ANALYSIS OF THE OPERATION OF A GENERATOR WITH SHARPENING OF THE FRONT OF HIGH-VOLTAGE PULSES ON AN ELECTRODE SYSTEM IN WATER

V. Ya. Simonov, A. F. Usov, V. Ya. Ushakov, A. T. Chepikov

(Presented by the scientific seminar of the High-Voltage Research Institute)

Introduction

The use of impulse-voltage generators—IVG—for generating shock waves in liquids for the purpose of beneficially using their energy has a number of special features. As a source of impulse voltage of hundreds of kilovolts, generators assembled according to the Arkad’ev–Marx multiplication circuit are used, with a capacitance in the discharge of not more than several tens of thousands of picofarads. The load of the generator is a liquid gap, whose resistance, when technical water is used as the liquid medium, may not exceed several tens of ohms. During operation of the generator, considerable unproductive energy losses occur due to the spreading of impulse currents in the volume of the liquid in the prebreakdown time, as a result of which the utilization factor of the discharge circuit is considerably less than 1 [1].

To eliminate these undesirable phenomena, in [2] it was proposed to use the principle of sharpening the front of high-voltage pulses [3], and a method was developed for selecting the circuit elements [4]. Without excluding the possibility of using, as the sharpening capacitance, pulse capacitors manufactured serially by domestic industry, in the developed method preference was given to low-inductance capacitors of special designs.

In the present work, results are considered of experimental investigations of the operation of a generator with sharpening of the front of high-voltage pulses on pulse capacitors of the IM 0.022/100 type, and an analysis of the results obtained is given.

Experimental Method

In the work an impulse-voltage generator was used, assembled according to the Arkad’ev–Marx multiplication circuit on KBGP capacitors. By disconnecting or short-circuiting part of the capacitors, the capacitance of the generator in the discharge was varied within the limits from 0.025 to 0.0625 μF. The nominal voltage of the generator was 400 kV. The sharpening capacitance of 0.0055 μF was made up of four IM 0.022 μF/100 kV impulse capacitors. As the sharpening gap, a spherical spark gap with

with an electrode diameter of 125 mm. The shape of the voltage pulses was recorded with an OK-19M oscilloscope. The generator load consisted of electrode systems of the type of parallel plates, parallel and coaxial cylinders, and asymmetric systems of the rod--plane and sphere--plane type.

In the work, the method developed in [1] was used to analyze the operation of the generator into a load made of a conducting liquid, according to the coefficient of reduction of the amplitude and steepness of the pulse front,

\[ k_{\mathrm{sn}}=\frac{U_{\mathrm{xx}}-U_a}{U_{\mathrm{xx}}}\cdot 100\%. \]

where \(U_{\mathrm{xx}}\) is the pulse amplitude with the load disconnected (no-load operation),

\(U_a\) is the pulse amplitude at the connected electrode device.

To analyze the experimentally obtained dependences, the parameters of the voltage wave on the load were calculated from its low-voltage resistance, using calculated nomograms of the output parameters of the pulse. To measure the load resistance and the specific resistance of tap water, a Kohlrausch bridge circuit was used with a vessel having platinized electrodes and an audio-frequency alternating-voltage source, ZG.

Results of Experimental Investigations

In the work, investigations were carried out of the dependence of the voltage reduction on the generator parameters (pulse amplitude and capacitance in the discharge) and the load parameters (interelectrode distance, surface over which the pulse currents spread, and electrical conductivity of the medium).

As a result of the experimental investigations it was shown that the coefficient of reduction of the pulse amplitude does not depend on the amount of energy stored in the generator when it is varied by changing the discharge capacitance or the operating voltage of the generator. In an electrode system of the type of parallel rods with cylindrical tips (diameter 20 mm, height 30 mm, length of the working gap 30 mm), the reduction coefficient \(k_{\mathrm{sn}}\) in the range of variation of the generator operating voltage from 100 to 350 kV and of the generating capacitance from 0.025 to 0.0625 \(\mu\mathrm{F}\) remained constant and equal to 17--20 percent.

Table 1 gives data on the dependence of the voltage-amplitude reduction coefficient on the magnitude of the interelectrode distance. As is seen from Table 1, changing the latter from 10 to 60 mm does not lead to a noticeable change in the reduction coefficient.

Table 1

The data presented were obtained for an electrode system of the type of solid coaxial cylinders (diameter 20 mm, length 30 mm).

Fig. 1. Dependence of the voltage-amplitude reduction coefficient on electrode area:
● — experimental data,
○ — calculated data \((C_{\mathrm{ud}} = 5.5 \cdot 10^{-9}\ \mathrm{F},\ L = 15 \cdot 10^{-6}\ \mathrm{H})\)

As the investigations showed, only the surface over which the pulse currents spread and the electrical conductivity of the medium have a substantial influence on the voltage-amplitude reduction coefficient.

