Comparison of a model for air fluorescence via electron beam excitation with experimental data

ARTICLE IN PRESS Nuclear Instruments and Methods in Physics Research A 597 (2008) 110–114

Contents lists available at ScienceDirect

Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima

Comparison of a model for air fluorescence via electron beam excitation with experimental data M.A. Nelson , L.A. Triplett, J.J. Colman, R. Roussel-Dupre´ Los Alamos National Laboratory, Earth and Environmental Sciences Division, Los Alamos, NM, USA

a r t i c l e in f o

a b s t r a c t

Available online 22 August 2008

Air fluorescence is a process that is important in a variety of subject areas including sprites, plasmas, cosmic ray showers, and Teller light from nuclear detonations. In 1968, Davidson and O’Neil published the results of an experiment that measured fluorescence efficiencies from about 300 to 1000 nm. In this paper, we model an electron beam from first principles and compare our air fluorescence efficiency results to these measurements. & 2008 Elsevier B.V. All rights reserved.

Keywords: Electrical discharge physics Air fluorescence Lightning

1. Introduction

2. Review of the O’Neil and Davidson experiment

Recent developments in our understanding of lightning have provided us with an entirely new perspective on how the Earth’s atmosphere couples to the cosmos. In many respects our atmosphere can be thought of as a giant scintillator that is continuously lit up by the passage of energetic radiation from space. Russian and Los Alamos scientists [1] have recently pointed out the fact that lightning could be initiated by cosmic rays. In other words thunderstorms can locally enhance the optical output of the atmospheric scintillator in a dazzling display, one that has fascinated man for millennia. This notion has far reaching implications both for the potential utility of lightning as a diagnostic to probe the mysteries of energetic cosmic ray showers and therefore the universe and for the very nature of the lightning discharge and its effects on the atmosphere. While measurements are the cornerstone of any science, modeling enables us to design sensors to better measure the phenomenon and helps us to integrate our knowledge of the measurements. The purpose of this paper is to outline our method of modeling the spectrum of light, from 300 to 1100 nm, that is initiated by a beam of electrons. Several experimentalists have reported measurements of the air fluorescence from a beam of electrons in air or nitrogen [2–6]. We will describe the O’Neil and Davidson experiment briefly [3]. We will then describe our modeling from first principles of the excitation rates and the amount of fluorescence light emitted at each transition wavelength. We will then elucidate where the models agree and disagree and explain how to resolve these discrepancies.

In their 1968 technical report ‘‘The fluorescence of air and nitrogen excited by energetic electrons’’, O’Neil and Davidson discuss the results of two types of experiments they performed. The experiments were performed with an experimental apparatus designed to provide high beam currents with kilovolt energy incident on target gases across a wide range of pressures. The major categories of measurements performed were of fluorescence efficiency and excitation cross-section of the two target gases, nitrogen and air. Fluorescence efficiencies were determined in the so-called ‘‘thick target’’ experiments, in which the incident electrons were stopped within the observation region of a target chamber and measurements of absolute intensity involving spectrometer measurements across the 200–1100 nm range yielded fluorescence efficiencies. Radiation emitted by the target gas was spectrally analyzed by a 1 m MacPherson f/10.0 scanning monochromator of the Czerny Turner design with photomultipliers being used as the detectors at the exit slit of the monochromator. Identical sets of experiments were performed for both nitrogen and air, with gas at 22 torr pressure excited by 10 keV electrons and gas at 600 torr excited by 50 kV electrons. The electron beam was provided by a gun of the type used in Van de Graaf accelerators and was modulated at the lower end of the voice frequency (VF) range at a few hundred Hz with a 10–20% duty cycle.

 Corresponding author.

