Figure
1.
Schematic diagram of the power supply source for the apokamp electrode system.
| Citation: |
Anastasiia KOZHEVNIKOVA, Igor ALEKSEENKO, Viktor TARASENKO, Dmitry SCHITZ. Application of holographic laser scanning to determine the electron concentration in the plasma forming the apokamp[J]. Plasma Science and Technology. DOI: 10.1088/2058-6272/adb828
|
Streamer discharges that do not transition to a spark channel are now being widely investigated. One of these discharges is the apokamp discharge, in which streamers start from a diffuse spark channel having a curved shape at a high repetition rate of voltage pulse. In this work, to estimate the electron concentration in the plasma forming the apokamp a digital holographic laser scanning method is applied for the first time. The method is based on a comparison of the phases of two optical wavefronts, registered at different time instants in the form of digital holograms. The result of the phase comparison between the wavefronts is presented in the form of a numerically calculated map of the phase difference of the reconstructed wavefronts. A gas-discharge plasma is a phase (transparent) object, and the interference fringes are formed as a result of the change in the refractive index introduced by the plasma with respect to the original unperturbed medium. The obtained value of the refractive index allows estimation of the concentration of electrons in the spark channel plasma. It is shown that at as the voltage pulse repetition rate increases from 5 to 50 kHz the concentration of electrons in the plasma forming the apokamp decreases by an estimated four times.
The development of a high-current contracted discharge in gases occurs as a result of the formation of streamers and subsequent ionization waves during the first stage and then spark leaders that close the gap and form a spark channel [1–3]. The concentration of electrons in streamers and subsequent ionization waves is relatively small and does not usually exceed 1014 cm−3 [1, 4]. When a spark channel is formed this concentration increases significantly and reaches 1017–1018 cm−3 [5, 6]. Nevertheless, for practical purposes, pulsed diffuse discharges, including those at atmospheric pressure [7, 8], that are formed due to spherical streamers are widely used [9, 10]. When the duration of the voltage pulse is limited, transition to the spark stage of discharge under these conditions does not have time to occur and the concentration of electrons in air is ~ 1014 cm−3 [6].
It is also possible to form a diffuse cold plasma in the reverse scenario, i.e. from the dense plasma of spark discharges. Such discharge modes are relatively rare phenomena. The best known are discharges propagating from the region of intense thunderstorm activity upward to the mesosphere [11–14]. Such discharges include blue jets and their varieties. These are blue starters, which have a relatively short length [15], and gigantic jets, which have the longest vertical length of upper-air discharges [16]. The blue jets appearing during thunderstorm discharges have been observed from the ground surface as well as from aeroplanes and the International Space Station [14]. They usually appear at an altitude of about 20 km and consist of two parts: a bright outgrowth that emerges from the clouds and streamers sprouting upward in parallel. It is estimated that the blue jets start from the lightning channel. The colour of the outgrowth is usually white, but streamers, which are significantly longer, have a blue colour that can change to red as their length increases. Photographs of the blue jets are given in many works (e.g. [15, 16]) and they can also be found on the Internet.
In addition, formation of mini blue jets starting from the dense plasma of a spark discharge has been reported recently under laboratory conditions [17, 18]. With a pulse-periodic discharge in atmospheric air and other gases between two pointed electrodes it is possible to obtain a cold plasma jet consisting of an offshoot and streamers originating on the surface of a curved pulse spark. It was proposed to call this mode an apokamp discharge, and the outgrowth together with the streamer was called the apokamp (from the Greek for ‘off’ and ‘bend’) [17, 18]. In this mode, a cold plasma jet is formed in atmospheric air using a relatively simple electrode system, and this has aroused the interest of researchers and developers. In a wide range of conditions an apokamp can be formed without additional gas pumping through the discharge region. In subsequent work (e.g. [19–22] and references therein) various properties of the apokamp have been investigated. In particular, the electron temperature and the electric field strength in the apokamp jet have been measured [21]. In addition, model calculations of the apokamp discharge have been initiated [19, 23, 24].
Various methods of measuring the electron concentration in plasma, including probe detection, spectroscopic methods based on the dynamic Stark effect [25] or Thomson scattering of probing radiation [26], and optical interference [27, 28], are used to diagnose gas-discharge plasmas, but each method has its own limitations. For example, the probing method cannot be realized for pulsed plasma and the use of spectroscopic methods requires expensive equipment with a sufficiently high resolution and does not provide information on the distribution of electron concentration in different parts of the plasma object under study.
