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Huang Jie, Yang Lin, Zhang Hongchao, Chen Lei, Wu Xianying. Temporal and spatial evolution of air-spark switch plasma investigated by the Mach–Zehnder interferometer. Chinese Physics B, 2019, 28(5): 055202  
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Temporal and spatial evolution of air-spark switch plasma investigated by the Mach–Zehnder interferometer
Huang Jie1, 2, Yang Lin2, †, Zhang Hongchao3, Chen Lei2, Wu Xianying1
College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China
Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621900, China
Nanjing University of Science and Technology, Nanjing 210094, China

 

† Corresponding author. E-mail: fuyunyufeng@163.com

Abstract

An air-spark switch plasma was diagnosed by the Mach–Zehnder laser interferometer with ultra-high spatial and temporal resolution. The interferograms containing plasma phase shift information at different time were obtained. The phase shift distributions of the plasma were extracted by numerically processing the interferograms. The three-dimensional (3D) electron density distributions of the air-spark switch plasma were then obtained. The working process of the air-spark switch was described by analyzing the temporal and spatial evolution of the plasma electron density.

PACS: 52.75.Kq;52.80.-s;07.60.Ly
Keyword:air-spark switch;Mach-Zehnder laser interferometer;arc channel;electron density
1. Introduction

Gas spark switches as the key component are widely used in pulsed power generators, pulse modulation networks, vacuum electron devices, particle accelerators, and other high pulsed power devices.[1–4] They have extraordinary capabilities that are well suited for applications that require switching of very high voltage, long life, and rather high currents. The main purpose of researching gas spark switches is to achieve high reliability. At the same time, high reliability of gas spark switch is also the guarantee for the safe operation of pulse power equipment. At present, the research on gas spark switch mainly focuses on the numerical calculation and experimental research of its circuit characteristic parameters, the numerical simulation of the main arc of the switching arc and the electrode ablation.[5–8] With the development of plasma diagnostic techniques, the accurate diagnosis of plasma parameters of gas spark switches has become possible. These new plasma diagnostic techniques help us to better understand the working process of gas spark switches.[9, 10]

The air-spark switch is a kind of gas spark switch that uses air as the insulating medium. The electron density distribution and evolution of the air-spark switch discharge plasma have a significant effect on the operating process of the air-spark switch. It is well known that the air-spark switch discharge is a transient and complicated physical process. Generally, the major physical processes of discharge contain two stages, plasma formation and plasma expansion. However, there is no clear threshold for the two stages. Once the plasma is produced, it will expand in the background gas and the shock waves will form because of the steep density gradient.[11, 12] Many works have been carried out to comprehend the processes of plasma formation and plasma expansion in the background gap. Zhang et al. studied laser induced plasma in air using the laser interferometry and a three-dimensional (3D) electron density profile was obtained.[13, 14] Hairlal et al. used laser shadowgraph and fluid simulation to study the shock wave propagation, estimating the pressure and the velocity of the shock front.[15] Yang et al. studied laser induced copper plasmas in air using fast spectral imaging and two-color laser interferometry, and the density profiles of Cu atoms and electrons were obtained.[16]

Obtaining the exact parameters of air-spark switch plasma is the key to understanding the working process of the air-spark switch, but it is a challenge because of the rapid changes of the plasma parameters in time and space. Fortunately, the laser interference imaging can “freeze” the plasma, obtain and analyze the transient parameters of the plasma by numerical processing the interferograms. In this paper, the Mach–Zehnder (M–Z) laser interferometer with laser wavelength 532 nm is used to diagnose the gas spark switch plasma. The interferograms containing plasma information are obtained, and the electron density distribution of the plasma is presented by numerical processing the interferograms. The spatiotemporal evolution of the plasma electron density is analyzed.

2. Theory and assumptions

Low temperature plasma is mainly composed of electrons, ions, and neutral atoms.[17] Different types of particles have different contributions to the refractive index of the plasma. So the refractive index of plasma can be written as[14]

where n is the refractive index of the plasma, λ is the wavelength of the probe laser beam, e0 is the elementary charge, me is the electronic mass, ɛ0 is the dielectric constant, c is the speed of light in vaccum, NA is the Avogadro constant. Ne is the number density of free electron, and Nk is the number density of particle of kind k. Ak and Bk denote the gas-specific constants for these particles. In Eq. (1), the first term is the contribution from free electrons and the second term from heavy particles (atoms and ions).

