# Influence of the dielectric thickness on the homogeneity of a diffuse dielectric barrier discharge in air

Antoine Belinger, Simon Dap, Nicolas Naudé

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Antoine Belinger, Simon Dap, Nicolas Naudé. Influence of the dielectric thickness on the homogeneity of a diffuse dielectric barrier discharge in air. Journal of Physics D: Applied Physics, 2022, 55 (46), pp.465201. 10.1088/1361-6463/ac9067. hal-03789351

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Submitted on 9 Feb 2026

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# Influence of the dielectric thickness on the homogeneity of a Diffuse Dielectric Barrier Discharge in air

Antoine Belinger¹, Simon Dap¹, Nicolas Naudé¹

¹ LAPLACE, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France

## Abstract

This work focuses on a diffuse Dielectric Barrier Discharge (DBD) in atmospheric pressure air using an original experimental approach. In air, the role of the capacitance on the discharge regime has not yet been studied even though it affects the discharge current. To address this gap in knowledge, the dielectric capacitance was modified by the means of the dielectric thickness in a plane-to-plane DBD configuration. The discharge regime was analyzed using short exposure time photographs and electrical measurements in order to remove any potential uncertainties regarding the diffuse nature of the DBD in atmospheric pressure air. The influence of the dielectric capacitance on the discharge regime was analyzed thanks to the working domain of the discharge. Additionally, using an original electrical model of the discharge, the effective surface and current density of the discharge was obtained only from electrical measurements. Thus, the crucial role of the maximum current density on the discharge regime was highlighted. The control of the current density by the means of the dielectric capacitance led to the obtention of a diffuse discharge at a frequency up to 5 kHz for the very first time. Considering this high frequency, the possibility of using a DBD in air at atmospheric pressure for coating applications is discussed.

## 1. Introduction

The Dielectric Barrier Discharge is an easy and robust way to obtain a cold plasma at atmospheric pressure [1,2]. The types of discharge produced by this device are generally made of multiple microdischarges or filaments independent from one another [3,4]. They have a very short lifetime (1-10 ns) and are randomly distributed throughout the volume of the discharge. The energy transferred to the discharge lacks uniformity and is thus not optimal, representing a major obstacle to the use of DBD for many applications, such as plasma coating or surface treatment. It is possible however to obtain a diffuse discharge, although this outstanding event is only observable under restricted conditions. The diffuse discharge is commonly the consequence of a memory effect resulting from previous discharges, producing seed electrons before the ignition of the discharge [5].

Diffuse discharges are divided in two types: the atmospheric pressure glow discharge (APGD) [6-8] and the atmospheric pressure Townsend discharge (APTD) [9-11]. The APGD is obtained in noble gases with a penning mixture, for example, Ar + NH₃ or He + impurities of N₂. The penning mixture enables the production of electrons by Penning ionization before the ignition of the discharge [12]. This Penning ionization is possible thanks to long lifetime metastable atoms produced by the former discharge. The APTD was first obtained in nitrogen, where the ionization level is too low to form the cathode fall [2]. The electric field is roughly constant, and the gas gap voltage is similar to the Townsend plateau value. The reason for the homogeneity of the APTD is well described, and is attributed to a memory effect from one discharge to the next. Indeed, the first discharges are filamentary, and several cycles are necessary to reach a perfectly homogeneous discharge [5]. In nitrogen, the long lifetime metastable molecules N₂(A³Σ⁺u) act as an important energy reservoir and thus play multiple important roles in the operation
of the discharge. For example, their diffusion towards the surfaces leads to the production of electrons by secondary emission [13]. Measurements of N₂(A³Σ⁺u) density and quenching rate by Laser-Induced Fluorescence [13,14] confirm that a significant amount of N₂(A³Σ⁺u) remains between two discharges. With the addition of a N₂(A³Σ⁺u) quencher, such as NH₃ or O₂, the discharge stays filamentary, confirming the key role played by N₂(A³Σ⁺u) molecules [15,16]. Surprisingly, the addition of a small quantity of oxidizing species (few ppm) leads to an increase of the memory effect. Tyl *et al.* and Lin *et al.* show that the enforcement of the memory effect in N₂/NO and N₂/O₂ mixtures is certainly due to associative ionization reactions [17,18]. Unfortunately, this memory effect drops above a threshold of 50-100 pm oxidizing species. The addition of oxidizing gases induces a serious decrease of the N₂(A³Σ⁺u) density, so that 500 ppm of O₂ is enough to cause the transition from a homogeneous to a filamentary discharge. In air, the N₂(A³Σ⁺u) concentration is very low, hence several years ago it was commonly accepted that obtaining a diffuse discharge in air is impossible, as reported for example by Mirlaï *et al.* [19]. The ambiguity of the terms "diffuse" and "homogeneous" in the literature seems to add confusion about the diffuse character of a DBD in air. For example, while Råhel' *et al.* claim to obtain a diffuse discharge in air, the image of this paper appears to be acquired with an exposure time of 1 s [20]. More recent studies suggest the existence of diffuse discharges in air [21,22], however electrical waveforms are similar to those observed in filamentary discharges. In addition, here again the long exposure time of the photography makes it difficult to conclude as to the diffuse character of the discharge. Indeed, as described by Fang *et al.* [22], a discharge constituted by a superimposition of many micro-discharges can be seen as "diffuse" with the naked eye. Thus, a single image accumulated on several periods cannot be considered a demonstration of the diffuse character of the discharge. The authors use the term "diffuse discharge" to describe a discharge exempt from any plasma filament or microdischarge (and resulting from a Townsend breakdown). The term "homogeneous" is used as a synonym for "uniform". Thus, a diffuse discharge can be non-homogeneous.

