Study of vacuum ultraviolet emission in helium and helium/nitrogen mixtures Free

Noble gases are commonly used as the working medium in many plasma discharges used in lighting, semiconductor manufacturing, and other plasma applications due to their low reactivity and well-known behavior relative to other gases. Emission of ultraviolet and visible radiation from noble gas plasmas is readily measured,^1,2 whereas the detection of more energetic radiation (⁠$120nm<λ<180nm$⁠) in the vacuum ultraviolet region requires a more sophisticated experiment.³ However, there is significant interest in even more energetic photons. High-energy photons are capable of acting as industrially important light sources, can play an essential role in streamer propagation, and can induce important plasma and surface chemistry. This work presents an experimental and computational study of VUV emissions in pure helium at wavelengths below 120 nm. Key radiation components in this region are the resonance transitions from atomic helium originating from the upper n$1$P states (n = 2, 3, 4, $…$⁠) to the lower 1$1$S ground state and radiation from the excited helium molecule (excimer, denoted $He2∗$⁠). The observation of atomic resonance emission at 58.4 nm (2$1$P excited state) at early times in transient events suggests that they play an important role in ionization wave propagation and surface effects. Time-resolved and spectrally resolved emissions clearly indicate the significant surface flux of this resonance emission, even though it is radiation trapped.

Particle-in-cell (PIC) with direct simulation Monte Carlo (DSMC) in combination with experiments is a strong tool for understanding the fundamental mechanisms impacting plasma discharges. The kinetic modeling approach directly simulates electron energy distribution functions (EEDFs) and emission spectra using a discrete photon approach.⁴ This simulated emission spectra are first compared to the experimental measurements for a pure helium system. The model is then extended to include a nitrogen admixture in order to investigate the impact of resonance radiation on ionization wave propagation. The model includes photoionization of the nitrogen molecule by atomic and molecular helium emission in the vacuum ultraviolet regime (VUV).

Such a situation is directly relevant to an atmospheric pressure plasma jet (APPJ) that is generated in a helium environment, flowing into ambient air, and brought into contact with a surface in many cases for decontamination.^5,6 These plasma devices have distinct advantages compared to other decontamination techniques and also have a number of biological applications such as wound treatment.⁷ APPJs are commonly generated in noble gases due to their desirable discharge properties and then injected into air to obtain reactive species. The resulting reactive oxygen and nitrogen are a key factor in the efficacy of APPJs.^8–10 The transition layer between the helium plasma and the surrounding air is an important region for the propagation of the plasma and the generation of reactive species. As a result, a number of investigative efforts have been undertaken to understand the dynamics of the APPJ.

As the plasma jet interacts with the surrounding air environment, the charged species, helium gas, and air interact to produce a complex plasma chemistry environment. Essential to this is the propagation and interaction of the helium plasma jet with the background environment. In particular, high energy photons are capable of generating nonlocal reactive species. Experimental characterization of the APPJ has been conducted to determine wave front speeds^11,12 and plasma species densities.¹³ In modeling studies, fluid approaches are frequently used that make an assumption of the electron energy distribution function (EEDF) in first-order models¹⁴ or calculate it assuming a local field or local mean energy approximation.¹⁵ As the plasma leaves the noble gas tube and flows into air, in the case of positive streamers, a propagation mechanism must be included in modeling to allow for the plasma wave to propagate. Commonly, this is done through the inclusion of photoionization processes where emission from a helium species photoionizes a nitrogen molecule. Specifically, it is often assumed that only the emission from the excited helium molecule causes photoionization and that resonance emission to the ground state does not contribute. However, recent modeling^4,16 and experiment¹⁷ results show these resonance emission lines even at higher pressures. As a result, these lines could indeed contribute to photoionization of molecular nitrogen contrary to past assumptions.

VUV spectra were measured in a plane-to-plane helium discharge using a differential pumping system designed to measure the spectrum of photons incident on a plasma cathode, while minimizing the trapping and loss of those photons in the transition to a vacuum spectrometer. A cross section of the discharge apparatus and the differential pumping flange can be seen in Fig. 1. The discharge apparatus was composed of a nylon insulator (in black), holding a copper ground plane (seen in white), onto which a degenerate silicon wafer was cemented with silver epoxy. The silicon wafer was coated with a 30 nm ZnO adhesion layer and then with a 310 nm layer of platinum. A 200 $μ$m orifice was laser cut into the cathode surface to allow the VUV flux to pass through into the differential pumping section. Not shown is the 37 mm diameter aluminum disk that served as the anode, located 5 mm away from the cathode.

