Plasma chemistry of sprite streamers

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113,, doi: /2007jd008941, 2008 Plasma chemistry of sprite streamers D. D. Sentman, 1 H. C. Stenbaek-Nielsen, 1 M. G. McHarg, 2 and J. S. Morrill 3 Received 9 May 2007; revised 8 December 2007; accepted 22 January 2008; published 10 June [1] A study is conducted of the principal chemical effects induced by the passage of a single sprite streamer through the mesosphere at an altitude of 70 km. Recent high-speed imaging of sprite streamers has revealed them to comprise bright (1 100 GR), compact (decameter-scale) heads moving at 10 7 ms 1. On the basis of these observations, a quantitative model of the chemical dynamics of the streamer head and trailing region is constructed using a nonlinear coupled kinetic scheme of 80+ species and 800+ reactions. In this initial study, chemical processes related to currents in the trailing column and to vibrational kinetics of N 2 and O 2 are not included. The descending streamer head impulsively (t 10 ms) ionizes the gas (fractional ionization density 10 9 ), leaving in its trail a large population of ions, and dissociated and excited neutral byproducts. Electrons created by ionization within the head persist within the trailing column for about 1 s, with losses occurring approximately equally by dissociative attachment with ambient O 3, and by dissociative recombination with the positive ion cluster N 2 O 2 +. The ion cluster is produced within the trailing channel by a three-step process involving ionization of N 2,N 2 + charge exchange with O 2, and finally three-body creation of N 2 O 2 +. On the basis of simulation results, it is concluded that the observed reignition of sprites most likely originates in remnant patches of cold electrons in the decaying streamer channels of a previous sprite. Relatively large populations (fractional densities ) of the metastable species O( 1 D), O( 1 S), N( 2 D), O 2 (a 1 D g ), O 2 (b 1 S g + ), N 2 (A 3 S u + ), and N 2 (a 0 1 S u ) are created in the streamer head. The impulsive creation of these species initiates numerous coupled reaction chains, with most of the consequent effects being of a transient nature persisting for less than 1 s. These include weak (1 kr), but possibly detectable, OI nm and O 2 (b 1 S g +! X 3 S g ) Atmospheric airglow emissions. Neutral active species created in the greatest abundance (fractional densities > 10 8 ) are N 2 (X 1 S g +, v), O( 3 P), N( 4 S), and O 2 (a 1 D g ), which, because of the absence of readily available chemical dissipation channels, persist for longer than 100s of seconds. Other long-lived (>1000 s) effects are very weak (1 10 R) OH(X 2 P, v =6...9 Dv) Meinel emissions produced by O( 3 P)-enhanced OH catalysis and O 2 (a 1 D g! X 3 S g ) Infrared Atmospheric emissions. Short-lived (100 s) populations of hydrated positive ions and negative ion clusters are also created in the streamer trail. Electron impact dissociated N( 2 D) interacts with O 2 to create a long-lived (>1000 s) increase (fractional enhancement 75%) of the ambient NO density within the streamer channel, for a net production of NO molecules for the streamer as a whole. It is suggested that in addition to the optical emissions from electron-impact excited electronic states of N 2, a substantial portion of the spectrum may be due to chemiluminescent processes derived from vibrational kinetics of nitrogen. Citation: Sentman, D. D., H. C. Stenbaek-Nielsen, M. G. McHarg, and J. S. Morrill (2008), Plasma chemistry of sprite streamers, J. Geophys. Res., 113,, doi: /2007jd Geophysical Institute, University of Alaska, Fairbanks, Alaska, USA. 2 Department of Physics, U.S. Air Force Academy, USAFA, Colorado, USA. 3 Space Sciences Division, Naval Research Laboratory, Washington, D. C., USA. Copyright 2008 by the American Geophysical Union /08/2007JD Introduction [2] The occurrence of transient upper atmospheric optical phenomena triggered by lightning in thunderstorms suggests there should occur accompanying local chemical perturbations within the optical emission regions. The detailed chemical kinetics of breakdown associated with these events and the follow-on chemistry have not previously been studied in detail, and are the subject of this report. 1of33

2 [3] The term Transient Luminous Event (TLE) is the generic name adopted by researchers to refer to a diverse collection of distinctive types of short-lived (<1 s) optical phenomena such as red sprites, blue jets, ELVES, sprite halos, and gigantic jets that have been found to be a common occurrence above thunderstorms. The nature of the effects associated with TLEs differs from other photochemical processes in the upper atmosphere in several key respects: [4] The first difference is that TLE breakdown is impulsive. The characteristic timescale for electrical breakdown in the upper atmosphere ranges from submillisecond in the case of sprites and ELVES to a few tens to hundreds of ms for blue jets and gigantic jets. This is much shorter than other kinds of external forcing processes that induce time varying chemical effects in the terrestrial system, such as day-night variations in solar photoionization [Roble, 1995] and X-ray flares [Zinn et al., 1990], precipitating particles, as for example in the aurora [Rees, 1989] or in relativistic electron precipitation [Callis et al., 1996], or by solar proton events or Forbush decreases associated with modulation of galactic cosmic ray flux by solar activity [e.g., Thorne, 1980]. [5] The second difference is that the system is in a nonequilibrium state. Impulsive ionization, dissociation and excitation in TLEs create mixtures of electrons, ions and chemically active species in an, initially, highly unstable configuration that is far removed from chemical equilibrium. Consequently, a dynamical description of the chemistry must be used to follow the evolution of the system that can resolve rapid variations that occur on collisional timescales. [6] The third difference is that the effects are highly localized spatially. The immediate chemical effects of breakdown in the upper atmosphere are confined to a relatively small volume of the upper atmosphere directly above a thunderstorm, in contrast to the large volumes affected by solar illumination, particle precipitation, or cosmic ray variations. [7] Of the various types of TLEs, sprites are the most commonly observed form of upper atmospheric breakdown, generally occurring in the mesospheric range of altitudes km above thunderstorms. Sprites appear to be electrical streamers initiated by gas breakdown from a strong quasielectrostatic impulse originating in an underlying lightning stroke, and can range