Time resolved N2 triplet state vibrational populations and emissions associated with red sprites

\ PERGAMON

Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 700Ð718

Time resolved N1 triplet state vibrational populations and emissions associated with red sprites J[ S[ Morrilla\\ E[ J[ Bucselaa\f\ V[ P[ Paskob\ S[ L[ Bergc\ M[ J[ Heavnere\ D[ R[ Moudrye\ W[ M[ Beneschd\ E[ M[ Wescotte\ D[ D[ Sentmane a

E[ O[ Hulburt Center for Space Research\ Naval Research Laboratory\ Washin`ton\ DC\ U[S[A[ b STAR Laboratory\ Stanford University\ Stanford\ CA\ U[S[A[ c Computational Physics Inc[\ Fairfax\ VA\ U[S[A[ d Institute for Physical Science and Technolo`y\ University of Maryland\ Colle`e Park\ MD\ U[S[A[ e Geophysical Institute\ University of Alaska Fairbanks\ Fairbanks\ AL\ U[S[A[ f Raytheon STX\ Lanham\ MD\ U[S[A[ Received 20 March 0886^ accepted 00 February 0887

Abstract The results of a quasi!electrostatic electron heating model were combined with a time dependent N1 vibrational level population model to simulate the spectral distributions and absolute intensities observed in red sprites[ The results include both N1 excited state vibrational level populations and time pro_les of excited electronic state emission[ Due to the long atmospheric paths associated with red sprite observations\ atmospheric attenuation has a strong impact on the observed spectrum[ We present model results showing the e}ect of atmospheric attenuation as a function of wavelength for various conditions relevant to sprite observations[ In addition\ our model results estimate the variation in the relative intensities of a number of speci_c N1 emissions in sprites "0PG\ 1PG\ and VK# in response to changes in observational geometry[ A recent sprite spectrum\ measured from the Wyoming Infrared Observatory "WIRO# on Jelm Mountain\ during July\ 0885\ has been analyzed and includes N1 0PG bands down to v?  0[ In addition to N1 0PG\ our analysis of this spectrum indicates the presence of spectral features which are attributable to N¦ 1 Meinel emission[ However\ due 1 to the low intensity in the observed spectrum and experimental uncertainties\ the presence of the N¦ 1 "A Pu# should be considered preliminary[ The importance of both the populations of the lower levels of the N1"B2P`# and the N1"B2P`#: 1 N¦ 1 "A P`# population ratio in the diagnosis of the electron energies present in red sprites is discussed[ While the current spectral analysis yields a vibrational distribution of the N1"B2P`# which requires an average electron energy of only 0Ð1 eV\ model results do indicate that the populations of the lower levels of the N1"B2P`# will increase with increases in the electron energy primarily due to cascade[ Considering the importance of the populations of the lower vibrational levels\ we are beginning to analyze additional sprite spectra\ measured at higher resolution\ which contain further information on the population of B"v  0#[ Þ 0887 Elsevier Science Ltd[ All rights reserved[

0[ Introduction Red sprites are recently!discovered luminous glows occurring above large thunderstorm systems at altitudes typically ranging from 29Ð89 km[ The lateral extent of sprites is typically 4Ð09 km and they endure for several milliseconds "e[g[\ Sentman et al[\ 0884^ Funkunishi et al[ 0885#[ Hampton et al[ "0885# obtained optical spectra of

 Corresponding author[ E!mail] morrillÝcronus[nrl[navy[mil

sprites from the Mt[ Evans Observatory on 11 June 0884[ The spectra of sprites were also acquired on 05 July 0885 from an observation site near Ft Collins\ Colorado\ by Mende et al[ "0884#[ The optical spectra were measured in the wavelength range from ½3499н7399 _\ and four distinct features in the 5999Ð6799 _ region have been identi_ed as the N1 First Positive System "0PG\ B2P` : A2S¦ u # Dv  1\ 2 and 3 band sequences which re~ect emission from vibrational levels 1 through ½7 of the B2P`[ Although the observed emissions were found to be primarily those of the 0PG of N1\ there were also

S9906Ð8209:87:,*See front matter Þ 0887 Published by Elsevier Science Ltd[ All rights reserved PII] 0 2 5 3 Ð 5 7 1 5 " 8 7 # 9 9 9 2 0 Ð 4

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J[S[ Morrill et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 700Ð718

1 1 ¦ indications of the N¦ 1 Meinel emission "A Pu : X S` # as discussed by Green et al[ "0885#[ More recently\ spec! troscopic measurements have been made from the Wyoming Infrared Observatory "WIRO# on Jelm Moun! tain "altitude ½2 km# "Heavner et al[\ 0885^ Bucsela et al[\ 0887# which extend to longer wavelengths "½8999 _#[ These recent measurements include the Dv  0 sequence of the N1 0PG which feature band emissions from the B2P` vibrational levels\ v  0\ 1 and 2[ Spectrally resolved emissions obtained by Mende et al[ "0884# and Hampton et al[ "0885# have been analyzed in detail by Green et al[ "0885# who used energy!dependent electron excitation cross sections and laboratory data to extract information on the energies of electrons pro! ducing the sprite radiance[ A similar analysis has been performed by Milikh et al[ "0886#[ The results of these steady state models indicate excitation by electrons with a Boltzmann temperature of 0 eV "range 9[3Ð1 eV#[ How! ever\ Green et al[ "0885# suggest that a Druyvesteyn dis! tribution with a suppressed high energy tail may be more realistic[ Green et al[ "0885# also suggest the presence of N¦ 1 Meinel to be important as an indicator of electron energies in sprites\ and they present upper bounds on the relative vibrational populations of the N1"B# and N¦ 1 "A#[ Our analysis of the recent sprite spectrum\ mentioned above\ also indicates the presence of emission features which appear to be due to N¦ 1 Meinel emissions in addition to the N1 0PG[ However\ due to the low intensity 1 the presence of the N¦ 1 "A Pu# and the relative popu! ¦ 1 lations of the N1 "A Pu# and N1"B2P`# states should be considered as being preliminary[ Nonetheless\ certain spectral features in the observed spectrum are best explai! ned as N¦ 1 Meinel emissions and\ if con_rmed\ this may have implications relative to the shape of the electron energy distribution[ Additional evidence of N¦ 1 emission is presented by Armstrong et al[ "0887# who report obser! vations of N1 PG "C2Pu*B2P`# and N¦ 0NG 1 1 ¦ ¦ "B1S¦ "B# state\ u !X S` #[ However\ unlike the N1 N¦ 1 "A# is reported to be strongly quenched "Vallance Jones\ 0863^ Piper et al[\ 0878#\ and this will be discussed below[ A detailed review of the current theories of sprite pro! duction is presented by Rowland "0887#[ However\ we will present here a brief discussion of the three primary theories[ The basic mechanism in the quasi!electrostatic model involves the buildup of positive charge in a thun! dercloud prior to the lightning discharge and the induced space charge in the conducting atmosphere above the thundercloud "Pasko\ 0885^ Pasko et al[\ 0886a#[ When the lightning discharge quickly removes the positive charge\ a large quasi!electrostatic _eld appears at all alti! tudes above the thundercloud[ The resulting _eld accel! erates the ambient electrons and collisionally excites the neutral atmosphere[ A similar mechanism to the quasi! electrostatic model is the EMP!induced breakdown which includes the addition of an upward propagating

electromagnetic pulse "EMP# associated with a large lightning stroke "Rowland et al[ 0885a\ b\ 0887^ Milikh et al[ 0884# which can produce breakdown at altitudes above 59 km[ The third mechanism involves the possible role of runaway electrons which has been considered by a number of groups "McCarthy and Parks\ 0881^ Gur! evich et al[\ 0881\ 0883^ and Roussel!Dupre et al[\ 0883# who showed that\ under certain conditions\ secondary cosmic ray electrons with energies of ½0 MeV can become runaway electrons[ Model results "Bell et al[\ 0884# suggest that runaway electrons produce optical emissions similar to the observed spectra when positive cloud!to!ground discharges involve 149 C or more[ The threshold runaway _eld is ½09 times lower than the threshold _eld of the conventional breakdown and\ on this basis\ it was suggested by Taranenko and Roussel! Dupre "0885# that the runaway mechanism could proceed at lower quasi!electrostatic _eld levels[ It is now well known "Sentman et al[\ 0885^ Wescott et al[\ 0885^ Taylor and Clark\ 0885# that\ rather than simply di}use and unstructured\ sprites are in fact highly struc! tured and that they continue to produce signi_cant emis! sion for relatively long periods "some tens of ms# and show {rebrightening|[ Indeed\ under certain geophysical conditions the electric breakdown associated with sprites may develop in the form of streamers "Stanley et al[\ 0885^ Fukunishi et al[\ 0885#[ The electric _eld in very narrow regions around the tips of streamers "scale ½0 m at 69 km altitude# can be much greater than the break! down _eld and generally lead to localized enhancements in N1 1PG and N¦ 1 0NG emissions in comparison with N1 0PG emissions "Pasko et al[\ 0886b#[ Within most of the volume of the sprite and during a majority of the time associated with the sprite\ the electric _eld is expected to remain at the level only slightly above the breakdown _eld[ From simple physical arguments\ it is clear that new ionization produced by the discharge would tend to reduce the electric _eld due to the enhancement in conductivity[ However\ rather than examine the detailed spatial structure observed in sprites\ in this paper we consider the spectrum summed over several scan lines to improve the signal to noise ratio[ Speci_cally\ in this paper we use a quasi!electrostatic "QE# model of lower ionospheric:mesospheric heating and ionization "Pasko et al[\ 0886a#\ a recently developed time dependent model of N1 triplet state vibrational populations "Morrill and Benesch\ 0889^ 0885#\ and an atmospheric transmittance model\ MOSART "Cornette et al[\ 0883#\ to perform detailed time dependent simu! lations of the N1 emissions associated with sprites[ Model N1"B# vibrational distributions\ summed over ½29 ms\ agree reasonably well with those resulting from _tting the spectral observations of Mende et al[ "0884# and Hampton et al[ "0885# to the 0PG system of N1 "Green et al[\ 0885#[ The current results also provide predictions for future spectral or photometric observations ranging

