We investigated the dynamic interactions between electric fields and space charges within an axisymmetric dielectric barrier discharge (DBD) configuration. Employing a square-wave AC, the DBD setup ensured spatial and temporal consistency in microdischarge occurrences. The Electric Field Induced Second Harmonic Generation (EFISH) technique was utilized to capture electric fields and space charge distributions, with special emphasis on the theoretical deduction of space charges from Gauss’s Law. After a microdischarge occurred, the measured electric fields diminished due to the destructive superposition of external electric fields and th fields induced by space charges. This reduction in electric field intensity prevented subsequent microdischarges from occurring. However, when the polarity changed, our results demonstrated an increase in the electric fields due to constructive reinforcement between the external electric fields and the space-charge-induced electric field. This enhancement in the electric field facilitated the occurrence of subsequent microdischarges. Notably, a dominant excess of negative charges was observed in the negative phase after the microdischarge, indicating a net negative-charge domain likely due to electron emission from a metallic electrode. This study confirmed the effectiveness of the proposed method for estimating space charges by showcasing the inherent operating mechanism of DBD.
Article
Measuring space charge and electric field in axisymmetric dielectric barrier discharge using EFISH technique
https://doi.org/10.21203/rs.3.rs-4868782/v1
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Dielectric Barrier Discharge (DBD)
Microdischarges
Electric Field Induced Second Harmonic Generation (EFISH)
Space charge
Electric field
Since Siemens developed it in 1857, dielectric barrier discharge (DBD) has found diverse applications ranging from surface treatment1–3, light source4,5, and contamination control6–9 to advancements in plasma medicine10–12. The inherent advantages of DBD, such as a straightforward structure and versatile operation across a wide range of pressures and alternating current (AC) frequencies, have solidified its role in various fields. Notably, DBD’s capability has extended to fundamental research exploring its physical mechanisms and chemical kinetics using it, highlighting its dynamic nature and contributing valuable insights into plasma chemistry13.
In DBD, memory charges are known to play a crucial role in discharge dynamics. The memory charges, generated by preceding microdischarges, lower the instantaneous electric field, leading to the temporal and spatial variability of microdischarges. Specifically, they cause the intermittent occurrence of successive microdischarges at certain locations14 and contribute to a consistent distribution of microdischarges across the entire barrier surface15–20. The reversal of AC polarity causes the externally applied electric field and the field generated by memory charges to reinforce each other. This amplification of the electric field within a gas gap facilitates following microdischarges to occur at consistent locations in subsequent half-cycle, illustrating the memory effect15–20. Despite a reasonably stable voltage across the gas gap during a discharge period21–24, the memory effect influences the electric field, resulting in dynamic behavior in microdischarges.
Research on the charges in DBD has mainly focused on surface charges deposited on dielectric surfaces, both experimentally25–31 and numerically32–34, due to their importance on discharge dynamics. Although some numerical studies have explored the transient behaviors of memory charges within the discharge channel33, experimental investigations have mostly concentrated on measuring surface charges. These measurements typically employ the Pockels effect, utilizing optical crystals such as Bi12SiO20 or Bi4Ge3O12 as the dielectric barrier25. Experimental results using the Pockels effect have not only precisely captured the dynamic behavior of surface charges25–31 but have also clearly demonstrated the spatial memory effect, where microdischarge tend to occur at location previously enriched with surface charges from earlier microdischarges. The electrical potential across a gas gap could be also estimated by simultaneously measuring surface charges on dielectric barriers at both electrodes31. Despite this method's effectiveness in capturing surface charge dynamics, its application does not extend to measuring space charge distribution within the gas gap. Thus, a spatiotemporally resolved investigation of the dynamic characteristics of space charges and electric fields has remained largely unexplored.
A promising method for mapping the spatial distribution of space charges is the electric-field-induced second-harmonic generation (EFISH) technique—a laser-based approach for measuring electric fields35–44. EFISH operates on the principle of interaction between an incident laser beam and the electric field. Since the polarization of the generated second harmonic signal (SHS) depends on the direction of the electric field, the electric field vector could be successfully reconstructed by measuring each SHS along each unit vector in a two dimensional (2D) coordinate system38. Due to its high spatial and temporal resolution, the electric field measured via the EFISH technique can be transformed into a detailed map of space charge distribution using Gauss’s law41.
