Investigation on the electrode surface roughness effects on a repetitive selfbreakdown gas switch

Fanzheng ZENG (曾凡正),Song LI (李嵩),Hao CAI (蔡浩),Quancai ZHANG(张全才),Jinhong WEI(韦金红),Junting WANG(王俊婷),Zhaohua LIU (刘照华),Lei WANG (王蕾),Jingming GAO (高景明),Hong WAN (万红),∗and Baoliang QIAN (钱宝良),∗

1 College of Advanced Interdisciplinary Studies,National University of Defense Technology,Changsha 410073,People’s Republic of China

2 The 93986 Unit,Hotan 848000,People’s Republic of China

3 College of Aerospace Science and Engineering,National University of Defense Technology,Changsha 410073,People’s Republic of China

Abstract In this work,the influence of the electrode surface roughness on the self-breakdown gas switch is investigated by physical analysis,computer simulation and experiment.Cu-W electrodes of different surface roughness were tested under the conditions of a pulse repetitive frequency of 50 Hz,self-breakdown voltage of ～30 kV,and peak current of ～2 kA for ～93000 shots (the total charge transferred was ～15 C).The coefficients of variation of the self-breakdown voltage of Cu-W 0.8,Cu-W 3.2 and Cu-W 12.5 electrodes were ～2.95%,～1.62% and ～1.16%,respectively.With the increase of electrode roughness,the erosion area decreased continuously,indicating that the breakdown positions were more stable and the coefficient of variation of breakdown voltage decreased.The method showed that decreasing the coefficient of variation of the self-breakdown voltage by increasing the surface roughness of electrode greatly improves the stability of the self-breakdown switch,which is significant for their application in compact highpower pulse power devices over a long time with stable operation.

Keywords: gas switch,self-breakdown,surface roughness,coefficient of variation

1.Introduction

High-power pulse generator technology,as an electrophysical technology where the electric power rising speed can be larger than 1015W s-1,has been widely used in high power microwave generation,nuclear physics,plasma physics and other scientific and engineering fields.High power switches,as the core device in high-power pulse generators to compress the electric pulse power,largely determine the application of such generators.Gas switches are widely used in high-power pulse generators due to their advantages of simple structure design,low cost,high voltage bearing range,large current carrying capacity and good conduction characteristics [1-3].

Generally,gas switches are divided into self-breakdown switches and triggered switches.Compared to self-breakdown switches,trigger switches have trigger poles which can decrease the jitter of output pulses.However,the structures of trigger switches are complex,and the trigger poles are easy to ablate,which will affect the lifetime and uses of trigger switches [4-6].Furthermore,an additional high voltage system for generating trigger pulses is needed,which also decreases the robustness and compactness of the whole system.Self-breakdown switches have the advantage of simple structures,but the jitters in these are larger than those of trigger switches.Therefore,research on a low jitter,long lifetime self-breakdown gas switch is an important prospect for application in compact high-power pulse power devices with a long life and stable operation,which is the motivation for this work [7-9].

The coefficient of variation of the self-breakdown voltage is a key evaluation factor for self-breakdown gas switches[10-13].The coefficient of variation of the self-breakdown voltage η can be calculated from equations (1)-(3),

where Uiis the self-breakdown voltage,Uis the average breakdown voltage,N is the shot number,and σ is the variation of the self-breakdown voltage [14].

According to the traditional concept,the smaller the surface roughness the switch electrodes have,the smaller the coefficient of variation that the self-breakdown voltage occupies.However,in our work,we find that the surface of the electrodes will be eroded in the experiment,and pitting and bulging will also be produced in the breakdown experiments,especially in long-time operating studies with a high repetition rate.The pitting and bulging will shift the surface state of the smooth electrodes,pulse by pulse,which will further affect the stability of breakdown processes.If the surface roughness of the electrodes increases,the electric field enhancement on the electrode surface will increase,and initial plasma electrons will be concentrated at fixed positions on the electrodes correspondingly,indicating that the erosion on the electrode surface will become more concentrated,which may reduce the coefficient of variation of the self-breakdown voltage.

In this work,the influence of the surface roughness on self-breakdown gas switches is investigated by physical analysis,computer simulation and experiment.The Cu-W electrodes of different surface roughnesses were tested under the conditions of a repetitive frequency of ～50 Hz,selfbreakdown voltage of ～30 kV,and peak current of ～2 kA for～93000 shots (the total charge transferred was ～15 C).The coefficients of variation of the self-breakdown voltage of Cu-W 0.8,Cu-W 3.2 and Cu-W 12.5 electrodes were ～2.95%,～1.62% and ～1.16%,respectively.The results show that,to some extent,the coefficient of variation of the self-breakdown voltage can be reduced by increasing the surface roughness of the electrodes,which is useful to expand the prospects for application of self-breakdown switches.

