Abridgment of corona ellipses

The purpose of this investigation is to give a mathematical theory of the cyclograms of corona obtained by a cathode ray oscillograph. In the case investigated a long wire of small diameter is connected to one terminal of an a-c. source; the other terminal of the source is connected to a concentric cylinder of considerable diameter, or to a metal plate at some distance from the wire. A cathode ray oscillograph with two pairs of deflecting plates, at right angles to each other, is so connected that one pair of plates causes deflections of the cathode beam proportional to the values of instantaneous voltage of the source, and the other pair of plates causes deflections proportional to the instantaneous values of the charging and loss current flowing into the wire. So long as the sinusoidal amplitude of the applied voltage is below the visual corona point, the charging current is also sinusoidal, in time quadrature with the voltage. The oscillograph record is therefore an ellipse, with the amplitudes of the voltage and the current as the principal semi-axes. When, however, the minimum ionization voltage is exceeded during a part of each alternation, the cyclogram ceases to be an ellipse, but consists of four portions per cycle, two of which correspond to the intervals of time during which the corona is extinct, and the other two when corona is present, with quite short transients in between. F. W. Peek, (A. I. E. E. TRANS., Vol. XLVI, 1927, p. 1009) published a number of such oscillograph records, with voltage amplitudes both below and above the visual critical point. In order to explain the mechanism of corona formation and the influence of the space charge upon the instantaneous critical voltage, he also produced “artificial corona,” by using two condensers in series, one of which was shunted by a sphere-gap. The purpose of the present investigation is to give a mathematical theory of the observed cyclograms, on the basis of two condensers in series,- with the space charge as a fictitious dividing line. To account for the actual motion of ions and the power loss, the condenser nearest the wire is assumed to be shunted by a conductance, and to have a resistance in series. Approximate equations are derived for the current and the voltage as functions of time. For the artificial corona it is shown that the composite curve consists of arcs of two ellipses, with their principal axes along those of the cyclograms. Assuming the visual critical voltage to be known, an expression is derived for the instant of the cycle at which the corona is re-established. For the actual corona, it is shown that the cyclogram also consists of portions of two ellipses, only their principal axes are at some angles with the principal axes of the cyclogram. The theory is applied to one of Mr. Peek´s records, and it is shown that both the shape of the experimental curves and the instants at which the corona is re-established check fairly well with the theory.