J[S[ Morrill et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 700Ð718

from UV "Vegard!Kaplan "VK#\ Second Positive "1PG## through the visible to the near!infrared "0PG#\ and the variety of observational geometries\ including obser! vations from the ground\ mountains\ aircraft and balloons[ We analyze one of the recent spectra measured from Jelm Mountain\ WY\ in July 0885 "Heavner et al[\ 0885^ Bucsela et al[\ 0887# and the resulting vibrational distributions of the N1"B# and N¦ 1 "A# states are presented below along with the recent populations determined by Green et al[ "0885#[ As is the case in the aurora "Car! twright\ 0867#\ it is found that the relative populations of the lower B2Pg levels are important indicators of the electron energies in red sprites[ In addition\ the possible presence of the N¦ 1 "A# Meinel emission has implications regarding the electron energy distribution "Green et al[\ 0885#[ The current N1"B# vibrational distribution\ as with Green et al[ "0885#\ indicates a low electron energy "½0Ð 1 eV#[ However\ the possible presence of the N¦ 1 "A# Mei! nel emission implies a much higher average electron energy "×½09 eV# or an enhancement in the high energy tail of the electron energy distribution[

1[ Atmospheric transmission Spectroscopic studies of sprites generally entail obser! vations made across long\ nearly horizontal paths through the atmosphere[ Observations of the aurora\ in contrast\ are seldom a}ected by path lengths more than a few percent longer than a single vertical path through the atmosphere[ Accordingly\ while auroral spectra in the visible and near ultraviolet are only minimally distorted by atmospheric absorption and scattering\ these pro! cesses constitute major factors in the production of the apparent spectrum of a sprite as observed from platforms at di}erent altitudes "e[g[\ ground\ aircraft\ or balloons#[ This distortion must be accounted for in order to deter! mine the vibrational distributions associated with an observed spectrum "Green et al[\ 0885#[ It is molecular absorption and scattering that primarily contribute to the attenuation of the spectra of sprites[ Ozone\ oxygen and water vapor are the main absorbers through the visible and near infrared\ while Rayleigh scattering dominates the shorter wavelengths[ The in~u! ences of these mechanisms have been taken into account in the present model[ Their impact on the sprite spectrum as calculated for various paths through the atmosphere is displayed by Fig[ 0[ The atmospheric transmission pro_les in Fig[ 0 were calculated by the Moderate Spectral Atmospheric Radi! ance and Transfer "MOSART# model "Cornette et al[\ 0883# as implemented in the Naval Research Lab! oratory|s Synthetic Scene Generation Model "SSGM# "Wilcoxen and Heckathorn\ 0885#[ This model was used to generate atmospheric transmittance with a spectral resolution of 4 cm−0 between an emission point at 54 km

702

and an observation point at a lower altitude "9Ð19 km#[ MOSART is local thermodynamic equilibrium "LTE# model and has combined the best features of the Air Force Phillips Laboratory|s MODTRAN code "Berk et al[\ 0878# and the Atmospheric Propagation and Radi! ative Transfer "APART# model "Cornette\ 0889#[ MOS! ART contains all of the atmospheric features of MODTRAN[ The MODTRAN one!dimensional Mid! latitude Summer model atmosphere was used for these calculations[ Figure 0 shows the wavelength dependent transmission of the atmosphere from an altitude of 54 km to the observation altitudes indicated on the _gure "9\ 4\09\ 19 km# along two di}erent path lengths "a# 099 and "b# 499 km[ The observation altitudes "9\ 4\ 09\ 19 km# were chosen to be representative of observations from the ground\ mountains\ aircraft and balloons\ respectively[ The 19 km altitude would also include high altitude air! craft such as the U1 and WB!46F[ The actual path lengths and zenith angles associated with Fig[ 0 are presented in Table 0[ As Fig[ 0 indicates\ the atmosphere permits the trans! mission of sprite radiation beginning at the long!wave! length end of the absorption by the ultraviolet bands of ozone at about 2999 _\ depending on path length[ For the longer path lengths\ transmission has already been much attenuated below 3999 _ by Rayleigh scattering[ Ozone again contributes signi_cant absorption via the Chappius bands which are broad and di}use with peaks at about 4629 and 5919 _[ Vibrational bands of water vapor then appear and become increasingly signi_cant into the infrared[ The sharp double peak near 6599 _ is due to molecular oxygen\ the "9Ð9# O1 Atmospheric band\ and serves to cut into the Dv  1 sequence of the sprites First Positive spectrum of N1[

2[ Spectral analysis Prior to the determination of the vibrational dis! tribution associated with an observed spectrum\ the atmospheric attenuation must be accounted for "Green et al[\ 0885#[ This was accomplished by scaling the synthetic 0PG v? progressions "common upper vibrational level# with the model atmospheric transmission and then using a least!squares spectral _tting procedure[ Our analysis of the N1 0PG spectrum measured from Jelm Mountain\ during July 0885\ mentioned above\ extends up to ½8999 _ and was done assuming a 419 km path length\ an emission altitude of 46 km and an observation altitude of ½2 km\ as determined from the video image taken simultaneously with the spectrum[ The superposition of the spectrograph slit on the video image of the sprite shows the spectrum to be of an upper portion of a tendril which extends downward from the main body of the sprite[ This 0PG spectrum includes emission of the Dv  0

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J[S[ Morrill et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 700Ð718

Fig[ 0[ Atmospheric attenuation between 54 km and observation altitudes of 9\ 4\ 09 and 19 km along "a# 099 km and "b# 499 km path lengths[

sequence and so provides a measure of the relative popu! lation of the v  0 level of the B2Pg through the intensity of the "0\9# band with a band origin at 7773 _ "Gilmore et al[\ 0881#[ We have also included the N¦ 1 Meinel tran! sition in our analysis and a number of bands of this system are indicated in the _t of this spectrum[ Previous measurements of sprite spectra were done for emission from higher altitudes "Mende et al[\ 0884^ Hampton et al[\ 0885# and our choice of altitudes for the modelling portion of this study "54 and 64 km# was based on these values[ However\ a detailed examination of the obser!

vational geometry determined the 46 km altitude of emis! sion associated with the sprite spectrum in Fig[ 1[ The details of the spectral analysis routine are given elsewhere "Bucsela and Sharp\ 0886# but we present a brief description here[ A multiple linear regression algo! rithm was used to determine the relative intensities of the molecular band progressions in the spectrum[ The procedure is similar to that employed by Fraser et al[\ "0877#[ A set of unit!intensity 0PG vibrational bands are each multiplied by an intensity scaling factor and combined with the other bands to produce a synthetic

J[S[ Morrill et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 700Ð718 Table 0 Atmospheric attenuation] actual path lengths and zenith angles Path length "km#

