Evolution of ionization waves in a multipulsed plasma jet: the role of memory charges

N Yu BABAEVA, G V NAIDIS, V F TARASENKO,D A SOROKIN, Cheng ZHANGand Tao SHAO

1 Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow 125412, Russia

2 Institute of High Current Electronics, Siberian Branch, Russian Academy of Sciences, Tomsk 634055,Russia

3 Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

4 University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China

Abstract In this paper, we discuss the properties of ionization waves (IWs) in a multi-pulsed plasma jet while using the two-dimensional computational approach.The IWs are generated by application of three short negative pulses with a repetition frequency 12.5 MHz.The simulations are performed continuously during a single run while accounting for charges accumulated inside(surface charges)and outside(space charges)the tube.The plasma forming gas mixture(He/O2=99.8%/0.2%)is injected through the discharge tube into the surrounding humid air.We show that an IW can emerge from the tube exit at a pulse rising edge(as a negative IW)and at a falling edge of the same pulse(as a positive IW).It is demonstrated that remnants of the negative and positive charges play an essential role in the discharge evolution.The first pulse travels the shortest distance as it propagates through the initially non-ionized environment.The IWs developing during the second pulse essentially enlarge the plasma plume length.At the same time,the IWs generated by the third pulse eventually decay due to the remnants of charges accumulated during the previous pulses.Accumulated memory charges can lead to the IW extinction.

Keywords: helium plasma jet, multiple pulses, positive and negative ionization waves

1.Introduction

Low-temperature plasma jets have numerous beneficial applications.The application areas include material science and polymer functionalization[1,2],surface modification[3],biotechnology and water treatment[4]as well as the new area of plasma medicine [5-7].The plasma jet setup is relatively simple.The conventional design includes a tube(usually of a dielectric material) and different configurations of powered,grounded and/or floating electrodes.Helium and argon are often used as the plasma forming gases [8-10].Different excitation sources were analyzed by Lu et al in [11].

The plasma jets are reliable sources of reactive species.These species are produced in the discharge region (and sometimes beyond it) and transported by the flowing gas to the treated target [12-17].There are two major types of atmospheric pressure plasma jets showing quite different physical phenomena [11].Applied voltage can have a sinusoidal (including a radio frequency range) [18, 19] or pulseshaped form.The frequencies used are usually in the kHz to GHz range.The jet plasma is perceived by the naked eye as a continuous luminous plume.However,the plume(typically at high frequencies) is often composed of ionization waves(IWs).The IWs have the same mechanism of propagation as conventional streamers albeit their propagation is guided by a gas flow channel.These IWs are often referred to as guided streamers or plasma bullets [20-28].For example, Parsey et al [29] compared the behaviors of the non-guided and guided plasma jets.The research on plasma jets is summarized in the recent comprehensive review by Viegas et al[30].In this review, both plasma jet experiments and modelling efforts are addressed.

The pulsing regime of plasma jets while using various pulsing schemes is a very promising technology.By changing the pulse duration, pulse voltage, pulse repetition frequency(PRF) and duty cycle, one can control the plasma jet dynamics[31-34].For example,Xian et al[35]demonstrated the increase of a plasma plume length with the increase of a pulse width.The most important(and still unsolved)problem for the pulsed plasma is the discharge repeatability.For the pulsed jets with relatively high repetition frequencies, the charges or long-lived metastables left from the previous pulses can drastically modify the plasma dynamics.For example, in the kiloHertz range of applied frequencies, estimates of charged species density left between the pulses give the values in the range of 106-1011cm-3[36].The plasma decay due to electron-ion recombination and attachment is usually longer than the time of the IW propagation along the jet.

