Computational study of simultaneous positive and negative streamer propagation in a twin surface dielectric barrier discharge via 2D PIC simulations
Q. Zhang, R.T. Nguyen-Smith, F. Beckfeld, Y. Liu, T. Mussenbrock, P. Awakowicz, J. Schulze
CComputational study of simultaneous positive andnegative streamer propagation in a twin surfacedielectric barrier discharge via 2D PIC simulations
Quan-Zhi Zhang , ∗ , R T Nguyen-Smith , ∗ , F Beckfeld , YueLiu , T Mussenbrock , P Awakowicz and J Schulze , School of Physics, Dalian University of Technology, Dailan 16024, P.R. China Chair of Electrical Engineering and Plasma Technology, Faculty of ElectricalEngineering and Information Sciences, Ruhr University Bochum, Germany Chair of Plasma Technology, Faculty of Electrical Engineering andInformation Sciences, Ruhr University Bochum, Germany ∗ Authors contributed equally to this work
E-mail: [email protected], [email protected]
Abstract.
The propagation mechanisms of plasma streamers have been observed andinvestigated in a surface dielectric barrier discharge (SDBD) using 2D particle incell simulations. The investigations are carried out under a simulated air mixture,80% N and 20% O , at atmospheric pressure, 100 kPa, under both DC conditionsand a pulsed DC waveform that represent AC conditions. The simulated geometryis a simplification of the symmetric and fully exposed SDBD resulting in thesimultaneous ignition of both positive and negative streamers on either sideof the Al O dielectric barrier. In order to determine the interactivity of thetwo streamers, the propagation behavior for the positive and negative streamersare investigated both independently and simultaneously under identical constantvoltage conditions. An additional focus is implored under a fast sub nanosecondrise time square voltage pulse alternating between positive and negative voltageconditions, thus providing insight into the dynamics of the streamers underalternating polarity switches. It is shown that the simultaneous ignition of bothstreamers, as well as using the pulsed DC conditions, provides both an enhanceddischarge and an increased surface coverage. It is also shown that additionalstreamer branching may occur in a cross section that is difficult to experimentallyobserve. The enhanced discharge and surface coverage may be beneficial to manyapplications such as, but are not limited to: air purification, volatile organiccompound removal, and plasma enhanced catalysis. Keywords: PIC/MCC simulation, atmospheric pressure plasma, SDBD, positivestreamer, negative streamer, floating surface discharge, ns voltage pulse
Submitted to:
Plasma Sources Sci. Technol. a r X i v : . [ phy s i c s . p l a s m - ph ] F e b omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations
1. Introduction
Dielectric barrier discharges (DBDs) are plasmadischarges incorporating at least one layer of dielectricmaterial separating the two electrodes. The dielectricbarrier limits the charge transfer and thus the currentflow typically producing a non thermal plasma atatmospheric conditions. This non thermal natureallows for the efficient generation of reactive speciesthereby providing multiple possibilities in biomedical,surface, and industrial applications [1, 2]. DBDsare classifiable into two main categorical descriptors:volumetric and surface DBDs. Volume dielectricbarrier discharges (VDBDs) are classifiable fromDBDs by having a gas gap and a dielectric barrierpresent between the two electrodes, producing eitherhomogeneous or filamantary like plasmas depending onthe conditions [3]. Surface dielectric barrier discharges(SDBDs) on the other hand, have only the dielectriclayer directly separating the two electrodes; a plasmais thereby only able to ignite along the surface ofthe dielectric. Due to the possibility of having athin structure, SDBDs may have particularly low flowresistance and are therefore commonly researched forgas treatment or flow control purposes [1, 2, 4–6].SDBDs have the capability of being built in manyunique geometrical configurations ranging in symmetryproviding either a single axis or multiple axes forplasma propagation. They may also allow for eithera single phase, anodic or cathodic plasma, or a dualphase ignition process.Throughout the 1990s SDBDs have been wellinvestigated as potential actuators for gas flow control[1, 2, 4, 6]. For such purposes an asymmetricgeometry, where one electrode is offset from theopposite electrode and possibly completely submergedby the dielectric, is typically used [6–22]. Much efforthas been put into controlling the plasma behaviors,such as densities and surface charge deposition, andtheir corresponding aerodynamic effects from saidSDBD configurations [6, 8, 21–23]. It has also beenshown that AC and pulsed waveforms can significantlymodulate the plasma profiles (at positive and negativevoltage phases) [7–10, 14–18, 20].In recent years, SDBDs have undergone exten-sive investigation for gas purification for industrialand environmental protection applications [1, 2, 5].Absolutely calibrated two wavelength emission spec-troscopy has been used in order to characterize a sym- metric SDBD under tailored voltage waveforms [24–26]. The waveform under experimental investigationis a damped sine wave with multiple µ s period, ad-justable peak to peak voltage, and pulsed in the kHzregime. Additional emission spectroscopy, absorptionspectroscopy, and Fourier transform infrared (FTIR)spectroscopy methods have also been used to mea-sure various species densities and chemical modifica-tions of cystine. Furthermore, flame ionization detec-tors, gas chromatography-mass spectroscopy, and ionenergy analyzer quadrupole mass spectroscopy are allbeing used to investigate and characterize the conver-sion of volatile organic compounds into non-harmfuland non-toxic compounds [27]. Furthermore, the inclu-sion of pre gas heating and catalyst coatings are beinginvestigated for higher conversion efficiencies [27, 28].In many applications, like chemical processingand gas purification, the interaction between a plasmaand a catalyst yields synergistic effects resulting inenhanced performances [2, 29]. As such, variousstructures of catalytic material are often inserted intotraditional DBD reactors including, but not limited to:spheres, honeycombs, 3D fibre deposition structuresand coatings of the dielectric barrier itself [29, 30].The synergistic effect is obtained via two primarymethods. Firstly, the altered geometry along withtailored voltage waveforms influence the dischargecharacteristics [1, 2, 30–32]. Secondly, the plasmadistribution determines the effective contact area ofthe catalyst thereby altering the morphology and workfunction of the catalyst [33, 34]. This leads to a greatimportance on generating a controllable plasma densityand spatial distribution [1, 2, 30, 31, 35].The above studies, although very interesting, weremostly based on experiments of submerged SDBDswhere the plasma discharge is confined to one side ofthe dielectric plate providing investigations only intoa single phase ignition process [4, 6–15, 23, 35]. Thatis to say that only either an anodic or cathodic phaseplasma is present, but never both simultaneously. Thissingle phase nature limits the effective volume andsurface area of the plasma which defines the effectivecatalytic surface area exposed to the plasma speciesin plasma enhanced catalysis. As such, the catalystperformance is potentially limited to a great extentin a single phase SDBD. In gas treatment conditions,an SDBD electrode system is very likely to be placedalong the central plane parallel to gas flow in orderto minimize flow resistance and increase the treatment omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations (a) AnodeCathode + + - E→ Propagation - - - - - - - -
Dielectric(b) AnodeCathode + ++ + +++--- -+++++++++++++++++++++ ++++++- - ++++++
E→ PropagationDielectric +++
Figure 1: Schematic detailing the negative streamerformed via an anode oriented electron avalanche.volume. Under these conditions, it is very clear thatutilizing an SDBD electrode system which ignites onboth sides of the dielectric plate will improve thetreatment volume, and as such efficiency of the process.Unfortunately, most theoretical investigations uti-lizing circuit models [36–38], global models, moleculardynamic models [33], fluid models [12, 17, 20], andeven particle-in-cell/Monte Carlo collision (PIC/MCC)models [30, 32, 34] of (S)DBDs and packed bed reac-tors provide limited insights into the underlying mech-anisms of the plasma propagation [39–41]. No contri-butions on the theoretical investigation of a dual phasesymmetric SDBD could be found by the authors, point-ing to a significant lacking of knowledge of such config-urations is present. The inherent mechanisms behindthe evolution of the plasma discharge in asymmetricand even more so symmetric SDBDs is still not fullyunderstood. It is not yet clear how a simultaneouspositive and negative surface streamer (above and be-low the dielectric) can interact with each other, and towhat extent, if any, do they enhance one another. It isnot clear how the streamers respond to tailored voltagewaveforms, nor what the optimized conditions are forgenerating large treatment volumes. It is unknown towhat extent the surface streamers interact with an ac-tive surface such as a catalyst. These are crucial piecesof information to ensure good plasma enhanced cataly-sis performance. Additionally, many experiments, suchas optical emission spectroscopy, still have open ques-tions as to whether the results are more representativeof the streamer bulk or the highly dynamic streamerhead. These concerns demand a more detailed sim-ulation for the dynamic behavior of the positive andnegative streamers in a dual phase symmetric SDBDduring the ignition process.Therefore, in the present work we computationallyinvestigate the plasma propagation of a symmetric,dual phase SDBD, hereby referred to as the twinSDBD, under various voltage waveform conditions.
