Phase-shifted counterpropagating atmospheric pressure plasma jets: Characterization and interaction with materials

Nonequilibrium plasmas have unique chemical and electrical properties that make them a powerful tool for surface modification and, thus, serve a vital role in microelectronics manufacturing,^1,2 biomedicine,^3,4 agriculture,⁵ and aerospace.⁶ A plasma jet is a distinct type of atmospheric pressure plasma source that is designed to propel a streamer discharge away from the source, a feature that allows for the treatment of remotely located objects of nearly any material. However, the highly collisional nature of atmospheric pressure plasmas makes it difficult to produce and sustain plasma jets with large diameters and uniform properties over the length of the plasma jet, thus exacerbating the challenges associated with their use in materials’ treatment. These limitations have spurred the development of approaches that employ multiple plasma jets operating in tandem^7–9 or gas flow controls^10,11 to increase the effective treatment areas. However, when multiple jets function concurrently in close proximity, the plasmas emitted from these jets interact with one another in ways that alter their properties. This study aims to explore these interactions by examining two counterpropagating plasma jets driven by independent AC waveforms that can operate with variable phase differences. This work demonstrates how the jets interaction is a strong function of the relative streamer ignition time, which impacts the streamer length, species density, and the energetics of the resulting plasma. We then show how phase-shifting can be advantageously applied to treat the surface of 3D objects placed between the jets.

To circumvent limitations derived from the small effective area of a plasma jet, many researchers have investigated the use of arrays of plasma jets where multiple jets operate simultaneously. Various jet configurations have been studied, including a brushlike array by Niu et al.,¹² a radial jet array by Wang et al.,¹³ a 10-jet array by Cao et al.,¹⁴ and a 12-jet design by Lalor et al.¹⁵ The effects of electrostatic repulsion between the streamers produced in the plasma jets have been reported in various plasma jet arrays.^8,16,17 In their study, Cao et al.¹⁴ highlighted that interactions between jets enhanced the uniformity of surface treatments. This observation emphasizes the critical need to understand these effects, as proper use of these jet–jet interactions can be beneficial for certain applications.

The propagation of a streamer produced within a plasma jet is driven by a complex interplay between photo-ionization and electron avalanche.^18,19 As such, the behavior of the streamer is subject to environmental conditions, where, for example, the introduction of an electric field can influence the streamer by affecting the electron avalanche process. It has been shown that the application of external electric fields²⁰ and magnetic fields^21–24 can impact the features of the plasma, such as the streamer trajectory, electron energy, and chemistry. Li et al.²⁵ showed that positioning two adjacent plasma jets—one grounded and the other driven by a high voltage—can increase the volume of the plasma. The streamer was guided between the jets by the strong electric field between the electrodes, increasing the propagation distance of the streamer and, thus, filling the gap with plasma.

Various researchers^26–32 have studied counterpropagating streamers, where two streamers travel toward each other within a helium background gas. It has been shown through both computational and experimental studies that when two symmetric, counterpropagating streamers approach each other, a dip in the electron density forms between them. This dip is the result of electrostatic repulsion, which prevents the streamers from colliding, thus creating a gap or reduction in plasma formation. In these previous works, it was shown that introducing a time delay in opposing streamer ignition shifts the location of this dip away from the center and toward one of the electrodes. Furthermore, the dip disappears when the polarity of one of the streamers is reversed such that a positive streamer interacts with a negative streamer, resulting in a uniform electron density between the jets.

In our earlier research, we demonstrated that the volume of a plasma jet could be enhanced by introducing additional noble gas streams that serve to guide and extend the length of a streamer.¹⁰ Interestingly, the additional gas streams enable a single plasma jet’s volume to increase sublinearly with input power, making this method a more energy-efficient means to expand plasma volumes than incorporating more jets in tandem. In another study, we demonstrated how the phase difference between two plasma jets intersecting at a surface alters the resulting plasma properties.³³ Changes in the electron density and plasma chemistry at the substrate could be used to control the plasma-surface interaction.