The reproducibility and the repeatability of the IWs depend on the residual charges (electrons) that are left from the previous pulse.Another source of residual charges could be due to the electron detachment from the-O2ions [36, 37].For relatively high frequencies,the remnants of charges could be accumulated from pulse to pulse and thus affect the propagation of plasma bullets.Chang et al[25]studied the effect of seed electrons on the repeatability of plasma plume propagation.The authors used the numerical approach by applying a global plasma chemical kinetics model.They showed the temporal evolution of electrons and-O2ions in the afterglow of a plasma plume.The main outcome of this research was the determination of the minimum seed electron density required for the plasma bullets to appear in a repeatable mode.This density was as high as 108cm-3for the pressure of 20 kPa and 107cm-3for 4 kPa and did not depend on the oxygen concentrations in the helium-oxygen mixture.

Wu and Lu [38] explored the repeatability of an atmospheric pressure plasma plume.They applied multiple voltage pulses and studied the behavior of a helium plasma jet after each pulse (the first, the second, and so on).The conclusion was made that the residual electrons greatly affect the discharge reproducibility.Wang et al [39] and Shao et al [40]studied the plasma jets driven by different pulse polarities.They showed that the polarity has a strong effect on the jet properties.

Temporal behavior of reactive species also depends on PRF.Ries et al [41] detected the OH fluorescence and temporal evolution of OH density between two voltage pulses(at a frequency of 2 kHz).The experimentalists showed the decrease of the OH density over the pulse period.Norberg et al[42,43]demonstrated that reactive oxygen and nitrogen species production depends on the PRF and flow rate.

Figure 1.Evolution of a plasma bullet in a helium jet(a)on a rising edge of a positive pulse and (b) at a falling edge.Experimental parameters: rising time 100 ns, falling time 100 ns, pulsed width 1 μs, applied voltage +10 kV at a frequency of 20 kHz.Helium flow rate is 3 l min-1, exposure time is 20 ns.The experiment was performed in the Institute of Electrical Engineering, Chinese Academy of Sciences.

In the present paper,we computationally study the effect of short negative pulses of the nanosecond time duration having short rising and falling edges.We discuss the consequences of accumulation of positive and negative space and surface charges on the IWs propagation and compare the morphology of positive and negative IWs.We show that the residual charges influence both the IW velocity and the propagation length.We observe two IWs emerging from the tube during each pulse.The first IW (negative) is generated at the rising edge of the negative pulse, the second (positive)appears at the falling edge of the same pulse due to the accumulated surface charges inside the tube.Similar observations were performed by Karakas et al[44](see also[45]).The experimentalists observed the secondary discharge appearing at the falling edge of the applied voltage pulse.

As an example, in figure 1 the primary discharge appearing at a rising edge of the pulse and a secondary discharge, ignited at the falling edge of the pulse are presented.The secondary discharge (which is negative for the indicated conditions) is due to the release of surface charges accumulated inside the tube.

Further information on plasma jets physics and, in particular, on pulsed discharges can be found in topical reviews by Viegas et al [30] and Zhao and Li [46].

A brief description of the model is given in section 2.Characteristics of negative and positive IWs at a rising and falling edge of each of the three negative pulses are discussed in section 3.Evolution of space charges during the second and the third pulse is demonstrated in section 4.Concluding remarks are provided in section 5.During the discussions in sections 3 and 4, we use the terms ‘plasma bullet’ and ‘IW’interchangeably as synonyms.

Figure 2.(a) Geometry used for simulation of multiple pulses.He/O2=99.8%/0.2%mixture is injected through the tube at a flow rate 3 l min-1.(b) Profile of three negative pulses.

Figure 3.Helium density (cm-3) after the steady state is reached.The contours are plotted on a linear scale.The densities of charged species are recoded along the line AB (see figures 7-9).

2.Description of the model

The description of the 2D hydrodynamics computational model, nonPDPSIM, and algorithms used in this study, is given in [42, 47].The list of equations incorporated in the modelling platform can be found in [48].

