Tomographic optical emission spectroscopy of an atmospheric pressure plasma jet and surface ionization waves on planar and structured surfaces

The plasma source used in this study is the APPJ described in Jiang et al [47] and used in [15, 48]. As shown in figure 1(a), this APPJ was powered with a nanosecond DC pulse of positive polarity at 5 kHz with pulse width of 200 ns (full width at half max) and 3 kV of applied voltage. The pulsed power supply consists of a DC power supply (Spellman, SL600) and a high voltage pulse generator (DEI, PVX-4110). Representative voltage and current waveforms can be found elsewhere [15, 48]. Nanosecond pulsed excitation is advantageous because it reduces the electrical energy consumption compared to sinusoidal excitation but can maintain the same densities of reactive species [49]. Timing of the high voltage pulse with respect to image acquisition is controlled with a delay generator (SRS, DG645). The APPJ has a co-axial geometry, with a 1 mm diameter tungsten electrode centered within a 2 mm inner diameter quartz tube for primary gas flow. The pulsed power supply is connected to the tungsten electrode through a 500 Ω ballast resistor. A copper ground ring 5.2 mm in height on the outside of the quartz tube is centered at the location of the electrode tip 3.5 mm from the tip of the quartz tube. Ultra-high purity helium gas (99.999% purity) is utilized to sustain the NTP due to its high ionization coefficient at relatively low reduced electric fields [50]. The flow rate of the helium was set using a mass flow controller at 1.0000 standard liter per minute. The flow rate and the pulse repetition rate influence the buildup of reactive species in the quartz tube and in the plume due to plasma species residing in those regions between shots and experiencing multiple IWs [51]. Care was taken to ensure the purity of the gas and repeatable operation of the APPJ over the course of hours.

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Two 25.4 × 25.4 × 5.4 mm (length, width, height) dielectric surfaces are considered, as represented in figure 1(b). The first has a flat planar surface and the second has rectangular periodic trenches across the entire surface. The width, height, and separation of the trenches are all 150 µm and each trench has a length of 25.4 mm. The surfaces were fabricated using a 3D printer (Formlabs, Form 3) with 25 µm resolution, sufficient to create the 150 µm trenches. A resin (Formlabs, Black Resin V4) was chosen so that the plastic dielectric material would have relative permittivity of 3.3 (according to the manufacturer). The color was black to minimize surface reflections. For all experiments presented here the plasma operating conditions were kept constant, the APPJ was oriented such that the plume is perpendicular to the dielectric surface, and when it was used the surface was placed 3.3 mm below the outlet of the quartz tube.

As shown in figure 1(c), the APPJ was mounted on a motorized rotational stage (Zaber, X-RSW60A-SV2) to acquire the multiple views required for tomographic reconstruction. An intensified charge-coupled device (ICCD), (La Vision, IRO), was positioned to image the region shown in green in figure 1(a) using a UV lens (Nikon, UV-105). A tilt stage and bubble leveler were used to ensure the optical axis of the camera was parallel to the dielectric surface and perpendicular to the plasma plume. This side-on imaging orientation was chosen so that plasma light emission scattered or reflected from the dielectric surface did not enter the solid angle of the detector. A delay generator (SRS, DG645) synced to the high voltage pulse was used for direct gating of the ICCD to reduce jitter and achieve 5 ns gate widths. A 11.4 cm extension tube was used to increase the magnification of the lens to 1.26 at a working distance of 13.5 cm to resolve SIWs. The f-number of the lens was set to f/32, corresponding to the smallest aperture size and largest depth of field, appropriate for applying a pin-hole camera model for calibration [44], discussed in section 3 below. Optical bandpass filters with 10 nm bandwidth were used to isolate light emitted at 706.5 nm (He_m ), 391.4 nm (N$_2^+$(B)), and 337.1 nm (N₂(C)). A fiber-coupled irradiance-calibrated spectrometer (StellarNet, BlueWave) mounted on a translation stage was used to monitor the APPJ, and an example spectrum acquired side-on below the outlet of the quartz tube is shown in figure 2. A LabView script was written to automate rotation of the motorized stage, timing of the high voltage pulse, and image acquisition with the ICCD. The DaVis software (La Vision, version 10.2) was used to set ICCD parameters and acquire images.

