A Model for Positive Corona Inception from Charged Ellipsoidal
Thundercloud Hydrometeors
Abstract
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 representative hydrometeor volumes
and typical thundercloud pressure, values between
$1.2\,E_k$ and $37\,E_k$ were 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 is minimum for semi-axes aspect
ratios between 0.04 and 0.07 depending on the considered hydrometeor
volume. For the simulated hydrometeors, the values of this onset charge
for typical pressures are between 1500\,pC and
3200\,pC. Including a size-correction for comparison to
in situ measurement shows agreement with measured precipitation charges.
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.