1.Introduction

Self-organized pattern,which is associated with instability and symmetry breaking is a fascinating and common phenomenon in physical,biological,chemical and economic systems[1,2].Pattern formation is also pervasive in gas discharge,which particularly occurs in the anode layer,and a variety of patterns could be observed in air discharge under different conditions[3,4].

In recent years,many researchers have investigated the characteristics of the self-organized pattern in a wide range of electrical discharges.With regard to the morphological characteristic,Shirai et al investigated the anode pattern in atmospheric DC glow discharge with a liquid electrode[5–7],and Maszl et al observed this phenomenon experimentally on both liquid and metal anode surfaces[8,9].Astrov et al studied the formation of the self-organized pattern in dielectric barrier discharges[10–15].Numerical simulation is an important method for understanding the origin of pattern formation.For example,Trelles presented the first attempt to simulate the spontaneous formation of anode attachment spot patterns in high-pressure and high-current arc discharge[16,17].

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Although　the　characteristics and　theories of self organization phenomena have been investigated,the external characteristics of the self-organized pattern on the surface of a metal anode electrode under low-pressure condition have not been completely clarified.In this paper,the authors carried out laboratory investigations of self-organization in a low pressure test platform for 100–200 mm rod-plane gaps with a needle tip,conical tip and hemispherical tip within 1–10 kPa,and analyzed the influence of the pressure,gap length and shape of the electrode on the pro file and development process of the pattern.

2.Experimental con figuration

Figure 1.Experimental setup.

Figure 2.Schematic diagram of the arrangement of the camera and rod-plane electrode.

Figure 1 shows the experimental con figuration for the test.The gas used in the test was air.The ambient temperature and relative humidity were constant at 20°C and 35%,respectively.During the test,the temperature inside the discharge chamber was kept at 20°C.This experimental system consists of a high-speed camera(54-kframes/s frame rates,960 × 16 pixelresolution),power system,measurement system,pressure-control system,test chamber and electrode system.Figure 2 gives the schematic diagram of the arrangement of the camera and rod-plane electrode.The camera focused on the upper surface of the metal plane electrode to observe the ionization phenomena.The angle between the camera and the surface of the plane electrode is about 35°.The DC voltage was generated by an AC transformer(50 Hz,20 kVA)and recti fier and filter,which was applied to the high-voltage rod electrode at 0.5 kV s−1.The discharge voltage was the mean value of 20 times the test,and was measured by a resistance voltage　divider and　a　digital oscilloscope　(Tektronix DPO2012,100 MHz,1GS s−1).The discharge current was measured by a high-frequency current transformer(Pearson 2100,20 MHz).In the measurement of the discharge process,we used current pulse trigger mode to record the process of pattern formation on the plane electrode for 400 ms.In order to make the charge distribute in the chamber adequately,the time interval for repeated discharges was set as 5min.The pressure ranged from 1–10 kPa in the test chamber and was adjusted by vacuum needle valve and ΔP = 2 kPa.

Figure 3.Test chamber and electrodes.(a)Test chamber.(b)Plane and three kinds of rod tips.

Figure 3 shows the chamber and electrodes.The effective radius of the stainless steel chamber and plane electrode are 400 and 200 mm,respectively,and the surface roughness of the plane is 1.6 μm[18].The cylindrical stainless steel rod with a diameter of 10 mm with three kinds of tips are common electrode con figurations in discharge tests.Table 1 shows the structure of the rod tip used in this experiment.The surface of the electrodes is cleaned by alcohol before the test.

It can be seen in figure 4 that with the increase of pressure,the adjacent U-P curves of different gap length are further apart from each other,which means the influence of gap length increment on the breakdown voltage is gradually strengthened with increasing pressure.Furthermore,tip shape has a Significant influence on breakdown voltage.Theamplitude of breakdown voltage at the same pressure value and gap length shows ‘needle ＜ conical ＜ hemispherical.’Therefore,tip shape may have obvious influence on the pro file and development process of the self-organized pattern.

3.Experimental result and discussion

3.1.The dependence of pattern formation on external parameters

Thus,it can be concluded that the self-organized pattern on the surface of a metal anode under low-pressure condition depends on the shape of the electrode and the pressure value.An upper limit pressure of pattern formation between 8 and 9 kPa exists for 200 mm gap length.Within the pressure range of pattern formation, first the diameter of the pattern increases and then decreases,which means a maximum value exists.

硫酸根的理论塔板数为8 974，钠离子与硫酸根的分离度为3.01，后相邻杂质与钠离子的分离度为2.55。

Table 1.Structure of the rod tip.

