A Model for Positive Corona Inception from Charged Ellipsoidal Thundercloud Hydrometeors

Lightning is observed to incept in thundercloud electric fields below the threshold value E_k for discharge initiation. To explain this, the local enhancement of the electric field by hydrometeors is considered. The conditions for the onset of positive corona discharges are studied in air for ellipsoidal geometries. A hydrometeor is simulated as an individual charged conductor in zero ambient field; there is only a field generated by the charge on the hydrometeor surface. By doing so, the feasibility of corona inception from ellipsoidal hydrometeors can be formulated based on the self-sustaining condition of electron avalanches. For hydrometeor dimensions of a few millimeters and typical thundercloud pressure, values above 2.4 E_k are found for the onset electric field at the tip of the ellipsoid. From simulations the required ambient electric field for corona onset from an uncharged hydrometeor can then be derived. This results in values between 0.07 E_k and 0.8 E_k for semi-axes aspect ratios between 0.01 and 1. The charge required on the hydrometeor surface for corona onset for typical pressures is minimum for semi-axes aspect ratios increasing from 0.12 to 0.22 for decreasing hydrometeor volume from 42 mm³ to 4.2 mm³. For representative simulated hydrometeors, onset charges are between 495 pC and 2430 pC. For a hydrometeor volume of 4.2 mm³ results are comparable to measured precipitation charges for aspect ratios between 0.16 and 0.32. From the results it is concluded that corona onset from ellipsoidal hydrometeors of a realistic volume can be achieved in thundercloud conditions for certain aspect ratios.