It is nevertheless possible to obtain a diffuse DBD in air as reported in [23–32]. In 2011, Osawa *et al.* showed for the first time the existence of a APTD discharge in air at low frequency (until 1 kHz) [23]. The electrical waveform suggests a diffuse discharge, the image of the discharge being unfortunately taken with a regular camera. One year later in [24], Osawa *et al.* clearly demonstrated the discharge’s homogeneity with an image acquired with a ICCD camera using an exposure time equal to a half cycle. They showed the feasibility of an APTD in air until 1.7 bar [25], while Li *et al.* presented a homogeneous DBD in a multilayer DBD [26]. Garamoon *et al* showed that the use of porous alumina helped obtaining an APTD, suggesting an important role of the dielectric surfaces [27]. This was later confirmed by Luo *et al.*, who studied the influence of the dielectric material on the discharge uniformity [28]. More recently, Ran *et al.* suggested that the roughness of the dielectric was a crucial factor to obtain a homogeneous DBD in air [29,30]. They showed that the use of a smooth ceramic was detrimental for a homogenous discharge. Similarly, Choi *et al.* studied the influence of the surface resistivity on the uniformity of the discharge powered by a pulsed voltage [31]. Up to now, no additional studies are available on this topic. We can gather from the literature that the impact of the surfaces on the memory effect is the main subject around the APTD obtained in air, where the density of N₂(A³Σ⁺u) is too low to sustain a memory effect [14,16]. Until today, no volume mechanism was evidenced in the literature to suspect a volume memory effect in air. Recent studies [33,34] suggest that negative ions could produce enough seed electrons to obtain a Townsend breakdown in other gases. There is no proof however of their involvement on the memory effect observed in air. Currently, the main hypothesis of the memory effect comes from a historical paper of Golubovskii *et al.* [35]. He demonstrated, using a model working in nitrogen, that the desorption of electrons from the surface could be sufficient to obtain a Townsend breakdown, and thus a Townsend discharge. Similarly, Luo *et al.* [32] suggested that the Townsend character of the discharge obtained in air, results from electrons stored in the shallow traps of the dielectric surfaces, which they were the first to quantify. They observed a homogeneous discharge only with materials capable of storing a large amount of charges.
We can note that the production of seed electrons is *sine qua non*, but not the only requirement for obtaining a diffuse discharge. It is also important to prevent the transition of electron avalanches to the streamer, which can be achieved by limiting the discharge current [2,5], mainly through limiting the variation of the applied voltage *i.e.* the applied voltage or the frequency. However, this option limits the power transferred to the discharge.

<figure><img src="image_2.png" /><figcaption>Figure 1: Experimental set-up</figcaption></figure>

A more efficient way to limit the current is to power the DBD using a current power supply [36,37]. The idea is to limit the current of the discharge while increasing the power. In this paper we present an alternative approach to reach the same goal, which relies on changing the capacitance of the dielectrics covering the electrodes.

The first part of the paper is dedicated to a clear demonstration of the possibility of obtaining a Townsend discharge in air, thus solving a historical controversy within the community. The diffuse regime is accurately characterized by the means of electrical measurements and ICCD imaging synchronized with the power supply. The influence of the dielectric capacitance on the discharge behavior is studied by varying the dielectric thickness. In a second part, a fine analysis of the working domains of the APTD, together with a study of the discharge area, highlight the crucial role of the current density on the DBD homogeneity. Finally, the impact of the dielectric thickness on the power dissipated in the discharge is discussed.

## 2. Materials and methods

The plane-to-plane Dielectric Barrier Discharge (DBD) was placed in a closed vessel to perform experiments in a controlled atmosphere. The vessel was pumped down to $10^{-3}$ mbar prior to any experiment. It was then filled up to atmospheric pressure using synthetic air (Alphagaz 1 from Air Liquide). In order to renew the atmosphere, a gas flow (1 slm) was injected from one side of the discharge (longitudinal gas injection, x-axis), keeping a constant pressure through a gentle pumping of the vessel. The experimental setup is presented in Figure 1. The discharge was ignited between two square electrodes ($A_e=3$ cm $\times$ 3 cm) made of silver paint deposited on alumina plate dielectric from KYOCERA (96% $Al_2O_3$, $115 \times 70$ mm$^2$, relative permittivity of $\epsilon_r=9.6$). Two glass wedges steered the flow between the electrodes and enabled to have a constant 1 mm gas gap along the discharge. The gas flow inlet consisted of a slit with the same size of the transverse section as the DBD (1 mm $\times$ 3 cm) located 3 cm before the beginning of the electrode to ensure a stable longitudinal gas flow from the entrance of the discharge.

