V.5 No 1

35

On physical processes in showering arcs

To understand the affection of nonlinearity introduced by the high-frequency breakdown of the gap onto the pattern of oscillations in the circuit, we can make a simple and visual analogy with oscillations in a mechanical system. Imagine some charged particle evenly moving along the axis x in a transverse electric field whose amplitude harmonically depends only on time. Then the resulting trajectory of the body will be some harmonic curve whose period will be determined by the external field, and the wavelength of these oscillations as to axis x will depend on the speed of particle's motion, as the system of modelling equations will be

where m, q are the mass and charge of the body, and  E₀ , , ₀  are the amplitude, frequency and initial phase of the outer electric field.

The solution of this system is

where x₀,  y₀ are the coordinates of initial location of the body, and V_x0 , V_y0   are the projections of initial speed of the body.

The shape of this solution at zero values of the initial location of the body, V_y0 and zero initial phase of the outer field is shown in Fig. 17.

Fig. 17. Trajectory of the body's motion in the transverse electric field

This curve corresponds to the trajectory of beam motion on the oscillograph screen. This is just the pattern which we would see on the screen, if free of limitations introduced by breakdown phenomena. The oscillation frequency would fully fit to our above calculation.

Now let us complicate the problem, introducing some horizontal boundaries from which the studied body reflects in its motion. For a full analogy with electric circuit, introduce that in reflection from the boundary, not only y-projection of the body's speed changes but the phase of outer field changes also in the same way, shifting just by the half-period. So we account the processes introduced to the oscillation process by breakdown phenomena, changing the phase of oscillation process in the circuit. Noting that out of boundaries the body still moves as (9), we can record the modelling equations for this sectionally-smooth motion as the first derivatives

where t_b is the instant when the body is reflected from boundary, and sign (t - t_b ) is the function of sign:

We can easily yield the solution for (11), using the sectionally-smooth type of model. The typical trajectory is shown in Fig. 18.

Fig. 18. Trajectory of the motion of charged body in the external transverse electric field, when its motion was limited by horizontal boundaries; red dotted line denotes the trajectory without limitation of motion

We see from the plot that when we introduced the horizontal boundaries, it considerably increased the frequency of body's oscillations as to axis x. The shape of oscillations also changed, they became acute-angled, with inequal inclination to x. This is well seen in Fig. 19 which repeats the trajectory shown in Fig. 18 in enlarged scale.

Fig. 19. Trajectory of the motion of charged body in the outer periodic transverse electric field in presence of boundaries, enlarged

Of course, this analogy is too limited, it does not take into account most features of high-frequency breakdown. None the less, if we compare the oscillation pattern in the beginning of Fig. 19 with typical curves of voltage change in the region of high-voltage oscillations in Fig. 14, especially in Fig. 14 a, we will find full analogy. This just corroborates the above statement of the cause of so much deformed shape of oscillation process. As the analogy with mechanical oscillation process showed, due to high-frequency oscillations in electric circuit superimposed on the gap breakdown process, there arises a limitation in oscillations and at the same time their frequency grows and shape is nonlinearly deformed. And this is just the nuance ignored by the linear equivalent circuit in Fig. 15. It is important to mark here, the gap breakdown cannot occur immediately after the monotonous section has been finished. A simple fact says of it: in this case the high-frequency would not be superimposed on the process forming the gap breakdown. With it, the gap resistance due to the breakdown has to fall abruptly and in this way to prevent the voltage surge, and the shown oscillograms corroborate it.

As a physical model of resistance able to shunt the gap, we considered three possible phenomena: decaying plasma, glow discharge and metallic bridge. This consideration showed that decaying plasma cannot shunt the gap during all time of monotonous charging of the capacitance, as the time of its dispersion is well less. So it has been found [27] that plasma decay time is estimated by the value (1 - 10) s. At the same time both after Mills oscillograms, Fig. 1.2, and after ours one of which we showed in Fig. 10, the time of capacitance charging can achieve  (40 - 50) s. And plasma dispersion occurs after exponential law and has not abrupt surges [28]; consequently, the transition between the monotonous and oscillation sections would be not so abrupt.

If we premise that the glow discharge takes part as the shunting resistance, we will have to admit that the discharge arises after short arc discharges, and surges are the sections of anomalous glow discharge which precedes the arc discharge. But the first admission contradicts the gas discharge theory [28, 29] and the second - electric circuit theory [30]. An anomalous discharge can arise only with increasing current going through plasma. While in the considered case, the source of current is the energy accumulated in the load inductance that can provide only descending current. The parasitic capacitance also cannot increase the current, as at this moment it just is charged by the current of inductance and shunts the gap. Besides, as we saw in the oscillograms and as Mills' study [2] corroborates, the monotonous section of process can begin both at positive and negative values of momentary voltage at the contacts and also after this, doing not changing the monotony, and pass to the positive region of momentary voltage. With such reverse polarity of voltage, the glow discharge would have to extinguish and arise anew in the positive region. This would certainly have a reflection in the pattern of monotonous section of voltage, but we already said, this is not seen in the oscillograms. It remains only to suppose that such resistance is the metallic bridge that arises each time during the whole showering arc process.