Spectroscopic analysis of the N₂ B³Π_g–A³Σ⁺_u in radiation-induced air ionization

Abstract

This article presents experimental results from probing atmospheric air irradiated by a Polonium-210 alpha particle source using both optical emission spectroscopy and continuous wave cavity ring down absorption spectroscopy to study the first positive (B³Π_g–A³Σ⁺_u) system of molecular nitrogen. Optical emission spectra were acquired between 11 000 and 17 391 cm⁻¹ (575–900 nm). Long exposure measurements showed definitive emission from the first positive system, atomic nitrogen, atomic oxygen, and atomic argon. A non-Boltzmann emission model was constructed and fit to the data to infer relative vibrational state populations of N₂(B³Π_g). In pursuit of more quantitative characterization of the air ionization, cavity ring down absorption measurements were performed between 12 800 and 13 070 cm⁻¹ (765–781 nm) using an external cavity diode laser targeting detection and quantification of electronically excited molecular nitrogen N₂(A³Σ⁺_u). The null result in this measurement provides experimental evidence that in atmospheric pressure air, the presence of N₂(A³Σ⁺_u) generated by alpha particle radiation is below the estimated 0.4 ppb detection limit of the experiment.

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1. Introduction

It is well known that as ionizing radiation deposits energy in the surrounding air it creates a reservoir of excited state gases that de-excite and emit photons. This phenomenon, known as radioluminescence, has been extensively studied with ultraviolet (UV) optical emission spectroscopy in an effort to understand the chemical processes taking place.^1–7

Specific to radioluminescence in air, the UV emission is dominated by photons emitted from the molecular nitrogen (N₂) second positive system (C³Π_u–B³Π_g) and the ionized molecular nitrogen (N₂⁺) first negative system (B²Σ⁺_u–X²Σ_g). In an effort to study the continued energy transfer and relaxation processes for various nitrogen based plasmas, researchers probe the metastable N₂ (A³Σ⁺_u) state.^8,9 Studies are typically done at reduced pressures or in environments devoid of oxygen due to the rapid quenching of N₂(A³Σ⁺_u) by collisions with atomic (O I) and molecular oxygen (O₂). Although this experimental modification can simplify measurement of N₂(A³Σ⁺_u), it leads to extrapolated interpretation of the energy transfer and state population dynamics in standard air.

Although similar work has been conducted in electron beams,⁵ to the author's knowledge, there are no reports studying the N₂ first positive system (B³Π_g–A³Σ⁺_u) in radiolytically-produced ionized air. To experimentally characterize this transition in true atmospheric conditions exposed to radioactive decay, we conducted long exposure optical emission measurements which provide qualitative access to ultra-trace transitions. In an effort to provide quantitative information on the state of the ionized air we also conducted continuous wave cavity ring down absorption spectroscopy measurements.

2. Emission spectroscopy

2.1. Experimental setup

An optical emission spectrometer captured radioluminescence in the visible to near infrared (NIR) from ²¹⁰Po (NRD, NUCLECEL Ionizing Air Cannon P-2035) which primarily decays through the release of an α particle. Because alpha particle emission has a short attenuation length in air (about 3 cm), it deposits energy throughout a small volume leading to more localized fluorescence that can be captured by the spectrometer. At the time of the experiment, the source activity was approximately 12.6 mCi for the passive radioluminescence measurements.

The radiation source was placed against the slit of a 0.32 m spectrometer (Teledyne IsoPlane 320) with a 600 groove per mm grating blazed at 500 nm. Focusing optics were avoided to minimize transmission losses. A wide slit width of 254 µm was chosen to capture as much light as possible from the very weak NIR signal while maintaining sufficient spectral resolution. Because the spectral range of 550–1000 nm contains overlap with 2nd order dispersion of the predominant UV emission lines, a 500 nm long-pass filter (Andover, 570FG05-50) was added after the slit in the spectrometer.

A CCD camera (Andor iKon) cooled to −90 °C was used to record the signal. The final spectrum is a composite of seven, 65 nm bandwidth measurements. Each section required a 9 hour exposure. The spectral resolution was estimated to be 0.83 nm from the full-width at half-maximum of Ar emission lines which were also used to spectrally calibrate the data. The nascent unit for the spectral data intensity is counts per pixel which become proportional to photons per nm after spectral calibration and efficiency correction. Thus, intensity was adjusted using independently measured transmission of the long-pass filter and quantum efficiency of the camera in combination with the manufacturer's data for the dispersive grating.

Spectral data was converted from photons per nm to W cm⁻¹ to linearize the intensity scale of the data relative to the constructed spectral model by applying eqn (1).¹⁰

where L_ṽ is a power spectrum with intensity proportional to W cm⁻¹, C_λ is the spectrum proportional to photons per nm, h is Planck's constant, c is the speed of light, λ is wavelength, and is the derivative of wavelength with respect to wavenumber. Since the data intensity is accurate on a relative scale, the conversion to a wavenumber basis may be simplified to a multiplication between the corrected intensity profile in photons per nm and the wavelength vector.

