An experimental and theoretical investigation of

An experimental and theoretical investigation of femtosecond laser excitation in N2 + O2 mixtures Yibin Zhang,∗ Mikhail N. Shneider,† and Richard B. Miles‡ Princeton University, Princeton, NJ, 08544, USA

Oxygen is found to have both a quenching and amplifying effect on Femtosecond Laser Electronic Excitation Tagging at different mixture fractions with nitrogen, through the production of long-lived emitting species. The strongest signal is still achieved in a pure nitrogen gas flow. When oxygen is initially added, the total signal quickly decreases before increasing again to a local maximum level around 50% nitrogen + 50% oxygen, and then decreases as the relative amount of oxygen in the mixture continues to increase. No obvious changes in the detectable first or second positive emission are observed to explain this effect. Experiments and modeling both suggest that long-lived secondary species, N O and O3 , could be responsible for UV radiation, adding to the overall signal. A zero-dimensional kinetics model is developed to study and explain the effects of oxygen on FLEET emission in mixtures of nitrogen and oxygen at atmospheric pressure and temperature.

Nomenclature F ve De k I I∗ δ QeV QV T Ev Ev0 τV T νe,N2 νex νc νev νm N ln Λ Te Tv Tg

flux density of electron energy electron velocity electron diffusion coefficient Boltzmann’s constant effective molecular ionization energy effective excitation energy 2m(XN2 MN2 +XO2 MO2 ) = , m = electron mass, M = neutral particle mass MN2 MO2 rate of vibration excitation energy transfer from collisions with electrons rate of vibration-translation energy transfer vibrational energy per unit mass equilibrium vibrational energy per unit mass VT relaxation time electron-neutral collision frequency electronic level excitation frequency electron-ion Coulomb collision frequency rate of electronic level excitation electron-neutral transport frequency molecular density Coulomb logarithm electron temperature vibrational temperature gas temperature

∗ Graduate

Student, Department of Mechanical and Aerospace Engineering, Princeton, AIAA Student Member Scientist, Department of Mechanical and Aerospace Engineering, Princeton, AIAA Associated Fellow ‡ Robert Porter Patterson Professor Emeritus, Department of Mechanical and Aerospace Engineering, Princeton, AIAA Fellow † Senior

1 of 14 American Institute of Aeronautics and Astronautics

I.

Introduction

Unseeded, laser-based velocimetry methods are becoming increasing popular as a result of improvements in laser technology and increased demand for more robust gas diagnostics. A number of existing methods, including scattering techniques and molecular tagging, take advantage of existing particles in the air to produce measurable signals from a standoff distance. Molecular tagging methods with a strong signal over a long lifetime are especially desirable in air-breathing testing facilities that mimic flight conditions. The discussion of laser diagnostics in mixtures of nitrogen and oxygen necessitates the mention of several methods that take advantage of long-lived species such as ozone and nitric oxide, or dominant reactive particles such as atomic oxygen. Several of these rely on emission in the δ, and γ bands from long-lived populations of nitric oxide. NO-LIF is a popular method for thermometry1 and velocimetry. In velocimetry, a laser is used to probe NO’s ground vibrational state at 226nm and short-lived (O(ns)) emission from the δ and γ bands are measured with CCD cameras. Vibrational energy exchange with N2 , O2 , and energy transfer with atomic oxygen can also excite the nitric oxide species. The VENOM2 (vibrationally-excited nitric oxide monitoring) technique is a modification of NO-LIF that uses a 355nm laser pulse to tag the flow by photodissociation of N O2 into N O(v = 0, 1) and O. The vibrationally-excited NO is subsequently interrogated with a 226nm ”read” pulse as it moves with the flow. The ratio of NO at each rotational state can provide insight into the translational temperature of the flow. Air photolysis and recombination tracking (APART3 ) relies on the photosynthesis of N O in air with an ArF excimer laser centered at 193nm and similarly uses a 226nm beam for excitation. Ozone tagging velocimetry (OTV) relies on tagging by the formation of ozone through the dissociation of oxygen and subsequent interrogation by ozone dissociation to form excited molecular oxygen that emits through the Schumann-Runge band.4 Raman excitation and laser induced electronic fluorescence (RELIEF5 ) relies on stimulated Raman scattering to vibrationally excite oxygen, and laser-induced electronic fluorescence by an ArF laser at 183nm to interrogate the long-lived (O(ms)) excited species. Atomic oxygen LIF uses a two-photon process to excite oxygen to the 2p3 3p 3 P0,1,2 level and produce radiation at 845nm, or collisionally transfer excited species to the 2p3 3p 5 P1,2,3 level, creating excitation at 777nm.6, 7 Considerations for choosing a method typically fall under cost and equipment availability, complexity of setup, and robustness of technique. Femtosecond Laser Electronic Excitation Tagging (FLEET) is a laser diagnostic method for velocimetry in nitrogen-containing gases, and provides the necessary spatial and temporal resolution for both high and low-speed flows.8 To produce the FLEET emission, a focused femtosecond laser pulse dissociates molecular nitrogen into atomic nitrogen, which produces long-lived fluorescence as the atoms recombine into excited electronic states of molecular nitrogen. Of primary interest is the first positive system, the transition from the nitrogen B state to the A state. Equations 1−5 describe the proposed mechanism by which the ionization and dissociation of molecular nitrogen into atomic constituents creates excited molecules that produce first positive emission through a long-lived recombination process. This emission, the LewisRayleigh afterglow, is a visible fluorescence that is swept with the flow and can be tracked with a camera. The detectable nitrogen first positive system (B 3 Πg − A3 Σ+ u ) creates emission in the 500 − 950nm range, 3 + whereas the shorter-lived second positive system (C 3 Π+ u − B Πg ) emits primarily in the 300 − 450nm range. N2 + hν → e− + N2+