in complexity from single streamers to dense networks of streamers. Streamers are weakly ionized, cold plasma phenomena, usually occurring as thin, rapidly propagating nonlinear ionization structures. Sprite streamers appear to be ignited primarily in the altitude range km, and can span vertical distances of several tens of km. [8] In this paper we investigate the chemical response induced by passage of a sprite streamer through the upper atmosphere, with the primary goal of establishing the dominant reactions that occur, their associated timescales, and possible connections to other elements of the atmospheric chemical system. Our approach generally follows that of conventional photochemistry of terrestrial and planetary atmospheres [e.g., Chamberlain, 1961; Banks and Kockarts, 1973; Levine, 1985; Brasseur and Solomon, 1986; Chamberlain and Hunten, 1987; Rees, 1989; Roble, 1995; Yung and DeMore, 1999], but with account being taken of several additional kinetic processes occurring in electrical discharges that are either absent or differ fundamentally from aeronomical processes driven mainly by solar photoionization or energetic particle interactions with the upper atmosphere. [9] A general framework is developed for following homogeneous chemical reactions in gases of arbitrary composition associated with transient electrical breakdown, and applied to the specific case of air breakdown of a single sprite streamer at 70 km. For this study the electrical parameters of the streamer are modeled to agree with optical observations of single streamers recently obtained with high-speed imagers. The detailed reactions triggered by a streamer are traced beginning with initial impulsive breakdown in the streamer head and followed through the subsequent evolution of the complex coupled chemical reactions in the trailing column to where transport effects become important. [10] The organization of the paper is as follows: In section 2 the background of TLE research and studies of relevance to chemical processes deriving from them are briefly outlined. Recent high-speed imaging observations of sprite streamers that form the basis for the physical model of the streamer used in the chemical calculations are described in section 3. In section 4 the streamer model based on these observations is described. Section 5 presents the chemical kinetic scheme adopted for the simulation and describes limitations due to the omission of possibly important vibrational kinetic processes in the reaction set. In section 6 is briefly described the modeling framework that was developed for quantitatively handling the very large number of processes in the nonlinear system of coupled chemical reactions. The principal results of the simulation are presented in section 7. The relationship of the present simplified streamer model to the geometry and dynamics of typically much more complex sprite structures is discussed in section 8, as well as possible connections to the larger terrestrial system. Finally, the conclusions are summarized in section Background [11] Observations have identified several distinctive types of transient upper atmospheric optical phenomena triggered by underlying lightning. The principle forms range from red sprites in the altitude range km (first reported by Franz et al. [1990] and subsequently elaborated on beginning with Vaughan et al. [1992], Sentman and Wescott [1993], Lyons [1994], and Sentman et al. [1995]); blue jets [Wescott et al., 1995] that are primarily confined to the stratosphere km; sprite halos in the km range [Barrington-Leigh et al., 2001; Wescott et al., 2001; Miyasato et al., 2002; Frey et al., 2007]; gigantic jets that extend from cloud top to the ionosphere [Pasko et al., 2002; Su et al., 2003; van der Velde et al., 2007]; and ELVES (ionospheric 100 km) [Fukunishi et al., 1996; Inan et al., 1996]. These phenomena have come to be collectively referred to as Transient Luminous Events (TLEs) [Lyons, 1996]. Two nearly simultaneous spectroscopic observations in the summer of 1995 independently identified the primary optical emissions from sprites as the 2of33

3 nitrogen First Positive (1PN2) band system [Mende et al., 1995; Hampton et al., 1996]. Heavner et al. [2000] provide an early review of spectroscopy studies, and Kanmae et al. [2007] have recently verified that sprite spectra observed at 300 fps retain the same spectral characteristics as at slower (30 fps) video rates. In the many thousands of images of sprites that have been obtained over more than a decade of research at both midlatitudes and low latitudes, no discernible relationship has been found between the highly structured morphology of sprites and the local geomagnetic field direction. [12] A steadily growing body of imagery, photometry and spectrographic observations at progressively higher spatial and temporal resolution indicate that sprites are well described by conventional gas discharge kinetic theory, in particular such as were originally proposed by Pasko et al. [1998] and Raizer et al. [1998] for sprite streamers. Recent theoretical work by Liu and Pasko [2003, 2004, 2005], ground-based sprite observations reported by Pasko and Stenbaek-Nielsen [2002] and topside observations made using the ISUAL instrument aboard the FORMOSAT-2 satellite [Mende et al., 2005; Kuo et al., 2005; Liu et al., 2006] have shown that the principal characteristics of sprites are consistent with a description of the events as large-scale (10s of km) upper atmospheric versions of conventional electrical breakdown processes. Fukunishi et al. [2005] briefly review current understanding of sprite processes. A more recent review by Pasko [2007] critically compares the physical kinetics of sprites with molecular dynamics of laboratory discharges. [13] With the discovery of large-scale transient electrical breakdown in the upper atmosphere, it was recognized that such discharges held potential for inducing concomitant chemical perturbations that would not otherwise occur [Sentman and Wescott, 1995; Green et al., 1996; Stenbaek-Nielsen et al., 2000]. Mishin et al. [1996], Mishin [1997], and Smirnova et al. [2003] studied the effects of NO production associated with blue jets using a kinetic approach based on a model of the blue jet as an ionization wave, as described by Lagarkov and Rutkevich [1994]. Armstrong [2000] and Armstrong et al. [2001] reported the results of kinetic modeling of the chemistry of sprites and similar calculations were independently undertaken by Sentman et al. [2000]. Hiraki et al. [2004] calculated the amount of metastable oxygen O( 1 D) produced in sprite halos in the altitude range of km using Monte Carlo methods, showing that density