In this study, we combine the previously described concepts to develop a large area plasma source, which uses two counterpropagating plasma jets, driven at only 25 V_amp. Our aim is to explore the behavior of colliding streamers with varying ignition time delays, both within a closed channel and when exposed to ambient air over substrates of different shapes. We specifically focus on the impact of ignition timing on the performance of these plasma jets by adjusting their relative phase difference to demonstrate how minor changes to phase can lead to significant changes in the plasma volume. As with our previous work,³³ the time delay is introduced by adjusting the phase of the AC waveforms that drive the jets. By shifting the ignition timing, we can prevent the positively charged streamers from repelling each other. Instead, with a sufficiently high shift in ignition time, each streamer will experience the field produced at the opposing electrode during the negative half-cycle of the AC waveform. Our findings suggest that controlling the timing of the jets by adjusting the phase shift between them extends the propagation length of each individual jet without increasing the overall power consumption or impacting the plasma properties. This approach can be used to enhance the ability of streamers to travel around objects, thus enabling the treatment of 3D objects located between the opposing jets.

To study how the phase shift influences colliding streamers, two needle electrodes were positioned 5 cm apart within a single, 6.35 mm OD, 4 mm ID glass tube, as shown in Fig. 1. The two plasma jets were driven by a phase-shifting circuit previously described,³³ which produces two sine waves of equal magnitude but different phases. The amplitude was set by an external power supply, which was 25 V for this work. Phase differences, ranging from 0° and 160°, were created using an all-pass filter with a tunable potentiometer (Bourns 3310Y-125-103L, 10 kΩ linear taper). Each waveform was then sent through a piezoelectric transformer to amplify the signal. When only one jet was active in this study, the opposing jet electrode was attached to the laboratory ground. When exploring jet-surface interactions, all substrates were fabricated from thermoplastic (polylactic acid) using an extrusion 3D printer.

For the configuration in Fig. 1, helium was passed into the tube from both ends at a rate of 1 l/min and was allowed to exit through a slit located in the tube’s center, assuring symmetric gas flow for both plasma jets. For the electron density and N₂(C) vibrational/rotational temperature measurements, 0.03 l/min of air was passed through a water bubbler and mixed with the He gas. This addition of N₂ and H₂O to the plasma enabled emission measurements of N₂ bands and the H_β line. This humidified air altered the propagation of the plasma jets, which was addressed by increasing the He flow rate to 3 l/min so that the plasma jet lengths in pure and diluted He were equivalent. For the jet-material studies, flow rates were increased to ensure that the plasma jets could navigate around the material.

Each needle electrode was connected to its own piezoelectric transformer (Steiner & Martins SMSTF68P10S9), which produced a high AC voltage to generate the plasma. Piezoelectric transformers (PTs) leverage the inherent electromechanical coupling found within piezoelectric materials to create a voltage gain comparable to electromagnetic transformers. PTs demonstrate significant promise for plasma generation, as their small size and high voltage gains make them an ideal candidate for a variety of plasma sources.^34–42 In this study, PTs were employed to amplify waveforms from 25 V_amp to considerably higher voltages (>1 kV).

Despite the distinct advantages of PTs, there are a few operating considerations that require attention for their proper usage. It is essential to account for the PT’s resonance frequency during operation to ensure that the maximum voltage gain is achieved. The use of two PTs adds further complications to driving the system at its resonance frequency, as even minor differences in the output impedance of one transformer can cause the resonance frequencies of the PTs to shift.⁴¹ The experimental design ensured that the loads attached to all transformers were equal to keep the resonance frequencies of each transformer as close as possible. As observed in our previous work with angled jets,³³ some resonance frequency variation is inevitable as the plasma introduces an additional load, which may vary between the two jets. This means that while the two jets will be similar, they will not be identical due to the frequency variation causing slight differences in the voltage gain produced by the transformers. The impact will be discussed in Sec. III C 1.

Measuring the output voltage is another challenge with piezoelectric transformers. Attaching a high voltage probe to the PT’s output alters its electrical characteristics, reducing the output voltage and shifting the resonance frequency. Although nonintrusive methods exist for measuring the PT’s output,^43–45 they were not employed in this study. Here, the input voltages were constant, and the transformers were always operated at their expected resonance frequency (≈63.45 kHz), unless stated otherwise. The relative phase of the output voltage in relation to the input voltage is influenced by both the resonance frequency of that transformer and the frequency of the input voltage.⁴⁶ As a result, any differences in the resonance frequency between the plasma jets will cause the relative phase of the plasma jets’ output to vary. To ensure the plasma jets’ relative phase was as intended, their phase was measured by measuring the displacement current formed on auxiliary electrodes positioned outside the shared channel and near each jet. It was determined that the relative phase between the plasma jets was accurate within an uncertainty of ±5°.