Zenith angle ">#

Observation altitude "km#

099

499

099

499

9 4 09 19

096[2 093[3 090[5 85[6

384[4 384[0 383[6 383[0

42[0 44[2 46[5 51[5

73[6 74[1 74[7 76[9

The actual path lengths and zenith angles used in the calculation of atmospheric attenuation[ The column headings {099| and {499| correspond to the nominal path lengths shown in Fig[ 0[

spectrum[ The intensities are varied independently to minimize the chi!square in _tting the features to the data[ The features included in the _t were the "0\ 9# band\ the "v?!vý# progressions "1\ 9Ð0#\ "2\ 9Ð2#\ "3\ 9Ð3#\ "4\ 9Ð4#\ "5\ 1Ð5#\ "6\ 2Ð7#\ "7\ 3Ð8# for the N1 0PG and the "v?!vý# progressions "1\ 9Ð0# and "2\ 9Ð1# for the N¦ 1 Meinel\ as well as a uniform continuum background[ Progressions originating from higher v? levels in both band systems proved too weak to yield meaningful intensities when _tted to the spectrum[ Also\ negative intensities for sev! eral band progressions resulted when the background level was allowed to vary freely in the _t[ Therefore the background was _xed at a level just below its _tted value so that all feature intensities were positive[ Shapes of the vibrational bands were calculated by synthesizing the rotational lines of molecular band pro! gressions and multiplying by an atmospheric trans! mittance pro_le\ as already described[ The attenuated features were convolved with a Gaussian function rep! resenting the instrumental line shape[ The resolution was varied from a full width at half maximum of 8 nm at the shorter wavelengths to 03 nm at 0999 nm and this was found to produce the best _t to the spectral data[ The rotational line strengths and wavelengths were calculated with a band synthesis algorithm that has been described by Bucsela and Sharp "0883#[ Molecular constants for ¦ the N1"A# and N1"B# states and the N¦ 1 "X# and N1 "A# states were obtained from Laher and Gilmore "0880# and Huber and Herzberg "0868#\ and the relative intensities of bands within the progressions were _xed according to the transition probabilities of Gilmore et al[ "0881#[ The temperature of all bands was set at 129 K but\ due to the current resolution\ the _t was relatively insensitive to the choice of rotational temperature[ Figure 1a shows the observed spectrum corrected for instrument sensitivity as well as our best _t which includes both 0PG and Meinel band emissions[ In this _gure the observed spectrum is shown by the solid line\ the full spectral _t "0PG¦Meinel# by the dashed line\ and the Meinel portion by the dotted line[ The resulting N1 "B2Pg#

704

vibrational distribution appears in Fig[ 1b as well as the 1 N¦ 1 "A Pu# populations for levels 1 and 2[ The overall scale is arbitrary but the relative population of the N1 "B# and N¦ 1 "A# vibrational levels has been preserved[ The presence of the Meinel band in the 44Ð59 km altitude region is di.cult to explain since this emission has a quenching height of 74Ð89 km "Vallance Jones\ 0863#[ Consequently\ we have attempted to _t the observed spectrum without the Meinel band and we are currently preparing these results for inclusion in a pub! lication discussing the analysis of a number of other sprite spectra "Bucsela et al[\ 0887#[ Our attempt to _t this emission without the Meinel band produced two basic scenarios regarding the observed emission in the 6799Ð 7199 _ region[ First\ if the spectral _tting model is con! strained as it is with the Meinel bands present "e[g[ the weight associated with the intensity at a speci_c wave! length is based on the noise in the calibrated spectrum at that wavelength#\ then the model produces a good _t to the emission at most wavelengths except the region between 6799 and 7199 _ which is very poorly _tted[ Furthermore\ the observed spectrum appears to have excess emission in this wavelength range[ Secondly\ if the model is constrained to _t only the longer wavelengths "×6299 _#\ then the 6799 to 7199 _ region is well _tted[ However\ in this case the model spectrum contains tremendous enhancements near 5449 and 6549 _\ largely due to v?  6 band emissions[ These enhancements are beyond anything explainable in terms of uncertainty in the observed spectrum[ In addition to the spectral _tting\ signi_cant e}ort has been expended to ensure that all data processing and calibrations have been done properly[ Although the possibility remains that the features in the 6799Ð7199 _ region are due to either an instrumental or processing artifact which has not been considered\ we are forced to conclude that the observed spectrum in this region is best explained as Meinel emission[ In order to con_rm these results\ we are currently examining additional sprite spectra to determine if the emission in the 6799Ð7199 _ appears during other observations[

3[ Quasi!electrostatic model The electric _eld transients capable of causing break! down ionization at mesospheric altitudes can be pro! duced by cloud to ground lightning discharges removing large amounts of positive thundercloud charge on a time scale of several milliseconds "Pasko et al[\ 0884\ 0886a#[ The quasi!electrostatic "QE# heating model quan! titatively describes the evolution of the electric _eld in the conducting atmosphere resulting from a given charge dynamics at tropospheric altitudes "e[g[\ accumulation of thundercloud charge and its removal by lightning#[ The electric _eld and charge density are calculated using the Poisson and continuity equations[ The conductivity of

705

J[S[ Morrill et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 700Ð718

Fig[ 1[ "a# Sprite spectrum and least!squares _t which consists of the 0PG spectrum of N1 and the Meinel spectrum of N¦ 1 ] "b# N1"B# and N¦ 1 "A# vibrational distributions determined by the _t[

the medium is calculated self consistently by taking into account the e}ect of the electric _eld on the electron component through changes in mobility "due to heating# and electron density "due to ionization#[ A detailed description of the QE model is presented by Pasko "0885# and Pasko et al[ "0886a#[ It is important to note that results of the QE model generally demonstrate large variability as a function of input parameters "e[g[\ altitude pro_le of atmospheric conductivity\ discharge duration and thundercloud

charge geometry "Pasko et al[\ 0886a##[ This is a direct consequence of the highly nonlinear nature of the inter! action of thundercloud electric _elds with the meso! sphere:lower ionosphere\ leading to large heating and ionization changes\ which signi_cantly modify the ambi! ent conductivity[ In spite of this large variability\ under a variety of conditions the magnitude of the electric _eld does not signi_cantly exceed the characteristic air break! down _eld Ek "which varies proportionally to the ambient air density\ N "e[g[\ Papadopoulos et al[\ 0882##[ This

J[S[ Morrill et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 700Ð718

e}ect is mostly de_ned by the fast "½0 ms# screening of the electric _eld due to enhancements of the conductivity produced by the breakdown ionization and leads to an important conclusion that spectral results obtained for the limited number of cases considered in this paper are valid for much wider range of input parameters "not only those chosen here for the calculations#[ It is important to note in this regard that heated electron energy dis! tributions are self similar at di}erent altitudes for the electric _elds E ½ Ek "i[e[\ remain the same for the same E:N ratios#[ For the purpose of the studies in this paper we take a case of the removal of 364 Coulombs of charge from altitude 09 km in 19 ms "called case "e# in Pasko et al[ "0885##\ associated with the formation of a columnar channel of breakdown ionization and relatively long optical emission[ This case leads to the intense production of excited electronic states at higher altitudes "×54 km# which makes it preferable in comparison with other simi! lar cases in "Pasko et al[\ 0885c\ d# from the point of view of the application of existing vibrational population models "see next section#[ The dynamics of the electric _eld and electron number density are readily calculated by the model at any time during the 099 ms period con! sidered[ Figures 2 and 3 show these two quantities as a

706

function of time and at two selected altitudes 54 and 64 km[ The characteristic breakdown _eld Ek at these altitudes is also shown in Fig[ 2 by horizontal dashed lines[ The electric _eld and electron density values shown in Figs 2 and 3 are used to calculate the temporal variation of the electron distribution function F"o# in units of "0:cm1!s!eV# "here o is the electron energy# using the solu! tion of the Boltzmann equation\ taking into account inelastic collisions consisting of rotational\ vibrational\ optical\ dissociative\ dissociative with attachment and ionizational losses "Taranenko et al[\ 0882a\ b#[ Results are shown in Fig[ 4a and b for altitudes 54 and 64 km\ respectively\ at selected instants of time[ The average energy of the electron distribution is shown in Fig[ 5\ demonstrating that the average energy does not exceed 4[4 eV[ This indicates that most of the ionization is produced by the relatively small number of electrons in the tail of the electron distribution function which appear in the region of energies of ½04 eV "cor! responding to the ionization threshold of N1 and O1#[ Lastly\ Fig[ 6 shows the temporal variation in the pro! duction rate of vibrationally excited N1 calculated using the electron energy distribution functions and known cross section of this process "Taranenko et al[\ 0882a\ b^ Phelps\ 0876#[

Fig[ 2[ The electric _eld as a function of time at two selected altitudes 54 and 64 km[ The characteristic breakdown _eld cor! responding to each altitude is shown by horizontal dashed lines[

Fig[ 3[ The electron number density as a function of time at two selected altitudes*54 and 64 km[

Fig[ 4[ The distribution of heated electrons as a function of energy at selected instants of time\ and at two selected altitudes "a# 54 and "b# 64 km[

707

J[S[ Morrill et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 700Ð718 Table 1 MSIS densities and temperatures

Fig[ 5[ The temporal variation of the average electron energy at two selected altitudes\ 54 and 64 km[

Fig[ 6[ The production rate of vibrationally excited N1 as a function of time at two selected altitudes\ 54 and 64 km[