Therefore, this study aimed to investigate the dynamic interactions between electric fields and space charges in a gas gap inside DBD by adopting the EFISH technique alongside theoretical insights from Gauss’s law. We established a well-defined axisymmetric DBD setup, ensuring spatial and temporal consistency in microdischarge occurrences by employing a square-wave AC. Note that we did not apply the EFISH technique during the discharge due to the mismatch in physical dimensions between the laser and the discharge channel, as well as the time jitter associated with both the lasing process and the microdischarges.
Our analysis encompassed the electric field and space charge distribution both after and before microdischarges in each phase. The study targeted to verify a self-suppressed electric field due to microdischarge-generated space charges and to comprehend the role of memory charges in enhancing the externally applied electric field, thus facilitating following microdischarges with reversed AC polarity. The findings not only illuminated the inherent characteristics of DBD but also highlighted the significance of electron emission from bare metal electrode within this specific setup.
2.1. Experimental setup
The experimental setup consisted of a DBD section, a power supply system, and a laser diagnostic system as shown in Fig. 1. An axisymmetric configuration of electrodes was considered for a simple two-dimensional (2D) approach using cylindrical coordinates. A stainless steel rod (4-mm diamter), with a domed end, was used as an upper electrode, while a lower electrode (identical to the upper one) was embedded in a ceramic cylinder (a-Al2O3, dielectric constant = 9.8, 20-mm diamter), leaving a 2-mm thickness of ceramic along the symmetric axis (Fig. 4). A (gas) gap between the tip of the upper electrode and the ceramic surface was set at 3.5 mm. To minimize spatial jettering of repeated microdischarges, we employed the bare-metal upper electrode; thus, the roots of the microdischarges could be reasonabley maintained at the tip of the upper electrode (along the y-axis)14.
A combination of a voltage amplifier (Trek, 30/20A) and a function generator (NF, WF1973) applied a high voltage (Va) to the upper electrode, while the lower electrode inside the ceramic was grounded. To obtain Lissajous diagram (QV plot), both Va and Vm (the voltage across a monitoring capacitance, Cm = 470 nF) were monitored using an oscilloscope (Tektronix, DPO4104B) with two voltage probes (Tektronix, P6015A and TPP1000, respectively). All measurements were conducted in open-air conditions (20oC and relative humidity = 70%) under a ventilation hood.
2.2. Design of discharge conditions
To effectively measure the electric fields associated with microdischarges, ensuring the spatiotemporal consistency of these microdischarges is crucial. This consistency enabled spatially and temporally resolved measurements, achieved by accumulating and averaging data from reasonably reproducible microdischarges. As mentioned in the previous section, the spatial occurrence of the microdischarges was controlled by the geometrical configuration of the electrodes. Furthermore, to regulate the temporal occurrence of the microdischarges, a square-wave AC of 18 kVpp at 1 kHz was applied.
This approach with the square-wave effectively limited temporal jittering, thereby resolving the issue of many successive microdischarges in time, a challenge encountered with sinusoidal waves14. Figure 2 shows the waveforms of Va and Q (= CmVm), averaged over 256-cycle, with an expanded time axis that highlights the discharge moments for the positive (a) and negative phase (b). For convenience, the time axis is set so that zero corresponds to the moment of phase change (Va = 0). The square wave's sharp change in Va resulted in a narrow jittering band, approximately 5 and 12 µs for the first and second microdischarges in the positive phase, respectively, and around 3 µs for the microdischarge in the negative phase. These jittering bands were confirmed to be identical to the temporal distribution of microdischarges observed by current spikes14. There was a 2 kV overshoot in Va following the phase change. As shown in Fig. 2a, two successive microdischarges were consistently observed in the positive phase, while only a single microdischarge was identified in the negative phase as depicted in Fig. 2b. Figure 3 shows each of the discharge moments captured by the ICCD camera (Princeton instruments, PI-MAX4: 1024i). The three discharge images in Figs. 3a − c confirm that the microdischarge occurs along the axis of the DBD. In addition, a continuous negative corona discharge was observed in the negative phase, followed by the microdischarge, as shown in Fig. 3d. Overall waveforms of Va and Q and the corresponding QV plot were illustrated in Figs. S1 and S2 (Supplementary Information).