Generally, we can obtain the accurate plasma electron density by measuring the refractive index distributions of plasma at two separate wavelengths.[18] However, in the plasma, the refractive index is primarily a function of the electron density, which is the main plasma parameter determined by refractive index measurements. In particular, when the electron density is above 2×1019 cm−3, the influence of electrons on the refractive index is dominants and the heavy particle influence is neglected entirely.[19] For air-switched plasma, in the arc-column region between the electrodes, we assume that the plasma is fully ionized. At the same time, we ignore the effect of ions on the refractive index. Thus the electron density N e can be calculated from a refractive index distribution at a single probing wavelength λ

Laser interferometry measures the change in refractive index of a tested plasma. When the probing laser beam passes the plasma, the phase shift will be recorded in the interferograms.[19] The can be expressed as[16]
where is the phase shift of the probing laser beam passed through the plasma, n is the refractive index of the plasma, n 0 is the refractive index of air ( ), and l is the propagation path of the probing laser beam in the plasma.

For axisymmetric plasma systems, digitizing the interferograms and performing the inverse Abel transformation, we can reconstruct the spatial distribution of the refractive index, and then the spatial and temporal distribution of the electron density in the plasma can be obtained. The inverse Abel transformation can be expressed as follows:

There is a simple approximation formula: if the electron density of the plasma is much lower than the critical electron density, then the phase shift is proportional to λ[20]
For a probing laser beam with wavelength of 532 nm, the critical electron density is 4×1021 cm−3. According to previous studies, the critical electron density is much larger than the electron density of the air-spark switching plasma.[21] Therefore, the electron density distribution of the air-spark switching plasma can be calculated according to the approximation formula.

3. Experimental setup

The experimental setup is shown in Fig. 1. The output laser (wavelength 1064 nm) of a Q-switch Nd: YAG laser is frequency-doubled with low efficiency (15%) to provide a probe pulse laser (λ = 532 nm), and the full width at half maximum (FWHM) of the laser pulse is about 7 ns. Then the probe pulse laser passes through an aperture that is used to adjust the intensity of the laser beam. A sample optical path delay system composed of two mirrors is used to adjust the direction of propagation of the laser beam. Then, the laser beam is separated into two beams by the Mach–Zehnder interferometer. The plasma is situated at one arm of the Mach–Zehnder interferometer. The laser beam which passes through the plasma is called the probe beam and the other beam that does not pass through the plasma is called the reference beam. The probe beam passed through the plasma interferes with the reference beam and produces an interferogram image on the charge coupled device (CCD) camera. The CCD camera is connected with a personal computer, which is used to display and store the interferograms in real time. To improve the spatial resolution of the device, a microscope (magnification of 10×) is installed on each arm of the interferometer. So, the spatial resolution of the interferometer can reach (for one pixel). The temporal resolution of the interferometer is determined by the FWHM of the laser pulse that is 7 ns. In order to eliminate the effects of plasma luminescence and other stray light and improve the contrast of the interferograms, a bandpass filter (λ =532 nm, FWHM =1 nm) is used in front of the CCD camera. To accurately “freeze” the plasma and obtain an interferogram containing plasma information, the digital delay pulse generator (DG535) is used to control the time series of the laser (Nd: YAG), the high voltage power supply (HV Power Supply), and the CCD camera.

Fig. 1. The experimental set for laser interferometry to diagnose the air-spark switching plasma. KDP: potassium dihydrogen phosphate, M: mirror, BS: beam splitter, CCD: CCD camera, PC: personal computer, DG645: digital delay pulse generator, HV power supply: high voltage pulse power supply.

In our experiments, for the convenience of observation and research, we chose a two-electrode gas switch and simplified the switch structure as a two-tip discharge structure, whose schematic diagram is shown in Fig. 1. The plasma was generated between two needle-type copper electrodes, the gap between them was 2 mm. The air-spark switch was ignited in self-breakdown mode. The output voltage amplitude of the high-voltage pulse power supply was −10 kV, and the discharge duration was . The typical waveforms of the air-spark switch ignited in air are shown in Fig. 2.

Fig. 2. Waveforms of the current I and voltage U of an air-spark switch ignited in air.
4. Results and discussions
4.1. Interferograms

All of our experiments are performed in air. In our experiments, the ignition of the air-spark switch is in the single ignition mode. Although the experimental device can obtain only one interferogram in a single discharge of air-spark switch, the stability of the high-voltage pulsed power supply ensures that the time jitter of the discharge is very small ( ). At the same time, the air-spark switch is simplified to a two-needle-type-electrodes discharge structure such that each discharge is produced at the tip of the needle. For the two reasons above, the good reproducibility of the experiment can be ensured. Time series is controlled by using DG535, the interferograms of different delay time can be obtained. The temporal and spatial evolution of the plasma electron density can be studied by processing the interferograms.