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The tomography inversion problem is defined by figure 3. We assume radiation trapping is negligible such that multiple camera views measure different projections of the light emitted by the entire plasma volume. This assumption is valid when measuring light emission from transitions between excited states with densities much lower than the ground state [52, 53], as was done here. Each pixel on the ICCD array will measure an intensity that is the integration along the pixel's line-of-sight, l, through the volume, given by [37]

$$\begin{equation} P\left(x^{^{\prime}},y^{^{\prime}},z^{^{\prime}}\right) = \int_{l} \mathrm{d}l ~\varepsilon\left(x,y,z\right), \end{equation} \tag{ 1 }$$

where, considering figure 3(a), $(x^{^{\prime}},y^{^{\prime}},z^{^{\prime}})$ designates the camera coordinate system, $(x,y,z)$ designates a position within the plasma, and $\varepsilon(x,y,z)$ is the emission coefficient. The aim of tomographic reconstruction is to recover $\varepsilon(x,y,z)$ from multiple measurements of $P(x^{^{\prime}},y^{^{\prime}},z^{^{\prime}})$. According to (1), a pixel image measured by a camera can be considered as a Radon transform of the plasma light emission [54]. Therefore, 2D images acquired at multiple views or projection angles can be used to invert the complete 3D scalar field. When the number of views or projection angles is limited, as is the case for practical experiments involving ICCD cameras, iterative reconstruction techniques like MART have been preferred for solving the inverse problem [55]. Discretizing (1) results in, for the ith pixel,

$$\begin{equation} P_i = \sum_j W_{ij} \varepsilon_j, \end{equation} \tag{ 2 }$$

where ε_j is the emission coefficient for voxel j and W_ij is a component of the weighting matrix W that represents the contribution of the jth voxel to the ith pixel. The weighting matrix W is sparse because each pixel does not 'see' many voxels.

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In the case of experiment, W is populated through a calibration procedure, as the radial lens distortion and orientation of each view with respect to the volume are unknown. Details of this procedure can be found in [37, 44]. Briefly, for each camera view, images are captured of a flat and rigid calibration target with a known dot pattern and fiducial markers that is placed at multiple positions. For each camera view, distances between the dots (measured in number of pixels) and the known dimensions of the ICCD pixel array are used to fit a set of parameters describing rotation and translation of the camera, perspective/image projection assuming a pinhole camera model, and radial lens distortion. The pinhole camera model depends on the distance from the pinhole to the detector. Once this distance is known, each pixel's line-of-sight, l_i , can be determined. A real camera will deviate from the ideal pinhole camera model through the introduction of radial lens distortion. Therefore, a lens distortion coefficient is also determined to correct the line-of-sight of each pixel. The weight, W_ij , can then be calculated as the voxel volume intersected by l_i divided by the total voxel volume, as shown in figure 3(b). For more details, see for example [36, 37, 44].

MART employs an iterative optimization procedure that reconstructs the emission coefficients ε_j when W and the pixel measurements P_i are known. In each iteration k, a multiplicative correction to the emission coefficient based on the ratio of P_i to the estimated pixel intensity, $\hat{P}_i = \sum_j W_{ij}\varepsilon_j^k$, is applied, expressed as

$$\begin{equation} \varepsilon_j^{k+1} = \varepsilon_j^k \left(\frac{P_i}{\sum_j W_{ij}\varepsilon_j^k}\right)^{\mu W_{ij}}, \end{equation} \tag{ 3 }$$