Holographic interferometry began to be used for plasma studies in the 1970s and 1980s (e.g. [29]). However, data collection was a rather labour-intensive process since the registration of interferograms took place on photographic plates. The development of digital holographic interferometry significantly accelerated the process of data acquisition. This is based on comparing the phases of at least two optical wavefronts recorded at different points in time as digital holograms. The result of the phase comparison between the wavefronts is presented as a numerically calculated phase difference map of the reconstructed wavefronts. Advanced digital tools provide a high degree of mutual synchronization for the study of dynamic events. The ability to acquire a large number of holograms in a relatively short time provides an array of data for further analysis.
The purpose of this work is to obtain data on the electron concentration in the plasma of a pulsed-periodic spark discharge initiating the apokamp using a digital holographic interferometry technique.
The apokamp is generated in atmospheric air using two stainless steel needle electrodes that are placed at angles of 80°–120°. The gap between the needles is 3.75 mm. High-voltage pulses of positive polarity are applied to one of the needle electrodes (figure 1) and the other is connected to ground through capacitor C3 with a capacitance of 50 pF.
High-voltage pulses are generated by means of a step-up transformer (Tr) serving as a load of the metal–oxide–semiconductor field-effect transistor (MOSFET) bridge (VT1–VT2), the DC bus of which is supplied with a voltage of 0–300 V. In order to synchronize the power supply, pulses of the apokamp discharge and the laser sensing system, each power supply pulse is triggered by the ‘start pulse’ input, which activates the ‘timing circuit’ producing the necessary control signals for each transistor, taking into account the dead time. This signal is then amplified by the MOSFET driver and applied to the gates of the transistors. As a result, pulses of 1 μs duration with amplitude up to 12.5 kV and a frequency of 1–50 kHz are obtained at the Tr output.
When high-voltage pulses are applied to the gap, a breakdown occurs and a spark channel with a curved shape is formed in the stationary stage of the discharge [17, 18]. Initially, the discharge shape is unstable and changes from pulse to pulse [30]. However, after about 100 pulses it stabilizes. The appearance of the apokamp depends on the pulse frequency, the amplitude and duration of the voltage pulses and their polarity. The results of apokamp discharge studies, as we have already noted, are detailed in references [17–24, 30]. Under the conditions of this experiment, the apokamp does not form at low frequency f ~ 5 kHz. As f increases, the apokamp jet appears and becomes longer (figure 2).
In holographic interferometry, the plasma is considered as a phase (transparent) object, and the phase difference is formed by hologram reconstruction in relation to the initial medium as a result of the changing refractive index introduced by the plasma [31]. The resulting refractive index value enables estimation of the electron concentration in the plasma [32].
The relation of phase difference to the refractive index is described by
| Δφ(x,y)=2πλl2∫l1[n(x,y,z)−n0]dz, | (1) |
where λ is the wavelength of laser radiation, l1 and l2 are the limits of the integral for the length, x, y and z are the coordinate system, n0 is the refractive index of the observed environment in its initial state and n(x, y, z) is the distribution of the current refractive index. The laser radiation propagates through a medium in the z-direction and the integration proceeds along the direction of propagation.
The plasma refractive index is based on the relation [33, 34]
| n−1=∑ki=1(Ai+Biλ2)Nai−4.5×10−14λ2Ne, | (2) |
where Ne and Nai are electron and atomic concentrations, respectively, and Ai and Bi are Cauchy constants. In reference [34] it was noted that the refractive index of atoms far from the absorption lines weakly depends on the wavelength. The first term of expression (2) corresponds to heavy particles slowly affecting the refractive index during the plasma process and immediately after its generation, and such an effect could be compensated. Thus, for the electron concentration, the phase difference is expressed as follows:
| Δφ(x,y)=2πλlΔn, | (3) |
| Δn=(4.5×10−14λ2Ne), | (4) |
| Ne=2.2×1013Δφ2πlλ. | (5) |
Digital holographic interferometry acquires image plane holograms on a charge-coupled device or complementary metal–oxide–semiconductor (CMOS) camera matrix. It allows monitoring of the plasma pulse and can also provide images of the observation area.
The acquired image intensity contains the phase of the object wave and can be extracted with Takeda’s numerical method, which uses the Fourier transform [35]. The Fourier transform of the recorded intensity allows separation in the Fourier domain of the intensity of the reference signal |RH(x,y)|2, the intensity of object signal |UH(x,y)|2 and the object signal that corresponds to the R∗H(x,y)×UH(x,y) term. The filtering of just the object part FFT(R∗H(x,y)×UH(x,y)) and the implementation of inverse Fourier transform on this term reconstructs the object’s phase.
The phase difference between two wavefronts UH1(x,y) UH2(x,y) corresponding to the two states of the object is given by [36]
| Δφ(x,y)=arg[e−i(φH2(x,y)−φH1(x,y))]. | (6) |
Therefore, based on expression (5), the phase difference allows for evaluation of the electron concentration.