4[ Vibrational level populations model In order to examine the details of the time dependent variations of red sprites\ we have adapted a number of steady state kinetic models of the vibrational level popu! lations of the N1 triplet states[ These models have been used to examine N1 emissions in low altitude aurora "Benesch\ 0870\ 0872^ Morrill and Benesch\ 0885# and under airglow conditions "Bucsela and Sharp\ 0886#[ They are both variations of the earlier model developed by Cartwright "0867#[ The time dependent model was originally developed for the analysis of laboratory obser! vations of pulsed laboratory discharges "Carragher et al[\ 0880a\ b^ Morrill et al[ 0877\ 0880^ Morrill and Benesch\ 0889\ 0883# which involved shorter excitation pulses and more complex afterglow processes "such as energy poo! ling "Piper\ 0877\ a b\ 0878## than were expected in sprites[ The current model has been adapted to work with a longer excitation and decay time and presently covers a 099 ms period[ The time resolution for each iteration has been kept short "9[4 ms# but the results have been binned into 19 ms bins[ Considering the photometric obser! vations of Fukunishi et al[ "0885#\ we regard this com! bination of decay period and time resolution to be adequate to model the emissions throughout the duration of a typical red sprite "½0Ð09 ms#[

Parameter

54 km

64 km

N1 ":cm2# O1 ":cm2# O ":cm2# T "K#

2[95e04 7[19e03 9[9 116[1

6[21e03 0[84e03 0[3e7 084[7

The MSIS 89 model atmosphere densities and temperatures used in the calculation of the excited electronic state populations[

In addition to electron impact excitation and radiative cascade\ the time dependent model also contains the col! lisional processes utilized in the steady state model dis! cussed by Morrill and Benesch "0885#[ The three col! lisional processes are simple quenching\ intersystem collisional transfer "ICT# "Benesch\ 0870\ 0872#\ and vibrational redistribution within the A2S¦ u vibrational manifold[ Brie~y\ quenching involves the complete loss of electronic excitation from the N1 triplet state manifold and is distinctly di}erent from the collisional transfer of electronic excitation and vibrational redistribution[ For these latter two processes\ electronic excitation is retained and is either transferred to an adjacent electronic state 2 2 − "e[g[ from B2P` to A2S¦ u \ W Du\ or B? Su # or retained by 2 ¦ the A Su with the loss of some number of vibrational quanta into the ground state vibrational manifold "Mor! rill and Benesch\ 0885#[ A similar analysis involving col! lisional transfer among the N1 singlet states has recently been presented by Eastes and Dentamaro "0885#[ The model requires density and temperature values from an atmospheric model[ Kinetic temperatures and densities for N1\ O1 and O from the MSIS 89 model atmosphere "Hedin\ 0880# were used as inputs and these values appear in Table 1[ Observations indicate that the N1 0PG is the dominant red emission in sprites "Mende et al[\ 0884^ Hampton et al[\ 0885# that is produced by emission from the B2P`[ Once the observed band intensities are corrected for atmospheric attenuation\ they are a direct measure of the populations of the vibrational levels[ In order to model these populations under steady state conditions\ the ratio of the production and loss rates are iterated until the model populations come to equilibrium[ With the time dependent model\ the e}ect of the production and loss rates on the population of each individual level is cal! culated for a small time step and then added to or sub! tracted from the population at the previous time interval[ These rates can vary with time due to changes in electron energy\ which a}ects direct electron excitation\ or with upper state population\ which a}ects cascade[ The vari! ation of the production and loss rates\ along with the short lifetime of the B2P`\ has determined the size of time

J[S[ Morrill et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 700Ð718

interval "9[4 ms# in the current calculation[ The _eld obser! vations have used video format with a time resolution of the order of 06Ð22 ms[ Consequently\ we examine B2P` vibrational distributions summed over a period of 29 ms for comparisons with these observations[ This time period includes the majority of the predicted emission at both altitudes modeled in this study "54 and 64 km#[ In the current model we have not included the time variation of the ground state vibrational distribution[ The ground state distribution determines the initial excited state vibrational distributions produced during electron impact excitation[ As has been noted elsewhere "Morrill and Benesch\ 0889#\ variation in the excited vibrational distribution can be signi_cant but only when the vibrational temperature increases from lower tem! perature "½099Ð299 K# to values on the order of 0499Ð 1999 K[ The temporal variation of the N1 ground state vibrational distribution is a complex process involving both production by electron impact excitation and loss by interactions with atomic and molecular species in the atmosphere "Caledonia and Center\ 0860^ Torr and Torr\ 0871^ Pavlov and Buonsanto\ 0885#\ and we will examine this in a future publication[ In the current model the vibrational temperature is chosen to be the kinetic tem! perature "Table 1# and this is maintained throughout the 099 ms period[

5[ Model results and data comparison The calculation of the time dependent populations uses the electron energy distributions shown in Fig[ 4[ These distributions were used with the electron impact exci! tation cross!sections "Trajmar et al[ 0872^ Zubek\ 0883^ Zebek and King\ 0883# to determine the excitation rates for the seven triplet states used in the current model\ 2 2 2 − 2 2 ¦ 2 ¦ A2S¦ u \ B P`\ W Du\ B? Su \ C Pu\ D Su \ E S` "See Cart! wright "0867# or Morrill and Benesch "0885##[ The result! ing excitation rates are plotted in Fig[ 7[ These results indicate that excitation continues for much longer at 54 km than at 64 km[ Note that at 64 km "Fig[ 7b# the excitation is con_ned to a single spike which is less than ½4 ms wide while our results at 54 km "Fig[ 7a# show that the excitation begins later "½4 ms# but continues until ½19Ð14 ms[ Also\ there is a plateau in the 64 km excitation rates between 4 and 19 ms "not shown#\ but the rates have dropped to such small relative values that there is no signi_cant e}ect on the model populations or predicted intensity during this period[ This behavior is a direct result of the faster relaxation of the electric _eld at higher altitudes "Fig[ 2#\ leading to faster cooling of the electron energy distribution "Fig[ 4a#[ Using the excitation rates in Fig[ 7\ we have calculated the time dependent vibrational populations of the seven triplet states presented above "Morrill and Benesch\ 0885#[ Due to di}erences in the excited state lifetimes and

708

excitation cross sections\ it is di.cult to illustrate the temporal behavior of the absolute value of the excited state populations predicted by the model[ Consequently\ we begin with an example comparing the population of v  9 of the A\ B\ W\ B?\ and C states\ normalized at the peak for 64 km with quenching only "Fig[ 8#[ As expected\ this _gure shows that the emission from the longer life! time species peaks later\ following the onset of the exci! tation pulse[ Figure 8 shows the decay of both A"9# and W"9# to be dominated by quenching\ since both levels have much longer lifetimes than indicated by these curves "t"A"9## ½1[3 seconds and t"W"9## ½9[06 seconds#[ Next\ the predicted number density of "v  9# for the above _ve states in Fig[ 8\ is shown in Fig[ 09 where we now examine the results for 54 km[ Figure 09b shows a number of e}ects when the additional collisional pro! cesses are included "QIR#\ the predicted enhancement in A"9#\ the equilibration of overlapping populations "B"9# and W"9##\ and an enhancement in B?"9# "compare Fig[ 09a and 09b#[ Note that in Fig[ 09b\ the number density of B"9# and W"9# levels overlap "the second curve from the top# and the levels are said to be collisionally coupled[ Similar behavior is predicted for these two levels at 64 km altitude[ Also\ Fig[ 09b shows the predicted enhance! ment in the B"9# population produced by including col! lisional transfer "ICT# in addition to simple quenching "Fig[ 09a#[ This enhancement will lead to increases in overall 0PG band intensity "Morrill and Benesch\ 0885#[ An important point regarding Fig[ 09 involves the sig! ni_cant density of A"9#[ At both altitudes and with either set of collisional processes\ the density is predicted to exceed 094 mol:cm2 for ½04Ð19 ms[ The rapid decay of A"9# compared to that expected due to radiative decay indicates the e}ect of strong quenching\ primarily by O1 "Cartwright\ 0867^ Morrill and Benesch\ 0885#[ Processes involving N1"A# energy pooling\ where energy transfer occurs from the N1"A# state to both the N1"C# and N1"B# states "Piper\ 0877a\ b^ 0878#\ are not included in the current analysis but we brie~y discuss these processes below[ Summing the B state populations over the _rst 29 ms gives the vibrational distribution that would be observed by a spectrograph operating at video frame rates[ Figure 00 is a comparison of a number of di}erent model vibrational distributions with those determined from the observations discussed above[ The distributions from the observations were determined by Green et al[ "0885# and our analysis presented earlier[ Figure 00a and b compares model distributions at 54 km and 64 km\ respectively[ All populations are expressed as a percentage of the total populations of level 1 and 3 through 7[ The populations of v  0 and 2 are excluded from the normalization of the observed populations due to uncertainties in both the 0PG "2\ 9# intensity associated with absorption by the O1 Atmospheric "9\ 9# band at 6483 _ and by the fact that v  0 is determined from a single band\ 0PG "0\ 9#\ at the very edge of the red sensitive portion of the spectrum[

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Fig[ 7[ Excitation rates of seven N1 triplet states at "a# 54 km and "b# 64 km[

