Rotational and vibrational temperatures of transient atmospheric glow plasma

Plasma ignition can significantly improve the efficiency and performance of combustion devices through the enhancement of combustibility limits. Investigating plasma development for fundamental experimental flame conditions (i.e. spherical flame experiments) can provide insight into how plasma thermalizes the combustible mixture and, therefore a better understanding of flame development in future experimental studies. This study observed an ignition system designed to produce spherical flames in quiescent gas inside a constant-volume combustion chamber. Rotational and vibrational temperature measurements of dry atmospheric air glow plasma are reported. Measurements were taken for a transient discharge with currents less than 0.5 A. The electrode wire geometry and discharge variation resulted in an ellipsoid-shaped kernel and plasma region with an abnormal glow discharge. The measured temperatures were compared to the conductive thermal kernel boundary observed with Schlieren imaging. Maximum rotational and vibrational temperatures of 3000 K and 10 000 K, respectively, were observed near the anode electrode for a 0.5 A current. The temperature decreased with the axial distance from the anode, while a constant temperature was observed in the radial direction. Lower currents resulted in a smaller temperature, with minimum measured rotational and vibrational temperatures of 1500 K and 5000 K, respectively. The results were compared with available experimental literature and the variation observed was a result of the transient nature, which resulted in hysteresis in temperature vs discharge current measurements.


Introduction
The plasma discharge observed was produced via a custom capacitive discharge circuit [1] comparable to devices used for internal combustion systems.Such discharge generally contains three stages of plasma generation [2]; breakdown, the Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.required first stage for initiating the discharge, where the conductivity of the gas is greatly increased by a large current (>10 A) flowing for a short duration (<µs) through a small size channel between the electrodes [3].If the current flow after breakdown is dominated by electric field emission of electrons [4], the plasma will transition to the second stage of glow discharge, which is typically described with a low current density near the cathode electrode [5].If the glow discharge is normal glow, the current density at the cathode will be a constant value regardless of what amperage is applied.Abnormal glow discharge has a changing current density through transient conditions.The abnormal glow condition in this study is a result of two main conditions preventing a steady state discharge: strong current variation and the cylindrical electrode geometry, which prevents the plasma geometry from reaching its normal steady state condition [5].The third stage, arc discharge, forms if the cathode is sufficiently heated (via the plasma sheath) to cause significant thermionic emission electrons.This transition would be characterized by a sudden increase in current density at the cathode surface.Arc discharge was avoided in this work by careful preparation of the electrodes and using moderate amperage during each pulse because it would affect the location of discharge from the cathode (i.e. the location will not be fixed), therefore preventing accurate spatial measurement.
Temperature measurements of atmospheric plasma discharge in literature are typically relegated to a sparkplug or flat electrode geometry with either a small current discharge (∼10 mA) or have an underlying flowing gas for continuous discharge.For example, Arkhipenko [6][7][8] studied steady plasma in pure flowing gases up to 1 A. These studies were done with a flat cathode and steady currents to allow for the glow plasma cathode to expand naturally according to the normal glow current density.N 2 and air temperatures were shown to approach a thermal equilibrium condition after ∼0.2 A. Gas temperature was also dependent on the location within the plasma, where measurements near the cathode (in the dark space) were much lower than the positive column closer to the anode.Staack et al [9] studied plasmas similar to Arkhipenko for several flowing pure gases and similar electrode geometries except with smaller current values (up to only 3.5 mA).Low rotational temperatures, 1320 K, and high vibrational temperatures, 5906 K, were observed for air.In addition, spatial measurement showed two interelectrode thermal regions at similar rotational temperatures in N 2 .
Oliveira et al [10] observed an automotive spark plug geometry with a maximum current of around 40 mA.This resulted in a rotational temperature of around 2300 K, which decreased with a decreasing current.The position of the measurement within the plasma was not specified and the result is for a short, pulsed plasma.Michler [11,12] reported temperature values for a sparkplug geometry of a pulsed plasma for glow and arc discharge with spatial dimensions.The results showed that the rotational temperature increased near the anode but was also significantly higher near the cathode.The dark space between the two plasma regions showed a higher temperature (as compared to [13]) given the higher current flow of the discharge (<150 mA).The vibrational temperatures appeared to deviate from the rotational temperature primarily at some small locations near the cathode.The temperature of the plasma closer to the anode (positive column) had a temperature of around 3000 K for glow plasma; however, comparison is challenging as this result was not directly compared to the discharge current.
Machala et al [14] observed glow plasma in flowing air between two wire electrodes under DC currents up to 5 mA.Rotational and vibrational temperatures were 2400 K and 3700 K, respectively.Spatial dimensions of the temperature were not provided in this result.Yu et al [15] used a significantly different electrode geometry, where two thin conductive wires were oriented parallel and transversely to each other such that the discharge was emitted from the cylinder wall.However, the flow of gas was significantly higher and preheated.This is relatively interesting because plasma from a 150 mA discharge did not cause a significant temperature change in the gas (suggesting the discharge would normally operate at the preheat temperature).
While the available literature provides insight into many common atmospheric plasma conditions, measurements of temperature values for the wire electrode geometry with the observed current pulse are desired.As a result, this study wanted to investigate how the change in current will affect the temperature of the plasma, and how the conical electrode shape will affect the temperature profile of the plasma.The authors believe such measurements would provide insight into the formation of plasma as well as useful data for describing the mechanisms that lead to the ignition of a self-sustained flame.This work will show that the shape of the cathode had a strong influence on the internal temperature profile of the plasma interrupting the normal manifestation of the glow plasma structure (negative glow, dark space, positive column) and that the hysteresis of temperature was consistent with the studied current pulse.This hysteresis was compared to previous research [16] (which also provides further details on this specific discharge event) and the thermodynamic model proposed to predict the generation of the thermal kernel based on the thermal energy of the plasma.This thermal kernel is primarily formed through conductive mechanisms from plasma high temperatures and was shown in this work through Schlieren images.
The experimental work in this study considered a welldefined discharge event, which was generated via a highly repeatable current pulse over a range of 0-0.5 A. The nature of the glow plasma resulted in identical plasma geometry between pulses, which formed around the surface of the cathode electrode.Measurements were taken with a spectrometer over several vibrational band transitions to measure the vibrational and rotational temperature described in the following methodology section.

