Discussion

A correlation between the sprites and the apparent periphery of the discharge would be surprising if the charge distribution throughout the flash were somewhat uniform, as assumed in the uniformly charged disk models of Section 2.5.2. The electric field will, of course, be maximized directly over the center of a uniformly charged disk. It was also shown in Section 2.5.2 that the electric field below the base of the ionosphere varies little for disk radii of 15 km or less for a given charge moment. This implies that the electric field is insensitive to the actual charge distribution for such small radii.

In order to produce sprites with plan positions near the periphery of the discharge in a purely quasi-electrostatic approximation, two things must both be true: 1) the charge must be localized at or just beyond the plan positions of the sprites 2) The horizontal dimensions must be sufficiently large so that the charge regions do not produce a high-altitude electric field maximum near the center of the charge distribution.

It should be stressed that the exact plan location of the sprites relative to the discharge boundary is unknown for several reasons:

1. The detection efficiency of the LDAR drops off rapidly with range (see Section 3.2.1)

2. The LDAR did not adequately detect the negative leader activity following the +CG. This leader activity will extend the horizontal dimensions of the discharge.

3. The sprite locations were obtained by assuming the uppermost luminous emissions were at 87 km altitude. This introduces an uncertainty of at most $\pm$6 km in the plan location, as discussed in Section 3.6.

4. The range errors in LDAR locations are on the order of a few kilometers at the distance of the sprite discharges.

The second point is particularly important for the localization of charge near the discharge periphery, since it is the outward propagation of the individual leaders which supplies the current, and hence the new charge regions, following the return stroke process. Optical measurements indicate that the two-dimensional return stroke velocity of natural positive return strokes is 0.9$\pm$0.4$\times$10$^8$ m/s and does not change with height (Mach and Rust, 1993). Thus, it should take a return stroke $\sim$300 $\mu$s to propagate to the end of a $\sim$30 km channel length which might be typical of the sprite-producing discharges. Thus, the dramatic increase in electric field after the initial $\sim$300 $\mu$s ramp would be due to new charge near the periphery of the discharge. This charge would be relatively localized since the leader velocities would be very much less than that of the return stroke. Even if the negative leader velocities were as high as 2$\times$10$^6$ m/s ($\sim$10 times the average shown earlier), they would only advance $\sim$8 km in 4 ms.