To track the temporal variations in the electric field and space charges due to the microdischarges, we selected specific temporal conditions for the EFISH measurement, focusing on periods before and after the microdischarge(s). The measurement points were divided into four categories: i) before the microdischarges in the positive phase (BP), ii) after the microdischarges in the positive phase (AP), iii) before the microdischarge in the negative phase (BN), and iv) after the microdischarge in the negative phase (AN). We designed the BP and BN to understand how memory charges from the preceding phase were redistributed spatially and how they enhanced the external electric field, facilitating the onset of following microdischarge. The AP and AN were studied to observe the decay of the electric field, anticipated to result from the screening effect of the newly generated space charges. Note that all measurement points were temporally separated from the discharge jittering bands by more than a few microseconds to avoid interference between the laser pulse (width of ~ 30 ps) and the discharge filaments. The jitter of the laser pulse was less than 1 µs. Further details and conditions are illustrated in Fig. 2 and summarized in Table 1.
|
Classification |
Cases |
Time before (tb) and after (ta) discharge band [µs] |
Instantaneous Va [kV] |
|
|---|---|---|---|---|
|
Before microdischarge in Positive phase (BP) |
BP-1 BP-2 BP-3 BP-4 |
tb = − 51 −43 −35 −27 |
−9.0 −4.5 0.0 4.5 |
|
|
After microdischarge in Positive phase (AP) |
AP-1 AP-2 AP-3 AP-4 |
ta = 5 15 30 100 |
10.3 8.9 8.4 9.0 |
|
|
Before microdischarge in Negative phase (BN) |
BN-1 BN-2 BN-3 BN-4 |
tb = − 29 −21 −13 −5 |
9.0 4.5 0.0 −4.5 |
|
|
After microdischarge in Negative phase (AN) |
AN-1 AN-2 AN-3 |
ta = 5 10 40 |
−8.4 −10.0 −9.0 |
|
2.3. 2D EFISH measurement
For the EFISH measurement, a picosecond Nd:YAG laser (Ekspla, PL2251A, 30 ps, 50 Hz, 1064 nm, 9.6 mJ/pulse) was employed. Laser pulses were synchronized with the applied voltage using a delay generator (BNC, Model 575). To measure the respective electric field component, a laser beam was polarized in either the radial (r) or axial (y) direction using a half-wave plate.
The polarized incident beam was focused in the DBD section using a convex lens (f = 500 mm). A long-pass filter (> 800 nm) was placed between the lens and the DBD section to filter out any parasitic second harmonic signal (SHS, 532 nm) beam. In the DBD section, the incident beam interacted with the electric field, generating SHS alongside it. In principle, the SHS depends on the inner product of the electric field and the polarization direction. This indicates that the component of the electric field of interest can be measured by appropriately adjusting the polarization direction. These beams (both incident and SHS) were then collimated using another convex lens (f = 400 mm), and the SHS was spatially separated from the incident beam using a dispersive prism. The intensities of both the incident beam and SHS were measured using a photodiode (PD, Thorlabs, DET025A) and a photomultiplier tube (PMT, Hamamatsu, H10721-01), respectively, in conjunction with the oscilloscope.
EFISH is a third-order nonlinear process that involves the interaction between a light field and an electric field. Assuming a Gaussian beam, the intensity of SHS, Ii(2ω), can be expressed as:
where 𝜒(3)ijkl is the nonlinear susceptibility depending on a gas composition (4th order tensor), N is the number density of particles participating in the non-linear interaction (usually assumed to be the number density of gas molecules), Ei is the electric field component to be measured, E(𝜔) is the electric field of incident beam at the fundamental frequency of 𝜔, ∆k is the phase mismatch between the incident beam and SHS, and L is the effective length of the interaction (i.e. region of overlap between the E(𝜔) and Ei). Here, z denotes the laser beam propagation axis. The use of a focused beam results in the majority of SHS occurring within the Rayleigh range. Therefore, the integration length L can be approximated as twice the Rayleigh range. To quantify Ei, Eq. 1 could be rewritten as Eq. 2 by introducing a coefficient C, which includes the information of N and 𝜒(3)ijkl. This coefficient C was calibrated by comparing a measured Laplacian field and a simulated one, following a methodology described in a previous study41. By measuring the intensities of both the SHS (Ii(2ω)) and the incident beam (I(ω)), Ei can be deduced:
To obtain planar information in the r-y plane, we conducted a multi-point measurement, as illustrated by the grid in Fig. 4. The measurement domain was 0 ≤ r ≤ 5 mm and 0.25 ≤ y ≤ 3.25 mm with intervals of 0.25 mm in both directions (273 points in total). To obtain the spatially resolved data, a scanning direction was orthogonal to the laser passage42, since the scanning of the EFISH signal along the laser beam direction required relatively longer measurement interval of several centimeters36,43. An incident direction of the laser was perpendicular to the plane shown in Fig. 4. The laser beam radius at the measurement point (beam waist) was approximately 40 µm, assuming a Gaussian profile. This measuring radius was smaller than the spacing between adjacent measurement points. This scanning scheme could provide significantly improved spatial resolution.
