Electrical characterization and imaging of discharge morphology in a small-scale packed bed dielectric barrier discharge

Packed bed dielectric barrier discharges (DBDs) exhibit an improved energy efficiency and selectivity in nonthermal plasma based gas conversion. They enable the direct interaction between plasma and catalyst. In this contribution a compact coaxial DBD reactor enabling the end-on imaging of the discharge with and without packed beds is studied. The discharge morphology is correlated with electrical measurements such as voltage-charge (V-Q) plots. The studies are performed for different packed bed materials, binary gas compositions of argon and carbon dioxide, voltage amplitudes, average powers, and pressures. The analysis points outs the role of parasitic capacitances and parasitic discharges as often overlooked aspects. The introduction of the packed bed material into the coaxial barrier discharge arrangement increases the total capacitance, but the barrier of the outer glass tube mostly determines the maximum effective dielectric capacitance. The choice of the packed bed material determines the voltage threshold and the average discharge power. The investigations leads to a revision of the equivalent circuit for packed bed barrier discharge reactors, which also accounts the properties of different filling materials.


Introduction
Dielectricbarrier discharges (DBDs) have gained significant attention as a versatile plasma source for various applications, including ozone generation, surface activation, and plasma Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
medicine [1][2][3][4].The inherent advantages of DBDs, such as simple design, robust operation, easy upscaling and no need for special high voltage power supplies, make them attractive for industrial use [5,6].Currently, gas processing and generation of green fuels or valuable chemicals are prominent research topics, encompassing CO 2 splitting or hydrogenation, NO x reduction and N 2 fixation, volatile organic compound decomposition, and dry reforming of methane [7][8][9][10][11].Despite their potential for applications, DBDs still face challenges related to energy efficiency and selectivity, hindering their widespread industrial utilization.Coaxial DBDs, either with or without a packed bed, have emerged as the preferred reactor configuration for addressing these challenges [12].The main benefit of this construction is that there is no slippage of the reaction gas.Research has shown that reactor geometry, such as electrode design and dielectric barrier material and thickness, as well as operational parameters, such as gas the flow rate, determine the reactor performance [13][14][15].
Compared to empty plasma reactors, packed bed DBDs (PB-DBDs) exhibit an improved energy efficiency and selectivity.Packed bed DBDs enable the direct interaction between plasma and catalyst, which is seen as very promising for selectivity and yield improvement.For example, Xu et al [16] employed Ru/MgAl as a catalyst for CO 2 hydrogenation and dry reforming of methane.With the packed bed 85% CO 2 conversion and 84% CH 4 selectivity were achieved, while the empty reactor operation resulted only in 5% conversion and no selectivity at all.One must take into account, that the presence of the bed materials can result in lower discharge power.
In PB-DBDs the plasma interacts with a complex surface on different lengthscales, ranging from mm (gas gap and void space between pellets) over µm (discharge channel diameters in volume and on surface) to nm (size of active catalytic centers).Understanding the complex interaction between the plasma and the packed bed material is still a challenge [17].The presence of a packed bed reduces the free discharge (i.e.gas space) volume.With catalyst one can enhance the reaction rates through the catalytic activity [8,16,[18][19][20][21] as well as by altering its electrical parameters [22][23][24][25][26][27][28][29][30].Chen et al [8] provided a comprehensive review about the impact of various packing materials utilized for CO 2 conversion.Due to the polarization of the dielectric bead particles, the electric field strength at its contact points is enhanced.The filaments or microdischarges ignite in the gas space between and around the contact points.Depending on the dielectric constant and the surface properties (such as roughness and pore size) the microdischarges continue to spread on the dielectric surface [18].For single DBDs generated between semispherical dielectric barriers and surface DBDs this phenomenon is also known as surface ionization wave.Since the discharge channel length as well as the relative permittivity and thickness of the barrier material determine the charge per microdischarge, the packed bed properties are expected to have an impact on the charge per microdischarge as well on its overall number and thus, the discharge morphology.Experiments and simulations on PB-DBDs in dry air [22,23,31], helium [25,26,32,33] and CO 2 [12] show a similar trend.Bead materials with a higher relative permitivity cause a higher enhanced electric field strength at the contact points.Consequently, the filaments are more concentrated at the contact points for such materials and gain a higher charge, while on beads with lower relative permittivity it is expected that they expand more over the dielectric surface since there is less charge being dissipated in the mirodischarge volume.Packed beds with higher relative permittivity materials or smaller bead diameters require a higher voltage amplitude for operation.At low operating voltage amplitudes, the discharge concentrates at the contact points; the expansion of the dielectric bead surfaces proceeds at higher amplitudes.For sufficient voltage amplitudes the plasma channels can connect the reactor electrodes.Although the electric field strength is expected to be stronger between the beads and between the beads and the dielectric layer of the coaxial reactor due to polarization, it is weaker across the entire gap, i.e. along the chains of dielectric beads connecting the electrode.
Furthermore, the uniformity (here in the sense of spatial distribution of microdischarges) may have consequences for the plasma chemistry.For example, Chawdhury et al [20] argue that the highest selectivity of partial oxidation of methane into methanol is correlated with a more uniform distribution of the microdischarges which was achieved with glass beads.Like mentioned before, with this material the surface ionization waves expand more than on Al 2 O 3 , TiO 2 , or CeO 2 and highest amount of power is dissipated in case of glass [21].
Despite the increase of the chemical performance there is still not a full understanding of the discharge physics in PB-DBDs.For example, a comprehensive equivalent circuit model which describes PB-DBDs is still a matter of debate.This is of importance insofar, that electrical diagnostics provides a relative simple approach for a macroscopic characterization of the overall plasma.It is not only useful to determine the average discharge power; it can give information about discharge uniformity as demonstrated by Peeters and van de Sanden [34].The simplest equivalent circuit considers the DBD as a line of two capacitances representing the discharge gap and the dielectric barrier(s).The gap capacitor is by-passed when there is plasma in the gap.The equivalent circuit for volume DBDs of Peeters and van de Sanden [34] accounts for discharging and non-discharging electrode area sections.Only in the discharging part the gas capacitance is bypassed by plasma current.Brandenburg et al [5] extended this with the presence of parasitic capacitances as introduced already by Falkenstein and Coogan [35].Although these have no impact on the determination of the discharge power, they often are an overlooked phenomenon.Their incorporation as a capacitor in parallel to the discharge arrangement avoids erroneous calculations of the discharge voltages and the elementary capacitances of the circuit.Butterworth [36] discusses equivalent circuits for a single pellet PB-DBD configuration based on video recordings of the discharge correlated with electrical measurements.These authors conclude that an equivalent circuit for PB-DBDs must consider aspects of partial surface discharging [34] and surface DBDs as proposed by Kriegseis et al [37,38].Mei et al [39] propose a third capacitance representing the packed bed in line with gas and barrier capacitance.This approach cannot mimic the behavior of PB-DBDs entirely as discussed later in this contribution.
This contribution aims to present a comprehensive electrical characterization of a small-scale coaxial DBD, both in empty and packed bed configurations, with end-on visual access to the discharge zone.This enables the correlation of the measured electrical characteristics with the overall discharge morphology.Most coaxial DBDs, which are mainly devoted for the plasma chemical investigation does not enable such a visualization of the discharge volume.The study is conducted for different pressures, gas mixtures (argon and/or CO 2 ) and packing materials.Based on these results we introduce a novel approach for an equivalent circuit for PB-DBDs, which can give advises for the construction of future PB-DBD reactors.

