Chemistry of sprite discharges through ion-neutral reactions

We estimate the concentration changes, caused by a single streamer in sprites, of ozone and related minor species as odd nitrogen (NO x ) and hydrogen (HO x ) families in the upper stratosphere and mesosphere. The streamer has an intense electric ﬁeld and high electron density at its head where a large number of chemically-radical ions and 5 atoms are produced through electron impact on neutral molecules. After propagation of the streamer, the densities of minor species can be perturbed through ion-neutral chemical reactions initiated by the relaxation of these radical products. We evaluate the production rates of ions and atoms using electron kinetics model and assuming the electric ﬁeld and electron density in the streamer head. We calculate the density 10 variations mainly for NO x , O x , and HO x species using a one-dimensional model of the neutral and ion composition of the middle atmosphere, including the e ﬀ ect of the sprite streamer. Results at the nighttime condition show that the densities of NO, O 3 , H, and OH increase suddenly through reactions triggered by ﬁrstly produced atomic nitrogen and oxygen, and electrons just after streamer initiation. It is shown that NO 15 and NO 2 still remain for 1 h by a certain order of increase with their source-sink balance predominantly around 60 km; for other species, increases in O 3 , OH, HO 2 , and H 2 O 2 still remain in the range of 40–70 km. From this a ﬃ rmative result of long time behavior previously not presented, we emphasize that sprites would have a power to impact on local chemistry at night. We also discuss comparison with previous studies and 20 suggestion for satellite observations.


Introduction
Sprites are lightning-induced secondary discharges with both lateral and vertical scales of tens of kilometer appearing at middle atmosphere all over the world. From telescopic imaging observations it is found that the structure of the emission dominates in a cluster (e.g., Morrill et al., 2002). Streamer is a highly conducting plasma channel; as the tip propagates with high electric field and high electron density, a large amount of ions and electrons is produced and released over its path, through collisions with neutral gases (mainly N 2 and O 2 ) of electrons accelerated by the field. Radical particles produced, neutral atoms and excited states as well as plasmas, are considered to induce various 10 chemical reactions. Because of no strong gas heating a technological application is expected such as reduction of toxic materials (Kulikovsky, 1997).
It has been suggested that sprites can have an impact on upper stratospheric and mesospheric ozone chemistry, which is triggered by a cluster of streamers having the above characteristics (Stenbaek-Nielsen et al., 2000;Sentman and São Sabbas, 2002; 15 Hiraki et al., 2004;Enell et al., 2005, private communication). Here, we make a rough estimation how large impact is actually expected from generation of ions and atoms (e.g., N + 2 , N, and O( 1 D)) through electron-molecule collision in high electric field. On the basis of laboratory and numerical studies the electron density at streamer tip is typically n es ≃10 14 cm −3 being approximately uniform (e.g., Kulikovsky, 1997 and ref-20 erences therein). The amount of ions and atoms produced is considered to be comparable to n es or larger, and is estimated to be ≈10 9 cm −3 at altitudes of 40-50 km by assuming a scaling relation of n es ∼N 2 , N being atmospheric gas density (Pasko et al., 1998). This corresponds to ≈1% of ozone density at this altitude range (Brasseur and Solomon, 1986). Meanwhile, the impact on nitric oxide NO is expected to be relatively 25 large because its ambient density is only 10 cm −3 or less at night. Impacts are also expected for other species as NO 2 with density of 10 8 -10 9 cm −3 and HOx with densities of 10 4 -10 7 cm −3 . It is, however, not so easy to understand whether the densities of ozone, NO x (NO Introduction EGU and NO 2 ), and HO x (H, OH, HO 2 , and H 2 O 2 ) finally increase or decrease. This is because the upper-stratospheric chemistry controlled mainly by NO x , HO x , and O x (O 3 and O) is a non-linear system. NO x and HO x species, which destroy ozone through catalytic reactions (Brasseur, 1999), can increase by one reaction and decrease by other reactions related with sprite products such as nitrogen atom N; for NO, an ex- 5 pected source reaction is N+O 2 →NO+O and a sink one is N+NO→N 2 +O. For OH, the source can be H 2 O+O( 1 D)→2 OH, which is a main ambient reaction in the D region, while the sink be OH+O→H+O 2 . In this study we perform a numerical simulation with one-dimensional ion-neutral chemical model including the effect of modeled sprite streamer. The purposes are to find the way to relax of minor species after the event 10 along with its altitude dependence and to make clear the above obscure point in the nighttime condition. It is worthy to mention the importance of the impact on NO x in the upper-stratosphere and mesosphere. The main ozone destroyer is generally considered to be HO x species in these regions (Brasseur, 1999). However, it is possible that NO x supersedes HO x as 15 the position of ozone-reactor if its amount increases considerably through, for example, oxidation of N shown above after the occurrence of sprites. No evidence implying this enhancement has been reported because of limited spatial and temporal resolutions and sensitivity of optical instruments. Obtaining some feature from detailed observation, we can suggest strongly enhanced and eccentric local chemistry above 20 thundercloud.