2.Analysis of the breakdown of gas switches

The schematic diagram of the electrodes is shown in figure 1.The electrodes consist of an anode and a cathode,and their breakdown points occur at the bulge ring.The microscopic diagrams of the anode and cathode are basically the same,so for simplicity,images of the cathode are not given.The radial width of the ring is L,the bottom width,height,and period of the tips are l,h,and w,respectively.The number of tips is n=L/w.

In order to study the relationship between the electrode surface roughness and the coefficient of variation of the selfbreakdown voltage,Cu-W electrodes of different roughnesses were processed.The Cu-W electrodes were processed into Cu-W 0.8,Cu-W 3.2 and Cu-W 12.5,where 0.8,3.2 and 12.5 represent the surface roughness.The smaller the value,the smoother the electrode surface is.The surface roughness is a rough estimated value,set by the manufacturer after comparing the electrode surfaces to standard parts.Before the experiment,the morphology of the electrodes’ surfaces was analyzed by a profilometer,shown in figure 2,and the observation position is the bulge ring,labeled in figure 1(b).It is obvious that with the increase of the electrode surface roughness,the height of tips will increase,the bottom width of tips will remain basically unchanged and the number of tips will decrease.

A physical model is established to investigate the generation and the development process of initial electrons on the tips,which is shown in figure 3.With the increase of the voltage between the electrodes,the initial electrons will escape continuously from the electrode surface,and cause an electron avalanche and form streamers between the electrodes.According to[15],in region ξ the number of the electrons produced by the field emission is α(βE)2,where α is a constant,β is the electric field amplification coefficient,and E is the macroscopic electric field strength.According to Townsend theory,the number of electrons can be calculated from equation (4) when the electron avalanche develops to the boundary of region ξ,

where λ is the mean free path of the electron,Wiis the ionization energy of the gas,and e is the charge of the electron [16,17].Ify=(y<0),the number of electrons can be calculated from equation (5)

If the breakdown probability caused by each electron in the boundary of region ξ is equal and can be expressed byF(1 ),then when the number of seed electrons is n,the breakdown probability can be calculated by using

It can be seen that with the increase of roughness,the heights of tips h and the electric field amplification coefficient β will increase.According to equation (5),the number of electrons on region ξ will increase,and the breakdown probability will increase according to equation(6).Therefore,with the increase of roughness,the breakdown probability at the electrode tip increases,which means the breakdown on the tips happens easily.The fewer the number of tips,the fewer points that are prone to breakdown,and the breakdown is more likely to occur in a few peak positions.Therefore,with the increase of the electrode surface roughness,the breakdown is more likely to occur in a few peak positions,which means the coefficient of variation of the self-breakdown voltage may be reduced.

Additionally,during the breakdown experiment,the surfaces of electrodes will be eroded,and pitting and bulging will be produced,especially in long-time operating studies with a high repetition rate.As for the electrodes with small surface roughness,the pitting and bulging are relatively larger than the tips on the electrode surfaces and will obviously shift the surface state of the electrodes,pulse by pulse,which will affect the stability of breakdown processes.As for the electrodes with the large surface roughness,the pitting and bulging are smaller than the tips on the electrode surfaces,which will have almost no effect on the stability of the breakdown processes.Therefore,with the increase of the electrode surface roughness,the pitting and bulging produced during the breakdown experiment will have almost no effect on the stability of the breakdown processes,which means the coefficient of variation of the self-breakdown voltage may be reduced.

3.Numerical simulation study

The emission process of the electron beam on the electrode surface was investigated with a 2.5D fully electromagnetic PIC code.In order to simplify the model,only the raised ring of the electrode surface (as shown in figure 1(b)) was simulated,and the results are shown in figure 4.The left and right ends are the cathode and anode respectively,and voltage of 30 kV is loaded between them.The thickness of the ring is 1 mm,the inner and outer radii of the ring are 10 mm and 10.8 mm respectively,and the gap between the ring is 5 mm.Table 1 shows the comparison of parameters of the tips shown in figure 1(b).Due to the accuracy of the 2.5D fully electromagnetic PIC code,the height of the tips was magnified about ten times correspond to that in figure 2.According to the model discussed in section 2,the electrodes with 2,4 and 8 tips can be denoted by roughness 12.5,roughness 3.2 and roughness 0.8 respectively for the convenience of description.It can be seen that the larger the roughness,the fewer the number of tips,the higher the height of tips,and the more uneven the electron beam emission.

Table 1.A comparison of parameters of the tips.

Figure 5 shows the current density curves of electrodes of different surface roughness at z=1.1 mm,which represents the surface of the electrodes.It can be seen that the larger the roughness,the more uneven the current density in the r direction,and the larger the peak value of the current density,indicating that the plasma electrons are generated on the more concentrated position.Therefore,the breakdown will happen on the concentrated position,which means the coefficient of variation of the self-breakdown voltage will decrease.The numerical results meet the analysis given in section 2.

