Frequency conversion by third class conductor and mechanism of the arcing ground and other cumulative surges

In high-voltage power circuits, such as transmission lines and the high-voltage coils of large power transformers, not infrequently disturbances are observed of a frequency differing from, and usually very much higher than that of the power supply, and differing from the typical transient of energy readjustment, in that they do not gradually die out, but increase in intensity until either destruction occurs, or they finally limit themselves. Such cumulative oscillations or arcing grounds derive their energy from the machine power of the system, and so constitute a frequency transformation, of which the mechanism has been little understood. Physically they may be derived from the typical condenser discharge by the conception of a negative resistance, in combination with a source of power, which supplies the energy given out by the negative resistance. Attention is drawn to a class of conductors — to which arcs and gas discharges belong — the so-called “third-class conductors,” in which the voltage decreases with increase of current, and it is shown that these conductors can be considered as a combination of a negative resistance with a source of power, and as such are capable of transforming the low machine frequency into a high oscillation frequency of alternating currents, and their presence in an electric system thereby may produce cumulative oscillations. The general equations are then derived of a system comprising a third-class conductor shunted by an inductive circuit containing capacity, and supplied with voltage over an inductive circuit from an alternating low-frequency source, and it is shown that in such a system currents and voltages of two distinct frequencies may continuously exist, of which the one is the machine frequency, the other a high oscillation frequency. It is further shown that the voltage of the latter is limited only by the resistance of the oscillating circuit, and in low-resistance circuits may build up t- very high values. Furthermore, the high oscillation frequency is essentially limited to the circuit shunting the third-class conductor and but little of it enters the supply circuit, while the supply frequency enters the shunt circuit to a limited extent only, and both frequencies are superimposed in the third-class conductor as the frequency converter.