Model description
Using an ion-neutral chemical model we calculate temporal density variations for various atmospheric species in the relaxing phase after occurrence of a sprite streamer at each altitude. The reaction rate coefficients between streamer electrons and major 25 species, N 2 and O 2 , can be expressed as a function of local electric field. For simplicity not solving the streamer dynamics directly, we assume its tip field magnitude 2314 EGU and its crossing time at a certain altitude and evaluate the production rates of radical particles. We consider that a reasonable evaluation of the impact as our approach will bring results of chemical model calculation with good accuracy even though the model generally has an uncertainty depending on schemes and rate coefficients.
2.1 Sprite model 5 Parameterization of streamer: We suppose that the radical particles are produced predominantly at the streamer tip. We assume roughly that the tip has an impulsive electric field with a width of r s and a uniform amplitude of E s , and the electron density at the region being uniform as n es . Here, we assume r s being in the same order as the streamer radius (Raizer, 1991).
We can consider that the lightning-induced electric field above thundercloud is directed almost vertically, and the streamer propagates along its direction with the constant velocity of v s . Therefore, the timescale of electron acceleration, i.e. particle production, at a certain altitude is given as t s =r s /v s . Numerical simulation results showed that E s , n es , r s , and v s characterizing streamer depend on boundary conditions (shapes of elec-15 trodes and applied field magnitude) and the polarity. For simplicity and maximum estimation we set as E s =150 kV/cm, n es =10 14 cm −3 , r s =10 −1 cm, and v s =10 7 cm/s taken from Kulikovsky (1997) neglecting factors of differences. These parameters are assumed to be scaled as ∼N, ∼N 2 , ∼N −1 , and ∼1, respectively, using atmospheric gas density N; for example, r s =10 −1 (N 0 /N) cm, N 0 being the ground value, and at 70 km 20 r s ≃10 m, t s ≃100 µs. We neglect here the effect of photoionization process excited through electron collisions, although it is an important process for local streamer dynamics and makes these parameters slightly shifted from the above N-scaling values (Liu and Pasko, 2004 (Hiraki et al., 2004), the relaxation time of the energy distribution is much smaller than the streamer lifetime t s at the altitude of our interest, and the major composition of atmosphere changes hardly in the timescale of t s . In what follows, the production rate of a particle j is given constantly as P j =k j (E s /N)Nn es all through the streamer propagation. We obtain the electron energy distribution function with a Monte Carlo technique.

10
Here we take the cross sections of e-N 2 , O 2 collisions from updated compilation by Itikawa (2006Itikawa ( , 1994, respectively. We consider, as radical particle j, atoms of O( 1 D), O( 3 P), N( 4 S), and N( 2 D), and adopt the cross section data in Cosby (1993a, b) and Itikawa (1994); the excited species of O 2 (a 1 ∆ g ) and N 2 (A 3 Σ Cross sections for all these particles are taken from Itikawa (1994Itikawa ( , 2006. We disregard other possible source processes. We obtain the most reliable set of production rates especially for atomic nitrogen and oxygen of critical importance in the following calculation by recalculating electron energy distribution with updated cross sections of N 2 by Hiraki and Fukunishi (2006).