Below the cathode is the intermediate vacuum region that is pumped through a small side port. The high vacuum region is brought to within 3 mm of the cathode orifice by a small hollow “finger” with a 500 $μ$m orifice in its tip. The entire system was pumped down by a Pfeiffer Vacuum HiPace 300 turbopump backed by an Edwards XDS10 scroll pump. An arrangement of throttling valves was used to independently control the pressure of the discharge chamber and spectrometer. The base pressure of the entire system is $3×10−6$ Torr. Under nominal operating conditions, the discharge was operated at 40 Torr as measured by an MKS 127 Baratron, and the pressure in the spectrometer was 1 mTorr as measured by a Pfeiffer Vacuum MPT 200 full-range gauge. Ultra-high purity helium was delivered by an MKS GE50A mass flow controller.

The differential pumping system was connected to a McPherson 234/302 vacuum spectrometer with a 2400 g/mm grating optimized for 80 nm. The differential pumping system was designed such that the cathode orifice defined the slit and was positioned at the focus of the system. Measurement of VUV photons was accomplished by the use of sodium salicylate phosphor and a Hamamatsu R928 photomultiplier tube. When measuring the time-averaged spectrum, a Keithley 6512 programmable electrometer was used to measure the current from the PMT. When photon counting, a PicoScope 6824E digital oscilloscope was used to obtain photon timing information.

The discharge was driven by 1.9 kV pulses, 1 $μ$s in length, supplied by a DEI PVX-4140 high voltage switch. These pulses were repeated at a rate of 4 kHz, and a 1 k$Ω$ ballast resistor was used to limit the current. As the ground plane was isolated from the vacuum chamber, current measurements were made on the return path by the use of a 50 $Ω$ shunt resistor. An SRS DG535 delay generator was used in order to synchronize the oscilloscope and the HV switch.

The time-integrated spectra of the pulsed discharge were measured in order to assess the relative importance of different transitions capable of inducing photoionization. For these measurements, the exit slit was closed to 400 $μ$m providing a resolution of approximately 0.5 nm. At each grating position, 128 electrometer samples were taken resulting in an uncertainty of 0.02 nA.

A portion of the helium VUV spectrum can be seen in Fig. 2, ranging from 55 to 93 nm. As was observed in previous pure helium simulation studies,⁴ the dominant transition originates from the 2$1$P state at 58.4 nm. No evidence was observed of transitions from the helium ion at 30.37 nm or from the forbidden transition originating from the 2$3$P state. Similarly, no emissions corresponding to the excimer continuua (60 nm and 80 nm) were observed, though these have been seen in the previous work.¹⁸ It is likely that the excimer population at these pressures is too low to produce detectable signals. Radiation from the helium excimer may be an important consideration for photoionization, particularly at higher pressures.

In the present measurements, the instrument function is too broad to draw any conclusions from the measured line shape. While self-reversal is expected to be present, its width is estimated to be several picometers under the current pressures, well below the resolving power of the system. This may change at higher pressures as pressure-broadening can significantly widen the line as well as its self-reversal. A reduction in the diameter of the cathode orifice would help with an investigation into the line shape properties by increasing the system resolution and reducing the background helium pressure of the spectrometer, though such a move would further reduce the relatively small photon flux. With a sufficiently small orifice, it should be possible to resolve the self-reversal at atmospheric pressures.

A key consideration in understanding photoionization processes in the context of ionization wave propagation is not just the spectrum of photons, but the flux dynamics. For this reason, it is necessary to assess not only the time-integrated spectrum of a discharge but to measure its evolution over time. This is a challenging prospect given the low detection efficiency and low duty cycle of the discharge in question. To address this challenge, a photon counting approach was used over the course of 350 000 discharge events. The spectrometer grating was set to allow the 2$1$P light through, and the exit slit was opened to 1.2 mm in order to maximize the VUV signal. The oscilloscope was set to trigger on the detection of a photon from the PMT, and the timing of the photon relative to the discharge was determined by a comparison to the delay generator signal.