[1]

e− + N2+ → N + N

[2]

N (4S) + N (4S) + M → N2 (

5

Σ+ g)

+M

[3]

3 N2 (5 Σ+ g ) + M → N2 (B Πg ) + M

[4]

N2 (B 3 Πg ) → N2 (A3 Σ+ u)

[5]

Previous work demonstrated that the FLEET signal is strongest at all delays in pure nitrogen and decreases by about an order of magnitude in air, a phenomenon attributed to the loss of nitrogen atoms to reactions with oxygen species.9 The main ion species following laser excitation is O2+ , which has an ionization energy of 12.07eV, compared to 15.58eV for nitrogen. Thus reactions involving oxygen species, especially odd oxygen species ((O, O3 ) at high pressures as suggested by Lopaev,10 are expected to be dominant. Oxygen is furthermore found to be a more efficient quencher of excited nitrogen states than molecular nitrogen, especially for higher vibrational states.11, 12 Signal intensity and lifetime become limiting factors when flows, such as in a wind tunnel testing facility, experience large pressure and density drops.


This study is conducted in order to understand the main processes that impact FLEET emission levels, which are beneficial to the study of FLEET’s perturbative effects on the flow, as well as to investigations dedicated to improving the diagnostic. Insight from these results can prove useful towards enhancing the FLEET signal in air. The rapid incorporation of the FLEET method into fluid diagnostic studies8, 13, 14 invites a better understanding of these femtosecond laser-produced plasmas at conditions relevant to flow applications.

II.

Experiments

The laser used in this study is a Spectra Physics Solstice laser with titanium sapphire oscillator and MaiTai regenerative amplifier operating at a fundamental wavelength centered at 800nm and emitting a beam with a 1/e2 intensity half-width of 1.95mm.15 Each pulse has a temporal full-width at half maximum duration of 60fs and a frequency doubling crystal is used to produce second harmonic generation at 400nm. Femtosecond laser pulses at both the fundamental and frequency-doubled wavelengths at 1kHz are focused with 30cm focal length AR-coated lenses into a custom-made optically clear quartz gas cell containing various mixtures of industrial-grade N2 and O2 at atmospheric gas temperature. The gases flow through the cell to avoid build-up of NO or other contaminants,and a vacuum pump maintains the pressure at 1atm in the cell throughout the experiment. Broad spectrum images and time-integrated spectra of the FLEET emission are taken in different mixtures of nitrogen and oxygen. Time-integrated spectra are taken of the FLEET emission with a Princeton Instruments PIXIS 512B camera and an Acton SpectraPro 300i spectrometer by collecting 150 shots at each spectral range and stitching them together with a matching algorithm. These spectra are first spatially averaged along the FLEET line and then calibrated by the spectral response of the camera. Emission from the tagged line in nitrogen-oxygen gas mixtures enable identification of key atomic and molecular participants in the reactions and the relative concentrations of prominent species as a function of gas mixture. To obtain broad-spectrum images of FLEET, we use a PCO.dimax camera system with a sensor resolution of 45.5LP/mm and maximum frame rate of 2128 frames per second. Signal amplification is achieved with a Quantum Leap gateable image intensifier module with a reported resolution > 60LP/mm and gate repetition of 2MHz. The intensifier serves the dual purpose of signal amplification and high-speed shutter. The MCP gain is held constant for the duration of the experiment.

2µs 5.5µs 10µs 15µs 20µs

180

Intensity (a.u.)