Chemical model
We represent the chemical impact of the sprite streamer with two parameters P j and t s , both of which are only functions of altitude through N. We estimate composition changes at altitudes of 40-90 km using one-dimensional chemical model after occurrence of the modeled streamers at each altitude. We adopt basically the chemical 25 model of neutral atmosphere by Iwagami et al. (1998) EGU range of 0-90 km; reaction coefficients are taken from DeMore et al. (1994). We include thermal electrons and 34 ionic species such as O ± i , N + i , and NO ± i (i≤4) into the above model on the basis of reaction data by Ogawa and Shimazaki (1975), Borisov et al. (1993), Rees (1989), Brasseur and Solomon (1986), Tochikubo andArai (2003), andMatzing (1991). 5 In order to obtain a reference diurnal density variation used for initial values we make firstly a temporal integration (hundreds of days) of rate equations d t n=P −Ln of all ions and neutrals at altitudes of 0-90 km with the day of year and moderate solar activity being fixed on the basis of Iwagami et al. (1998). Here we include the vertical eddy and molecular diffusions for neutral species. Adding the production terms P j of radical 10 particles and using the reference density data at an arbitrary local time t 0 , we solve rate equations for all species separately without assumption of families until the time t=t 0 +t relax by an implicit method. It is noted that the sprite impacts P j are non-zero at each altitude at t≤t s . Here we disregard the vertical diffusion term in order to focus the streamer effect on each-altitude local chemistry. The altitude interaction makes no 15 sense because the initiation of actual streamer at all altitudes does not coincide at t 0 . The electron temperature, used for calculation of reaction coefficients, is assumed to be 10 eV at the period of t 0 <t<t 0 +t s , after which it equals to the neutral temperature, while the ion temperature is not perturbed at all. We assume the neutral temperature unchanged from the ambient values because Joule heating by sprite discharge may 20 be negligibly small. One can estimate the secondary sprite impact at the same site using the same initial density data because the air parcel with composition change by primary sprite is advected to other site by a horizontal wind. Hereafter, we redefine t=t 0 as t=0.

25
We focus the chemical impact of sprites in the nighttime stratosphere and mesosphere where most of events are observed. In this paper we estimate only the impact of Introduction EGU streamer head where large amount of radical particles are produced in strong electric field. We show first in Fig. 1 the production rate coefficients of N( 4 S), N( 2 D), O( 3 P), and O( 1 D) atoms through electron impact dissociations of molecular nitrogen and oxygen calculated with a Monte Carlo method. Streamer electric field, 150 kV/cm at ground level, corresponds to a reduced value of E/N=600 Td; in this field the average electron 5 energy ≈12 eV exceeds dissociation limit. The coefficients of the above atomic production and ionization show the largest values at this field among inelastic processes such as metastable-state excitation. It is also found that these values are much larger than a typical ion-molecular reaction coefficient (≈10 −10 cm −3 s −1 ) in the atmosphere. It is clear from a simple estimation that the amount of produced N atom written as 10 k diss Nn es t s overwhelms the ambient one, which is negligibly small below 70 km altitude: Furthermore it is in the same order or exceeds the nighttime NO density at altitude range of 40-70 km.
We solve rate equations to calculate the density changes for various species when a single streamer effect as source term P =k j Nn es is given at altitudes of 40-90 km. Here 15 we assume the fixed conditions such as temperature being at mid-latitude equinox (Iwagami et al., 1998). Firstly, we show in Fig. 2 the density distributions of NO x (NO and NO 2 ) species one second and one hour after initiation of a single streamer. We find that the NO density increases strongly at t=1 s, whereas NO 2 does not change so much except below 55 km since NO 2 is abundant as NO x below 70 km at night, and 20 above the altitude the sprite impact itself is too small. We find that a decrease of NO 2 below 55 km is due to negative-ion reactions related with strongly enhanced N, O, and NO. The key reactions of increase in NO density (up to 10 11 cm −3 at t≤1 s) are electron impact dissociation of N 2 and oxidation of N atom as a series below, This response is consistent with the maximum production of N, P diss t s ≈1.2×10 12 cm −3 at 40 km. The saturation around 40 km is caused by the NO x reduction process as 2318 EGU N+NO→N 2 +O. Note that the N atoms in the second equation are mostly in the state of 4 S, while the excited state 2 D is already lost at all at this moment. It is, however, confirmed that the effect on NOx species continues over 1 s in spite of assumed lifetime of sprites less than 1 ms (maximum at 90 km). The increasing rate of NO is the order of 10 5 -10 9 at altitude range of 40-70 km. We would investigate the response at 1 h after 5 the event, even if it is an order-estimation, in order to discuss the effect on atmospheric chemistry. The noticeable enhancements sustain around 60 km altitude for NO and 40-60 km for NO 2 (Fig. 2). Especially, we show in Fig. 