Counter-propagating streamers in an atmospheric-pressure helium plasma jet

This study explores an atmospheric pressure plasma jet impinging on a downstream dielectric surface using a 2D numerical plasma fluid model. It is demonstrated that a counter-propagating discharge ignites at the exposed dielectric surface when the discharge is ignited using negative polarity voltage pulses with fall times in the microsecond range. Two distinct streamer discharges are created, a cathode-directed streamer propagating upstream toward the cathode, and an anode-directed streamer propagating parallel to the dielectric surface facing the gas flow. The surface discharge propagating parallel to the dielectric surface deposits negative surface charge. It is also shown that driving an APPJ with a negative applied potential significantly increases the O2− time-averaged flux to the dielectric surface while decreasing the O2+ time-averaged flux.


Introduction
In the last decade, atmospheric pressure plasma jets (APPJs) have attracted considerable attention due to their ability to generate a long and reactive plume of plasma species that extend several cm's beyond the jet's exit. Such characteris tics mean APPJ systems are ideally suited for a wide variety of applications, including surface decontamination [1], mat erials processing [2], wound healing and dental hygiene [3,4]. Given their application potential, APPJs have been the subject of intensive experimental and computational invest igation. It is well established that the discharge produced by an APPJ is in the form of a train of fast propagating streamers (also known as plasma bullets, fast ionization wave, or pulsed atmo spheric plasma streamers). These propagate in the noble gas channel at velocities much higher than that of the background flow velocity [5,6]. When a dielectric surface is placed down stream, the impinging plasma bullets deflect at the surface and propagate in a parallel direction to the di electric surface, depositing positive surface charge [7,8]. Under certain gen eration conditions, it has been shown that a plasma bullet can ignite at the dielectric surface and propagate in the opposite direction, toward the powered electrode [9][10][11][12][13]: this can be considered as the 'reverse' direction of propagation in the region outside the dielectric tube [11]. This phenomenon has mainly been observed in the presence of a dielectric sur face downstream on the negative cycle of the applied voltage waveform.
In general, most computational studies have focused on the propagation of the discharge generated by a positive applied potential. Few studies have focused on plasma bullets pro duced by a negative applied potential, in spite of many exper imental reports which show clear differences between the two types of operation in terms of structure, intensity and chem istry [14,15]. Of the numerical studies focusing on negative pulsed operation of APPJs. Nadis studied the operation of a This study explores an atmospheric pressure plasma jet impinging on a downstream dielectric surface using a 2D numerical plasma fluid model. It is demonstrated that a counterpropagating discharge ignites at the exposed dielectric surface when the discharge is ignited using negative polarity voltage pulses with fall times in the microsecond range. Two distinct streamer discharges are created, a cathodedirected streamer propagating upstream toward the cathode, and an anodedirected streamer propagating parallel to the dielectric surface facing the gas flow. The surface discharge propagating parallel to the dielectric surface deposits negative surface charge. It is also shown that driving an APPJ with a negative applied potential significantly increases the − O 2 timeaveraged flux to the dielectric surface while decreasing the + O 2 timeaveraged flux.
Keywords: atmosphericpressure, plasma jet, plasma model (Some figures may appear in colour only in the online journal) Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. negatively driven APPJ in open air [17] and Norberg et al con sidered the interaction between a negatively driven APPJ dis charge and a partially conductive surface downstream of the jet [17][18][19]. In these reports, the discharge was operated under conditions where the generated plasma bullet was observed to propagate from the driven electrode to the dielectric surface.
In this work, a 2D axisymmetric fluid numerical model is used to study the characteristics of the counterpropagating bullet in a helium APPJ, driven by a negative applied potential. In essence, the discharge configuration simulated in this work is similar to that reported by Norberg et al [17][18][19]; however, the major difference is a considerably longer rise time of the applied potential, which is 1 µs in this work compared to 5 ns in the work of Norberg et al [17][18][19]. Surprisingly, this longer rise time initiates a counterpropagating mode of operation, where the generated streamer propagates from the dielectric surface to the driving electrode. The model is also used to study the timeaveraged fluxes of − O 2 and + O 2 associated with the counterpropagating discharge and provide a comparison with those produce in the conventional propagation direction.