To research the dependence of pattern pro file on pressure value and tip shape,we take a 200 mm rod-plane gap as an example.The effects of pressure and tip shape are shown in figure 5 and the diameter of the self-organized pattern varies with pressure,as shown in figure 6.With the increase of pressure,several transitions are observed obviously.With the needle tip at 1 kPa,the pattern presents irregular layer structure,and the structure of the pattern is unstable.With the increase of pressure within 1–3 kPa,the pattern enlarges and a ring-like structure gradually becomes visible,and the diameter of this pattern then gradually decreases with increasing pressure.When the pressure increases to 5 kPa,the pattern presents double ring and is constricted at the anode plane to a small spot at 9 kPa.It can be seen in figure 5(b)that the pattern has the obvious characteristic of ring-like structure.Within 1–6 kPa,the pattern enlarges and becomes a regular ring with increasing pressure.However,when the pressure continues increasing,the ring-like structure gradually forms separate spots,which will subsequently develop into an anode streamer.The distinct difference between figures 5(b)and(c)is that distinct anode spots could be clearly observed inside the ring,and the luminance and the number of spots increase with increasing pressure.The outer ring forms separate spots within 6–7 kPa and is unable to form a regular pattern when the pressure increases to 8 kPa.

Figure 4.U-P curves of different electrode con figurations.(a)Needle tip.(b)Conical tip.(c)Hemispherical tip.

This research mainly aims at the characteristics of the self organization phenomenon over a metal-surface electrode in low-pressure DC discharge with different electrode con figuration.Figures 4(a)–(c)show the discharge voltage U dependence of pressure P for different rod tips with gap length increases from 100–200mm.The pressure ranges from 1–10 kPa.

However,the formation of different pattern pro files in figure 5 should be interpreted in terms of the formation mechanism of the self-organized pattern.Other studies have shown that every anode spot in the pattern represents a discharge filament,and filaments are ‘indistinguishable’under low-pressure condition[19].Figure 7 shows the discharge pro file of a 200 mm rod-plane gap at 6 kPa,and the exposure time is set as 1000 μs.It can be seen in figure 7 that the discharge pro file could be divided into the filament region and pattern region,and the holistic morphology of the filament region appears cone-shaped and ‘indistinguishable’.Therefore,we speculated that the influence of rod tip shape on the distribution of filaments within the filament region is the main reason for the different pattern pro file with different rod tip.In consideration of the difficulty to observe the filament distribution inside the filament region,numerical simulation is needed in the future.

We carried out laboratory experiments to investigate the characteristics of the self-organized pattern on the surface of a metal electrode under AC voltage for 100–200mm rod-plane gaps with a needle tip,conical tip and hemispherical tip within 1–10 kPa.The influence of the pressure,gap length and shape of the electrode on the pro file and development process of the pattern was analyzed.The following results were obtained.

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Figure 8 shows the influence of gap length on the pro file of the self-organized pattern at 5 kPa.As shown in figure 8,the diameter of the pattern increases gradually with the increase of gap　length.The possible reason　for this phenomenon can be explained by the motion of free electrons.When free electrons move towards the anode electrode,the deviation to axis caused by thermal motion and elastic collision increases gradually,which in turn increases the ionization area on the plane[21,22].Besides,the pro file of the pattern is also significantly affected by gap length.With the needle tip,the pattern changes from layer structure to ring structure with the increase of gap length.With the conical tip,ionized stripes with a more luminous ring on the outside are seen for the gap length between 100 and 150 mm,and the pattern becomes single ring when the gap length is 200 mm.With the hemispherical tip,there are anode spots inside the ring structure,and the luminance and the number of spots increase with increasing gap length.Thus,it can be seen that,in the aspect of pattern pro file,the effect of increasing gap length is similar to that of increasing pressure.

Figure 5.Self-organized pattern of 200 mm rod-plane gap varies with pressure.Exposure time is set as 350 μs.(a)Needle tip(3000 frames/s frame rates,200 × 87 pixel resolution).(b)Conical tip(3000 frames/s frame rates,300 × 130 pixel resolution).(c)Hemispherical tip(3000 frames/s frame rates,550 × 238 pixel resolution).

Figure 6.Diameter of self-organized pattern of different electrode con figurations varies with pressure.

Figure 7.Discharge filament of a 200 mm rod-plane gap with hemispherical tip.Exposure time is set as 1000 μs.

3.2.The development process of the self-organized pattern with a metal anode

It can be seen in section 3.1 that the self-organization phenomenon is observed on the surface of the metal anode within a certain pressure range.Hereafter,we take the 200mm rod-plane gap as an example to describe the development process of the self-organized pattern.