Experimental setup
The sketch of the reactor and the experimental setup are shown in figures 1(a) and (b).The reactor consist of two cylindrical electrodes and a 3 cm long quartz tube as the wall as well as the dielectric barrier.Detailed information about the experimental setup, reactor's dimensions, material properties and suppliers are given in table 1.The inner (grounded) electrode, is a stainless steel tube enabling the gas input.The feed gas then hits the optical window of the reactor and passes through the discharge volume between the inner electrode and the quartz tube before it enters the gas outlet.Binary gas mixtures of Ar and CO 2 with a total flow rate of 100 sccm are applied.The fraction of gases Ar:CO 2 is changed by varying the gas flow rates at two separate mass flow controllers.The optical window is a round quartz plate, placed on top of the quartz tube by two Teflon holders.Two different high voltage electrodes were used during this work, namely a copper foil tape (wrapped around the quartz tube) and a silver film (applied as silver-conductive varnish and dried for several hours).The discharge gap is 1 mm, according to the outer radius of the inner electrode and the inner radius of the quartz tube.The reactor is sealed and tested to have no leakage for pressures up to 4 bar.The pressure inside the reactor is monitored and controlled with a digital pressure gauge (installed at the reactor outlet) and a valve after the pressure gauge, respectively.With open valve the gas flushes against the actual pressure, which was p = (1015 ± 37) mbar during the period of our measurements (this condition is referred as 'atm' in this work).The information regarding the power supply, transformer, high-voltage probe, current probe, and measuring capacitor is given in table 1 as well.The electrical parameters are monitored by voltage probes and recorded with a digital oscilloscope.Photos of the discharge zone were taken through the optical window (end-on) and from the side (side-on) by a Canon EOS 77D camera (ISO800, exposure time 10 s).
The electrical measurements are analyzed based on equivalent circuits.In its simplest form, the discharge arrangement (see figures 2(a) and (b)) is represented by the capacitance of the gas gap, C gap , and the dielectric tube, C diel .The overall capacitance, C cell is determined by equation ( 1) When plasma appears, the gap capacitance is by-passed by the time-dependent resistivity R plas (t).In coaxial DBDs, the capacitance values C diel and C gap can be calculated using the following formulas: where L is length of electrode, ε r is dielectric constant of quartz, ε 0 is permittivity of vacuum (dielectric constant of gas mixtures is considered as 1), a and b are outer and inner diameters (OD, ID) of quartz tubes, respectively and c is outer diameter (OD) of inner electrode.Total capacitance is measured with a LCR meter as well as from the lower slope of the V-Q plot, see figure 2(c).Other parameters that can be determined from V-Q plots are the minimum sustaining voltage, V min , and the discharge voltage, ∆V.The larger slope of the V-Q plot represents C diel in the simplest equivalent circuit.
The results obtained in this study are derived with three different reactor configurations (labeled R1, R2 and R3) which resemble three stages of its gradual improvement.In the first stage R1, the copper foil or the silver film are serving as the outer electrode.The silver-conductive varnish should adheres better on glass and therefore avoid air voids between the metal electrode and the glass tube.In the second step R2, silicone rubber is applied around the outer electrode in order to avoid parasitic discharges there.Finally, in version R3 the packed bed is introduced.Glass beads with 1 mm diameter as well as Al 2 O 3 and ZrO 2 beads with diameters ranging from 0.4 to 0.7 mm are examined.The information regarding the reactors in their different stages is provided in table 2. The results compare copper foil and silver film reactor operation.The capacitance is slightly higher for the silver film.This is attributed to non-identical electrode areas and a better adhesion of the painted silver compared to the self-adhesive copper tape which can include voids of air.The capacitance values are independent on pressure and gas, and the range of the error bars (representing three sets of experiments at different times) is also similar.The gap capacitance is not influenced by the gas composition and the pressure since the dielectric constant is nearly 1 for most gases (1.0009 for CO 2 and 1.0005 for Ar) and only changes by about 0.01% when the pressure increases from 1 to 2 bar.The influences of gas composition reported in some literature [6,12,39] can be explained by edge effects and parasitic discharges as discussed in the following.