The DBD section was mounted on a translation stage to vary the measurement points, while the laser was introduced orthogonally to the measurement domain. At each point, both the radial (Er) and axial (Ey) components of the electric field were measured by adjusting the polarization axis of the incident beam. The validity of the reconstruction of 2D electric fields through the analysis of the SHS polarization has been confirmed by Chng T. L. et al.38. Note that the azimuthal electric field was negligible in our experiment due to the axisymmetric electrode configuration. A detailed description of the resulting EFISH signal intensities for radial and axial polarization in axisymmetric configuration is provided in Supplementary Information. At each point, data were averaged over 256 laser pulses.
EFISH technique is known to have two major sources of uncertainty: i) the generation of SHS in the Rayleigh range (~ 5.2 mm in this study) outside the measuring r-y plane and ii) the Gouy phase shift due to the phase mismatch between the incident beam and the SHS44. Nevertheless, this uncertainty was estimated to be less than 15% by comparing the EFISH signal quantified by Eq. 2 with a simulated Laplace field (Fig. S4 in Supplementary Information).
To deduce the space charge distribution from the measured electric field, we applied Gauss’s law41 in the cylindrical coordinate system:
$$\:\nabla\:\bullet\:E=\:\frac{d{E}_{y}}{dz}+\frac{1}{r}\frac{dr{E}_{r}}{dr}=\:\frac{\rho\:}{{\epsilon\:}_{0}},$$
3
where E (= Ey + Er) is the total electric field, ε0 is the permittivity of free space (= 8.854 × 10− 12 C/Vཥm), and 𝜌 is the charge density. For the numerical derivation, the central difference method was used, except at the boundaries where the forward or backward difference method was applied instead. Note that there are two different sources of E: the Laplace field caused by the external electric field and the electric field formed by space charges. However, Eq. 3 does not require specific knowledge of the electric field created by space charges, since the derivative of the Laplace field term naturally vanishes (equals zero).
3.1. Discharges in positive phase
The measured electric fields and deduced space charge profiles coherently explained their dynamic behaviors, which facilitated the microdischarges in the positive phase before discharge. After the discharge, we observed self-decayed electric fields due to the ambipolar diffusion of the discharge-produced cations. Figures 5 and 6 illustrate the measured E/N and deduced r for the BP and AP cases, respectively. For enhanced visual clarity, areas where |r| < 5 nC/cm3, which might be due to numerical differentiation, are colored white. E/N was calculated under standard temperature and pressure conditions. In all figures, the y-axis (r = 0) indicates the electrodes’ axis, where the microdischarge spatially occurred.
It should be noted that the EFISH measurement provides only the magnitude of the electric field, and thus the field direction must be carefully determined. The overall field direction could be easily determined from the applied voltage to the gas gap, which was obtained by the voltage waveform14. If there were a reversal in the electric field direction within the gap, the SHS would be expected to drop to zero, based on the intermediate value theorem41. However, in the present measurements, no measured region returned zero SHS, indicating that no inversion of the field direction occurred within the measure domain.
During the transition from the negative to the positive phase in the Va cycle (BP cases, Fig. 5), a notable redistribution of memory charges from the preceding negative-phase microdischarge was observed, along with a significant augmentation in field intensity near the upper electrode due to the inversion of the electric field direction. In the BP-1 case (Fig. 5a and e)—at the end of the preceding negative phase, high E/N concentrated near the tip of the upper electrode, demonstrating upward field direction due to the applied negative potential (Va = − 9 kV). The maximum E/N was relatively modest (~ 69 Td, Fig. 5e) with negligible space charges in the domain (Fig. 5a). In this case, we conceived that anions and electrons from the preceding microdischarge accumulated over the ceramic surface, while cations neutralized at the surface of the metallic upper electrode. Consequently, the overall weaker E/N could be attributed to the electric field screening effect done by the memory charges on the ceramic surface.