E-mail address: [email protected] (M.A. Nelson). 0168-9002/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2008.08.059

3. Modeling of experiments When a beam of energetic electrons is injected into the air, these high-energy electrons create a large number of lower energy secondary electrons. Collisions by these secondary electrons cause

ARTICLE IN PRESS M.A. Nelson et al. / Nuclear Instruments and Methods in Physics Research A 597 (2008) 110–114

a molecule to transit to an excited state. Decay of the excited state happens in one of the two ways. The excited molecule may collide with another molecule, undergo radiation-less thermal decay and transfer its energy. On the other hand, the excited molecule may transfer an electron to a lower state and emit a photon. The wavelength of light emitted is determined by the excited state and the lower state. The intensity of light produced is a competition between the lifetime of radiation of the excited state (fluorescence efficiency) and the number of collisions of the excited state with other molecules (quenching). It is also a function of the number and the energy of high-energy (primary) electrons and the time between collisions of electrons with air molecules. We modeled the Davidson and O’Neil experiment [3] using a model we developed called Physics based Optical Emission Model (POEM) to determine fluorescence efficiency as a function of excitation rates in conjunction with models for the primary and secondary electrons, known as SWARM and PLUME, also developed by our group, to determine the excitation rates as a function of incident primary electron energy and flux. SWARM models non-relativistic secondary electrons by performing a full 2-D (cylindrically symmetrical) solution to the Boltzmann equation using collision integrals to describe electron transport in a gas subject to a uniform, steady-state electric field. Modeling of the secondary electrons is essential, as they dominate the excitation that leads to air fluorescence. The excitation crosssections at the primary electron energies are an order of magnitude lower, but more importantly, there are orders of 1500 times as many secondary electrons as primaries. (The energetic electron expends 34 eV per ion pair created, so the 50 keV primary electron produces 1500 secondary electrons.) PLUME models high-energy electrons via solution to the relativistic Fokker–Planck equation [16]. POEM uses the excitation rates calculated by use of SWARM and PLUME to predict the fluorescence efficiencies. To model the light power from the decay from the excited state, we assumed a 2-D cylindrical geometry:   Z Z Joules c R Z ab P annb0 ¼ 107  h A 0  Zan  Nðr; z; tÞ2pr dr dz (1) 3 l 0 0 nn cm s where the symbols a and b denote excited electronic states and n and n0 denote vibrational levels. Nðr; z; tÞ is the free electron density (the density of secondary or primary electrons in the vicinity). We included the following nitrogen electronic states in our model: N2 X (ground state), N2 a1 Pg , N2 a0 1 Su , N2 A3 Suþ , N2 B3g (1st Positive or 1P lines), N2 C3u (2nd Positive or 2P lines), N2 D3uþ , N2 E3gþ , N2 B0 3u , N2 þ X1gþ (the ground state of the positively ionized species), N2 þ B2uþ (1st Negative or 1N transitions), and N2 þ A2u . Zan is the number density (in units of per centimeter cubed) of the n-th vibrational level of electronic state a and is found by solving the following equation [7,8]: 2 3 X X ba b X X aj a X a5 a 4 Ain0 Zi ¼ An0 r þ Q n0 Zi . (2) kn0 0 Z0 þ b b;a

i

j

r

Ai;j is the Einstein spontaneous transition probability (in units of per second) from the vibrational level i of state b to level j of state a. Z is the number density of electrons (in a specified electronic and vibrational state). Q an0 is the total quenching rate (in units of per second) of level n0 of state a. ZX0 is the ground state number a density (in units of per cubic centimeter). kn0 ;0 is the electron impact excitation rate (in units of per second) of state a of the 0-th vibrational level of the ground electronic state. Note that population of levels via collisional de-excitation of higher energy levels is neglected in the above expression, although a particularly

