V.5 No 1

33

On physical processes in showering arcs

3. Analysis of improved model of showering arc

The full amount of yielded results, and especially the two-stage pattern of processes in each period of unstable discharges having the exponential pattern of monotonous section and high-amplitude oscillation pattern of the section of break of monotony, requires to apply a basically other than before approach to the model of processes occurring in the contact gap.

According to the theories of electric [15, 23, 24] and radio [25, 26] circuits, no one circuit with constant either smoothly varying parameters can give so complicated curve for transient voltage, the more complicated by passing from the monotonous regime to that oscillation with an abrupt change of the process amplitude. The abrupt transition from one process to another is possible only in case of surge-like change of some parameter of any element of circuit. Noting the specific pattern of between-the-stages transition, we have to conclude, in the studied case only electric contacts can be such elements, when by some physical reasons their resistance changes in the surge-like way.

To clear this issue, consider the conditions under which the monotonous and oscillation processes occur at the contacts. Let us analyse the switched electric circuit for two cases: when the contacts after the bridge break were shunted only by a parasitic capacitance, as it was thought before, and when they were additionally shunted by a resistance.

The equivalent circuit in which the contacts can be presented as a parasitic capacitance is shown in Fig. 15.

Fig. 15. Equivalent for the contact circuit in which the contact gap has been substituted by the parasitic capacitance

First of all, we see here the source of current I₀ inserted in parallel with the inductance. As we have revealed in the experimental part of this work, just the energy accumulated in the capacitance causes the overvoltage appearance and its consequence - unstable discharges. In the monotonous section it plays part of additional source charging the capacitance of gap, and in the section of voltage surges its affection just causes the high-voltage pattern of oscillation process in the circuit.

The characteristic equation for the chain shown in Fig. 15 is the following (see, for example, [23. 26]):

According to (1), the studied oscillation process in the circuit will be possible with complex roots of equation, namely with

If we substitute to (2) the approximate orders of the values of parasitic capacitance and resistance of inductance C_p=100 F and R_L = 1000 Ohm, we will yield that the periodic process in this circuit takes place under L > 25 H . This value is well less not only than the inductive load used in the circuit but even than the parasitic capacitance of wires typical for the circuits having contacts. Thus, should during the capacitance charging the contact gap was shunted only by the capacitance, in this circuit, at trivial conditions, there could arise only periodic high-voltage oscillation processes interrupted by short arcs, and monotonous sections would be absent.

According to (1), the resonance frequency of voltage oscillation in this circuit is

which means the oscillation frequency

When we substitute into (4) the above value of parasitic capacitance and inductance corresponding to the start of periodic process in this circuit, we will yield the estimated limiting value of the resonance frequency f₀ =   1,0065 MHz  or the oscillation process period T₀ =  0,9934 s .   The order of these values is in quite good agreement with the results shown in the oscillograms Fig. 14. At the same time, if we substitute to (5) the values at which we yielded the oscillogram Fig. 14a, we will yield f₀ =  1,0065 kHz and  T₀ =  770 s ; this evidences, the equivalent circuit in Fig. 15 is incomplete.

Thus, we can conclude, equivalent circuit in Fig. 15 describes on the whole the stages of voltage surges, though needs to be well improved.