A sinusoidal power supply was used to power the DBD. Its frequency and amplitude were adjusted by a low voltage waveform generator (AGILENT 33210A) before being amplified by a power amplifier (Crest Audio 8001). The output of the power amplifier was applied to the primary winding of a step-up transformer in series with a 4 Ω resistance in order to match the impedance of the power amplifier. The DBD was connected to the secondary winding in series with a shunt resistor of 100 Ω, helping the current measurement of the DBD. The DBD voltage
(V_a) was measured with a high voltage probe (Tektronix P6015A). The current and voltage of the DBD were then recorded by means of a 1 GHz oscilloscope – 10 bits (Rohde and Schwarz – RTA 4004). Each electrical measurement included between 2 and 4 periods of the signal with a maximum of 200 000 samples. Depending on the signal’s frequency, the number of recorded periods and the sampling rate of the oscilloscope, the sampling time was in between 16 and 64 ns. The discharge current I_g and the gas voltage V_g were calculated from an electrical model of the discharge presented in [38].

Short-exposure time photographs were taken with an intensified CCD camera (PI-MAX-3, Princeton Instruments) synchronized with the power supply and equipped with a visible lens (Nikkon NIKKOR 50 mm f/1.2). As shown in Figure 1, the images presented in this paper were taken either perpendicular to the flow direction (position 1) or in the gas flow direction (position 2). For this last configuration, a thin quartz wedge was used facing the camera in order not to distort the image.

<figure><img src="image_3.png" /><figcaption>Figure 2: Example of a picture of a discharge taken during the negative half-period) of the applied voltage (f=3kHz) with the camera in position 2</figcaption></figure>

The DBD configuration presented in Figure 1 enabled to keep the gas capacitance C_g constant while adjusting the equivalent capacitance of the dielectric C_ds by the means of the thickness of the dielectric (d) as reminded below:

$$C_{ds} = \frac{\varepsilon_0 \cdot \varepsilon_r \cdot A_e}{2 \cdot d} \qquad \text{Eq. 1}$$

where A_e is the area of the electrode, ε_0 the vacuum permittivity and ε_r the relative permittivity of the dielectric plates. We used two kinds of dielectric plates with thicknesses of d= 1.016 mm and d= 1.27 mm respectively.

A specificity of this study concerns the location of the discharge. Under certain conditions, the discharge was ignited mainly on a reduced area as we can see in Figure 2. From this image it could be possible to have a rough estimation of the discharge area by cross section analysis.

We also used an original method to quantify the discharge area. It is based on the electrical model presented in [39] and adapted to a discharge, which does not fill the total area of the electrodes as presented in [40]. The main advantage of this method is the possibility to determine the discharge area only from electrical measurements. It enables the estimation of the current density with only one measurement, while other methods rely on both electrical and optical measurements, the synchronization between which is not always easy to achieve.

As for other electrical methods [41], this method is based on the calculation of the capacitance of the DBD. The equivalent model is presented in Figure 3. The black part represents the parasitic elements due to the wire, the connection and so forth. The values of the different parameters were determined with an open circuit test, i.e. when the discharge was turned-off. We found R_p = 300 MΩ and C_p=1.6 pF.

The DBD cell is divided in two parts: the red one and the blue one. In both parts C_ds is the total dielectric capacitance and C_g the gas capacitance. The blue part takes into account the effective area of the discharge A_d. The red part represents the area of the electrode where the discharge is extinguished. For this reason, one can define a coefficient K = A_d/A_e as the ratio of the discharge area A_d over the electrode area A_e with K ∈ [0,1]. When the discharge covers the full electrode (K=1), the red part of the circuit disappears.

The measured current can be expressed as:

$$I_a = I_p + I_{o-d} + I_g \qquad \text{Eq. 2}$$

If we disregard the current through the parasitic resistance, the measured current is equal to:
$$ I_a = C_p \cdot \frac{dV_a}{dt} + (1 - K) \cdot \frac{C_{ds} \cdot C_g}{C_{ds} + C_g} \cdot \frac{\frac{dV_a}{dt} + K \cdot C_{ds}}{\frac{d(V_a - V_g)}{dt}} \quad \text{Eq. 3} $$

<figure><img src="image_4.png" /><figcaption>Figure 3 : Electrical model of the DBD</figcaption></figure>

When the discharge is ignited and if the gas voltage $V_g$ is almost constant (which is a good approximation for an established Townsend discharge), then:

$$ I_a \approx C_{eq} \cdot \frac{dV_a}{dt} \quad \text{Eq. 4} $$

where the equivalent capacitance $C_{eq}$ is equal to:

$$ C_{eq} = C_p + (1 - K) \cdot \frac{C_{ds} \cdot C_g}{C_{ds} + C_g} + K \cdot C_{ds} \quad \text{Eq. 5} $$

When the discharge is ignited, i.e. $V_g$ is almost constant, the measured current $I_a$ is proportional to the time derivative of the applied voltage $dV_a/dt$ as shown by Eq. 4. A fitting procedure was then used to find the value of $C_{eq}$ (and thus the discharge area) providing the best agreement between the measured current (black curve) and the calculated current (purple curve), as illustrated by Figure 4. The light purple zone is the validity zone of the fit i.e. when the gas voltage $V_g$ is almost constant.

