Square grid pattern with direction-selective surface discharges in dielectric barrier discharge

Jianhua ZHANG(张建华),Yuyang PAN(潘宇扬),2,*,Jianyu FENG(冯建宇),Yunan HE (贺玉楠),Jiahui CHU (褚佳惠) and Lifang DONG (董丽芳),*

1 College of Physics Science and Technology,Hebei University,Baoding 071002,People’s Republic of China

2 College of Quality and Technical Supervision,Hebei University,Baoding 071002,People’s Republic of China

Abstract A new phenomenon that a filament discharged only once instead of twice in a cycle of the applied voltage is observed in a square grid pattern in a dielectric barrier discharge (DBD) with a larger gas gap,which is named intermittent discharge.Its spatiotemporal dynamics and the formation mechanism are studied by the multiple photomultiplier tubes and an intensified charge-coupled device.Corresponding to the positions of spots in the picture with an exposure time of 40 ms,there are some bright spots(discharge spots)and black spots(non-discharged spots)in the instantaneous image with an exposure time of 10 μs (a half cycle of the applied voltage).There are at least two bright spots around one black spot and vice versa.The surface discharges(SDS)can be observed between any two adjacent spots.The intensity of the SDS between the bright spot and the black spot is 2.5 times greater than that between two adjacent bright spots,which indicates that the SDS are directional-selective.The intermittent discharge with positive(negative)current polarity changes to that with negative(positive)current polarity,after it sustains up to 14 voltage cycles at the longest.The spatial distribution of the electric field component is calculated through COMSOL software to solve the Poisson equation numerically.It is found that the inhomogeneous distribution of surface electric field is caused by the inhomogeneous distribution of wall charges,which leads to direction-selective SDS.The intermittent discharge is formed by the competition between the direction-selective SDS and volume discharges(VDS) in DBD.This is the reason why the intermittent discharge is generated.

Keywords: dielectric barrier discharge,pattern,direction-selective surface discharges,intermittent discharge

1.Introduction

Self-organization patterns far from equilibrium are complex and intriguing phenomena,which are commonly presented in diverse types of physical,chemical,and biological systems[1,2].Dielectric barrier discharge (DBD) is one of the most interesting nonlinear systems for the study of pattern formation because of its richness of luminous filament patterns.DBD is an AC gas discharge,the generating device contains two parallel plate electrodes,at least one of which is covered with a dielectric.Driven by the high-voltage power supply,the discharge starts when the applied electric field reaches the breakdown threshold of the gas.The gas will be ionized,generating positive and negative particles that collide with each other.Charges move to both poles under the action of the applied electric field.Ultimately,they are deposited on the surface of the dielectric layer,forming wall charges with double affection [3].The wall charges must be considered in the study of the physical mechanism of DBD patterns.The effect of wall charges is demonstrated in two aspects: in the time scale,the time interval of a single discharge filament has a long and short alternate change rule [4,5]; in the spatial scale,deposited wall charges on the dielectric surfaces act as an activator,each filament array tends to coincide spatially with that of the preceding half cycle(HC),which is known as the‘memory effect’of wall charges[6].The‘memory effect’of the wall charges is an essential mechanism for pattern formation.In 2000,Walhoutet alresearched the distribution of isolated filaments in an effectively 1D system,which found the localized site of charges deposited in one HC as a probable site of filamentation in the next HC to ensure each filament in nearly the same place[7].In 2006,Purwinset alfound that the filaments considered as self-propelled quasi-particles due to mutual interaction of the particle and the surface in DBD systems can revisit sites that have been visited long ago[8].In 2009,Stollenwerketet alfound that the surface charge distribution in the zero of the driving voltages was an image of the preceding breakdown using the method of optical measurement[9].With the in-depth study of patterns in DBD,some patterns which were inconsistent with ‘memory effect’ of the wall charges have been reported [10-12].In 2012,Boeufet aldiscovered a novel discharge phenomenon in the ‘quincunx’structure.It was shown that the position of the new filament did not exist at the exact location as the previous one,which was caused by the movement of the filaments in pairs [13].Here,we report a type of internment discharge with temporal interval discharge and spatial ‘memory effect’ disappearance and reappearance,which relates to surface discharges (SDS).