Experimental design
Plasma ignition experimentally refined for spherical expanding flame initiation was observed at atmospheric pressure in quiescent dry air (21% O 2 , 79% N 2 ).The experimental schematic is presented in figure 1, where each observed discharge occurs in a cylindrical constant volume combustion chamber (CVCC) with a diameter and height of 13.3 cm.The discharge was observed through a 1 inch thick sapphire window and the image of the discharge was collected by two 15.3 cm diameter, 150 cm focal length spherical mirrors.The first mirror is placed one focal length from the experiment and the second mirror is placed to focus the image onto the fiber optic input of the spectrometer.The use of mirrors is important to prevent chromatic aberrations and inaccuracies in the spectral data.The spectrometer (Isoplane, model SCT 320) was coupled to an ICCD camera (Teledyne Princeton Instruments, model PI-MAX4).The optical fiber (Thorlabs, model BFL105HS02) that delivers the signal from the CVCC to the spectrometer slit entrance was a high OH fiber bundle consisting of seven 105 µs fibers.The entrance of the fiber was placed on an x-y-z stage motion platform with a linear resolution of 0.1 mm.The spectrometer had a slit of 0.2 mm, and a grating of 600 g mm −1 .Wavelengths were calibrated using a mercury lamp.The spectral response of the optical arrangement was nearly flat for the observed wavelengths and was not considered to have any significant effect on the overall analysis of the spectra.
The discharge was generated using a 100:1 automotive transformer with the initial energy stored in a capacitor on the primary coil circuit.The circuit arrangement shown in figure 1 resulted in a pulse discharge which produced a high voltage discharge on the secondary circuit with the electrode gap.A variac on the primary circuit allowed for control of the total energy through variation in the maximum discharge current.A discharge was selected which after breakdown increased from 0 A to its maximum value of 0.5 A around 250 µs and then falls back to 0 A at 700 µs, as shown in figure 2.
This discharge was selected for its repeatable nature since the time and spatial characteristics of the plasma were captured with ∼630 discharge events (recorded only after achieving repeatable events).Only glow plasma was selected because the geometry of the plasma remains identical between experiments (given the electrodes were not adjusted for the duration of the experiment).Arc plasma cathodic location could fluctuate which resulted in uncertainty in the location of measurement within the plasma.The spectra were captured using 48 µs exposures with each exposure starting at 50 µs intervals (see figure 2).The camera captures two exposures per experiment using a fast double frame feature.The breakdown exists between the very tips of the electrode and occurs during the first exposure but was not captured by the fiber because of its location in the experiment.The electrodes were 0.5 mm in diameter with the tips polished to a fine point.Polishing was crucial to the repeatable nature of the observed plasma.More details on the effect of polishing are provided in [16].The discharge was measured using a voltage probe (NorthStar) with a 2000:1 scale connected to the high voltage side of the discharge and an inductive coil (Pearson, model 6595) to measure the current placed around the grounded electrode.The voltage and current were observed to ensure the discharge remained the same for all experiments and did not transition to arc discharge.
Figure 3 shows additional details regarding the discharge as well as a demonstration of experimental repeatability and control.To show optical repeatability, figure 3(a) presents the Schlieren image of two discharge events with equivalent input energies.While the thermal conduction of energy away from the glow plasma is evident, the plasma is barely visible as a white spot within the electrode since Schlieren imaging uses a secondary light source as opposed to the incident light of the experiment.These kernel images were captured separately and used only as a reference since both the spectra and kernel images could not be captured simultaneously.Figure 3(b) shows that the electrical variation between experiments was roughly 1%-2% of the maximum measured value (0.5 A), which was minimal when compared to the uncertainty introduced by the time-integration of the spectral data.Figure 3(c) shows the effect of the energy deposited to the discharge.The peak intensity was limited to 0.5 A to minimize the effect of a large number of required discharges on the electrode surface micromorphology, which would then affect the shot-to-shot plasma repeatability [16].