Figure 8.Self-organized patterns of 100–200 mm rod-plane gaps at 5 kPa.(a)Needle tip.(b)Conical tip.(c)Hemispherical tip.Exposure time is set as 350 μs.

Figure 9 shows the development process of the self organized pattern of a 200mm rod-plane gap with a needle tip at 5 kPa.This process contains three key stages:pattern enlargement,pattern stabilization and pattern shrink.As shown in figure 9,the frame before seeing the pattern for the first time is set as t = 0 μs.At t = 604 μs,a small homogeneous spot is generated at the anode.During 604–11461 μs,the spot gradually enlarges and reaches its maximum size at t = 11461 μs.In terms of the pro file of the self-organized pattern,the change of pro file with the time increasing can be divided into three stages:small anode spot,ring-like structure and double-ring structure.During 11461–17493 μs,the diameter of the outer ring basically remains unchanged,but the diameter of the inner ring gradually decreases.The outer ring of the pattern begins to shrink from t = 18099 μs and nearly extinguishes at t =23525μs.Furthermore,the development process of the pattern is accompanied by the transformation from a pattern to a positive column.The degree of ionization at the outer ring increases during 12046–19303μs,and some filaments gradually develop into positive columns with high charge density.More than one positive column could develop forward simultaneously,but when one positive column develops faster due to some accidental reason,its strong axial electric field may inhibit other positive columns and discharge filaments.Therefore,the pattern on the anode surface eventually disappears.

步骤3：计算各洪水场次的评价指标：纳什效率系数(NSE)、洪峰误差百分比以及洪峰出现的时差，如果符合精度要求则结束，如果不符合要求则根据原始值与预测值得到新的误差序列再一次建立ARIMA模型来对误差进行修正；

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It can be seen in figure 13 that the variations of pattern pro file with a hemispherical tip include two aspects:the outer structure and inner structure.As for the outer structure,with the time increasing,the outer part of the pattern becomes a ring-like structure,which gradually forms separate spots and eventually disappears.In terms of the inner structure,the anode spots change from the separate state to connected state.

Figure 9.Development process of the self-organized pattern of a 200 mm rod-plane gap with a needle tip at 5 kPa.

Figure 10.Voltage and current waveform of a 200 mm rod-plane gap discharge with a needle tip at 5 kPa.Discharge voltage is 9.6 kV.Current peak value is 6.69 mA.

Figure 11.Development process of the self-organized pattern of a 200 mm rod-plane gap with a conical tip at 5 kPa.

In order to analyze the influence of tip shape on the development process of the self-organized pattern, figures 11–14 give the development process and waveform of the pattern formation with a conical tip and hemispherical tip at 5 kPa,respectively.As shown in figure 11,the pro file of the pattern maintains a ring-like structure from its origin to extinction.The development process of the pattern also contains three key stages:pattern enlargement,pattern stabilization and pattern shrink.From this research,we believe that the formation of the positive column may be due to the accumulation of positive ions in the pattern.The reason could be that during the shrink process of the pattern within 27247–44740 μs,positive ions in the ringlike pattern drift towards the center of the anode plane,which in turn strengthen the field strength of the area ahead of the center.As the formation of electron avalanches is significantly affected by the polarity effect,the positive column with high charge density will initiate from the center of the pattern.It can be seen in figure 12 that regions A,B and C correspond to the stage of pattern enlargement,pattern stabilization and pattern shrink,respectively.The change law of the pattern pro file could be described as follows.The pattern increases with the decrease of voltage in region A.The voltage increases slightly when the pattern is stable and decreases again during the transformation from the pattern to the positive column.Two peak value positions of current waveform correspond to the maximum size of the pattern and positive column,respectively.

Figure 12.Voltage and current waveform of a 200 mm rod-plane gap discharge with a conical tip at 5 kPa.Discharge voltage is 10.3 kV.Current peak value is 9.4 mA.

Figure 13.Development process of the self-organized pattern of a 200 mm rod-plane gap with a hemispherical tip at 5 kPa.

Figure 14.Voltage and current waveform of a 200 mm rod-plane gap discharge with a hemispherical tip at 5 kPa.Discharge voltage is 13.7 kV.Current peak value is 12.8 mA.