Figure 1.A schematic structure and diagram of the switch electrodes,(a)basic structure of switch electrodes,(b)microscopic diagram of the anode.

Figure 2.The morphology of the electrodes’surfaces observed by a profilometer.

Figure 3.A physical model of the switch electrodes,where the distance between the electrodes is d,the bottom width and height of the tip are l and h.The seed electrons are produced in region ξ,where h＜x≪d.

Figure 4.Comparison of electron emission from electrode surfaces with different roughnesses,(a)roughness 12.5,(b)roughness 3.2 and(c) roughness 0.8.

Figure 5.Comparison of current densities on electrode surfaces with different roughnesses at z=1.1 mm (shown in figure 4 as dotted lines).

Figure 6.Schematic diagram of the test platform.

Figure 7.Typical voltage waveforms of charge voltage and load voltage.

Figure 8.The coefficients of variation of the self-breakdown voltage of Cu-W electrodes with different roughnesses.

Figure 9.The self-breakdown voltage of Cu-W electrodes with different roughnesses for 16000 shots.

4.Experiment

4.1.Experimental setup

A test platform was established,as shown in figure 6.The platform includes a DC primary source,a solid-state high voltage pulse forming line (SHVPFL),a self-breakdown gas switch,a load (low-inductance resistor group) and an oscilloscope(600 MHz).The working process can be described as follows.Initially,the DC power source is used to charge the SHVPFL.The charge voltage continues to increase.As the charge voltage hits the breakdown voltage of the self-breakdown gas switch,the gap of the switch will be closed,and the modulated energy is transferred to the load.After one discharge cycle ends,the next cycle starts.The measurement system includes the electrical measurement system and the microstructure observation system.The electrical measuring system includes two high voltage probes,a Rogowski coil and a digital oscilloscope,which will be used to measure the charging voltage,the load voltage and the load current.The microstructure observation system contains a laser confocal scanning microscope (LCSM),which is used to observe the surface roughness and microstructures of the electrodes.For insulation,observation,and safety reasons,the external wall of the gas switch cavity is made of plexiglass,and the cavity is filled with nitrogen at 1.0 atmosphere during the experiment.

4.2.Roughness contrast experiment

In order to study the relationship between the electrode surface roughness and the coefficient of variation of the self-breakdown voltage,a contrast experiment with electrodes of different roughnesses was designed.Under the same experimental conditions: a repetitive frequency of 50 Hz,electrode gap of 5 mm and nitrogen pressure of 1.0 atmosphere,the Cu-W electrodes of different roughnesses of 0.8,3.2 and 12.5 were tested for the breakdown experiment.For each pair of electrodes of different roughnesses,the experiment was divided into 3 rounds and 15 steps.Steps 1 to 5,steps 6 to 10 and steps 11 to 15 serve as the first,the second and the third rounds of experiment respectively,in which the shots number doubles from 1000 to 16000.So,each pair of electrodes of different roughnesses were tested for ～93000 shots (the total charge transferred was ～15 C).Typical voltage waveforms are illustrated in figure 7,which shows the 3rd step of the experiment with Cu-W 3.2 for 4000 shots.The voltage waveforms of other steps with different roughnesses are almost the same,except the coefficient of variation of the self-breakdown voltage and the peak voltage of the load.In the experiment,the charge voltage continued to increase.As the charge voltage hit the breakdown voltage of the selfbreakdown gas switch,the gap in the switch was closed,and the modulated energy was transferred to the load.After one discharge cycle ended,the next cycle started.Owing to the 5 mm gap and the cavity filled with nitrogen at 1.0 atmosphere,the self-breakdown voltage,the peak voltage of the load and the peak current of the load were maintained at ~30 kV,~15 kV,~2 kA,for each step.

4.3.Experiment result and discussion

Figure 8 shows the coefficients of variation of the self-breakdown voltage of Cu-W 0.8,Cu-W 3.2 and Cu-W 12.5 electrodes.Each point represents the average value of the coefficient of variation of the self-breakdown voltage of different electrodes at different shot numbers of the three round experiments,while the vertical line through each point stands for the error range of that average value.It can be seen that with the increase of roughness,the coefficients of variation of the self-breakdown voltage decrease continuously.The coefficients of variation of the selfbreakdown voltage of Cu-W 0.8,Cu-W 3.2 and Cu-W 12.5 electrodes are ～2.95%,～1.62% and ～1.16%,respectively.Additionally,with the increase of roughness,the error range of the average value decreases continuously.

Figure 10.The electrodes with different roughnesses after the experiment,(a) Cu-W 0.8,(b) Cu-W 3.2 and (c) Cu-W 12.5.