Numerical model
The model used in this study is similar to our previous work described in Hasan et al [8], it is a 2D axisymmetric fluid model describing a helium jet impinging on a dielectric surface in ambient air conditions. Several minor modifica tions have been done to the model described in [8] for this work, including a reduction in the number of species consid ered: electrons, He + , He * (helium excited to 2 3 S state), * He 2 , + He 2 , + N 2 , + O 2 , − O 2 , and their associated reactions. Moreover, a second modification was also made to the electrode geometry; which is depicted in figure 1(a) and comprised of an electrode needle 1 mm in length with an internal radius of curvature of 10 µm at the tip. The downstream dielectric surface was situated 3 mm from the exit of the dielectric capillary. The secondary electron emission coefficient of the pin electrode was set to 0.1 for all ions. The discharge was driven by the voltage profile shown in figure 1(b), which is a ramp func tion having a rise time of 1 µs. The model was solved for a total of 5 µs of discharge time. Three values of the applied potential were chosen: −4 kV, −6 kV, and +6 kV for com parison. For all cases considered, the rate of voltage change was adjusted to ensure the maximum voltage was reached at 1 µs. Additionally, the feed gas flow rate was assumed to be 1.5 SLM with a negligible level of impurities. This gas feed is introduced in the domain through the boundary between the dielectric tube and the pin electrode as shown in figure 1(a). For the initial conditions, it was assumed that the plasma den sity in the vicinity of the pin electrode was 10 15 m −3 which decayed exponentially over a distance of 3 mm to a value of 10 12 m −3 everywhere else in the computational domain. This assumption accounts for the seed electrons and is motivated by the fact that the electric field is strong at the pin tip due to its curvature, even for low applied potentials. This implies that the electrons near the tip experience ohmic heating constantly, causing an increase in the local plasma density. This situa tion mimics what is observed in experiments where repetitive pulses are used and the discharge relies on seed electrons from previous pulses.

Results and discussion
This section will focus solely on the negative applied poten tials, as positive applied potentials have been studied widely. Under negative potential excitation, a continuous plasma channel forms between the pin electrode and the dielectric sur face downstream, the ignition and the expansion of this channel occurs through three phases. The first phase is a discharge driven by secondaryemitted electrons and ignited at the pin electrode, approximately 0.3-0.6 µs from the simulation initia tion. This discharge is followed by the ignition of two streamers, the counter propagating streamer and the surface streamer (in a parallel direction along the downstream dielectric surface). These three distinct phases are discussed further in section 3.1, followed by a discussion on the timeaveraged fluxes of − O 2 and + O 2 to the dielectric surface for the three investigated cases in section 3.2. For simplicity, the timeaveraged fluxes will be referred to simply as fluxes in the remainder of this work.

Phase 1: pin electrode discharge
This discharge phase begins as soon as the applied potential begins to increase at the pin electrode (increase in absolute terms). The negative applied potential accelerates electrons in the initial plasma away from the pin electrode and accelerates ions toward it. The accelerated electrons aided by the secondary emitted electrons from the pin electrode start to ionize the gas around the pin electrode, causing the local plasma density to increase. This occurs at approximately 0.5-0.6 µs from the beginning of the applied pulse in the −4 kV case. Following this, the plasma spreads further into the dielectric tube driven by the strong axial electric field, extending beyond the region having a high initial plasma density, as figure 2 shows.