False color images of radioluminescence generated from the Polonium-210 (²¹⁰Po) sources used in this study are shown in Fig. 1. The images were acquired with the Andor iKon camera using a LaVision 85 mm lens and an Andover 570 nm long-pass filter. The left image of Fig. 1 shows the radioluminescence generated from the ²¹⁰Po NUCLECEL Ionizing Air Cannon P-2035 source used in the emission spectroscopy experiment. The false color image on the right of Fig. 1 shows the radioluminescence generated from the ²¹⁰Po NUCLESPOT Compact Ionizer used in the CRDS measurements discussed later. These images show the spatial distribution of NIR photons generated by the alpha particles from this study's ²¹⁰Po sources interacting with air.

Fig. 1 Radioluminescence images of the ²¹⁰Po sources used in this work. (left) “Can” source containing diametrically opposed ²¹⁰Po sources used in spectroscopic analysis. Image taken over 1 h exposure (right) “Puck” source used in cavity ring-down spectroscopy analysis. The laser passed about 3 mm above the surface of the puck. Image taken over 2 hour exposure.

2.2. Emission model and fitting

The optical emission spectrum was fit with a custom, non-Boltzmann model that includes contributions from N₂(B³Π_g−A³Σ⁺_u), atomic oxygen (O I), atomic nitrogen (N I), and atomic argon (Ar I). Based on previous work analyzing the vibrational population distribution in the N₂ (C³Π_u) state, a vibrational temperature (T_vib) was not assumed and therefore the vibrational distribution function (VDF) of the N₂ (B³Π_g) state was solved for in a similar method.² The N₂ emission was calculated assuming a Boltzmann distribution across the rotational levels within each vibrational state calculated at 296 Kelvin (i.e. T_rot = 296 K).

The contributions from atomic emission were included largely to aid in the complex fitting of the N₂ VDF, but provide some of the first characterization of atomic species in radiation-induced air ionization. The model fit to experimental data is shown in the top row of Fig. 2 along with an inset comparing the experimental data and the fitted model below 14 000 cm⁻¹. This region accounts for the majority of the fitted signal for vibrational states higher than v′ = 10. In the middle panel, vibrational states higher than v′ = 10 are colored gray to distinguish them from lower vibrational states. Due to wavelength and relative intensity calibration uncertainties, these vibrational states, primarily fit above 14 000 cm⁻¹, have a higher degree of uncertainty compared to vibrational states less than v′ = 10. Contributions from N₂ and the atomic emitters are depicted in the middle and bottom rows respectively.

Fig. 2 (top) Long-exposure emission spectrum of Polonium-210 radioluminescence with non-Boltzmann model fit degraded by estimated instrument resolution. (middle) Fitted emission contribution from the N₂(B³Π_g−A³Σ⁺_u) color coded by upper vibrational state (v′) shown at full physical resolution. (bottom) Non-Boltzmann emission contributions from atomic species identified in the spectrum also shown at full physical resolution.

For a given transition in this model, the emitted power (I_ṽ) is calculated according to eqn (2) where h is Planck's constant, ν is the transition line center in Hz, n_u is the upper state number density, A_ul is the Einstein A coefficient in s⁻¹, and ϕ_ṽ is the Voigt line shape function which was calculated as the real part of the Faddeeva function. Although spectral lineshapes are well below the spectral resolution of the measurement, the translational temperature was assumed to be 296 K and used in calculation of the Doppler width for Gaussian component of the line shape function. A 0.1 cm⁻¹ Lorentz component was added for inclusion of nominal pressure broadening effects.

The N₂ (B³Π_g–A³Σ⁺_u) model was constructed from the venerable line list of Western et al.¹¹ obtained from the ExoMol database.¹² At the time of this article, the state-specific energy levels were not separated by contributions of electronic, vibrational, and rotational modes. Therefore, to construct the non-Boltzmann model, the rotational energies of each state were isolated by subtracting out electronic, vibrational, and spin–orbit coupling contributions. Vibrational and spin–orbit energies were taken from Western's publication while the electronic term was obtained from the NIST Constants of Diatomics.¹³ Close attention should be paid to the zero of energy when working between the various resources as was done in the present work. To remove any remaining state contributions, we zero the lowest rotational level in each vibrational state by subtracting off any remaining energy contribution.

For each vibrational level, the upper state number densities are calculated according to eqn (3). The rotational partition function (Z_rot,v) is calculated with a direct numerical summation over rotational states. The direct summation showed good agreement when compared to the analytical expression using the characteristic rotational temperature calculated from the rotational constants (B_v) in Western's publication.¹¹g_i is the statistical weight, E_i is the rotational energy of the state, k_B is Boltzmann's constant, and T_rot is the rotational temperature which was assumed to be 296 K.

n(B³Π_g,v) is the number density of N₂(B³Π_g) molecules in a given vibrational state (v). In this model, vibrational states up to v′ = 20 are included. Due to the spectral range covered in the experimental data, no transitions originating from the N₂(B³Π_g, v = 0) are able to be included in the fit.

