Figure
1.
Schematic diagram of the experimental setup.
| Citation: |
Caixia LI, Jianyu FENG, Shuchang WANG, Cheng LI, Junxia RAN, Yuyang PAN, Lifang DONG. Formation mechanism of bright and dark concentric-ring pattern in dielectric barrier discharge[J]. Plasma Science and Technology, 2024, 26(8): 085401. DOI: 10.1088/2058-6272/ad386a
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In this work, a bright and dark concentric-ring pattern is reported in a dielectric barrier discharge for the first time. The spatiotemporal dynamics of the bright and dark concentric-ring pattern are investigated with an intensified charge-coupled device and photomultiplier tubes. The results indicate that the bright and dark concentric-ring pattern is composed of three concentric-ring sublattices. These are bright concentric-ring structures, dark concentric-ring structures and wider concentric-ring structures, respectively. The bright concentric-ring structures and dark concentric-ring structures are alternately distributed. The bright concentric-ring structures are located at the centre of the wider concentric-ring structures. The wider concentric-ring structures first form from the outer edge and gradually develop to the centre. The essence of all three concentric-ring structures is the individual discharge filaments. The optical emission spectra of different sublattices are acquired and analysed. It is found that the plasma parameters of the three concentric-ring sublattices are different. Finally, the formation mechanism of the bright and dark concentric-ring pattern is discussed.
Dielectric barrier discharges (DBDs) are well known for ozone generation, surface modification, as a light source, in ammonia synthesis, plasma display panels and so on [1–6]. In recent years, there has been much evidence that the DBD system is an excellent vehicle for studying pattern formation. A wide variety of patterns, such as square patterns, hexagonal patterns, superlattice patterns and concentric-ring patterns, have been realized in DBD systems [7–11]. Among them, concentric-ring patterns have always attracted much attention because of their extremely high symmetry. In more detailed research, simple concentric-ring patterns to concentric superlattice patterns formed by interleaving multiple sets of sublattices have been reported and studied in computational and experimental studies. For example, Gurevich et al observed a concentric-ring pattern in a dielectric barrier gas discharge system in 2003 [12]. In 2009, Duan et al exhibited a concentric-ring pattern in a dielectric barrier glow discharge [13]. In 2011 and 2014, Dong et al reported a sparse–dense dot concentric-ring pattern and a concentric-ring pattern in a DBD system, respectively [10, 14]. In 2016, Feng et al presented a concentric superlattice pattern with three different sublattices in a DBD system [9]. In 2019, Shang et al realized a concentric pattern in an atmospheric helium DBD through a two-dimensional axisymmetric fluid model [15]. Recently, Wu et al and Li et al described various concentric-ring patterns in a water-anode atmospheric glow discharge [16, 17]. In general, the above-mentioned concentric-ring patterns can be roughly divided into three categories. Firstly, the patterns have a simple structure, comprising only concentric-ring structures or concentric-dot structures. Secondly, the pattern is composed of two sublattices. That is, the pattern is a combination of concentric-ring structures and concentric-ring structures, concentric-ring structures and concentric-dot structures, or concentric-dot structures and concentric-dot structures. In general, the sublattices of this type of concentric-ring pattern have the characteristics of alternating discharge. In addition, it is worth mentioning that the brightness of different sublattices is not obviously different. Thirdly, the pattern is a concentric superlattice pattern formed by interleaving three sublattices. The three sublattices have totally different performances. Here, a concentric-ring pattern with complex structures is reported in a DBD system. The three sublattices are all composed of concentric-ring structures and the brightness of different sublattices is obviously different. In a word, the bright and dark concentric-ring pattern is not only different in terms of appearance from the previously reported concentric-ring pattern but may also have a completely different formation mechanism.