The emission spectrum of the plasma was captured using a scanning monochromator (McPherson model 2035) with 2400 g/mm grating equipped with an Andor 334 T iStar ICCD. Light was fed into the monochromator using a fiber optic cable with a 5 mm diameter collimating lens. Additionally, an Ocean Insight HR2000+ and an Ocean Insight HR4 spectrometer were used to measure the intensity of the emission from 650 to 950 nm along the path of the two jets. Photographs were taken with a Canon PowerShot SX710 camera. High-speed images were captured using the Andor 334 T iStar ICCD and were subsequently analyzed using Andor Solis software. The high-speed images shown in the present work were generated by employing a numerical filter in postprocessing that amplifies the differences in emission from the streamer against the background captured by a high-speed camera. This filter is beneficial for highlighting a dimming streamer, as it can provide clearer images even when the signal-to-noise ratio decreases due to reduced light emission from the streamer.

Schlieren photography, a common flow visualization technique, uses variations in the refractive index caused by differences in the gas density to visually capture fluid motion within a flow. In this study, the Schlieren images were captured using a single mirror setup that incorporated a Canon PowerShot SX710 camera, a 160 mm spherical mirror (Cassini Telescopes), an LED light source, and a razor blade.

Images of the plasmas formed within the shared tube are shown in Fig. 2. When one jet is driven and the other is grounded, each plasma jet generates a streamer that travels slightly beyond the channel’s center. When both plasma jets are operated in phase, the propagation length of both streamers shortens due to the electrostatic repulsion from the opposing streamer, creating a dark space around the point of intersection. For a symmetric system, the intersection is expected to be in the center. The images indicate some asymmetry between the left and right jets. This asymmetry and its implications will be discussed in Secs. III B and III C. As the phase difference between the jets is increased, the position of the dark space moves toward the right electrode until about 90°, where it is no longer visible. This implies that a phase shift of approximately 90°, delaying the ignition of the streamers by about 4 μs, effectively alters the streamer-to-streamer interaction. At higher phase differences, the light emission becomes nearly uniform across the distance between the electrodes, with the brightest emission near the electrodes and slightly dimmer emissions in between.

These findings closely match the calculations of Naidis²⁶ and Jánský,²⁷ who both added time delays between opposing streamer ignition into their simulations. When there was no time delay, a predicted decrease in the electron density and emission occurred at the system’s midpoint, where the streamers intersected. Introducing a time delay caused this minimum point to shift toward one electrode, reflecting the change in the intersection point of the streamers.

To understand how the interaction between streamers impacts their propagation, a series of high-speed images were taken to provide spatial and temporal information about the streamers’ trajectory. Figure 3(a) shows the high-speed images of a single plasma jet active while the other jet is grounded. As shown in the time-averaged images in Fig. 2, the streamer travels about half the distance between the electrodes before it eventually dissipates. After the positive streamer, a small plasma glow forms on the powered electrodes during the negative half-cycle and persists until the next streamer is produced. When both jets are active with no phase shift, as shown in Fig. 3(b), the streamers simultaneously travel toward each other until both dissipate. Figure 3(c) compares the location of the streamers when only one jet is active and when both jets are active. The locations of both the individual and simultaneous streamers follow similar trends, differing primarily in the duration of emission.

To quantify the duration of emission, the normalized total light emission from the plasma jets operating individually and simultaneously with no phase shift is shown in Fig. 4. In each case, there is a significant increase in emission at approximately 5 μs, attributed to the formation and propagation of the streamer, as shown in Figs. 3(a) and 3(b). The emission intensity displays similar trends across all cases, increasing after formation until it reaches its peak and then quickly dissipates. As noted earlier, there is a notable difference in the duration of emission produced by the plasma jets when operated individually and simultaneously. Specifically, when the jets operated independently, the streamer’s normalized emission intensity exceeded 10% for a longer duration: 42% of the cycle for the right jet, 35% for the left jet, and only 28% when both jets were active. An asymmetry was observed between the left and right jets, with the right jet active for a longer period than the left. This asymmetry, along with the off-center dark region observed for a 0° phase difference in Fig. 2, may be attributed to variations in the piezoelectric transformers or turbulence from the gas outlet.