111

significant case of this phenomenon is treated in the model as described in Section 5. a The electron excitation rate kn;n0 and the electron number density for 600 and 5 torr were calculated by Colman and RousselDupre´. The modeling of the excitation rates is described in more detail in a forthcoming publication and in a published technical report [9]. In summary, a solution was performed of a full 2-D (momentum space) Boltzmann equation applied to the behavior of electron swarms (the model is called SWARM). Swarm studies allow one to connect experimental macroscopic quantities in the form of transport parameters and rate coefficients with crosssections for all the processes found in the investigated physical system. In the regime of a weakly ionized gas, electron-neutral collisions dominate the collision of electrons with other electrons, ions, or excited molecules. The relevant processes included in their modeling are: elastic scattering, three-body attachment, two-body attachment, rotational excitation, vibrational excitation, electronic excitation, and ionization. They compared their model with a variety of data including drift velocity, characteristic energy, two- and three-body attachment coefficients, ionization rates, and with other models for the electronic states and found good agreement with much of the domain. Our modeling indicated that there was a small self-consistent electric field from the beam of about 43 V/m. The inclusion of this small field in the model increased the excitation rates by about a factor of 10. The electronic excitation is a threshold process, so there can exist a very high sensitivity of the excitation cross-section to electron energy—a small increase in the energy due to the presence of a small electric field can result in a very large increase in excitation rate. A more detailed investigation of this rather surprising result and an examination of whether this phenomena is actually manifested in typical laboratory air florescence experiments is a subject of a future paper. Our modeling required that we know the fraction of the excitation rate of a given electronic state that went into exciting the ground vibrational state of the vibrational band associated with that of the electronic state. We approximated this by multiplying the electronic state excitation rates by the Franck– ;X Condon factor qan;0 . We obtained our Einstein and Franck–Condon factors from Gilmore et al. [10] and obtained electronic tabulations from the following website: http://spider.ipac.caltech.edu/ staff/laher/fluordir/fluorindex.html. To calculate the efficiency, we divided the power in each wavelength by the input power of the beam (50 W, the product of the electron gun current (1 mA) and the energy of the electrons emitted by the gun (50 keV)).

4. Quenching Selection of appropriate quenching or collisional de-excitation rate coefficients is made difficult by the fact that measurements of quenching have been performed in a variety of ways with different quantities being reported in each case. In some cases measurements reported in the literature were performed in air, whereas in others experimental data with regards to quenching rates in pure nitrogen and pure oxygen environments from different sources obtained using different measurement techniques must be interpreted to obtain a result for air quenching. Various authors have reported quenching results in terms of the quenching coefficient K ðtorr1 Þ, the collisional de-excitation rate coefficient a ðcm3 =sÞ, and the characteristic pressure P0 , which is the pressure at which the radiative lifetime is equal to the collisional de-excitation lifetime. The vibrational state dependent quenching coefficients for quenching by ‘‘air’’ (treated as 79% N2 and 21% O2 , thus neglecting

ARTICLE IN PRESS 112

M.A. Nelson et al. / Nuclear Instruments and Methods in Physics Research A 597 (2008) 110–114

4.2. Nitrogen 2nd Positive

Quenching Coefficient (cm3/molecule-sec)

1.00E-08 0

5

10

15

20

25 N2 2nd Positive 2P(0,0) transition (337.1 nm)—quenching of the C3 Pu state. Although measurements of the collisional deactivation rate, the characteristic pressure P 0 , and radiative lifetime for the upper state of this transition have been reported from various sources, the level of agreement between the collisional de-excitation rates we calculated based on these various measurements is poor.

1.00E-09

1.00E-10

1.00E-11 4.3. Nitrogen 1st Negative

1.00E-12

N2 A N2 B, W, a1, w1,D,E N2 B’, a’1 N2 C N2 +A (M) N2 +B (1N)

1.00E-13

Nþ 2 1st Negative 1N(0,0) transition (391.4 nm)—quenching of the B2 Sþ u state. The agreement amongst the available data for the quenching of this state is by far the best amongst the three upper level states associated with the transitions of greatest interest to us.

Vibrational State Fig. 1. Vibrational state dependence of quenching coefficients for quenching by air used for the various electronic states.