Spectroscopic properties for the atomic transitions identified in the data were collected from the NIST Atomic Spectral Database.¹⁴ Emitted power was again calculated according to eqn (2). All of the atomic transitions identified in the data originate from highly excited electronic states and span a relatively narrow upper state energy range. For the purpose of including atomic contributions in the fit, the upper state number densities for all transitions of a given atom were assumed proportional to their upper state degeneracy. This is likely an oversimplification, and to extract meaningful upper state number densities a line-by-line Voigt fit would be required for each atomic transition. Nevertheless, the primary purpose for including the atomic emission in the model was to provide definitive attribution to a given atom, and to minimize any bias in the VDF fitting of molecular structure.

The model was fit to the data by floating the N₂(B³Π_g) VDF normalized to N₂(B³Π_g, v = 1) with additional contributions from each of the atomic species subject to the same normalization condition. The fully resolved model was degraded with an estimated instrument resolution of 12 cm⁻¹ (full-width at half-max) by convolution with a Gaussian function. The Voigt profile from the Doppler and pressure broadening effects are negligible with respect to the instrument broadening but were included in the spectral modeling for completeness. There is one strong, atomic transition near 13 326 cm⁻¹ (750.4 nm) that was not well captured in the model. It is believed that this transition is the 108 722–95 400 cm⁻¹ transition of Ar I.¹⁵ This transition is actually included in the modeled atomic emission, however it would suggest the simplified model is under predicting the relative upper state number density. The narrow spectral window containing this transition was assigned a higher uncertainty in the optimization algorithm so that the global fit to the N₂ structure was not biased by it. The model fits to atomic line emission provide high confidence assignment to the spectrum, but unfortunately lack the fidelity needed to report intra-material, number densities relative to N₂(B³Π_g, v = 1). The vibrational state densities fit to the data are collected in Table 1. The uncertainties provided in Table 1 are the fitting uncertainties from the covariance values of the optimizer and do not capture other significant sources of a full uncertainty budget. These values are the lowest bound and likely under-predict the true level of uncertainty in the VDF.

Table 1 Relative vibrational state number densities in N₂ (B³Π_g) inferred from the model fit to data

Vibronic state	Relative number densities
N2 (B, v = 0)	– ± –
N2 (B, v = 1)	1.000 ± –
N2 (B, v = 2)	0.771 ± 0.002
N2 (B, v = 3)	0.259 ± 0.001
N2 (B, v = 4)	0.199 ± 0.001
N2 (B, v = 5)	0.189 ± 0.001
N2 (B, v = 6)	0.175 ± 0.001
N2 (B, v = 7)	0.078 ± 0.001
N2 (B, v = 8)	0.040 ± 0.001
N2 (B, v = 9)	0.048 ± 0.001
N2 (B, v = 10)	0.037 ± 0.001
N2 (B, v = 11)	0.022 ± 0.001
N2 (B, v = 12)	0.045 ± 0.001
N2 (B, v = 13)	0.035 ± 0.002
N2 (B, v = 14)	0.066 ± 0.002
N2 (B, v = 15)	0.012 ± 0.002
N2 (B, v = 16)	0.087 ± 0.003
N2 (B, v = 17)	0.053 ± 0.002
N2 (B, v = 18)	0.075 ± 0.003
N2 (B, v = 19)	0.048 ± 0.003
N2 (B, v = 20)	0.057 ± 0.004

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The floated VDF approach to fitting the molecular spectra was taken primarily due to previous work suggesting non-Boltzmann vibrational populations in the N₂(C³Π_u–B³Π_g).² To evaluate this hypothesis, the fitted VDF was regressed to a vibrational temperature assuming a Boltzmann distribution. For this regression, the vibrational state energies were again taken from the publication of Western et al.¹¹ The relative vibronic populations from Table 1 fit to a Boltzmann temperature are shown in Fig. 3. The Boltzmann fit only includes vibrational states up v′ = 10. Fig. 3 shows strong deviation from a Boltzmann distribution for vibrational states higher than v′ = 10. A similar N₂(B) VDF with a secondary maximum have been previously observed^16–18 in pulsed plasmas. The initial portion of the VDF can be reasonably well-described with a vibrational temperature around 6000 Kelvin and follows a Franck–Condon factor (FCF) VDF distribution.¹⁸ The higher vibrational levels, v′ > 10, are dominated by gas kinetics as shown by.¹⁸ Interestingly, the dip in relative population at v′ = 13–15 has also been previously observed and is attributed to predissociation.¹⁸

Fig. 3 Boltzmann temperature fit to the vibrational distribution function measured from the N₂(B³Π_g–A³Σ⁺_u) emission spectrum including upper state vibrational levels from v′ = 1 to v′ = 10.