Figure 5(a) shows the high-speed images of when the phase between the plasma jets is shifted by 90°. At this intermediate phase shift, there appears to be more cycle-to-cycle inconsistencies in streamer propagation, leading to less distinct streamers when viewed with high-speed images. An asymmetry forms between the two jets, with one jet extending further than the other. This asymmetry can be explained by examining the voltage waveforms applied to the two jets, shown in Fig. 5(b). When the left streamer forms, the right electrode is at a negative voltage, generating a favorable electric field for the left streamer to propagate. In contrast, the right streamer forms when the left streamer has already traveled about halfway down the channel, consequently diminishing the electric field encountered by the right streamer. As a result, the right streamer has a short lifetime and only travels about 1 cm from its origin. This explains the formation of a dark space closer to the right electrode with phase differences of 20° and 50°, shown in Fig. 2, as at those phase differences, the streamer has a weaker background electric field that prevents it from traveling far from the electrode. The location of the dark region is determined by the interaction point of the streamers, which depends on how long they have been active and their velocity.

Figure 6(a) shows the high-speed images of the plasma jets shifted in phase by 160°. At this high phase shift, some symmetry returns between the plasma jets, as both streamers last about the same amount of time and travel about the same distance. At this large phase shift, both streamers move farther from their origin than they do under smaller phase shifts or when operated in isolation. This behavior occurs because the streamers are ignited during the positive voltage swings of each electrode and are, thus, never active simultaneously. This prevents the direct interaction between them and allows each streamer to benefit from the attractive force of the opposite electrode and the residual species left by the previous opposing streamer. This observation also indicates that the positive charge within the streamer head has largely dissipated within 6 μs after the streamer ceases, as evidenced by the subsequent streamer passing through the previous streamer’s end location seemingly unimpeded approximately 6 μs later.

Figure 7 shows the normalized total emission from the jets operating at different phase shifts. At a 160° phase shift, two roughly equivalent increases in emission were observed, corresponding to the two temporally separated streamers. Each streamer produced light for a duration similar to the individual streamers in Fig. 4, effectively doubling the plasma lifetime. At 160°, the normalized emission exceeded 10% of the max emission for 65% of the cycle. Conversely, the 90° phase shift did not significantly impact the duration of emission, with emission surpassing 10% of max emission for 31% of the cycle, compared to 28% with no phase shift. The asymmetry between the streamers is clear as the right streamer, peaking at about 10 μs, produced less peak emission, and did not last as long as the left streamer.

By ensuring that the streamers are never active at the same time, the system can be driven synergistically by increasing the electric field in the tube and enabling each streamer to travel further and exist for longer than if the opposing electrode were grounded. One potential reason for this phenomenon is that the maximal phase shift might equate to doubling the voltage on one electrode and grounding the other, as two identical AC signals in antiphase effectively double the voltage differential between the electrodes. However, if the voltage difference were the only parameter driving plasma propagation, plasma would not form when there is no phase shift between the jets, as the absence of a phase shift would cause the fields of the two opposing jets to cancel each other. Figure 3(b) shows that when the same voltage is applied to both electrodes, two streamers form but are hindered by the presence of the other. Another possible explanation for this phenomenon is the larger population of charged species and metastables lingering from the previous streamer. As shown in Fig. 7 for the 160° case, the right streamer forms only ≈3 μs after the left streamer is extinguished. This suggests that with maximal phase shift, the frequency of positive streamers doubles, thus allowing a greater number of residual species to promote streamer propagation.^18,47,48

To summarize, the total volume of the plasma in Fig. 3(a) could be increased by introducing an additional plasma jet. However, as demonstrated in Fig. 3(b), the repulsion between the plasma jets leads to a decrease in the volume of each individual jet. This can be circumvented by adjusting the timing between the jets, ensuring that the streamers are not active simultaneously. However, depending on the timing, this can enhance the propagation of the streamers, as shown in Fig. 6(a), or suppress propagation as shown in Fig. 3(b).