SDSmean that the gas discharge is always initiated in the inhomogeneous field at or close to the edge of one electrode and moves along the dielectric surface (creeping discharge,sliding discharge) [14].There are two types of devices to generate SDS,one is the along-surface DBD device(S-DBD)[15-18],and the other is the volume-discharge DBD device(V-DBD) [19].The SDSare induced by the wall charges deposited on a dielectric surface and diffuse in all directions during the V-DBD with a larger gas gap [20,21].In 2014,Gaoet aldiscovered the existence of the ‘competition’behavior of SDSbetween two spots,which resulted in bending of electric field lines at the location of the midperpendicular of two neighboring spots,and the ‘Voronoi’diagrams can be formed[22].In 2015,Liuet alfound that the dim spot was formed by the confluence of the SDSof the surrounding other three bright spots in the hexagonal superlattice pattern with SDS[23].In 2018,Miet aldiscovered the direction-selective SDSdue to the electrostatic force of the surrounding wall charges.The spatiotemporal dynamics of the superlattice patterns with direction-selective SDSwere different from the previous ones.The distribution of spots violated the conventional interpolation discharge,and an incomplete nest structure with discharge holes appeared[24].Here,we discovered the direction-selective SDScaused by the inhomogeneous distribution of the surface electric field.The intermittent discharge with the ‘memory effect’ of the wall charges disappearance and reappearance was formed by the competition between the direction-selective SDSand volume discharges (VDS) in DBD.

In this work,the intermittent discharge is first observed in the square grid pattern in a DBD with a larger gas gap.The spatiotemporal dynamics and the formation mechanism of the square grid pattern are researched by a photomultiplier tubes system(PMTS) and an intensified charge-coupled devices (ICCD).The spatial distribution of the electric field componentin the dielectric surfaces is calculated through COMSOL software to solve the Poisson equation numerically when the discharging of the bright spot(Sbr)is extinguished.It is believed that the results not only deepen the understanding of the interaction between SDSand VDS,but also enrich the theory of wall charges.

2.Experimental setup

The schematic of the experimental setup is shown in figure 1.Two cylindrical containers with a diameter of 80 mm are filled with water,and both sides of each container are sealed with quartz glass of thickness 1.5 mm.A metallic ring is immersed in container and connected to an AC power supply with a frequency off= 51.19 kHz.As the discharge area,the rectangular gap with a face size of 55 mm×40 mm and thickness (d) of 4.7 mm is clamped between the two water electrodes.The whole cell is placed in a transparent vacuum chamber,which contains a mixture gas of argon and air.The voltage waveform is detected by a high-voltage probe (Tektronix P6015A,1000X)and recorded by a digital oscilloscope(Tektronix DPO 4054B).A four-channel measuring device has been designed based on the luminescent characteristics of the self-organizing pattern.The principle is to use a plane mirror to change the direction of light propagation,and the light is converged through a convex lens.The image can be formed in the lens of photomultiplier tubes (PMTs).The system (temporal resolutions: 2 ns;spatial resolutions: 1 mm)is used to simultaneously measure the optical signals of spot structures at four different positions in a unit cell.According to the high transparency of the electrode,evolution images of the patterns are taken by a normal digital camera(Canon EOS 6D).The temporal correlation of filaments is studied by optical signals measured by the PMTs.The instantaneous images of substructures are captured by an intensified chargecoupled device (ICCD,HSFC Pro).

3.Results and discussions

3.1.Bifurcation sequence and phase diagram of patterns

Figure 2 shows the bifurcation sequence for the square grid pattern with the increasing the applied voltage (U).The discharge filaments regularly arrange and form the square pattern at 3.80 kV (figure 2(a)).When theUrises to 4.16 kV,the square grid I pattern (figure 2(b)) with lattice constantsa1= 6.40 mm appears.AtU= 4.20 kV,the square grid II pattern (figure 2(c)) with lattice constantsa2= 5.40 mm occurs in the discharge area.Sstands for the spot,andLstands for the line.For the convenience of future study,five spots in a unit cell enclosed by‘◇’are denoted asS,S1,S2,S3,andS4respectively.At the same time,an enlarged cell(figure 2(c1)) is shown on the left side of figure 2(c).When increasing theUto 4.50 kV,the pattern is the coexistence of square and hexagon(figure 2(d)).Among them,the positions of square and hexagon patterns in figure 2(d) are marked by using quadrilateral and hexagon respectively.Other experimental parameters are as follows: gas pressurep= 15.2 kPa,argon concentration Ф= 59.6%,driven frequencyf= 51.19 kHz,gas gapd= 4.7 mm,and exposure time of the picturest= 40 ms.