The uncertainty in vibrational state population densities is challenging to asses given the complexity of the model and data. Due to the spectral range of measured data, only one depopulating transition from the v′ = 1 state is available for the fit. Furthermore, this vibronic transition lies at the low-frequency edge of the detectors response and so the signal to noise ratio (SNR) is lower than other portions of the spectrum. States with higher upper vibrational quanta lie in a more favorable portion of the detector's response band, but have a weaker emission and consequently lower SNR. Last, since the spectrum is a composite, there is a variable uncertainty in the accuracy of spectral calibration which also affects the fit.

3. Absorption spectroscopy

3.1. Continuous wave cavity ring down spectroscopy

Cavity ring down spectroscopy (CRDS) is an extensively documented method for trace gas detection.¹⁹ The technique leverages an optical cavity to generate long effective absorption path lengths to enable very low spectroscopic detection limits. Over time, researchers have evolved CRDS in many different ways to meet various measurement requirements. Specific to the present manuscript is the development of continuous wave cavity ring down spectroscopy (CW-CRDS) using tunable diode lasers (TDL). The backbone of the CW-CRDS body of literature is formed by the many venerable publications of Romanini and colleagues.^20–23

The primary nuance of CW-CRDS arises from the Fabry–Perot etalon that is formed between the mirrors of the optical cavity. Frequency locking a narrow linewidth laser to one of the cavity modes is extremely difficult and would require stabilization. In the original CW-CRDS publication, Romanini et al. demonstrate a greatly simplified approach that exploits coincidental cavity build up and a triggering circuit to shutter the laser and initiate a ring down event.²⁰ This foundational effort leveraged a ring dye laser and generated periodic build up by very slightly tuning the cavity length with piezo mounted mirror to scan the cavity modes across the laser.

This method of CW-CRDS was quickly adapted to be usable with tunable diode lasers.²¹ The use of tunable diode lasers enabled a different approach to generating periodic build up events. Instead of dithering the length of the ring down cavity with a piezo mirror mount, the wavelength of the laser was periodically fine tuned with piezo modulation. Advances in commercially available optics and electronics have only further simplified the implementation of Romanini's methods for CW-CRDS.

3.2. Ring down cavity design

To overlap the optical path of the CRDS cavity with the irradiated volume of air, we employed an open-path set up (i.e. not a gas cell). The ring down cavity in the present work was constructed from two identical, concave mirrors (Layertec, P/N 140966) with 1000 mm radius of curvature and manufacturer specified reflectivity >99.995% at 760 nm. The mirrors were spaced approximately 400 mm apart. Using eqn (4) through (6) from the texts of Gagliardi²⁴ and Bush¹⁹ where c is the speed of light, n is the index of refraction of air, L is the length of the cavity in meters, and R is the refelectivity of the mirrors, we calculate that the cavity has fundamental transverse mode (TEM₀₀) free spectral range (FSR) of 375 MHz, mode full width at half maximum (Δν_FWHM) of 0.006 MHz and empty cavity ring down time (τ₀) of 26.7 µs.

The cavity parameters are useful in determining other experimental details such as amplitude of the piezo modulation on the laser and the required frequency bandwidth of the ring down detector. They also help understand the expected spectral resolution in terms of the cavity mode spacing relative to the linewidth of the absorbing gas being probed. A step-by-step procedure for how the cavity was aligned can be found in Appendix A.

3.3. Mode matching

After designing the optical cavity for CRDS it is still necessary to align and mode match the laser to it. We follow procedures in the literature using a Helium–Neon laser to align the cavity through the same fiber collimator that is used by the CRDS laser.²⁵

The methods of Kogelnik and Francois were followed to calculate the location and focal length of the mode matching optic.^26,27 Kogelnik²⁶ provides an expression to calculate the physical spacing between beam waists and a matching lens of specified focal length, while Francois²⁷ reformulates the problem to calculate the required focal length of the matching lens given specified distance between waists. Both resources arrive at the same solution and provide useful guidance to the process.

Using eqn (7) (from Kogelnik), we calculate the radius of the cavity waist (w₂) to be 313 µm at 770 nm. Here R₁ and R₂ are the radius of curvature of the CRDS mirrors and not to be confused with the reflectance in the previous section. L is still the length of the cavity (i.e. distance between the mirrors) and λ is the wavelength of the laser. Eqn (7) could be reduced for the symmetric cavity since R₁ = R₂ however we leave it in the original form for completeness.

Eqn (8) through (10) (again from Kogelnik) are used to calculate the distance between the fiber aperture and mode matching lens (d₁) and between the mode matching lens and cavity waist (d₂) for a mode matching lens with focal length f. The 5 µm mode field diameter (MFD) of 780HP fiber is used for the beam waist diameter (2w₁).²⁸

f₀ = πw₁w₂/λ (8)

A seemingly elegant solution to the practical application of mode matching fiber coupled lasers to optical cavities is the use of an adjustable fiber optic collimator.²⁹ Following this example, a 7.5 mm focal length adjustable aspheric collimator (Thorlabs, CFC8A-B) was chosen as the mode matching lens. The resulting calculations suggest d₁ = 7.6 mm and d₂ = 865 mm at 770 nm. There are very slight changes to these distances as the wavelength of the laser is tuned over a its full spectral range, but no adjustment was made during the course of a scan.