Since the voltage applied to the electrodes was not directly measured due to the absence of a high voltage probe on the piezoelectric transformer’s output, obtaining the plasma power at the plasma jet origin was not possible. Instead, we calculate the power input into each transformer by measuring both the voltage and current entering each transformer.^33, Figure 8(a) shows the total power consumption of the system when one of the jets is operating (the opposing electrode is grounded) and when the jets are operated in and out of phase (i.e., 0° and 160° phase differences). The power consumption of the system at 0° phase difference is marginally less than twice that of a single jet, due to the slight variations in resonance frequencies between the two individual plasma jets. This is shown in Figs. 8(c) and 8(d), where peak power into the individual jets occurs at slightly different driving frequencies, similar to what was found in our previous work.³³ This discrepancy is attributed to the piezoelectric transformers, whose resonance frequencies are affected by their respective loads.⁴¹ The variation in the resonance frequency likely contributes to the asymmetry observed in Fig. 2. That is, when driving the jets at the same frequency, one jet is operating nearer to resonance than the other, causing a difference in the amount of power into the respective jets. This can result in different propagation distances and lifetimes of the streamers. The variation in the frequency also explains the approximately 10% less power required for the maximum phase-shifted (160°) jets, where introducing a phase difference between the jets further alters the resonance frequency.

The introduction of a second, phase-shifted plasma jet adds an additional electric field within the system, impacting the electron energy distribution within the plasma. Upon interaction with an energetic electron, molecules within a plasma can dissociate or be excited into different electronic, vibrational, and rotational states, which can lead to gas heating. To quantify the energetics of the plasma, it is useful to measure how the energy is partitioned into these different states. Generally, the temperatures of species and their internal energies are not equal: T_t ≤ T_r ≤ T_v ≤ T_ex ≤ T_e. However, it is often assumed that the rotational temperature (T_r) is in equilibrium with the translational temperature (T_t), which suggests that the use of emission spectroscopy is a convenient approach to measure the background gas temperature (T_t = T_g). While there are many caveats to this assumption of equilibrium and the associated spectroscopic measurements, the second positive system of nitrogen (C³Π_u-B³Π_g) in atmospheric pressure helium plasmas is an established system to study.⁴⁹ In this work, the rotational and vibrational temperatures of N₂(C) were determined by fitting the measured emissions of the second positive N₂ system to simulations using MassiveOES.^50–52 An example of this fit is shown in Fig. 9(a), where the measured N₂(C-B) from 381 to 370 nm was fit to simulations.

The vibrational and rotational temperatures of the excited gas as a function of phase difference are shown in Fig. 9(b). In agreement with the discussion above, the vibrational temperatures are well above the rotational temperatures, which, in turn, are slightly above the room temperature (300 K). Compared to one active jet, two active jets operating in phase resulted in a marginally higher (<2%) rotational and vibrational temperature compared to just one jet. With a phase difference of 160°, the results were similar although the rotational temperature increased to about 5% above the single jet temperature. Given the assumption that the rotational/translational energies are in equilibrium, the increase could be attributed to the additional heating of the feed gas by the second jet. The trend with increasing phase difference is not clear but may well indicate that these are simply marginal differences, and, thus, gas heating is not significant near the electrode surfaces. It is interesting to note, however, that the total input power (Fig. 8) decreases with increasing phase difference. The absence of any temperature change is in line with previous research indicating a lack of direct dependence between input power and rotational/vibrational temperatures.⁵³ It is important to note that the rotational temperature might have spatial dependencies across the length of the plasma not captured in this measurement, which was taken at a single location near the left electrode.

Figure 10(b) shows that the electron density calculated from the H_β line generally largely stays the same regardless of the phase. The largest difference between these cases is that at the 160° phase difference, the plasma is able to produce strong enough emission along the length of the tube to enable electron density approximation at each point across the space between the electrodes. Away from the left electrode, the electron density of the phase-shifted plasma was uniform. This is a positive attribute of the plasma, as enhancing the propagation length while maintaining uniformity is necessary for several applications.⁵⁸ 

Operating outside the shared channel, the system retains its functionality but experiences more cycle-to-cycle variability, likely due to increased turbulence from the colliding gas streams mixing with ambient air. Operation in the open air enables this system to be used for surface treatment applications, as atmospheric pressure plasmas are highly effective in treating insulating materials, such as polymers⁵⁹ and biomaterials.^60,61 The counterpropagating, phase-shifted jets presented in this work exhibit a remarkable feature when interacting with insulating 3D objects positioned between the jets, as the plasma jets can navigate around complex surfaces. For instance, Fig. 11(a) shows a schematic of a dielectric barrier positioned between two jets open to ambient. Figure 11(b) shows the images of the two plasma jets operating with different phase shifts. When a single jet is active, or when the jets are in phase, the streamers terminate as they collide with the sides of the barrier. However, when the jets are phase-shifted, the plasma jets appear to maneuver around the barrier and connect. The high-speed images in Fig. 11(c) indicate that the streamer, indeed, navigates across the barrier and emerges on the other side.