<figure><img src="image_5.png" /><figcaption>Figure 4 : Measured current, gas voltage and derivative of the applied voltage smoothed with moving average (100 points) for two values of $C_{eq}$ (f= 4kHz, V= 12 kVpp)</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Figure 5: Diffuse discharge in air at f=2 kHz and V=13.8 kVpp. a) Electrical waveforms (measured and discharge currents, gas and applied voltage) compared with the luminous intensity extracted from imaging. b) Imaging with camera in position 1. Images (+) an (−) correspond to the positive and negative half-period (exposure time = 250 µs, without accumulation). Images (1) to (6) correspond to the times indicated in a) (exposure time = 250 ns, 1000 ICCD accumulations)</figcaption></figure>

For comparison, a calculation of the current was performed considering that the discharge covered the full electrode area ($K=1$). The corresponding curve is the orange one. The fitting coefficient was then equal to the geometric capacitance $C_{eq}=32$ pF. We can clearly see that there is no matching with the experimental current $I_a$ (black curve), whereas a fairly good agreement was obtained considering $C_{eq}'=23.5$ pF (purple curve) corresponding to $K=0.66$. This example shows the need to take into account the area that is actually covered by the discharge in the electrical model of the DBD, as presented in Figure 3. Importantly, this approach is only valid for Townsend discharges. Indeed, gas voltage must be constant during the discharge to be able to determine the discharge area using the fitting procedure.

As described earlier, this method requires to calculate the time derivative of the applied voltage $V_a$. It is then mandatory to smooth the electrical signal to make a proper analysis. We chose to smooth the signal with a moving average filter between 50 and 150 points to minimize the noise and avoid signal distortion.

The determination of the fitting coefficient $C_{eq}$ depended both on the smoothing procedure of the electrical measurement and on the part of the signal considered for the analysis (previously defined as the validity zone). When the current and the discharge duration were low, as in Figure 4, this method was very sensitive to the choice of the two aforementioned parameters. It resulted in an important uncertainty in the evaluation of the discharge area. For this reason, several fitting procedures were performed for each experimental measurement taking into account a wide range of conditions (number of points for the moving average, several experimental signals). The uncertainty related to the determination of $K$ was then estimated to be in the range 20 - 40%, which was sufficient for providing a tendency of the area evolution.

### 3. Results

#### 1. Analysis of the discharge regime
The main features of a typical discharge in air powered by a sinusoidal voltage (f=2 kHz, V=13.8 kVpp) are presented in Figure 5. The electrical characteristics are presented in Figure 5.a, while short ICCD images taken perpendicular to the gas flow direction (position 1) are presented in Figure 5.b. The two first images (noted + and -) were respectively acquired on the positive and negative polarities with an exposure time equal to the half period and without accumulation. The discharge appeared diffuse, covering the whole electrode. The bright region was always located on side of the anode, and no filament was observed. The images 1 to 6 were acquired with a shorter exposure time (250 ns) to display the development of the discharge for each polarity. For these short exposure times, we used 1000 CCD accumulations to increase the signal-to-noise ratio. This high number of accumulations was required given the very low brightness of the discharge. The effect of the accumulations on the image morphology has been experimentally verified: it only affected the light intensity and, therefore, the signal-to-noise ratio. It illustrates the stability of the discharge in time and the reproducibility of the optical measurements. Moreover, the partial covering of the electrode in image 4 confirms a good reproducibility of the discharge.

Images 1 to 3 correspond to the measurements on the negative half-period of the applied voltage and images 4 to 6 to the positive half-period. The discharge did not cover the whole electrode at the beginning of the ignition (images 1 and 4), while it fully covered it after few micro-seconds. At the current peak (images 2 and 5) the light emitted by the discharge was maximal and decreased afterwards (images 3 and 6). These six images are representative samples from a record of 2000 images, which was used to quantify the light emitted by the discharge during the whole period. The intensities of all the pixels located from the midway of the gap to the anode were added. According to images in Figure 5.b, the discharge was less luminous during the negative half-period. This effect was due to a slight horizontal misalignment of the ICCD camera with the cell discharge. That is why the evolution was normalized for each half-cycle to unity and plotted in Figure 5.a (blue dotted line). When the discharge turned on, the light increased slowly with the current. No light was present between the two discharges. The luminous intensity followed the evolution of the discharge current ($I_d$). The current clearly showed one large peak for each half period and no series of many narrow peaks typical of filamentary discharges. No filament was observed in the large number of pictures taken during the experiment. All these arguments lead to the conclusion that the discharge is purely diffuse. Whether the discharge is Townsend or glow still remains to be addressed at this point.

During each half cycle, from ignition to extinction, the light was always located close to the anode and the gas voltage of the discharge was almost constant during the discharge. The discharge observed in air was thus very similar to the APTD discharge observed in nitrogen [9]. To confirm the Townsend character of the discharge, we plotted the global distribution of the light across the gap (Z-axis), as presented in Figure 6. To realize this intensity profile, all the pixels in the Y direction were integrated (camera in position 1). We noted an exponential growth of the light from the cathode to the anode as indicated by the red fit curve. In air at atmospheric pressure, and close to ambient temperature, the light is mainly emitted by the $N_2$ second positive system, which is dominantly exited by direct electron impact from the ground state [42]. It is thus reasonable to consider that the light is directly proportional to the electron density $n_e$. Accordingly, the electron density grew exponentially from the cathode to the anode, in perfect agreement with the typical electron density profile of a Townsend discharge [43,44]. The related alpha coefficient of Paschen was estimated to be 41 cm⁻¹. As a result, one electron produced by secondary emission at the cathode produced 41 electrons while traveling to the anode.
<figure><img src="image_7.png" /><figcaption>Figure 6: Light intensity evolution between the cathode and the anode on the image noted + in Figure 5.b.</figcaption></figure>

This value of alpha corresponds to an electric field of 153 Td calculated from Bolsig+ [45] with the IST-Lisbon database [46]. Considering a constant electric field across the gap (typical of Townsend discharges), the corresponding gas voltage is $V_g=3.8kV$, which is close to the gas voltage observed experimentally (see Figure 5.a). In summary, the diffuse discharge obtained in air was a Townsend discharge similar to the APTD obtained in nitrogen.