The effects of mode matching in CRDS data have been studied extensively.^30,31 We did not quantify the higher order mode suppression ratio in our data, however it was fairly clear in the processed spectra when the mode matching focus was insufficient as the mean-shifted ringdown times of higher order modes created secondary copies of the spectrum at offset times.

3.4. System integration

An overview of the CW-CRDS system is shown in Fig. 4. The external cavity diode laser used was a TLB-6712 (Newport) with a TLB-6700-LN (Newport) controller. The laser tunes from 765 to 781 nm, supplies up to 50 mW of free spaced power, and has a manufacturer suggested linewidth <0.2 MHz. An important note is that the laser head includes an optical isolator and so no additional feedback isolation was needed in this setup.

Fig. 4 Overview of experimental layout for CW-CRDS. Red color indicates free-spaced laser propagation, blue indicates in-fiber propagation, and black indicates electrical cable connection. AWG: arbitrary waveform generator. OAP: off-axis parabolic mirror. AOM: acousto-optic modulator. PD: photodiode. MM-FC: mode matching fiber collimator. APD: avalanche photodiode. DAQ: data acquisition.

The free space laser beam is coupled into a polarization-maintaining, single mode fiber using a fiber-coupled off axis parabolic mirror collimator (Thorlabs, RC04FC-P01). Once sufficient cavity build up has occurred, a fiber-coupled, acousto-optic modulator (AOM, AeroDiode, 780AOM-2) is used to shut off the cavity injection. The AOM has a manufacturer specified 70 dB of isolation and <10 ns rise time.

Coarse wavelength tuning of the laser was driven by the TLB-6700 diode laser controller and typically scanned at a speed of 0.01 nm s⁻¹ (≈5 GHz s⁻¹). Even at this minimum tuning rate, ringing could be seen in the CRD signal leading up to the AOM shutting.^32,33 After the AOM blocked the cavity injection, the CRD signal returned to the desired exponential decay. The fine wavelength tuning of the laser was controlled with an arbitrary waveform generator (Tektronix AFG31152) supplying a triangular function. The frequency and amplitude of the modulation were 50 Hz and 70 mV respectively. The superposition of coarse and fine tuning was intended to produce multiple ring down measurements on a given cavity mode.

After passing through the AOM, the light is separated using fiber splitters (Thorlabs, TN785R3A1, TN785R5A1). A portion of the light is directed to a 1 GHz fiber coupled photodiode (Thorlabs DET02AFC) to monitor the shutoff timing of the AOM. This photodiode also serves as a power reference for optimizing the initial fiber insertion. The 1 GHz bandwidth of the AOM reference photodiode is only leveraged during set up to verify the 10 ns function time of the AOM. During a typical spectral scan, the oscilloscope is operated at a lower bandwidth to balance memory and tuning range.

A different arm of the fiber split couples into a wavemeter (Bristol, 871A-VIS). The wavemeter has a manufacturer specified accuracy of 60 MHz and is triggerable such that the wavelength readout can be synchronized with ringdown events. The wavemeter is located after the AOM so that the 200 MHz AOM-imposed frequency shift is captured in the spectral calibration.

The third arm of the fiber split is directed into the ring down cavity described in Section 3.2 using the mode matching optics described in Section 3.3. Ringdown events are measured on a avalanche photodiode (APD, Thorlabs, APD130A) with an aspheric condensing lens (Thorlabs, C110TMD-B). The APD has a 50 MHz–3 dB bandwidth.

The reference photodiode and the ring down APD voltages are recorded on a 12-bit oscilloscope (Tektronix, MSO64B) sampling at 125 MS s⁻¹ and a 20 MHz bandwidth limit to suppress noise. The voltage threshold for triggering the oscilloscope is set such that ring down events are expected only from the TEM₀₀ cavity mode. Once the APD channel reaches the trigger threshold, the oscilloscope begins recording and sends a sync-out TTL to an AWG (BK Precision, 4055B). The AWG fires the AOM to shut off the laser and sends a falling edge trigger to the wavemeter to record the wavelength. The Aux output from the triggered oscilloscope has a 950 ns delay. This is important to be aware of, however it is readily overcome in post processing by regressing the ring down signal only after the AOM has blocked the laser.

The strength and geometry of the ²¹⁰Po source differed from the one used to capture radioluminescnece. Here, a NUCLESPOT Compact Ionizer, P-2042 from NRD whose activity was estimated to be 4.3 mCi at the time of the experiments was placed in the center of the cavity directly underneath the beam.

3.5. Data processing

Each ring down event was fit using eqn (11) where the floated parameters were I₀, τ_ṽ, and C. I₀ is the initial voltage amplitude at the beginning of the ring down, τ_ṽ is the ring down time constant at a given spectral point, and C is a constant voltage offset to allow for compensation of any DC offset in the baseline of the signal.

