The influence of pulse repetition frequency on reactive oxygen species production in pulsed He+H₂O plasmas at atmospheric pressure

Low temperature plasmas generated at atmospheric pressure have seen great interest in recent years due to their ability to be operated in ambient air and close to room temperature.^1–8 These properties make them well suited to biomedical applications, including cancer therapy, microbial sterilization, and the treatment of chronic wounds.^9–11 If small admixtures of oxygen or water vapor are introduced to the feed gas, the electron-driven plasma chemistry can produce high densities of reactive oxygen species (ROS). The resulting mixture of species can exhibit a complex array of effects on the human body; for example, the OH radical is highly reactive and readily oxidizes proteins and DNA molecules, causing cell damage and instability in healthy and cancerous tissues alike.¹² H $2$O $2$ primarily acts as a cell signaling molecule, mediating immune responses.¹³ Depending on its concentration, it can also inhibit the growth of bacterial infections, while at too high a dose, it causes damage to human cells due to oxidative stress.¹⁴ Like H $2$O $2$⁠, O $3$ is known to stimulate the immune system and inactivate micro-organisms; however, it is toxic in high concentrations.¹⁵ Given this array of functionality, it is evident that the plasma chemistry must be tightly controlled when optimizing a plasma for a specific application.

O $3$ is produced in abundance in helium plasmas with admixtures of O $2$⁠, and thanks to extensive research, the mechanisms governing this are now well understood.^16–19 Similarly, helium plasmas with admixtures of H $2$O have garnered attention due to their ability to produce tunable amounts of H $2$O $2$ and OH.^6,8,20 It has also been established that these two admixtures can be used in tandem, with He+O $2$+H $2$O plasmas offering a high degree of selectivity between hydrogen-containing species and those containing only oxygen.^2,21,22

For discharges operated with pulsed power schemes, the number of pulses per second can be modified, while the pulse itself is left unchanged. This parameter, the pulse repetition frequency, presents a seemingly straightforward way of tuning the plasma chemistry. This is due in part to the parameter being altered by purely electrical means. The lack of mechanical action reduces the risk of component wear over time, while also allowing the plasma chemistry to be modified at a rate restricted only by the effluent transit time. Previous works have investigated the use of pulse repetition frequency as a control parameter for pulsed-power atmospheric pressure plasmas. The influence of pulse repetition frequency on discharge behavior^23,24 and electron parameters^25,26 in dielectric barrier discharges has been reported, in addition to its effects on efficiency and selectivity in the conversion of methane and CO $2$⁠.²⁷ It has also been demonstrated that the repetition frequency of He+O $2$ plasmas can be altered to improve their effectiveness in biomedical roles, such as for triggering apoptosis in cancerous cells²⁸ or for treating tissue beneath a thin layer of liquid.²⁹ 

When considering pulsed plasma sources, operation with nanosecond-scale pulses can efficiently generate energetic electrons, driving an active plasma chemistry while also suppressing excessive gas heating due to the long afterglow period relative to the pulse.³⁰ Fundamental studies have been conducted that investigate the influence of pulse repetition frequency on atmospheric pressure, nanosecond-pulsed plasmas for a number of gas compositions, including helium,³¹ air,^32,33 Ar+CH $4$⁠,^30,34 Ne+Ar,³⁵ H $2$+air,³⁶ and CH $4$+air.³⁷ However, the influence of pulse repetition frequency on ROS production, and the overall plasma chemistry, in the bulk of a He+H $2$O plasma has not yet been studied in detail. This paper presents a model study in which the pulse repetition frequency is varied so as to characterize its effect on ROS production across the power cycle.

where $n$ is the number density of species $i$⁠. The first term describes the gas phase chemistry, where $a i j R$ is the stoichiometric coefficient of species $i$ in reaction $j$ on the right-hand side of the reaction and $a i j L$ is the stoichiometric coefficient on the left-hand side. The bracketed term is, therefore, the difference between these coefficients, giving the change in species $i$ per reaction. $k j$ is the rate coefficient of reaction $j$⁠, and $∏ l n l a l j L$ accommodates for the reaction partners. The second term quantifies the gain and loss of particles due to collisions with the vessel wall, where $S V$ is the surface area to volume ratio of the plasma, $D$ is the diffusion coefficient, $γ$ is the sticking coefficient of a heavy particle colliding with the reactor wall, $Λ$ is the diffusion length, $v t h$ is the thermal velocity of the particle, and $f$ is the return fraction of a species from the walls.