enhancements of cm 3 could occur within sprite halos. Ennel et al. [2005] have presented preliminary results of a study of NO x production from TLEs using a coupled ion-neutral chemical model. Lehtinen and Inan [2007] have used an ion chemical model to show that gigantic jets may leave a trail of persistent ionization. [14] Streamers are well described in a large literature of numerical and laboratory research [e.g., Kunhardt and Tzeng, 1988; Lowke, 1992; Babaeva and Naidis, 1996, 1997; Raizer, 1997; Aleksandrov et al., 1997; Kulikovsky, 1997a, 1997b, 1998a, 1998b, 1998c, 2000a, 2000b, 2001a, 2001b; Georghiou et al., 1999; Pancheshnyi et al., 2000, 2001, and references therein]. The conventional kinetic description of electrical breakdown of gases (see the review of the early primary literature by Lister [1992]) and its associated plasma chemistry together form the basis for the understanding of gas discharges of many different types, ranging from terrestrial lightning [Raizer, 1997; Bazelyan and Raizer, 1998], to widespread industrial applications [Roth, 1995, and references therein]. Breakdown kinetics and photochemical modeling are combined in the present work. [15] Modeling studies of the chemical kinetic effects of microwave breakdown in the stratosphere have brought together much of the data required to evaluate the effects of other types of electrical breakdown on the upper atmosphere [e.g., Kossyi et al., 1992; Borisov et al., 1993, and references therein]. Similar investigations of the production of chemically active species by positive streamers in air have been reported by Kulikovsky [1997a, 1998b, 2001a] and Pancheshnyi et al. [2000]. [16] Experimental investigations to determine the overall magnitude and extent of possible chemical effects of TLEs on the upper atmosphere have not been systematically undertaken. To our knowledge the only observational studies performed to date to search for a large-scale upper atmospheric chemical signature associated with lightning were by Armstrong [2000] and Armstrong et al. [2001]. In those studies, suggestive evidence for regional-scale effects was found in observations made by the HALOE instrument on the UARS satellite. A plume of stratospheric NO was observed to extend westward from regions of summer thunderstorms in the American Midwestern plains states, and it was speculated that this plume may have had its origins in the effects of lightning-induced chemical perturbations in the middle atmosphere. 3. Observational Basis of Model [17] There are two sets of recent optical observations that yield important insights into the processes involved in sprite streamers. These observations provide both the evidence for persistent chemical effects of sprites in the upper atmosphere and the constraints necessary to construct an approximate kinetic model of the processes. A detailed discussion of these observations and their implications for chemical modeling are presented below High-Speed (1000 fps) Imagery of Sprites [18] High-speed ICCD observations of sprites at frame rates of fps [Stanley et al., 1999] and 1000 fps [Stenbaek-Nielsen et al., 2000; Moudry et al., 2003] revealed them to consist of a complex mixture of streamer-like structures that propagate both upward and downward from initiation points from within a relatively narrow altitude range km. Association with +CG causative lightning makes the downward propagating structures positive streamers (cathode-directed in the parlance of the discharge literature), and the upward ones negative streamers (anode directed). High-resolution telescopic imaging of these structures at TV rates has revealed that they are of decameter-scale size [Gerken et al., 2000]. [19] The millisecond-resolution images reveal the temporal development of sprites significantly better than was possible with 30 frames/60 fields per second video. These images show that the initial phase of a typical sprite event is very short, lasting on the order of a few ms. During this phase the complex spatial structure of the sprite develops. It 3of33

4 Figure 1. Sequence of 1000 fps images showing a reactivated sprite, taken from Stenbaek-Nielsen et al. [2000, Figure 2]. (top) The initial sprite and (bottom) the reignited event after a 44 ms break. The detailed analysis of the text and Figure 2 of this paper is of the dashed regions from frames 118 and 165 in the above sequence. is followed by a longer phase extending over many ms in which the largely static optical emissions slowly decay. The optical features or phases of an event may morphologically be placed in three, largely sequential groups: Elves, sprite halos, and sprites. The sprite group may be further subdivided into, using terminology established largely on the basis of video data, tendrils (downward propagating features), branches (upward propagating features), afterglow (largely static features), and beads (spatially small optically bright features) lasting significantly longer than the sprite itself. [20] Optical emissions from elves are typically the first to appear. They are created by the electromagnetic impulse launched by the initial lightning strike and are of very brief (a few ms) duration [Inan et al., 1996]. Elves can be very bright and have been observed even in video recordings. Mende et al. [2005], using data from the ISUAL instrument on FORMOSAT, report a brightness of 40 MR. Because of the very short duration the elves can be difficult to distinguish from other features in sprite images. [21] Following the brief appearance of an ELVE, a sprite halo and/or sprite appears. In some events both are present, but there are many in which only the halo or the sprite appear. The physical processes leading to their appearance have not yet been fully characterized, but is thought to be associated with transient quasi-electrostatic electric field between the ionosphere and the ground created by the removal of charge from a thunderstorm clouds by a lightning strike (Pasko et al. [1997] and subsequent publications). The sprite halo is a large ( km) horizontal pancake-like optical feature at an altitude of 80 km [Stenbaek-Nielsen et al., 2000; Barrington-Leigh et al., 2001; Wescott et al., 2001]. The sprite halo is largely devoid of spatial structure and typically persists for only a few milliseconds. [22] The sprite is the most spectacular part of an event. It starts with downward and upward propagating structures, tendrils and branches, which appear within 1 or 2 ms, too fast for their temporal development to be resolved at 1000 fps. Moudry et al. [2002] and McHarg et al. [2007] derived propagation speeds for the tendrils and branches of 10 7 m s 1. This initial burst leaves behind