Temperature measurement
The spectrometer was centered at a wavelength of 362 nm and captured many significant vibrational transitions of N 2 and N + 2 , as shown in figure 4. The spectra were fitted to find the rotational and vibrational temperatures as a function  of both space and time using open-source software (Massive OES [17][18][19]).Simulation of the spectra for both observed species were used to fit the experimental spectra.The temperature of the N 2 species is the only value reported in this work given its greater signal strength.However, it was important to consider the effect of N + 2 on spectra to achieve accurate fittings.While both rotational and vibrational temperatures are reported, the rotational temperature was assumed to be near the gas temperature [20] when interpreting the results and conclusion, because of fast relaxation at atmospheric pressures compared to vibrational states [21].Average Signalto-Noise (SNR) ratios of the reported spectra were from ∼10 to 70 depending on the time and location of the captured data.
The spatial characteristic of the plasma was captured by translating the fiber optic along 3 different paths (labeled radial paths: a, b, and horizontal paths: c) in 0.1 mm increments, shown in figure 5.The spectra captured along the path at 250 µs is displayed alongside the image.The emissions were observed for a diameter of 2 mm along the radial axis and 2 mm in length along the axial path.This matched well with the Schlieren image which represents the thermal kernel produced by plasma in the center of the kernel.The Schlieren image was not used for any analysis other than to illustrate the size and dimension of the ionized region (relative to the electrode and thermal kernel).The size of the emissive region reached its maximum value at the time (250 µs) presented in figure figure 5, with a reduction in size beyond this point.The (schlieren) thermal kernel boundary continued to grow as it represents thermal conduction from the plasma as the plasma continued to behave as an energy source despite its reduction in size.The wrinkled tail near the left most part of the Schlieren image was produced by some transport mechanisms from the formation of the cathode sheath.The lines shown in the image in figure 5 were scaled to 2 mm, with the origin of measurements at the center of the a measurement line.