Figure 1.A schematic diagram of the experimental setup.

Figure 2. The bifurcation of pattern types with the applied voltage increasing.(a)The square pattern,U = 3.80 kV.(b)The square grid I pattern, U = 4.16 kV,lattice constants a1 = 6.40 mm.(c) The square grid II pattern,U = 4.20 kV,lattice constants a2 = 5.40 mm.S,S1,S2,S3 and S4 stand for five spots in a unit cell respectively and L stands for the line.(c1) The enlarged view of the single cell in figures 2(c).(d) The coexistence of square and hexagon,U = 4.50 kV.Other experimental parameters: gas pressure p = 15.2 kPa; argon concentration Ф = 59.6%; driven frequency f = 51.19 kHz,gas gap d= 4.7 mm; exposure time of the pictures t = 40 ms.

Self-organization pattern is a nonlinear phenomenon that exhibits dynamic or stationary structure due to the influence of various parameters.A phase diagram of the patterns as a function ofpandUis shown in figure 3(a1),which reflects the existence range of each pattern corresponding to figures 2(a)-(d).TheUcorresponding to each pattern grows with the increase of thepin figure 3(a1).The square grid II pattern occurs over a wide range of parameters.The phase diagram of patterns as a function of the argon concentration Ф and theUis displayed in figure 3(a2).In the experiment,it is found that the square grid II pattern is the most stable under the case (p= 15.2 kPa,Ф = 59.6%,andU= 4.20 kV).Accordingly,it is selected as the research condition of this experiment.

3.2.The spatial-temporal dynamics of square grid pattern and intermittent discharge

For studying the spatiotemporal structure of the square grid II pattern,the optical signals of filaments at different positions are simultaneously measured by using two highly sensitive PMTs.In figure 4,theS,L,Sbr,andSblstand for spot,line,discharge and non-discharging spots,respectively.Figure 4(a)displays the temporal correlations betweenSandL.From figure 4(a),it can be seen thatSdischarged only once during one cycle of the applied voltage,and the discharge moment corresponds to the first current pulse of the rising edge of the applied voltage.Ldischarged twice in a whole cycle of the applied voltage,and the discharge moment corresponds to the second current pulse of the rising edge of the applied voltage.Compared with the discharge moment ofS,the discharge moment ofLis delayed by approximately 0.2 μs,which indicates thatLis induced by the SDSofS.As shown in figure 4(a),the temporal correlations between different filaments indicate that the discharge sequence of filaments isS(i,j)-L-S(i±1,j±1)-Lin a cycle of the applied voltage,whereistands for the row,jrepresents the column,and ± represents the adjacent row and column.To measure the light signals of SDS,the distance between the PMTSand the pattern is adjusted,so that more light enters the PMTSaperture.The temporal correlations betweenS+Land individualSare measured simultaneously,as shown in figure 4(b).The partial enlargement image on the right side of figure 4(b) indicates that the optical signal ofS+Lhas two distinctive signal pulses with half-widths of about 0.057 μs and 0.066 μs respectively.Nevertheless,the pulse half-width of individualSis only 0.025 μs.It indicates that the optical signal ofS+Lmeasured by PMT contains the optical signal of SDS,because the deposition time of wall charges produced by SDSis longer than that of VDS,which will cause the half-width of the optical signal to increase.A new phenomenon thatSis ignited only once in a cycle of the applied voltage attracts our attention,which is named intermittent discharge.To investigate the spatial distribution of the intermittent discharge,the exposure time of the ICCD is set to 10 μs,and the instantaneous images of the square grid II pattern within the HC of the applied voltage are taken.For simplicity,figure 4(c)shows an instantaneous image,which is one of the repetition experimental results.Corresponding to the positions ofSin the picture with an exposure time of 40 ms,there are someSbrandSblin the instantaneous image with an exposure time of 10 μs(a HC of the applied voltage).There are at least twoSbraround oneSbland vice versa.From figure 4(c),it can be seen that the claw-like discharge filaments are extended fromSbr,which should be SDS[25].Obviously,the directions of SDSare different.To clearly present the selective distribution of SDS,the positions ofSbrandSblare marked with a rectangular frame in figure 4(c).It can be clearly seen that the SDSof theSbrextending to theSblare strong,while the SDSbetween two adjacentSbrare almost invisible.The above results show that the SDSofSbrare preferentially extended to the position of adjacentSbl.Furthermore,the light intensity between different filaments in the rectangular frame in figure 4(c) is measured,as shown in figure 4(d).It is found that the light intensity between two adjacentSbris not zero.If it is the background of the picture,the light intensity between theSbrand theSblshould be equal to that between two adjacentSbr.However,the light intensity between theSbrand theSblis significantly greater than that between two adjacentSbr.The light intensity between two adjacentSbrand the light intensity of a singleSbrhas a ratio of 1:5.However,the light intensity betweenSbrandSbland the light intensity of a singleSbrhas a ratio of 1:2.This means that the SDSlight intensity between theSbrand theSblis 2.5 times greater than that between two adjacentSbr.This shows that the SDSofSbrare direction-selective,and the accumulated charge preferentially mobile to the adjacentSbl.