static and typically highly structured optical features which slowly decay over ms. The maximum brightness of the sprite has been estimated at 12 MR on the basis of the 1000 fps images [Stenbaek-Nielsen et al., 2000]. [23] Sprite decay times vary significantly from event to event. For example, a large sprite shown by Stenbaek- Nielsen et al. [2000] decayed to below the limit of detection in just 6 ms, while most other events lasted for several tens of ms. This variability in decay time suggests there may exist an associated variability in some characteristic property of the underlying medium. [24] The first detailed evidence that there are local effects produced by sprites that persist beyond their optical lifetime was presented by Stenbaek-Nielsen et al. [2000] in a report of sprites recorded on 18 August 1999 from the Wyoming Infrared Observatory. A detailed analysis was performed of a very large compound sprite imaged at 1000 fps. It consisted of a primary event whose optical emissions died down over a period of several ms, but was followed less than 50 ms later by a secondary event that exhibited very clear signatures of reignition from the darkened tendrils of the previous event. Figure 1, reproduced from Stenbaek- Nielsen et al. [2000] follows the sequence of events. The sequence shown on the top row shows a carrot sprite in the process of optical decay. After a 44 ms break, a second sprite develops in the same general region as the first event. What is not immediately evident from this sequence is the detailed spatial correlation of the second event with the structure of the first event. [25] Figure 2 shows expanded and contrast enhanced regions indicated by dashed boxes from ms 118 and ms 165 of Figure 1. In Figures 2a 2c are shown three frames. Figure 2a is the frame from ms 118 of Figure 1, and Figure 2b is from ms 165. The views in Figures 2a and 2b are identical. In Figure 2c are shown the common regions of Figures 2a and 2b as determined by performing a pixel multiplication of Figures 2a and 2b. In Figure 2d, Figure 2c has been colored red and added to a negative of Figure 2b. The black plumes extending away from the central spine of the sprite in Figure 2b, as color coded in red, are clearly seen to emanate from small regions corresponding to features in Figure 2a, labeled streamer 4of33

5 Figure 2. (a d) Detail of the reignition event captured at 0544:59 UT on 18 August The images here correspond to sections of images in the second column of Figure 1 and have been contrast enhanced to bring out detail. launch sites. The correlation provides remarkably clear evidence that the first sprite produced an effect that persisted within its decaying tendrils for at least 44 ms, and which then became sites for reignition in the second sprite. Evidence for persistent effects surviving a sprite to influence the ignition of a secondary sprite is also present in standard video imagery [Gerken et al., 2000]. One of the questions motivating the present work is, what are the kinetic mechanisms that connect the two sprites? 3.2. Higher-Speed (10,000 fps) Imagery of Sprite Streamers [26] While the fps imagery described in the previous section revealed many new features of sprites not captured in slower speed video imagery, they still did not fully resolve the temporal development of the downward propagating streamers in the tendrils. This came in 2005 when Cummer et al. [2006] and McHarg et al. [2007] separately fielded new, much faster intensified cameras that were finally able to achieve the temporal resolution required to resolve the development and propagation sequence of sprites. A critical equipment feature is the intensifier phosphor. The intensifier used by McHarg et al. [2007] had a 1 ms (P24) phosphor, so even at 10,000 fps there was no persistence between successive frames. Sprite images were recorded from the Langmuir Laboratory (latitude N, longitude W, altitude 3130 m) near Socorro, New Mexico. The recordings were made at 10,000 frames per second and the intensifier was gated at 50 ms; that is, the exposure time of each image is equivalent to what would be achieved using 20,000 fps at 100 percent duty cycle. The observations were made unfiltered, so that images represent luminosity integrated across the full intensifier wavelength range, nm. [27] Only with the short phosphor persistence has the true nature of the tendrils and branches been revealed. Rather than being leaders, as perhaps may be suggested by the form of the branched structures observed in lower time resolution images, tendrils and branches are formed by bright, spatially compact, fast moving streamer heads. The downward propagating streamer heads forming the tendrils appear first, followed a few hundred microseconds later by the upward propagating streamer heads forming the branches [Stanley et al., 1999; Cummer et al., 2006; McHarg et al., 2007; Stenbaek-Nielsen et al., 2007]. The upward propagating streamer heads start from a lower altitude than the earlier downward propagating structures and are initiated from preexisting luminous sprite structures. This behavior is in distinct contrast to that of bidirectional streamers whereby both upward and downward streamers are simultaneously launched from a common point of initiation. Not all events have both upward and downward streamers. If an event only has downward propagating streamer heads we would classify the sprite as a C-sprite, or column sprite [Wescott et al., 1998]. If both are present it would be a carrot sprite. Analysis by McHarg et al. [2007] indicates the speed and brightness of the upward moving streamer heads are similar to those of the downward propagating structures, and the speed generally follows the brightness. The observed speeds of the streamer heads are in the range m s 1. Van der Velde et al. [2006] have presented evidence suggesting that c-sprites and carrot sprites are associated with cloud-to-ground and intracloud activity, respectively, in the underlying thunderstorm. [28] The streamer heads appear to be much brighter than earlier estimates of a few tens of MR based on video data. In the 50 ms exposure images the signal can be as bright as a magnitude 6 star. The streamer heads are also spatially compact. Telescopic observations of tendrils and branches by Gerken et al. [2000] and theoretical models [Liu and Pasko, 2004, 2005] suggest that the transverse dimensions of streamers are actually much smaller that the 140 m resolution in the McHarg et al. [2007] images, so that in the image analysis the streamer heads must be treated as point sources. High-speed (300 fps) spectroscopic observations of sprites [Kanmae et al., 2007] show the spectrum is primarily nitrogen First Positive (1PN2) emissions, with no significant difference compared to previous observations made at lower (30 fps) speeds [Mende et al., 1995; Hampton et al., 1996]. On the basis of these results, Stenbaek-Nielsen et al. [2007] find streamer head emission rates to be in the range to photons s 1. For a 25 m physical streamer head size, as modeled by Liu and Pasko [2005], the average brightness in the 1PN2 band 5of33