AnodeCathode -- ++ + ++ + ++ + ++ + Dielectric(a) ++ + ++ + -- E→ Propagation ++ AnodeCathode +- --- ++ + ++ + ++ + ++ + ++ + ++ + ++ + ++ + ++ + ++ + ++ + ++ + ++ + ++ + ++ ++ + ++ + Dielectric(b) ++ + ++ + -- ++ + ++ + E→ Propagation - ---- -
Figure 2: Schematic detailing the positive streamer,which forms via a cathode oriented propagation front.The particular geometry of the twin SDBD ensuresthat both an anodic and cathodic phase plasma aresimultaneously ignited, separated by the dielectricbarrier, and are physically symmetric about themetallic electrodes. The symmetric geometry does notonly give rise to a higher plasma surface coverage,but also enables a direct comparison between thepositive streamers on the anode side versus thenegative streamers on the cathode side as well asthe interaction between the two. The numericalinvestigations are carried out by means of a 2DPIC/MCC simulation software known as VSim, amulti-physics simulation tool, which combines theFinite-Difference Time-Domain (FDTD), PIC, andCharged Fluid (Finite Volume) methods for simulatingelectrical gas discharges. [42]. The insights provided bythis work are not only applicable to the twin SDBD andsimilar geometries, but also to other SDBD geometries,asymmetric ones included via a deeper understandingof the streamer propagation and form.To provide a basis of understanding the streamerdynamics in a twin SDBD, that will be revealedin this work, we briefly recall the fundamentals ofpositive and negative streamer dynamics in a DBD.A negative streamer, see fig. 1, ignites through ananode oriented electron avalanche: electrons, which areaccelerated against the direction of the electric field,collide with the background gas. Ionization takes placecausing an exponential growth of electrons and ions,creating a quasineutral bulk plasma that propagatesfrom the cathode to the anode. A positive streamer,see fig. 2, is also created via electron collisions, butis somewhat more complex. The cathode orientedpositively charged streamer head attracts the electronswhich cause ionization in front of the streamer head,resulting in an ionization wave. This ionizationwave propagates from the anode to the cathode,leaving behind a quasineutral bulk plasma. Branchesmay form from the streamer head creating additionalionization waves; branching is more readily observed in omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations O dielectric barrier(light grey material). Due to the strong curvatureof the electric field lines when under operation, theplasma (purple structure) ignites along the edges ofthe metallic lattice.gas mixtures that are susceptible to self induced photoionization. Under short timescales, a few nanosecondsand less, a feature very similar to a low pressure sheathforms. The positive streamer head floats above thecathode due to an absence of available electrons, thuscreating a region with a very strong electric field.Given an appropriate amount of time, the positive ionsdo reach the cathode due to their own velocities. Atthe dielectric(s), any charges that reach the surfaceadhere to it and charge it. These surface charges repelincoming like charges along the surface, causing bothpositive and negative streamers to spread out. Due tothe lightweight electrons, this effect is more prominentin negative streamers; however, the floating nature ofpositive streamers can also facilitate a similar effect.For a deeper understanding we refer the reader toNijdam et. al. and to Zhang et.al. [43, 44] wherethe dynamics of positive and negative streamers of aVDBD via PIC/MCC simulations are detailed.This paper is structured as follows: First insection 2 the computational model and geometry aredescribed. Following this, in section 3 the results ofthe various simulations are presented: the DC resultsin sub-sections 3.1 and 3.2, and the AC results in sub-section 3.3. Finally, in section 4 our closing remarksand conclusions are discussed.