160

140

120

100

80

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

N2/(N 2+O2) Ratio

Figure 1. FLEET emission intensity as a function of time and mole fraction, 400nm, 1atm total pressure


Figure 1 depicts the spatially-averaged peak emission intensity as a function of nitrogen fraction for several different delays following excitation. The camera gate width is fixed at 1µs for each data point. The introduction of small percentages of oxygen into the nitrogen mixture causes the signal to drop steeply by a factor of two or three, forming a local signal intensity minimum. The signal intensity in industrial-grade air under the same experimental conditions at a 5µs delay (not shown) falls approximately on the curve indicated by the 5.5µs delay line at 78%N2 . At 12% mole fraction, the ratio of oxygen to nitrogen in air unfortunately falls close to that minimum well, affecting FLEET’s attractiveness as a non-seeded diagnostic method for air flows. The signal appears to have a local maximum in a mixture of 50% nitrogen and 50% oxygen before dipping to immeasurable values as the mole fraction of nitrogen in the mixture continues to decrease.

v'=0 → v"=0

100%N 2 80%N2 +20%O 2 50%N2 +50%O 2

Intensity a.u.

v'=0 → v"=1

320

340

360

380

400

420

440

460

480

v'=0 → v"=2

v'=0 → v"=3 v'=1 → v"=3

v'=1 → v"=4 v'=2 → v"=5

340

360

380

400

420

440

wavelength (nm)

Figure 2. Time-integrated FLEET second positive spectra as a function of mixture, λ = 800nm

× 10-35

× 10-35

3.8 100%N 2

3.2

80%N2 +20%O 2

3.6

50%N2 +50%O 2

Intensity a.u.

3.4

3.1

v'=11 → v"=8

3

3.2

2.9

3

2.8 2.7

2.8

O

v'=12 → v"=9

v'=8 → v"=7 v'=9 → v"=8

v'=10 → v"=9

2.6 2.6 2.5 605

610

615

620

720

730

740

750

760

770

780

wavelength (nm)

Figure 3. Time-integrated FLEET first positive spectra as a function of mixture, λ = 800nm

Figures 2 and 3 depict the second and first positive regimes in detail. These spectra are averaged over 150 individual shots with a pulse energy of 2 millijoules. Time integrated spectra taken at the v 0 = 0 → v” = 0 transition at λ = 337nm show strong, monotonic quenching behavior with increasing oxygen levels (Figures 2). The second positive system typically has a short lifetime of several hundred nanoseconds to a microsecond in air or nitrogen. In Figure 3, the visible spectrum in oxygen mixtures shows a strong transition near v 0 = 8 → v” = 7 that corresponds to the 777nm transition of atomic oxygen. No other measurable features


were found outside of these spectral ranges. Fast reactions rates, low emission levels and equipment sensitivity currently limit the availability of temporally-resolved full-spectrum analyses in air-like gas mixtures. A kinetic model is able to provide physical insight over the entire time range of interest and spectrum of initial conditions with computation time being the only cost. To minimize computing time without losing important physics, the model incorporates only major species and reactions following validation under experimental conditions presented by other studies. Figure 4 depicts the FLEET emission intensity created with × 10 8 a the 800nm fundamental beam, 2mJ/pulse, taken at six differdirect ent mixtures of nitrogen and oxygen with a PCO.dimax inten7 blocked UV sified camera at constant gain. Intensity is computed for each 6 case by summing the bright pixels of the emission of an aver5 aged set of images. The camera delay here is 2µs and gate, 1µs. Differences between these curves and that in Figure 1 4 can be attributed to differences in multiphoton ionization us3 ing 800nm vs 400nm. A transparent glass window with 3mm 2 thickness is used to block the UV spectrum below 300nm. Intensity a.u.

6

1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

III.

1

Model

N2 /(N 2 +O 2 )

The temporal behavior of different concentrations of oxygen and nitrogen following femtosecond laser dissociation is studied using a zero-dimensional kinetics model with the reactions listed in Tables 1 - 3. The creation of 24 different + 3 3 + species (e, N2 (A3 Σ+ u ), N2 (B Πg ), N2 (C Πu ), N , N , N2 , + + + − − + + − + N3 , N4 , O2 , O2 , O3 , O3 , O, O , O , N O, N O , N O2 , O4 , O2 (a1 ∆g ),O2 (b1 Σ+ g )) is taken into account, and the initial vibrational temperature is assumed to be equal to that of the ambient gas (Tv ≈ Tg ≈ T0 ). Reaction rates are primarily taken from papers by Shneider et al.,16 Kossyi et al.,17 initial ionization rates of gaseous species from Mishima et al.,18 and electron-neutral collision frequencies are approximated from energy losses.19 Electron and vibrational temperatures are calculated using Equations 7 and 8,16 respectively. The electron temperature is calculated using an ordinary first order differential equation approximation of the hydrodynamic equation20 in Equations 6-7. Vibrational temperature is found using the Landau-Teller approximation since no additional pumping is added to the system after the initial excitation pulse. Species formed immediately as a result of multiphoton ionization (e, N2+ and O2+ ) are calculated from available rates using femtosecond laser intensity-clamping ranges for 800 and 400nm.21 Other initial excited atom and molecule populations are assumed to be zero. Electron-ion Coulomb collisions are computed using Equation 17.22, 23 The resulting system of differential equations is found using a variable-order stiff equation solver and mass and charge conservation are realized. More details about a similar model can be found in Zhang et al.24 This work extends the model presented in Zhang et al14, 24 by taking into account the rapid vibrational relaxation caused by oxygen atoms in the mixture and heat lost to the gas through vibrational-translational relaxation. The gas temperature is described by Equation 19, which takes into account heat production from VT relaxation and recombination processes. The model assumes that most of the gas vibrational energy is assumed to be stored in nitrogen while estimating the VT relaxation time. Figure 4. FLEET emission intensity as a function of mixture, imaged directly and through a UV-blocking filter (glass).