Two di}erent model distributions are shown in Fig[ 00 for the case of quenching only "solid line# and for the case where all collisional processes are included "dashed line#[ It is notable that\ although the model distributions generally _t those derived from the observed spectra\ neither model result is able to reproduce the enhancement in v  1 or the de!enhancement in the higher levels[ Simi! lar di.culties appear to have been encountered by Green et al[ "0885^ Fig[ 2#[ In addition\ the population of v  0 appears low based in comparison with model results as well as laboratory pulsed discharge spectra "Morrill and

Benesch\ 0877\ 0889\ 0883#[ This low value is possibly due to calibration uncertainties since the "0\ 9# band occurs at a wavelength where the spectrograph sensitivity is rapidly decreasing "½8999 _#[ To estimate the di}erence between the model and observed v  0 populations\ the observed value has been scaled by 0[4 and 1[9\ and is also plotted in Fig[ 00[ Preliminary estimates of the v  0 populations measured at higher resolution and with bet! ter red sensitivity "see above# indicate that the v  0 popu! lation is on the order of twice the value implied by the lower resolution spectrum shown in Fig[ 1a[

J[S[ Morrill et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 700Ð718

710

Fig[ 8[ Normalized triplet populations "v  9# with quenching "Q# only at 64 km[

Also shown in Fig[ 00 is the model vibrational dis! tribution characteristic of an aurora at 009 km "Morrill and Benesch\ 0885^ Fig[ 7#[ The most obvious di}erence between the auroral distribution and those observed or modeled in sprites is the enhancement of the populations of the lower N1"B# vibrational levels in the auroral case[ The auroral distribution re~ects excitation by a higher energy distribution of electrons than that expected in sprites[ In fact\ the enhancement in the lower vibrational level populations under auroral conditions is due largely to increases in cascade from the N1"C# via the 1PG "C2Pu : B2P`# "Cartwright\ 0867#[ The e}ect of increas! ing the electron energy distribution can be seen by com! paring the model vibrational distributions in Fig[ 00\ where the average energy has a larger peak value at 64 km "Fig[ 00a# than at 54 km "Fig[ 00a#\ as shown in Fig[ 5[ In addition\ the observed auroral N1"B# vibrational distributions "Vallance Jones and Gattinger\ 0865\ 0867# show an enhancement in v  1 not completely explained by the model "Morrill and Benesch\ 0885^ Fig[ 7#\ similar to the enhancement in the sprite distribution[ Similar strong enhancements in v  1 have also been observed in the laboratory between 29 and 0999 mTorr in radio frequency discharge and during the afterglow "either fol! lowing a pulsed discharge or in a ~ow reactor#[ These enhancements in the B"v  1# population are produced by a number of processes[ In a laboratory dis! charge at constant pressure\ the enhancements are due to a combination of quenching and energy transfer "ICT# as well as energy pooling reactions "Benesch and Fraedrich\ 0873^ Morrill 0875#[ In the afterglow the enhancements

are primarily due to energy pooling processes involving reactions of the N1"A# state with other N1"A# molecules or with vibrationally excited ground state molecules "Piper\ 0877a\ b^ 0878#[ The apparent enhancement in the aurora at 009 km "Vallance Jones and Gattinger\ 0865^ 0867# is more di.cult to explain and may imply a larger ICT or smaller quenching rate coe.cient associated with v  1 than are currently used in the steady state model "Morrill and Benesch\ 0885#[ Finally\ in an e}ort to estimate the e}ect of errors associated with the rate coe.cients\ a single model run at 54 km was performed with all of the collisional rate coe.cients increased by 19)[ This resulted in an approximately 5) reduction in the overall population of the N1"B# state\ indicating that the model populations are relatively insensitive to small errors in the rate coe.cients[ However\ at 54 km and below\ where col! lisions are much more frequent than at 64Ð099 km\ the e}ect of errors ×19) in the collisional rate coe.cients will have a larger impact on the _nal distributions pre! dicted for the lower altitudes[ In an e}ort to improve the _t between the model and observed vibrational dis! tributions\ we are currently reexamining both the quen! ching and collisional transfer rate coe.cients used in our kinetic model[

6[ Discussion The nature of sprite observations involves long atmo! spheric path lengths which result in signi_cant attenu!

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J[S[ Morrill et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 700Ð718

Fig[ 09[ Predicted number density of v  9 for "a# quenching only "Q# and "b# quenching\ ICT\ vibrational redistribution "QIR# at 54 km[

ation of the emitted spectrum[ This leads to uncertainties in the vibrational distribution determined by the spectral _t and estimates of absolute intensities[ Such information is important in determining of the role of initial electron excitation and subsequent energy transfer and relaxation processes[ The accurate evaluation of these processes will be aided by improvements in both kinetic rate coe.cients and data quality[ Improvements in rate coe.cients may require further laboratory studies[ Improvement in data

are expected as improvements in instrumentation and observing conditions are implemented[ However\ given the faint and elusive nature of the observed phenomenon\ this is a demanding requirement[ As shown in Fig[ 0\ by reducing the path length between the sprites and the observer as well as increasing the altitude of the obser! vation point\ substantial improvement in data quality can be achieved without any changes in instrumentation[ This improvement is especially evident for emissions

J[S[ Morrill et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 700Ð718

712

Fig[ 00[ Relative vibrational populations comparing quenching only "Q# and "b# quenching\ ICT\ vibrational redistribution "QIR# at "a# 54 km and "b# 64 km\ with various measured vibrational distributions[ The names refer to the conventions of Green et al[ "0885# except for {Heavner| "Heavner et al[\ 0885#[

occurring in the shorter wavelength visible and near! UV spectral ranges "2999Ð4999 _#[ This spectral region contains numerous N1 and N¦ 1 emission features\ pri! 0 ¦ marily the Vegard!Kaplan "VK\ A2S¦ u : X S` #\ and Second Positive Group of N1 and the First Negative 1 ¦ ¦ Group "0NG\ B1S¦ u : X S` # of N1 "Vallance Jones\ 0863^ Cleary et al[\ 0884^ Broadfoot et al[\ 0886#[ The current model does not contain N¦ 1 species\ and so we initially focus our discussion on the N1 emissions[

In order to compare the e}ect of attenuation on a set of emission features in the 2999Ð4999 _ spectral range\ we have chosen two observing conditions[ First\ an obser! vation altitude of 4 km and a 499 km path length\ and second\ a 09 km observation altitude and a 099 km path length\ both observing emissions from 54 km altitude[ Model time pro_les of emission associated with three spectral features are shown in Fig[ 01[ The features are the 0PG "1\ 9#\ 1PG "9\ 2#\ and VK "0\ 09# vibrational

713

J[S[ Morrill et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 700Ð718

Fig[ 01[ Predicted temporal variation of emission for 0PG "1\ 9#\ 1PG "9\ 2#\ VK "0\ 09# bands "a# from altitudes of 54 km to 4 km\ along a 499 km path^ and "b# from altitudes of 54 km to 09 km\ along a 099 km path[

bands[ The band origins\ transition probabilities\ and predicted atmospheric transmission for the above two cases are listed in Table 2[ A comparison of Fig[ 01a and b shows the increase in the observed intensity of all features by factors of 1\ 12\ 069 for the 0PG\ 1PG\ VK bands\ respectively\ when the observation altitude is increased from 4 to 09 km and the path length is decreased from 499 to 099 km[ Further improvement can be realized by increasing the observation altitude from 09 km "nor! mal aircraft# to 19 km "high altitude aircraft#[ Attenu! ation by aircraft windows has not been included\ but this

e}ect could be minimized by use of quartz viewing ports[ The choice of 1PG and VK bands was based on their spectral position so that well!chosen passband _lters would allow them to be observed without overlap by nearby bands "Vallance Jones\ 0863\ Broadfoot\ 0885#[ There are other emission features associated with the measurement of sprites which would bene_t from measurements at higher altitudes and shorter path leng! ths[ This involves the measurement of the lower levels of the N1"B# and N¦ 1 "A# states[ The N1 0PG "9\9# band "N1"B\ v  9## emits at approximately 09\499 _ while the

714

J[S[ Morrill et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 700Ð718 Table 2 Transition parameters for N1 emissions Transmission Band

Origin "_#

Transition Probability "0:sec#

4 kmÐ499 km

09 kmÐ099 km

Ratio

0PG "1\ 9# 1PG "9\ 2# VK "0\ 09#

6621 3947 2316

2[85e3 0[09e5 8[76e!1

3[52e!0 2[16e!1 2[48e!2

8[31e!0 6[37e!0 5[05e!0

1 12 069

Transition parameters for N1 emissions used in Fig[ 01[ The distances under {Transmission| are the observing altitude and path length through the atmosphere\ respectively[