Figure 3.The phase diagram of patterns.(a1) The phase diagram of patterns in figures 2(a)-(d) as a function of the gas pressure p and the applied voltage U.(a2) The phase diagram of patterns in figures 2(a)-(d) as a function of the argon concentration Ф and the applied voltage U.

Figure 4.The time correlation and instantaneous image of square grid II pattern in half cycle of the applied voltage.(a)The optical signals of spot(S) and line (L).(b) The optical signals of S + L and S.(c) Instantaneous image of the square grid II pattern with an exposure time of 10 μs(a half cycle of the applied voltage)taken by an intensified charge-coupled device.Bright spot(Sbr)stands for the position of discharge,black spot (Sbl) stands for the position of non-discharge.(d) The distribution of light intensity between different filaments.

Figure 5.Images of square grid II pattern integrated over 50 voltage cycles.(a)Waveform of the applied voltage and the current.(b1)Image in positive half cycle of the applied voltage.(b2) Image in negative half cycle of the applied voltage.The exposure time of (b1) and (b2)correlated with Δt1 and Δt2 current pulse phases in figure 5(a).

To study the spatial distribution of intermittent discharge,images are taken by the ICCD.First,intermittent dischargeSin the square grid II is integrated over 50 voltage cycles to obtain sufficient light signals.The waveform of the applied voltage and current of the pattern is presented in figure 5(a).Figure 5(b1) shows the image of intermittent dischargeSintegrated over 50 times in the positive HC of the applied voltage,and its exposure time is correlated with the current pulse phases denoted byΔt1= 950 ns in figure 5(a).The result shows that allSdischarged instead of the predictably partialSdischarge.Figure 5(b2) exhibits the image of intermittent dischargeSintegrated over 50 times in the negative HC of the applied voltage and its exposure time is correlated with the current pulse phases denoted byΔt2= 950 ns in figure 5(a),the result is consistent with the result in figure 5(b1).The phenomenon indicates that there may be a transformation moment for the intermittent discharge between positive and negative HCs of the applied voltage.That is to say,intermittent discharge lasts for a while in the positive HC of the applied voltage and then shifts to the negative HC of the applied voltage.The number of continuous voltage cycles does not exceed 50.Therefore,allSdischarges in an image which is integrated over 50 voltage cycles.

Figure 6.The intermittent discharge in continuous voltage cycles in square grid II pattern.There is a transformation moment (Si) of the current direction of a single discharge.

Figure 7. Instantaneous images of square grid II pattern in single exposure mode.(a) Instantaneous image in a positive half cycle of the applied voltage.(b) Instantaneous image in a negative half cycle of the applied voltage.(c) The superposition of (a) and (b).The exposure time of (a) and (b) correlated with Δt1 and Δt2 current pulse phases in figure 5(a).

Based on the above results,the intermittent discharge in continuous voltage cycles was further studied.The measurement scale of PMTSis varied to 20,40 and 80 voltage cycles respectively.It reveals that there are transformation processes between positive and negative HCs of the applied voltage for theS.To see the transformation process more clearly,the part of the optical signals after one transformation ofSis intercepted,and the result is displayed in figure 6.The intermittent discharge with positive(negative)current polarity changes to that with negative (positive) current polarity,after it sustains up to 14 voltage cycles at the longest.There is a transformation moment (Si) of the current direction of a single filament.