Similar behavior is observed when obstacles with different geometries are placed between the electrodes. In Fig. 12(a), a glass tube is placed between the jets. This results in the plasma jets shown in Fig. 12(b), where a single jet and nonphase shifted jets simply terminate on the sides of the tube. At higher phase differences, the tube is enveloped by plasma. Figure 12(c) shows a single streamer navigating around the surface of the tube. For both barrier shapes, the high-speed images show that the individual streamers do not extend far beyond the barriers. However, since the streamer from the left jet traces a similar path in the opposite direction, the images of Figs. 11(b) and 12(b) appear as a continuous jet extending between the electrodes when the phase difference is 160°. These findings suggest that phase-shifted plasma jets can enable the effective treatment of complex, three-dimensional substrates, due to the streamers’ ability to navigate around complex geometries.

However, different geometries come with different considerations, as the shape of the substrate will impact surface charging and will distort the flow of the feed gas in different ways. While surface charging is outside the scope of this work, altering the flow can change the local concentration of noble gas and, thus, the streamer trajectory. This is important because the trajectory of the plasma jet is also influenced by the local concentration of noble gas,¹⁰ which requires a consideration of fluid mechanics. Most notably, a sufficient concentration of the feed gas along the desired path of the streamer is needed. As shown in the Schlieren images in Figs. 13(a) and 13(b), positioning a substrate between the jets deflects the feed gas, which can adversely impact the noble gas density above the substrate. If the flow rate was inadequate, the plasma jets would simply terminate upon reaching the sides of the substrate, regardless of the phase. However, if the flow rate were high enough, the plasma jets could traverse the substrate. The requisite flow rate is dependent on the geometry of the substrate placed between the jets. This is shown in Fig. 13, where a flow of 7 l/min was necessary to travel around a triangular substrate [Fig. 13(a)] and 5 l/min was sufficient to travel around a square substrate [Fig. 13(b)]. Alternatively, it could be possible to maintain lower flow rates by adding more feed gas flows along the length of the surface to further augment the noble gas density and promote plasma propagation.¹⁰ 

In this work, counterpropagating plasma jets with varying time delays between their ignitions interacted within a closed channel and were exposed to ambient air across different shaped substrates. The timing of ignition of the positive streamers from each plasma jet was adjusted by shifting the relative phase of the high voltage AC powering the plasma jet, facilitating a study on how altering the relative timing of the plasma jets impacts their properties. Operating two jets simultaneously led to an increase in the overall plasma volume but a decrease in the length of each individual jet due to electrostatic repulsion between the streamers. Increasing the phase difference between the jets caused the dark space, created by the electrostatic repulsion between the streamers, to shift toward one jet until it eventually dissipates. At high enough phase differences, a uniform plasma column formed that spanned the two powered electrodes. High-speed images showed the trajectory of individual streamers at various phase differences, revealing that the phase difference impacted the distance the streamers were able to travel and their lifetimes. The impact varied with the magnitude of the phase shift. Intermediate phase adjustments significantly reduced the propagation length of one of the jets. Larger phase shifts prevented direct interaction between the streamers, while still enabling them to benefit from residual species left by the opposing streamer. Increasing the phase difference between the plasma jets led to a minor decrease in power consumption, while the electron density and rotational/vibrational temperature of N₂(C) remained relatively constant. It was demonstrated that the attractive force of the opposing plasma jet could be used to pull streamers across different substrates, suggesting that this technique could be employed to treat 3D substrates.

The authors would like to thank Dr. David B. Go for his insightful discussions. G.H.B. held an internship at NRL through the Office of Naval Research supported by the Naval Research Enterprise Internship Program (NREIP). This work was supported by the NRL base program.

The authors have no conflicts to disclose.

Michael J. Johnson: Conceptualization (equal); Data curation (equal); Investigation (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Gabriel H. Brown: Conceptualization (equal); Investigation (equal); Visualization (equal); Writing – review & editing (equal). David R. Boris: Conceptualization (equal); Methodology (equal); Writing – review & editing (equal). Tzvetelina B. Petrova: Writing – review & editing (equal). Scott G. Walton: Conceptualization (equal); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.