where $N g$⁠, $c p$⁠, and $κ$ are the gas mixture’s total density, specific heat, and thermal conductivity, respectively. $P i o n$ is the power supplied to the ions at time $t$⁠, and $T w$ is the temperature of the bounding surfaces. Equations (1)–(3) are passed to an ODE solver module, which extracts the relevant parameters and passes them back to the chemistry and transport module for the next iteration. A Boltzmann solver module is also periodically called to solve a two-term approximation of the Boltzmann equation, allowing the rates of electron impact reactions and corresponding diffusion coefficients to be updated. This module is called less frequently than the ODE solver to save on processing power, as very small changes in the electron energy distribution function should have minimal impact on the overall plasma chemistry.

In this study, GlobalKin is supplied with a chemistry set containing 46 species and 577 reactions covering He, H $2$O, and O $2$ gas mixtures, listed in Ref. 2. This chemistry set has been validated in previous studies against experimental measurements of O and OH densities, alongside time-resolved electron density measurements.^2,39 Despite being a spatially averaged model, GlobalKin requires geometric inputs in the forms of the surface-area-to-volume ratio and radius of the plasma. As such, the dimensions used in this model were matched to an existing experimental setup described in Ref. 39 and illustrated in Fig. 1.

The plasma source is a nanosecond-pulsed, pin-to-pin discharge housed in a 67 mm cubic vessel. The two pin-type electrodes are made of stainless steel. They are conical in shape with a parabolic tip, with an approximate radius of curvature of 500  $μ$m.⁴⁰ They are fixed at 3 mm separation. The plasma produced between them has a radius of roughly 1 mm. Assuming the discharge to be approximately cylindrical, the initial plasma volume is $9.42× 10 − 3$ cm $3$⁠. The volume of the vessel is 300 cm $3$ and the plasma is generated at its center, meaning that interactions with the plasma and vessel walls are negligible and the surface area of the vessel is ignored in the model. The surface area in contact with the plasma is instead set to 0.0524 cm $2$⁠, the approximate area of the parabolic electrode tips that bulk plasma emission extends across. A helium feed gas with a 0.25% water vapor admixture, equivalent to 2500 parts-per-million by volume, is supplied to the vessel.

The width and amplitude of the power profile are based on current and voltage measurements of the physical setup, with a typical pulse shown in Fig. 2. The scheme utilizes a negative voltage pulse with an amplitude of 2.5 kV, a rise time of 3 ns, and a duration of roughly 80 ns. Plasmas generated in this manner have been observed to be reasonably homogeneous along the discharge channel.³⁹ It is, therefore, expected that the 0D model described above will provide a good approximation of the plasma chemistry. The current and voltage signals are multiplied together to find the power supplied to the plasma over time, before being simplified slightly to streamline the model input. The experimentally measured pulse and its approximation are also shown in Fig. 2. The power deposition used in the model is 0 outside the width of the simplified profile. The duration of power deposition is 89 ns per cycle, with a rise time to peak of 67 ns. The pulse amplitude and duration are kept constant for all repetition frequencies. As such, by altering the pulse repetition frequency, the afterglow is the phase of the cycle that is modified. The use of this pulse scheme produces model electron densities comparable to the experimentally measured ones presented in Ref. 39.

The pulse repetition frequency is varied in the range of 1–100 kHz. Across this frequency range, the pulse width is significantly shorter than the overall cycle time. In addition to this, the plasma chemistry during and shortly after the pulse is driven by electron interactions occurring on very short timescales, whereas the late stage of the cycle is dominated by heavy particle interactions on comparatively longer timescales. Consequently, the time steps used in the model must allow the plasma chemistry in the pulse to be captured in high resolution, while using longer time steps in the afterglow phase to relax computational demand and produce a more efficient output. This is achieved by setting each subsequent time step to increase by a constant factor determined by the given repetition frequency. The time step then resets with the following cycle.