Total and cell capacitance: parasitic discharges and capacities
The total measured capacitance is much higher than the calculated value of C cell (1.1 pF).The reasons for this discrepancy can be manifold, but uncertainties of the discharge geometry parameters (gap distance and dielectric thickness, dielectric constants of barrier material) does not explain this difference sufficiently.Photos of (R1) with Ag and Cu high     illustrates the operation of (R1) with pure argon at atmospheric pressure (at 5 kV pp ), while figure 4(b) shows the operation at 2.5 bar and 7.5 kV pp .From the circular end-on view photo it is seen that the entire volume of the gas gap is illuminated by plasma.It is clearly evident that the plasma extends beyond the electrode edges; thus, covering a larger area than determined by the outer electrode.The equivalent electrical circuit includes this by assuming an extension of the electrode area leading to a higher capacitance than calculated.However, the expansion estimated from the photos is about 10%, which is again not explaining the more than 3-fold higher measured total capacitance.Thus, there must be an additional, parasitic capacitance, which is attributed in the equivalent circuit as a capacitance C p in parallel to the discharge arrangement, see figure 3(c) [5,35,40].Taking the calculated C cell of 1.1 pF into account the value of C p is about 2.8 pF.
The presence of parasitic capacitances is somewhat unavoidable due to high-voltage throughputs, connectors and cables as well as stray capacitances.The latter are assumed as the main contributor in our arrangement.Table 3 compares calculated values for C cell and C tot obtained from the slope of V-Q-plots from the literature.The calculation of C cell uses the dielectric constant of the gas mixtures equal to 1 according to the results in figure 3(a) and in our previous work [41].The difference between calculated and measured values is significant in all studies.Although there are always uncertainties from the dimensions of the reactors, this does not explain the up to 18-fold higher measured capacities.As it appears in smaller reactors more significantly, this difference tends to be lower for larger electrode areas.Thus, working with a large electrode area helps to minimize the impact of the parasitic capacitance while for small-scale discharge arrangements the parasitic capacitance can be higher than for the discharge arrangement as demonstrated in our example.Using the cell capacitance corrected with the parasitic capacitance the difference between the Ag and Cu high voltage electrode of about 0.15 pF (see figure 3(a)) corresponds to an about 13% larger effective area and capacitance in case of the Ag film compared to the Cu foil.
Independent on the electrode material, but depending on the voltage amplitude there appear parasitic discharges outside the dielectric tube at the electrodes edges, as shown in the photos in figure 5. Figure 5(a) shows the plasma in a gas mixture Ar:CO 2 (4:1) at atmospheric pressure, which is operated in the entire discharge volume at 7 kV pp .The increase of pressure (figure 5(b)) or CO 2 fraction (figure 5(c)) requires a higher voltage amplitude.Even at 11 kV pp or 12 kV pp the expansion of the plasma beyond the electrode is not seen on the photos, but the parasitic discharges clearly are.With an electrical insulation by silicone rubber around the high voltage electrode in the stage R2 (see figure 6(b)), no parasitic discharges appear.
Figure 6(a) compares the total capacitance for the reactor stages R1, R2 (i.e.R1 with outer insulation) and R3 (filling of R2 with glass beads) as a function of pressure and gas mixture.The solid lines in the figure represents the capacitances measured by a LCR meter, while the dashed lines represent the average values measured from the V-Q plots.The measured values obtained by the LCR meter are in good agreement with the values obtained from the V-Q plots, taking into account the uncertainty of the LCR meter (±0.1 pF).
The silicone rubber insulation in R2 increases the total capacitance by about 15% or 0.7 pF.A schematic diagram of the reactor with the outer insulation in figure 6(c) illustrates that there is also an electric field outside of the discharge arrangement, which forms the stray capacitance.The presence of a material with a higher dielectric constant than air around the outer electrode increases the stray capacitance.Its increase by rubber insulation is about (C tot −C cell ) = 3.4 pF (for R2 and R3).
The discharge power is a parameter that may define the energy efficiency of any plasma chemical process in such reactors.The energy efficiency of a reactor is important, because it allows the comparison between different reactors.An incorrect measurement of the discharge power can lead to erroneous interpretation.When comparing the discharge power between Ag film and Cu foil high electrode in stage R1 (see figure 7), the copper foil results in slightly lower values (up to 20%) due to the slightly lower effective electrode area being provided by the Ag film.The results in the figure are for pure Ar, but the same difference is measured for other gas mixtures (see supplementary material).
As mentioned above, the operation with CO 2 requires higher voltage amplitudes, which favors parasitic discharge ignition.Figure 8 displays the discharge power measured at the same input voltage for R1 and R2, both with Ag electrode, in different gas mixtures and pressures.As depicted, the difference between R1 and R2 becomes evident for voltage amplitudes above 10 kV pp and, there is a clear correlation between the voltage amplitude and the difference in the discharge power.The data points for 2.5 bar in figure 8(a) indicate that there is no discharge ignited at 10.5 kV pp and 2.5 bar in R2, but in R1; i.e. the electric field is sufficiently high to generate the parasitic discharge outside (in air at atmospheric pressure), but not the plasma inside the reactor (operated with CO 2 and Ar at elevated pressure).
The parasitic discharge consumes more than 20 mW.To summarize these results the difference between the power in R1 and R2, taken as an indicator for parasitic discharge power losses is presented in figure 9.The "wasted" power only depends on the voltage amplitude and can reach up to 23 mW, which is about 40% more than the actual discharge power.It might be less for longer electrodes (because of the lower ratio between electrode area and electrodes edge length), but should be considered in any situation.In the case of small laboratory reactors, the appearance of parasitic discharges can lead to a significant overestimation of the power.Therefore, the choice of appropriate electrical insulation becomes crucial in ensuring accurate power measurements, especially in small-scale setups.