Due to the development of experimental devices and diagnostic techniques, a new category of pattern with bright and dark structures has been reported and is attracting much attention. In general, different types of discharges or different discharge intensities lead to differences in the brightness of the different sublattices comprising the patterns. This may give rise to the formation of new patterns with more complex structures. In 2014, Itoh and Suzuki observed a hexagonal arrayed pattern with bright and dark spots in a plasma chamber equipped with a piezoelectric transformer and a dielectric electrode [18]. In 2015, Liu et al reported a hexagon pattern with bright spots and dim spots in a DBD system. The reason for the formation of the dim spots was explained as the surface discharges produced by the adjacent different bright spots coming together at the position of the dim spots [19]. In 2019, Li et al presented a bright–dim hollow hexagonal superlattice pattern based on selective discharges in a DBD system [20]. In 2022, a hexagonal superlattice pattern composed of bright spots and dim spots was observed by Pan et al. Surprisingly, the hexagonal superlattice pattern, which appears to the naked eye to be composed only of dim spots and bright spots, is actually formed of three completely different sublattices [21]. The formation mechanism of the pattern with the bright and dark structures seems to have its own characteristics. Here, there is a significant difference in the brightness of adjacent concentric-ring structures of the pattern. Therefore, study of this bright and dark concentric-ring pattern is very valuable.
In this work, a bright and dark concentric-ring pattern is observed in a DBD system for the first time. An intensified charge-coupled device (ICCD) and photomultiplier tubes (PMTs) are used to investigate the spatiotemporal dynamics of the pattern. The plasma parameters are studied by optical emission spectroscopy. The formation mechanism of the pattern is discussed. It is believed that research into these bright and dark concentric-ring patterns will not only enrich or knowledge about the types of concentric-ring patterns and patterns with bright and dark structures but may also provide further ideas about the different formation mechanisms for self-organized patterns.
The experiments were carried out in a DBD system based on water electrodes which can be operated at a higher pd (p, pressure; d, discharge distance) value. Figure 1 shows a schematic diagram of the experimental setup. The critical part of the discharge device is the water electrode. The water electrodes are machined from two cylindrical containers. The cylindrical containers are sealed with glass plates on both ends and filled with water with a conductivity of about 3.2×10−2 S m–1. The circular metal rings made of copper are immersed in the pre-filled water in the cylindrical containers and used to connect a sinusoidal AC power supply with a driven frequency of 53 kHz. The discharge space is achieved by inserting a 5 mm thick glass plate with a diameter of 50 mm in a hollow circular frame between the two water electrodes. The whole discharge unit is installed in a transparent chamber having adjustable gas composition and pressure. In this work, the process gas consists of an 80% argon/20% air mixture, and the pressure is fixed at 15 kPa. The high-voltage probe (Tektronix P6015A 1000×) and current probe (Tektronix TCP0030A) are introduced into the circuit and connected to an oscilloscope (Tektronix TDS 3054B) to measure and record the voltage and current waveforms. The discharge images of the patterns can be recorded by a digital camera (Canon Power Shot G16). An intensified CCD (HSFC-Pro. three channels) is used to capture the instantaneous images in successive current pluses. The optical signals of the discharge are acquired by the photomultiplier tubes (PMTs; RCA 7265) with high sensitivity. The optical emission spectra are acquired by a spectrograph (Acton Advanced SP 2750A, CCD 1 340 400 pixels).
Figures 2(a)–(d) show the evolution of the bright and dark concentric-ring pattern with increase in the applied voltage. At the beginning, the gas in the discharge space has just broken down, and a few random discharge filaments are generated in the discharge space. As the applied voltage increases to 4.4 kV, more and more discharge filaments are generated, and the discharge filaments gradually show a regular arrangement (figure 2(a)). With a further increase in the applied voltage, a perfect honeycomb superlattice pattern is formed in the discharge space (figure 2(b)). The evolution process of the bright and dark concentric-ring pattern is similar to that of the concentric superlattice pattern [9] under lower applied voltage conditions. Random discharge filaments and hexagonal or honeycomb patterns appear during the formation of the two kinds of concentric-ring patterns. With further increase in the applied voltage, the honeycomb hexagonal pattern gradually disappears, and the fingerprint pattern begins to be generated (figure 2(c)). When the voltage increases to 8.8 kV, the bright and dark concentric-ring pattern is formed, as shown in figure 2(d). From figure 2(d), it can be clearly seen that the bright and dark concentric-ring pattern is composed of wide bright concentric-ring structures and narrow dark concentric-ring structures. The bright and dark concentric-ring structures are alternately distributed. Figure 2(e) shows the distribution of light intensity of the bright and dark concentric-ring pattern based on the greyscale distribution. It is an undoubted fact that the light intensity of the bright concentric-ring structures is much higher than that of the dark concentric-ring structures. It is worth mentioning that this is the first observation of a concentric-ring pattern with bright and dark concentric-ring structures in a DBD system.