2. Computational model
The geometry to be simulated is chosen toresemble that of the twin SDBD electrode intendedfor use in gas treatment applications and was firstexperimentally presented in [24] and subsequently in[25–27, 45]. The authors defer the readers to these Figure 4: SEM image of electrode cross section. Thebulk, homologous material is the Al O dielectric. Thehump like structure with larger grains is the metallicelectrode trace.references for a detailed description of the twin SDBDsystem under question. It is important to reiterate thatthis device consists of a dielectric plate, with metallicgrids placed on the surface of the dielectric on bothsides. A computer rendered sketch of the system canbe seen in fig. 3. These grids serve as electrodes. Thesystem is built with both a geometric and electricalsymmetry, such that both a positive and negativestreamer are simultaneously ignited on either side ofthe dielectric under any given sufficiently high voltageconditions, which thereby warrants the name ”twinSDBD”. The metallic traces of the electrode systemhave been imaged with a scanning electron microscopefor a more accurate depiction of the electrodes withinthe simulations. An example image of the crosssectional view of the metallic traces can be seen infig. 4, which shows the curved nature of the metallictraces located on the dielectric, which is included inthe simulation. A 2D PIC/MCC model is used to study theplasma propagation of the twin SDBD based onthe VSim simulation software [42]. VSim isbeing widely used and has been validated [32,34, 42]. As these investigations taken placeunder similar conditions presented here (atmosphericpressure DBDs, nanosecond timescales and micrometerlength scales), we operate under the assumption thatour model is also valid. Additionally, the usage ofPIC/MCC simulations to investigate the COST-Jetat atmospheric pressure yield realistic results thatagree well with experiments, [46–48], proving thatPIC/MCC models can indeed be used at atmosphericconditions. The PIC/MCC simulations performed omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations and 20 % O , at300 K. Free electrons, N +2 , O +2 and O − ions are tracedthroughout the simulation, which are represented assuper-particles, i.e. one super-particle corresponds toa certain number of real particles defined by theirnumerical weighting, initially starting at 20 · realparticles per super particle [49].In order to numerically initiate the plasmadischarge, a uniform distribution of seed electrons isplaced within the free space of the simulated geometry.These seed electron super-particles have a densitycorresponding to 1 · m − . Realistically, seedelectrons are present due to cosmic radiation andenvironmental photo-ionization producing backgroundelectrons, as well as remaining charges from previousplasma discharges. The initial electron densitywas chosen as such in order to increase the initialweighting of the super particles, and thereby thesimulation speed. The high initial density increases thespeed of the initial electron avalanches and streamerbreakdown. As seen later on, maximum achieveddensities are on the order of 1 · m − , which ismuch higher than the initial density; therefore, thefinal profiles and mechanisms would not change if alower initial density was chosen. Thus, the high initialdensity serves to increasing the simulation speed whilenot altering the results of the simulations. It shouldbe noted that the usage of uniform seed electrons does not consider local effects of previous discharges.As the plasma streamers evolve, the particlenumber of each considered species will rapidly increasedue to the ionization avalanches. To account for thisand to reduce the computation time, the weight ofeach super-particle is adaptive. A merger algorithmconserving both momentum and energy will combinesame species super-particles when the number of saidsuper-particles exceeds a threshold value of 10 super-particles respective to each cell of the simulationmesh. As the particle numbers only increase withinthe considered simulated time, no de-merger algorithmis implemented. This adaptive weight and mergeralgorithm is described in more detail in [34].Elastic, excitation, ionization, and attachmentcollisions of electrons with O and N gas moleculesmake up the considered reaction mechanisms asexplained in more detail by [34]. The correspondingcross sections and threshold energies are adoptedfrom the LXCat database and literature [50–54]. Atthe surface of the dielectric barrier, only electronabsorption is considered, i.e. no electron reflection orsurface electron emission is considered. Reported in[32, 34], the inclusion of secondary electron emission,SEE, surface coefficients do not significantly alterthe form of the simulated positive streamers, dueto the floating nature of the streamer head. Thenegative streamer; however, propagates along thesurface of the dielectric barrier, and as such, SEEcoefficients would be more critical. The inclusionof SEE coefficients would theoretically increase thenumber of ”background” electrons available forstreamer propagation, and as such the streamers wouldpropagate faster; however, their forms should notstrongly change. Additionally, due to the lower electricfields of the negative streamer and the very shortconsidered timescales, the effect of ion induced SEEwould be very limited within this investigation.With each successive timestamp of the model,a particle pusher, particle merger, and Monte Carlocollision algorithms for all particle species follow insuccession. After the collisions, a new electron superparticle is added to the simulation regime, the densityof each cell is calculated, and Poisson’s equation issolved in order to get the electric forces being applied toeach particle, after which the cycle repeats. A diagramof the general flow is shown in fig. 5. The geometry to be simulated is a crosssection of the twin SDBD described in [24–27,45], and shown in fig. 3. The twin SDBDsimultaneously produces positive and negative phasedplasma streamers along the edges of the metallictraces; however, the two phases are separated by omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations and20 % O ), II) Al O dielectric, III) grounded electrode, IV) powered electrode. The boxed in regions denotedwith (i) correspond to the regions that are presented in greater detail for the rest of the publication.the Al O dielectric barrier. On either side of thedielectric barrier, ignition on opposite edges of therespective metallic trace can be considered as twoindividual but same-phased streamers. Two differentsimulation geometries, referred to as geometry(a) andgeometry(b), are considered in order to appropriatelyresolve the interaction of both the same-phasedand respectively opposite-phased plasma streamers.Simulation geometry(a) and simulation geometry(b)are presented in fig. 6. In total geometry(a) contains a2D plane that is 9 . . . µ m resulting in a squarelattice of 4000 x 500 cells. The grid size was chosenbased off of the Courant limit, c · dt < dx , where c isthe speed of light and dx is the grid size. Geometry(b)utilizes the same size grid cell, but uses only 1000 x500 cells resulting in a total width of 2 . i ) in fig. 6.Firstly, to investigate the interactivity of two same-phase streamers, positive-positive or negative-negative, two anodes and two cathodes are includedin simulation geometry(a). The two same-phaseelectrodes are simulated with the same potential underDC conditions and are separated in the X-directionby 9 . . omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations Y po s . [ mm ] Figure 7: Electric field distribution of the simulated electrode geometries for an applied +8 kV and − · V/m. The normalized directionof the electric field is shown via the vector field. -8 -6 -4 -2 0 2 4 6 8Electric Potential [kV] Y po s . [ mm ] Figure 8: Electric potential distribution of the simulated electrode geometries for an applied +8 kV and − omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations .
500 mm thick andexpands the whole X-direction, and is simulated witha dielectric constant of 9. In this representation, theZ-direction would equate to the length (or width) ofthe physical electrode setup but is mathematicallytreated as constant/homogeneous. This results ina simulation regime that is most valid for a planarsection in the middle of any grid structure. Inboth geometries, the electrode structure itself isa geometrical composition of multiple tangent arcsresulting in a ”hump” like structure. This electrodestructure is used to approximate the real geometricstructure of the metallic traces which can be seenin fig. 4. It should be noted that the simulatedaspect ratios of the electrode thickness and width tothe dielectric thickness is significantly different fromreality; however, this was chosen as such in order toavoid numerical issues which would arise from usingan appropriately sized simulation grid for realisticaspect ratios. Furthermore, the reduced dielectricthickness of the simulations versus the actual electrodeconfiguration should not lead to any major differencesin the interpretations of this paper, as it is the surfaceof the dielectric that plays a much more important role.By using a reduced dielectric thickness, we are able toincrease the number of computational cells available forthe plasma propagation, without increasing the entiresimulation domain.Particle densities and electric fields are resolvedusing a cutting-cell technique in order to handlethe irregular geometry, through contributions ofneighboring cells. The authors refer the reader toreferences [55–57] for more information. Neumannboundary conditions are used in all directions toensure a smooth electric potential distribution at theboundaries of the simulation walls. The timestepsare non adaptive and fixed at 2 · − s. Similar to[58], a singular new electron super-particle is randomlyadded to the simulation domain at each timestep inorder to account for random events such as cosmicradiation, photo-ionization, etc. as described in [59–61]. These random events are beyond the scope ofthe available VSim functions. The seed electrons, both background and newly loaded electrons, are bothsufficient in the simulation region to support streamerpropagation as well as to not interfere with the plasmabulk as they are far fewer compared to the generatedplasma. The generated plasma density profile is alsomuch smaller than the simulation domain in bothconsidered geometries. In all considered simulations and both geometries,the electrode(s) above the dielectric barrier aretreated as the powered electrode(s) while the bottomelectrode(s) are held constant at 0 V. This choice isarbitrary and due to the physical symmetry of thesystem would provide only mirrored results if theopposite choice, either inverse polarity and/or choiceof powered electrode, was made. Initially, a constantpositive 8 kV potential is applied to geometry(a), thusthe two powered electrodes take the role of the anodeswhile the bottom two are the cathodes. The initialelectric field distribution can be seen in fig. 7(a)and the initial potential distribution can be seenin fig. 8(a). Within both figures, the magnitudesof the presented quantity are shown via the colorscale, and the normalized direction of the electric fieldare additionally presented for further clarity. Thenormalized direction is presented as a vector field,where the X and Y directions of the vectors are thenormalized X and Y values of the electric field at thatgrid cell. Naturally, the magnitude of the electric fieldis obtained from the square root of the sum of the Xand Y components squared: E mag = (cid:112) E X + E Y .First, in order to investigate solely the role of thepositive streamers, only the top half of the simulationarea is seeded with the initial electrons. Likewise,the bottom half is subsequently seeded in a secondsimulation in order to solely investigate the negativestreamers. Third, both halves are identically seededthereby investigating the interplay and differencesof both discharges igniting simultaneously under theDC voltage conditions. These three conditions areapplied to geometry(a) only. Lastly, a varying voltagewaveform is investigated.Geometry(b) is only investigated under the ACconditions shown in fig. 9. Under these conditions,the role of the anode and cathode switches twice;thereby giving insights into the extreme dynamics offast voltage streamer switching. Initially, the appliedvoltage potential sharply rises within 0 . . . − omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations A pp li e d V o lt a g e [ k V ] c d e ffedcba ba Figure 9: Applied voltage waveform of the ACsimulations. Dashed lines labeled a through f at 0.8,0.9, 1.0, 1.7, 1.8, and 2.0 ns respectively representthe timestamps at which results are presented insection 3.2.Again, this minimum value is held constant for 0 .