Partial discharging in the discharge volume
To discuss the discharge morphology further, we take into account the partial surface discharging effect as it was pointed out by Peeters and van de Sanden for volume barrier discharges [34].We pay attention to the observation in many DBD arrangements that at low over-voltages only a distinct part of the electrode cross section is illuminated by plasma, which is related with a lower discharge power [40].As also discussed in [42], the most likely reasons for this effect are slight variations of the discharge gap width and the thickness of the dielectric barrier due to tolerances of the tube walls, non-parallel alignments, improper electrode adhesion, local surface contaminations or edge effects at the electrodes.The extended equivalent circuit is given in figure 10(a).The discharged pathway is characterized by the parameter β ⩽ 1 while the non-discharging part acts like an additional parasitic capacitance αC cell .Consequently, the sum of both parameters is one, α + β = 1.The value of the higher slope in the V-Q plots, called effective dielectric capacitance, ζ diel , can be lower than C diel .The experimentally measured value of the higher slope is the sum of the effective dielectric capacitance and the parasitic capacitance (ζ diel + C p , always determined for the negative half-period) as suggested by the equivalent circuit in figure 10(a).Due to the identification and quantification of the parasitic capacitance in the previous experiments, ζ diel can be extracted for all reactor configurations.This study is combined by the investigation of plasma morphology via the end-on view photos.Figures 11 and 12     photos (results for pure CO 2 are available in the supplementary material).For higher pressures the values increase with the voltage amplitude and saturate slightly above the calculated C diel (given by red dashed line).In particular for 1.5 bar it is seen, that this increase correlates with the radial expansion of the discharge in the circular discharge gap.The plasma also expands along the electrode length (see figure 4) leading to higher effective and dielectric capacitance C diel than calculated.This can be suggested in the end-on photos by a higher overall luminosity.The higher luminosity at the wall of the dielectric is due to the internal reflection of light in the dielectric wall, but also in the gas gap itself the luminosity is changing.For example, in case of atmospheric pressure, a voltage amplitude of 8.5 kV pp leads to a value of ζ diel higher than C diel while the end-on photos does not show a full radial discharging.
The photos for 1.5 bar also do not show the complete filling of the discharge gap with plasma.However, the luminosity and the value of ζ diel increase.The most general statement to be drawn from these results is, that as higher the voltage amplitude, the more 'complete' does the discharge appear and that ζ diel reaches the value of a 'real' or 'actual, expanded' C diel for sufficient high voltage amplitudes (the maximum capacity of ζ diel measured in this study of 5.5 pF is represented by the dark blue dash-dotted line).Furthermore, the upper right radial segment has the highest local ignition voltage threshold.It is most likely because of the discharge gap tolerance.For a higher CO 2 fraction the full radial breakdown requires a much higher voltage amplitude, in particular at higher pressures (the voltage thresholds scales with pressure linearly).
This behavior becomes apparent in figure 12 for Ar:CO 2 = 1:4.The black squares in part (a) represent ζ diel at atmospheric pressure, and figure 12(b) shows the photo of the discharge gap taken simultaneously.The first value and the corresponding photo (first one in the top line) show partial discharging, whereas the third point photo in the line indicates full radial discharging which is also confirmed by the capacitances, namely ζ diel > C diel .The second data point suggest full discharging, which is not resembled in the corresponding second photo in the top line.Thus, the discharge has expanded along the electrode length, but not in the entire ringshaped gap.For the higher pressures only partial discharging is obtained.The values are below the theoretical limit of 4.1 pF and the photos show the absence of plasma in the upper right  radial segment of the gap.But in all cases the expansion along the electrode length can be suggested from the values and the overall luminosities.The maximum voltage amplitude of the power supply (18.5 kV pp ) enables full radial breakdown with ζ diel ≈ C diel in pure CO 2 at 2 bar, (see supplementary material).