where µ is a relaxation parameter typically chosen between 0 and 2 to improve convergence. The MART update in (3) can be understood as a projection onto a convex set of solutions [56]. Iterative application enables convergence to a solution at the intersection of all convex sets, implying that several solutions exist. Therefore, the inversion is ill-posed and the reconstructed solution is sensitive to noise in the observed data and the limited number of projections. This problem can be addressed by having a sufficient signal to noise ratio (SNR) and number of projections and applying Gaussian spatial filtering between iterations to force convergence to a physically realistic smooth solution. Manipulating the relaxation parameter, µ, can further improve the reconstructions by modifying the iterative correction to ε_j according to (3), causing convergence to a different solution. Using these procedures, the tomographic reconstruction is of high fidelity when using eight or more angular projections, as was done here [37, 45, 46]. This has been validated through comparison of optical tomography with planar LIF [43].

For each tomographic reconstruction of the APPJ and SIWs presented in section 4 below, 10 different views were acquired with 15^∘ of separation between each view using the experimental methods described in section 2. For each view, 50 images were acquired and averaged. Each image accumulated at least 5000 plasma discharge events, with some variation depending on the bandpass filter used. Many accumulations were required given the small aperture used in the experimental setup, however this provided the best match possible to the pinhole model used in the calibration procedure. The gain of the ICCD and CCD were kept the same for each acquisition and were well below their maximum values to reduce noise. Gate widths of either 300 ns or 5 ns were used to study the spatial structure of the discharge and its temporal evolution.

Processing was performed using the DaVis software (La Vision, version 10.2). The image processing included: (i) background subtraction, (ii) thresholding, (iii) flatfield correction, (iv) nonlinear filtering, and (v) linear scaling. The flatfield image was acquired using a white light source illuminating a white business card and was used to correct for variations in detection efficiencies across the image. The nonlinear median filter removed the 'salt and pepper' noise that is common in ICCD images. The linear scaling corrected for differences in optical bandpass filter transmission, detector efficiency, and measurement accumulation times at 706.5 nm, 391.4 nm, and 337.1 nm. The processed images were used for tomographic reconstruction as described above.

The SNR of the raw image data was calculated as the mean of the 50 unprocessed images divided by the standard deviation and found to be 24, 24, and 22 at 706.5 nm, 391.4 nm, and 337.1 nm, respectively. The SNR of the processed images (after averaging) was estimated to be about 160 using the mean and standard deviation of regions of the images. The reconstruction quality was similar at each wavelength because the same reconstruction parameters were used and the SNRs are comparable. For each reconstruction, 100 iterations were run to ensure convergence, µ was set equal to 1, and the same minimal Gaussian spatial filter was used. The computational time for each reconstruction depends on the spatial resolution and volume that is reconstructed, and here was about 2.5 h on a desktop computer (Intel i7-11700 processor, 2.5 GHz, 8 cores). Each reconstruction data file was 3.5 GB and the total size for all reconstructions presented here was 178.5 GB. The spatial resolution is uniform and determined by the reconstruction voxel size, which depends on the image magnification and the spacing between pixel line-of-sights in the volume. To check the relative differences in the line emission values, designated here in arbitrary units (a.u.), tomographic reconstructions at 706.5 nm, 391.4 nm, and 337.1 nm were spatially integrated and compared to irradiance-calibrated spectra like those shown in figure 2 captured along the plume and found to agree well.

