Condition of Inception of DC Positive Corona in Air

Summary form only given. A problem of evaluation of corona inception voltages is of great importance for many applications. The inception voltage is commonly calculated using the criterion int₀ ^z0a_ef(z)dz=K, where a_ef is the net ionization coefficient (the difference between the ionization and attachment coefficients), governed by the reduced electric field, z is a distance coordinate along the field line, counted from the surface of a stressed electrode, z₀ is the critical avalanche length (that is, the electric field at the distance z₀ from the electrode is equal to the critical field, corresponding to a_ef=0), and K is a dimensionless parameter, typically in the range 5-20. At known distribution of electric field near the stressed electrode, the integral in the criterion may be calculated with high accuracy, so the problem of evaluation of the inception voltage consists mainly in an appropriate choice of the value of parameter K. The latter is determined by efficiency of a physical process that governs production of secondary electrons: emission of electrons at the cathode in negative coronas, or volume ionization of gas molecules by photons emitted in the near-anode region in positive coronas. In this work the parameter K is calculated for spherical and cylindrical anodes in air, using the condition of equality of numbers of ionizing photons produced by primary and secondary avalanches. The values of parameter K are presented for a wide range of gas densities and the radii of spheres and cylinders. Approximating expressions for K are given. It is shown that K increases substantially with the growth of air density, because of increasing role of quenching of radiating states of nitrogen molecules in collisions with heavy particles. A comparison is given of calculated inception voltages in a sphere-plane gap versus air density with experimental data. In agreement with the experiment, calc- lated inception voltages for the positive corona are noticeably lower than those for the negative corona, the difference decreasing with growth of the gas density. It is shown that at low r₀d, where r₀ is the radius of a sphere or a cylinder and d is the relative gas density (the ratio of gas density to its value under standard conditions), the effect of electrode geometry on the parameter K is weak. This result allows one to use the same values of K, at given r₀ and d, for calculation, on the basis of the criterion, of onset voltages for positive DC coronas in more general cases (e.g., for points of various configurations)