Effect of packed bed in the discharge volume
As already shown in figure 6(a), the addition of the glass beads introduces an additional capacitance of about 0.5 pF.To investigate the plasma formation in PB-DBDs further, three different dielectric packings, namely Borosilicate glass beads, alumina Al 2 O 3 , and zirconium oxide ZrO 2 are examined.Figure 13(a) shows the V-Q plots for powers between 22 and 40 mW in R2 and R3 filled with beads made of glass, Al 2 O 3 and ZrO 2 (for Ar:CO 2 = 4:1 at 2 bar) and figure 13(b) depict the total measured capacitance for R2 and R3 with different packing materials.The total measured capacitance is independent on the voltage amplitude and gas composition, as expected from the previous discussions (total capacitance for R3 in two gas mixtures of Ar:CO 2 (4:1 and 1:4) at atm and 2 bar with a different packing materials are available in the supplementary material).
The gas composition determines the ignition voltage threshold but not the values of the capacitance.The higher the dielectric constant of the packing material the higher the total capacitance.The difference between the empty reactor total capacitance and packed bed total capacitance ∆C PB is in the order, ∆C PB GB < ∆C PB Al2O3 < ∆C PB ZrO2 .Figure 14(    slightly higher than the calculated C diel .This indicates a nearly full discharged reactor volume.The end-on photos support this suggestion.A higher fraction of CO 2 (see figure 15) shows the same trend although higher voltage amplitudes are required.Lower values are obtained, similar as in the case of R2.Due to the transparency of glass beads, the interpretation of the end-on photos is difficult.But, it is evident that the discharge develops in the entire gap and expands beyond the electrode area in case of a lower CO 2 fraction.Some distinct spots of higher luminosity can be seen in the photos, in particular between the beads and the dielectric tube surface.For a higher admixture of CO 2 , the discharge is less bright; but still, uniform distribution of microdischarge can be concluded.Similar as for the empty reactor the values of ζ diel to not reach more than 6.5 pF.
Obviously, the presence of the glass beads supports uniform microdischarge distribution and plasma expansion in axial direction, but the maximum capacitance in the active phase is still limited by the dielectric capacitance value.The same finding was obtained in a larger plasma reactor in [41].Figures 16(a  R2 from the measured slope of the V-Q plots for the active phases.Both materials are non-transparent.Thus, the corresponding end-on photos allow the investigation of the very first bead layers in the reactor only.While the gas mixture and the pressure determine the ignition voltage, the trends are similar, namely an increase with a saturation around the calculated dielectric capacitance. The lower saturation values of ζ diel of Al 2 O 3 and ZrO 2 are in agreement with the photos suggesting much less uniform plasma formation.Distinct discharge spots between the dielectric tube and the particles as well as between the beads are clearly observed, but do not in the full entire volume in radial direction.Furthermore, the plasma does not spread over the entire beads surface.The concentration of the discharge spots with less surface expansion is more evident for ZrO 2 , the material with the highest dielectric constant being studied here.These observations are in agreement with the findings summarized in the introduction.Figure 17 depicts the distribution of the electric field in the discharge gap for both empty and with bead particles made of Al 2 O 3 and ZrO 2 .This analysis was performed using COMSOL Multiphysics ® [43], solving the Laplace equation ∇ (−ε 0 ε r ∇φ ) = 0 in 3D Cartesian coordinate system in empty reactor and with one bead for different voltage amplitudes U a .The potential at the anode (φ = U a ) and grounding at the cathode (φ = 0) were considered.Placing a dielectric bead (diameter of 0.7 mm) in the discharge gap, comparing figures 17(b) and (c), alters the geometry of the electric field due to polarization.The magnitude of the electric field is visualized using the color bar.The figure illustrates the electric field enhancement between the bead and the dielectric layer or the inner electrode.As it is shown in figure 17(c), as higher the dielectric constant of the bed material as higher the polarization and as higher the electric field enhancement at the particles.Thus, microdischarge will be formed predominantly in the small gaps between bead particles and bead particle and electrode as illustrated in figure 18(a).Experiments by Butterworth and Allen as well as Kim et al [23,36] have shown such discharge morphology being investigated by optical imaging.Butterworth and Allen focused on discharges on single beads and observed the ignition and propagation of discharges around the bead's surface by photos and video recordings.Kim et al demonstrated the propagation of the microdischarges on the surface of the beads in case of packings by ICCD camera imaging.For sufficient high voltage amplitudes microdischarges may also form beside the beads (in the 'gas gap').As it is shown in figure 18(b), in such a complex overall discharge region there is no distinct discharge gap width and the determination of the discharge voltage is not universal as pointed out by Butterworth and Allen [36].The task of an equivalent circuit is to provide a general description of the conditions that averages the entire volume.The equivalent circuit should describe the partial breakdown performance, the increase of the total capacitance by beads addition, the limitation of the effective capacitance by the expanded 'real') dielectric capacitance and the dependence of the discharge formation on the relative dielectric permittivity of the bead material.
Starting from a limited number of beads (and thus, discharge spots) one can consider the discharge volume to consist of two capacitances in line.The capacitance C gas (which is not equal to C gap ) describes the small discharge gaps between beads and electrodes.The capacitance C bead represents the dielectric bead.C gas , and C bead form the packedbed capacitance C pb = (C gas .C bead ) ⁄ (C gas + C bead ).This capacitance is higher than C gap (2.3; 9.4 and 17.9 pF for glass, Al 2 O 3 and ZrO 2 , respectively), obviously because of the much lower distances for microdischarge ignition in the packed bed and the higher dielectric permittivity of the bead material.The higher the relative permittivity the higher C pb .The microdischarge develop as a channel (streamer) in the gas phase and then spread along on the gas-dielectric interfaces of the beads.To account for this and to explain that the extended C diel values can be reached, both C gas and C bead must be by-passable by a variable resistor, representing the overall plasma.Single microdischarges operated with barriers with higher dielectric constants generate a higher charge, but the spreading on the dielectric surface is lower.It is also known for surface DBDs (also referred to as surface ionization waves) that their expansion on the surface is less for higher dielectric constants.
Thus, in case of glass and Al 2 O 3 the plasma expands more on the surface of beads than for ZrO 2 , the material with highest dielectric constant being examined.Consequently, the plasma appears more 'spot-like' and non-uniform in case of ZrO 2 .Furthermore, the 'by-passing' of C bead is less likely for ZrO 2 which explains the lower maximum effective capacities compared with the other bead materials.
In a more general expression averaging the entire volume with a multitude of beads the equivalent circuit in figure 19 is proposed.It adapts the concept of Peeters and van de Sanden with a discharging and a non-discharging fraction, summarizes all gas gaps as the capacitance C gas , summarizes the overall capacitance of the packed bed as C PB , and includes stray      the power.This is also explainable by the equivalent circuit in figure 19 since a lower voltage drop over the capacitance C PB has to be expected when the capacitance increases diel :U PB = C PB :C diel .Furthermore, full discharging is inhibited for the materials with a higher relative permittivity which leads to a higher αC PB and β < 1.For the same the minimum sustaining voltage will increase, as it is shown in figure 21.From this viewpoint, the choice of the packing material can significantly influence the discharge power and a low as possible relative permittivity as a bead and catalyst carrier material in PB-DBDs appears favorable.The different morphology of the plasma in the packed bed in dependence of the material also manifest in the current signal and the V-Q plots of individual high voltage periods.The current measurements in figure 22(a) provide a qualitative understanding of the operational conditions.The current spikes represent individual microdischarges, which are ignited in the active phases.In contrast to the averaged, parallelogram-shaped V-Q plots, the slopes for R3 with glass beads in figure 22(b) show distinct steps or stairs in the active phases because the microdischarges transfer a certain amount of charge in a very short time.The highest current spikes are obtained in the empty reactor (R2).The addition of the packed bed leads to weaker microdischarges and a higher number.The current pulse amplitude decreases with the relative permittivity of the bead material and its number seems to be become larger.
The same feature can be obtained in the individual V-Q plots by the higher number but the lower step size of the stairs.They appear at random positions in each individual V-Q plot, but always as multiples of about 1 nC (i.e.probably between one and ten (more or less simultaneous) microdischarges with a charge of 1 nC per active phase).
In case of Al 2 O 3 and ZrO 2 the amount of charge per microdischarge is lower and the ignition is more distributed in time, thus no distinct 'stair treads' can be observed in the individual V-Q plots.These trends are observed for all pressures and gas mixtures being investigated.The weaker microdischarges in the presence of packed bed are due to the smaller discharge pathway and the weaker pronounced surface discharge for the higher relative permittivity.This is in agreement with findings for microdischarges in volume DBDs [31].