Figure 1 gives the dependence of the reduction coefficient on the area of the electrode surface in contact with the conducting medium. When the latter is varied from 13 to \(450\ \mathrm{cm}^2\), \(k_{\mathrm{sn}}\) increases from 10 to 50 percent. It should be noted that, in the case of symmetrical electrodes, the reduction in voltage amplitude at a constant area of the uninsulated electrode surface does not depend on the geometry of the plate electrodes. The points shown in Fig. 1, 1–5, correspond to the case in which the electrode surface is varied by increasing their length; points 5–7 correspond to increasing the height of the electrodes at their constant length. As can be seen from the graph, no breaks or bends are observed in the curve \(k_{\mathrm{sn}} = f(F)\). The parameters of the electrode systems are given in Table 2.

Table 2

Figure 2 presents the dependence of the reduction coefficient on the specific resistance of the liquid, \(\rho\). A change in the \(\rho\) of water from \(5.1 \cdot 10^{1}\) to \(8 \cdot 10^{4}\ \Omega \cdot \mathrm{cm}\) is accompanied by a decrease in the reduction coefficient from 88 percent practically to zero. The data presented indicate the advisability of applying methods for increasing the specific resistance of water when using it as a liquid medium in processes of electron-ion technology.

Analysis of the Research Results

In [1] it was shown that, with accuracy sufficient for practical application, the parameters of the voltage wave at the load made of an electrically conducting liquid can be calculated from the low-voltage resistance of the load. The coefficient of reduction of the pulse amplitude, introduced for estimating the operating conditions of the generator, is related to the utilization coefficient of the discharge circuit by the relation

\[ k_{\mathrm{sn}} = \frac{k_{\mathrm{rxx}} - k_{\mathrm{rn}}}{k_{\mathrm{rxx}}}\cdot 100\%, \tag{2} \]

where \(k_{\mathrm{rxx}}\) and \(k_{\mathrm{rn}}\) are the utilization coefficients of the discharge circuit, respectively with the load disconnected (no-load operation) and connected.

Figure 3 presents the equivalent circuit of a generator with sharpening of the front of high-voltage pulses. Calculation of the transient process with respect to the voltage at the load for this complete equivalent circuit is rather complicated and, most importantly, for the existing ratios of the parameters of the primary and secondary circuits does not give a noticeable increase in accuracy in comparison with simplified equivalent circuits.

Fig. 2. Dependence of the coefficient of reduction of the voltage amplitude on the specific resistance of water:
● — experimental data,
○ — calculated data

A feature of this circuit is that, after operation of the sharpening spark gap, a simultaneous discharge of the sharpening capacitance onto the load and onto the generating capacitance occurs. In [4] the latter is neglected, and the utilization coefficient of the generator discharge circuit is determined as \(k_{\mathrm{r}} = k'_{\mathrm{r}}\cdot k_{\mathrm{ro}}\), where \(k'_{\mathrm{r}}\) and

Fig. 3. Equivalent circuit of the discharge loop of a generator with pulse-front sharpening (a) and its Carson operational representation (b).

\(k_{\mathrm{ro}}\), respectively, is the recharge coefficient of the capacitances of the primary circuit and the utilization coefficient of the sharpening circuit. Since \(k'_p\) is determined only by the ratio of the generating and sharpening capacitances and does not depend on the load, formula (2) can be rewritten in terms of the utilization coefficients of the sharpening circuit at no load and with the load connected.

The utilization coefficients of the discharge circuit at no load and with the load connected are measured relative to the voltage on the sharpening capacitance at the instant the sharpening arrester operates, \(U_a\). In the computational processing of the data from the voltage oscillograms at no load, \(k_{\mathrm{rxx}}=1.1\) was adopted. The utilization coefficient of the sharpening circuit is determined using calculated nomograms of the output parameters of the voltage pulse.

The discharge of the sharpening capacitance into the generator can be taken into account by introducing a correction coefficient, for estimating whose magnitude the following procedure is proposed. In Fig. 3b an equivalent circuit of the generator is given for the instant at which the sharpening gap operates; moreover, the initial voltage is taken as the voltage at this instant on the sharpening capacitance, \(U_c=U_a\). The correction coefficient \(\Delta k_p\) is determined from the calculation of the decrease in voltage on the sharpening capacitance \(\Delta U_{c_2}\) when it discharges into the generating capacitance, assuming that the mean value of the voltage of the sharpening capacitance in the time interval \(0 \le t \le t_\phi\) is

\[ U_{c_y}=\frac{1+k_p}{2}U_a. \]

As a result of the calculation we obtain

\[ \Delta k_p=\frac{\Delta U_{c_2}}{U_a} =\frac{(k+k_p)k}{2(1+k)}\cdot(1-\cos \omega t_\phi), \tag{3} \]

where \(k\) is the capacitance-ratio coefficient,

\[ k=\frac{C_2}{C_1}; \]

\(\omega\) is the angular frequency of the primary circuit,

\[ \omega=\sqrt{\frac{C_1+C_2}{(L_1+L_2)C_1C_2}}, \]

\(k_p,\, t_\phi\) are, respectively, the utilization coefficient and the front duration of the pulse in the sharpening circuit.