## 2 Working domains and discharge ignition

A Townsend discharge was successfully obtained in air with the two dielectrics used in this study. However, the diffuse / filamentary nature of the discharge is dependent on the excitation conditions, i.e. the frequency and the amplitude of the sinusoidal voltage applied. The conditions leading to the Townsend discharge are illustrated by an amplitude vs frequency plot in

Figure 7. The maximum voltage applied, for which the discharge remained in APTD, is plotted as a function of the excitation frequency for two different dielectric thicknesses. Throughout the following paragraphs, the area under the curve is referred to as the (diffuse) working domain (WD) of the discharge. For each measure, the frequency was fixed and the voltage was progressively increased until the transition to the filamentary discharge. The transition between the two modes was however not always obvious. For example, some filaments could appear from time to time (few events per minutes) very close to the limit. For this reason, we considered a colored space around the experimental points to indicate that the discharge was mainly diffuse, but some filaments could exceptionally appear.
<figure><img src="image_8.png" /><figcaption>Figure 7: Working domain of the DBD in air for two dielectric thicknesses.</figcaption></figure>

The maximum voltage applied in this experiment was fixed at 22 $kV_{pp}$ in order to protect the device from parasitic discharges outside the electrode zone (connecting wire, insulated connector, transformer, ...). This voltage limitation corresponds to the first part of the WD (horizontal line at 22 $kV_{pp}$) after being referred as the voltage-limited zone. An increase of the dielectric thickness enabled work in a Townsend mode at a higher frequency for a given applied voltage, as shown in

Figure 7. To the best of our knowledge, it is the first time that an APTD at 5.1kHz is reported. Indeed, up to now the higher frequency reported for an APTD in air was 1.5 kHz [30].

A DBD is a capacitive dipole from an electrical point of view. Consequently, at a given voltage, an increase of the frequency increases the current and then the ionization rate within the discharge. Thus, to avoid the transition to the filamentary regime, the applied voltage had to be decreased, as shown in

Figure 7. This decrease was first linear. To illustrate this, two linear curves were plotted for each dielectrics thickness. These curves are located after the last point of the maximum voltage limitation, for $d=1.016$ mm it corresponds to the frequency of 1.2 kHz, and 1.8 kHz for $d=1.27$ mm. For higher frequencies, a flattening of the WD boundary was observed. In the following paragraphs, these two regions are respectively referred to as the linear zone and the flat zone.

To understand the difference between these two zones, we have to focus on the applied voltage at the ignition of the discharge. Figure 8 shows the evolution of the applied voltage $V_a$ and the discharge current $I_d$ for two points of the WD boundary with excitation frequencies of 1800 Hz (linear zone, blue curves) and 4700 Hz (flat zone, red curves). The dielectric thickness was $d=1.27$ mm. The x-axis represents the normalized period to have a direct comparison between both conditions.

As a rule of thumb for a DBD, the discharge turns-off when the applied voltage reaches its maximum value, whereas the ignition of the discharge can be observed on the current growth and when the gas voltage $V_g$ is equal to the breakdown voltage.

In the linear zone (blue curve), the ignition always occurred when the applied voltage was close to zero, as shown by the vertical blue line in Figure 8. The discharge was ignited during 27% of the period. In contrast, in the flat zone, the ignition occurred "later", i.e. when the applied voltage was close to its maximum value. The discharge only lasted during 11% of the period. For all the points located at the border of the working domain, the higher the frequency, the lower the maximum applied voltage. Consequently, as the frequency increased, the applied voltage grew closer and closer to its maximum value and the corresponding discharge duration was then shorter. This phenomenon went together with an evolution of the discharge area as presented in the following section.
<figure><img src="image_9.png" /></figure>

Figure 8: Evolution of the applied voltage $V_a$, gas voltage (dashed curves) and the discharge current $I_d$ versus the normalized period for two different frequencies $f= 1.8$ kHz (blue) and $f = 4.7$ kHz (red). Dielectric thickness is $d=1.27$ mm. The vertical grey curve indicates the extinction of both discharges, the blue one shows the ignition for $f=1.8$ kHz and the red one the ignition for $f=4.7$ kHz

<figure><img src="image_10.png" /></figure>

Figure 9: (a) Image of the positive half-period of the applied voltage (exposure time = 1/(2·f), 10 ccd accumulations, camera in position 2). The 3 images correspond to 3 working points at the limit of the WD for the 3 frequencies indicated in Figure 7. (b) Corresponding normalized intensity profiles.
<figure><img src="image_11.png" /><figcaption>Figure 10: Evaluation of the discharge area versus the frequency</figcaption></figure>

### 3 Evolution of the discharge area

The evolution of the discharge area with the excitation frequency is illustrated for $d=1.016$ mm in Figure 9, which shows images of the discharge along the flow direction (camera in position 2). These three pictures correspond to the points indicated in purple in

Figure 7 and Figure 10. Each image results from the accumulation of 10 positive half-periods of the applied voltage. In the first picture ($f=1.5$ kHz – $V_{pp}=18.5$ kV, linear zone), the discharge filled the whole electrode, while this was not true for the two other pictures ($f = 2.2$ kHz – $V_{pp}=13.7$ kV, flat zone) and ($f = 3$ kHz – $V_{pp}=12$ kV, flat zone). Thus, the length of the discharge decreased with the increase of the excitation frequency. Indeed, the discharge ignited later but also extinguished sooner.