6 Figure 3. (top) Time and spatial development of a single streamer observed at 10 kfps [McHarg et al., 2007]. (bottom) A single frame from the observations showing multiple streamers. The streamer indicated by the arrow in Figure 3 (bottom) is shown in Figure 3 (top) in 100 ms time slices. emissions would be to R(1 100 GR). Conversely, if we know the volume emission rate we can obtain the scale size. The 1PN2 band emissions calculated in this paper peaks at photons cm 3 s 1, which corresponds to decameter-scale head sizes, in agreement with Gerken et al. [2000]. [29] In Figure 3 are shown frame-by-frame slices of sprite streamers at 100 ms intervals obtained by McHarg et al. [2007]. The bright leading edges of the descending structures are nonlinear solitary-wave-like ionizing fronts that comprise the streamer heads. They are reminiscent of highspeed images of laboratory streamer structures reported by Ebert et al. [2006], reproduced in Figure 4. In Figure 4 it is seen that tendril structures observed at exposure times longer than 1 ns are images of compact, temporally unresolved propagating emission regions smeared over the exposure interval. Assuming that the characteristic times of processes we observe scale inversely as the pressure, the equivalent exposure time of the left-most image in Figure 4 scaled to mesospheric altitudes is 15 ms, similar to that of a single field in a standard 30 fps TV image. The equivalent exposure time of the right-most image of Figure 4 scaled to mesospheric altitudes is 50 ms, similar to the 50 ms exposure time of the 10 kfps image of a sprite streamer shown in Figure 3. Conversely, the frame rate required to observe an event such as Figure 3 at STP at equivalent temporal resolution is about 1.5 Gfps. These results strongly suggest that the leader-like structure of sprite tendrils observed in low-speed imagery are most likely produced by smearing of the emissions from compact head structures moving at speeds too fast to be resolved. [30] As noted above, despite the apparent similarity between sprite tendril structures as observed in images at low temporal resolution and images of leader channels in laboratory discharges, the dynamics of the streamer heads in the 10 kfps images reported by McHarg et al. [2007] and Figure 4. High-speed images of laboratory streamers at various time resolutions (reproduced from Ebert et al. [2006, Figure 1] with kind permission of authors and editor). These images demonstrate that the long tendril structures observed at exposure times longer than 1 ns are of temporally unresolved compact propagating emission regions smeared over the exposure interval. When scaled to the pressure at 70 km altitude the equivalent exposure time of the right-most image is 50 ms, similar to the 50 ms exposure time of the 10,000 fps image of a sprite streamer shown in Figure 3. 6of33

7 Stenbaek-Nielsen et al. [2007] does not appear to follow the development sequence of step leaders [e.g., Niemeyer et al., 1989]. The observed streamer heads propagate smoothly (down or up). When descending streamer heads split, each of the split segments continues as a separate streamer without a pause in the process, in particular at the point where splitting occurs. This is in contrast to the development sequence of step leaders, where streamers momentarily pause while the trailing channel heats and fills with charge, followed after some time by emission of one or more new streamers from the bottom terminus of the preceding streamer channel. [31] The distinction between streamers and leaders has important implications for the chemistry that occurs in the interiors of the respective structures. In addition to a hotter interior, a leader possesses a longer lifetime than a streamer, permitting the buildup of active species to levels where interactions among them and with the heated neutral background play a significant role in the chemistry. The short dosing time of a streamer head limits the build up in the density of such species, hence also the interactions in the trailing column. Consequently, streamers should possess a relatively simpler chemistry compared to leaders. [32] Finally, it is noted that the streamer structure discussed in section 3.1 above and the apparent motion observed in the 10,000 fps images do not appear to be discernibly influenced by the local geomagnetic field. The downward direction of streamer development and absence of magnetic effects would appear to rule out a mechanism for sprite formation involving runaway electrons, such as has been proposed by Roussel-Dupre and Gurevich [1996] drawing on ideas first proposed by Wilson [1925] and further elaborated on by Babich and Stankevich [1973] and by Gurevich et al. [1992]. The runaway mechanism appears to account well for thunderstorm-associated gamma ray bursts [e.g., Fishman et al., 1994; Smith et al., 2005] but works in the wrong direction to be able to account for the observed top-down development of sprite streamers Afterglow in the Trailing Column [33] The approximately 1 ms delayed rise in the trailing afterglow emissions behind the descending streamer heads (Figure 3, top) and the high-speed spectral observations of Kanmae et al. [2007] suggest they may be chemiluminescent emissions. These processes are separate from the direct electron impact excitation of electronic states and subsequent prompt emission cascade that have previously been assumed in interpretations of sprite optical observations. A preliminary analysis of the time and space resolved structures of sprite streamers indicates that in many cases the integrated brightness of these afterglow regions is comparable to or exceeds that of the streamer heads. [34] Several mechanisms for generation of chemiluminescent afterglow in nitrogen discharges have been proposed [e.g., Anketell and Nicholls, 1970; Center and Caledonia, 1971; Guerra et al., 2004, 2007], all of them involving vibrational kinetics of N 2. Morrill et al. [1998, 2002] and Buscela et al. [2003] have discussed one possible mechanism for afterglow generation in sprites as a secondary process involving vibration-electronic (V-E) interactions between vibrationally excited N 2 (X 1 S + g, v > 0) and metastable N 2 (A 3 S + u, v) [Piper, 1989]. Both N 2 (X 1 S + g, v > 0) and N 2 (A 3 S u +, v) populations are created by electron impact within the head of a streamer (see section 7 below). [35] The 1 ms observed delay time for the onset of afterglow behind the streamer heads suggests that in addition to excitation of vibrational states, an energy storage and slow release mechanism is involved. One way in which this might occur is in the formation of a Treanor distribution in N 2 (X 1 S g +, v). Here, vibration-vibration (V-V) interactions among electron impact-excited ground state nitrogen molecules with low vibrational temperature produce a migration of states up the vibration ladder to higher states where they are able to interact with N 2 (A 3 S u +, v) populations [e.g., Center and Caledonia, 1971; Billing, 1986; Capitelli et al., 1986, 2000; Cacciatore et al., 1986; Gordiets and Zhdanok, 1986; Guerra et al., 2001]. In this scenario the afterglow may correspond to 1PN2 emissions from N 2 (B 3 P g )-state excitation by way of V-E interactions, as described by Morrill et al. [2002] and Buscela et al. [2003], but with V-V interactions introducing a delay in the onset of the V-E pumping of N 2 (B 3 P g ). N 2 V-V and V-E interactions compete with vibration-translation (V-T) and collisional deactivation processes, so this effect is pressure, hence altitude, dependent. [36] Guerra et al. [2007] have discussed recent work on afterglow processes that derive from V-V up-pumping and V-E transfer processes involving interactions among N( 2 P), N 2 (a 1 P g ), N 2 (A 3 S u + ) and N 2 (a 0 1 S u ) metastables. Another proposed source of nitrogen afterglow is the well known Lewis-Rayleigh Afterglow [Becker et al., 1972], but in the laboratory this process produces 1PN2 spectra different than observed in sprites so it is unlikely to be a dominant mechanism. Yet another source is proposed by Kamaratos [2006], who invokes complex interactions between vibrationally excited N 2 (A 3 S u +, v) and O 2 (a 1 D g ) to explain N 2 (B 3 P g ) vibrational distributions with enhancements in the high-v level populations. [37] An additional process that may affect N 2 vibrational lifetime in the km altitude range has been discussed by Picard et al. [1997]. Here, vibrational energy in electron impact-produced N 2 (X 1 S g +, v > 0) is near-resonantly transferred to CO 2 (n 3 ), followed by 4.3 mm radiation and radiation trapping, and finally transfer back to N 2 (X 1 S g +, v > 0). The characteristic timescale of this process is 5 7 min. [38] The afterglow in sprite streamers, the absence of any apparent influence by the local geomagnetic field, the longlived (1 ms) emissions from the central bright region of complex sprites, and the persistence of emissions in the compact glowing balls that occur at the splitting junctions of sprite tendrils all point to neutral chemiluminescent processes involving vibrationally active nitrogen as playing an important, but heretofore unaccounted for, role in sprite kinetics. However, in this initial study we focus on the principal, nonvibrational chemical processes in sprite streamers and defer a detailed treatment of vibrational kinetics to a later work. 4. Streamer Model 4.1. Model Justification [39] The observations presented in section 3 showing that sprite branches and tendrils, so distinct in TV recordings of sprites, are formed by fast moving, very bright, and 7of33

8 Figure 5. Simplified positive sprite streamer based on kinetic considerations and the observations of Figures 2 and 3. The calculations of the text are carried out in the gas frame along the longitudinal axis of the streamer. See text for discussion. compact streamer heads [McHarg et al., 2007; Stenbaek- Nielsen et al., 2007] followed by more or less stationary afterglow behind the head, suggest a simple model sufficient for working out the associated chemical dynamics. Figure 5 shows our model for a positive sprite streamer (streamer head propagates in the direction of the electric field) which is broadly consistent with the results of numerous studies of streamer structure [e.g., Babaeva and Naidis, 1996; Kulikovsky, 1998b; Liu and Pasko, 2005, and references therein]. [40] At the leading edge of the streamer is the streamer head, region 1 in Figure 5, in which the bright optical emissions are assumed to be caused by a strong electric field localized to within the small volume of the streamer tip. In the stationary gas frame this electric field is impulsive with a characteristic duration determined by the thickness of the head and its propagation speed. In the trailing column behind the streamer head we observe first a dark region followed by a region of afterglow, regions 2 and 3, respectively in Figure 5. The absence of optical emissions in region 2, immediately behind the streamer head, indicates the electric field there is too small to support significant ionization, at least compared to the intensities within the tip. This is consistent with simulations of Kulikovsky [1998c], who showed there is a current free, hence field free, region in the streamer region behind the head. The optical emissions farther down the trailing column, region 3, are assumed to be afterglow processes, and are labeled as such. We therefore model the electric field along the central axis of the streamer behind the tip to be equal to zero. [41] Since the electric field parameters and dimensions of the streamer head are based on observations, no other additional theoretical information is needed for the modeling. The model details will vary with altitude, particularly with regard to the relative importance of two- and three-body processes. In this paper we will not explore altitude variations, but concentrate on describing the model and the effects of the large number of chemical processes involved in a single streamer near the observed altitude of sprite streamer onset. For this we have chosen an altitude of 70 km, which is a standard altitude that has been adopted in many sprite modeling studies (e.g., Pasko et al. [1997] and subsequent papers and Liu and Pasko [2004, 2005]). However, we emphasize that the model, as presented, can be adapted to any altitude over which streamers are observed. [42] It should be noted that it is the amplitude E 0 several E k and duration Dt several microseconds of the strong electric field within the streamer head, rather than the amplitude and duration of the earlier initiating electric impulse of the causative lightning stroke, that are the primary determinants of the streamer dynamics, and consequently the associated chemistry. Although a lightning impulse initiates the streamer and a small external maintenance field is required for its continued existence and propagation, once the streamer is launched it rapidly transitions into a nonlinear ionizing wave capable of propagating in an undervoltage environment. The chemical chains initiated by passage of the streamer are entirely determined by impulsive ionization of the embedding background gas and the accompanying creation of populations of dissociated and active species within the relatively small volume of the streamer head. Our model describes the reactions within the fully developed streamer in the most energetic phase of its existence. Following head passage the interconnected chemical chains spawned within the streamer head interact among themselves and the ambient atmosphere within the trailing column as they evolve back toward equilibrium Streamer Electron Dynamics [43] The electron dynamics of the streamer is described by the conventional diffusion-drift þr ð n ev e þ D e rn e Þ ¼ S e L e ð1þ 8of33