Typical interferograms obtained at different delay time are shown in Fig. 3. The interferogram in Fig. 3(a) is obtained when the electrode gap has just been broken down and the current in the electrode gap has just been generated. For the convenience of record and research, the moment of obtaining this interferogram is defined as time zero. In the interferogram in Fig. 3(a), the interference fringes are shifted in a small area of the electrode gap, especially near the cathode, which indicates that there is an electron cloud near the cathode. The interferogram in Fig. 3(b) is obtained at t = 10 ns. The plasma channel completely forms and a typical columnar plasma region can be observed in the electrode gap.

Fig. 3. The interferograms of air-spark switch discharge plasma obtained at different delay time: (a) 0 ns, (b) 10 ns, (c) 75 ns, (d) 130 ns, (e) 240 ns, (f) 420 ns.

The interferogram in Fig. 3(c) is obtained at t = 75 ns. A spherical plasma region is observed, which indicates that the plasma has expanded into the surrounding air. From the interferogram in Fig. 3(d) that is obtained at t = 130 ns, we find that the plasma has expanded into the surrounding air completely. The interferograms in Figs. 3(e) and in 3(f) are obtained at t = 240 ns and t = 420 ns, respectively. The plasma area then becomes bigger and bigger.

4.2. Phase shift distribution

The interferograms obtained in the experiments have a high quality and can be used to calculate the phase shift of the interference fringes. The phase shift ( ) is the most critical parameter to calculate the electron density of the plasma. First, the interferograms are digitized and low pass filtered. We perform a fast Fourier transformation (FFT) analysis to extract the phase shift from the fringe pattern, select the phase main value of the interferograms in the frequency domain, and then perform inverse FFT transformation to obtain the phase distribution.[22] Air-spark switching plasmas have high electron densities and density gradients. When the plasma expands into the atmosphere, high-speed diffusion of plasma always induces shock waves, which will cause phase shift discontinuity. The resulting phase is wrapped into interval ]. To obtain a continuous phase, a phase unwrapping algorithm that uses graph cuts is applied.

To avoid confusion, we consider the condition when the arc channel is a column, and the electron density distribution is radially symmetric. The electron density is uniform in the z direction as shown in Fig. 4. The obtained phase shift distribution is shown in Fig. 5 as a false color image. According to formula (1), we know that the refractive index of plasma is mainly composed of two parts, one is the contribution of electrons, and the other is the contribution of ions and neutral atoms. Electrons and heavy particles have opposite contributions to the refractive index of plasma. The contribution of electrons to the refractive index makes the refractive index smaller, but the contribution of heavy particles to the refractive index makes the refractive index larger. Therefore, according to formula (3), when the contribution of electrons to the refractive index dominates, the phase shift is negative on the phase shift distribution. Conversely, when the contribution of the heavy particles to the refractive index dominates, the phase shift is positive on the phase shift distribution. From Fig. 5, we find that some areas have darker colors (positive phase shift) surrounding the arc channel boundary. The dense compressed air layer contains lots of neutral atoms. The air-spark switching plasma is generated between the electrodes and then expands into the surrounding air at supersonic speed, this will compress the surrounding air to form a dense compressed air layer. The dense compressed air layer shows a clear plasma boundary, so we can observe the plasma shape after complete diffusion.

Fig. 4. Probing diagram of an arc channel in the air medium.
Fig. 5. Phase shift distribution of air-spark switch plasma obtained at different delay time: (a) 0 ns, (b) 10 ns, (c) 75 ns, (d) 130 ns, (e) 240 ns, (f) 420 ns. The phase shift is expressed in radian.
4.3. Electron density distribution

For axisymmetric plasma systems, the inverse Abel transform is applied to calculate the 3D electron density distribution from the phase shift distribution. From Fig. 5, we can see that the air-spark switch plasma has good symmetry, so the inverse Abel transformation based on the Hanke–Fourier method[23] is applied to calculate the refractive index of the plasma. The result is shown in Fig. 6. Although the electron density in the arc channel is lower than 2×1019 cm−3, we estimate the influence of the atom on the refractive index.[24] The estimation results show that the contribution of an electron to the refractive index is 1000 times that of an atom. Therefore, in the arc channel, the contribution from atoms to the refractive index is still negligible.

Fig. 6. The 3D electron density distribution extracted from the phase shift distribution at different delay time: (a) 0 ns, (b) 10 ns, (c) 75 ns, (d) 130 ns, (e) 240 ns, (f) 420 ns.