In doing so, an array of photon timing information was built up over the course of the experiment. A histogram of this array was formed with bin widths of 8 ns, which can be seen in Fig. 3. Also plotted is the plasma discharge current in black, with an uncertainty of several nanoseconds in the relative timing. The dashed line in the plot indicates the mean number of dark counts per bin which is approximately 10.

A significant amount of discharge current is observed in advance of any detectable VUV photons. Despite the possible implication that VUV photons are not important at these early times, earlier work has shown that even a small flux of VUV photons can play a significant role in discharge formation, particularly in positive streamers.¹⁹ Following breakdown, the VUV photon flux generally follows the current trend, albeit delayed by approximately 150 ns. The cause for this delay has not been identified but may represent the time required for photons to diffuse to the surface, or the time needed for a significant density of the 2$1$P state to be established near the cathode. Emissions from the 2$1$P state continue to be detected well after the discharge current returns to zero. In part, these emissions may originate from photons diffusing out of the system, but also likely come from cascading transitions from higher excited states.

During a helium discharge, strong emission lines in the VUV are produced from the helium atom between 50 nm and 60 nm and the helium excited molecule (dominant transition at 66 nm).^17,20–22 To study the role of photons originating from different transitions on the propagation of an ionization wave front, a kinetic approach is utilized where particle-in-cell (PIC) is used for collective charged particle behavior, and direct simulation Monte Carlo (DSMC) handles binary particle collisions. The kinetic approach enables a higher fidelity description of electrons in the tail of the energy distribution function which contribute most to electron-impact ionization. The PIC/DSMC code, Aleph, developed at Sandia National Laboratories is used for this study.

The PIC method uses computational particles that represent many (often $>1010$⁠) real particles and thereby weight charged particles to the mesh through a linear weighting scheme²³ and solves for the electric potential and the electric field. The particle positions and velocities are updated using a velocity Verlet method. A constant electric field in the element is assumed for all particles within an element and provides the acceleration field for particle movement inside a given element. In the DSMC approach,²⁴ binary collisions between particles in the same element occur through the modified no time counter (NTC) method to account for particles with different macroparticle weights.²⁵ Here, we treat all species (electrons, ion, neutrals, and photons) as computational particles which can collide with each other through specified interactions such as elastic, excitation, charge exchange, photoionization, etc., using experimental (or numerical) cross section data vs relative collision energy for each process. Three-body interactions (such as $He2$ excimer formation) are treated with rate equations based on the reactant densities in each element.

Photon transport is modeled with a more first-principles approach where photons are directly emitted from excited atomic and molecular states rather than assuming a continuum radiation approach or ionization frequency. The recently developed discrete photon approach generates photons from excited states based on a random sampling as a function of the Einstein coefficient.⁴ Central to accurately modeling the helium atomic emission is accounting for line broadening mechanisms due to radiation trapping. Radiation trapping is the process in which an emitted photon is strongly self-absorbed over a length scale that is small with respect to the system’s characteristic dimensions. This often occurs for allowed transitions to the ground state, in this case 1$1$S. One example of this in helium is

where $21$P is the first excited state for the helium atom, $11$S is the ground state, and $hν$ is the photon energy with wavelength $λ0=c/ν$⁠. Photons emitted by transitions to the ground state are readily reabsorbed, for example,

The resulting excited state emits a new photon shortly thereafter which is once again absorbed. This process occurs repeatedly, resulting in a diffusive process. However, the wavelength emitted from the $21$P state is not a delta function, but rather a distribution of wavelengths caused by line broadening. Additionally, the process of absorption is also wavelength dependent and highest on the center wavelength (⁠$λ0$⁠) for transition. Wavelengths emitted away from the line center are less easily absorbed and can propagate further away from their emission location. To account for this, the discrete photon approach implemented into Aleph⁴ generates a random wavelength for the transition that is sampled from a Voigt profile that is ultimately a function of gas pressure and temperature.^26,27 These photons are pushed through the spatial domain similar to other particles (e.g., electrons) and are evaluated based on the DSMC procedure for a collision (i.e., absorption) event.