To quantify the evolution of the discharge area, were used intensity profiles along the gas flow direction obtained by integration on the vertical axis from the middle of the gap to the anode for each horizontal position 2 (Figure 9-b). Then, each curve was normalized to unity.

The picture taken at $f=1.5$ kHz was used as the reference, since the discharge covered the whole electrode area: $K = A_d/A_e = 1$. For this condition, the electrode length corresponded to the luminous length, where the normalized intensity was above 30% of the maximal value. This value was used for the other conditions to determine K. Following this procedure, we obtained $K=0.8$ at $f= 2.2$ kHz and $K=0.75$ at $f= 3$ kHz.

The discharge area was also determined using the electrical approach developed in section 2 for each experimental point of the WD presented in

Figure 7. The corresponding results are presented in Figure 10 where the colored areas surrounding experimental points represent the standard deviation of the electrical method. The results provided by both methods are consistent.

Firstly, at low frequency i.e. in the voltage-limited zone and in the linear zone, the discharge approximately filled the whole electrodes. Secondly, in the flat zone and for both dielectrics, the discharge area decreased with the frequency until the worst case, where it occupied less than half of the electrode surface.

### 4 Evolution of the maximum current and current density of the discharge

Figure 11 represents the evolution of the maximum discharge current $I_{d-max}$ (a) and the maximum average discharge current density $J_{d-max}$ (b) for which a Townsend discharge was obtained (i.e. at the limit of the WD) versus the frequency.
<figure><img src="image_12.png" /><figcaption>Figure 11: Maximum discharge current (a) and average current density versus the frequency for the two dielectric thicknesses.</figcaption></figure>

In Figure 11 (a) the maximum discharge current $I_{d-max}$ increased when the voltage was limited at 22kVpp (voltage-limited zone of the WD). It was then roughly constant and equal to 4 mA, in the linear zone of the working domain. The current decreased for the higher frequencies corresponding to the flat zone, which goes in hand with the discharge area reduction. This result is not surprising since it is well known that the discharge current must remain below a given value to work in APTD mode [5,47]. This is clearly illustrated in previous studies [36,37] using a current converter to impose a constant current in the discharge: above a given value of the current, the discharge turns into a filamentary one whatever the excitation frequency.

To get more insight into the decrease of $I_{d-max}$, we must look at the average current density at the limit of the working domain $J_{d-max}$. The latter was calculated using the values of $I_{d-max}$ and $K: J_{d-max} = \frac{I_{d-max}}{K \times A_e}$. The corresponding results are presented Figure 11 (b), where the colored areas represent the standard deviation. Except when the voltage was limited by the power supply (voltage-limited area) where it followed the evolution of $I_{d-max}$, $J_{d-max}$ was mostly constant and nearly equal to 0.4 mA.cm$^{-2}$ for the two dielectric thicknesses. The observed decrease of $I_{d-max}$ could thus be attributed to the decrease of the discharge area. Interestingly, the same order of magnitude of the very maximum average current density (0.4 mA.cm$^{-2}$) was obtained for DBD working in Townsend mode in nitrogen [5,15].

## 5 Discharge development

The discharge was not ignited on the whole electrode, as observed in Figure 5 (b). Moreover, the discharge was not completely homogeneous, as shown in Figure 9. Even when it covered the whole electrode (f=1.5 kHz) a deviation of almost 20 % was observed. The discharge was then a diffuse APTD, with certainly some local differences. In order to understand this non-uniformity, we focused on the discharge ignition.
<figure><img src="image_13.png" /><figcaption>Figure 12: Horizontal cross sections calculated from images presented in Figure 5 (camera in position 1)</figcaption></figure>

To study the development of the discharge carefully, the beginning of the ignition for the positive half cycle, when the current started to grow i.e. between 274 and 282 µs, was considered. For each horizontal position (y direction), the intensity of the vertical pixels (Z) between the middle of the gap and the anode were summed. A smoothing filter was applied to each curve for noise reduction. The corresponding results are presented in Figure 12. The discharge was always ignited first in the left part of the electrode represented by the blue background (t=274 µs and t = 275 µs) before spreading on the whole surface of the electrode. When the maximum intensity was reached at this position (276 µs), the applied voltage continued to grow, the current increased (see Figure 5), and the discharge spread on the full electrode surface.

The zone with the green background on the right side of the electrode reached the maximal value of the light emission at t = 279/280 µs.

