation inductors; 9—high-voltage brush; 10—high-voltage inductors; 11—generator stators

The constructed generator was tested during operation in a hydrogen atmosphere. In Fig. 2 the short-circuit characteristics of the generator at various pressures are presented.

Let us estimate the obtained values of the generator current. For this purpose we shall use the method applied to an ESGD [3], namely: we shall find the magnitude of the charge density \(\sigma\) removed from the working surface

of the rotor disk, i.e., the surface occupied by the transporters in the short-circuit mode,

\[ \sigma=\frac{I_{\text{s.c.}}}{n\cdot S\cdot p}, \tag{1} \]

where \(S\) is the working surface of the rotor disk on both its sides.

\[ S=2\pi\cdot\left(\frac{D_2^2}{4}-\frac{D_1^2}{4}\right) =2\pi\left(\frac{22.8^2}{4}-\frac{13.8^2}{4}\right) =520\ \text{cm}^2 . \tag{2} \]

At a hydrogen pressure \(P=16\ \text{ati}\) and an excitation voltage \(U_{\text{v}}=21\ \text{kV}\), in accordance with curve 7 in Fig. 2, the short-circuit current is \(I_{\text{s.c.}}=1000\ \mu\text{A}\). Then

\[ \sigma=\frac{1000\cdot 10^{-6}}{47.6\cdot 520\cdot 10^{-4}\cdot 2} =2.02\cdot 10^{-4}\ \text{C}/\text{m}^2 =60.5\ \text{CGSE units}. \]

Fig. 2. Short-circuit characteristics of a disk and rod ESG, taken in a hydrogen atmosphere at various pressures \(P\):
1—\(P=16\ \text{ati}\); 2—\(P=13\ \text{ati}\); 3—\(P=8.5\ \text{ati}\); 4—\(P=6.4\ \text{ati}\); 5—\(P=4.9\ \text{ati}\); 6—\(P=2.4\ \text{ati}\); 7—\(P=1.3\ \text{ati}\).

It is known from [4] that industrial cylindrical ESGs have

\[ \sigma' = 60\div 90\ \text{CGSE units}. \]

Thus, for a small-size generator of size “70,” operating in hydrogen at a pressure of \(15\ \text{ati}\), one has: \(\sigma=90\) CGSE units in the short-circuit mode and \(\sigma=70\text{–}75\) CGSE units at the nominal voltage of \(90\ \text{kV}\).

From a comparison of the data obtained by us for the disk ESG and the literature data for the cylindrical ESG, it follows that the averaged surface density \(\sigma\) of the charges transported in the disk ESG is approximately \(2/3\,\sigma'\) for the ESG on one side of the rotor. Taking into account the fact that in the disk ESG both sides of the rotor disk are usefully employed, one may state that the overall efficiency of the disk ESG with respect to the density of the transported charge exceeds that for the ESG, amounting to

\[ \eta=\frac{2\sigma}{\sigma'}=\frac{4}{3}. \]

This value, however, still remains considerably smaller than \(\eta=2\), which follows from theoretical estimates, and is explained by the fact that the rotor–stator gap in our generator was comparatively large (1 mm). For the ESG, the obtained charge densities \(\sigma'=90\) CGSE units correspond to a gap of 0.3 mm. By reducing the gap in the disk ESG to the value of the gap in the ESG, it is possible to increase significantly the charge density \(\sigma\) and the efficiency \(\eta\to 2\).

The tests carried out on a single-disk electrostatic gyroscope with a large number of transporters placed in a dielectric thus prove the possibility of creating an ESGP with improved specific energy characteristics in comparison with an ESGD.

REFERENCES

1. A. F. Kalganov, V. V. Patsevich. Izv. vuzov. “Elektromekhanika”, 1963, No. 8.
2. V. V. Patsevich, Some questions of the theory and calculation of an ESG with conductor transporters. Dissertation, Tomsk, 1964.
3. N. J. Felici, A. F. Kalganov. ZhTF, 22, 1001, 1962.
4. Ed. by K. G. V. Ivetonova and Ph.D. A. P. Lyapina. The application of electric forces in industry and agriculture. Based on the materials of the International Colloquium devoted to the physics of electrostatic forces and their application (Grenoble), VNIIZEM, Moscow, 1964.