9 where n e is electron density, V e = m e E is the electron drift speed, E is the electric field, m e is the electron mobility, D e is the electron diffusion coefficient, and S e and L e are local source and loss terms, respectively, for electrons, plus Poisson s equation r 2 8 = r/e 0, where r =r + + r is the electric charge density, e 0 is the dielectric permittivity of free space, and r + and r are positive and negative charge densities, respectively. Continuity equations similar to (1) may be written for the ions, but on account of their low mobility the ion transport terms are small and may be neglected. The self consistent solution of the full set of electron and ion continuity equations coupled to Poisson s equation is a nonlinear problem that generally requires numerical modeling to solve (see Pasko et al. [1997] and subsequent works). [44] The diffusion-drift equation (1) does not include nonlocal contributions to ionization, such as photoionization. For positive (cathode directed) streamers, upstream photoionization of O 2 by electron impact-excited N 2 singlet state emissions from within the streamer head is thought to be important [Zheleznyak et al., 1982; Kulikovsky, 1997b, 2000a, 2000b, 2001b; Pancheshnyi et al., 2001] (see Liu and Pasko [2004] for a detailed discussion of the role of photoionization in sprite streamers). Since our model is based on observations, these effects are implicitly included in our simulation as described following expression (2) below. [45] Electrical streamers can propagate in substantially undervoltage fields. In the case of positive streamers associated with sprites, the ratio of the minimum external field E to the breakdown field E k required to sustain propagation is E/E k 0.14 [Phelps and Griffiths, 1976], while negative streamers can propagate in undervoltage fields E/E k 0.3 [Allen and Ghaffar, 1995]. Numerical modeling has shown that for positive streamers electron thermal diffusion does not play a significant role within the streamer head [Kulikovsky, 1998a] over short timescales. However, it is expected that within the trailing region of a sprite streamer thermal diffusion will spread the populations of chemically produced neutral species, and ambipolar diffusion will similarly act to spread populations of electrons and ion products. [46] The critical parameter driving the system is the electric field within the small volume of the streamer head. This parameter may be estimated either by modeling or by observations. We use the optical observations to estimate the amplitude and duration of the electric impulse delivered to the gas within the streamer head. This effectively models the flux term in expression (1) as required to be consistent with observations, and allows the electron continuity equation to be written as dn e dt ¼ dn e dt þ S e L e div where the flux term is assumed to include effects from nonlocal ionization. Its value is modeled to be consistent with optical observations of Stenbaek-Nielsen et al. [2007]. ð2þ [47] The impulsive electric field within the streamer head is modeled as t t0 E h ðþ¼ t E 0 e ð Þ2 =Dt 2 ð3þ where E 0 is the maximum electric field within the streamer head, and Dt is the characteristic duration of the impulse centered at t = t 0. For an impulse duration shorter than the timescales of the chemical reactions the overall influence of the impulse should be relatively insensitive to its specific functional form. The maximum electric field E 0 in the streamer head is estimated on the basis of self-consistent modeling of streamers in an undervoltage environment at 70 km [Liu and Pasko, 2005], which is in turn consistent with modeling based on emission line ratios obtained with the ISUAL experiment aboard the FORMSAT-2 satellite [Kuo et al., 2005]. The specific values used in the following simulation are Dt =6ms, and E 0 =5E k. We note that although our model is not strictly Poisson self-consistent in a formal sense, the electron avalanche multiplication factor of 10 6 in the streamer head (Meek number of 13.8) is broadly consistent with the Raether-Meek criterion for streamers in attaching gases with high internal fields and small electron diffusion [Montijn and Ebert, 2006] Macroscopic Plasma Parameters of the Sprite Streamer [48] The simulations described below produce an electron density in the head and in the immediate trailing region of n e 10 6 cm 3. Below it is shown that the electrons in the trailing column rapidly thermalize to the ambient gas temperature. For a neutral gas with temperature of 200K and density N = cm 3 at 70 km, the mean free path for electron neutral collisions in the trailing column is l en = 3.3 cm, the electron thermal speed is v th = cm s 1, the electron-neutral collision frequency is n en = s 1 the electron plasma frequency is w pe = s 1, and the electrical conductivity is s = Sm 1. For these parameters the electric field will be excluded from the trailing plasma column on a timescale of microseconds, consistent with our modeling the electric field to be zero along the central axis of the streamer channel behind the head. [49] Diffusion of electrons and ions in the trailing plasma column will be determined by ambipolar processes. Assuming an ambipolar diffusion coefficient of D a 10 3 cm 2 s 1 [Capitelli et al., 2000, p. 98] for cold plasma at 70 km altitude, the characteristic time t a(l) for ambipolar diffusion transverse to the axis of a channel of radius 10 m [Gerken et al., 2000] is approximately 1000 s. For neutral species, the collisional diffusion coefficient is approximately D n cm s 1 [Capitelli et al., 2000, p. 97], which corresponds to a diffusion time of 500 s transverse to the channel axis. The ambipolar and neutral diffusion times are of similar magnitude, and together define the upper limit of 1000 s for the present simulation beyond which transport lateral to the streamer axis becomes important. [50] Several processes included in the set of chemical reactions, e.g., recombination lifetime and thermal dissociative ionization of N 2 (X 1 S g + ), strongly depend on electron temperature. For an electron gas with a temperature signif- 9of33