quenching by Ar, CO2 , H2 O, and trace constituents of air) used in the model are displayed in Fig. 1. Many are calculated via a combination of separately collected data for quenching of a given species by O2 and N2 . The vibrational state dependent N2 ðAÞ quenching coefficients were taken from the data reported by Cartwright [8] based on the experimental measurements for quenching by N2 by Dreyer and Perner [11] and for O2 by Dreyer et al. [12]. The N2 ðBÞ quenching coefficients for quenching by N2 from Cartwright [8] were combined with measurements for quenching of N2 ðBÞ by O2 from Piper [13]. The N2 ðCÞ state quenching rates measured by Pancheshnyi [14,15] were selected for both N2 and O2 quenching. The quenching of N2 ðB0 Þ by N2 was taken from Morrill and Benesch [17]. Quenching coefficients for the N2 ðB0 Þ and N2 ða0 1Þ states were assumed to be identical and thus served as a lumped parameter. Similarly the quenching coefficients of N2 ðBÞ were assigned to N2 ðWÞ, N2 ða1 Þ, N2 ðw1 Þ, N2 ðEÞ, N2 ðDÞ, the whole set forming another lumped parameter. Cartwright [7] argued that the quenching rates of the N2 a1 Pg and N2 B3 Pg states should be very similar due to the fact that the two states have the same electronic configuration and differ only in their spin coupling. Due to unavailability of experimental data regarding vibrational state dependent quenching rates for most of the electronic states of interest, the assumption of similar quenching behavior to that of N2 ðBÞ was made by the authors for the other N2 states as in Cartwright [8]. The quenching of the Nþ 2 ðBÞ state was taken from Kemper and Bowers [18] value for quenching by N2 and the Comes and Spier [19] value for quenching by O2.

4.1. Nitrogen 1st Positive N2 1st Positive 1P(0,0) transition (1050.8 nm)—quenching of the B3 Pg state. The available information regarding quenching of the upper state of this transition in air is very limited. The Cartwright [8] numbers for quenching for both O2 and N2 are based on their extrapolation and interpolation of experimental data they obtained from various sources. They combined N2 quenching data for v0 ¼ 0,1,2 from Dreyer and Perner [11] with v0 X2 from Polak et al. [20]. They assumed that the vibrationally dependent O2 quenching rates for the N2 B electronic state and all other N2 states were the same as those measured for N2 A ðv0 ¼ 028Þ by Dreyer et al. [12].

5. Intersystem collisional transfer of excitation In addition to quenching, higher vibrational levels of some transitions can de-excite into higher vibrational levels of other transitions. This process, known as intersystem collisional transfer (ICT) of excitation, occurs between vibrational levels of the lowlying N2 triplet states. Excited state population is transferred between vibrational levels of the B3 Pg and the A3 Su þ, W3 Du , 3 B0 Su  electronic states as per N2 ðBÞ þ N2 ðXÞ !N2 ðA; W; B0 Þ þ N2 ðXÞ. We implemented the ICT mechanism described in Morrill and Benesch [17] and used their ICT of excitation rate coefficients. The rate coefficients for transfer from the N2 ðBÞ state to the N2 ðAÞ, N2 ðWÞ, and N2 ðB0 Þ states were based upon the overall collisional transfer rates (assumed to be the sum of those between individual vibrational states) measured by Rotem and Rosenwaks [21], with an approximation being used by Morrill and Benesch [17] as follows. They assumed that only ICT to nearest energy neighbor vibrational levels from N2 ðBÞ to the overlapping N2 ðAÞ, N2 ðWÞ, and N2 ðB0 Þ states are significant and that the rates scale as ðg g =g B Þ  expðjEjÞ, where g g =g B is the degeneracy ratio of the two electronic states, and E is the energy difference between the two vibrational levels involved in the transition; this expression having the effect of weighting ICT transitions with similar energies more heavily. Due to what are apparently dipole selection rules, the ICT transitions within the N2 triplet manifold are modeled as occurring only between the B3 Pg and the A3 Su þ, 3 W3 Du , B0 Su states, with no ICT transitions allowable between the A, W, and B0 states. The ICT mechanism was implemented in our code in an attempt to model more accurately the N2 1P transitions. Equilibrium vibrational populations of the N2 triplet excited states involved in the ICT were determined via the Morrill and Benesch [17] formulation, using equations of statistical equilibrium. For a vibrational level n, in an electronic state a, the number density ðnan Þ=ðnN2 Þ at statistical equilibrium is given by X X ba A K aei;n þ ½Ai;n þ dAb  di;nþ2ð3Þ ½nbi =nN2  I

b

2 3 X X ag ag A ðAn;j þ K ICT;n;j þ K VR;n;j Þ5  ½nan =nN2  ¼ K q;n  ½nan =nN2  þ 4 a

