Sprite Streamer Formation and Propagation: Theory and Observations
Sprites are finely-structured, large scale electrical discharges typically initiated near the lower boundary of the ionosphere at 70-85 km altitudes [Pasko, 2010; Ebert et al., 2010; Pasko et al., 2011, 2013; Liu, 2014; Liu et al., 2015b]. Their lateral extent is ∼5-10 km and vertical extent is ∼50 km, and hence the atmospheric volume electrically and chemically affected by sprites is thousands of cubic kilometers [Sentman et al., 1995; Lyons, 2006]. Halos are relatively uniform, descending glows that may give rise to more structured features, from which sprites are initiated. A large amount of observational [e.g., Gerken et al., 2000; Cummer et al., 2006; McHarg et al., 2007; Stenbaek-Nielsen et al., 2007; Stenbaek-Nielsen and McHarg, 2008; Stenbaek-Nielsen et al., 2013] and modeling [e.g., Liu and Pasko, 2004; Liu et al., 2009a; Luque and Ebert, 2009; Celestin and Pasko, 2010; Luque and Ebert, 2010; Qin et al., 2011; Liu, 2012; Liu et al., 2012; Qin et al., 2012; Qin et al., 2014] work has recently been conducted to understand the dynamics of the constituent electrical discharge of sprites - streamers. The modeling results have shown that many physical parameters (e.g., velocity, radius, and brightness) of sprite streamers exponentially increase in time [e.g., Liu and Pasko, 2004; Liu et al., 2009a; Liu, 2010; Kosar, 2010; Celestin and Pasko, 2011]. These results have been verified by high-speed video observations of sprite streamers [e.g., McHarg et al., 2007; Stenbaek-Nielsen et al., 2007; Stenbaek-Nielsen et al., 2013]. As discussed in several recent review papers [Pasko, 2010; Ebert et al., 2010; Pasko et al., 2011, 2013; Liu, 2014; Liu et al., 2015b], many important science questions regarding the physics of sprite streamers and their collective effects in the lower ionosphere are still unanswered. The purpose of this dissertation is to investigate and address several outstanding problems on sprite streamer initiation. A previously-developed plasma discharge model [Liu and Pasko, 2004; Liu et al., 2012] is used and improved to conduct detailed simulations of streamer initiation process and to compare the obtained results with recent high-speed images of sprite streamers. The first research problem addressed in this dissertation is sprite streamer initiation at subbreakdown conditions. Recent high-speed images of sprites combined with electromagnetic measurements of lightning field have demonstrated that the lightning field is often below Ek when sprite streamers are initiated in the lower ionosphere. The plasma discharge model has been used and further improved to investigate a theory of streamer initiation at subbreakdown conditions that dense ionospheric columniform patches can initiate streamers in a lightning field below Ek. Numerical simulation results show that positive streamers are able to form from the tip of an ionization column for a variety of electric fields with the lowest field of 0.3Ek when a dense ionization column with proper dimensions is introduced. Even though positive streamers are formed and propagated through a substantial distance, negative streamers do not form from the other tip of the ionization column, consistent with observations showing sprites are initiated with downward propagating positive streamers. The simulation results also indicate that the initial ionization patch from which streamer is initiated may become very bright following the streamer formation and its brightness persists as the streamer continues its propagation. The brightness of the patch depends on its initial density, and the patch with smaller density is brighter than the denser one. An analytical formula describing the temporal and spatial variation of the electric field in the streamer channel is derived to explain the brightening of the ionization column as well as the luminous streamer trail. Finally, comparisons between the streamers forming from the ionization patch and those forming in the vicinity of a conducting sphere in an electric field below Ek show that the exponential growth rates associated with the streamer characteristics are similar. Those results also indicate that ionospheric inhomogeneities are required for sprite streamer initiation. However, the peak plasma density of the inhomogeneity used is about 2-3 orders of magnitude larger than the ambient density at lower ionospheric altitudes, posing a very strong constraint on the source processes in the lower ionosphere. Our further investigation indicates that positive streamers can also be initiated from large ionospheric patches with a density comparable to the sprite halo density (<108 m−3 ). In addition, modeling results on the associated optical emissions show that a luminous spherical-like cap appears around the lower tip of the ionization patch before streamer initiation and the streamer is initiated from the bottom of this cap. These results appear to be consistent with the observations reported by Stenbaek-Nielsen et al.  and Takahashi et al.  in terms of the shape, size and brightness of the halo structure initiating streamers. This study suggests that if the sprite halo front is unstable, inhomogeneities developing from it can initiate sprite streamers at subbreakdown conditions. The last part of this dissertation studies the origin of the ionospheric inhomogeneities in the lower ionosphere leading to initiation of sprite streamers. In the previous studies it is assumed that plasma inhomogeneities already exist at sprite initiation altitudes and the density and dimension of the inhomogeneities may be unrealistic. New simulations from a modified plasma discharge model show that sprite streamers can be initiated from naturally-existing small-scale neutral density perturbations created by gravity waves at mesospheric altitudes. In addition, numerical simulation results are compared with the results of highspeed observations to explain the initiation of prompt sprites. The time scales, spatial scales, and speeds associated with the initiation process reach a close agreement between the simulation results and high-speed observations.