Figure 6 shows the temporal and spatial evolution of the air-spark switch plasma. In the initial discharge, at the tip of the cathode, the field emission provides the seed electrons for discharge. These seed electrons move toward the anode under the action of the electric field and collide with the background gas (air), producing a large amount of secondary electrons. The seed electrons and secondary electrons both move toward the anode and ionize the background gas under the action of the electric field. The electron avalanche effect causes a dense cloud of electrons formed near the cathode in a very short period of time. The electron cloud is shown in Fig. 7(b), the blue area near the cathode tip. Figure 7(b) indicates that the electron density near the cathode is higher than that near the anode in arc channel at the beginning of discharge. From Fig. 7(c), the electron density is up to 4.2×1019 cm−3 near the cathode, but the electron density near the anode is very small. The electron density distribution between the electrodes is shown in Fig. 7(c) and approximately fitted by a Boltzmann function (the red-solid line).

Fig. 7. Electron density distribution and phase shift distribution at the beginning of discharge (t = 0 ns) when the arc channel is just formed: (a) the interferogram, (b) the phase shift distribution, (c) the electron density distribution between the electrodes.

The electrons accelerate toward the anode under the action of the electric field, and continuously ionize the neutral atom during the movement. The electron avalanche effect causes the arc channel to form quickly. So the initial plasma is generated in a short time. A large number of high-energy electron bombardment of the anode results in a large number of secondary electrons generated at the anode. The newly generated secondary electrons are attracted and accelerated by the anode, this results in more secondary electrons generated at the anode. So a dense electron cloud will form near the anode. Two high-density areas of electrons are observed near the electrodes when the arc channel is fully formed. This result is shown in Figs. 8(b) and 8(c). For the electron cloud near the cathode, there are three main sources of electrons: (i) the electrons from field emission, (ii) the secondary electrons from ionized neutral atoms, and (iii) the secondary electrons from ion bombardment cathode. For the electron cloud near the anode, there are also three main sources of electrons: (i) the electrons from field emission, (ii) the secondary electrons from ionized neutral atoms, and (iii) the secondary electrons from electron bombardment anode.

Fig. 8. Electron density distribution and phase shift distribution at t = 75 ns. The arc channel is completely formed at t = 75 ns. Two high-density areas of electrons are observed near the electrodes. The compressed air layers are observed due to the diffusion of the plasma. (a) The interferogram, (b) the phase shift distribution, (c) the electron density distribution between the electrodes.

Intense collision and ionization lead to dense plasma generation during the formation of arc channels. This high temperature and high density plasma will expand into the air due to the pressure gradient in the plasma. The compressed air layer is generated because of the diffusion of the plasma, and is shown in Figs. 8(a) and 8(b). At the same time, this compressed air layer reveals the clear profile and diffusion radius of the plasma.

The plasma expanding into air is accompanied with the density decrease, the radius increase, and the temperature reduction. In our experiment, we select two reference locations, y1 located near the cathode and y2 located near the anode, as shown in Fig. 9(a). The distance between the reference position and the electrode tip is about . Figure 9(b) shows the radial electron density distribution at t = 0 ns at y 1. The electron density profile is approximately fitted by a Gaussian function (the red-solid line). Figure 7(b) indicates that the arc channel is very narrow about when it is just formed, but the electron density of the plasma is very high (4×1019 cm−3) at position y1. In the same manner, the radial distribution of electron density is obtained at different time, the result is shown in Fig. 10. Figure 10(a) and 10(b) show the evolution of electron density and radius of plasma with time at positions y1 and y2, respectively. Figure 10(a) shows that near the cathode, the electron density continues to decrease and the radius of plasma continues to increase due to the diffusion of the plasma. However, figure 10(b) shows that the electron density increases first and then decreases near the anode because of the formation of arc channels and subsequent diffusion of the plasma. The maximum density is up to 2.5×1019 cm−3 at t = 75 ns. The radius of plasma continues to increase near the anode.

Fig. 9. Two reference locations y1 and y2, which are located near the electrodes. The distance between the reference position and the electrode tip is about . (a) The interferogram obtained at t = 0 ns, and two reference locations y1 and y2 are illustrated with two red solid lines. (b) The radial electron density distribution at t = 0 ns at y1.
Fig. 10. Electron density distributions at different time superposed with Gaussian fit curves on a common radial coordinate system, which is center around the axes of the arc channels. (a) Electron density distributions at y1 and (b) y2.