<figure><img src="image_14.png" /><figcaption>Figure 13: Evolution of the light on the left and right part of the discharge</figcaption></figure>

To study the discharge spreading, let us now focus on the time evolution of the electrode's left (blue) and right (green) zones. For this purpose, the intensities of the pixels contained in these zones were summed at each time, and then normalized to unity, as shown in Figure 13.
The same procedure was applied for both half-periods of the applied voltage, and the absolute value of the discharge current was added for comparison (red curve). It helps to determine the time delay in the ignition of the discharge between the right and the left zones of the electrodes. Indeed, for both half-periods, the discharge ignited 2 µs before in the left part. Then, it shows that the electron avalanche was not uniform along the dielectric surface and whatever the polarity, it systematically started earlier on the left part of the discharge.

At "steady state" i.e., when the discharge was fully established, the intensity of the light emitted in the left part was higher than in the right part by approximately 20%. Although the ICCD sensor response could be not fully uniform, such a discrepancy is too large to be solely due to the sensor. The same observation can be made in Figure 5 and Figure 9. Overall, the discharge was not fully homogeneous (i.e. non uniform) while at the same time it was obviously diffuse.

## 4. Discussion

Major findings of this studies are summarized below. In air a non-uniform Townsend DBD was observed in this manuscript. The ignition of the discharge was also non uniform. For higher frequency, the discharge covered only a part of the electrode. We also observed that the dielectric capacitance changed the working domain area, while keeping the maximum value of the average current density constant.

Interestingly, these phenomena are directly linked, as discussed below. The working domain (WD) of the air DBD was composed of three different zones (see

Figure 7): the voltage-limited zone, the linear zone, and the flat zone. The voltage-limited zone was unable to provide information on the transition between the filamentary and diffuse discharges. For both other zones, the average current density at the boundary of the domain $J_{d-max}$ was constant and equal to 0.4 mA/cm² for the two dielectric thicknesses studied (Figure 11). The transition between the diffuse and filamentary discharges was thus strongly related to this average current density limitation, whether in the linear or the flat zone.

According to the Meek criterion, streamer breakdown leading to filamentary discharges occurs when the electron multiplication factor exceeds a given value (generally around 18-20 [43]). In an APTD, the electric field is nearly constant across the gas gap. Since the gas voltage $V_g$ was roughly the same regardless of the experimental conditions, the current density can be considered as a good picture of the electron multiplication factor. The observed average current density limitation at the boundary of the WD was thus probably related to the Meek criterion: a moderate ionization rate was necessary to obtain a Townsend breakdown. This was true regardless of the dielectric capacitance and whether in the flat or in the linear zone.

According to the electrical model presented above, the discharge current is given by:

$$ 
\begin{aligned}
I_d = C_{ds} \cdot \frac{dV_{ds}}{dt} & - C_g \cdot \frac{dV_g}{dt} \\
& = C_{ds} \cdot \frac{d(V_a - V_g)}{dt} \\
& - C_g \cdot \frac{dV_g}{dt}
\end{aligned}
\qquad \text{Eq. 6}
$$

During the Townsend discharge ($V_g \approx constant$), Eq.6 becomes:

$$ I_d = C_{ds} \cdot \frac{dV_a}{dt} \qquad \text{Eq. 7} $$

Thus, the discharge current density can be expressed as:

$$ J_d = \left. \frac{C_{ds} \cdot dV_a}{A_d \cdot dt} \right|_{\text{Ignition}} \qquad \text{Eq. 8} $$

where $A_d$ is the discharge area and $\left. \frac{dV_a}{dt} \right|_{\text{Ignition}}$ is the time derivative of the applied voltage when the discharge was ignited, and the gas voltage was almost constant.
Eq.8 indicates that reducing the dielectric capacitance $C_{ds}$ decreases $J_d$, helping the DBD to work in APTD mode at higher frequency and/or higher voltage. Thus, the working domain observed in

Figure 7 for $d=1.27$ mm was wider. In other words, the modification of $C_{ds}$ enables to slow down the ionization rate. As a result, in the flat zone i.e. for the highest frequencies, the discharge ignited later and later, leading to two major consequences (see Figure 8). First, $\frac{dV_a}{dt}|_{Ignition}$ was lower, leading to the resulting current density remaining below the limit of 0.4 mA/cm$^2$. In addition, the discharge duration was lower.

An originality of the diffuse DBD in air is the reduction of the discharge area on the flat zone of the WD: the higher the frequency, the lower the area of the electrode occupied by the discharge (see Figure 10). This area reduction can be related to the memory effect. As reminded in the introduction, a memory effect able to release seed electrons between two discharges is necessary for a Townsend breakdown. For the sake of argument and according to the literature [27,32,35], the memory effect in our conditions is mainly due to surface processes such as spontaneous electron desorption. Let us now consider two different locations, such as the green and blue parts in Figure 12 and Figure 13. In the blue zone, the discharge ignited earlier. Moreover, when the discharge was fully developed, a higher light intensity was emitted suggesting a higher electron density in front of the anode. As a result, a larger amount of electrons was probably stored in the shallow traps of the dielectric. The polarity was reversed for the next half-period and the old anode become the new cathode. The larger number of trapped electrons in the blue region could therefore: 1. facilitate the breakdown which occurs earlier (i.e. for a lower voltage) because of a larger release of seed electrons, and 2. result in a higher discharge current. Consequently, a larger amount of electrons could be stored at the anode surface. The same process then repeated during the next half-periods resulting in the non-uniformity of the discharge in the stationary state, as observed experimentally in Figure 5 and Figure 9. This illustrates the high sensitivity of the discharge to the initial conditions during the ignition i.e. to the memory effect. The non-uniformity of the memory effect is even more true when we observe a reduction of the discharge area (i.e. at high frequencies). In this case, the discharge is barely ignited that it turns-off (Figure 8). The number of electrons stored onto the dielectric surface was likely too low because of the lower deposited charges due to the short duration of the discharge. It could even be insufficient at some locations to ignite the discharge under low electric field. The non-uniformity of the memory effect implies a reduction of the discharge.