It should be taken into account that the sensitivity for phase difference detection can basically determine the measurement error. Thus, in analogue holographic interferometry [34] the accuracy of interference fringe detection is restricted by the criterion 2π/10 (10%). However, digital holographic interferometry allows such sensitivity to be extended. For example, in reference [37] determination of the phase difference is achievable in the range of 2π/100 (1%).
The investigation of apokamp pulse-periodic discharges by digital holographic interferometry methods is based on previous works on the study of spark discharges [38, 39], where the feasibility of assessing the concentration of electrons in the plasma channel is presented. However, study of a discharge in the apokamp mode is more challenging since it appears at frequencies higher than 20 kHz, is accompanied by a strong heat flux and does not have a constant location between the electrodes.
In order to investigate the parameters of a pulsed spark discharge, an automated holographic setup has been developed that allows observation of dynamic changes in the plasma. A holographic dual-beam Mach–Zehnder interferometer is implemented to acquire optical information using a pulsed Innolas SpitLight II Nd:YAG laser emitting at a wavelength of 532 nm and 50 Hz repetition rate. A FASTCAM Nova S16 (Photron) CMOS 16-bit CMOS camera with resolution of 1024×1024 pixels and a pixel size of 20 μm is used as the detector. The corresponding optical setup is presented in figure 3.
The efficiency of the proposed setup depends on precise synchronization between laser, camera and plasma operation. Based on a National Instruments DAQ-board NI-6602, synchronization was established for the entire diagnostic system. The current plasma discharge duration is 1000 ns, the camera exposure time is 200 ns and the laser pulse duration is 10 ns. It is worth noting that the intensity of plasma emission is quite low and does not affect the optical signal (hologram).
Due to the fact that the apokamp can be realized at a frequency range from 20 to 50 kHz and the laser pulse frequency and the camera frame rate are 50 Hz, N-periods of plasma discharges are skipped between each acquired hologram. Assuming that the discharge condition remains the same from pulse to pulse, it should be considered that the plasma emission and related processes (e.g. thermal) are similar from period to period. Thus, it is possible to scan a plasma not only during one pulse but also by grabbing independent discharges at different moments of their existence.
The effect of relative signal desynchronization occurs between mutual signals with frequencies varying by several orders (50 Hz versus 50 kHz). Thus, the signal formed at a higher frequency will be shifted in relation to the synchronized signals with lower frequencies during one measurement session. In this way, the scanning procedure can be realized. Figure 4 shows the time diagram corresponding to the scanning synchronization mode used in this study.
For the primary evaluation it is necessary to choose two holograms, one of which is acquired when the plasma is switched off (φ0) and the second at the moment of plasma existence (φ0+g+p). As a result, we provide information about the phase distribution (Δφg+p) associated with plasma generation and the thermodynamic changes in the environment caused by plasma emission. Figure 5 shows the processing algorithm for the digital holograms.
It has been found that the thermodynamic processes affected the phase difference more strongly than the plasma itself. In order to estimate the plasma parameters only, qualitative compensation of the thermodynamic contribution during the plasma process was implemented. The thermodynamic components in the plasma are present in space for longer than the discharge, so that there is a time between two plasma pulses when the plasma channel is no longer present but the thermodynamic processes in the gas remain (φ0+g). For the best compensation, it is worth choosing two holograms in which the direction and shape of the spatial distortions in phase difference distribution are similar but the detected times from the beginning of the plasma pulse are different. Figure 6 represents the compensation algorithm for extracting the contrast (Δφp) associated with the presence of the plasma.
Figure 6 shows the result of qualitative compensation, namely residual thermodynamic phenomena in the gas that cannot be fully compensated, the emission of a plasma channel where the phase difference contrast is related to the presence of electrons and the perturbation of the gas environment caused by explosive effects after the breakdown.
It is known that at low frequencies the apokamp does not occur, which means that the plasma localization area is only within the boundaries of the spark breakdown channel; therefore, a frequency of 5.25 kHz was chosen to determine the limit of electron concentration for this plasma source. The acquired spark discharge data should be able to estimate the electron concentration in the apokamp jet.
In this work a colour representation of the data is used for better perception of the phase difference associated with small changes in the refractive index of the environment and a graphical representation of the data is used to determine the exact values and subsequently calculate the electron concentration in the plasma channel. Figure 7(a) shows the full-field of phase difference changes Δφp after compensation for thermodynamic components, where the red colour highlights an area along which the phase difference changes (Y-axis; figure 7(b)). The graph shows a dip at OY coordinates (660:710), which corresponds to the existence of a plasma channel, and on both sides of the channel boundaries there is an area with sharp edges, which apparently corresponds to the area of shock wave propagation.
The results of the study of the apokamp discharge with pulse generation at 30.2 kHz and 49.2 kHz are presented in figures 8 and 9, respectively. In figures 8(a) and 9(a), the contrast associated with the existence of the plasma channel is very low, but in figures 8(b) and 9(b) it is still possible to identify the channel boundaries in the near-electrode area since this is a point of maximum electron concentration. All data in figures 7(b), 8(b) and 9(b) have the phase difference offset to zero level.