¦ N¦ 1 "9\ 9# and "0\ 9# Meinel bands "N1 "A\ v  9\ 0## emit at approximately 00\099 and 8199 _[ The 0PG "9\ 9# occurs in a region between water absorption features\ while the two N¦ "A# features would be strongly 1 absorbed unless the path length were kept short and the observing altitude were kept high "−09 km^ see Fig[ 0#[ Observation of these bands could be done photo! metrically and the population of these levels would pro! vide important additional information about the electron energies present in red sprites[ Regarding the observed spectrum in Fig[ 1\ we discuss two signi_cant points[ The _rst is the possible presence of N¦ 1 Meinel bands and the second is the observed N1"B# vibrational distribution[ With regard to the Meinel emis! sion\ the _t to the spectrum in Fig[ 1 gives us portions of the relative populations of the N1"B# and N¦ 1 "A# states\ and these are presented in Table 3 "see Fig[ 1b#[ Also in Table 3 are the N1"B# and N¦ 1 "A# vibrational distributions measured during an ½IBC1¦aurora observed by Vall! ance Jones and Gattinger "0867#[ As mentioned above\ low intensity and experimental uncertainties make the

Table 3 N1"B# and N¦ 1 "A# vibrational distributions*aurora vs sprite Aurora "IBC II¦# v

N1"B#

9 1[79 0 1[93 1 1[26 2 0[35 3 0[99 4 9[47 5 * 6 * Sv1Ð2 2[72 N¦ 0[02 1 "A#:N1"B#v  1Ð2

Red sprite

N¦ 1 "A#

N1"B#

N¦ 1 "A#

4[64 4[96 1[77 0[34 9[41 9[06 * * 3[22

* 0[02 2[97 0[49 0[99 9[53 9[25 9[03 3[47

* * 9[72 9[24 * * * * 0[07 9[15

N1 "B# and N¦ 1 "A# vibrational distributions in the aurora "Vall! ance Jones and Gattinger\ 0867# and in a red sprite "see Fig[ 1#[

present relative populations of the N1"B# and N¦ 1 "A# states preliminary and are best considered upper bounds for the N¦ 1 "A# population in this spectrum[ However\ it is worthwhile examining estimates of the average electron energies required to produce the observed ratio of N¦ 1 "A# to N1"B# populations in levels 1 and 2[ These estimates were made using a simpli_ed steady!state model involv! ing N1"C#\ N1"B# and N¦ 1 "A# excited by Boltzmann and quasi!electrostatic electron distributions\ which includes both quenching of N1"B# "Morrill and Benesch\ 0885# and N¦ 1 "A# "Piper et al[\ 0874#\ as well as radiative cascade "Gilmore et al[\ 0881#[ The results for 1 eV show the N¦ 1 "A#:N1"B# ratio to be on the order of 09−2 and 09−4 for these two types of distributions\ respectively[ In order to achieve a ratio of ½9[15 for the N¦ 1 "A\ v  1Ð2#:N1"B\ v  1Ð2# ratio "see Table 3#\ average ener! gies in the Boltzmann and quasi!electrostatic electron distributions in excess of 09 eV were required[ However\ Bell et al[ "0884# predict volume emission rates for 0PG and Meinel excited by runaway electrons[ From the ratio of the volume emission rates at 44 km ""4[6e2 ph:cc!s#: "0[5e5 ph:cc!s## and the average radiative lifetimes "03[2e!5s:4[8e!5s#\ the predicted N¦ 1 "A# and N1"B# popu! lations have a ratio of ½9[975[ This ratio is scaled up by factor of 0[27 in accordance with the recent branching ratio for the N¦ 1 "A# state "9[43# "Van Zyl and Pendleton\ 0884# rather than the value "9[28# used by Bell et al[ "0884#[ Further\ to compare to the N¦ 1 "A#:N1"B# ratio in Table 3\ the fraction of the population in levels 1 and 2 of these two states is accounted for with a scaling factor of 0[0 "i[e[ the fraction of the total population in levels 1 and 2 is roughly the same for both states\ ½22)#[ This yields a ratio of N¦ 1 "A\ v  1Ð2#:N1"B\ v  1Ð2# ½ 9[02 which is 49) of the observed ratio[ Given the uncer! tainties in the observed ratio and the lack of an obvious explanation for the presence of the Meinel band by either the Boltzmann or quasi!electrostatic electron distri! butions\ production of the observed spectrum*at least in part*by runaway electrons appears to be a reasonable possibility[ The above results have assumed that quenching rep! resents a loss of population from the N¦ 1 "A# state based

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on quenching rates reported by Vallance Jones "0863# which are similar to the values measured by Piper et al[ "0874#[ However\ Katayama et al[ "0879# and Katayama "0873# have shown collisional energy transfer\ similar to that discussed above "ICT#\ to occur rapidly between the ¦ N¦ 1 "A# and N1 "X# states[ This type of process tends to increase the apparent lifetime of an emitting state when it is collisionally coupled to a state with a longer lifetime\ as in this case[ Consequently\ the results by Bell et al[ "0884# would underestimate the N¦ 1 "A# state population[ An increase in this population would tend to further support the above analysis of the Meinel emission[ The strongest observed spectral features are the 0PG bands[ The results of Green et al[ "0885# show the N1"B# vibrational distributions associated with a number of spr! ite spectra "Fig[ 00#\ and indicate an average electron energy on the order of 0 eV[ This is signi_cantly lower than the auroral case "see Table 3# where\ for example\ the electron energy distribution in an IBC1¦aurora is expected to have an average energy on the order of ½2Ð 4 eV "Cartwright\ 0867^ Fig[ 1#[ We have reached similar conclusions to those of Green et al[ "0885# regarding the magnitude of electron energies in sprites based on the model N1"B# vibrational distribution shown in Fig[ 00a produced by electrons with an average energy of 0Ð1 eV "Fig[ 5#[ As shown in Fig[ 00\ the observed vibrational distributions peak at v  1\ unlike the auroral dis! tribution that peak at v  9[ Although the population for v  0 from the current spectral _t appears low\ an increase in the observed intensity of the 0PG "0\ 9# band at 7899 _ on the order of a factor of 1[4Ð2 would be required to have the observed distribution peak at v  0[ We are currently re!examining the intensity calibration near 8999 _ which could e}ect the corrected intensity of the Dv  0 sequence and so the populations of v  0 of the N1"B# state[ As mentioned above\ we are currently analyzing additional sprite spectra taken with higher resolution and better red sensitivity "Bucsela et al[\ 0887# that yield a preliminary estimate of the v  0 population at about twice the currently determined value[ However\ it is not necessarily the case that the summed spectrum of di}erent regions of sprites will be identical\ or nearly so\ given the variability and spatial structure of sprites[ Nonetheless\ the persistence of the v  1 enhancement observed by numerous groups "see Fig[ 00# is an indication of a pre! dominant process occurring during the 06Ð22 ms period of the video spectral data analyzed thus far[ Finally\ an additional mechanism that is known to produce 0PG emission but which has not been included in our model is energy pooling involving the N1"A# state "Piper\ 0877a\ b^ 0878#[ Here we refer to both N1"A#¦N1"A# and N1"A#¦N1"X\ v × ½4#[ Since the predicted N1"A# density only reaches values on the order of 094 molecules:cm2\ the N1"A#¦N1"A# process is not likely to produce signi_cant 0PG emission[ However\

since the vibrational excitation is ½099Ð0999 times larger than electronic excitation "Figs 6 and 7#\ there is a possi! bility that the process involving N1"A#¦N1"X\ v × ½4# could contribute to the 0PG emission[ However\ this process leads to N1"B# vibrational distributions that are strongly peaked at the lower levels\ unlike the observed distribution in Fig[ 00[ The spectral observations used in this paper represent data taken with TV _eld rate "06 ms resolution#\ so that portions of the observations could contain a portion due to an {afterglow| which may have a signi_cant e}ect on the observed spectrum[ Higher time resolution data can be extracted from the spectrograph and the afterglow process can be modeled with further e}ort[ Given the di}erences between the observed dis! tribution and those produced by the model\ further mod! elling and analysis of existing spectral data are warranted to determine the spatial and temporal variation of N1 excited state vibrational distributions and the processes which produce them[

7[ Conclusion We have presented the results of a quasi!electrostatic heating model\ combined with a time!dependent vibrational level populations model\ in order to examine the temporal behavior of N1 excited state populations in red sprites[ In order to compare the model results with spectral observations\ we have analyzed a recent sprite spectrum measured from the Wyoming Infrared Observ! atory "WIRO# on Jelm Mountain "Heavner et al[\ 0885\ Bucsela et al[\ 0887# and have included the recent spectral analysis made by Green et al[ "0885#[ The spectral analysis incorporates atmospheric attenuation models "e[g[ MOS! ART#\ and we have discussed the e}ect of atmospheric attenuation on various N1 emissions "0PG\ 1PG\ and VK#[ The e}ect of collisional processes other than simple quenching has also been presented and this represents a potential source of additional 0PG emission intensity[ The current spectral analysis indicates the possible presence of N¦ 1 Meinel emission in addition to the N1 0PG[ However\ due to the low observed intensity and experimental uncertainties the relative population of the 1 N1"B2P`# and N¦ 1 "A Pu# states should be considered as being preliminary[ The current analysis yields a vibrational distribution of the N1"B2P`# that requires an average electron energy of only 0Ð1 eV[ Model results show that the populations of the lower levels of the N1"B2P`# increase with increases in the electron energy[ If the presence of the N¦ 1 Meinel emission is con_rmed in other sprite spectra this may imply the presence of runaway electrons or enhancements in the electron energy distribution[ However\ further spectral and photo! metric observations will be required at both longer and shorter wavelengths in order to improve our under!