3. Results and Discussion
Under the 8kV DC conditions with seed electronspresent only on the anodic side of geometry(a), thepropagation of an anodic phased plasma streamer, alsoknown as positive streamer is simulated and presentedin fig. 10. The initial electric field distribution is shownin fig. 7(a) and the initial electric potential distributionis shown in fig. 8(a). Under these conditions, a cathodeoriented positively charged streamer head that is ableto freely move from the metallic anode to the dielectricsurface is able to form.The streamer structure is anchored to the anodejust above where the highest electric fields are located.It would be expected that the anchoring would takeplace at the location of the highest electric field;however, under these conditions this is located atthe intersection of the electrode and the dielectricsurface. At this point, and immediately next toit, due to the strong curvature of the electric field,electrons do not have enough space to gain sufficientenergy for ionization. Multiple executions of thesimulation produce anchored positions at the samelocation; furthermore, the anchor position is also at asymmetrical position on the opposite anode, which isnot presented in fig. 10. This suggests that the anchoris positioning itself based on the strong curvatureof the anode, and not through the randomness ofthe ionization events. Indeed, when looking at thecurvature of the simulated electrode, it appears as ifthe plasma is next to the strongest curvature. Under noconditions did the simulated positive streamers extenda significant amount into the X-direction, such thatinteractions between the two positive streamers do notneed to be considered.At 0 . .
12 mm meaning a propagation speed of 0 .
62 mm/ns.By the end of the simulated time, 1 . .
31 mm resulting in an averaged speed of0 .
31 mm/ns. The actual instantaneous speed of thestreamer would be significantly slower at this times-tamp, as the average includes the faster propagationof the early streamer. It was observed via multipletest executions that these propagation speeds and dis-tances were highly dependent on the initial backgroundelectron density. With lower initial densities, the sim-ulated streamer propagates a shorter distance. Like-wise, larger background densities would result in fasterspeeds and longer propagation distances.Initially the positive streamer began to propagatealong the electric field lines at an angle offset from thesurface of the dielectric barrier. The positive streamer omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations . i.e. sheath like feature, III) potential/failed positive streamer branch.head, which is not directly visible in fig. 10, formsin front of the streamer and along the bottom sidebetween the bulk plasma and the dielectric barrier.The streamer head is annotated in fig. 10 with an arrowlabeled (I). Between the dielectric barrier and thepositively charged streamer head is located a sheathlike region, annotated via (II), where free electronsare attracted to the streamer head; however, they donot have enough space in order to promote furtherpropagation towards the dielectric. Therefore, the onlydirection possible is outwards along the X- and positiveY-directions, towards the center of the simulated area.As the streamer continues to propagate along thisdirection, the electric field gets weaker proportional to1 /r (in 2D) or 1 /r (in 3D), where r is the distancefrom the electrode. Thus the positive streamer is ableto advance in a somewhat straight line, parallel tothe initial trajectory, which is at some angle to thedielectric surface; under these presented conditions thistrajectory angle was determined to be 20 . ◦ . Thefurther the streamer propagates, the more space isavailable for propagation into the negative Y-direction,towards the dielectric surface. Therefore, in fig. 10(b), a potential branch had began to take shape, annotatedwith (III); however it is not able to fully develop.As the cathode is located underneath the positivestreamer, that is the only location of the streamer head;therefore, no branching occurs above the streamerbulk.Due to the location of the failed branch infig. 10(b)(III), it would be extremely difficult toexperimentally observe, and is noticeable within thesesimulations because of the kinetic nature of PIC/MCCmodels. Naturally, without experimental evidence, thereader might question the reality of whether branchingforms or not at these orientations. The authors believethat the simulations are indeed accurate in predictingthese features.In fig. 11 the same simulation conditions arepresented, except the initial seed electrons are on thecathode side of the dielectric barrier, thus the negativestreamer is simulated. The seed electrons are stillaccelerated in the opposite direction of the electric fieldlines shown in fig. 7(a). An electron avalanche directedtowards the anode initiates the discharge. Underthese conditions the electrons are pushed towards the omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations . i.e. sheath like feature.dielectric, where they begin to collect on and charge thesurface of the dielectric. A positively charged spatialregion forms next to the cathode, but is unable toanchor to the cathode, as it must float at some distanceaway from the cathode.Newly created background electrons are pushedaway from the cathode. Simultaneously, the electronsare attracted towards the positively charged region.Outside of the sheath region between the two, markedvia an arrow labeled (II) in fig. 11, these twodirections are opposite one another. Only a verysmall amount of electrons are sufficiently acceleratedto the positive charges with enough energy in orderto cause ionization. Therefore, minimal propagationof the negative streamer parallel to the cathodesurface takes place, as depicted via (I). Newly createdbackground and avalanche electrons that reach thedielectric surface, instead of the positively chargedspatial region, help to promote the propagation of thenegative streamer along the surface of the dielectric inthe X-direction away from the cathode and towards thecenter of the simulation area. However, no distinctlyvisible negatively charged streamer head is directly observable.At 0 . .
077 mm meaning a propagation speed of 0 .
39 mm/ns.By the end of the simulated time, 1 . .
25 mm resulting inan averaged speed of 0 .
25 mm/ns. The actualinstantaneous speed of the streamer would besignificantly slower at this timestamp, as the averageincludes the faster propagation of the early streamer.As with the positive streamer, lower and higherinitial electron densities result in a shorter and longerpropagation distance, respectively. Furthermore,under no conditions did the two simulated negativestreamers next to both cathodes extend a significantamount into the X-direction, such that interactionsbetween the two negative streamers do not need to beconsidered.
Presented in figs. 12 and 13 is the completeDC scenario, where seed electrons are present on omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations . . .
15 mm while the negativestreamer has advanced 0 .
088 mm away from the anodesand cathodes, respectively. By 1 . .
41 mmwhile the negative streamer advanced a total of0 .