To study spatial distribution ofSon square grid II pattern,instantaneous pictures of it in the positive(negative)HC of the applied voltage are taken by single mode of ICCD,when it does not transform within 14 voltage cycles.Figures 7(a) and (b) show images whose exposure time is correlated with Δt1and Δt2in figure 5(a).Figure 7(c) is the superposition of figures 7(a)and(b).It can be seen that theSbrandSblcoexist in figures 7(a) and (b).Figure 7(c) indicates that the filaments appear at random positions in the positive(negative)HC of the applied voltage,and at a complementary position in the negative (positive) HC of the applied voltage.The complete square structure is formed at the positions of theS.To sum up the above,the results of the PMTs and the ICCD are used to demonstrate the intermittent discharge in time scale and spatial scale,respectively.Sdischarged only once during a whole voltage cycle in time scale,SbrandSblappeared alternately in space scale.

Figure 8.The time correlation among four spots (S, S1, S2,and S3 denoted in figure 2(c)) in a cell in a square grid II pattern.

Figure 9.The spatial distribution of electric field component after the discharging of bright spots(Sbr)of each half cycle of applied voltage on the dielectric surface. X stands for the long and Y stands for the wide.The unit of E is V m-1.

To investigate the time and space situation of intermittent discharge during multiple consecutive HCs of the applied voltage,the optical signals ofSat different positions in a unit cell denoted with ‘◇’ in figure 2(c) are measured by PMTs with highly sensitive.As shown in figure 8,the characteristic of the intermittent discharge is suitable for eachS.Compared with central locationS,it can be clearly seen that discharge moment ofS1andS2is delayed for HC of the applied voltage,the discharge moment ofS3around it is the same.The result indicates that there are interactions among multipleSat the different positions [26].It is shown in the instantaneous images within two consecutive HCSof the applied voltage:in the first HC of the applied voltage,the positions ofSandS3formSbr,the positions ofS1andS2formSbl;while in the latter HC of the applied voltage,the positions ofS1andS2start to discharge and formSbr.The result of multi-channel PMTSis good agreement with the result of ICCD with external trigger:there are at least twoSblaround oneSbrand vice versa.

3.3.The simulation of the spatial distribution of the electric field in square grid II pattern with intermittent discharge

3.4.Formation mechanism of the pattern with intermittent discharge

To analyze the formation process of intermittent discharge distinctly,figure 10 displays the schematic diagram of the distribution of wall charges and SDSat different moments.Figures 10(a)-(c) are anode plates in the positive HC of the applied voltage and figures 10(d)-(f) are cathode plates in negative HC of the applied voltage.A cell is encircled by‘◇’,in which a small circle represents the position ofSand the arrow stands for the direction of the equivalent movement of charges produced by the SDS.The distributions ofSbr(S,S3)andSbl(S1,S2,S4) within the positive HC of the applied voltage can be determined by the experimental results in figure 8,as shown in figure 10(a).While the positions of theSbrandSblin the negative HC of the applied voltage are exactly opposite to those in the positive HC of the applied voltage.Before Δt1,the distribution of residual wall charges at positions ofSon the anode plates shows that there are clear differences in figure 10(a).The number of residual wall charge at positions ofS(SandS3) is more than that at positions ofS(S1,S2,andS4).During Δt1,S(SandS3) in multiple locations are prior to ignite and formSbrin the positive HC of the applied voltage,due to the stronger promotion effect of more residual wall charges.The wall charges with the negative polarity are accumulated on the anode plates after the discharging ofSbr(SandS3),which establishes an opposite internal electric field with the present applied field,leading theSbr(SandS3) to progressively extinguish,as shown in figure 10(b).After Δt1,the direction-selective SDSalong the direction of the arrows (the SDSbetweenSbrandSbl)are induced by the VDSofSbr(SandS3)[35].However,the direction-selective SDSvanish at these positions between two adjacentSbr(SandS3),because the wall charges ofSbr(SandS3)are passed away,thebetween two adjacentSbr(SandS3) is lower than the breakdown threshold of SDS,as shown in figure 10(c).The distribution of wall charges is shown in figures 10(d)-(f)when the polarity of the current is reversed.Figure 10(d)shows the distribution of residual wall charges before Δt2.Compared with the positions ofSandS3,most of wall charges deposit in these positions ofS(S1,S2andS4),because theseS(S1,S2andS4) accumulate a large number of wall charges from the equivalent movement of the charges produced by the SDS,as shown in figure 10(d).At Δt2,these positions ofS(S1,S2andS4)will be preferentially ignited to formSbrand accumulate positive charges on the cathode plate in the negative HC of the applied voltage,due to the activation effect of residual wall charges,as shown in figure 10(e).In general,Sbl(SandS3)with a few residual wall charges will be ignited later as the voltage continues to increase.Here,Sbl(SandS3) cannot be ignited again and converted to formSbr,because of the inhibition effect of wall charges that come from surroundingSbr(S1,S2,andS4)in this HC of the applied voltage.After Δt2,the residual negative charges atSbl(SandS3) positions are neutralized and accumulated positive charges from the surrounding multiple dischargingSbr(S1,S2,andS4) [36],as shown in figure 10(f).Eventually,the distribution of wall charges returns to the initial situation,as shown in figure 10(a).The above process is repeated over and over again,resulting in the intermittent discharge phenomenon that filament at the same position is ignited only once in a whole cycle of the applied voltage.It is worth pointing out thatLbetween adjacentScan be clearly seen by the naked eyes,and it is formed by direction-selective SDSmultiple superimposed.According to the above analysis,it can be found that the formation of the square grid II pattern is closely related to the double effects of wall charges.The intermittent discharge with the ‘memory effect’ of the wall charges disappearance and reappearance is formed by the intense competition between direction-selective SDSand VDSin DBD with a larger gas gap.