J[S[ Morrill et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 700Ð718

standing of the details of the electron energy distributions which occur in sprites[

Acknowledgements The computer time was supported by the Solar Physics Branch and X!Ray Astronomy Branch in the Space Sci! ence Division of the Naval Research Laboratory and STAR Laboratory of Stanford University[ The atmo! spheric transmission calculations were performed using the MOSART model as implemented in the SSGM "Syn! thetic Scene Generation Model# at the Space Science Division of the Naval Research Laboratory[ E[ J[ Bucsela was supported by an ASEE Postdoctoral Fellowship[ J[ S[ Morrill was supported in part by the Edison Memorial graduate training program at the Naval Research Lab! oratory^ V[ P[ Pasko was supported by an NSF Post! doctoral Fellowship under NSF grant ATM!8411705 to Stanford University^ and D[ R[ Moudry\ M[ J[ Heavner\ D[ D[ Sentman\ and E[ M[ Wescott were supported by NASA grant NAG4!4908[ The authors would like to thank B[ D[ Green for providing the B2Pg vibrational distributions\ G[ R[ Swenson for numerous interesting conversations on red sprites\ and U[ S[ Inan\ T[ F[ Bell\ and S[ G[ Queen for their critical review of the manu! script[

References Armstrong\ R[A[\ Shorter\ J[A[\ Taylor\ M[J[\ Suszcynsky\ D[M[\ Lyons\ W[A[\ Leong\ L[S[\ 0887[ Photometric measure! ments in the SPRITES |84 + |85 campaigns\ nitrogen second positive "288[7 mn# and _rst negative "316[7 nm# emission[ J[ Atmos[ Sol[ Terr[ Phys[ 59\ 676Ð688[ Bell\ T[F[\ Pasko\ V[P[\ Inan\ U[S[\ 0884[ Runaway electrons as a source of red sprites in the mesosphere[ Geophys[ Res[ Lett[ 11\ 1016Ð1029[ Benesch\ W[\ 0870[ Mechanism for the auroral red lower border[ J[ Geophys[ Res[ 75\ 8954Ð8961[ Benesch\ W[\ 0872[ Intersystem collisional transfer of excitation in low altitude aurora[ J[ Chem[ Phys[ 67\ 1867Ð1872[ Benesch\ W[\ Fraedrich\ D[ 0873[ The role of intersystem col! lisional transfer of excitation in the determination of N1 vib! 2 ronic level populations[ Application to B?2S− u −B P` band intensity measurements[ J[ Chem[ Phys[ 70\ 4256Ð4263[ Berk\ A[\ Bernstein\ L[S[\ Robertson\ D[C[\ 0878[ MODTRAN] A Moderate Spectral Resolution Model for LOWTRAN6\ Phillips Laboratory Report No[ GL!TR!78!9011[ Broadfoot\ A[L[\ Hat_eld\ D[B[\ Anderson\ E[R[\ Stone\ T[C[\ Sandel\ B[R[\ Murad\ E[\ Hecht\ D[J[\ Pike\ C[P[\ Viereck\ R[A[\ Gardner\ J[A[\ 0886[ The N1 triplet band systems and atomic oxygen in the dayglow[ J[ Geophys[ Res[\ 091\ 00456Ð 00473[ Bucsela\ E[J[\ Sharp\ W[E[\ 0886[ NI 7579 and 7518 _ multiplets in the dayglow[ J[ Geophys[ Res[ 091\ 1346Ð1355[ Bucsela\ E[J[\ Heavner\ M[J[\ Morrill\ J[S[\ Pasko\ V[P[\ Berg\

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J[S[ Morrill et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 700Ð718

Desroschers\ J[T[\ 0885[ Spectral observations of sprites "abstract#[ Eos Trans[ AGU\ 66 "35# Fall Meet[ Suppl[\ 59[ Hedin\ A[E[\ 0880[ Extension of the MSIS thermosphere model into the middle and lower atmosphere[ J[ Geophys[ Res[ 85\ 0048[ Huber\ K[P[\ Herzberg\ G[\ 0868[ Molecular Spectra and Molec! ular Structure] IV Constants of Diatomic Molecules[ Van Nostrand Reinhold\ New York[ Inan\ U[S[\ Reising\ S[C[\ Fishman\ G[J[\ Horack\ J[M[\ 0885[ On the association of terrestrial gamma!ray bursts with light! ning and implications for sprites[ Geophys[ Res[ Lett[ 12\ 0906Ð0919[ Katayama\ D[H[\ 0873[ Collision induced electronic energy transfer between the A1Pui "v  3# and X1S¦ ` "v  7# rotational manifolds of N¦ 1 [ J[ Chem[ Phys[ 70\ 2384Ð2383[ Katayama\ D[H[\ Miller\ T[A[\ Bondybey\ V[E[\ 0879[ Col! lisional deactivation of selectively excited N¦ 1 [ J[ Chem[ Phys[ 61\ 4358Ð4364[ Laher\ R[R[\ Gilmore\ F[R[\ 0880[ Improved _ts for the vibrational and rotational constants of many states of nitro! gen and oxygen[ J[ Phys[ Chem[ Res[ Data 19\ 574Ð601[ Lehtinen\ N[G[\ Walt\ M[\ Inan\ U[S[\ Bell\ T[F[\ Pasko\ V[P[\ 0885] g!ray emission produced by a relativistic beam of run! away electrons accelerated by quasi!electrostatic thunder! cloud _elds[ Geophys[ Res[ Lett[ 12\ 1534Ð1537[ Lehtinen\ N[G[\ Bell\ T[F[\ Pasko\ V[P[\ Inan\ U[S[\ 0886[ A two!dimensional model of runaway electron beams driven by quasi!electrostatic thundercloud _elds[ Geophys[ Res[ Lett[ 13\ 1528Ð1531[ McCarthy\ M[P[\ Parks\ G[K[\ 0881[ On the modulation of X ray ~uxes in thunderstorms[ J[ Geophys[ Res[ 86\ 4746Ð4753[ Mende\ S[B[\ Rairden\ R[L[\ Swenson\ G[R[\ Lyons\ W[A[\ 0884[ Sprite spectra] N1 0PG band identi_cation[ Geophys[ Res[ Lett[ 11\ 1522Ð1525[ Milikh\ G[M[\ Papadopoulos\ K[\ Chang\ C[L[\ 0884[ On the physics of high altitude lightning[ Geophys[ Res[ Lett[ 11\ 74Ð 7[ Milikh\ G[M[\ Valdivia\ J[A[\ Papadopoulos\ K[\ 0886[ Model of red sprite optical spectra[ Geophys[ Res[ Lett[ 13\ 722Ð725[ Morrill\ J[S[\ 0875[ The e}ect of collisions and plasma pre! conditioning on the vibrational level population of molecular nitrogen[ Thesis\ Univ[ of Md[\ College Park[ Morrill\ J[\ et al[\ Carragher\ B[A[\ Benesch\ W[\ 0877[ Popu! lation development of auroral molecular nitrogen species in a pulsed discharge[ J[ Geophys[ Res[ 82\ 852Ð866[ Morrill\ J[\ Benesch\ W[\ 0889[ Plasma preconditioning and the role of elevated vibrational temperature in production of excited N1 vibrational distributions[ J[ Geophys[ Res[ 84\ 6600Ð6613[ Morrill\ J[S[\ Benesch\ W[M[\ Widing\ K[G[\ 0880[ Electron temperatures in a pulse electric discharge and the associated N1 electron excitation rate coe.cients[ J[ Chem[ Phys[ 83\ 151Ð158[ Morrill\ J[S[\ Benesch\ W[M[\ 0883[ The role of N1"A?4S¦ ` # in the enhancement of N1 B2Pg "v  09# populations in the after! glow[ J[ Chem[ Phys[ 090\ 5418Ð5426[ Morrill\ J[S[\ Benesch\ W[M[\ 0885[ Auroral N1 emissions and the e}ect of collisional processes on N1 triplet state vibrational populations[ J[ Geophys[ Res[ 090\ 150Ð163[ Papadopoulos\ K[\ Milikh\ G[\ Gurevich\ A[\ Drobot\ A[\ Shanny\ R[\ 0882[ Ionization rates for atmospheric and iono! spheric breakdown[ J[ Geophys[ Res[ 87\ 06482Ð06485[