The single electrode two-dimensional planar jet geometry(the powered electrode is inserted into a quartz tube)is shown in figure 2.The grounded plane is located 1.5 cm downstream from the jet exit.This plane functions as a pump for the helium/air flow.The voltage profile is shown in figure 2(b).We simulate three pulses, each pulse has a 5 ns rising edge and 5 ns falling edge, while the duration of the pulse plateau at the level of -17 kV is 40 ns.The inter-pulse period is 30 ns.It is important to notice that the present simulations are computationally intensive and performed continuously through all the three pulses while accounting for the charges accumulated from previous pulses.As such, we intentionally chose the short pulse duration and the short inter-pulse period.The charge dissipation is small during the inter-pulse period.This allowed us to demonstrate the main features of an IW propagation through accumulated space charges.The applied voltage and the distance to the grounded plane is chosen in such a way that none of the IWs immersed from the jet exit can reach the grounded electrode.The IWs decay before reaching the right boundary of the computational domain.

The computational domain is covered by unstructured meshes with several refinement zones.A small cloud of electrons and ionsplaced near the electrode served as a seed plasma to initiate the discharge.The probability of secondary electron emission by the ion impact on all surfaces is γ=0.2.We also included the possibility of accumulation of surface charges on the walls of the tube.

3.Negative and positive IWs at a rising and falling edge of each pulse

As simulations start, the discharge is off and only the flow field for neutral component is computed during 20 ms by integrating the Navier-Stokes equations.After the steady state for the neutral flow is reached, the discharge is ignited.Helium flow field is shown in figure 3.The mixing zones shown in figure 3 indicate that helium diffuses into the surrounding air thus producing downstream a wider channel of helium.Certain amount of O2(as well as N2) gases diffuses towards the jet axis.

In the simulation, the IW is represented by the electron impact ionization source Se(cm-3s-1).In the experiments,this source corresponds to the luminous IW front (plasma bullet).The Seis shown in figures 4-6 for the first,second and third pulses, respectively.

The bullet first emerges from the tube during the plateau region of the first pulse (22 ns) as shown in figure 4.It then decays at the falling edge of the first pulse (45-47 ns)approximately in the middle of the gap.The positive bullet appears at the end of the falling edge of the first pulse(49 ns).It travels much shorter distance, stalls in vicinity of the tube and decays during the inter-pulse period (54-57 ns).

Evolution of plasma jet bullets during the second negative pulse is shown in figure 5.For the second pulse, the negative bullet appears not at the pulse plateau but rather at the rising edge of the second pulse (83 ns).The simulations were arranged in such a way that the very first IW propagates via a pristine environment and is driven only by the photoionization emission from its own front.This is a conventional mechanism for the IW propagation.The second IW starts when there are already essential values of the electron density left from the first pulse.These remaining electrons facilitate the ignition of the next IW and accelerate the process of the IW evolution.As a result,the appearance of the second pulse occurs earlier.The discharge originates from the electrode(in this region the electric field is high when the pulse is turned on)and/or inside the tube.The resulting IW propagates along the already ionized media.

Figure 4.(a)-(j) Evolution of an IW during the first pulse.The contours are plotted on a log scale within the range indicated at the top of the figure.(k)Pulse profile.The blue circles indicate the time moments that correspond to the position of a negative bullet (left column)during the first pulse.The red circles are for positive bullets(right column).

Figure 5.(a)-(j) Evolution of an IW during the second pulse.The contours are plotted on a log scale within the range indicated at the top of the figure.(k)Pulse profile.The blue circles indicate the time moments that correspond to the position of a negative bullet (left column) during the second pulse.The red circles are for positive bullets (right column).

The plasma bullet decays by the end of the second pulse plateau(113 ns).In this case,the negative bullet travels much longer distance.For example,the negative bullet from the first pulse stops at the distance of 0.8 cm from the tube exit,while the negative bullet from the second pulse decays at the distance of 1.2 cm.The stopping position of the IW is defined as the position where no more than 107cm-3of electron density is produced in front of the IW,as shown in figures 7-9 below.The distance travelled by the negative bullet during the second pulse is the greatest for all three pulses.During the second pulse,the positive bullet emerges at the falling edge of the second pulse (128 ns) and decays during the pulse-off period (135-161 ns).The distance travelled by the positive bullet is smaller than that for the negative one.

