Sprites and their Parent Discharges

It has been known for about a century that the electric field required to produce breakdown scales as the air number density, $N$. Wilson (1925) insightfully realized that $N$ would decrease at a rate faster than the decrease in $E$ above a net charge in a thundercloud ($e^{-z}$ vs. $z^{-3}$, respectively). He theorized that for a sufficiently large dipole moment of the charge and its below ground image, the electric field would exceed the ``sparking limit'' at high altitude.

The ionosphere is sufficiently conductive for electric fields to rapidly decay on submillisecond time scales. In the region just below the base of the ionosphere, the conductivity of the atmosphere is such that electric fields will decay on time scales of milliseconds. The electric field will take increasingly longer to decay at lower altitudes, but it is still sufficiently fast just above cloud tops ($\sim$10 s) that any charge separation on the time scale between sprite-producing discharges (typically minutes) will be screened by charge motion in the atmosphere. Thus, the electric field above a storm and particularly at high altitude will only be of concern when charge is rapidly transported, such as during CG discharges. Figure 1.1 shows an example of how $E$ would decrease above a CG, relative to the rapid decrease in the electrical breakdown strength of air, $E_k$, with increasing altitude. If the discharge was sufficiently energetic, $E$ would exceed $E_k$ below the base of the ionosphere, resulting in electrical breakdown.

Figure 1.1: Charge at 8 km altitude is removed to ground by a CG discharge. As predicted by Wilson (1925), the electric field, $E$, decreases at a slower rate than the electrical breakdown strength of air, $E_k$, with increasing altitude. In this example, $E$ exceeds $E_k$ between an altitude of $\simeq$77 km and the base of the ionosphere at $\simeq$81 km, resulting in electrical breakdown in that altitude range.

Based on a self consistent model of conductivity, ionization, and electron heating, Pasko et al. (1995) predicted that optical emissions would extend down to $\sim$65 km altitude for very large CG charge moment (charge times height) changes of 3000 C$\cdot$km in 1 ms, corresponding to an exceptionally large average current of 300 kA. In order for there to be luminous sprite emissions below 50 km altitude, it was realized that space-charge field enhancements in the form of streamers would likely be involved (Pasko et al., 1996; Fernsler and Rowland, 1996). However, these early models lacked the fine spatial resolution needed to accurately model streamers and thus a minimum altitude could not be determined.

Streamers would be initiated below the base of the ionosphere from localized regions of breakdown ($\sim$1-100 m wide) at altitudes of $\sim$70-80 km (Raizer et al., 1998; Pasko et al., 1998a). The streamers would have radii of $\sim$100 m or less (Raizer et al., 1998) below the base of the ionosphere, consistent with the observations of fine scale structure in sprites (Wescott et al., 1998; Stanley et al., 1996b). It was also shown that streamers could propagate down to altitudes well below 50 km (Pasko et al., 2000; Raizer et al., 1998), consistent with the observed lower terminal altitudes of sprites (Sentman et al., 1995).

Early measurements of extremely low frequency (ELF) atmospherics (``sferics'') showed that sprites were typically associated with positive cloud-to-ground (+CG) discharges which removed unusually large quantities of positive charge to ground (Boccippio et al., 1995). The apparent exclusive association of sprites with +CGs along with the detection of terrestrial gamma-ray flashes (Fishman et al., 1994) led some researchers to theorize that sprite optical emissions were associated with an energetic upward runaway electron breakdown process (Roussel-Dupré and Gurevich, 1996; Yukhimuk et al., 1998; Taranenko and Roussel-Dupré, 1996; Bell et al., 1995).

Time resolved sprite imagery showed that sprites typically began 1.5-4 ms after the occurrence of the parent +CG (Rairden and Mende, 1995). Cummer and Inan (1997) used ELF measurements to show that the charge moment changes of 6 sprite-producing discharges had each attained at least 250 C$\cdot$km during the initial 5 ms. They noted that several of the charge moments were less than required to produce significant optical emissions by the quasi-electrostatic heating or runaway electron breakdown models, suggesting that some other mechanism was involved.

Though the charge moment of sprite-producing discharges had been measured by remote ELF measurements, the height of the charge and hence the charge and current values could not be determined from this technique. Possible average charge heights used in the sprite literature range from 4 km to 10 km or even higher.

Numerous studies have shown that sprites occur only over large thunderstorm systems known as Mesoscale Convective Systems (MCSs) (Lyons, 1996; Lyons, 1994; Winckler et al., 1996; Winckler, 1995; Boccippio et al., 1995), MCSs are highly-organized storm systems with the upper-level anvil outflows from convective cells joined together into a solid cloud shield known as the ``stratiform region'' (MacGorman and Rust, 1998, p. 258). Observations of sprites show that they occur primarily over the stratiform region of MCSs (Lyons, 1996). Balloon soundings through the stratiform region and away from the ``transition zone'', which is near the convective region, show that there is a high-density of positive charge near the 0$^\circ$C level at an altitude of $\simeq$4 km MSL (Stolzenburg et al., 1994; Marshall and Rust, 1993). Based on this and other measurements, Williams (1998) concluded that the altitude of positive charge removed by sprite-producing discharges would be at 4-6 km MSL.