Overall rotational temperatures
First, 3D plots of the intensity and rotational temperature of each path are shown in figure 6. Maximum temperatures occurred along the a and c paths, which were the closest to the anode spot.The variation with time or discharge current was expected, where the highest temperature along each path occurred slightly after 250 µs (∼0.5 A) because of the transience.Spatial data beyond what is displayed was captured.However, signal intensities were too small (SNR < 10), which greatly increased the uncertainty in the measured temperature.Inadequate SNR resulted in a sudden increase in temperature as the fitting algorithm predicts the maximum temperature limit.The beginning of this trend can be observed in the radial paths for figures 6(a) and (b), where the temperature beyond the 1 mm radius is slightly elevated.
The spatial trends observed were unexpected, with variation in temperature only along the axial dimension observed in figure 6(c).The spatial-temporal paths show that the discharge temperature was most affected by the current and energy supplied to the plasma, with a smaller geometry effect.Given the cylindrical nature of the electrodes, the total length in the axial dimension c is heavily influenced by the current, where the total plasma length has significant growth (as seen in figure 6(c)).
The temperature profile parallel to the measurement path (through the kernel) would typically be calculated using the Abel transform assuming radial symmetry.The observed temperature radially is shown to be constant (figure 6(a) and (b)) which would suggest the temperature in the line-of-sight is constant (or much smaller than the changes present on path c).
The variation of plasma temperature vs current, which is displayed in figure 7, shows the hysteresis that results from the time-varying current, where the early discharge was cooled through growth and mass gain of the plasma, while the temperature of the receding discharge was higher as the plasma relaxed to smaller geometries.The separation between the rising current and the falling current is expected to be smaller if the pulse were longer, therefore a smaller rate of change in the discharge current.The uncertainty in measurement is displayed as the dashed boundary lines, which encompass the horizontal and vertical error bars of each measurement.The vertical error bars represent the uncertainty associated with the best fit of spectral data, which was ∼100 K for rotational fittings.The horizontal error bar represents the gate exposure duration.Given the exposure will capture spectra from a range of amperage, the temperature measurement will represent some average temperature for the current levels within this gating frame.The data point was placed at the current within the center of the frame temporally.This interpretation of uncertainty assumes the weighting of the temperature measurement is equal at all temperatures which is likely not the case as the signal intensity would vary with temperature and the path both current and temperature take is not linear across time.This would only cause the location of the The temperature variation along the radial and axial paths in figure 8 shows an interesting trend such that the radial paths maintain a nearly constant value as opposed to the linear decrease of the axial path.Initially, this result was thought to be caused by a stigmatism in the optical design (from two spherical mirrors), which would cause the vertical axis to blur and could blend the temperature into one value.If this was the case, the spatial dimension of the temperatures should no longer match the geometry observed through the Schlieren image of the kernel (i.e. the stigmatism should cause the vertical emissions to appear longer in the vertical dimension).Given the geometric accuracy, this source of error is unlikely to be the cause of this uniform temperature.Instead, the spatial temperature profile is expected to be physically realistic for this plasma geometry.The best hypothesis is that the current density throughout the plasma is heavily influenced by the electrode intrusion.Since the magnitude of current is the primary factor in determining the temperature, the current density within a unit volume of plasma should be the most universal variable to determine the local temperature within the plasma.The width of the plasma naturally constricts as it approaches the anode spot, which would increase the current density and naturally result in a higher temperature in the positive column of plasma near the anode.The conical electrode shape would likely enhance this variation in the current density as compared to electrode geometries, which use flat geometries [6,11].An illustration  is also provided in figure 8(d) for the proposed justification of the observed temperature measurement where the primary current density varies because of electrode geometry.This interpretation treats the plasma as a continuous structure (i.e.does not consider the normal plasma internal structures) because, given the intrusion of the electrode, it was impossible to determine experimentally the separation of the plasma into structures such as the positive column near the anode.