∂ ∂t

3 ne kTe 2

3 3 + ∇ · F = − ne k(Te − Tv )νev − kne (Te − Tg )δ(νm + νc ) − ne (νi IN2 + νex I ∗ ) 2 2 5 F = ne k (Te ve − De ∇Te ) 2

[6]

Here, F represents the flux density of electron energy, ve is electron velocity, De is the electron diffusion coefficient, and k is Boltzmann’s constant. The first and second terms on the right-hand side represent the electron inelastic energy losses through electron-impact vibrational excitation of ground state nitrogen, and energy loss to other heavy particles, respectively. The third term on the right-hand side represents second-order collisions: νex is the rate of electronic level excitation and I ∗ is the corresponding excitation energy. Because initial electron temperatures are assumed to be high (> 1eV), excitation energies of nitrogen


molecules are realized through collisions with electrons in second-order reactions, allowing us to neglect the ne νi,N2 IN2 process in the energy balance. Simplifying Equation 6 into its zero-dimensional form, we arrive at Equation 7. 2 Te n˙e dTe = νev (Tv − Te ) − (Te − Tg )δ(νm + νc ) − (νex I ∗ ) − [7] dt 3k ne εv

Tv =

ln 1 + dTv = dt

−εv 1 + NE2vεv ln 1 +

εv N2 Ev

N 2 εv Ev

2

[8]

εv dN2 εv N2 dEv − Ev dt Ev2 dt

[9]

v Variables Ev , Ev0 , dE dt , νev , δ, τV T,N2 are defined in Equations 10-13. εv and Ev are in units of eV , and all other temperature values are in units of Kelvin. εv Ev = N2 [10] εv e Tv − 1 εv Ev0 = N2 [11] εv e Tg − 1

dEv = QeV − QV T dt Ev − Ev,0 3 = ne k(Te − Tv )νev − 2 τV T

[12]

√ −1 1/3 τV T = (N2 + O2 )(7 ∗ 10−16 e−141/Tg + XO2 ∗ 5 ∗ 10−18 e−128∗ Tg )

[13]

The first term of Equation 12 is the molecular vibration excitation energy transfer rate from collisions with electrons and the second term is the rate of vibration-translation energy transfer. A subscript ”0” indicates thermal equilibrium values. When the harmonic oscillator approximation holds at small displacements from equilibrium, we can approximate Ev − Ev,0 QV T = τV T . Rate coefficients (Equation 15) and threshold energies are used to obtain the electron energy loss rate as a function of electron temperature [K]. From the sum of energy losses due to vibrational and electronic excitation, Equation 14,19 we can approximate νev in Equation 15. Various rates from Huba22 and Raizer25 are found in Equations 15-18. In Equations 14-18, Te , ε, I are expressed in units of electron volts. qv + qex = 8.917 ∗ 1010 ∗ Te−3 (9.93 + Te5 ) ∗ ne 3 1 8.917 ∗ 1010 ∗ Te−3 (9.93 + Te5 ) ∗ ne e−2.36/Te − νex I ~ω0 2 N = 5.53 ∗ 106 ∗ Te2 ∗ 1812.23 + Te−15 ∗ e−1.7835/Te N0

[14]

νev ≈

[15]

νex

[16]

νc = 2.907 ∗ 10−12 ne Te−1.5 ∗ ln(Λ) νm = 2.91 ∗ 10−14 N2 ρcp

p

Te

X dTg Ev − Ev0 3 = + kne (Te − Tg ) (νe,i ) dt τV T,ef f 2 i


[17] [18] [19]

N2 O2

10 18 e 10

16

10

14

O3

number density [cm-3]

N +2 N(4S) N 2 (C) N

10 12

O

-

O -2

NO +

+

O +2 N 2 (A)

10 10

O

10 8

N +3

NO

O -3

10 6 N 2 (B) O+

N +4

10 4

10 -12

10 -10

10 -8

10 -6

10 -4

Time [s]

Figure 5.