2 þ4

g

XX g

j

3

dA;g  dn;jþ2ð3Þ 5  ½nan =nN2 

(3)

j

where K aei;n is the electron impact excitation rate (per N2 molecule) of vibrational level n in state a; AbI;na the transition a probability from bðIÞ to aðnÞ; K bICT;i; n , the ICT rate from bðIÞ to aðnÞ;

ARTICLE IN PRESS M.A. Nelson et al. / Nuclear Instruments and Methods in Physics Research A 597 (2008) 110–114

K AVR;i;n , the vibrational redistribution rate from AðIÞ to AðnÞ; K aq;n ¼ kq ðO2 Þ; na ðnO2 Þ þ kq ðN2 Þ; na ðnN2 Þ, the total quenching rate; a; b; g, the electronic states and i; j the source and sink vibrational levels, respectively. The rates are in (1/s). We have not yet incorporated vibrational redistribution coefficients in our model and are thus neglecting vibrational redistribution of the N2 ðAÞ state to the extent that it is not imbedded in the experimental quenching coefficient data used for the N2 ðAÞ state, therefore the expression we implement in our code is simplified to X X ba b K aei;n þ ½Ai;n ½ni =nN2  2

b

I

a

¼ 4K q;n þ

XX g

3 ag ðAn;j

ag

þ K ICT;n;j Þ5  ½nan =nN2 .

(4)

j

6. Results The electron excitation rates computed using our PLUME and SWARM models for the various electronic levels of N2 and N2 þ which we include in our POEM model are displayed in Table 1, for the 50 keV e 600 torr air O’Neil and Davidson experimental scenario. In Figs. A1 and A2 of Appendix A, the fluorescence efficiencies calculated by the POEM model are compared with those reported by O’Neil and Davidson in their 1968 technical report [3], for 50 keV e targeted on air at a pressure of 600 torr. Fig. A1 displays the lines corresponding to N2 2P and N2 + 1N transitions, and Fig. A2 the lines corresponding to N2 1P transitions. The efficiency ratio of the data from the POEM model to the experimental data is displayed for all of the transitions in Tables A1 and A2 in Appendix A.

7. Discussion The level of agreement of the model predictions for efficiencies of the various N2 2P and N2 þ 1N transitions (Fig. A1) with the O’Neil and Davidson data is much higher than that with the N2 1P transition data (Fig. A2). This we believe to be a result of both the difficulty of selecting quenching coefficient data for the N2 ðB3 Pg Þ state vibrational levels due to the very low level of agreement between the available data sources and perhaps also to a need for refinement in the implementation of the ICT algorithm. Implementation of the ICT mechanism in the code resulted in a better match to the experimental data for many transitions, but a worse match for others.

There are some ambiguities regarding the O’Neil and Davidson experiment which may effect interpretation of their data. The spectra were collected with the monochromator aligned with the center of the fluorescing volume. The f/10 monochromator was positioned such that the field of view was slightly underfilled, this ensuring that the total fluorescing region was observed with a slight sacrifice in solid angle collecting efficiency. This means that if the fluorescing region was not uniform in its spectral output due to existence of more low energy secondary electron based excitations towards the edges and due to non-uniformity of temperature, the measured spectra is a representation of the total spectral output of the glowing region rather than that of the gas excited by the primary electrons. Thus the reported spectra are not necessarily an accurate representation of the spectra of gas excited by the primary electron energies. Furthermore, in the interpretation of their spectral data, which was collected at a single position, O’Neil and Davidson assumed isotropic emission from the source region, which contained a non-spherically symmetric distribution of electrons and electron energies. The level of variation of the spectral content of the emission as a function of angular position in a gaseous glow region upon excitation by energetic particles is an issue which does not seem to have been thoroughly addressed.