The numerical value \(\Delta k_p\), determined by formula (3), for conditions corresponding to the experimental dependence \(k_{\mathrm{en}}=f(C_{\mathrm{ud}})\), does not exceed 0.025 at \(C_{\mathrm{ud}}=0.025\ \mu\mathrm{F}\) and 0.01 at \(C_{\mathrm{ud}}=0.0625\ \mu\mathrm{F}\), i.e., it is comparable with the accuracy of processing the experimental data. This makes it possible, when calculating the pulse parameters on the load, not to consid-

be associated with reverse recharging of the capacitances and the calculation carried out using simplified equivalent circuits. The calculated values of \(k_{\mathrm{sn}}\) for the dependence \(k_{\mathrm{sn}}=f(C_{\mathrm{ud}})\) correspond to the experimental data. In the calculation it was assumed that \(L_{\mathrm{ob}}=15\cdot10^{-6}\ \mathrm{H}\), \(C_{\mathrm{ob}}=5.5\cdot10^{-9}\ \mathrm{F}\), \(R_{\mathrm{n}}=145\ \Omega\), and the following were obtained: \(k_{\mathrm{r}}=0.88\), \(k_{\mathrm{sn}}=20\%\).

The dependences of the voltage-amplitude reduction coefficient on the interelectrode distance, voltage, and specific resistance of the water are analogous to those obtained earlier for the rod–plane system, which indicates the generality of the generator operating conditions for various types of electrode devices. The parameters of the voltage wave on the electrode device are determined not by the type of electrode system and the specific features of the conditions of its use, but by the parameters of the generator discharge circuit. In this sense the electrode systems differ only in the magnitude of the resistance and capacitance of the load, which depend not only on the geometry of the systems but also on the dielectric properties of the medium: the dielectric permittivity and specific resistance of the solution.

The coefficients of utilization of the discharge circuit \(k_{\mathrm{r}}\) and of reduction of the voltage amplitude \(k_{\mathrm{sn}}\) vary in accordance with the change in load resistance. The small change in \(R\) with increasing interelectrode gap (Table 1) corresponds to the practical constancy of \(k_{\mathrm{sn}}\). A considerable decrease in load resistance with an increase in the electrode area (Table 2) and a decrease in the specific resistance of the liquid medium (Fig. 1) is the cause of the substantial increase in \(k_{\mathrm{sn}}\).

As calculations show, the reduction of the voltage amplitude may be neglected if the resistance of the electrode system in water is brought to \(500\ \Omega\). Two-electrode systems have this order of resistance even when technical water with a specific resistance of \(3\cdot10^{3}\ \Omega\cdot\mathrm{cm}\) is used. In multielectrode systems, these values of load resistance can be obtained only when water with an increased specific resistance is used.

Conclusions

1. The operating conditions of a pulse-voltage generator on a load consisting of an electrically conducting liquid are determined not by the type of electrode system and the specific features of the conditions of its application, but by the load parameters as an element of the discharge circuit. Similar dependences in different electrode systems have one and the same character.

2. A significant dependence of the reduction coefficient is found only on the electrode area and on the specific resistance of the liquid medium. Accordingly, a substantial increase in load resistance can be achieved only by reducing the electrode surface and by using, as the liquid medium, liquids with considerable specific resistance. From the standpoint of the possibility of obtaining a voltage wave with the required parameters, it is sufficient to bring the specific resistance of the medium to values of \(5\cdot10^{4}\div10^{5}\ \Omega\cdot\mathrm{cm}\). A further increase in \(\rho\) is hardly economically expedient.

3. In the work a number of circuit problems have been solved; in particular, a method has been developed for calculating the parameters of the voltage wave on the load in a circuit for sharpening the front of high-voltage pulses, taking into account the reverse recharging of the capacitances.

References

1. I. I. Kalyatskii, A. F. Usov. Breakdown of dielectrics and semiconductors. In: Proceedings of the Fourth Interuniversity Conference on the Breakdown of Dielectrics and Semiconductors, “Energiya,” Moscow–Leningrad, 1964.

2. A. F. Usov. Izv. TPI, vol. 139, pp. 88–96, 1965.

3. G. A. Mesyats. Author’s certificate No. 156616 of June 19, 1962.

4. A. F. Usov. Izv. TPI, vol. 152, pp. 24–31, 1966.