Figure 10 gives the voltage and current waveforms of a 200 mm rod-plane gap discharge with the needle tip at 5 kPa,and the region between the two dash lines corresponds to figure 9.The discharge voltage and peak current are 9.6 kV and 6.7 mA,respectively.As shown in figure 10,the development process of the self-organized pattern is accompanied by current.The chopped wave of voltage waveform represents the beginning of the pattern.In the subsequent process of voltage drop,the pattern experiences enlargement,shrinks and subsequently transforms from the pattern to a positive column.In addition,the elongation of the positive column is the main reason for the surge of the current.

4.Conclusions

Therefore,the reason to form a different pattern pro file could be explained as follows.Due to the sufficient time for electron diffusion at 1 kPa, filaments could occupy more electrode surface to form a layer structure[20].Taking figure 5(b)as an example,the flocculent or liner structure in the middle of the ring-like structure at 3 kPa corresponds to the motion track of the discharge filament during the exposure time of the picture.When discharge filaments which appear randomly are too close to each other,they will interact with each other and move quickly to form the flocculent or liner structure.As for figure 5(c)within 6–8 kPa,the axial electric field of discharge filaments which form the outer ring of the pattern may inhibit other filaments,so the outer ring forms separate spots.

(1)The self-organized pattern can be observed only on the surface of the metal anode,and an upper pressure limit of pattern formation exists.

(2)With increasing pressure,the pattern diameter first increases and then decreases,which means the size of the pattern has a maximum value.

(3)With increasing pressure,the pattern presents a layer structure,single-ring structure and double-ring structure with a needle tip,and the ring-like structure forms separate spots with a conical tip.With a hemispherical tip,there are anode spots inside the ring structure.

首先，应在各种联系过程中不断对变量与不变量之间存在的关系进行了解与分析。其次，结合最终需要的函数关系式列出该函数表达式，不能对两者之间具有怎样的关系进行凭空想象。最后，对于函数动点问题具有的问题若呈现出较为明显的递进关系时，学生则可结合问题第一问的答案对下一问题进行解决，不能仅根据自身的想象对问题进行解答。同时在课后还应让学生们进行深入锻炼，结合实际教学情况布置相应的作业。

(4)With the increase of gap length,the diameter of the pattern increases and the pro file of the pattern changes.

(5)The development process of the pattern contains three key stages:pattern enlargement,pattern stabilization and pattern shrink.

This work is supported by National Natural Science Foundation of China(Grant No.51277063).

三是流量调节不及时，对水闸效益发挥及工程安全带来不利影响。当长江水位下降时，闸门开高不及时增加，造成引水不足，影响工程效益发挥；当长江水位上涨时，闸门开高不及时降低，会造成超设计工况运行，给水闸工程本身及输水河道的安全运行造成威胁。

References

[1]Kanazawa S et al 1988 J.Phys.D App.Phys.21 838

[2]Fang Z,Qiu Y and Luo Y 2003 J.Phys.D App.Phys.36 2980

[3]Purwins H G J and Berkemeier J 2011 IEEE Trans.Plasma Sci.39 2116

[4]Zhu W et al 2014 Plasma Sources Sci.Technol.23 054012

[5]Shirai N,Uchida S and Tochikubo F 2014 Plasma Sources Sci.Technol.23 054010

[6]Verreycken T,Bruggenman P and Leys C 2009 J.Appl.Phys.105 083312

[7]Wilson A et al 2008 Plasma Sources Sci.Technol.17 045001

[8]Maszl C,Laimer J and Störi H 2011 IEEE Trans.Plasma Sci.39 2118

[9]Shirai N et al 2011 IEEE Trans.Plasma Sci.39 2652

[10]Astrov Y A,Lodygin A N and Portsel L M 2015 Phys.Rev.E 91 032909

[11]Zheng P C et al 2015 Plasma Source Sci.Technol.24 015010

[12]Zhu P et al 2015 Phys.Plasma 22 023507

[13]Wang Y J et al 2014 Phys.Plasma 21 073505

[14]Stauss S et al 2013 Plasma Sources Sci.Technol.22 025021

[15]Li Z F et al 2013 IEEE Trans.Plasma Sci.41 3135

[16]Trelles J P 2013 Plasma Sources Sci.Technol.22 025017

[17]Trelles J P 2014 Plasma Sources Sci.Technol.23 054002

[18]Yang Y Q et al 2017 Plasma Sci.Technol.19 105401

[19]Liu W B and Dong L F 2015 Acta Phys.Sinica 64 245202(in Chinese)

[20]Li X C et al 2008 Acta Phys.Sinica 57 1001(in Chinese)

[21]Rizk F A M and Trinh G N 2014 High Voltage Engineering(New York:CRC Press)

[22]Meek J M and Craggs J D 1953 Electrical Breakdown of Gases(London:Clarendon)