27 mm. Table 1 summarizes the streamer height,length, propagation angle, and propagation speedfor the positive and negative streamers under allthree simulation conditions. The propagation angleis determined as the angle at which the positivestreamer propagates away from the dielectric surface,and is treated as 0 ◦ for the negative streamer. Thestreamer length and thickness are respectively thesize of the streamers with respect to the parallel and perpendicular axes about the streamer propagationangle.On the anodic side of the dielectric, the positivelycharged streamer head of the positive streamer is facingthe dielectric surface, which can be seen as the redcharges in fig. 13. This positively charged area acts asa virtual anode that leads to an enhanced electric fieldin both the X- and Y-directions below the dielectricsurface on the cathodic side. Additionally, the positivestreamer has a high charge density. The enhancedfield and high density promote the expansion of thenegative streamer along the surface of the dielectric inthe X-direction. The negative streamer thus chargesthe surface of the dielectric even more. These negativesurface charges along the dielectric barrier on thecathodic side act as a virtual cathode, enhancing theelectric field in both the X- and Y-directions above thedielectric. Thus, the negative streamer also facilitatesan easier expansion of the positive streamer in theX-direction. Here it is clear, that both streamerswork together in a unison that increases the effectiveplasma surface coverage and volume of both streamers.Naturally, the electric field reduces proportional to the omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations -150 -100 -50 0 50 100 150Charge Disparity [a.u.] Y po s . [ mm ] I II I IIIII III II I IIIII II
Figure 13: Spatial profiles of the charge disparity plotted on a diverging intensity scale of the dual streamersimulations with constant voltage. Sub figures (a) and (b) correspond to the timestamps of 0.2 and 1 . . − . . − . Due to the minimal extension of the plasma intothe free space above and below the dielectric surface ofthe simulations discussed in sections 3.1 and 3.2, thesimulated area was shifted horizontally to be centeredabout a single electrode pair, and reduced in width.Under this geometry, geometry(b), a bipolar AC squarevoltage profile with fast rise and short pulse times issimulated, shown in fig. 9. Seed electrons are placedboth above and below the dielectric barrier. Undersuch conditions, during the first positive pulse theplasma propagates near identically to the DC casediscussed in section 3.2 and figs. 12 and 13. However,here it is observed that two near-mirror dischargessimultaneously propagate about the horizontal centeraxis of both the anode and cathode. For reasonsof consistency, only the right half of the simulatedarea is shown, as seen in fig. 6b. If shown, minimaldifferences between the left and right discharges wouldbe seen, but may be attributed to the stochasticnature of the PIC/MCC code and the random seedelectrons implemented each time step. Additionally,the implemented rising time of the voltage waveformfrom 0 V to +8 kV at 0 . omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations µ m] Length [ µ m] Angle [ ◦ ] Speed [ µ mns ]Average Maximum Average Maximum Propagation LateralPositive 38.39 49.20 123.4 170.4 20.60 617.1 577.7Negative 63.66 133.2 77.70 158.4 – – 388.5Full (+) 40.27 54.00 149.72 206.4 14.80 748.61 723.770 . . . . i.e. summation of N +2 and O +2 ions, charge disparitydistribution, and electric field magnitude and directionare shown in figs. 14 to 17, respectively. Sub-figures (a)through (f) of each correspond to identical timestampsof interest, shown with respect to the voltage waveformin fig. 9.Between 0 . . . . − . st Polarity Shift - Positive to Negative streamer
Paying attention to the top half of the simulationregime focuses on the shift from a positive streamerto a negative streamer. As the voltage drops on thetop electrode from +8 kV to 0 V between 0 . . i.e. becomesmore quasi neutral. As the electrons are not asstrongly/no longer attracted to the metallic anode, apositive space charge builds up at the streamer anchoron the anode. These two effects respectively lead to theelectric field strength reducing between the streamerand the dielectric surface, and a very strong electricfield between the anode and the streamer anchor.At 0 . . . omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations i.e. sheath like feature., III) potential/failed/completed positive streamer branch. omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations P o s iti v e I on D e n s it y [ / m ] Figure 15: Spatial profiles of the positive ion density, i.e. the summation of N +2 and O +2 ions, plotted on alogarithmic intensity scale at six chosen time stamps of the multi streamer simulations with switching voltage.Sub figures (a) through (f) correspond to the timestamps of 0.8, 0.9, 1.0, 1.7, 1.8, and 2.0 ns, respectively. Theapplied voltages are respectively written within the electrode profiles. omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations -150-100-50050100150 C h a r g e D i s p a r it y [ a . u . ] I III I IIIII IIIIIIIIII I III IIII, IIIIII IIII, III
Figure 16: Spatial profiles of the charge disparity plotted on a diverging intensity scale at four chosen timestamps of the multi streamer simulations with switching voltage. Sub figures (a) through (f) correspond to thetimestamps of 0.8, 0.9, 1.0, 1.7, 1.8, and 2.0 ns, respectively. The applied voltages are respectively written withinthe electrode profiles. Features of importance are labeled with arrows, where the annotations are as follows: I)positively charged region leading to streamer propagation, II) surface charges which are visually hidden by themask of the dielectric barrier, III) potential/failed/completed positive streamer branch. omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations E l ec t r i c F i e l d M a gn it ud e [ V / m ] Figure 17: Spatial profiles of the absolute value of the electric field plotted on a linear intensity scale as wellas directional arrows at four chosen time stamps of the multi streamer simulations with switching voltage. Subfigures (a) through (f) correspond to the timestamps of 0.8, 0.9, 1.0, 1.7, 1.8, and 2.0 ns, respectively. The appliedvoltages are respectively written within the electrode profiles. Cut off value for minimum intensity scale (white)chosen as 1e6 V/m. The direction of the electric field is shown via the normalized vector field as discussed insection 2.3 omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations . . . . st Polarity Shift - Negative to Positive Streamer
Focusing now on the bottom half of the simulationregime tracks the shift of the negative streamer to apositive streamer between 0 . . − . omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations . nd Polarity Shift
Between 1 . . − . . . V at 1 . . . . . . During both polarity shifts, similar and importantevents take place on the respective positive andnegative streamers. The Negative streamer is initiallyattached to the anodic dielectric surface, and floatingaway from the metallic cathode. As the polaritychanges, the electrons reverse in direction, attachingto the metallic anode and forming a positively chargedstreamer head near the dielectric surface. Newlycreated electrons are quickly attracted to the streamerhead and as such allow for the now positive streamerto further propagate into the X- and Y-directions,thereby increasing the volume and overall density ofthe streamer. The positive streamer is initially floatingaway from the cathodic dielectric surface, and attachedto the metallic anode. As the polarity changes,electron avalanches are instigated and rush towardsthe dielectric surface, thereby drastically increasingthe plasma density, volume, propagation length, andsurface coverage. Additionally, as a positively chargedstreamer head and sheath like region form near themetallic cathode, newly created electrons are able toinstigate an additional positive streamer branch thatfloats above the metallic cathode. This branchingfeature also drastically increased the electron densityand volume. Given a high enough initial voltage, it isexpected that this positive streamer branch could formon the negative streamer before any polarity switchingoccurs.The increase in plasma densities, volume, andsurface coverage are expected to be directly beneficialto various applications such as plasma enhancedcatalysis and gas treatment. In plasma enhancedcatalysis, the dielectric surface will typically be coatedwith a catalyst, such that any increase in surfacecoverage directly increases the active area of thecatalyst. Additionally, any increase in plasma volumeand density will naturally increase the radical densitieswhich are available to react with either the catalyticsurface and or the treatment gas that the plasma isignited in, thus directly affecting the efficiency of theprocess.