There are some examples in the literature of diffuse discharges filling only a part of the electrode. They are often self-organized discharges [48,49] consisting of several filaments and static structures. These structures or domains extinguish at each half cycle, but tend to re-ignite at the same location because of the charge deposited onto the dielectrics [50]. Due to the gas flow, this behavior is less susceptible to occur when a significant volume memory effect exists. Thus, this is consistent with the initial assumption that the memory effect is mainly due to surface processes.
<figure><img src="image_15.png" /><figcaption>Figure 14: Evolution of the maximal value of the power transmitted to the discharge in Townsend regime.</figcaption></figure>

Previous studies on diffuse air DBD show a weak maximum frequency (above 1 kHz) [24,30,32], which implies a low power dissipation, representing a real drawback for the future applications of diffuse DBD in air. In this manuscript we successfully worked at a higher frequency by decreasing the value of the capacitance. It is then interesting to have a look on the discharge power. Figure 14 shows the evolution of the maximal value of the discharge power in Townsend regime as a function of the frequency for both dielectric thicknesses.

It was possible to transmit a higher power with a thicker dielectric when the voltage was not limited by the power supply *i.e.* above 1.2 or 2 kHz depending on the dielectrics thickness. Indeed, below these frequencies, the maximum discharge current was higher for the thinner dielectrics as shown in Figure 11. In both cases, the maximum power was obtained for the point at the boundary between the voltage-limited zone and the linear zone of their respective WD. It was 4.5 W for d=1.016 mm and 5W for d=1.27 mm which corresponded to an increase of the dissipated power of 11%. These optimum values of the discharge power can be improved by increasing the maximum applied voltage, which requires a better insulation of the experimental setup. It is worth mentioning that the discharge covers the whole electrodes surface in these conditions of large deposited power.

The increase of the maximum discharge power and the WD of the Townsend regime with the dielectric thickness support the development of the diffuse DBD applications in air. For example, in coating applications, an increase of the power directly leads to the rise of the growth rate [51]. Here the power was almost 0.5 W/cm² which is close to the surface power generally reported in the literature for the first coating in nitrogen atmosphere [52,53]. Moreover, the increase of the WD enables to tune the operating parameters (applied voltage, frequency) in a wider range. It provides more flexibility in the process. However, this result should not be interpreted as the thicker the dielectric the better. Increasing the dielectric thickness also increases the resulting voltage across the dielectric thus requiring to increase the applied voltage to rather high values. A compromise is thus necessary to take benefit of a more stable discharge in a wider range of parameters and with a slightly higher dissipated power with reasonable applied voltage.

**5. Conclusion**

An Atmospheric Pressure Townsend Discharge (APTD) was generated in air at atmospheric pressure with a DBD powered by a sinusoidal voltage. This discharge was clearly diffuse but a non-uniformity was also observed.

Two discharge cells with two different dielectric thicknesses (1.016 and 1.27 mm) were used. The working domains - corresponding to the applied voltage and frequency ranges for which a Townsend regime is possible - were determined for both dielectric thicknesses.
An important result concerns the role of the dielectric thickness. Reducing the capacitance of the discharge make it possible to work at both higher frequency voltage. Indeed, an APTD was obtained up to 5 kHz with the thicker dielectric plates. Our work is the first report of a Townsend discharge in air for such a high frequency. In addition, higher dissipated powers were measured, together with the increase of the working domain with the dielectric thickness. The surface power density obtained in these conditions is on the same order of those observed in nitrogen APTD at the beginning of the 2000 s.

The boundary between the Townsend regime and the filamentary regime was characterized by a constant value of the maximum average current density about 0.4 mA/cm². This behavior is probably related to the well-known Meek criterion: the ionization rate within the discharge must remain sufficiently low to avoid streamer breakdown to occur.

Within the working domain, the discharge is diffuse, while the ignition is not always uniform over the whole surface of the electrodes. The non-uniformity of the ignition is certainly related to a non-uniformity of the memory effect and can implies in some case a reduction of the discharge area. To determine the discharge area, a new method was presented in this paper, which can be very useful for other DBD applications. It was found that the discharge covered the whole electrode surface only for the lower frequencies whereas at higher frequencies a diminution of the discharge area is observed. This phenomenon is similar to what is observed in self-organized DBDs and probably due to memory effects originating from the dielectric surfaces.

The possibility of generating diffuse DBD in air in a wide range of experimental conditions, and with reasonable discharge power, makes APTD a promising tool for the development of applications based on the use of DBD in air.

# 6. Acknowledgements

The authors would like to acknowledge financial support from Agence Nationale de la Recherche (DECAIR project: ANR-20-CE08-0014).

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