Ion and excited species populations in a mixture of 20%O2 + 80%N2 as a function of time [s]

10 14

50% O2

10 13

100% N 2 10

50% O2

10 12

10 10

density [cm-3]

density [cm-3]

100% N 2 12

80% O2 10 11

10 10

80% O2 20% O2

20% O2

10 9

10 8

10 -12

10 -10

10 -8

10 -6

10 -4

10 -12

(a) N2 (B 3 Πg )

10 -10

10 -8

10 -6

(b) N2 (C 3 Πu )

Figure 6. Predicted temporal variation of excited nitrogen number densities [cm−3 ] as a function of time [s] in different mixtures of nitrogen and oxygen at 300K and atmospheric pressure. The laser pulse used in this model has a central wavelength of 400nm, duration of 50fs and pulse energy of 1mJ/pulse. The x-axis depicts elapsed time in seconds.

The model is computed for a number of mixtures ranging from 1%O2 + 99%N2 to 80%O2 + 20%N2 . Populations of excited nitrogen species are plotted, from which the first positive system (FPS) and second positive system (SPS) emission levels can be deduced. C-state nitrogen appears to be strongly quenched at later lifetimes by any addition of oxygen, and their overall populations vary indirectly with the amount of oxygen in the mixture. B-state nitrogen is similarly quenched at delays after ten nanoseconds. The averaged


densities of N O and O3 in the timespan from 1 to 10 microseconds are plotted as a function of mixture in Figure 7, and while the ozone density decreases with the increase of nitrogen, nitric oxide exhibits nonmonotonic behavior. From the predicted populations, we can induce the production of excited species and subsequent radiation.

Table 1: Relevant O2 + N2 reactions and their respective rate constants (m3 /s or m6 /s, unless otherwise indicated), Tv , Te , Tg [K] e + O2 + O2 → O2− + O2 e + O2 + N2 → O2− + N2 O2+ + O2 + O2 → O4+ + O2

k37

k39 = 2.5 ∗ 10−16 4 = 3.3 ∗ 10−12 300 e−5030/Tg Tg q k41 = 1.4 ∗ 10−12 300 Te k42 = 2 ∗ 10−13 300 T e1.5 −13 300 k43 = 4 ∗ 10 Te

17

k44 = 10−43 k45 = 1.5 ∗ 10−16 = 1.1 ∗ 10−20 Tg e−3150/Tg k47 = 10−41 k48 = 2.8 ∗ 10−16 k49 = 2.5 ∗ 10−16 k50 = 10−18 k51 = 5 ∗ 10−16 k52 = 8 ∗ 10−16 k53 = 3 ∗ 10−18 k54 = 10−18 k55 = 3 ∗ 10−18 k56 = 6 ∗ 10−17 k57 = 1.3 ∗ 10−16 0.2 k58 = 10−17 300 Tg

17

O4+ + O2 → O2+ + O2 + O2

k40

O4+ + e → O2 + O2 e + O2+ → O + O e + N O+ → N + O e + O + O2 → O2− + O O2− + O → O3 + e O2 + N → N O + O O + +N + (O2 , N2 ) → N O+ + (O2 , N2 ) N + + O2 → O2+ + N N + + O2 → N O + + O N + + O → N + O+ N + + O3 → N O+ + O2 N + + N O → N + N O+ N + + N O → N2+ + O N + + N O → O+ + N2 O + + N2 → N O + + N N2+ + O2 → O2+ + N2 N2+ + O → N O+ + N

k46

N2+ + O → O+ + N2 N2+ + O3 → O2+ + O + N N2+ + N O → N O+ + N2 O2+ + N2 → N O+ + N O O2+ + N → N O+ + O O2+ + N O → N O+ + O2 N4+ + O → O+ + N2 + N2 e + O3 + O2 →

+ O2

N4+ + N O → N O+ + N2 + N2 O4+ + O → O2+ + O3 O4+ + N O → N O+ + O2 + O2 O2− + O2 → e + O2 + O2 e + O + O2 → O− + O2 e + O3 → O + O2− e + O3 → O− + O2

17

N4+ + O2 → O2+ + N2 + N2

O3−

e−600/Tg e700(Te −Tg )/(Te Tg ) 2 = 1.07 ∗ 10−43 e−70/Tg 300 e1500(Te −Tg )/(Te Tg ) Te 3.2 k38 = 2.4 ∗ 10−42 300 Tg

k36 = 1.4 ∗ 10−41

k65 = 1.4 ∗ 10

k69

300 Te

k59 = 10−16 k60 = 3.3 ∗ 10−16 k61 = 10−23 k62 = 1.2 ∗ 10−16 k63 = 4.4 ∗ 10−16 k 2.5 ∗ 10−16 64 =