3 the time variation in NO and NO 2 densities at 60 km. We find from this figure and by checking dominant reactions that NO sustains its amount through the relaxation of ions and atoms as N at the initial 10 phase (t≤100 s), after that, almost all convert to NO 2 through the following processes: This is because the response of NO 2 is in anti-phase to NO, resulting in the remarkable 15 increase at t=1 h. On the other hand, it is confirmed that the dominant loss reactions of NO 2 are NO 2 +O→NO+O 2 and NO 2 +H→NO+OH. Thus, the loss rate of NO becomes relatively small around 60 km due to the source-sink balance in NO x as the above five reactions. Contrary to the linear response to sprite impact at t=1 s, these particles are strongly coupled each other along with weak couplings with O x and HO x in this 20 timescale. It is mentioned that the final sink of NO x to sprite impact is NO 2 , which has a large lifetime; its density amounts to ≈6×10 9 cm −3 at 40 km. The increasing rates at t=1 h are summarized as, for NO, up to the order of 6 with its maximum around 60 km, while, for NO 2 , the order of 1 at the range of 40-60 km. We emphasize from this result that the impact can sustain for a few hours. In addition to the above key reactions 25 ineffectiveness of the reaction N+NO→N 2 +O has a critical role because the impact will diminish perfectly if this reaction rate is so fast. It is slightly seen as a saturation 2319 Introduction EGU of the increasing rate of NO 2 at t=1 h at 40 km. However, we can interpret that the conversion of N→NO→NO 2 is smoothly proceeded in a scale of 1 h with negligible contribution of this reaction since the production rate of N atom is smaller at higher altitude and its loss timescale is smaller at lower altitude (≈1-10 s). We also confirmed that the contribution of ion-molecular reactions to the NO x chemistry is restricted within is P diss t s ≈5×10 11 cm −3 through the process (R6), other processes such as ionization (O + 2 , O + ) and excitation (O 2 (a)) of O 2 , and process (R2) also have large contribution to the ozone production within a scale of 1-100 s.
Next we show density distributions of HO x (H, OH, HO 2 , and H 2 O 2 ) at t=1 s and 1 h in Fig. 6, and these time variations at 40 km and 60 km in Fig. 7. The response of HO x is found to be more complicated and unexpected than those of other species NO is made by produced electrons through the following reactions up to the time of 1 ms: Thus both H and OH increase exclusively. However, these reactions concede position of a main trigger to the following ones through relaxations of ions and electrons to the initial densities until t≈1 s, showing a successive multiplication. In addition, Fig. 6 shows that increases in HO 2 15 by the order of 1-4 in the range of 40-55 km and in H 2 O 2 by several factors in the range of 55-65 km follow. We would mention briefly the difference of the latter two particles' responses at t≈1-100 s. We confirmed that HO 2 is produced with not only oxidation of H We would discuss possible uncertain factors for our calculation shown above even though it is only an order-estimation: (i) accuracy in molecular chemical reaction co-tions are unchanged except for Reaction (R3) having a difference of <1% at 250 K, while for HO x the difference is less than 30% at 250 K. From these facts we consider that uncertainty in rate coefficients is under our estimation.
(ii) Next, we perform a response study how much the results vary with the streamer electric field value. When the field value is set to be in the range of 400-800 Td, the 10 NO density at t=1 h varies in the scale of 1 order around the value in Fig. 2. However, our conclusion remains essentially unchanged because the difference is found to be almost linear to the amount of first product, i.e. k. Here it is difficult to mention the details about the effect on other species with their increasing scales of 1-2 orders, which is the same order as the above uncertainty. (iii) We focus in our model only the impact of the streamer tip with strong electric field. It is suggested that the tail part is actually formed after the tip passes away, in which a slight-amplitude electric field exists despite not causing strong electron acceleration and optical emission (Liu and Pasko, 2004); ≥60 Td. From optical measurement of sprites, the bead-like structures with strong emissions are found to be formed in the region a cluster of streamers exists 20 (Gerken and Inan, 2002;Moudry et al., 2003). Both lifetimes are in the order of ≈1-10 ms. We guess in this paper that the former effect is negligibly small and the latter one cannot be evaluated because of lack of its mechanism to date; these should be done in our future studies. Our some speculation to this problem is made as follows. We consider that the predominantly produced particles in streamer tail are metastable 25 states such as N 2 (v=1) and N 2 (A) rather than N and O atoms of great importance in our calculations. As a mechanism, the multiple excitation is needed to gain dissociation energy and to cause the density variation of NO x and HO x triggered by these particles; the highly excited secondary and ternary products dissociate N 2 and H 2 . However, EGU these processes are expected not to be so dominant in our transient discharge with small lifetime and small particle production, different from stable glow discharge.