Figure 4 shows tomographic reconstructions of the APPJ plume in ambient air at 706.5 nm, 391.4 nm, and 337.1 nm using an ICCD gate width of 300 ns, integrating the temporal dynamics. Figures 4(a)–(c) show isosurface plots of constant values designated by the colorbars to convey 3D morphology and figures 4(d)–(f) plot slices through the volume along the yz plane at constant x = 0 mm and along multiple xy planes at constant $z = -2, -5$, and −10 mm (top to bottom). It is clear from these plots that the plume is nearly axisymmetric, and its core contains He_m . In figures 4(c) and (f), emission of N₂(C) caused by an instability of the plasma operation is visible outside of the quartz tube in the region beneath the copper ground ring near z = 3 mm. In the region from z = 0 to about −5 mm, the He_m is surrounded by an inner layer of N$_2^+$(B) and an outer layer N₂(C) due to mixing with the ambient air. In the region from $z = -5$ to −10 mm, there is sufficient N₂ diffused into the core of the plume for there to be a peak in N$_2^+$(B) emission, primarily due to Penning ionization (He_m + N₂ $\rightarrow$ N$_2^+$(B) + He). In the region from $z = -10$ to −20 mm, the high N₂(C) emission, low N$_2^+$(B) emission, and low He_m emission suggest lower electric fields (and lower mean electron energies) of about 10 kV cm⁻¹ compared to about 15–25 kV cm⁻¹ in the region from $z = -3$ to −10 mm [48, 57]. A more precise determination of electric field strengths from line ratios [58] is left to future work. Figures 5, 6, and 7 show tomographic reconstructions of the APPJ plume in ambient air at 706.5 nm, 391.4 nm and 337.1 nm, respectively, using an ICCD gate width of 5 ns to resolve temporal dynamics. Isosurface plots of constant values designated by the colorbars are shown, revealing the formation of the 'plasma bullet.' Using this data set, the axial speed of the IW was calculated as $9 \times 10^4$ m s⁻¹. Streamer models based on photoionization are proposed to explain the high speed of the IW [16, 17, 53].

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The species considered in figures 4, 5, 6, and 7 are populated and depleted through various mechanisms. He_m (3³S) is populated primarily through electron impact excitation and is depleted through electron impact excitation to higher levels, spontaneous emission (3³S to 2³P, $A_i = 1.54 \times 10^7$ s⁻¹ [59]), collisions with N₂, O₂, H₂O, and He atoms [60, 61], and three-body collision reactions with H₂O and He molecules [62]. Penning ionization of N₂ and O₂ is a key process in helium APPJs and leads to fast decreases in emission at 706.5 nm on the timescale of the discharge [63], as can be seen in figure 5. N$_2^+$(B) is produced primarily by Penning ionization (He_m + N₂ $\rightarrow$ N$_2^+$(B$^2\Sigma_u^+$) + He, $k = 7.1\times10^{-11}$ cm³s⁻¹) [60]. It is also produced by electron impact ionization and charge transfer reactions with helium dimer ions (He$_2^+$ + N₂ $\rightarrow$ N$_2^+$(B$^2\Sigma_u^+$) + 2He, $k = 8.3\times10^{-10}$ cm³s⁻¹) [60]. N$_2^+$(B) is depleted through spontaneous emission (B$^2\Sigma_u^+$ to X$^2\Sigma_g^+$, $A_i = 1.67 \times 10^7$ s⁻¹ [64]), electron dissociative recombination (k = 2 × 10⁻⁷ cm³s⁻¹) [65], and deactivated by N₂ and O₂ ($k_\mathrm{N_2} = 2.1\times10^{-10}$ cm³s⁻¹ and $k_\mathrm{O_2} = 5.1\times10^{-10}$ cm³s⁻¹ [66]). The rotational temperature of N$_2^+$(B) depends on how the ion is created, and is expected to be near to room temperature [63]. Considering figures 6 and 7, the slower decrease in emission at 391.4 nm in the region from z = 0 to about −9 mm compared to the region from $z = -9$ to about −18 mm is consistent with a lower density of N₂ and O₂ diffused into that region.