Conclusion and outlook
This contribution focused on the electrical characterization of a small-scale coaxial DBD with and without different dielectric packed beds.The DBD reactor provided the end-on view on the plasma morphology.First, the parasitic capacitance was determined since this needs to included in the interpretation of the measured electrical quantities, such as the discharge voltage or the effective dielectric capacitance.The latter allows conclusions about the morphology of the plasma in the discharge volume.In the discharge arrangement, it is possible to correlate the electrical analysis results with end-on view photos of the plasma.The plasma volume is not limited entirely by the electrode area; a significant expansion due to edge effects and parasitic discharges outside is observed.At conditions with low breakdown values (i.e.low pressure, high fraction of argon) the expansion of the plasma is more likely, while conditions with high breakdown voltages favor the parasitic discharges.Both processes complicate the interpretation of the measurement results.However, the parasitic discharges, which can also lead to a significant overestimation of the discharge power (up to 40% in this study), can be avoided by an insulation around the high voltage electrode, but, it must be considered that this increases the parasitic capacitance.
The introduction of the packed bed material increases the total capacitance of the discharge arrangement, but the barrier capacitance of the outer tube, like in an unfilled reactor, mostly determines the maximum effictive capacitance.The choice of the packed bed material determines the threshold and the dependence of the discharge power on the applied high voltage amplitude.The analysis of the measured reactor capacitances and voltage thresholds for the different packed bed materials allows the suggestion of an equivalent circuit model for packed-bed DBDs.It includes the partial breakdown phenomenon, i.e. non-uniform distribution of microdischarges in the volume for low-overvoltage and mimics the packed bed by two virtual capacitances representing the beads and the gas between the beads, respectively.Despite other equivalent circuits, we propose that both capacitances are be by-passed by a resistivity representing the discharges in the gas and on the bead surfaces, respectively.
As higher the relative permittivity of the packed bed material, as higher the minimum sustaining voltage, as less uniform the plasma distribution and as lower the average discharge power at the same high applied voltage amplitude.A higher number of weaker microdischarge events appears.Consequently, the most uniform plasma with a higher power is obtained when a packing material with a low relative permittivity is used.On the other hand, the relative permittivity of the dielectric barrier should be as high as possible to have maximum power input.
The proposed equivalent circuit needs further verification, in particular for larger discharge arrangements.However, the complexity of the discharge space consisting of voids with difference sizes and volume-to-surface ratios limits the applicability of 'macroscopic' concepts, such as the universal breakdown voltage known from volume DBDs.Further dedicated experiments on single microdischarges in packed beds also are necessary to understand the discharge formation and the plasma surface interaction at the beads.The influence of other properties, such as the presence of catalytic materials or humidity must be examined.Despite the simple electrotechnical analysis used in this study, it is applicable to any DBD arrangement as it is based on universal quantities such as the dielectric capacitance, the gap capacitance or parasitic capacitances.The values of these capacitances depend on the reactor geometry and design.The parasitic capacitance in particular has a significant influence in the relatively small discharge arrangement investigated here.Although we assume that the partial surface discharging is a phenomenon that occurs (sometimes more, sometimes less pronounced) in all DBD reactors, the formation of the plasma can be different in larger packed beds and in case of other gases.This will make adjustments or modifications of the equivalent circuit necessary.Therefore, the study of the applicability of the equivalent circuit to large discharge reactors requires further studies.
We hope that the findings presented here have implications for optimizing DBD designs and improving the control and performance of plasma-based gas-conversion systems.