I_t = I₀ exp(−t/τ_ṽ) + C (11)

A representative model fit of a ring down event is shown in Fig. 5. Note the 2.01 µs delay between the trigger time of the scope and the closure of the AOM. This is due to the 950 ns latency in sync out trigger from the scope combined with a latency in the AOM closure. The delay is actually necessary for the wavemeter to accrue sufficient light to render a precise frequency reference. The ringdown signal is fit from 50 ns after the measured AOM closure out to 150 µs. The square root of the covariance matrix from the optimizer as well as the mean squared error (MSE) between data and model are recorded for each ring down as metrics of uncertainty and goodness of fit.

Fig. 5 Representative data and model fit to exponential decay. Top panel shows the cavity fill and subsequent ring down event. Bottom panel shows the measured acousto-optic modulator (AOM) closure used to monitor the start time of ring down. Time constant uncertainty is two times the square root of covariance matrix.

The measured ring down time constants are converted to the spectral absorption coefficient (α_ν) using eqn (12).³⁴ Here, d is the path length over which the absorbing gas is present and L is still the full length of the cavity. This fill fraction of the cavity length (d/L) is important to keep track of in the present work as different absorbing species are present across different portions of the optical cavity. The attenuation length scale of alpha particles in air is on the order of a few centimeters and so the radiolytically-produced gases likely only exist over a fraction of the total cavity length. This differs from the ambient molecular oxygen in the room air that exists over the entirety of the cavity.

3.6. Absorption results

Several measurements over the entire tuning range of the laser (12 800–13 070 cm⁻¹) were collected with and without the Polonium alpha source near the ring down cavity. The measured spectral absorption coefficient showed no evidence of additional radiolytically-produced species. Data did contain rotationally resolved absorption features belonging to the molecular oxygen O₂(b¹Σ⁺_g–X³Σ⁻_g) A-band. This atmospheric gas was present throughout the open-path ring down cavity. Although it was not the targeted measurement, it provided quantitative evidence of the resolving power of the CRDS system. Only the wings of each transition could be measured as the absorption around line center was too strong for our system to build up power in the cavity. We analyzed the O₂ absorption features and conducted additional model-informed calculations for the detection limits for electronically excited molecular nitrogen ¹⁴N₂(B³Π_g–A³Σ⁺_u) first positive system.

For both O₂ and N₂, calculation of the absorption coefficient was done using eqn (13)³⁵ where h is Planck's constant, ṽ is the transition line center, c is the speed of light, n is the lower or upper state number density, and B is the lower-to-upper or upper-to-lower Einstein B coefficient. ϕ_ṽ is the lineshape function.

The calculation of upper and lower state number densities differs between the two species under study. The ambient atmospheric oxygen is expected to be in local thermal equilibrium (LTE) while any electronically excited nitrogen would potentially be out of LTE.²

3.7. Atmospheric oxygen

The spectroscopic parameters for molecular oxygen were taken from the HITRAN database.³⁶ The state populations are calculated with the standard Boltzmann fraction shown in eqn (14) where g_i is the total degeneracy, E_i is the total energy of the state, k_B is Boltzmann's constant, T_gas is the gas temperature, and Z is the total internal partition sum. The total number density, n_tot, is constrained through the ideal gas relation to pressure and mole fraction which enables inclusion of the air and self broadening coefficients in calculation of the lineshape function.

Lineshape modeling was done using the real part of the Faddeeva function for the Voigt profile with the broadening coefficients applied following the procedure recommended by HITRAN.

The spectroscopic model was fit to the data by floating temperature, ¹⁶O₂ mole fraction, ¹⁶O¹⁸O mole fraction, and three terms for to reconstruct the non-absorbed background. The three term background effectively creates a second order polynomial approximation to the spectral variation in the empty cavity ring down time. Pressure was fixed in the optimization to be 0.81 atm. Which is a nominal value for local ambient pressure at 1620 m elevation.

A representative model fit to data is shown in Fig. 6. The ratio of fitted mole fractions for ¹⁶O₂ relative to ¹⁶O¹⁸O is 250.42. This value agrees with the terrestrial isotopic ratio curated in the HITRAN database (249.35). Quantifying the ambient, molecular oxygen spectra was not the focus of this effort, but the analysis provides extraordinary evidence as to the resolving power and accuracy of the cavity ring down spectrometer. The fitted temperature, absolute mole fractions, and relative isotopic ratios are all as expected.

Fig. 6 Representative full-spectrum CRDS data set including a model-fit of molecular oxygen (¹⁶O₂ and ¹⁶O¹⁸O) that was present in the optical cavity. Right panel is showing an expanded view highlighting the fully resolved line shapes.

3.8. Detection limits of N₂ (A³Σ⁺_u)

CRDS measurements of air irradiated by the ²¹⁰Po source did not contain measurable absorption from the first positive system of nitrogen. To maximize the utility of the current measurements, we developed a spectroscopic model to quantify the detection limit of the CRDS system. Construction of the non-Boltzmann absorption model followed the same procedure that was described previously for the emission model with the only difference being the emission model was characterizing the N₂(B³Π_g) state while the absorption model is characterizing the N₂(A³Σ⁺_u, v = 0).