Phase 2: the counter-propagating streamer
The counterpropagating streamer starts to ignite at the di electric surface approximately 0.5 µs from the start of the applied voltage pulse, at a position close to the axis of sym metry. The electrons from the initial plasma are driven away from the negatively biased plasma and pushed toward the dielectric surface; depositing their charge and limiting the flow of other electrons to the same spatial position. This pro cess directs the electron flux to another point on the di electric surface that is further radially from the axis of symmetry. The directed electrons accelerated by the electric field gain enough energy to ionize the background gas, increasing the local plasma density near the dielectric surface and initiating streamer propagation. Given that the streamer is ignited at the surface of the di electric, there are two possible paths for it to propagate; the first is in the upstream direction, creating the counterpropagating streamer. Alternatively, propagation can occur along the surface, creating the surface streamer (discussed in the following section). The counterpropagating streamer moves from the dielectric surface toward the pin elec trode. Since the pin electrode is negatively biased, the counter propagating streamer is in the form of a cathodedirected streamer. While propagating outside of the di electric tube (between the di electric surface and the exit of the di electric capillary), it follows a path along the radial mixing layer, which is defined as the transition zone between the helium jet and the surrounding ambient air. As the counterpropagating streamer approaches the exit of the tube, it can no longer prop agate along the radial mixing layer. Instead, the propagation of the streamer head continues along the axis of symmetry, eventually entering the dielectric tube through its exit. As it enters the tube, the electric field in the streamer head and its propagation velocity increase noticeably. Figure 3 shows the axial electric field at various times as the counterpropagating streamer propagates inside the dielectric tube. The propaga tion in the dielectric tube continues until the streamer head reaches the diffusing plasma emanating from the pin elec trode. At that point, the streamer structure is lost and a single glowlike discharge forms in the gap between the plasma sur rounding the pin electrode and the plasma channel created by the counterpropagating streamer. The glowlike discharge can be seen by observing the uniformity of the electric field, by comparing figure 3(b), which shows the point before the transition, and figure 3(c) the point following the transition in to a glowlike discharge. Under −6 kV excitation the same process occurs, but at a faster rate. For instance, the streamer head enters the dielectric tube at approximately 0.9 µs and propagates with an average velocity of 70 kms −1 until it transitions into a glowlike dis charge. Under −4 kV excitation, the streamer head does not enter the dielectric tube until 1.5 µs, and then propagates at 15 km · s −1 . Both of these velocities are similar to those reported for the downstream propagating streamers [5,10], and are consistent with the experimental observations of the velocity of the counterpropagating streamer [11].
From a practical perspective, the ignition of a glowlike discharge in the dielectric tube could have a significant impact on the chemistry of the discharge in comparison with the con ventional streamer discharge, particularly in cases where an admixture is added to the helium flow.

Phase 3: the surface discharge
The surface streamer ignites approximately 0.1 µs after the counterpropagating streamer is created as described in sec tion 3.2. Both the surface streamer and the counterpropagating streamer are ignited from the same point on the dielectric surface. The counterpropagating streamer creates a plasma channel extending from the dielectric surface to the streamer head. This plasma channel is located slightly off the axis of symmetry. As the plasma channel is held at a negative poten tial compared to its surroundings, the electrons experience a radial electric field that increases their energy enabling them to ionize the background gas. Some electrons are deposited on to the dielectric surface as they move parallel to it due to dif fusion, charging the surface negatively at that spatial location. The deposited surface charge causes the maximum radial elec tric field to shift slightly in the radial outward direction where there is no surface charge covering the dielectric surface and the ground electrode under the dielectric surface is still 'visible' to the electrons. This shifted electric field, presented in figure 4, initiates a new cycle of ionization and surface charge deposition, resulting in a further shift in the field. It is through this mechanism that the surface streamer prop agates. By the end of the simulation, the total surface charge deposited on the dielectric surface is negative for the negative applied potential cases compared to a positive surface charge for the 6 kV case, as seen in figure 5.
The association of a counterpropagating streamer with negative surface charge was reported experimentally by Wild et al [13]. The peak electric field in the surface streamer is on the order of 4 kV · cm −1 as shown in figure 4. This is noticeably less than the 12 kV · cm −1 observed in the counterpropagating streamer, indicating that the surface streamer is significantly weaker in comparison.
Since the surface streamer is essentially propagating toward the ground electrode from the negatively biased plasma channel, it can be classified as an anode directed streamer, which has significantly different characteristics to those of a surface discharge seen when using a positive applied potential, which has characteristics akin to a cathode directed streamer [8]. The main difference lies in the elec tric field. With a negative applied potential, the radial elec tric field is weaker (peak of 4-6 kV · cm −1 ) and is spread over a wider area compared to its counterpart in the positive applied potential case, where the electric field is relatively strong (peak of ~40 kV · cm −1 ) and is highly localized in the streamer head. These differences in the electric field between positively induced and negatively induced streamers were examined in [16].   The propagation mechanism described here for the surface streamer holds true for both cases of −4 kV and −6 kV. The only difference is that the surface streamer starts earlier for the −6 kV and ignites at a stronger electric field with a max imum of at 6 kV · cm −1 compared to that of −4 kV.