In figure 6, the evolution of a bullet during the third negative pulse is presented.As for the second pulse,the bullet emerges at the rise edge of the third pulse(164 ns)and decays before the end of the pulse plateau (180 ns).Opposite to the previous cases, the bullet intensity is much smaller due to the IW extinction in a cloud of accumulated negative charges as shown in the frame for 180 ns.The effect of the IW extinction depends on many factors of which the pulse rise time is perhaps the main factor.Here again,the positive bullet appears at the falling edge of the third pulse (209 ns) and decays during the pulse-off period.Note that in all cases the path travelled by a positive bullet is shorter when that for negative.

Distributions of charges species (negative and positive ions) along the jet axis are shown in figure 7 for the first pulse.The time moments are chosen in such a way as to show the densities during the evolution of both negative (32 and 45 ns)and positive(49 and 57 ns)IWs.The negative IW stalls at the falling edge of the first pulse(45 ns)while reaching the location of 0.8 cm(for the electron density the reference level of 107cm-3is adopted).The positive IW travels much shorter distance.It only increases the electron densities near the jet exit as shown in figure 7(d).It should be noted that launching the first IW into the initially non-ionized gas where there are no background electrons is computationally problematic.As mentioned above, the very first IW propagates in the pristine environment driven only by its own photoionization mechanism.As such, it takes a longer time for the IW’s formation and development.Many computational works do not include photoionization procedure, but, rather, assume that the IW propagates via uniform background of electron density [36].In this case, the launching of the first bullet is easier.

Figure 6.(a)-(j) Evolution of the IW during the third pulse.The contours are plotted on a log scale within the range indicated at the top of the figure.(k)Pulse profile.The blue circles indicate the time moments that correspond to the position of a negative bullet (left column) during the third pulse.The red circles are for positive bullets (right column).

Figure 7.Axial distributions of electrons,positive ionsand negative ionsndalong line AB(shown in fgiure 3(b))during the frist pulse.(a)and(b)Negative IW.(c)and(d)Positive IW.The densities are shown for the time moments indicated in fgiure 10 for the frist pulse.

In figure 8, the evolutions of charged species during the second pulse are presented.During the second pulse, the negative IW advances towards the end of the simulation region(16.5 cm)as shown in figures 8(c)and(d).In this case,the negative IW propagates along the channel where the residual charges still exist.The recombination during the offpulse period is small due to the short inter-pulse period.As follows from the axial distribution of the species, the dominant positive ions areandThedensity is depleted by the associative charge exchange resulting in the formation ofion.

The dominant negative ions areand O-.In the IW head where the electric field is high, the reaction of dissociative attachment leads to the formation of O-ions.In rather weak fields (in the IW channel), the process of threebody attachment to formions is essential.The positive IW enhances the electron density during the second pulse, as shown in figure 8(d).However, this IW only slightly advances the length of the plasma plume.

Figure 8.Axial distributions of electrons,positive ionand negative ionsandduring the second pulse.(a) and (b)Negative IW.(c) and (d) Positive IW.The densities are shown for the time moments indicated in figure 10 for the second pulse.

Figure 9.Axial distributions of electrons,positive ioand negative ionsandduring the third pulse.(a) and (b)Negative IW.(c) and (d) Positive IW.The densities are shown for the time moments indicated in figure 10 for the third pulse.

Figure 10.Three pulses marked by the time moments that correspond to those indicated in frames of figures 7-9.Blue circles are for negative IWs, red circles for positive.

The evolutions of charged species during the third pulse are presented in figure 9.During the third pulse,both negative and positive IWs propagate through the previously accumulated and not yet dissipated charges (due to the short interpulse period).These IWs quickly decay after travelling a short distance from the tube exit.As such, the plasma plume elongation is only incremental during the third pulse.

Our results on the production of ions,neutral species and radicals reasonably correlate with those presented work by Murakami et al[49](see figure 3 in this paper)and also with the results of the paper by Van Gaens and Bogaerts [50](figure 4 in this paper).Note that in the latter paper results for argon are presented.