To account for electron–helium interactions, a plasma chemistry set compiled for a pure helium discharge and compared to experiment is used.²⁸ The helium excimer is created through a three-body interaction,

Here, the $11$S represents the ground state helium atom and $23a$ (with $a$ taking on a value of $S$ or $P$⁠) is the metastable state of the helium atom. This three-body reaction creates a short-lived helium excimer, $He2∗$⁠, that emits a photon and subsequently dissociates due to the repulsive ground state. Though the continuua of the excimer emissions are not modeled directly as with the discrete transitions, other works assume a nominal cross section value of $3×10−21m2$^22,29 for this broad excimer emission and is the same value used in this work. Both the excimer and the resonance emission states have lifetimes on the order of $10−9$ s. As a result, radiationless quenching of the resonant and excimer states is neglected. Therefore, differences in the photoionization rate will be due to their generation rate and, for the resonance emission, the rate of self-absorption. This self-absorption rate is determined by an absorption cross section that is proportional to the emission cross section.⁴ Pressure broadening is assumed to be constant for a given total pressure. Therefore, the emission and absorption profiles are constant as well.

Analagous to the experiment, a one-dimensional simulation was constructed in 40 Torr of pure helium and applies a step voltage of 1.9 kV (infinite rise time) between the anode and the cathode. To enable simulations at longer time scales, photons from radiation trapped lines (2$1$P, 3$1$P, 4$1$P to 1$1$S) only emit if their mean free path before absorption is greater than $1×10−6$ m. It is assumed that these states radiate photons that are immediately re-absorbed at the location of the emission source. This ultimately relaxes the smallest time step required to resolve photon absoprtion events as the collision frequency for emitted photons becomes smaller. This absorption distance is much smaller than the gap length, and the implications of this approximation and implementation are discussed elsewhere.³⁰ 

In this simulation case, a value of $109cm−3$ helium ions and electrons are seeded uniformly in the simulation domain and given velocities sampled from a Maxwellian velocity distribution with a temperature of 300 K. This seed plasma reflects the remainder of the previously generated plasma, as in the case of the repetitively pulsed experiment. Heliums ions impacting the cathode produce secondary electron emission at a rate of 0.25 electrons per ion. A fixed spatial step of 1.6 $μ$m is used for a 5 mm gap distance resulting in a total of 3000 elements. The time step used is fixed at a value of $2×10−15$ s.

Figure 4 at time t = 10 ns shows the densities of the electrons, ions, 2$1$P, and excimer states as a function of location in the plasma. It can be seen that a normal ion sheath forms near the cathode at x = 5 mm where the ion density is greater than that of the electron density. The 2$1$P density is very close to that of the charged densities, while the excimer density is 5 orders of magnitude lower. Neglecting radiation trapping of the 2$1$P state, this would imply that the resonance transition should have an intensity of roughly 5 orders of magnitude higher than that of the excimer transition. In reality, when radiation trapping is included, the two intensities are much closer as shown in Fig. 5. This spectrum is calculated by counting the number of photons of each wavelength over a 100 ps window reaching the cathode at t = 10 ns.

Here, the intensities shown are integrated over the emission profile for each transition to give a single intensity value. An example emission profile is shown in the inset of Fig. 5 for the 2$1$P $→$ 1$1$S radiative transition. The roughness of this emission profile is due to the stochastic nature of the emission from the upper energy level. This simulated emission spectrum includes resonance trapping and indicates the dominance of the resonant transition 2$1$P in intensity over other resonant transitions and the excimer profile. At the simulated time, the 2$1$P transition is roughly 100 times more intense than the excimer transition and 10–15 times higher than the 3$1$P transition.

Additionally, the intensities of the 2$1$P transition and excimer transition reaching the cathode are compared in Fig. 6 as a function of time. The intensity given here is once again integrated over the entire emission profile for each transition. When the voltage is initially applied at time t = 0 s, the initial room temperature electrons gain energy in the applied electric field and collide with the background gas. Some collisions result in direct excitation of the 2$1$P state or the 2$3$a state which convert to excimer states as given by Eq. (3). Population of these states is then followed by subsequent spontaneous emission and the detection of these photons on the cathode surface. This process takes a finite amount of time resulting in the slow ramp up of the intensity of the 2$1$P and excimer states.

As can be observed, although radiation trapped, the 2$1$P state is approximately 50–100 times greater in intensity at the cathode than the excimer intensity over the 10 ns simulation. These results are in agreement with the results obtained from the experiment (Fig. 2). It should be noted that wavelengths near the line center when their mean free path is shorter than $1×10−6$ m are neglected. If these wavelengths were included, it would only be expected to further increase the ratio of the intensity from the 2$1$P state to the excimer state.