Figure 3 (
Figure 3(a)  shows the total measured capacitance as a function of pressure in different gas mixtures for configurations R1.Examples of the V-Q plots from averaged signals are presented in figure3(b).The results compare copper foil and silver film reactor operation.The capacitance is slightly higher for the silver film.This is attributed to non-identical electrode areas and a better adhesion of the painted silver compared to the self-adhesive copper tape which can include voids of air.The capacitance values are independent on pressure and gas, and the range of the error bars (representing three sets of experiments at different times) is also similar.The gap capacitance is not influenced by the gas composition and the pressure since the dielectric constant is nearly 1 for most gases (1.0009 for CO 2 and 1.0005 for Ar) and only changes by about 0.01% when the pressure increases from 1 to 2 bar.The influences of gas composition reported in some literature[6,12,39] can be explained by edge effects and parasitic discharges as discussed in the following.The total measured capacitance is much higher than the calculated value of C cell (1.1 pF).The reasons for this discrepancy can be manifold, but uncertainties of the discharge geometry parameters (gap distance and dielectric thickness, dielectric constants of barrier material) does not explain this difference sufficiently.Photos of (R1) with Ag and Cu high

Figure 1 .
Figure 1.(a) Scheme of the small-scale coaxial DBD enabling end-on view, (b) experimental set up.