Simulations are run until the plasma reaches an equilibrium, with the time-averaged density of a species found by taking the mean of its density across ten cycles in equilibrium. This allows a good degree of confidence in the results. For the same reason, the average peak electron density per cycle is taken as the mean of the peak electron density across ten cycles. Time-resolved measurements are taken across one cycle in equilibrium. Analysis of time-resolved parameters is achieved by normalizing the time in the cycle to the total duration of a cycle at the given repetition frequency, with $t=0$ being the moment of maximum power deposition. Data on reaction pathways in the plasma are extracted and streamlined to find dominant reaction rates using the software package PumpKin.⁴¹ 

The effect of pulse repetition frequency on the average peak electron density when the plasma is in equilibrium is shown in Fig. 3. The peak electron density is only weakly affected by pulse repetition frequency, changing by 9% between the maximum and minimum values recorded. This is unsurprising, as most of the electrons created by the pulse recombine on timescales significantly shorter than the cycle time.

A very small increase in the peak electron density is observed from 1 to 2 kHz. This can likely be attributed to the memory effect,⁴² with its dependence on repetition frequency identified in previous studies.^24,25 Here, increasing the repetition frequency reduces the duration of the afterglow such that larger electron population remains by the end of the cycle. The presence of residual electrons at the start of the next pulse shortens the breakdown phase of the plasma and increases the peak electron density. In this case, the memory effect is near-negligible due to the rapid recombination of the electrons at all repetitions frequencies investigated. At higher frequencies, the memory effect is offset by an expansion of the plasma that arises as a result of an increased gas temperature, increasing the overall volume occupied by the electrons and, therefore, reducing the electron density. The data presented here are in good agreement with previous experimental measurements of the pin-to-pin discharge setup modeled in this study.³⁹ For the same gas composition, nanosecond pulsing at a repetition frequency of 5 kHz yielded a similar electron decay curve with time. The peak spatially averaged electron density measured in those conditions was around $2.5× 10 14$ cm $− 3$⁠, which is close to $3.5× 10 14$ cm $− 3$ found in the present study.

Figures 4–6 show the change in time-averaged H, O, and OH densities, respectively, with pulse repetition frequency. H and O exhibit similar density trends, undergoing a minimal change at low repetition frequencies and a more substantial increase in the high frequency range. Meanwhile, OH increases more steadily with repetition frequency.

In spite of the 100-fold increase in power supplied per unit time as the pulse repetition frequency is increased from 1 to 100 kHz, the density of these radicals only increases by factors of 13–50. However, this is still a stark increase when compared to the electron density, especially as these species are predominantly formed through electron impact processes. To investigate this further, the densities of these radicals are plotted as a function of relative time within a cycle in Figs. 7–9. Density maxima occur shortly after the pulse for the radicals due to the associated peak in the electron density. The density of all three radicals drops substantially over the course of the afterglow at low pulse repetition frequencies. This effect is reduced toward higher repetition frequencies, where the reduced afterglow period limits the time available for the densities to decay. Indeed, once equilibrium is reached at a repetition frequency of 100 kHz, the time-resolved density of H is nearly constant. Additionally, an increase in the background gas temperature slightly enhances the radical densities in the range of 50–100 kHz.

The H, O, and OH radicals decay significantly slower than the electrons; even at lower frequencies, the electron density decays by several orders of magnitude more than that of the radicals. This leads to the radical densities experiencing a more pronounced memory effect compared to the electrons, with the latter decaying to near background densities at low repetition frequencies. In contrast, the significant radical densities remaining at the start of the next pulse further increase their peak densities until an equilibrium is reached. Similar effects were noted in a modeling study of pulsed He+O $2$ plasmas, where increasing the pulse repetition frequency was found to increase the density of the O radical and the excited states O(⁠ $1$D) and O $2$(⁠ $1Δ g$⁠).²⁶ Likewise, an increase in the H radical density with repetition frequency is also seen in Ar+CH $4$ mixtures,^30,34 and an increase in OH with repetition frequency is seen in CH $4$+air and H $2$+air mixtures.^36,37 As with the present work, the authors of these previous studies attribute the increased radical densities to accumulation with decreasing afterglow duration. These results indicate that the afterglow period is important for determining the final densities of H, O, and OH despite their short lifetimes.

Figure 10 shows the relationship between the pulse repetition frequency and the average H $2$O $2$ density. The density of H $2$O $2$ initially increases with the repetition frequency, before peaking at 20 kHz and dropping sharply toward 100 kHz.

This reaction is generally accepted to be the main mechanism of H $2$O $2$ production in atmospheric pressure plasmas with water vapor admixtures.^8,43 There is also a small spike in H $2$O $2$-producing ion interactions close to the pulse. The peaks of these reaction rates are mostly unaffected by the pulse repetition frequency, although their duration relative to the cycle period increases as the repetition frequency is raised.