8. Conclusions Future goals include further benchmarking of the results by comparison with those of other models [22], modeling of scenarios involving a wide range of electron energies incident on both nitrogen and air across a range of pressures, and detailed investigation of the effect of small electric fields. A number of experiments making measurements of air fluorescence in the 300–400 nm region exist due to the interest of the cosmic ray community with which to benchmark the model. However, our primary interest is in modeling of sprites and other transient luminous events (TLEs) associated with upper atmospheric electrical discharges, which have significant emissions from the N2 1P system, for which very limited laboratory data are available, making it difficult to select accurate model input parameters such as quenching coefficients in this region. As the model is refined via the process of benchmarking it with laboratory data, more accurate modeling of optical emissions of sprites and other upper atmospheric electrical discharges of interest will become possible, which would be useful in design of sensors enabling a better understanding of the relationship between the phenomenon of runaway electron breakdown, cosmic rays, and the mechanism by which TLEs and conventional cloud-to-ground and cloud-to-cloud lightning discharges occur. Wavelength (A) 1.00E-04 3000

Electronic level

Excitation rate (1/s)

1.00E-05

N2 B23 Pg (1P band) N2 W

9:7  105

N2 B0

2:1  105

N2 a0

1:7  105

N2 a

2:1  105

N2 w1

6:0  105

N2 C23 Pu (2P band) N2 E

2:3  104

5:6  105

N2 D

2:3  10

N2 A (Meinel band)

1:6  106

N2 B (1N band)

1:6  106

Absolute Efficiency

Table 1 Excitation rates for 50 keV primary electrons incident on air at 600 torr with 1 mA gun current

8:0  105

113

3500

4000

4500

5000

5500

6000

1.00E-06

1.00E-07

1.00E-08

4

O & D 1968

POEM

1.00E-09 Fig. A1. N2 2P and N2 þ 1N transitions, 50 keV e incident on 600 torr air.

ARTICLE IN PRESS 114

M.A. Nelson et al. / Nuclear Instruments and Methods in Physics Research A 597 (2008) 110–114

Acknowledgment This work was funded by the United States Department of Energy, Nonproliferation Office.

Appendix A. Efficiency data Fig. A1 displays the lines corresponding to N2 2P and N2 + 1N transitions, and Fig. A2 the lines corresponding to N2 1P

Absolutely Efficiency

1.00E-06 5000

6000

7000

8000

9000

10000

11000

1.00E-07

1.00E-08

O & D 1968 POEM model 1.00E-09 Wavelength (A) Fig. A2. N2 1P transitions, 50 keV e incident on 600 torr air.

Table A1 N2 2P and N2 þ 1N transitions with ratio of fluorescence efficiency as determined by the POEM model to that reported by O’Neil and Davidson [3] Wavelength (A˚)

Transition

Efficiency ratio

3371 3577 3805 4058 4344 4667 5032 5452 3537 3656 3998 4270 4574 4917 5309 3501 3711 3943 4490 4815 5179 3285 3469 3672 4142 4417 5066 3914 4278 4709 5228 5149 5011

N2 2P(0–0) 2P(0–1) 2P(0–2) 2P(0–3) 2P(0–4) 2P(0–5) 2P(0–6) 2P(0–7) 2P(1–2) 2P(1–3) 2P(1–4) 2P(1–5) 2P(1–6) 2P(1–7) 2P(1–8) 2P(2–3) 2P(2–4) 2P(2–5) 2P(2–7) 2P(2–8) 2P(2–9) 2P(3–3) 2P(3–4) 2P(3–5) 2P(3–7) 2P(3–8) 2P(3–10) N2 þ 1N(0–0) N2 þ 1N(0–1) N2 þ 1N(0–2) N2 þ 1N(0–3) N2 þ 1N(1–4) N2 þ 1N(3–6)

1.47 1.39 1.38 1.18 1.13 1.14 0.84 0.83 1.96 1.57 1.24 0.27 1.38 1.22 2.11 2.50 1.42 1.64 1.21 0.69 1.90 0.34 0.04 0.89 0.96 0.94 0.85 2.56 No OD data 2.91 3.14 3.57 0.00

Table A2 N2 1P transitions with ratio of fluorescence efficiency as determined by the POEM model to that reported by O’Neil and Davidson [3] Wavelength (A˚)

Transition

Efficiency ratio

10 508 8912 7754 8723 9942 6875 7627 8543 9682 6187 6789 6127 6789 7387 9202 6070 6624 7274 8047 6014 6545 7165 7987 5959 6469 5906 6395 5854 6336 5804 6253 5755