Figure 2 .
Figure 2. Scheme of the discharge arrangement R1 (a), simplest equivalent circuit (b) and corresponding voltage-charge plot (c).

Figure 3 .
Figure 3. Ctot as function of pressure (a) comparing Cu foil and Ag film as high voltage electrodes for different gas ratios Ar:CO 2 in R1; (b) V-Q plots (averaged over 512 samples); (c) adapted equivalent circuit.

Figure 4 .
Figure 4. Side view of plasma in pure Ar showing the expansion due to edge effects: (a) at atmospheric pressure, (b) at 2.5 bar.(c) Schematic illustrating the extended capacitance due to edge effect and discharge expansion outside the tube.

Figure 5 .
Figure 5. Side view of the reactor operating in a mixture of Ar:CO 2 (4:1): (a) at atmospheric pressure, (b) at 2.5 bar, and (c) in pure CO 2 at atmospheric pressure.

Figure 6 .
Figure 6.Ctot as function of pressure comparing different reactor stages R1, R2, and R3 (a).(b) Photo of R2 (silicone rubber around the high voltage electrode) and (c) schematic representation of reactor's cross-section with electric field lines.

Figure 7 .
Figure 7. Discharge power for stage R1 in pure Ar, pressure ranges from atmospheric pressure to 2.5 bar.
a) presents ζ diel obtained in R3 with glass beads for a mixture of Ar:CO 2 (4:1) at 2 and 2.5 bar.The parasitic capacitance of 3.4 pF has been subtracted from the values extracted from the active phase of the V-Q plots.Also in the PB-DBDs the effective dielectric capacitance increases with the voltage amplitude and saturates at values

Figure 10 .
Figure 10.(a) Adapted equivalent circuit and (b) V-Q plot considering partial surface discharging.

Figure 11 .
Figure 11.(a) Effective capacitance in R2, taking into account Cp, at various pressures in Ar:CO 2 = 1:1 with corresponding end-on view photos (b).
) and (b) present ζ diel vs. amplitude for the configuration R3 filled with beads made of Al 2 O 3 and ZrO 2 for two gas mixtures Ar:CO 2 (4:1 and 1:4) at atmospheric pressure and 2 bar, respectively.Figure 16(c) shows the corresponding end-on view photos of the highest effective capacitance with different packing materials.Similar to the procedure used for glass beads, ζ diel values are derived by subtracting the parasitic capacitance of reactor

Figure 12 .
Figure 12.Effective capacitance in R2, taking into account Cp, at various pressures in Ar:CO 2 mixture (1:4), (b) corresponding end-on view photos of the reactor.

Figure 13 .
Figure 13.(a) V-Q plots obtained for different reactor configurations (averaged acquisition of signals) (b) comparison of Ctot for different packing materials.

Figure 17 .
Figure 17.Electric field lines in (a) empty DBD arrangement, (b) Al 2 O 3 and (c) ZrO 2 PB-DBD.Note that the cross section through the middle of the bead is presented.

Figure 18 .
Figure 18.Possible microdischarge locations in the packed bed (a), (c) the equivalent circuit for an arrangement with n beads as sketched (b).

Figure 20 (
Figure20(a) displays the discharge power at atmospheric pressure for Al 2 O 3 and ZrO 2 with two gas mixtures, Ar:CO 2 (4:1) and (1:4).The power always increases with the voltage amplitude steadily.The pressure and the CO 2 fraction increase the voltage threshold.For the same gas and pressure, the higher the relative permittivity of the bed material the lower

Figure 22 .
Figure 22.(a) Current measured over 3.5 high voltage periods for powers between 32 and 40 mW in R2 and R3 filled with beads made of glass, Al 2 O 3 and ZrO 2 (for Ar:CO 2 = 4:1 at 2 bar).(b) V-Q plots acquired as high resolution individual samples for powers between 22 and 40 mW in R2 and R3 filled with beads made of glass, Al 2 O 3 and ZrO 2 (for Ar:CO 2 = 4:1 at 2 bar).
2 O 3 , ZrO 2 /CeO 2 voltage electrodes in different gas mixtures at different pressures are available in the supplementary material.Figure 4(a)

Table 3 .
Parasitic capacities determined from similar studies and in this work.