As the intensity of the resonance line has been shown to be far more intense than the excimer emission line in a pure helium discharge at 40 Torr, it is necessary to include this resonance helium emission in discharge studies in both pure helium and gas mixtures including helium. For example, ionization wave propagation requires a new source of electrons ahead of the ionization front. It is often assumed that only excimer emission contributes to photoionization and a source of new electrons for the propagation of an ionization wave in helium and nitrogen gas mixtures (e.g., an atmospheric pressure plasma jet). Here, this assumption is studied in an ideal cathode-directed ionization wave case where an initial seed of quasineutral plasma is placed near the anode and allowed to propagate via only photoionization mechanisms in various concentrations of helium and nitrogen gas mixtures.

A one-dimensional simulation with a total pressure of 250 Torr is utilized to conduct ionization wave studies in 10% helium and 90% nitrogen, 50% helium and 50% nitrogen, and finally 90% helium and 10% nitrogen. The gap distance is fixed at 5 mm with a space step resolution of 1.6 $μ$m. As the helium concentration is increased, the time step required to resolve the self-absorption collision frequency of the radiation trapped emission must decrease. To alleviate any inaccuracies introduced by neglecting self-absorption on near the line center for resonance transitions, the full model is used where no photons are neglected. Consequently, a time step of $2×10−16$ s is used for the 10% helium concentration, $5×10−17$ s for 50% helium concentration, and $2×10−17$ s for the 90% helium concentration.

To isolate the effect of photoionization, the only source for new electrons generated ahead of the ionization wave front is generated through photoionization of molecular nitrogen by either resonance emission or excimer emission. A photoionization cross section for molecular nitrogen^31,32 is given as input to the simulation. While the photoionization cross section is wavelength dependent, it has a nominal value of $2–3×10−21m2$ for the resonance and excimer transitions. To further isolate the photoionization propagation mechanism, no surface feedback mechanisms were included from the cathode (i.e., photoemission, ion-induced electron emission).

In addition to the pure helium model previously described, a nitrogen chemistry that was set was compiled from multiple literature sources (such as³³), included in addition to the helium chemistry, and is summarized elsewhere.³⁴ Nitrogen collisions include excitation, ionization, and dissociation. Additionally, interactions between helium and nitrogen were included and are shown in Table I.

A quasineutral plasma density of $1020m−3$ is seeded uniformly within a distance of 200 $μ$m near the anode. Electrons are accelerated into the anode region causing excitation and ionization of both the background nitrogen and helium. Photoionizing radiation generated from these excited states (specifically the 2$1$P and $He2∗$⁠) propagates in all directions, but some ahead of the ionization front. Newly generated electrons are accelerated toward the anode and field-enhanced regions, further avalanching and producing new regions of excitation. This process repeats until the volume is filled with plasma.

The evolution of the electron, $He2∗$⁠, and 2$1$P are shown in Fig. 7 in a series of time snapshots with 100 ps increments for different concentrations of helium gas.

The underlying plasma chemistry leads to a complicated competition between the self-absorption of resonance photons, production of excimer and resonance states, and photon generation. For example, the increase in nitrogen concentration lowers the average electron energy due to the excitation of low lying vibrational, rotational, and electronic states. As the helium concentration is increased, the radiation transport diffuses much slower because spontaneously emitted photons are rapidly self-absorbed many times. Eventually, the photon either ionizes a neutral particle or reaches the wall. In the 10% helium concentration case, the transport is not clearly described by a diffusion problem due to the stochastic appearance of long-range photoionization events. This generates a region of elevated electron density and 2$1$P excited states. These regions of small avalanches fill the volume with plasma. In contrast, the 90% concentration of helium leads to strong self-absorption, and photoionization events (new electrons) only occur very near the initial plasma seed. This plasma development is closer to a propagating ionization wave front.

At 10% helium concentration, new electron avalanches can be generated far from the initial ionization and the excitation source. The mean free path for photoionization with a nominal value of cross section of $2×10−21m2$ is approximately 69 $μ$m with 10% helium (225 Torr partial pressure of nitrogen). This is roughly 1% of the simulation domain. When the mean helium concentration is increased to 90% (nitrogen concentration is lowered to 10%), the photoionization mean free path increases to 625 $μ$m. The difference in the mean free path for photoionization, however, cannot be responsible for the observed results as the simulation with the most helium should cause photoionization events further from the source. A competing process when the helium concentration is increased is the shorter mean free path for resonance photon emission. As a result, the results indicate that the reduction in the mean free path for photon travel (due to increased neutral helium density) greatly affects the location of photoionization events.