The three pulses marked by time moments that correspond to those shown in frames of figures 7-9 are presented in figure 10.Note that during the three pulses the shift of the neutral gas between the pulses is negligible.It is much shorter than the length of plasma IW propagation.As such,each new plasma bullet propagates in a gas excited by previous plasma bullets [36].

Figure 11.(a)-(e) Negative space and surface charges (cm-3) at the rising edge of the second pulse (80, 82, 84, 86 and 94 ns).(f)-(j)Positive space and surface charges (cm-3) shown at the same time moments.The contours are plotted on a log scale within the range indicated in the top frames.(k) Pulse profile.The blue circles indicate the time moments that correspond to the position of negative and positive charges in each frame.

4.Space charges resolved for the second and third pulses

More details on the IWs evolution are presented in figures 11 and 12 where the charges are shown for shorter time intervals.In figure 11, negative and positive space and surface charges are shown for the rising edge of the second pulse.During the second pulse rise time (80-86 ns), there is no visible dissipation of the negative charge remnants from the previous pulse.These remnants are shown as blue objects in frames for 80-86 ns.The appearance of a new negative IW is demonstrated in figure 11 by the two bright parallel strips at 82, 84 and 86 ns.The strips correspond to negative charges removed from the top and bottom tube surface (as perceived in a 2D planar geometry).At 94 ns, a new IW injects new negative charges.They are added to the previously accumulated charges.At the same time, partial neutralization of positive charges (shown in the right column of figure 11) with negative occurs.

Figure 12.(a)-(e) Negative space and surface charges (cm-3) at the rising edge of the third pulse (160, 161, 163, 166, 171 ns).(f)-(j)Positive space and surface charges (cm-3) shown at the same time moments.The contours are plotted on a log scale within the range indicated in the top frames.(k) Pulse profile.The blue circles indicate the time moments that correspond to the position of negative and positive charges in each frame.

Figure 13.Comparison of the plasma bullet shape for (a) negative and (b) positive phases of the second pulse.

The IW evolution for the rising edge of the third pulse is presented in figure 12.More intense memory charges appear during the rise time of the third pulse.Here again the negative charges from the previous(second)pulse do not yet dissipate.At the same time, the new IW appears at the tube exit (perceived as two red strips in the left column of figure 12).The memory charges from the previous pulse prevent the IW from further propagation (see figure 6(e) for 180 ns).

In experiments, the re-ignition of the bullets at the end of the voltage pulse was observed and explained by Hubner et al[51].Similar results were also obtained in references [52, 53].The experimentalists suggested that this effect might be related to the discharging of the dielectric tube after the pulse is on/off.

Wu and Lu[38]explored(in a pulsing regime)the effect of residual charges on repeatability of the plasma plume.The experimentalists observed the longest plasma plume during the first pulse.The plasma plume decreased in length during the second pulse.Starting from the third pulse the plume length was same for all the following pulses.In our simulations, on the contrary, the length of the first pulse was the shortest.This contradiction can be explained that we did not have any initial seed electrons in front of the bullet.As such,the bullet travelled in the pristine environment driven by the photoionizing emission from its own head.In experiments,a priory,there are some seed electrons, at the level of 104cm-3[54].In our simulations, the second and third bullets propagated along the path pre-ionized by the previous IW and, despite the accumulated charges, the plume length gradually increased.

It should be noted that in figures 11 and 12 the space as well as surface charges is presented (both have dimensions cm-3).The left column shows only the negative charges ρ ＜ 0, while the positive charges ρ ＞ 0 are plotted in the right column.Each sort of ions, contributed to the charges, has its own recombination and attachment/detachment rates as well as its own drift velocity.It is seen that the layers of positive and negative charges can exist near the surface.These charges (positive or negative)are pushed outside the tube at each rising or falling edge of a pulse.At the same time, there is a tendency of a discharge appearing near the electrode as shown, for example, in figures 11(b)-(d).We believe that the manner the discharge appears (from the walls or near the electrode) depends on the conditions.For cases shown in figures 11 and 12,the discharge appears mostly from the tube walls and the new IW is a consequence and continuation of the above mentioned strips.