Figure 11.LCSM images of the Cu-W electrodes.(a) The central part of Cu-W 0.8 before the experiment,(b)the central part of Cu-W 3.2 before the experiment,(c)the central part of Cu-W 12.5 before the experiment,(d)the ring part of Cu-W 0.8 after the experiment,(e)the ring part of Cu-W 3.2 after the experiment and (f) the ring part of Cu-W 12.5 after the experiment.

Figure 9 shows the self-breakdown voltage of Cu-W 0.8,Cu-W 3.2 and Cu-W 12.5 electrodes for 16000 shots.The self-breakdown voltage of Cu-W 0.8,Cu-W 3.2 and Cu-W 12.5 electrodes stayed at approximately 28.0-32.0 kV,28.5-31.0 kV and 29.5-30.7 kV,respectively.It is obvious that with the increase of roughness,the coefficients of variation of the self-breakdown voltage decrease continuously.

Figure 10 shows the Cu-W electrodes with different roughnesses after the experiment.The erosion of the anode and cathode was basically the same,so for simplicity the images of cathode are not shown.An erosion ring can be seen on the surface of the electrodes.The widths of the erosion ring of Cu-W 0.8,Cu-W 3.2 and Cu-W 12.5 are 2.1-3.0 mm,1.3-2.1 mm and ～1.1 mm,respectively.It illustrates that with the increase of the surface roughness,the widths of the erosion ring are decreased and become more uniform,indicating that the erosion on the electrode surface becomes more concentrated.As a result,the coefficient of variation of the self-breakdown voltage is decreased,which verifies our analysis and simulation results.

In order to analyze the influence of the microcosmic structure,an LCSM was used to observe the surface roughness and microstructure of the electrodes.Figure 11 shows the observation images of the Cu-W electrodes before and after the experiment.The field of view of the LCSM is 694 μm×520 μm.The color label and numbers stand for the surface roughness,and the unit is μm.The green label represents the height of zero.With the increase of height,the color turns to red and with the decrease of height,the color turns to black.

Figures 11(a)-(c)show the central parts of the electrodes before the experiment.It can be seen that there are several raised rings on the surface of the Cu-W electrodes,and the raised rings represent the tips which have been shown in sections 2 and 3.With the increase of roughness,there is a decrease in the number of tips and an increase on the height of tips.This is consistent with the analysis and simulation mode in sections 2 and 3,which confirms the feasibility of the analysis and simulation results.

Figures 11(d)-(f) show the bulge ring parts of the electrodes after the experiment.It can be seen that the surfaces of electrodes were eroded,and the height of the tips on the electrode surfaces were clearly decreased,while pitting and bulging were produced.As for the Cu-W 0.8 electrodes,after the experiment the tips almost disappeared and the pitting and bulging shifted the surface state of electrodes,which would affect the stability of breakdown processes,and the coefficient of variation of the self-breakdown voltage would be large.With the increase of surface roughness(especially for the Cu-W 12.5 electrodes),after experiment the tips still existed,and the pitting and bulging were smaller than the tips on the electrode surfaces,which had little effect on the stability of the breakdown processes and the coefficient of variation of the self-breakdown voltage would be small.Therefore,with the increase of the electrode surface roughness,the pitting and bulging produced during the breakdown experiment would have no affect on the stability of the breakdown processes,which means the coefficient of variation of the self-breakdown voltage would decrease.

5.Conclusions

In this work,the influence of electrode surface roughness on the coefficient of variation of the self-breakdown voltage is investigated.First,the influence is analyzed from physical analysis and computer simulation,which to a certain extent illustrates that the larger the surface roughness,the smaller the coefficient of variation of the self-breakdown voltage.Then,the Cu-W electrodes of different roughnesses were tested for breakdown in an experiment for ～93000 shots(the total charge transferred was ～15 C).The coefficients of variation of the self-breakdown voltage of Cu-W 0.8,Cu-W 3.2 and Cu-W 12.5 electrodes were～2.95%,～1.62%and ～1.16%,respectively.With the increase of electrode roughness,the erosion area decreased continuously,indicating that the breakdown positions were more stable and the coefficient of variation of the self-breakdown voltage decreased.The method of decreasing the coefficient of variation of the self-breakdown voltage by increasing the surface roughness of the electrode greatly improves the stability of self-breakdown switches,which is of significance to their application in compact high-power pulse power devices over a long time and with stable operation.

Acknowledgments

This work was supported by Huxiang Youth Talent Support Program (No.2020RC3030) and State Key Laboratory of Pulsed Power Laser Technology (No.SK2021ZR02).The authors wish to thank Professor H W Yang for his encouragement and valuable suggestions.

Authors’ contributions

Bao-liang QIAN and Hong WAN are corresponding authors.Fan zheng ZENG and Song LI are co-first authors.