As is well known, self-organized patterns respond very quickly to changes in the experimental parameters. A phase diagram of the bright and dark concentric-ring pattern in relation to the gas pressure p and the concentration of argon φ is shown in figure 3. The pattern is observed within the pressure range of 12–20 kPa and argon concentrations from approximately 70% to 100%. When the concentration of argon is 80% and the pressure is 15 kPa, the bright and dark concentric-ring pattern presents a perfect state and exists for a longer time. Therefore, the bright and dark concentric-ring pattern corresponding to this experimental condition is studied in detail.
The voltage and current waveforms of the bright and dark concentric-ring pattern are depicted in figure 4(a). It is obvious that there are three distinct pulses with different widths or intensities within half the current cycle for the current waveforms. Normally, there is a strong relationship between the number of sublattices of the pattern and the number of current pulses in the DBD system [20]. As we described earlier in figure 2(d), the bright and dark concentric-ring pattern is composed of wide bright concentric-ring structures and narrow dark concentric-ring structures. It can be assumed that the bright and dark concentric-ring pattern is composed of two sublattices at most, namely wide bright concentric-ring structures and narrow dark concentric-ring structures. But to which sublattice should the third pulse of the three current pluses belong? Is it a repetition of the wide bright concentric-ring structures or narrow dark concentric-ring structures, or is it one sublattice which is invisible to the naked eye, just like the invisible honeycomb sublattice in the honeycomb Kagome hexagonal superlattice pattern with dark discharges reported previously [21]? It is this confusion that made us eager to uncover this mystery.
To investigate the spatiotemporal dynamics of the bright and dark concentric-ring pattern, time-resolved images of the pattern were acquired by the ICCD camera. Figures 4(b)–(d) present the time-resolved images correlated with the three current pulse phases with integration over 100 applied voltage cycles. The widths of the three current pulse phases are 880 ns, 880 ns and 1000 ns (labelled by ∆t1, ∆t2 and ∆t3, respectively, in figure 4(a)). Figure 4(e) is a superposition of figures 4(b)–(d). The result shows that the bright and dark concentric-ring pattern is an interleaving of three kinds of concentric-ring sublattices, namely bright concentric-ring structures, dark concentric-ring structures and wider concentric-ring structures. The width of the different concentric-ring structures is about 0.25 cm, 0.2 cm and 0.4 cm, respectively. From figure 4(e), it can be found that the bright and the dark concentric-ring structures are alternately distributed. The bright concentric-ring structures are located at the centre of the wider concentric-ring structures. The discharge sequence of the bright and dark concentric-ring pattern is also confirmed. It is followed as bright concentric-ring structures, dark concentric-ring structures and wider concentric-ring structures. In the following half cycle, the discharge sequence follows bright concentric-ring structures, dark concentric-ring structures and wider concentric-ring structures.
An ICCD camera is usually utilized to obtain the time-resolved images with the integration of multiple applied voltage cycles in order to investigate the intuitive structure of the pattern. However, the single-exposure images proved to be crucial for understanding the intrinsic properties of the formation of the pattern. We also tried to acquire single-exposure images for the bright and dark concentric-ring pattern. Unfortunately, the images contained no obvious information because the luminous intensity of the pattern was relatively weak. The integration of the time-resolved images was gradually increased. The time-resolved images correlated with the three current pulse phases (labelled by ∆t1, ∆t2 and ∆t3 in figure 4(a)) with integration over five applied voltage cycles are shown in figures 5(a)–(c). It is worth pointing out that the brightness of the time-resolved images is artificially increased for the purpose of clear display. It can be found that the profile of three different concentric-ring structures can basically be observed. The three different concentric-ring structures are not continuous, as marked by the red circle in figure 5. Some randomly individual discharge filaments can be observed. That is to say, the three different concentric-ring structures are all composed of discharge filaments although their appearances are different.