The increase in H $2$O $2$ density in the low repetition frequency range is likely a consequence of the steady increase in OH over the same frequency range. However, the peak and subsequent decrease in the H $2$O $2$ density seen at repetition frequencies above 20 kHz does not match the trend shown for OH in Fig. 6. To investigate this, Fig. 12 shows the density of H $2$O $2$ as a function of normalized time over one cycle in equilibrium. H $2$O $2$ is seen to accumulate through the early to mid afterglow at 1 kHz and throughout the full afterglow at 10 kHz and 100 kHz, primarily through OH recombination in reaction (4). Another feature of importance is the decrease in the H $2$O $2$ density during and shortly after the pulse.

Figure 13 shows that this is tied to a significant increase in the rates of dissociation reactions between electrons and H $2$O $2$ shortly after the pulse, along with an increase in the rate of H $2$O $2$ dissociation by the electronically excited He(⁠ $2 3S$⁠).⁴⁴ As the pulse repetition frequency is increased, these reactions remain at high rates for increasingly longer fractions of the cycle. Though less significant than during the pulse phase, H $2$O $2$ consumption is relatively consistent in the afterglow after these processes die out. The dominant contribution comes from a reaction with OH. Despite this, the consumption from OH is lower than the production from OH via reaction (4), meaning that there is still a net increase in H $2$O $2$ from OH. Another source of consumption is the reaction between H $2$O $2$ and atomic hydrogen, a process whose rate in the late afterglow increases significantly with pulse repetition frequency.

It so follows that a reduction in the afterglow period with increasing repetition frequency restricts the time available for OH to react to form H $2$O $2$⁠, while also increasing the fraction of the cycle where H $2$O $2$ is destroyed by electrons and metastables. This is the case despite the high OH densities seen at higher pulse repetition frequencies. It can be concluded that at the peak in H $2$O $2$ density at 20 kHz, the limiting factor in its production changes from OH availability at lower repetition frequencies to the afterglow duration at higher repetition frequencies. Another factor that impacts the density of H $2$O $2$ is the temperature of the background gas. Figure 14 shows the change in the time-averaged gas temperature with the pulse repetition frequency. It can be seen that the gas temperature increases steadily with repetition frequency, with a minimum of 300 K at 1 kHz and peaking at 455 K at 100 kHz.

H $2$O $2$ is known to undergo thermal decomposition at high temperatures, with this effect contributing to the drop in H $2$O $2$ seen above 20 kHz as the gas temperature increases appreciably in the same range.⁴⁵ Nevertheless, the influence of gas heating only exacerbates the existing trend seen for H $2$O $2$⁠. Simulations with a constant gas temperature of 300 K show the same trend, albeit with the peak and drop in the H $2$O $2$ density shifted toward higher pulse repetition frequencies.

O $3$ is produced in significantly lower quantities in plasmas with water vapor admixtures when compared to plasmas with admixtures of oxygen gas due to the preferential formation of hydrogen-containing species over O or O $3$⁠. Analysis of the reaction chemistry suggests that this phenomenon arises from the plasma conditions supporting hydrogen catalytic cycles, whereby hydrogen-containing radicals catalyze the decay of O and O $3$ into O $2$⁠.^46,47 The densities of the radicals, namely, H, OH, and HO $2$⁠, are largely unaffected by these cycles. Figure 15 shows a complex relationship between the density of O $3$ and pulse repetition frequency. The maximum O $3$ density occurs at a frequency of 1 kHz, with this density dropping toward 2 kHz and rising to a second, smaller peak at 10 kHz. The O $3$ density drops sharply as the repetition frequency is increased above this.

The rate of this reaction is consistent across the full cycle at higher pulse repetition frequencies, while at low repetition frequencies, the longer afterglow duration causes the rate to drop by around two orders of magnitude by the end of the cycle as O is depleted. O $3$ is also produced through ion interactions close to the pulse, with these processes increasing in rate and extending through a larger portion of the afterglow toward higher pulse repetition frequencies, although this effect becomes insignificant compared to the rising gas temperature.

Examining the change in the O $3$ density over one cycle at 1, 10, and 100 kHz, given in Fig. 17, shows that the peak density of O $3$ is reached shortly after the pulse. Its magnitude decreases with repetition frequency. In all cases, this peak is followed by a decline in the O $3$ density. This decline persists throughout the full afterglow at 10 and 100 kHz. At 1 kHz, a minimum is reached a quarter of the way through the cycle, with the O $3$ density increasing again through the remaining afterglow.