Figure 10.A schematic diagram of the distribution of wall charges and surface discharges on a dielectric surface in one cycle of the applied voltage.(a)-(c)In the positive half cycle of the applied voltage,(d)-(f)in the negative half cycle of the applied voltage.(a)The distribution of the residual wall charges before Δt1.(b)The distribution of accumulated wall charges during Δt1.(c)The equivalent mobility of charges of direction-selective SDS after Δt1.(d) The distribution of the residual wall charges before Δt2.(e) The distribution of accumulated wall charges during Δt2.(f)The equivalent mobility of charges of direction-selective SDS after Δt2.The ring stands for the position of S and the arrow stands for the direction of the equivalent movement of the charges produced by the SDS.

4.Conclusions

A new phenomenon that a filament discharged only once in a cycle of the applied voltage is observed in a square grid pattern in a DBD with a larger gas gap,which is named intermittent discharge.Its spatiotemporal dynamics and the formation mechanism are studied by the multiple PMTSand an ICCD.The experimental results show that the pattern consists of two different sub-lattices,which are spots (S)and lines (L),and the discharge sequence in a cycle of the applied voltage follows as:S(i,j)-L-S(i±1,j±1)-L.Corresponding to the positions ofSin the picture with an exposure time of 40 ms,there are some bright spots (Sbr) and black spots(Sbl)in the instantaneous image with an exposure time of 10 μs (a half cycle of the applied voltage).There are at least twoSbraround oneSbland vice versa.The SDScan be observed between any two adjacentS.The intensity of the SDSbetween theSbrand theSblis 2.5 times greater than that between the two adjacentSbr,which indicates that the SDSof theSbrare directional-selective.The wall charges at the position of theSbrare preferentially transferred to the position of neighboringSbl.The results of PMTs show that the intermittent discharge with positive (negative) current polarity changes to that with negative (positive) current polarity,after it sustains up to 14 voltage cycles at the longest.The SDSenhance the interaction amongSat different positions formed by the volume discharge(VDS).The spatial distribution of the electric field componentwas calculated through COMSOL software to solve the Poisson equation numerically.It is indicated that direction-selective SDSofSblare formed by the strongly inhomogeneous distribution of wall charges.Finally,the distribution process of wall charges and SDSon the dielectric surface is described by the theory of wall charges.The above analysis shows that intermittent discharge is formed by the competition between direction-selective SDSand VDSin DBD with a larger gas gap.

Acknowledgments

This work is supported by National Natural Science Foundation of China (No.12075075).The Natural Science Foundation of Hebei Province,China (Nos.2020201016 and A2018201154).