Comparing figures 4(c) and (d), it can be found that 120 ns after the dark concentric-ring structures are generated, the wider concentric-ring structures with a completely different appearance from the dark concentric-ring structures are formed. This is because the individual filaments are the basic units that make up the two concentric-ring structures. That is to say, within one voltage cycle some individual filaments are generated in the second current pulse which belongs to the dark concentric-ring structures. Those individual filaments cannot form complete dark concentric-ring structures. After 120 ns, some individual filaments are also generated in the third current pulse, which belongs to the wider concentric-ring structures. The dark concentric-ring structures and the wider concentric-ring structures only have different appearances in the integrated images with multiple voltage cycles. The essence of the two concentric-ring structures is individual filaments within one voltage cycle. This further illustrates that both the integrated images with multiple voltage cycles and the images with a single exposure mode are important for studying pattern formation.
Among the three different concentric-ring structures, the wider concentric-ring structures attract our attention. Therefore, the time-resolved images correlated with the third current pulse phase, which is labelled by ∆t3 in figure 4(a), are investigated in detail to clarify the formation process of the wider concentric ring structures. The width of ∆t3 is further divided into successive ∆t4 and ∆t5. The widths of ∆t4 and ∆t5 are set to 800 ns and 1000 ns, 800 ns and 1500 ns, 600 ns and 400 ns, respectively. The time-resolved images corresponding to different ∆t4 and ∆t5 with integration over 100 applied voltage cycles are shown in figures 6(a)–(c). When the width of ∆t4 is fixed at 800 ns and the width of ∆t5 is increased from 1000 ns to 1500 ns, the time-resolved image corresponding to ∆t4 shows no obvious difference. The time-resolved image corresponding to ∆t5 just shows that the concentric-ring structures have become a little diffuse. However, when the width of ∆t4 is decreased to 600 ns, it is obvious that there should be much wider concentric-ring structures but only the edge of the wider concentric-ring structures appears, as marked with the red arrows in figure 6(c1). The concentric-ring structures corresponding to ∆t5 are the missing part of the structure presented in figure 6(c1), as shown in figure 6(c2). This proves that the wider concentric-ring structures are gradually formed from the outer edge and develop towards the centre.
With the purpose of further determining the basic constituents of the three concentric-ring structures of the pattern, the optical signals of different concentric-ring structures were also collected using PMTs with higher sensitivity through the two optical windows, which are set at both ends of the vacuum chamber. The two PMTs were calibrated with the optical signal from the same position before the measurements. The temporal correlations of optical signals between different concentric-ring structures are shown in figure 7. The bright concentric-ring structures, dark concentric-ring structures and wider concentric-ring structures are represented by B, D and W in figure 7(a). The temporal correlations between B and D, D and W are shown in figures 7(b) and (c), respectively. The results show that the bright concentric-ring structures, dark concentric-ring structures and wider concentric-ring structures are ignited in the first, second and third pulse phases of the current, respectively. It is also confirmed that the discharge sequence is as follows: bright concentric-ring structures, dark concentric-ring structures and wider concentric-ring structures. It can be clearly seen that the three concentric-ring structures are not all ignited in every half-applied voltage cycle. This implies that the three concentric-ring structures are actually composed of individual discharge filaments. These results are consistent with those obtained by the ICCD camera.