Pasko\ V[P[\ Inan\ U[S[\ Taranenko\ Y[N[\ Bell\ T[F[\ 0884[ Heating\ ionization and upward discharges in the mesosphere due to intense quasi!electrostatic thundercloud _elds[ Geophys[ Res[ Lett[ 11\ 254Ð257[ Pasko\ V[P[\ 0885[ Dynamic coupling of quasi!electrostatic thundercloud _elds to the mesosphere and lower ionosphere] sprites and jets\ Ph[D[ dissertation\ Stanford[ University of California[ Pasko\ V[P[\ Inan\ U[S[\ Bell\ T[F[\ 0885[ Sprites as luminous columns of ionization produced by quasi!electrostatic thun! dercloud _elds[ Geophys[ Res[ Lett[ 12\ 538Ð541[ Pasko\ V[P[\ Inan\ U[S[\ Bell\ T[F[\ Taranenko\ Y[N[\ 0886a[ Sprites produced by quasi!electrostatic heating and ionization in the lower ionosphere[ J[ Geophys[ Res[\ 091\ 3418[ Pasko\ V[P[\ Inan\ U[S[\ Bell\ T[F[\ 0886b[ Gravity waves above mesoscale thunderstorms and small scale structure of sprites\ "abstract#[ Eos Trans[ AGU\ Spring meet[ Suppl[ Pavlov\ A[V[\ Buonsanto\ M[J[ 0885[ Using steady state vibrational temperatures to model e}ects of N 1 on cal! culations of electron densities[ J[ Goephys[ Res[ 090\ 15\830Ð 15\834[ Phelps\ A[V[\ 0876[ Excitation and ionization coe.cients[ Gase! ous Dielectric 4\ 0Ð8[ Piper\ L[G[\ 0877a[ State!to!state N1"A2S¦ u # energy pooling reac! tions[ I[ The formation and quenching of N1"C# 2Pu# and Herman infrared system[ J[ Chem[ Phys[ 77\ 120Ð128[ Piper\ L[G[\ 0877b[ State!to!state N1"A2S¦ u # energy pooling reactions[ II[ The formation and quenching of N1"B2P`\ v  0Ð 01#\ J[ Chem[ Phys[ 77\ 5800Ð5810[ Piper\ L[G[\ 0878[ The excitation of N1"B2P`\ v  0Ð01# in the reaction between N1"A2S¦ u # and N1"X\ v − 4#\ J[ Chem[ Phys[ 80\ 753Ð762[ Piper\ L[G[\ 0882[ Reevaluation of the transition!moment func! 0 ¦ tion and Einstein coe.cients for the N1"A2S¦ u −X S` # tran! sition[ J[ Chem[ Phys[ 88\ 2063Ð2070[ Piper\ L[G[\ Holtzclaw\ K[W[\ Green\ B[D[\ 0878[ Experimental determination of the Einstein coe.cients for the N1"B−A# transition[ J[ Chem[ Phys[ 89\ 4226Ð4234[ Richard\ A[\ de Souza\ A[R[\ 0883[ Active species in N1 ~owing post!discharges[ J[ Phys[ III France 3\ 1482Ð1599[ Roussel!Dupre\ R[A[\ Gurevich\ A[V[\ Tunnell\ T[\ Milikh\ G[M[\ 0883[ Kinetic theory of runaway air breakdown[ Phys[ Rev[ E 38\ 1146[ Roussel!Dupre\ R[A[\ Gurevich\ A[V[\ 0885[ On runaway break! down and upward propagating discharges[ J[ Geophys[ Res[ 090\ 1186[ Rowland\ H[L[\ Fernsler\ R[F[\ Huba\ J[D[\ Bernhardt\ P[A[\ 0885[ Lightning driven EMP on the upper atmosphere[ Geophys[ Res[ Lett[ 11\ 250[ Rowland\ H[L[\ Fernsler\ R[F[\ Bernhardt\ P[A[\ 0885[Breakdown of the neutral atmosphere in the D!region due to lightning driven electromagnetic pulses[ J[ Geophys[ Res[ 090\ 6824Ð6834[ Rowland\ H[L[\ 0887[ Theories and simulations of elves\ sprites\ and blue jets[ J[ Amos[ Solar Terr[ Phys[ 59\ 720Ð733[ Sentman\ D[D[\ Wescott\ E[M[\ Osborne\ D[L[\ Hampton\ D[L[\ Heavner\ M[J[\ 0884[ Preliminary results from the Sprites 83 campaign] Red sprites[ Geophys[ Res[ Lett[ 11\0194Ð0197[ Sentman\ D[D[\ Wescott\ E[M[\ Heavner\ M[J[\ Moudry\ D[R[\ 0885] Observations of sprite beads and balls[ EOS Trans[ AGU\ 66\ F50\ Fall Meet[ Suppl[\ A60B!6[

J[S[ Morrill et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 700Ð718 Stanley\ M[\ Krehbiel\ P[\ Rison\ W[\ Moore\ C[\ Brook\ M[\ Vaughan\ O[H[\ 0885[ Observations of sprites and jets from Langmuir laboratory\ New Mexico[ EOS Trans[ AGU\ 66\ F58\ Fall Meet[ Suppl[\ A00A!6[ Taranenko\ Y[N[\ Inan\ U[S[\ Bell\ T[F[\ 0882a[ The interaction with the lower ionosphere of electromagnetic pulses from lightning] heating\ attachment\ and ionization[ Geophys[ Res[ Lett[ 19\ 0428Ð0431[ Taranenko\ Y[N[\ Inan\ U[S[\ Bell\ T[F[\ 0882b[ The interaction with the lower ionosphere of electromagnetic pulses from lightning] excitation of optical emissions[ Geophys[ Res[ Lett[ 19\ 1564Ð1567[ Taranenko\ Y[N[\ Roussel!Dupre\ R[A[\ 0885[ High altitude discharges and gamma!ray ~ashes] a manifestation of run! away air breakdown[ Geophys[ Res[ Lett[ 12\ 460Ð463[ Taylor\ M[J[\ Clark\ S[\ 0885[ High resolution CCD and video imaging of sprites and elves in the N1 _rst positive band emission[ EOS Trans[ AGU\ 66\ F59\ Fall Meet[ Suppl[\ A60B!3[ Torr\ D[G[\ Torr\ M[R[\ 0871[ The role of metastable species in the thermosphere\ Rev[ Geophys[ Space Phys[\ 19\ 80Ð033[ Trajmar\ S[\ Register\ D[F[\ Chutjian\ A[\ 0872[ Electron scat! tering by molecules by molecules\ II\ Experimental methods and data[ Phys[ Rep[\ 86\ 108Ð245[ Vallance Jones\ A[\ 0863[ Aurora\ Geophysics and Astrophysics Monographs\ D[ Reidel\ Hingham\ Mass\ U[S[A[

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Vallance Jones\ A[\ Gattinger\ R[L[\ 0863[ Quantitative spec! troscopy of the aurora\ IV^ the spectrum of medium intensity aurora between 7799 _ and 00399 _[ Can[ J[ Phys[ 43\ 1017Ð 1022[ Vallance Jones\ A[\ Gattinger\ R[L[\ 0867\ Vibrational devel! opment and quenching e}ects in the N1"B2P`−A2S¦ u # and 1 1 ¦ N¦ 1 "A Pu−X S` # system in aurora[ J[ Geophys[ Res[ 72\ 2144Ð2150[ ¦ ¦ Van Zyl\ B[\ Pendleton\ Jr[\ W[\ 0884[ N¦ 1 "X#\ N1 "A#\ and N1 − "B# production in e ¦N1 collisions[ J[ Geophys[ Res[ 099\ 12\644Ð12\651[ Wescott\ E[M[\ Sentman\ D[D[\ Heavner\ M[J[\ Moudry\ D[R[\ 0885[ Blue jets\ lightning and large hail[ EOS Trans[ AGU\ 66\ F56\ Fall Meet[ Suppl[\ A61C!2[ Wilcoxen\ B[\ Heckathorn\ H[\ 0885[ Synthetic Scene Generation Model "SSGM R6[9#\ in Targets and Backgrounds] Charac! terization and Representation II[ Proceedings of the Inter! national Society for Optical Engineering 1631\ 46Ð57[ Zubek\ M[\ 0883] Excitation of the C2Pu state of N1 by electron impact in the near!threshold region[ J[ Phys[ B] At[ Mol[ Opt[ Phys[ 16\ 462Ð470[ Zubek\ M[\ King\ G[C[\ 0883[ Di}erential cross sections for − electron impact excitation of the C2Pu\ E2S¦ ` \ and a?Su states of N1[ J[ Phys[ B] AT[ Mol[ Opt[ Phys[ 16\ 1502Ð1513[