This increase in helium density also increases the production rate of excimer states due to the dependence on the density of helium ground states. As shown, the density of excimer states increases roughly 2–3 orders of magnitude for each increase in helium concentration. Though this radiation is not self-absorbed, it does not contribute to the observed difference in the location of photoionization events as the 90% helium case produces the most excimer states with the longest photoionization mean free path. However, new electrons are only generated near the initial plasma source. The density of these excimer states is roughly 3–4 orders of magnitude smaller than the density of the resonance states as well.

The photoionization cross section for nitrogen was split into two discrete domains. A higher energy domain where photoionization occurs through absorption of resonance helium emission, and a lower energy domain where photoionization occurs through excimer emission. As a result, a quantitative comparison between the amount of photoionization produces from each state can be shown (Fig. 8). In all concentrations of helium, the amount of photoionization produced from the resonance emission states is larger than the amount produced from excimer states. The greatest difference is observed for the 10% helium case where resonance emission photoionization is 5 orders of magnitude stronger than excimer emission photoionzation. As the helium concentration is increased, the excimer photoionization becomes increasingly more comparable relative to the resonance photoionzation but still is 2 orders of magnitude smaller at 90% helium.

The reason for photoionization attributable to the excimer radiation being smaller than that of the resonant radiation can be attributed to the excimer’s smaller density as shown previously (Fig. 7). Furthermore, though the atomic 2$1$P state is self-absorbed, it can emit quickly, get re-absorbed very near the original emission location, and re-emit. This process repeats many times before emitting a photon that with as wavelength sufficiently far from line center such that it can photoionize. The time scale for this process must be shorter than the process for excimer creation, emission, and resulting photoionization from the amount of photoionization that occurs.

The experiments at 40 Torr confirm that resonant photons from helium can play a role in discharge dynamics. Despite being strongly trapped, a significant flux of photons from the $21P→11S$ transition is measured within 150 ns of the onset of discharge current. No emissions were detected from higher energy resonant transitions, ions, or forbidden transitions. While these are expected to be present, they appear to be secondary effects in the propagation of ionization waves based on their comparatively low flux.

Simulations of a 40 Torr helium discharge also show the presence of 2$1$P transition with much higher intensity than the other nearby resonance transitions and excimer emission. In the densities of the upper states, the 2$1$P atomic state is 5 orders of magnitude higher in density than the excimer $He2∗$ state. Even accounting for reabsorption, this leads to a discharge where the resonant photons play a dominant role in both experiment and simulation. This suggests that there is a need to include resonant emissions in simulation models of helium discharges, particularly in admixtures.

In the modeling of positive ionization waves, it is often assumed that photoionization of the background gas produces new seed electrons ahead of the ionization front.^35–37 In simulations where the background medium is air or a general nitrogen/oxygen mixture, a photoionization source term can be included through the equation³⁸ (or a more computational efficient approach such as in Refs. 39 and 40),

where $R=|r−r′|$⁠, $XN2$ is the partial pressure of molecular nitrogen, $Sexc(r′)$ is the excitation rate at $r′$⁠, $kph$ is the absorption coefficient, and $ξ$ is the number representing a photoionization efficiency typically varied from 0.1 to 1.

This model has been adapted for plasma discharges in helium/nitrogen mixtures. In this case, it is assumed that photoionization of nitrogen only occurs via energetic photons emitted from the excimer state, neglecting all resonant photon emissions.²² Furthermore, a value of up to 10 for $ξ$ has also been used to better match experimental results.²⁹ This could potentially be attributed to not including resonance states in the model formulation. In solving for this photoionization source term, the amount of photoionizating radiation generated is proportional to this excitation rate, $Sexc(r′)$⁠. To first order, this approach is reasonable as regions of high excimer density coincide with the 2$1$P state as shown in Fig. 7 for helium concentrations of 50% and 90% with only a scale factor in difference. The absorption term for photon propagation in Eq. (4) is represented by a smooth exponential as a function of the absorption coefficient. Thus, this model cannot capture the stochastic and long-range photoionization processes observed in the lower concentration helium case.