Vibrational temperatures
Similar trends for vibrational temperatures were observed across both space and time.Figure 9 shows the magnitude near the center of the discharge, where the maximum temperature is around 10 000 K. Vibrational temperatures were significantly larger than rotational temperatures by several thousand degrees.A similar disparity was observed by Staack et al [13], where the temperature at the small discharge currents (3.8 mA) is 1200-1500 K rot and 4000-5000 K vib .Machala et al [14] also presented similar rotational and vibrational temperature.Both results show the vibrational temperature decreases with increasing rotational temperature, which would suggest approaching thermal equilibrium.Arkhipenko showed that for air at 0.5 A the electron temperature should be slightly higher than ∼4000 K (close to the rotational temperature), further indicating nearly equilibrium plasma.The vibrational temperature showed the opposite trend, with a value of 9-10 000 K. This was a result of electronic excitation (through the strong electric discharge), which increased the population of the vibrational transitions (because of the Franck-Condon principle).
The vibrational states are populated through both thermal and electronic excitation.Therefore, they are not necessarily representative of the thermal translational system and cannot be used to make inferences about the gas.The issue of electronic states interfering with vibrational temperature measurements is discussed in detail in Dilecce et al [22].The work of Staack et al [23] shows in detail the contributions of both electronic and vibrational excitation.Given the fitting routine does not account for electronic excitation, the reported 'vibrational temperature' was not the true temperature value but was still reported as an observed and fitted quantity of the experimental data, which the reader should only cautiously consider as the real vibrational temperature is much smaller.

Comparison to literature
Figure 10 presents two comparisons for the analysis of the temperature (rotational) measurement.Figure 10(a) is a direct comparison of available temperature measurements in the literature to the data in this study.The available literature represents a wider range of experimental conditions (electrode geometry, gas conditions), which makes comparison challenging.However, it will be assumed that those data represent steady normal glow plasma.The current effect on temperature (for large currents >10 mA) is indicated with a linear dashed line.It was also assumed that the measurement near the anode is comparable to the literature data (often measured in the positive column).Moving away from the anode introduces additional effects of geometry on temperature by excluding the higher current density regions effectively and lowering the observed temperature (visible through the second dashed curve (path b) also plotted with the data).
The path a is shown to be centered around the literature data.The hysteresis of the measurement resulted in the early measurements (<150 µs) having a lower temperature and the rest of the measurements (>150 µs) exceeding the trend in literature.The path of the falling current appears to also be on a trajectory to reach the literature values after some time.This observed behavior appears to be relevant to previous experimental and modeling work leading to figure 10(b).
Shaffer et al [16] models the discharge to predict kernel behavior based on the electrical power measurement (P → dr dt ).The power deposited within the gas (as heat) can be described as some fraction of the voltage measurement across the gap (as shown in figure 10(b)).Here, the gap voltage is the upper dotted line, and the thermal power is characterized by the region above either the steady sheath (dashed line) or the nonsteady sheath curve (solid line).This model found a 10%-15% discrepancy from the experimental propagation data.The difference was attributed to the initial assumption of normal glow plasma, where abnormal glow plasma could have a timevarying sheath formation (changing loss/sheath-dashed vs solid line figure 10(b)).The ideal sheath was calculated based on the measured kernel propagation (and proposed model).When these sheath measurements were plotted against the current, as shown in figure 10(c), the comparison between the sheath and temperature was clear.The development of the unsteady sheath compared to the steady sheath is like the unsteady and steady plasma temperature.
When the temperature was under the steady condition, the sheath drop (plasma losses) was also lower than the proposed steady condition, increasing the overall supplied thermal energy, hence driving the temperature up.This steady state temperature was eventually overshot, therefore requiring a further increase of the losses (greater than steady state) and lower thermal energy to bring the plasma back down to the normal temperature.Ultimately, the behavior of both sheath formation and temperature were dependent primarily on the current waveform, and the physics that describes the internal plasma behavior is complicated.However, these observations suggest that the assumption about the thermal energy balance of the plasma was accurate, and the inefficiencies were accurately described by the sheath (if the sheath can be accurately described).