As mentioned earlier, the evolution of the bright and dark concentric-ring pattern is similar to that of the concentric superlattice pattern [9] under lower applied voltage conditions. In general, the formation of a complex pattern often occurs gradually through random discharge filaments and simple patterns or simple superlattice patterns. Comparing the experimental parameters of the two patterns, both are generated in the 5 mm discharge gap. At the lower voltage, there are fewer discharge filaments or the interaction between different discharge filaments is weak. Therefore, the bright and dark concentric-ring pattern has a relatively similar evolution process to that of the concentric superlattice pattern. However, the driven frequency of the applied voltage, argon concentration and pressure are different for those two patterns. As is well known, the pattern is a self-consistent process caused by interaction between the discharge filaments under appropriate experimental conditions and is very sensitive to changes in the experimental parameters. In addition, a higher argon concentration and lower gas pressure make it easier to form the discharge filaments with a small radius and low brightness that constitute the basic unit of the bright and dark concentric-ring pattern instead of the discharge filaments with a large diameter and higher brightness that constitute the concentric dots in the concentric superlattice pattern. In this work, the pressure for the bright and dark concentric-ring pattern is slightly lower than that for the concentric superlattice pattern. Therefore, there are no discharge filaments with a large diameter and higher brightness that form the concentric dots of the concentric pattern generated in the bright and dark concentric-ring pattern.
To a certain extent, the brightness of the discharge is often closely related to the plasma state. As described in the discharge images in figure 2(d), the brightness of the different concentric-ring structures is obviously different. This implies that different concentric-ring structures are in different plasma states. To further clarify the differences between them, the emission spectra of the N2 second positive band (C3Πu→B3Πg) and the Ar spectral lines 763.51 nm (2P6→1S5), 772.42 nm (2P2→S3) and 696.56 nm (2P2→1S5), whose full width at half maximum (FWHM) can be used to reflect electron density, were collected and are shown in figures 8–10. The molecular vibration temperatures (Tν) for the different sublattices were investigated based on the six spectral bands of ∆ν = −2 (0–2, 1–3, 2–4) and ∆ν = −3 (0–3, 1–4, 2–5) in the N2 second positive band [21–23]. The electron excitation temperature (Texc) was calculated based on 763.51 nm and 772.42 nm [24, 25]. The electron density is positively related to the FWHM of the Ar I 696.56 nm spectral line. To be specific, a narrow FWHM of the 696.56 nm spectral line corresponds to a small electron density, while a wide FWHM corresponds to a large electron density [9, 19]. The results show that the Tν are 2600±20 K for B, 2780±20 K for D and 2860±20 K for W. The Texc of B, D and W are 7000±200 K, 8800±150 K and 9300±200 K, respectively. The FWHMs of B, D and W are about 0.01819 nm, 0.01638 nm and 0.01527 nm, respectively. Therefore, B has the highest electron density and W has the lowest electron density, as shown in figure 11. In a word, different sublattices have different molecular vibration temperatures, electron excitation temperatures and electron densities and different concentric-ring structures possess different plasma states.
The formation of the bright and dark concentric-ring pattern is determined by the arrangement of the effective field of the wall charge field and the applied field. It is well known that the working gas in the discharge space is ignited when the effective field, which is the vector sum of the internal electric field generated by the wall charges and the applied field, exceeds the threshold of the working gas. Thus, some discharge filaments are generated between the two water electrodes in the discharge space. The wall charges are generated by the discharge filaments and gradually accumulate on the dielectric layer at the corresponding discharge positions. The wall charges accumulated on the dielectric layer establish an internal electric field, which has a pivotal influence on the positions of subsequent discharge generation.