Figure 9 shows the plasma development when photoionization from the 2$1$P state is neglected in the 50% helium, 50% nitrogen case. As expected, and consistent with other works, propagation of the ionization wave is still possible. However, the rate of propagation is vastly different compared to when photoionization due to resonance emission is included. The density of excimer states is small, but it only takes a single photoionization event to create a new electron. Electron avalanches amplify with an exponential relationship and even a single photoionization event can significantly increase electron density.

Although out of the scope of this work, future work will examine the quantitative differences in the PIC/DSMC model and the commonly used model given in Eq. (4). The simulations presented here are extremely computationally expensive, even in one-dimension, and were run on the Sandia National Laboratories Ghost Supercomputer utilizing 288 processors for over 192 h. Consequently, the future work will also investigate photoionization models more conducive to fluid approaches at a lower computational cost but still including both the excimer and resonance emissions.

As the helium concentration is increased, it appears that the excimer emission plays a more prevalent role in photoionization. To increase the concentration of helium further would require even smaller time steps. Meanwhile, the excimer may become just as important as the resonance emission at 250 Torr if a concentration of 99% helium was used. Higher total pressures could reveal a regime where the excimer emission results in a photoionization amount that is dominant over resonance emission. However, two competing processes contribute to the photoionization amount for resonance emission as the pressure is increased. First, the increase in total pressure with a fixed helium concentration percentage would result in stronger radiation trapping. However, pressure broadening from the increased total pressure would increase the number of photons emitted in the wings of the emission profile leading to longer absorption lengths. Thus, the pressure scaling for the relevance of either the resonace or excimer emission is not straightforward.

With any model, there are questions of accuracy of the results. Aleph has been verified and benchmarked against various capacities for correctness of the underlying equations it solves.⁴¹ In addition, validation studies have been performed between Aleph and different experimental arrangements.^42–44 These increase the confidence in the simulation capabilities to real-world problems. However, these verification and validation tests do not imply correctness of the input data. A significant effort has been placed on compiling a helium and nitrogen chemistry set for this work and others. Furthermore, the criteria for stability of the numerical methods have been met (e.g., space step, time step). As such, the simulation results presented here are believed to be correct to within the accuracy of the numerical methods and input data given to the simulation.

The presence of helium atomic emission from resonance states was studied using an experimental apparatus that allowed for a discharge in higher pressure and measurement in lower pressures to alleviate any self-absorption mechanisms. The experimental effort measured line radiation eminating from the 2$1$P state at a discharge pressure of 40 Torr. Further time-resolved emissions show a slight delay between detection of the emissions from the 2$1$P state relative to the measured current signal. During the current pulse, however, the emission strongly follows that of the current pulse until the current stops. After zero current flow, there is still detectable 2$1$P emission likely due to cascading transitions or photons still diffusing out of the system. Simulations of a similar plasma system agreed with the experimental results indicating the presence of radiation eminating from the 2$1P$ state with little detection of the excimer emission. The simulation studies attributed this to the 5 orders of magnitude lower excimer density than the 2$1$P state.

Modeling studies confirmed the importance of resonant emissions on photoionization processes, indicating their inclusion for gas admixtures. One-dimensional simulations including a complex chemistry set for nitrogen and helium were conducted at a total pressure of 250 Torr. Increasing helium concentrations were studied to quantify the photoionization from both resonance and excimer states. The simulations showed that the $He2∗$ excimer emission does not contribute as much to ionization wave propagation due to its much lower density than the resonant 2$1$P density. It is clear that although radiation trapped, the atomic helium species can indeed contribute to the photoionization of the nitrogen molecule in the test cases simulated. The plasma formation in the smallest helium concentration case (10% He) did not necessarily follow a traditional ionization wave formation but instead exhibited volume plasma formation due to long-range photoionization events (relative to gap size) that occurred. When the helium concentration was increased (50% and 90% He), the plasma formed in a more typical ionization wave propagation mechanism.

The included plasma chemistry leads to complex interactions between helium and nitrogen and produces scaling relationships (such as the amount of photoionization or wave speed) that is not necessarily linear. Thus, there are a wide range of operating parameters that could potentially be adjusted in helium/nitrogen plasmas to optimize various plasma aspects.

Support was provided by the Sandia National Laboratories Laboratory Directed Research and Development (LDRD) program under Project No. 209241. 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 No. DE-NA0003525.

The data that support the findings of this study are available within the article.

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.