4. Conclusions and Outlook
In this work, the plasma streamer propagationof a twin SDBD setup by means of PIC/MCCcode modeled in dry air under DC and AC voltageoperation. The AC driving voltage waveformcorresponded to a nanosecond square waveform withsub-nanosecond risetimes. The twin SDBD geometrybeing fully exposed and symmetric about the dielectriclayer promotes both positive and negative streamerdischarges to ignite simultaneously, along the edges omputational study of positive and negative streamers in twin SDBD via 2D PIC simulations
5. Acknowledgements
This work is supported by the German ResearchFoundation (DFG) with the Collaborative ResearchCentre CRC1316 projects A4 and A5 and theScientific Research Foundation from Dalian Universityof Technology, DUT19RC(3)045, and the NationalScience Foundation of China Grant No. 12020101005.
EFERENCES ORCID iDs
Q. Z. Zhang: https://orcid.org/0000-0002-5726-0829
R. T. Nguyen-Smith: https://orcid.org/0000-0002-5755-4595
F. Beckfeld: https://orcid.org/0000-0001-8605-2634
Y. Liu: https://orcid.org/0000-0002-2680-1338
T. Mussenbrock: http://orcid.org/0000-0001-6445-4990
J. Schulze: https://orcid.org/0000-0001-7929-5734
References [1] Ronny Brandenburg. “Dielectric barrier dis-charges: progress on plasma sources and on theunderstanding of regimes and single filaments”.In:
Plasma Sources Science and Technology url : http : / / stacks . iop .org/0963-0252/26/i=5/a=053001 .[2] Hyun-Ha Kim. “Nonthermal Plasma Processingfor Air-Pollution Control: A Historical Review,Current Issues, and Future Prospects”. In: Plasma Processes and Polymers doi :
10 . 1002 / ppap . 200400028 .eprint: https : / / onlinelibrary . wiley . com /doi / pdf / 10 . 1002 / ppap . 200400028 . url : https://onlinelibrary.wiley.com/doi/abs/10.1002/ppap.200400028 .[3] U Kogelschatz. “Collective phenomena in volumeand surface barrier discharges”. In: Journalof Physics: Conference Series
257 (2010),p. 012015. doi :
10 . 1088 / 1742 - 6596 / 257 / 1 /012015 . url : https : / / doi . org / 10 . 1088 %2F1742-6596%2F257%2F1%2F012015 .[4] Eric Moreau. “Airflow control by non-thermalplasma actuators”. In: Journal of Physics D:Applied Physics doi : . url : https://doi.org/10.1088%2F0022-3727%2F40%2F3%2Fs01 .[5] S. M¨uller and R.-J. Zahn. “Air Pollution Controlby Non-Thermal Plasma”. In: Contributions toPlasma Physics doi :
10 . 1002 / ctpp . 200710067 . eprint: https :/ / onlinelibrary . wiley . com / doi / pdf /10 . 1002 / ctpp . 200710067 . url : https : / /onlinelibrary.wiley.com/doi/abs/10.1002/ctpp.200710067 . [6] Thomas C. Corke, C. Lon Enloe, and Stephen P.Wilkinson. “Dielectric Barrier Discharge PlasmaActuators for Flow Control”. In: Annual Reviewof Fluid Mechanics doi : .eprint: https://doi.org/10.1146/annurev-fluid - 121108 - 145550 . url : https : / / doi .org/10.1146/annurev-fluid-121108-145550 .[7] Yu Akishev et al. “Spatial–temporal develop-ment of a plasma sheet in a surface dielectricbarrier discharge powered by a step voltage ofmoderate duration”. In: Plasma Sources Scienceand Technology doi : . url : https ://doi.org/10.1088%2F0963-0252%2F22%2F1%2F015004 .[8] P Audier et al. “Experimental investigation ofa surface DBD plasma actuator at atmosphericpressure in different N2/O2gas mixtures”. In: Plasma Sources Science and Technology doi :
10 . 1088 / 0963 - 0252 /23 / 6 / 065045 . url : https : / / doi . org / 10 .1088%2F0963-0252%2F23%2F6%2F065045 .[9] I Biganzoli, R Barni, and C Riccardi. “Temporalevolution of a surface dielectric barrier dischargefor different groups of plasma microdischarges”.In: Journal of Physics D: Applied Physics doi :
10 . 1088 / 0022 - 3727 /46 / 2 / 025201 . url : https : / / doi . org / 10 .1088%2F0022-3727%2F46%2F2%2F025201 .[10] Antoine Debien, Nicolas Benard, and EricMoreau. “Streamer inhibition for improving forceand electric wind produced by DBD actuators”.In: Journal of Physics D: Applied Physics doi : . url : https://doi.org/10.1088%2F0022-3727%2F45%2F21%2F215201 .[11] Guoqiang GAO et al. “Parametric study onthe characteristics of a SDBD actuator witha serrated electrode”. In: Plasma Science andTechnology doi :
10 .1088/2058- 6272/aa5b39 . url : https://doi.org/10.1088%2F2058-6272%2Faa5b39 .[12] Bangfa Peng et al. “Experimental and numericalstudies of primary and secondary streamers ina pulsed surface dielectric barrier discharge”.In: Journal of Physics D: Applied Physics doi :
10 . 1088 / 1361 - 6463 /ab16b7 . url : https : / / doi . org / 10 . 1088 %2F1361-6463%2Fab16b7 .[13] Xiaohua Qi et al. “Experimental Study onSurface Dielectric Barrier Discharge PlasmaActuator with Different Encapsulated ElectrodeWidths for Airflow Control at Atmospheric EFERENCES
Plasma Science and Technology doi :
10 . 1088 /1009 - 0630 / 18 / 10 / 07 . url : https : / / doi .org/10.1088%2F1009-0630%2F18%2F10%2F07 .[14] V R Soloviev et al. “Evolution of nanosecondsurface dielectric barrier discharge for negativepolarity of a voltage pulse”. In: Plasma SourcesScience and Technology doi : . url : https : / / doi . org / 10 . 1088 % 2F0963 - 0252 %2F26%2F1%2F014001 .[15] A Yu Starikovskii et al. “SDBD plasma actuatorwith nanosecond pulse-periodic discharge”. In: Plasma Sources Science and Technology doi :
10 . 1088 / 0963 - 0252 /18 / 3 / 034015 . url : https : / / doi . org / 10 .1088%2F0963-0252%2F18%2F3%2F034015 .[16] T Unfer and J-P Boeuf. “Modeling and compar-ison of sinusoidal and nanosecond pulsed sur-face dielectric barrier discharges for flow con-trol”. In: Plasma Physics and Controlled Fusion doi :
10 . 1088 / 0741 -3335/52/12/124019 . url : https://doi.org/10.1088%2F0741-3335%2F52%2F12%2F124019 .[17] Xueke Che et al. “Numerical simulation ona nanosecond-pulse surface dielectric barrierdischarge actuator in near space”. In: Journalof Physics D: Applied Physics doi :