As for the formation of the bright and dark concentric-ring pattern, the gas is initially broken down at the positions of the bright concentric-ring structures. This implies that the positions with the maximum values of the effective field in the discharge space are the positions of the bright concentric-ring structures. The wall charges generated by the filaments of the bright concentric-ring structures will accumulate at the corresponding positions. As mentioned above, the internal electric field established by the wall charges has an essential impact on the positions of the subsequent discharge. In general, the arrangement of the internal electric field near the positions where wall charges have accumulated has an inhibitory effect on the generation of subsequent discharges. Therefore, subsequent discharges are prone to generate far from the positions where the discharge filaments were previously generated, because those positions possess the weakest inhibitory effect from the internal electric field. There is no doubt that the discharges after the bright concentric-ring structures will be generated between two adjacent bright concentric-ring structures since these positions are the furthest away from the positions of the wall charges generated by the bright concentric-ring structures in the entire discharge space. It is reasonable that the dark concentric-ring structures occur at these positions. This gives rise to the alternate arrangement of the bright concentric-ring structures and the dark concentric-ring structures. Similarly, the wall charges also accumulate at the positions of the dark concentric-ring structures. That is to say, the positions for the generation of the subsequent discharge will be jointly affected by the wall charges produced by the bright concentric-ring structures and dark concentric-ring structures. From figure 2(d), it can be clearly seen that the bright concentric-ring structures and dark concentric-ring structures have a significantly different brightness. This may imply that different concentric-ring structures may produce different amounts of wall charges which accumulate on the dielectric layer. However, the wall charges cannot yet be accurately obtained by experiment. In general, the amount of the transferred charge is proportional to the amount of wall charge, so the estimated amount of transferred charge can be used to roughly reflect the amount of wall charge. The amount of transferred charge of the bright concentric-ring structures (∆t1) and dark concentric-ring structures (∆t2) can be calculated by Q=∫Idt [21, 26]. The amounts of transferred charge of the bright concentric-ring structures and dark concentric-ring structures are about QΔt1= 78×10−9 C and QΔt2=63×10−9 C, respectively. It can be found that the amount of transferred charge of the bright concentric-ring structures is slightly greater than that of the dark concentric-ring structures. That is to say, the amount of wall charge produced by the bright concentric-ring structures is slightly greater than that of the dark concentric-ring structures. This fact causes the subsequent discharge to occur more easily at positions far away from the bright concentric-ring structures and close to the dark concentric-ring structures. Therefore, the wider concentric-ring structures first form at the positions of the outer edges, that is, close to the positions of the dark concentric-ring structures, and the wall charges accumulate at the corresponding positions. The positions of the subsequent discharge of the wider concentric-ring structures are affected not only by the bright concentric-ring structures and dark concentric-ring structures but also by the wall charges produced by the discharge filaments at their outer edges. This further promotes the formation of wider concentric-ring structures towards the centre.
In short, the formation mechanism of the bright and dark concentric-ring pattern is associated with the arrangement of the effective field, which is the sum vector of the wall charge field and the applied field. The arrangement of the internal electric field produced by the wall charges has an effect on the positions of the subsequent discharges. The formation of the dark concentric-ring structure provides more favorable conditions for the generation of the wider concentric-ring structure. The self-facilitation of the wider concentric-ring structure enables its formation from the outer edge toward the centre.
In conclusion, the bright and dark concentric-ring pattern in a DBD system is investigated for the first time. The spatiotemporal dynamics of the pattern measured by an ICCD camera and PMTs indicate that the pattern is composed of three different kinds of concentric-ring sublattices, namely bright concentric-ring structures, dark concentric-ring structures and wider concentric-ring structures. The bright concentric-ring structures are arranged alternately with the dark concentric-ring structures, and the bright concentric-ring structures are located at the centre of the wider concentric-ring structure. The formation of the wider concentric-ring structures starts at the outer edges and then gradually develops towards the centre. The essential elements that comprise the three kinds of concentric-ring structures are individual discharge filaments. The formation of the dark concentric-ring structures provides more favorable conditions for the generation of the wider concentric-ring structures. Study of the optical emission spectra shows that the plasma parameters of the three different concentric-rings structures are different. We hope that our results will contribute to the further understanding of this category of concentric-ring patterns with more complex structures and patterns with bright and dark structures.
This work is supported by National Natural Science Foundation of China (No. 12075075), the Natural Science Foundation of Hebei Province, China (Nos. 2020201016, A2018201154 and A2023201012) and Scientific Research and Innovation Team of Hebei University (No. IT2023B03).
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