Therefore, the working process of the air-spark switch can be described as follows: at the initial stage of discharge, the seed electrons are generated at the tip of the cathode by field emission. Under the action of the electric field, the seed electrons are accelerated to move toward the anode and ionize the background gas. So a large number of secondary electrons are produced. At this time, the electron density near the cathode is larger than that near the anode. The arc channel is rapidly formed due to the avalanche ionization mechanism. A large number of electrons bombard the anode and produce more secondary electrons. Then, the electron density near the anode increases rapidly. So two high-density regions are formed near the cathode and anode. When the arc channel is fully formed, the plasma in the arc channel will expand into the air under the pressure gradient. As the diffusion progresses, the plasma density decreases, the radius increases and the temperature decreases. Finally, the plasma disappears into the air.

5. Conclusion

Laser interferometry has an ultra-high spatial and temporal resolution, and is a powerful tool for studying plasma evolution. In this paper, we studied the working process of air-spark switches by laser interference technology. A series of interferograms that contain plasma information were obtained. The three-dimensional electron density distributions were obtained by numerical processing the interferograms. The electron density near the cathode up to 4.2×1019 cm−3 is higher than that near the anode in the arc channel at the beginning of discharge. Subsequently, the arc channel is rapidly formed under the action of the electric field. Due to the plasma expanding into air, the radius of the arc channel is increasing and the shock wave is formed in the front of the compressed air layer. The working process of the air-spark switch was described by analyzing the temporal and spatial evolution of the plasma electron density. The electron density near the anode increases first and then decreases, but the electron density near the cathode continues to decrease. The laser interferometry is demonstrated to be a valuable method to diagnose transient physical processes such as gas switching plasmas. The data of these experiments also provides a good reference for understanding the working process of the air-spark switch.

Reference
[1] Yalandin M I Sharypov K A Shpak V G Shunailov S A Mesyats G A 2010 IEEE Trans. Dielectr. Electr. Insul. 17 34
[2] Golnabi H 2000 Rev. Sci. Instrum. 71 413
[3] Kefu L Yaqing T Liu X L Jian Q 2013 IEEE Trans. Electron Devices. 60 875
[4] Cheng X B Liu J L Qian B L 2010 IEEE Trans. Plasma Sci. 38 516
[5] Rahaman H Nam S H Nam J W Lee B J Frank K 2010 Appl. Phys. Lett. 96 141502
[6] Lee L Cai L Qi X D Lin F C Pan Y 2012 J. Appl. Phys. 111 053306
[7] Kharlov A V 2010 IEEE Trans. Plasma Sci. 38 2474
[8] Anaraki A P Kadkhodapour J Taherkhani B 2014 J. Fai. L Anal. Preven 14 784
[9] Inada Y Matsuoka S Kumada A Ikeda H Hidaka K 2012 Phys. D: Appl. Phys. 45 435202
[10] Jiao Z H Wang G L Zhou X X Wu C H Zuo Y L Zeng X M Zhou K N Su J Q 2016 Plasma Sci. Technol. 18 1169
[11] Harilal S S Brumfield B E Phillips M C 2015 Phys. Plasmas 22 063301
[12] Grun J Stamper J Manka C Resnick J Burris R Crawford J Ripin B H 1991 Phys. Rev. Lett. 66 2738
[13] Zhang H C Lu J Ni X W 2009 Opt. Commun. 282 1720
[14] Zhang H C Lu J Ni X W 2009 J. Appl. Phys. 106 063308
[15] Harilal S S Miloshevsky G V Diwakar P K LaHaye N L Hassanein A 2012 Phys. Plasmas 19 083504
[16] Yang Z F Wu J Wei W F 2016 Phys. Plasmas 23 083523
[17] Weber B V Fulghum S F 1997 Rev. Sci. I Nstrum. 68 1227
[18] Breitling D Schittenhelm H Berger P Dausinger F Hügel H 1999 Appl. Phys. A: Mater. Sci. Process 69 S505
[19] Alexander B Burkhard J Sergey P 2005 IEEE Trans. Plasma Sci. 5 1465
[20] Ivanov V V Anderson A A 2016 Appl. Opt. 55 498
[21] Magesh T John S 2008 J. Appl. Phys. 104 013303
[22] Takeda M Ina H Kobayashi S 1982 J. Opt. Soc. Am. 72 156
[23] Álvarez R Rodero A Quintero M C 2002 Spectrochim. Acta Part. B At. Spectrosc 57 1665
[24] Lu Y H Wu J Shi H T Zhang D Y Li X W Jia S L Qiu A C 2018 Phys. Plasmas 25 072709