10 . 1088 / 0022 - 3727 / 45 / 14 /145201 . url : https : / / doi . org / 10 . 1088 %2F0022-3727%2F45%2F14%2F145201 .[18] Xu Hu, Chao Gao, and Jiangnan Hao. “Influenceof SDBD plasma aerodynamic actuation on flowcontrol by AC power supply and AC-DC powersupply”. In: IOP Conference Series: Earth andEnvironmental Science
108 (2018), p. 052051. doi : . url : https : / / doi . org / 10 . 1088 % 2F1755 - 1315 %2F108%2F5%2F052051 .[19] Tao Shao et al. “Time behaviour of dischargecurrent in case of nanosecond-pulse surface di-electric barrier discharge”. In: EPL (EurophysicsLetters) doi : . url : https : / / doi .org/10.1209%2F0295-5075%2F101%2F45002 .[20] Victor R Soloviev and Vladimir M Krivtsov.“Numerical modelling of nanosecond surface di-electric barrier discharge evolution in atmo-spheric air”. In: Plasma Sources Science andTechnology doi :
10 .1088/1361- 6595/aae63e . url : https://doi.org/10.1088%2F1361-6595%2Faae63e . [21] D. F. Opaits et al. “Surface charge in dielectricbarrier discharge plasma actuators”. In: Physicsof Plasmas doi : . eprint: https://doi.org/10.1063/1.2955767 . url : https://doi.org/10.1063/1.2955767 .[22] Shintaro Sato et al. “Successively acceleratedionic wind with integrated dielectric-barrier-discharge plasma actuator for low-voltage opera-tion”. In: Scientific Reports doi : . eprint: https : / / doi . org / 10 . 1038 / s41598 - 019 -42284 - w . url : https : / / doi . org / 10 . 1038 /s41598-019-42284-w .[23] D F Opaits. “Dielectric Barrier DischargePlasma Actuator for Flow Control”. Financialsupport by NASA Glenn Research Center.PhD thesis. Princeton, NJ, USA: PrincetonUniversity, 2012.[24] Bj¨orn Offerhaus et al. “Spatially resolvedmeasurements of the physical plasma parametersand the chemical modifications in a twinsurface dielectric barrier discharge for gas flowpurification”. In: Plasma Processes and Polymers doi : . eprint: https : / / onlinelibrary .wiley . com / doi / pdf / 10 . 1002 / ppap .201600255 . url : https : / / onlinelibrary .wiley . com / doi / abs / 10 . 1002 / ppap .201600255 .[25] Bj¨orn Offerhaus. “Characterisation of a noveltwin surface dielectric barrier discharge designedfor the purification of gas streams”. PhD thesis.Bochum, NRW, Germany: Ruhr UniversityBochum, 2018.[26] B. Offerhaus et al. “Determination of NOdensities in a surface dielectric barrier dischargeusing optical emission spectroscopy”. In: Journalof Applied Physics doi : . eprint: https://doi.org/10.1063/1.5094894 . url : https://doi.org/10.1063/1.5094894 .[27] Lars Sch¨ucke et al. “Conversion of volatile or-ganic compounds in a twin surface dielectric bar-rier discharge”. In: Plasma Sources Science andTechnology (2020). url : http://iopscience.iop.org/10.1088/1361-6595/abae0b .[28] Niklas Peters et al. “Catalyst-enhanced plasmaoxidation of n-butane over α -MnO2 in atemperature-controlled twin surface dielectricbarrier discharge reactor”. In: Plasma Processesand Polymers n/a.n/a (), e2000127. doi : https://doi.org/10.1002/ppap.202000127 . eprint: https : / / onlinelibrary . wiley . com / doi / EFERENCES pdf / 10 . 1002 / ppap . 202000127 . url : https :/ / onlinelibrary . wiley . com / doi / abs / 10 .1002/ppap.202000127 .[29] Hyun Ha Kim et al. “A novel plasma reactorfor NO/sub x/ control using photocatalystand hydrogen peroxide injection”. In: IEEETransactions on Industry Applications issn : 1939-9367. doi : .[30] Quan-Zhi Zhang and Annemie Bogaerts. “Plasmastreamer propagation in structured catalysts”.In: Plasma Sources Science and Technology doi :
10 . 1088 / 1361 - 6595 /aae430 . url : https : / / doi . org / 10 . 1088 %2F1361-6595%2Faae430 .[31] Hyun-Ha Kim, Yoshiyuki Teramoto, and AtsushiOgata. “Time-resolved imaging of positive pulsedcorona-induced surface streamers on TiO2and γ -Al2O3-supported Ag catalysts”. In: Journalof Physics D: Applied Physics doi :
10 . 1088 / 0022 - 3727 / 49 / 41 /415204 . url : https : / / doi . org / 10 . 1088 %2F0022-3727%2F49%2F41%2F415204 .[32] Ya Zhang et al. “Two-dimensional particle-incell/Monte Carlo simulations of a packed-beddielectric barrier discharge in air at atmosphericpressure”. In: New Journal of Physics doi :
10 . 1088 / 1367 - 2630 /17 / 8 / 083056 . url : https : / / doi . org / 10 .1088%2F1367-2630%2F17%2F8%2F083056 .[33] E C Neyts and A Bogaerts. “Understandingplasma catalysis through modelling and simula-tion—a review”. In: Journal of Physics D: Ap-plied Physics doi : . url : https://doi.org/10.1088%2F0022-3727%2F47%2F22%2F224010 .[34] Ya Zhang et al. “Formation of microdischargesinside a mesoporous catalyst in dielectric barrierdischarge plasmas”. In: Plasma Sources Scienceand Technology doi : . url : https://doi.org/10.1088%2F1361-6595%2Faa66be .[35] Kefeng Shang et al. “Characterization of anovel volume-surface DBD reactor: dischargecharacteristics, ozone production and benzenedegradation”. In: Journal of Physics D: AppliedPhysics doi : . url : https : // doi . org /10.1088%2F1361-6463%2Fab538d . [36] A. V. Pipa et al. “The simplest equivalent circuitof a pulsed dielectric barrier discharge and thedetermination of the gas gap charge transfer”. In: Review of Scientific Instruments doi :
10 . 1063 / 1 . 4767637 . eprint: https://doi.org/10.1063/1.4767637 . url : https://doi.org/10.1063/1.4767637 .[37] F J J Peeters and M C M van de Sanden. “Theinfluence of partial surface discharging on theelectrical characterization of DBDs”. In: PlasmaSources Science and Technology doi :
10 . 1088 / 0963 - 0252 / 24 / 1 /015016 . url : https : / / doi . org / 10 . 1088 %2F0963-0252%2F24%2F1%2F015016 .[38] Andrei Pipa et al. “Dependence of dissipatedpower on applied voltage for surface barrierdischarge from simplest equivalent circuit”. In: Plasma Sources Science and Technology (2020). url : http://iopscience.iop.org/article/10.1088/1361-6595/abc415 .[39] Zaka ul Islam Mujahid and Ahmed Hala.“Plasma dynamics in a packed bed dielectricbarrier discharge (DBD) operated in helium”.In: Journal of Physics D: Applied Physics doi :