10 icantly larger than that of the ambient neutral medium, such as is the case for the region of ionization within the streamer head, the characteristic time t c for electrons of temperature T e to cool once the electric field has been removed is given by t c 1 dn en ¼ 1 dns en m 1=2 e ð4þ 2T e where d is the mean fractional energy lost by an electron in air per collision with neutral species taking into account inelastic losses, N is the neutral density, s en is the electron-neutral collision cross section, m e is the electron mass, and T e is the electron temperature in ev. Estimates of electron temperature in sprites vary, from T e 1eV[Green et al., 1996] from ground-based observations, T e 2.2 ev [Morrill et al., 2002] derived from airborne observations, T e 2 ev[miyasato et al., 2003] (for sprite halos) derived from ground based observations, and T e = 6 9 ev [Kuo et al., 2005] derived from satellite observations. These studies do not differentiate between processes in the head and in the trailing column, but may be assumed to apply to the head. [51] As argued above, if the optical observations on which the electron temperature is derived contain a significant afterglow component, then the electron temperature within the head could be higher than these estimates. This would be consistent with the results of Adachi et al. [2006], who found that if the sprite emissions observed by the photometer array on the FORMOSAT2 satellite were interpreted assuming they were solely due to electron impact followed by prompt emissions, then the inferred reduced electric field is on the order of E k in the altitude range of interest. This value is smaller than typical values of the electric field in the streamer head in models, and the discrepancy could similarly be due to the presence of chemiluminescent emissions not accounted for in the model used to interpret the ISUAL observations. [52] For purposes of computing the electron cooling time, the reported range of electron temperatures 1 10 ev are not significant, however, so we adopt a maximum electron temperature of 7.5 ev at the center of the impulse (see following paragraph). With N = cm 3 at 70 km and s en = cm 2, the characteristic cooling time is on the order of the duration of the electric impulse. Hence, the electrons rapidly cool in the zero electric field region behind the head and reach equilibrium with the neutral population within a few tens of microseconds, roughly within a distance behind the streamer head comparable to its longitudinal thickness. The electrons in the trailing region are therefore cold, with a temperature of the ambient neutrals, T g = 200K. [53] To provide continuity in the description of the electron temperature between the regions of strong ionization within the head and the trailing region we adopted a model for the electron temperature based on the reduced electric field E/N. Within the ionization region of the head of the streamer, solution of the electron Boltzmann equation using the 2-term spherical harmonic approximation may be used to construct the parametric dependence of electron temperature on reduced field q = E/N larger than about 65 Td (1 Td = 1 Townsend = Vcm 2 ). We piecewise model the dependence of the electron mean energy E e [ev] on the reduced electric field as 8 < 2:31ð 2Þq; q < 65Td E e ¼ h i : 3 ðq=65þ 2:6 = 1 þ ðq=65þ 2 ; q > 65 Td: where for q < 65 Td we assume the electron temperature scales linearly with the reduced field. The mean electron energy is related to the electron temperature by T e (E/N) [ev] =2E e /3. In the simulation we therefore use for the electron temperature T e = T g + T e (E/N), where T g is the temperature of the background gas and T e (E/N) is the electron temperature within the region of strong ionizing electric field. With E 0 =5E k we have q = 615 Td, and from (5) the mean electron energy E e =11eV,T e (E/N) =7.5eV. [54] As mentioned previously, if there is a significant amount of nonelectron impact excited emissions in the spectrum, such as the afterglow emissions observed in the 10,000 fps images, then the brightness calculated assuming that cascade processes alone are responsible for the observed N 2 (B 3 P g ) emissions may lead to an underestimation of the actual impact-associated temperature within the head. Under certain circumstances involving heated electrons, the vibrational distribution of ground state nitrogen N 2 (X 1 S g +, v) can become enhanced, resulting in vibrational temperatures T v K, well above the gas kinetic temperature. Once created, this enhanced vibrational distribution can interact with the heated electron gas because of the large electron impact cross sections for superelastic collisions between e* and N 2 (X 1 S g +, v) such that the N 2 (X 1 S g + ) ground state vibrational manifold acts as an energy reservoir for the rapidly cooling electrons. In these cases the vibrational and electron temperatures equilibrate and the two populations cool together. However, the conditions that produce these distributions are long residence times in a discharge [e.g., Cacciatore et al., 1982] or numerous excitation pulses applied to the same volume [Morrill and Benesch, 1990]. Since these conditions do not occur in rapidly propagating single streamers, the role of vibrations is likely limited in the case treated here. However, it may be important in the context of multiple lightning pulses acting in rapid succession on a region containing chemical remnants of previous discharges. 5. Chemical Kinetics Scheme [55] With the electric field profile being specified as an a priori input into the model according to (3) and the electron temperature given by (5), all electric field-driven electron impact processes such as ionization, dissociation, attachment and excitation of electronic states are completely specified. When coupled with chemistry, the detailed chemical evolution of the system, from initial excitation through relaxation, may then be computed. [56] The processes selected for study comprise the numbered gas phase reactions of Table A1. This complex, interconnected set of reactions includes both electron impact processes and the standard set of two- and three-body processes used in discharge studies, as well as the reactions of aeronomy [e.g., Roble, 1995] with the exception of photoionization and photoexcitation. ð5þ 10 of 33