The spectral range measured via CRDS is expected to be dominated by absorption from the N₂(A³Σ⁺_u, v = 0) to N₂(B³Π_g, v = 2). Without spectroscopic information on N₂(B³Π_g) absolute number densities, we make the assumption that n_l ≫ n_u to allow solving eqn (13). The rotational state number densities for the N₂(A³Σ⁺_u, v = 0) are modeled using eqn (15) where g_i are still the state specific degeneracies, T_rot is the rotational temperature for calculating the Boltzmann distribution across that energy mode, and Z_rot is the rotational partition function for N₂(A³Σ⁺_u, v = 0) molecules.

Z _rot in eqn (15) is evaluated by direct numerical summation over rotational states within N₂(A³Σ⁺_u, v = 0). As was done previously, we isolate the rotational contribution of energy to a given state, by subtracting out the N₂(A³Σ⁺_u, v = 0) energy relative to N₂(X¹Σ⁺_g, v = 0). This resulted in state specific rotational energies for the N₂ line list that compared well with what are obtained using the expressions from Herzberg³⁷ for ³Σ states and the spectroscopic constants from Western's original publication.

A calculated absorption coefficient for N₂(A³Σ⁺_u, v = 0) is shown overlaid on the measured data in Fig. 7. The model is shown at approximately 5 ppb with a cavity fill fraction (d/L) of 0.1. This was based on the attenuation length scale of alpha particles in air being a few centimeters and therefore the irradiated portion of the cavity length was approximated as 4 cm for this comparison. The Doppler component of the lineshape for each transition was calculated at 296 Kelvin and a 0.1 cm⁻¹ Lorentz component was included for nominal contributions of collisional broadening.

Fig. 7 Modeled absorption coefficient for N₂ (A³Σ⁺_u, v = 0) calculated at roughly 5 ppb overlaid on measured data.

The lack of N₂ Herman Infrared emission bands³⁸ in the optical emission in Fig. 2 is another indication of low concentrations of N₂(A³Σ⁺_u). The production of the Herman Infrared system is generated by the energy pooling process of N₂(A³Σ⁺_u)^39,40 and is therefore driven by the density of the A³Σ⁺_u electronic state.

The standard deviation (1σ) of the measured absorption coefficient from 12 900 to 12 905 cm⁻¹ is used to estimate the noise floor of the spectrum. In Fig. 6, the standard deviation (σ) of the absorption coefficient is measured to be 2.18 × 10⁻⁶ m⁻¹. Taking 2σ as a noise floor threshold and assuming ambient pressure and temperature at 1620 m elevation suggests a detection limit near 0.4 ppb for N₂(A³Σ⁺_u, v = 0).

3.9. Under resolved temporal dynamics

The absence of detectable quantities of excited state N₂ in the cavity ring down spectrum motivates a brief discussion on a fundamental challenge of probing radiation-excited gases with temporally varying laser techniques. Specifically, the transient nature of the ionizing radiation's interaction with a given volume of air relative to the temporal scale of the laser probe. The nominal source strength at the time of measurement was approximately 4.3 mCi which is equivalent to 1.6 × 10⁸ disintegrations per second into 4π steradians. The ring down time in the cavity is on the order of 10's of µs, so the probability of interaction between a CRDS measurement and a disintegration may be quite low.

There is a second order consideration which is the persistence of any excited state species. For example, the duration of excited state N₂ molecules will be much shorter than quasi-stable radiolytic molecules such as ozone. In fact, UV CRDS was leveraged to quantify ozone (O₃) production in alpha-irradiated air.⁴¹ However, because this species is shown to build up over time in closed chambers probing it using temporally varying methods may be greatly simplified in part due to mixing time. Although excited state laser absorption of the N₂ second positive system in alpha-irradiated air has been claimed, our own efforts to reproduce that result were unsuccessful.⁴²

In an effort to overcome these effects, experiments with spectral averaging were conducted. Specifically, the laser was modulated over a small spectra window and ring down events were spectrally binned in postprocessing. The conclusions were unchanged.

4. Conclusions

This article details the results and analysis derived from optical emission and laser absorption measurements of the N₂(B³Π_g–A³Σ⁺_u) spectrum in ionized air generated by alpha particle radiation from a ²¹⁰Po source. Emission spectra showed definitive evidence of emission from N₂(B³Π_g), N I, O I, and Ar I. A non-Boltzmann vibrational emission model was developed to analyze the observed optical spectra from N₂(B³Π_g). Vibrational populations up to v′ = 20 of N₂(B³Π_g) were observed with the vibrational population distribution of N₂(B³Π_g) shown to be non-Boltzmann. A fit of the VDF of N₂(B³Π_g) shows an average vibrational temperature of ∼6000 K. This is in contrast to our previous measurements of second positive system, N₂(C³Π_u–B³Π_g) and the first negative system N₂⁺(B²Σ⁺_u–X²Σ⁺_g) which had much lower vibrational temperatures of ∼3800 K and 1500 K, respectively. This serves to highlight how Franck–Condon excitation and de-excitation along with collisional-radiative quenching^17,18 can drive different vibrational distributions of multiple diatomic nitrogen electronic states in air irradiated by a Polonium-210 source.