While leaving the tube with its small density of oxygen(the injected mixture is He/O2=99.8%/0.2%) the bullet encounters much larger amount of oxygen.The created halo of electron density at the edges of the tube (and, as a result,the accumulation of space charges as seen in figures 11 and 12 for negative charges) is a consequence of the photoionization.In experiments [55], these halos have also been observed in optical emission in arrays of micro-jets.

Finally,the shape of negative and positive IWs appearing during the same (second) pulse at its rising and falling edges is shown in figure 13.The shape of the negative bullet has an elongated form while the positive IW is more of the spherical form.Similar bullet shapes were observed in experiments and simulations [56-59].

5.Conclusion

In this paper, we discuss the properties of IWs generated by application of three negative pulses of nanosecond duration(repetition frequency 12.5 MHz)to the powered electrode.The two-dimensional simulations were performed continuously during a single run with account for the space and surface charges accumulated within the tube.The plasma-forming mixture of He/O2was injected through the discharge tube into the air.

We show that the IW can emerge from the tube exit at a pulse rising edge(as a negative IW)and at the falling edge of the same pulse (as a positive IW).The remnants of negative and positive charges play an essential role in the discharge evolution.The first pulse travels the shortest distance as it propagates through the initially non-ionized environment.The IWs developing during the second pulse essentially enlarge the plasma plume length.At the same time,the IWs generated by the third pulse decay due to the accumulated charges from the previous pulses.Accumulated memory charges lead to the IW extinction.This is the case for rather short inter-pulse periods considered in this work.The results presented in this paper are applicable for jets with lower repetition frequencies,such as jets operating in a kHz range.As indicated in [36],even for the frequency of tens of kHz, each new IW propagates in a gas excited by previous IWs.In this frequency range, the electron density decrease between the pulses is noticeable.The electron-ion recombination process is very slow.For example, with the typical value of recombination coefficient βei= 5 × 10-8cm3s-1and typical electron density ne=1012cm-3, the characteristic time for the electron-ion recombination is of the order of 20 μs.Note that the recombination coefficient depends on the sort of ions and the electric field.In the electronegative gas such as air, O2molecules have a very strong attachment.For air, two types of attachments including three and two-body attachments should be taken into account.In a weak or zero fields(as is the case for the inter-pulse period) the three body attachment rate is rather high νatt3=(2-5) × 107s-1[60,61].Reactions of dissociative attachment (two-body attachment) are essential only for rather high values of electric field(E ＞ 10-15 kV cm-1).As such,in the inter-pulse period most of the electrons attach to O2molecules forming negative ionsThe electron level decreases very rapidly, with the typical time of 50 ns determined mainly by three-body attachment of electrons to O2molecules.The characteristic time of the decrease of positive and negative ions is determined by the ion-ion recombination which depends on the type of ions and their temperature and is a much slower process [62].During propagation of the every next IW,a considerable number of electrons are detached fromin the region of the strong electric field in the IW front.The detachment coefficient(which corresponds to an abundance ofions) is of the order of Kdetach=2 × 10-10cm-3s-1for ions with the effective temperature of 0.5 eV [62].The rapid electron detachment fromcreates space charges which can advance or, on the contrary, interfere the IW propagation.As such, the results presented in this paper can be applicable for jets in a kHz frequency range.

In our research we did not intend to show when and from which pulse the discharge becomes repeatable.Probably,working with this high frequency, the problem will always persist due to a very short time between the pulses, when a large amount of charges accumulate.This would lead to the extinction of the discharge or at least to its unstable jet operation.

Acknowledgments

This work was inspired and initiated by Prof Mark Kushner(University of Michigan), to whom the authors express their sincere appreciation.The research was supported by the Ministry of Science and Higher Education of the Russian Federation (No.075-15-2021-1026 of November 15, 2021),and jointly by the National Key Research and Development Plan of China (No.2021YFE0114700).

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