−41

300 Te

e

−600/Tg 700(Te −Tg )/(Te Tg )

e

k66 = 4 ∗ 10−16 k67 = 3 ∗ 10−16 k68 = 10−16 −16 −6030/Tg = 8.6 ∗ 10 e ∗ 1 − e−1570/Tg k70 = 10−43 k71 = 10−15 k72 = 10−17


17 17

17 17 17 17

17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17

O− + O → O2 + e O− + N → N O + e O− + O2 → O3 + e e + O2 →

O2+

k73 = 5 ∗ 10−16 k74 = 2.6 ∗ 10−16 k75 = 5 ∗ 10−21

+e+e

e + N O2 → O− + N O O2− + N2 → O2 + N2 + e O2− + O2 → O2 + O2 + e

k76 = P

107 √ Te

(1.43 + 2.47Te +

0.456Te2 )e−12.06/Te 1/s

−17 k77 = 10 q Tg −4990/Tg k78 = 1.9 ∗ 10−18 300 e q Tg −5590/Tg 3 −16 k79 = 2.7 ∗ 10 m /s 300 e

O3− + O → O2 + O2 + e O2− + N2 (A3 Σ+ u ) → O2 + N2 + e O2− + N2 (B 3 Πg ) → O2 + N2 + e O− + N2 (A3 Σ+ u ) → O + N2 + e O− + N2 (B 3 Πg ) → O + N2 + e O + O2 + (O2 , N2 ) → O3 + (O2 , N2 )

k85

O3− + O → O2− + O2 O2− + O → O2 + O− O2− + O3 → O2 + O3− O− + O3 → O + O3− O2− + N → N O2 + e O2− + O2+ → O2 + O2 O2− + N2+ → O2 + N2 O + O3 → O2 + O2 O + N O2 → N O + O2

k80 = 3 ∗ 10−16 k81 = 2.1 ∗ 10−15 k82 = 2.5 ∗ 10−15 k83 = 2.2 ∗ 10−15 k84 = 1.9 ∗ 10−15 2 = 6.55 ∗ 10−34 300 Tg k86 = 3.2 ∗ 10−16 k87 = 3.3 ∗ 10−16 k88 = 4 ∗ 10−16 k89 = 5.3 ∗ 10−16 k90 = 5 ∗ 10−16 k91 = 2.2 ∗ 10−12 k92 = 2.2 ∗ 10−12 k93 = 2 ∗ 10−11 k94 = 1.13 ∗ 10−11

17 17 17 23 17 17 17 17 26 26 26 26 27 28 28, 29 28, 29 28, 29 28, 29 17 17 27 27

Table 2: Relevant reactions involving O2 metastables 3 (O2 (a1 ∆g ),O2 (b1 Σ+ g )) and their respective rate constants (m /s 6 or m /s, unless otherwise indicated), Tv , Te , Tg [K] O2− + O2 (a) → O2 + O2 + e O2− + O2 (a) → O2 + O2 + e O2 (a) + O3 → O2 + O2 + O O2 (a) + N → N O + O O2 (a) + N2 → O2 + N2

29, 30

O2 (a) + O2 → O2 + O2

km1 = 2 ∗ 10−16 km2 = 2 ∗ 10−16 km3 = 9.7 ∗ 10−19 e−1564/Tg km4 = 2 ∗ 10−20 e−600/Tg km5 = 3 ∗ 10−27 0.8 Tg km6 = 2.2 ∗ 10−26 300

O2 (a) + O → O2 + O O2 (a) + N O → O2 + N O O2 (b) + O3 → O2 + O2 + O O2 (b) + N2 → O2 (a) + N2 O2 (b) + O2 → O2 (a) + O2 O2 (b) + O → O2 (a) + O O2 (b) + N O → O2 (a) + N O O + O + N2 → (O2 (a), O2 (b)) + N2 O + O + O2 → (O2 (a), O2 (b)) + O2

km7 = 7 ∗ 10−22 km8 = 2.5 ∗ 10−17 km9 = 1.8 ∗ 10−17 km10 = 4.9 ∗ 10−21 e−253/Tg km11 = 4.3 ∗ 10−28 Tg2.4 e−241/Tg km12 = 8 ∗ 10−20 km13 = 4 ∗ 10−20 km14 = 13 ∗ 2.76 ∗ 10−46 e720/Tg km15 = 13 ∗ 2.45 ∗ 10−43 Tg−0.63