N2 1P(0–0) 1P(1–0) 1P(2–0) 1P(2–1) 1P(2–2) 1P(3–0) 1P(3–1) 1P(3–2) 1P(3–3) 1P(4–0) 1P(4–1) 1P(5–1) 1P(5–2) 1P(5–3) 1P(5–5) 1P(6–2) 1P(6–3) 1P(6–4) 1P(6–5) 1P(7–3) 1P(7–4) 1P(7–5) 1P(7–6) 1P(8–4) 1P(8–5) 1P(9–5) 1P(9–6) 1P(10–6) 1P(10–7) 1P(11–7) 1P(11–8) 1P(12–8)

0.09 0.19 0.26 0.21 0.30 0.33 0.62 0.92 0.58 0.42 0.55 0.37 0.29 0.28 0.30 0.72 0.52 0.34 No OD data 0.35 0.43 0.77 0.22 0.62 0.69 1.36 0.34 0.51 1.07 2.22 0.67 1.41

transitions. The efficiency ratio of the data from the POEM model to the experimental data is displayed for all of the transitions in Tables A1 and A2 in Appendix A. References [1] A.V. Gurevich, K.P. Zybin, R.A. Roussel-Dupre, Phys. Lett. A 79 (1999) 254. [2] G. Davidson, R. O’Neil, J. Chem. Phys. 41 (1964) 3946. [3] R. O’Neil, G. Davidson, The florescence of air and nitrogen excited by energetic electrons, AFRCRL-67-0277, Air Force Cambridge Research Laboratories, Bedford, MA, 1968. [4] M. Nagano, K. Kobayakawa, N. Sakaki, K. Ando, Astropart. Phys. 22 (2004) 235. [5] F. Kakimoto, E.C. Loh, M. Nagano, H. Okuno, M. Teshima, S. Ueno, Nucl. Instr. and Meth. A 372 (1996) 527. [6] P.L. Hartmann, Planet. Space. Sci. 16 (1968) 1315. [7] D.C. Cartwright, S. Trajmar, W. Williams, J. Geophys. Res. 34 (1971) 8368. [8] D.C. Cartwright, J. Geophys. Res. 83 (1978) 517. [9] J.J. Colman, R.A. Roussel-Dupre´, L.A. Triplett, B.J. Travis, Development of a new Electromagnetic Pulse (EMP) code at Los Alamos National Lab (LANL), LANL Technical Report LA-UR-07-0245, 2006. [10] F.R. Gilmore, R.R. Laher, P.J. Espy, J. Phys. Chem. Ref. Data 21 (1992) 1005. [11] J.W. Dreyer, D. Perner, Chem. Phys. Lett. 16 (1972) 169. [12] J.W. Dreyer, D. Perner, C.R. Roy, J. Chem. Phys. 61 (1974) 3164. [13] L.G. Piper, J. Chem. Phys. 97 (1992) 270. [14] S.V. Pancheshnyi, S.M. Starikovskaia, A.Yu. Starikovskii, Chem. Phys. Lett. 294 (1998) 523. [15] S.V. Pancheshnyi, S.M. Starikovskaia, A.Yu. Starikovskii, Chem. Phys. 262 (2000) 349. [16] E.M.D. Symbalisty, R.A. Roussel-Dupre´, V.A. Yukhimuk, IEEE Trans. Plasma Sci. 26 (1998) 1575. [17] J.S. Morrill, W.M. Benesch, J. Geophys. Res. 101 (1996) 261. [18] P.R. Kemper, M.T. Bowers, J. Chem. Phys. 81 (1984) 2634. [19] E.J. Comes, F. Speier, Chem. Phys. Lett. 4 (1969) 13. [20] L.S. Polak, D.I. Slovetskii, A.S. Sokolov, Opt. Spectrosc. USSR 32 (1972) 247. [21] A. Rotem, S. Rosenwaks, Opt. Eng. 22 (1983) 564. [22] F. Arqueros, F. Blanco, A. Castellanos, M. Ortiz, J. Rosado, Astropart. Phys. 26 (2006) 231.