Ionic oxygen fluxes to the dielectric surface
In this section, the fluxes of − O 2 and + O 2 to the dielectric surface under positive and negative excitation are compared as these are of considerable practical importance. Figure 6  As detailed in section 3.3, the surface streamer is driven by a weaker electric field in the V peak = −4 kV case compared to V peak = −6 kV case. Consequently, the corresponding elec tron temperature in the V peak = −4 kV case is lower than that in V peak = −6 kV, which leads to more − O 2 ions being gener ated in the former case. As a result, the − O 2 flux to the surface is higher for the V peak = −4 kV case as indicated by figure 6.

Conclusions
To unravel the mechanisms behind the counterpropagating streamer propagation a pin electrode based helium atmospheric pressure plasma jet (APPJ) was studied using a 2D plasma fluid model. The influence of negative and positive applied potentials to the pin electrode was considered. By driving the discharge with a rise time on the order of a µs causes the discharge to operate in a counterpropagation mode for negative applied potentials. In this mode, the discharge evolves through three distinct phases. In the first stage the discharge forms around the pinelectrode, where electrons are repelled by the negative potential and ignite a local discharge sustained by the secondary emitted electrons. The second phase of the discharge involves the generation of a counterpropagating streamer, where a cathodedirected streamer is ignited at the dielectric surface and propagates into the dielectric tube. Eventually the counter propagating streamer turns into a glowlike discharge in the gap between the pin electrode and dielectric surface. Finally, in the third phase of the discharge the surface streamer is formed, which ignites shortly after the counterpropagating streamer. This is an anode direct discharge that propagates as a result of negative surface charge deposition on the dielectric surface.
The influence of a negative applied potential on the ionic fluxes to the dielectric surface is also considered. It was observed that the − O 2 flux to the dielectric surface is significantly increased when the discharge is driven by a negative applied potential, while the + O 2 flux decreases slightly. The increase in the − O 2 flux to the surface occurs due to the propagation mechanism of the surface streamer, where negatively charged species are attracted to the grounded electrode under the dielectric surface in areas where the surface charge density is low. The increase in the − O 2 flux is more noticeable in the −4 kV case compared to −6 kV case, as a result of the electric field driving the surface streamer being weaker in the former case, which corresponds to lower electron temperature and higher attachment rate of the electrons to O 2 .
The results of this study indicate that there may be a pos sibility of controlling the timeaveraged fluxes of − O 2 and + O 2 (and positively/negatively charged species in general) by changing the driving polarity of the discharge. Comparing this study to other studies with similar jet configurations, it also indicates that the rise time can be used to operate the discharge in conventional mode or counterpropagating mode for the same polarity of the applied potential. From an application perspective, the ability to control the nature of charged species flux to a downstream surface is extremely important and such techniques could be employed in both materials processing and biomedical applications.