32


26 31 32 33 28

34 33 35 35 33 36 27 27

Table 3: Relevant N2 plasma reactions and their respective rate constants (m3 /s or m6 /s, unless otherwise indicated), Tv , Te , Tg [K] e + N2+ → 2N N2 (C 3 Πu ) → N2 (B 3 Πg ) + hν N2 (B 3 Πg ) → N2 (A3 Σ+ u ) + hν N4+ + N → N3+ + N2 N4+ + N2 → N2+ + 2N2 e + N2 → N + N + e N + + N2 + e → N + N2 N + + 2e → N + e N + + e → N + hν N + + N2 → N + N2+ N + + 2N2 → N3+ + N2 3 2N2 (A3 Σ+ u ) → N2 (C Πu ) + N2 3 + 2N2 (A Σu ) → N2 (B 3 Πg ) + N2 N2 (A3 Σ+ u ) + N → N2 + N e + N2 → N2+ + 2e N3+ + e → N + N2 N3+ + N → N2+ + N2 N2 (B 3 Πg ) + N2 → N2 + N2 N2 (C 3 Πu ) + N2 → N2 + N2 N2+ + N2 + N2 → N4+ + N2 N + N + N2 → N2 (B 3 Πg ) + N2 N2+ + N + N2 → N3+ + N2 N2+ + N → N + + N2 N4+ + N → N + + 2N2 N2+ + N2 → N3+ + N N2+ + N2 → N + + N + N2 + N2+ + N2 (A3 Σ+ u ) → N3 + N + N2+ + N2 (A3 Σ+ u ) → N + N2 + N + + N3 + N2 → N + 2N2 + + N3 + N2 (A3 Σ+ u ) → N + 2N2 3 N + N + N2 → N2 (B Πg ) + N2 e + N4+ → 3 3 N2 + N2 (A3 Σ+ u , B Πg , C Πu ) e + N2 → N + + N + 2e e + N2 → N2+ + 2e

k16

k1 = 2 ∗ 10−13 (300/Te )0.5 k2 = 2.74 ∗ 107 1/s k3 = 2 ∗ 105 1/s k4 = 10−15 k5 = 2.1 ∗ 10−22 eTg /121 5 k6 = 6.3 ∗ 10−12 Te−1.6 ∗ e−1.1368∗10 /T e 1.5 k7 = 6 ∗ 10−39 300 Te 4.5 k8 = 7 ∗ 10−32 300 Te k9 = 7 ∗ 10−18 k10 = 10−19 k11 = 1.7 ∗ 10−41 (300/Tg )2.1 k12 = 2 ∗ 10−16 k13 = 7 ∗ 10−17 k15 = 9.6 ∗ 10−17 5 Te −19 = 4.7∗10 ( 11600 )0.5 (1+1.12∗10−5 Te )e−1.82∗10 /Te p k17 = 2 ∗ 10−13 300/Te k18 = 6.6 ∗ 10−17 k19 = 3 ∗ 10−17 k20 = 1.4 ∗ 10−17 k21 = 5.24 ∗ 10−41 (300/Tg )2.2 k22 = 8.3 ∗ 10−46 e500/Tg k23 = 0.9 ∗ 10−41 e400/Tg k24 = 7.2 ∗ 10−19 e300/Tg k25 = 10−17 k26 = 5.5 ∗ 10−18 k27 = 1.2 ∗ 10−17 k28 = 3 ∗ 10−16 k29 = 4 ∗ 10−16 k30 = 6 ∗ 10−16 k31 = 6 ∗ 10−16 k32 = 8.3 ∗ 10−46 ∗ e500/Tg p k33 = 2.6 ∗ 10−13 300/Te

√ −2.96∗105 k34 = 4 ∗ 10−20 Te (1 + 6.9 ∗ 10−5 Te )e Te k35 = 7 P ∗ √10T 14.093 + 27.366Te + 1.386Te2 e−15.58/Te 1/s

17 37 38 39 40 41 42 42 42 43 43, 44 45, 46 45, 46 46, 47 41 17 40 47 47 44 47, 48 40, 43 40, 43 40, 43 40, 43 40, 43 40, 43 40, 43 40, 43 40, 43 47, 48 49

23

e

IV.

Discussion

These results suggest that the increase in fluorescence at approximately 50%O2 + 50%N2 (Figure 1) are not the result of changes in the nitrogen first or second positive emission systems, but rather emission from oxygen-containing species. The time-integrated visible spectra in oxygen mixtures shows a strong transition at the 777nm line, suggesting a minor contribution at earlier delays from atomic oxygen. This feature at 777nm is present for both 50%O2 and 20%O2 with no noticeable change in signal strength over the spectra 10 of 14 American Institute of Aeronautics and Astronautics

O3

density (a.u.)