This reaction dominates the afterglow phase because of an abundance of H atoms due largely to the electron-impact dissociation of H $2$O and H $2$ during the pulse. There is also a spike in electron-impact processes that destroy O $3$ near the pulse. The rate of reaction (6) is dependent on afterglow duration, staying roughly constant at high repetition frequencies but dropping by two orders of magnitude in the 1 kHz case wherein the afterglow lasts for long enough for the density of H to be severely depleted. Increasing the repetition frequency also increases the overall peak rate of reaction (6). It can, therefore, be concluded that the production of O $3$ seen in the afterglow at 1 kHz is due to the lack of availability of atomic hydrogen. Thus, the decrease in the average O $3$ density at 2 kHz shown in Fig. 15 can be attributed to a reduction of the afterglow as compared to the 1 kHz case such that the density of H is not depleted significantly. This limits the late-afterglow buildup of O $3$ at 2 kHz. The change in the O density from 1 to 2 kHz is minimal, resulting in negligible extra O $3$ production from reaction (5). As the pulse repetition frequency is increased from 2 to 10 kHz, a more appreciable increase in the density of O enhances O $3$ production through reaction (5), outmatching the effects of the reduced afterglow and H abundance and increasing the overall mean density. The subsequent decay seen from 10 to 100 kHz is heavily dictated by the rising gas temperature, as O $3$ is highly sensitive to thermal decomposition.⁴⁸ This is corroborated by simulating the plasma with a constant background gas temperature; under these conditions, a minimum is still reached at 2 kHz and the density of O $3$ rises above 10 kHz rather than decaying.

To summarize, the observed dependence of O $3$ density on pulse repetition frequency results from the interplay between O and H reactant availability and afterglow duration at low frequencies, while at high frequencies, the influence of background gas heating dominates.

Pulse repetition frequency shows potential as a parameter for controlling ROS production in pulsed-power He+H $2$O plasmas. The changes made are electrical, thus having rapid response times and relatively convenient implementation. In this study, a pulsed-power, pin-to-pin He+H $2$O plasma is modeled using GlobalKin with a PumpKin plugin. The plasma is simulated at different pulse repetition frequencies with a constant pulse shape, thus varying the duration of the afterglow phase. The plasma chemistry is subsequently analyzed with focus on biomedically relevant species and their precursors. The reduction in afterglow duration with increasing repetition frequency increases the influence of the memory effect. This results in a greater residual electron population by the end of the cycle, in turn causing a slight increase in the peak electron density at 2 kHz. However, this effect is outmatched by gas expansion in the 5–100 kHz range. The densities of short-lived species (namely H, O, and OH) decay much more slowly than the electron density, dropping by several orders of magnitude less than the electron density by the end of the cycle. This results in a more pronounced memory effect, boosting the peak radical densities until an equilibrium is reached. The density of H $2$O $2$ exhibits a more complex relationship with frequency as it has a comparatively longer lifetime and is mainly produced throughout the afterglow. As such, the pulse repetition frequency can be used to modulate the density of H $2$O $2$ provided that its relationship with this parameter is clearly understood. Finally, the density of O $3$ is dependent on the afterglow duration and availability of O and H as reactants, although at high repetition frequencies, an increase in the gas temperature drives a strong O $3$ decay. This work serves to highlight the importance of the pulse repetition frequency, and by extension the afterglow duration, when optimizing a pulsed plasma for biomedical applications. Though the pulse repetition frequency can indeed be used to tune the plasma composition, it is clear that the effects on the plasma chemistry are significant and a thorough understanding of the chemistry is needed to effectively utilize this parameter to optimize a plasma.

The authors would like to thank Dr. Helen Davies for many productive discussions. They would also like to thank Dr. Kari Niemi and Dr. Alexandra Brisset for their help with setting up the simulations. We also acknowledge financial support from the UK EPSRC (Nos. EP/S026584/1 and EP/S025790/1) and the Norma Ann Christie Scholarship.

The authors have no conflicts to disclose.

B. Harris: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (equal); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). E. Wagenaars: Conceptualization (equal); Funding acquisition (lead); Methodology (equal); Project administration (lead); Resources (lead); Supervision (lead).

The data that support the findings of this study are openly available in the York Research Database at https://doi.org/10.15124/a16dce57-8907-457a-b2cc-5b60e7c446fc.