Conclusion
This study investigated the temperature profiles of thermal ignition plasma for electrode geometry common in the study of spherically expanding flame and atmospheric air composition.Nitrogen spectral emission in the plasma region was used to determine the variation of temperature across space and the duration of the plasma.
The electrode geometry and the discharge path had a significant effect on the reported temperature.Significant variation in current resulted in a path-dependent temperature, which would introduce uncertainty in the value of temperature if not accounted for when measuring pulsed applications.The electrode geometry effect seems almost limitless on the temperature distribution within the plasma.Specifically, any slight change to the electrode will affect how the plasma forms and how the energy dissipates within this region.The geometry presented here represents an extreme case but is useful for other researchers interested in spherical flame development.For those that study similar electrode geometries, the plasma formation could be approximated as a prolate spheroid, with a linear temperature profile along the electrode and a constant temperature profile in the radial direction.Of course, there are many factors (e.g.electrode material, surface roughness/geometry, discharge circuit (current waveform), gas temperature, gas pressure composition) that would need to be considered in determining the exact plasma characteristics for a given experimental setup.For example, variation of the surface roughness can cause the transition to arc a lower current and would also affect the characteristic of the glow plasma through variation of the surface work function, hence affecting the local electric field at the surface and the plasma sheath.Such a property is hard to control and while it likely would not affect the overall shape and trend of the reported temperatures it could be a source of uncertainty (magnitude and transience of the temperature profile) for future studies which use these results.
issued through the Combustion and Fire System program and by West Virginia Higher Education Policy Comission under grant number RCG-12.The authors also gratefully acknowledge the MMAE department and WVU's Center for Innovation in Gas Research and Utilization (CIGRU) for their support.

Figure 1 .
Figure 1.Experimental setup illustrating spectrometer and optic arrangement as well as discharge circuitry.

Figure 3 .
Figure 3. Discharge repeatability and characteristics: (a) two discharge events with equivalent input energies, (b) voltage and current waveform of three separate discharges (including the differences in current magnitude), and (c) effect of input current (i.e. total supplied energy) on kernel size.

Figure 4 .
Figure 4. Vibrational transitions and fitted spectra of the observed plasma.

Figure 5 .
Figure 5. Spectrally imaged paths at 250 µs showing the scaled 2 mm path against a schlieren image of the discharge.

Figure 6 .
Figure 6.Intensity (left) and rotational temperature (right) measurements vs time and position for each respective experimental path: (a) path a, (b) path b, and (c) path c.

Figure 7 .
Figure 7. Temperature vs discharge current at the center of (a) radial path a, and (b) radial path b.

Figure 8 .
Figure 8. Spatial temperature distributions along (a) radial path a, (b) radial path b, and (c) axial path c; and (d) the interpretation of current density within the plasma base on experimental results.Temperature profiles were captured at 250 µs, when the temperature and current were near their maximum.

Figure 9 .
Figure 9. Significant (a) temporal and (b) spatial vibrational temperature variations, from axial path c.

Figure 10 .
Figure 10.Comparison of literature or previous data with present measurements: (a) plasma temperature in literature [7, 9, 10, 13-15, 23, 24] compared to path a (solid) and path b (dashed) temperatures, (b) transient electrical characteristics of abnormal glow plasma from prior experimental and modeling results [16], and (c) sheath measurements plotted against.