NO

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

N2 /(N 2 +O 2 ) Ratio

Figure 7. Predicted temporal variation of nitric oxide number and ozone (normalized to NO) densities as a function of nitrogen fraction in the mixture. These densities are those predicted by the model averaged over the time range t = 1 − 10µs.

integration time. In contrast, the v 0 = 11 → v” = 7 and v 0 = 11 → v” = 8 lines of the first positive system dominate in pure nitrogen, with no additional transitions. Direct quenching of excited nitrogen states (reactions 81-84) by O− and O2− ions is virtually the same for both the C and B electronic states and also does not explain the non-monotonic behavior. Quenching of the lower vibrational levels of the B-state fall in the infrared spectrum, outside the detection limits of our equipment. Further experiments would be necessary to explore the possibility of selective quenching of excited nitrogen states by oxygen. High levels of nitric oxide at long delays following laser excitation suggest that UV and infrared fluorescence from N O, whose spectrum lies outside the sensitive range of most imaging equipment, may also contribute to the signal levels. N O lifetime at low pressures has been previously measured and modeled to be about 10s-100s of milliseconds50 and is expected to have a slightly shorter lifetime at higher pressures. N O can initially be produced through a series of recombination, charge transfer and ion-neutral reactions, followed by continued production from dissociation of the secondary species N O2 , reactions 77, 94 in Table 1, and excited through collisions with molecules and atoms. Our model predicts a high level of N O species in the 1-100 microsecond range at 50%O2 as compared to in mixtures with higher or lower levels of oxygen, supporting the theory that N O contributes to the overall fluorescence either directly through UV emission or indirectly through the creation of other emitting species. Figure 7 echos the trend seen in Figure 1. Studies of nitric oxide radiation in the upper atmosphere have shown that collisional energy exchange with O is primarily responsible for the observed infrared emission.51 Kinetic modeling predicts vanishingly low levels of atomic oxygen at the microsecond timescale, so this is unlikely to be a large contributor. Another long-lived particle of interest is ozone. Ozone formation is governed by the reaction O + O2 + (O2 , N2 ) → O3 + (O2 , N2 ) and it has an extremely long lifetime at atmospheric conditions. Ozone can be collisionally excited by other species present in the reaction. The predicted lifetimes of these species show that both N O and O3 are candidates for emission at our timescales of interest, although modeled ozone populations do not reflect the trend observed in our FLEET experiments. Unfortunately neither the PCO.dimax nor the PIXIS 512B camera equipment calibration tests show their responses in the UV range, and existing QE data suggest very little sensitivity in those wavelengths. Spectral information below the second positive range is difficult to acquire, so a simple UV-blocking filter was used to determine the role of UV-emissions. Figure 4 suggests that the UV contribution is greater than what is presented if we take into account the camera’s low QE below 300nm. The difference between the UV-blocked and unblocked emission is especially pronounced at 50%N2 + 50%O2 , supporting the hypothesis. To measure the indirect impact of the long-lived species on measured emission, further experiments must be considered.


A.

Impact of metastable oxygen species

The electron impact excitation of O2 (a1 ∆g ) has the highest excitation cross section within the metastable oxygen states. The inclusion of the two lowest oxygen metastables O2 (a1 ∆g ), τ ≈ 4400s and O2 (b1 Σ+ g ), τ ≈ 11.8s in Table 2, where τ is the radiative lifetime, have negligible impact on the concentrations of other reacting species. No significant population of O2 (b1 Σ+ g ) builds up in the simulated FLEET plasma, and the concentration of O2 (a1 ∆g ) plateaus to a population that is orders of magnitude smaller than that of all oxygen ions. Lopaev suggested that in the presence of nitrogen, these metastable species become insignificant.10

V.

Conclusions

The physical mechanisms of FLEET in oxygen and nitrogen mixtures is studied. It is observed that while the strongest signal is found in a pure nitrogen flow, a half nitrogen, half oxygen mixture produces a local maximum signal intensity under atmospheric conditions. These observations open the possibility of selectively seeding a flow with oxygen for increased signal levels at the local maximum, or taking advantage of naturally-occurring systems that have high oxygen levels, such as in rocket exhaust. No significant changes in the first or second positive radiating systems are observed. It is hypothesized that N O is an important participant in producing increased emission in the UV, and small contributions from atomic oxygen are observed in the near-infrared. High levels of long-lived N O across different mixture ratios suggest that optimal conditions for FLEET to be used in combination with NO-LIF occur at approximately 50%N2 + 50%O2 . Combining the two diagnostics open opportunities for enhanced signal intensities and lifetimes, as well as extended capabilities to combustion applications.

Acknowledgments This research was conducted with government support from the Air Force Office of Scientific Research under Dr. Ivett Leyva and student support was provided by a National Defense Science and Engineering Graduate (NDSEG) Fellowship, 32 CFR 168a.

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