The excitation of N₂ to N₂(C) is by electron impact and metastable pooling reactions (N₂(A$^3\Sigma_u^+)$ + N₂(A$^3\Sigma_u^+)$ $\rightarrow$ N₂(C$^3\Pi_u$) + N₂(X$^1\Sigma_g^+$), $k = 1.5\times10^{-10}$ cm³s⁻¹) [67, 68]. The lifetime of N₂(A$^3\Sigma_u^+)$ in the guided streamer is about 5 µs [69]. Depletion of N₂(C) is by spontaneous emission (C$^3\Pi_u$ to B$^3\Pi_g$, $A_i = 2.74 \times 10^7$ s⁻¹ [64]), and quenching by He, N₂, and O₂ ($k_\mathrm{He} = 9.3\times10^{-12}$ cm³s⁻¹, $k_\mathrm{N_2} = 1.1\times10^{-11}$ cm³s⁻¹, and $k_\mathrm{O_2} = 4.37\times10^{-12}$ cm³s⁻¹ [63]). The higher spontaneous emission rate and quenching by He, N₂, and O₂ lead to decreases in emission at 337.1 nm that are faster than 391.4 nm. The high 337.1 nm light emission at $z = -18$ mm is consistent with electron densities above 10¹¹ cm⁻³ predicted by simulation [50].

Figures 8, 9, and 10 show tomographic reconstructions of the APPJ incident on the planar dielectric surface using an ICCD gate width of 5 ns to resolve temporal dynamics. In figure 8, isosurface plots of constant values designated by the colorbars convey 3D information at 337.1 nm. In figure 9, yz slices from the tomographic reconstructions are shown for plasma light emission at 706.5 nm, 391.4 nm, and 337.1 nm. In figure 10, edge contours drawn from figure 9 highlight difference in plasma light emission at different time points. Figures 8(a) and (b) and the top two rows of figure 9 correspond to time points before and after the IW contacts the surface. The surface was placed 3.3 mm below the quartz tube, or in the region where the He_m is surrounded by converging regions of N$_2^+$(B) and N₂(C), as shown in figure 4. As the IW approaches the surface, charging of the surface creates electric field components parallel to the surface [18], causing the regions or rings of N$_2^+$(B) and N₂(C) to diverge and then propagate over the surface as part of the SIW. Considering figures 9 and 10, the SIW appears as a layer of He_m , a layer of N$_2^+$(B) above the He_m , and a layer of N₂(C) above the N$_2^+$(B) due to mixing with the ambient air.

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In figure 9(a) corresponding to 50 ns, a high central emission is observed with low emission bulges on either side. The bulges may be created by weak radial components of the electric field caused by the surface leading to space charge induced field enhancement and avalanche in the radial direction. The wavefront of the SIW does not propagate with an orientation parallel to the surface but with a slight vertical angle, likely because the surface ahead of the wavefront is not charged and the fields at the wavefront are not parallel to the surface. This effect can be seen more clearly in figure 9(a) than in figures 9(b) or (c), consistent with the He_m being closer to the surface, as highlighted in figure 10. As discussed above in section 4.1, a transition from higher electric fields to lower electric fields seems to occur around 100 ns when the emission from N$_2^+$(B) and He_m decrease while the emission from N₂(C) does not. The charging of the surface weakens the SIW as it propagates [17], causing the plasma light emission to decrease and eventually the SIW is extinguished. Figures 8(e) and (f) suggest that the weakening of the SIW is position dependent, leading to non-axisymmetric distributions of the plasma light emission at later times. This may be caused by gas flow, small differences in electrical material properties, or localized non-uniform areas on the surface. The radial speed of the SIW on the planar surface was calculated as $3.2 \times 10^4$ m s⁻¹.

Figures 11, 12, and 13 show tomographic reconstructions of the APPJ incident on the structured dielectric surface using an ICCD gate width of 5 ns to resolve temporal dynamics. In figure 11, isosurface plots of constant values designated by the colorbar convey 3D morphology at 337.1 nm. In figure 12, xy slices of the tomographic reconstructions through the SIW are shown. In figure 13, slices along planes perpendicular to the trenches are shown to highlight variations along the z dimension and the effects of gas mixing. The trenches are oriented nearly parallel to the y-axis, as shown by the dashed white lines in figure 13, and were large enough for plasma to enter the trench (150 µm, much greater than the expected Debye length [24]). Using conservative estimates of the electron density and temperature in the SIW (10¹³ cm⁻³ and 3.5 eV [50, 70]), the Debye length is expected to be 4.4 um, or 34 times smaller than the size of the trench. The spatial resolution of each tomographic reconstruction was 7.4 µm, sufficient to see effects of the structured surface on the SIW. As multiple view angles are required for tomographic reconstruction, the plasma within the trenches could not be reconstructed because of the side-on view of the ICCD shown in figure 1. Therefore, the structure of the plasma just above the surface was investigated tomographically.