10 . 1088 / 1361 - 6463 /aaa8cd . url : https : / / doi . org / 10 . 1088 %2F1361-6463%2Faaa8cd .[40] Zaka ul Islam Mujahid et al. “Formation ofsurface ionization waves in a plasma enhancedpacked bed reactor for catalysis applications”.In: Chemical Engineering Journal
382 (2020),p. 123038. issn : 1385-8947. doi : https://doi.org/10.1016/j.cej.2019.123038 . url : .[41] Zaka ul-islam Mujahid and Julian Schulze. Plasma propagation dynamics in a patterneddielectric barrier discharge at different lengthscales . 2020. arXiv: .[42] Chet Nieter and John R. Cary. “VORPAL: aversatile plasma simulation code”. In:
Journal ofComputational Physics issn : 0021-9991. doi : https://doi.org/10 . 1016 / j . jcp . 2003 . 11 . 004 . url : .[43] Sander Nijdam, Jannis Teunissen, and UteEbert. “The physics of streamer dischargephenomena”. In: Plasma Sources Science andTechnology doi :
10 .1088/1361- 6595/abaa05 . url : https://doi.org/10.1088/1361-6595/abaa05 . EFERENCES
Plasma Processes and Polymers n/a.n/a(), e2000234. doi : https : / / doi . org / 10 .1002 / ppap . 202000234 . eprint: https : / /onlinelibrary . wiley . com / doi / pdf / 10 .1002 / ppap . 202000234 . url : https : / /onlinelibrary.wiley.com/doi/abs/10.1002/ppap.202000234 .[45] Friederike Kogelheide et al. “Characterisation ofvolume and surface dielectric barrier dischargesin N2–O2 mixtures using optical emission spec-troscopy”. In: Plasma Processes and Polymers n/a.n/a (n/a), e1900126. doi : . eprint: https : / / onlinelibrary .wiley . com / doi / pdf / 10 . 1002 / ppap .201900126 . url : https : / / onlinelibrary .wiley . com / doi / abs / 10 . 1002 / ppap .201900126 .[46] L Bischoff et al. “Experimental and computa-tional investigations of electron dynamics in mi-cro atmospheric pressure radio-frequency plasmajets operated in He/N2 mixtures”. In: PlasmaSources Science and Technology doi :
10 . 1088 / 1361 - 6595 / aaf35d . url : https://doi.org/10.1088/1361- 6595/aaf35d .[47] I Korolov et al. “Control of electron dynamics,radical and metastable species generation in at-mospheric pressure RF plasma jets by VoltageWaveform Tailoring”. In: Plasma Sources Sci-ence and Technology doi :
10 . 1088 /1361 - 6595 / ab38ea . url : https : //doi.org/10.1088/1361-6595/ab38ea .[48] I Korolov et al. “Helium metastable speciesgeneration in atmospheric pressure RF plasmajets driven by tailored voltage waveforms inmixtures of He and N2”. In: Journal of PhysicsD: Applied Physics doi :
10 . 1088 /1361 - 6463 / ab6d97 . url : https : //doi.org/10.1088/1361-6463/ab6d97 .[49] C. K. Birdsall. “Particle-in-cell charged-particlesimulations, plus Monte Carlo collisions withneutral atoms, PIC-MCC”. In: IEEE Transac-tions on Plasma Science issn : 1939-9375. doi : .[50] Alan J. Lichtenberg Michael A. Lieberman. Principles of plasma discharges and materialsprocessing . Second. Jonh Wiley & Sons, Inc.,2005. [51] M. A. Furman and M. T. F. Pivi. “Probabilisticmodel for the simulation of secondary electronemission”. In:
Phys. Rev. ST Accel. Beams doi : . url : https://link.aps.org/doi/10.1103/PhysRevSTAB.5.124404 .[52] A V Phelps and Z Lj Petrovic. “Cold-cathodedischarges and breakdown in argon: surface andgas phase production of secondary electrons”.In: Plasma Sources Science and Technology doi :
10 . 1088 / 0963 - 0252 /8 / 3 / 201 . url : https : / / doi . org / 10 . 1088 %2F0963-0252%2F8%2F3%2F201 .[53] S. Pancheshnyi et al. “The LXCat project: Elec-tron scattering cross sections and swarm pa-rameters for low temperature plasma model-ing”. In: Chemical Physics
398 (2012). ChemicalPhysics of Low-Temperature Plasmas (in hon-our of Prof Mario Capitelli), pp. 148 –153. issn :0301-0104. doi : https : / / doi . org / 10 . 1016 /j.chemphys.2011.04.020 . url : . 2008, pp. 217–218. doi : .[56] C. S. Meierbachtol et al. “Conformal Electro-magnetic Particle in Cell: A Review”. In: IEEETransactions on Plasma Science issn : 1939-9375. doi : .[57] John Loverich et al. Charge Conserving Emissionfrom Conformal Boundaries in ElectromagneticPIC simulations . May 2010.[58] Alexandre Likhanskii et al. “Limitations of theDBD effects on the external flow”. In: . doi : . eprint: https:/ /arc.aiaa.org/doi/pdf/10.2514/6.2010-470 . url : https://arc.aiaa.org/doi/abs/10.2514/6.2010-470 .[59] U Ebert et al. “The multiscale nature ofstreamers”. In: Plasma Sources Science andTechnology doi :
10 .1088 / 0963 - 0252 / 15 / 2 / s14 . url : https : / /doi . org / 10 . 1088 % 2F0963 - 0252 % 2F15 % 2F2 %2Fs14 . EFERENCES
Journal of Physics D:Applied Physics doi :
10 . 1088 / 0022 - 3727 / 35 / 17 / 313 . url : https : / / doi . org / 10 . 1088 % 2F0022 - 3727 %2F35%2F17%2F313 .[61] Y. Qiu et al. “Effect of background ionizationon plasma ignition dynamics”. In: Physics ofPlasmas doi : . eprint: https://doi.org/10.1063/1.4977805 . url : https://doi.org/10.1063/1.4977805 .[62] Quan-Zhi Zhang, Wei-Zong Wang, and AnnemieBogaerts. “Importance of surface charging duringplasma streamer propagation in catalyst pores”.In: Plasma Sources Science and Technology doi :
10 . 1088 / 1361 - 6595 /aaca6d . url : https : / / doi . org / 10 . 1088 /1361-6595/aaca6d .[63] Natalia Yu Babaeva, Dmitry V Tereshonok, andGeorge V Naidis. “Fluid and hybrid modeling ofnanosecond surface discharges: effect of polarityand secondary electrons emission”. In: PlasmaSources Science and Technology doi :
10 . 1088 / 0963 - 0252 / 25 / 4 /044008 . url : https : / / doi . org / 10 . 1088 /0963-0252/25/4/044008 .[64] Wen Yan et al. “Two-dimensional modelingof the cathode sheath formation during thestreamer-cathode interaction”. In: Physics ofPlasmas doi : . eprint: https://doi.org/10.1063/1.4861613 . url : https://doi.org/10.1063/1.4861613https://doi.org/10.1063/1.4861613