When Va rapidly changed to − 4.5 kV (BP-2) and then to 0 (BP-3), no noticeable changes in the overall space charge distribution were observed (Figs. 5b and c). This suggested that the time duration of 16 µs, from BP-1 to BP-3, was insufficient for the release of accumulated anions under the relatively weak electric fields (Figs. 5f and g). Considering O2− as the anion representative, its estimated movement over 16 µs was only about 0.26 mm based on the mobility of 2.06 cm2s− 1V− 1 and E ~ 12.5 kV/cm45. This limited movement was primarily due to the low E as shown in Figs. 5f and g. Although the surface charges could not be measured due to laser-surface interaction, the presence of surface charges on the ceramic was indirectly evidenced by the electric field at Va = 0 (BP-3); despite the externally applied field being null in this case, the electric field direction had already changed, illustrating a gradient of E along both y and r (Fig. 5g). This observation was likely due to the anions accumulated on the ceramic, with the highest charge density at r = 0.
In addition, at BP-3, the presence of cations (N2+ and O2 + 46) near the upper electrode can be attributed to electron impact ionization, caused by electrons released from the ceramic surface. Given that electron mobility (~ 480 cm2s− 1V− 1 at 50 Td) is two orders of magnitude higher than that of O2− 47, these fast-moving electrons moved away from the ceramic surface more rapidly than the anions. Thus, even though the absence of a visible region with negative charges in BP-3, these fast-moving electrons might be capable of generating cations along their path. This effect became even more evident in the BP-4 case, as shown in Fig. 5d.
In the BP-4 case, just before the microdischarges (BP-4 case, Fig. 5h), there was a noticeable increase in the electric field near the tip of the upper electrode. This increase was due to the redistributed memory charges (Fig. 5d), which facilitated the onset of microdischarges. Figure 5d shows a concentrated net positive charges (up to ~ 25 nC/cm³) in the upper part of the domain (y > 1.5 mm), resulting from ionization, and net negative charges (up to ~ − 22 nC/cm³) in the lower part (y < 1.25 mm), originating from the released memory charges. These space charges were predominantly aligned along the y-axis (r < 1 mm), intensifying the electric field as depicted in Fig. 5h. This intensification was due to the superposition of two electric fields generated by the space charges and Va = 4.5 kV, with the maximum E/N reaching up to 100 Td. Consequently, this enhanced downward electric field might effectively initiate the microdischarges in the positive phase.
At BP-4 (Fig. 5d), we also observed locally concentrated negative charges (− 15 nC/cm3) at a radially distant location (r > 3.3 mm) near the ceramic surface (y < 0.8 mm). Since these negative charges were produced during the preceding discharge phase, they likely resulted from surface discharges along the ceramic surface due to locally enhanced radial electric fields (Er) at the edge of the accumulated negative charges in the preceding discharge phase. Previous studies, which utilized the Pockels effect to measure surface charges, also identified similar ring-shaped secondary surface charge patterns30. The associated local increase in E/N will be further discussed in the subsequent section.
In the AP cases, we found that the temporal changes in the measured electric field and the deduced charge density accurately captured the dynamics of the space charges generated by the microdischarges. Additional space charges were produced by the microdischarges. Specifically, cations quickly disappeared from the domain and accumulated on the ceramic surface due to ambipolar diffusion. This resulted in a reduction in the electric field, effectively preventing subsequent microdischarges.
At AP-1 (Va = 10.3 kV, ta = 5 µs), we observed a column of net positive charges along the y-axis, with a radius of ~ 2 mm and the charge density reaching up to 90 nC/cm3 (Fig. 6a). Contrary to the electric field seen at BP-4, significantly lowered E/N was observed along the y-axis due to the cations generated by the microdischarges. Radially diffused net positive charges were identified near the lower ceramic surface, creating a cone-shaped area of low E/N centered on the y-axis (Fig. 6e). As time progressed to AP-2 and AP-3 (Figs. 6b and c), the column of net positive charges diminished, illustrating a lower charge density (up to ~ 50 nC/cm3) and a narrower distribution in r-direction (r < 1 mm for AP-2 and r < 0.5 mm for AP-3). This change was attributed to the ambipolar diffusion of the charges toward their respective electrodes. The cations accumulated on the ceramic surface and screened the potential of the lower electrode. Concurrently, electrons and anions were absorbed and neutralized at the upper electrode’s surface, leaving minimal memory charges in this region. Therefore, as shown in Figs. 6f and g, the electric field became weak due to the presence of the positive charges at the ceramic surface.