A continuous wave cavity ring down spectrometer was constructed to study N₂(A³Σ⁺_u v = 0) state in absorption. The performance of the CRDS spectrometer was tested by measuring the O₂(b¹Σ⁺_g–X³Σ⁻_g) A-band at ambient conditions. CRDS measurements with the ionizing radiation source present showed no evidence of absorption from N₂(A³Σ⁺_u, v = 0) suggesting the concentration was less than the estimated detection limit of 0.4 ppb. The null result highlights the significant challenge of using laser-based methods to study such a rarefied plasma.

Conflicts of interest

There are no conflicts to delcare.

Data availability

The DOE will provide public access to these results of federally sponsored research in accordance with the DOE public access plan https://www.energy.gov/downloads/doe-public-access-plan.

Appendix A. Cavity alignment procedure

After integrating the system and ensuring correct distancing between the cavity mirrors and the MMFC, the cavity could be aligned. Because the cavity mirrors were removed and replaced throughout the procedure, they were mounted into optics tubes that could easily be threaded into optics mounts. Irises were placed near the MMFC and about 40 cm downstream of the last focusing mirror. A beam camera (OPHIR, BGP-USB3-SP932U) was used to visualize the beam after the last iris, and care was taken to not saturate the camera throughout the alignment process. For these steps, the CRDS laser was used. A summary of the procedure follows:

1. Initial injection alignment: with the cavity mirrors removed, the MMFC was roughly focused into the center of the cavity. The MMFC was then aligned through the near and far irises using an X–Y translation stage and the tip-tilt optic mount adjustments, respectively. Alignment was achieved by closing an iris and using the appropriate adjustments to maximize signal on the beam camera.

2. Detector alignment: the APD was placed between the downstream cavity mirror location and the downstream iris. X–Y translation was used to align the center of a cross-hairs cap to the beam's axis. A lens tube and cross-hairs cap was placed on the detector which was then rotated to align the cross-hairs to the beam's axis. These steps were repeated as needed for proper alignment. Final positioning was marked such that the APD could be easily removed and replaced after alignment.

3. Upstream cavity mirror alignment: using the downstream iris as the target, the upstream cavity mirror was aligned to the center of the beam using X–Y translation while maximizing signal on the beam camera. Next, a NIR pinhole card was placed at the aperture of the MMFC such that the beam could pass through the card and the upstream mirror back reflection could be seen. Tip-tilt on the upstream mirror optic mount was used to direct the back reflection to the pinhole center.

4. Cavity focus refinement: with the upstream cavity mirror in place, the NIR pinhole card was then moved to the center of the cavity, and the downstream beam camera was referenced. Small adjustments were made to focus the MMFC until the camera captured maximum signal. Because of the nature of the mechanical translation of the MMFC's lens, focusing could lead to misalignment. In these cases, it was necessary to repeat steps 1 and 3.

5. Downstream cavity mirror alignment: the NIR pinhole card and the upstream cavity mirror were both removed and the downstream cavity mirror was put in place. The mirror was aligned similarly to Step 3 by using the downstream iris and X–Y translation of the cavity mirror while referencing the beam camera. The NIR pinhole card was repositioned at the MMFC aperture and the beam reflection was centered on the pinhole using the tip-tilt of the mirror's optical mount.

6. Cavity alignment: both mirrors were put in place for the final cavity alignment. Room lights were turned off and ND filters were removed from the beam camera which was then set near its maximum exposure. With proper alignment during the previous steps, faint structures were visible on the beam camera. The multi-beam pattern on the camera was adjusted into a single beam with an approximately Gaussian profile and faintly emanating Airy disks. The downstream iris and tip-tilt of the upstream mirror were used to roughly center the beam, then the upstream mirror was slightly X–Y adjusted to maximize the beam intensity on the camera. Slight adjustments of the downstream mirror were made as necessary.

After completing the above procedure, the APD was replaced after the final cavity mirror and ring down signal was collected on the oscilloscope. The ring down signal could be optimized by making very slight adjustments to the tip-tilt of the downstream cavity mirror. In this case, the ring down time of the signal changed while the intensity of the signal was roughly unaffected.

Acknowledgements

The authors sincerely wish to thank R. K. Harrison for years of technical mentoring in the field of radiation-induced air chemistry and optical diagnostics. We also greatly appreciate the technical review of this manuscript by John Murray (SNL) and Brian Bentz (SNL). Finally, we would like to thank the anonymous reviewers whose comments improved this article's quality. This work was supported by the National Nuclear Security Administration (NNSA), Office of Defense Nuclear Nonproliferation Research and Development (NA-221). Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

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