Daytime Sprite Initiation Threshold

It has been estimated that a parent discharge charge moment change of 8000 C$\cdot$km would be required to initiate a daytime sprite at 50 km altitude (Fernsler and Rowland, 1996). In order to better assess the possibility of conventional breakdown onset as a function of charge height and horizontal extent parameters, the parent discharge is modeled as a uniformly charged disk of radius $R_d$, height $Z_d$, and total charge $Q_d$. This static field approximation is nearly identical to that used in Section 2.5.2 for nighttime calculations, with the main difference here being that the base of the ionosphere is approximated as 62 km altitude (where $\tau_{r}\!\lesssim\!1$ ms) instead of 81 km.

Figure 4.7a shows that conventional breakdown ( $\frac{E}{E_{k}}\!\geq\!1$) probably would have occurred at 54 km altitude (where $\tau_{r}\!\gg\!t_{s}$ for profile A of Figure 4.6b) for $Q_{d}Z_{d}$ = 6000 C$\cdot$km (ie, the first sprite-producing discharge) if $R_{d}\!<$ 25 km. Table 3.1 shows that $R_{d}$ is typically $<\!25$ km for nighttime sprite-producing +CGs, which supports the possibility that the radius of even this unusually energetic flash might have been small enough to produce conventional breakdown for Profile A. However, it is clear from Figure 4.7b that the first sprite-producing discharge would probably not have been able to initiate conventional breakdown at altitudes where $\tau_{r}\!>\!t_{s}$ in Profile B.

Figure 4.7: A static field approximation for a uniformly charged disk of radius $R_{d}$ and height $Z_{d}$ along with an ionosphere conducting plane at $Z\!=\!62$ km is used to calculate a) The ratio of the electric field to the breakdown field at $Z\!=\!54$ km due to a total charge moment ($Q_{d}Z_{d}$) of 6000 C$\cdot$km. b) The minimum $Q_{d}Z_{d}$ required to initiate breakdown for a $Z_{d}\!=\!15$ km point charge and a more realistic example of $R_{d}\!=\!20$ km and $Z_{d}\!=\!10$ km.

The charge moment changes at the onset of the second and third sprite field changes was shown to be 4300 C$\cdot$km and 3900 C$\cdot$km, which would have been insufficient to initiate conventional breakdown at 54 km according to Figure 4.7b. One speculative possibility is that the conductivity above 54 km altitude had somehow been decreased by the energetic first sprite event on the time scale of minutes, leading to a higher initiation altitude and hence lower initiation threshold.