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Considering first figure 11, the transition of the guided streamer to a SIW is similar to the planar surface case, with charging of the surface causing the regions of N$_2^+$(B) and N₂(C) emission to diverge and then propagate over the surface as part of the SIW. Using the reconstructed data, the radial speed of the SIW on the structured surface was calculated as $3.2 \times 10^4$ m s⁻¹, the same as the planar surface case. While the speed of the SIW could be expected to decrease on structured surfaces, this was not easily seen within the precision of the measurements presented here.

Considering next figure 12, effects of the surface on the plasma light emission are more obvious. Slices are shown through the volume along the xy plane at constant $z = -3.15$ mm, or 150 µm above the surface (300 µm above the bottom of the trenches). Plasma light emission is shown in column (a) at 706.5 nm (He_m ), column (b) at 391.4 nm (N$_2^+$(B)) and column (c) at 337.1 nm (N₂(C)). For comparison, slices for the planar dielectric surface are shown in column (d) at 337.1 nm. The influence of the surface appears as regions of lower light emission above the trenches. For the case of a positive bias applied to the APPJ, as was done here, the resulting SIW is expected to adhere to the surface, propagating into and out of the trenches [24]. Therefore, the regions of lower light emission above the trenches are likely a geometric effect. Considering figure 12 columns (c) and (d), the transition of the IW to a SIW at early times is similar for the planar and structured surfaces. The differences include the reduced emission in the regions above the trenches and an increase in emission in the regions above the apex of the trenches. The cause of this increase in emission may be due to effects of field enhancement at the corners of the apex of the trenches. At later times, there is a 'crescent moon' shaped asymmetric feature, where higher light emission is seen in the top right of the SIW as compared to the bottom left. A similarly shaped feature can be seen in figure 4(f), suggesting the effect could be due to the APPJ itself.

In figure 12(b), at the 110 and 160 ns time steps, an inner ring of N$_2^+$(B) emission is observed that does not appear in the He_m or N₂(C) emission. The same effect is also observed for the planar surface, as can be seen in figure 9(b). The cause is not immediately clear, but may be due to gas mixing at the surface and the slower quenching rate of N$_2^+$(B) when compared to He_m and N₂(C) as seen in figures 5, 6, and 7. The final time point shown in the bottom row of figures 12(c) and (d) suggests that the weakening of the SIW due to charging of the surface occurs differently for the structured surface than the planar surface. This can also be seen by comparing figures 11 and 8. This could be due to cumulative effects of variable local surface capacitance or field enhancements at the apex of the trenches, as the gas flow is the same in each case.

In figure 13, slices through the SIW at 80 ns after the start of the high voltage pulse are shown in column (a) at 706.5 nm (He_m ), column (b) at 391.4 nm (N$_2^+$(B)) and column (c) at 337.1 nm (N₂(C)). Slices along the xy plane at constant $z = -3.15$ mm are shown again with white dashed lines added that designate the locations of the trenches. Slices along planes perpendicular to the trenches are also shown to convey structure in the z dimension. The position of these planes is designated by the three red lines, which correspond from top to bottom with the lower figures. The effects of mixing with the ambient air at the wavefront of the SIW can be seen, including layering of N$_2^+$(B) above the He_m and N₂(C) above the N$_2^+$(B), consistent with figure 10(b) and the flat surface. As discussed above, the wavefront propagates with a slight vertical angle, likely due to charging of the surface ahead of the SIW. Considering figures 1(c) and 3(a), figures 12 and 13 demonstrate the ability of tomographic reconstructions to recover complex spatial structure in the plane perpendicular to the camera fields of view.