By the time AP-4 was reached (as shown in Figs. 6d and h at Va = 9 kV and ta = 100 µs), it appeared that all the positive charges were completely removed from the domain, indicating that a layer of cations accumulated on the ceramic surface. Given the predicted drift velocity of N2+ (~ 0.6 mm/µs at 140 Td and ~ 0.1 mm/µs at 20 Td, based on the mobility of N2+ in N2 of 1.72 and 1.94 cm2s− 1V− 1 at 140 and 20 Td, respectively)48, the observed decay of the space charges within 100 µs was credible. However, in Fig. 6d, we also noticed the region of net negative charges ( < − 25 nC/cm3) near the upper electrode (y > 2.5 mm and r < 2.5 mm). Since the last discharge’s electrons and anions (O2−) possessed sufficiently high drift velocities to exit the domain, this phenomenon might indicate ongoing electron-attachment of O2 facilitated by free electrons. In the last stage of the positive phase (BN-1 at Va = 9 kV and ta = 400 µs) as shown in Figs. 7a and e, the region of net negative charges disappeared; however, it remains unclear whether the anions were completely neutralized at the electrode or still lingered near the electrode’s surface due to the physical limitation of the mentioned laser-surface interference.
In addition, at AP-1 (Fig. 6e), we identified high E/N region (~ 100 Td) near the ceramic surface (y < 1 mm and 3 < r < 4.5 mm), comparable to the E/N near the upper electrode. Comparing to the charge distribution in Fig. 6a, this augmented E/N region suggested it originated from a radially outward accumulation of surface charges at this location. A similar strong radial electric field (forming a ring shape on a dielectric surface) was also observed in a previous study using the Pockels effect30. At the radial edge of the cation layer on the ceramic surface, the radical electric field could be intensified due to the surface charges. This augmentation is known to facilitate a secondary discharge channel along the dielectric surface, resulting in the deposition of additional cations near the radial edge of the cation layer. Afterwards (AP-2 to AP-4), the strong radial electric field in the radial direction gradually diminished.
3.2. Discharges in negative phase
Contrary to the dynamic behaviors of E/N and r observed in the BP cases, we found a significant presence of space charges in the domain during a transient phase when Va decreased to 0 from 9 kV. Counterintuitively, the domain became predominantly filled with net negative charges in following the microdischarge in the negative phase (AN cases). Figures 7 and 8 illustrate the measured E/N and deduced r for the BN and AN cases, respectively. Consistent with Figs. 5 and 6, regions where |r| < 5 nC/cm3 were marked in white for visual clarity.
In the BN-1 and BN-2 cases, unlike in BP-1 and BP-2, we observed regions of both net positive and net negative charges within the domain, as shown in Figs. 7a and b. Given the downward direction of the vertical electric field (towards the ceramic), the detected space charges likely did not originate from the memory charges generated by the preceding microdischarges. This indicated that the observed charges were generated within the domain and were migrating towards their respective electrodes—cations to the lower ceramic and anions to the upper electrode—driven by ambipolar diffusion. Consequently, we conceived that free electrons may generate both cations and anions through electron impact ionization and attachment, respectively for given electric fields.
At BN-3 (Va = 0, shown in Fig. 7g), with the electric field direction inverted by memory charges, released cations from the ceramic surface were detected for r < 1.5 mm and 2.3 < r < 4.5 mm. The concentrated positive charges in regions y < 0.5 mm and 2.3 < r < 4.5 mm reflected the residual effect of cations deposited earlier, as depicted in Fig. 6.
In addition, the anions, likely generated continuously by the free electrons, were observed in r < 1 mm. By the time of BP-4 (Va = − 4.5 kV, Fig. 7d), an enlarged area of anions might be explained by the boosted electron attachment due to the continuous electron emission from the upper electrode, extending the affected zone down to y = 1.5 mm. Concurrently, the reversed polarity of Va further intensified the electric field, drawing the cations (max r = 29 nC/cm³) deeper into the domain. This resulted in a significant increase in E/N near the upper electrode (114 Td), facilitating subsequent microdischarge in the negative phase.