Discussion
On the basis of our calculation results we try to evaluate roughly the sprite impact on local chemistry at nighttime. Here we examine whether the mean density variation for 5 a certain species survives or not when the impact is mixed in a local area as a similar approach by Hiraki et al. (2004). We focus nitric oxide NO of the most possible one. The variation in the NO density by a single streamer is over the order of 6 at 60 km altitude. Here we assume the horizontal scale of sprites with a cluster of streamers being 100 km 2 at their maximum. The local area is defined to be 10 6 km 2 as the resolution of 10 some satellite, e.g. Envisat-Sciamachy (limb emission sounder), in which the increasing rate of NO is reduced as 1/10 4 through mixing without any loss. However, our calculated variation can survive evidently with the order of 2 in spite of the wide-range mixing. Our estimation being only for one event, the impact is expected to be larger in the area such as Africa where many events of lightning and sprites are possible within 15 several hours. It is also expected to be still large even though this kind of estimation depends certainly on the initial condition; we discuss this point in the next paragraph. We emphasize that the density increase of at least NO is detectable if a certainly resolved and qualified observation is performed. Note that this discussion is limited in the nighttime impact because the daytime ambient density of NO becomes, through 20 photolysis of NO 2 , the same order as that produced by one streamer event at night. It is one of future studies of this field whether integration of nighttime local variation in NO x by many sprite events affects on these diurnal variations. We would suggest some ideas to the future observational studies including this point. Our estimation is done on purpose to determine the upper limit with uncertainty in a few orders due to streamer electric field and scale parameters so that it needs verification with observation. Since the sprite impact on chemical species vary widely with altitude, sub-millimeter wave detectable limit becomes higher and traces in several particles except NO such as O 3 and OH can be achieved. Finally we compare our calculation results with other studies. To date the similar calculation is done by Enell et al. (2005). They showed the increasing rate of the NO density after initiation of a sprite streamer in the nighttime condition at equator (in 10 summer and low solar activity). The increasing rate is the order of 2-3 at 40-50 km at its maximum, and no increase is seen above the altitude range. They also show the longtime behavior that the NO density relaxes to the initial value within 1 h. The response at this altitude range is very similar to our results, however, that above the altitude is quite different. We elaborate to mention the response around 60 km, being 15 important in the viewpoint of atmospheric chemistry, where in our case the rate is instantaneously the order of 6. The difference in this rate is undoubtedly due to the difference in the evaluation of sprite first products as input parameters. It remembers that we give altitude dependence of the production rate on the basis of scaling law of streamer dynamics and include all possible particles produced through e-N 2 , O 2 20 inelastic collisions. On the other hand, Enell et al. (2005) considered only some N 2 excited states and N + 2 identified from recent optical measurements, not including N and O atoms, which are of great importance in our calculation results. Furthermore, the magnitude itself of their particle production is considerably smaller than ours. It would be due to the time averaging effect on the measurement of streamer emission 25 intensity, causing an underestimation of the production rates derived. We additionally mention dependence of the results on the initial values of chemical model adopted. At 60 km the initial value of NO density is in our case ≈10 2 cm −3 , while in theirs ≈10 6 cm −3 . It is not clear in details but the difference is considered to be due to the difference in the Introduction EGU referring latitude and data set of reaction rate coefficients. It is, however, asserted that the increasing rate of NO density in the order of 2-3 would be obtained if we calculate with their initial values, and be detectable with satellite sounder observations if 100 sprites occur within 1 hour, as discussed in the above paragraph.

5
We investigate density variations of NO x , O x , and HO x species after the initiation of a single sprite streamer using a specified ion-neutral chemical model with modeling chemically radical particle production by non-thermal electrons. constructed by sprite products. We suggest that the sprite impact on these minor species will be detectable with highly qualified satellite observations, even though it has an uncertainty by ≈1 order due to initial conditions and magnitudes of particle production. Introduction