Comparing the E/N at BN-4 (Va = − 4.5 kV, illustrated in Fig. 7h) with BP-4 (Va = 4.5 kV, shown in Fig. 5h), we observed that E/N was 10–30 Td higher across the domain at BN-4 than at BP-4. Given that the Laplace fields remained the same for both BN-4 and BP-4, this increase in electric field intensity could be attributed to the quantity and distribution of space charges unique to BN-4. Thus, as shown in the QV plot (Fig. S2), the lower breakdown voltage (− 6.5 kV) in the negative phase compared to the positive phase (8.5 kV) could be explained by this higher E/N for the BN-4.
In the AN cases following the microdischarge in the negative phase (Fig. 8), we noticed that the discharge trail was completely filled with net negative charges. At 5 µs from the end of the jittering band (AN-1, Fig. 8a), net negative charges were exclusively presented in the domain, contrasting with the net positive charge prevalence observed in the AP cases (Fig. 6a). The dominance of net negative charges persisted up to ta = 40 µs (AN-3), even though most space charges vanished from the domain due to ambipolar diffusion. This was somewhat counterintuitive; considering electrical neutrality and the high mobility of electrons, one would expect the discharge channel to predominantly contain net positive charges, similar to the observation in the AP cases (Fig. 6).
This observation can be explained by the fact that the negative corona discharge that follows the microdischarge shown in Fig. 3d introduces surplus electrons into the domain. A significant number of these electrons attach to O2 becoming anions. Anions stay in the domain longer than the electrons due to their differing mobilities. The rather continuous charge flow pattern observed in the third quadrant of the QV plot (Fig. S2) signified the negative corona discharges persisting after the microdischarge until Va peaked.
Observable differences in the electric field for AN, compared to AP, included a weaker Er and relatively plain gradient of E. This was due to a wider spread of net negative-charge areas with lower charge density in AN compared to AP. An augmented E/N near the ceramic surface for r > 4 mm (Figs. 8d, e, and f), echoing findings from AP (Fig. 6e). Since the ring-shaped area of augmented E/N in AN was approximately 1 mm wider in radius than in AP, it might suggest a broader distribution and potentially a higher quantity of deposited anions compared to the deposited cations in AP.
We conducted an experimental investigation into the dynamic characteristics of electric fields and space charge distribution over time in a microdischarge(s) in an axisymmetric dielectric barrier discharge (DBD) setup. The DBD setup was optimized to generate a single microdischarge along its axis, significantly reducing time jittering by adopting a square wave alternating current (AC). The Electric Field Induced Second Harmonic Generation (EFISH) technique was effectively employed to capture the electric field in the r-y plane, facilitating the indirect measurement of charge density deduced from Gauss’s Law.
In both the positive and negative phases of the microdischarges, the deduced charge density successfully revealed the dynamic behavior of memory charges, primarily due to ambipolar diffusion. Simultaneously, the measured electric field clearly illustrated the phenomena of constructive superposition of electric fields (due to applied voltage and space charges) preceding the microdischarge and destructive superposition following it. These phenomena resulted from the interaction between space charges and the applied voltage as the AC polarity changed. The constructive superposition (enhanced electric field) facilitated subsequent microdischarge, while the destructive superposition (diminished electric field) restrained them until the AC polarity shifted.
The analysis also highlighted that surface charges accumulated on the ceramic surface exhibited a broader radial distribution. Near the radial edge of these surface charges, we observed an intensified electric field, potentially triggering secondary surface discharges. This observation aligns with finding from a previous study using the Pockels effect30, thus validating our approach that combined EFISH and Gauss's Law for analyzing DBD dynamics.
In addition, following the microdischarge in the negative phase, we detected a predominant excess of negative space charges over positive ones, resulting in a net negative-charge domain. This unusual phenomenon is possibly linked to continuous corona dischcarge, which generates surplus electrons, from the bare metal electrode on one side. This intriguing observation suggests further exploration for numerical modelers who might be interested in elucidating the underlying mechanisms.
Author Contribution
J. Park conceived of the experimental method, conducted the experiment, collected the data, prepared all figures and supplementary information, and wrote the main manuscript. M.S. Cha supervised the project, analyzed the data, revised figures 5-8, and wrote the main manuscript. All authores reviewed the manuscript.
Acknowledgements
The research reported in this publication was funded by King Abdullah University of Science and Technology (KAUST), under award number BAS/1/1384-01-01.
Data Availability
The experimental data presented in this study will be available upon request to the corresponding author (J.P.).
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No competing interests reported.