Table 1 shows the values of electron concentration in the plasma numerically according to the data presented in figures 7–9.
| Frequency (kHz) | Plasma channel width (cm) | Phase difference (rad) | Electron concentration (1017 cm−3) |
| 5.25 | 0.033 | 0.7 | 13.9 |
| 30.2 | 0.021 | 0.17 | 5.3 |
| 49.2 | 0.021 | 0.12 | 3.7 |
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It has also been found that the concentration of electrons in the discharge at a frequency of 49.2 kHz is less than those at frequencies of 30.2 kHz and 5.25 kHz. Consequently, there is a physical process that significantly reduces the concentration of electrons in the channel if the oscillograms of voltage pulses on the gap and the discharge current through the spark channel are identical. Two processes are the most probable: the heating of the air in the area of the electrode tips and the space above them, or the transfer of some of the electrons to the apokamp component of the plasma discharge. However, measurements of the discharge emission intensity between needle electrodes and the apokamp jet have shown that they differed by more than an order of magnitude [30]. The emission spectra from the spark discharge zone indicate the transition of the spark channel to the diffuse discharge form in this field. The measurements also show that the main reason for this is gas heating and a decrease in the concentration of neutral particles in the near-electrode region. The spark discharge becomes more diffuse and its cross section increases. This phenomenon was observed in reference [30] when photographing the discharge with a high-speed camera. In the steady-state regime at which the apokamp appears, the diameter of the spark discharge increased. Moreover, it can be assumed that the absence of the apokamp at a voltage pulse repetition rate of less than 5 kHz is due to the high concentration of neutral particles in the region of apokamp formation. As the frequency increases, the power injected into the discharge plasma increases in proportion to the number of pulses, and the gas temperature increases. Therefore, the concentration of particles decreases and the core area of the discharge increases.
The technique of digital holographic laser scanning was developed for relatively large electron concentrations, so the channel widths at frequencies of 30.2 and 49.2 kHz were the same. The cross section of the spark discharge at higher frequencies is larger, and the electron concentration at the edge in the diffuse area of the channel is lower and difficult to determine by holographic laser scanning. As a result, the electron concentration is only detected in the central part of the spark channel in the area with the highest discharge current density.
The application of digital holographic laser scanning interferometry allows measurement of the electron concentration in the plasma of the spark channel, from which the apokamp begins. It has been determined that when the frequency of voltage pulse repetition is increased from 5 to 50 kHz the concentration of electrons in the plasma, which creates the apokamp at the electrodes, decreased by a factor of about four. It has been assumed that this phenomenon was caused by the expansion of the spark channel diameter due to gas heating in the area of the electrodes and above. Therefore, the discharge current density in the channel decreases and the concentration of electrons is measured only on its axis.
A value of Ne of more than 1018 cm−3 was obtained for a frequency of 5.25 kHz (see table 1), which is higher than the maximum electron concentration measured, for example, in reference [5]. We associated this deviation with the near-electrode space in measurements, where Ne is expected to be higher than in the interelectrode gap. Additionally, it is also worth discussing the restrictions of the proposed approach. In order to observe apokamp formation, the essential challenge lies in the instability of the plasma state in the space between the electrodes, which significantly complicates the compensation of thermal disturbances. The thermal effects accompanying the plasma formation process are more unstable compared with existence of the plasma. The implementation of compensation requires longer times. Thus, we present data with maximum compensation for thermal processes to confirm the functionality of our method. In order to provide higher accuracy and reliability it is necessary to increase the sensitivity of the method by using a long-wavelength spectrum and improved synchronization system.
According to equation (2) we have not directly considered the effect of heavy particles and ions on the refractive index and the resulting phase difference. Reference [40] described a similar optical method resembling conventional interferometry for pulsed plasma and took into account neutral atoms for correction of the phase difference related to the refraction of plasma. However, this correction does not lead to a significant change in electron density and it remains of the order of magnitude of the resulting concentration. In order to generally solve equation (2) it is necessary to acquire holograms at two different wavelengths. In the case of dynamic plasma, the simultaneous recording of holographic images using independent sources at two wavelengths increases the reliability of the resulting data.
Furthermore, we have to specify that in our case the sensitivity of the method was restricted to the range of 2π/50 (2%).
It is expected that this setup will be used to measure the electron concentration in spark discharges and in other modes.
This study was performed in accordance with the support of the Russian Science Foundation (RSF) (No. 23-79-00023).
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| Frequency (kHz) | Plasma channel width (cm) | Phase difference (rad) | Electron concentration (1017 cm−3) |
| 5.25 | 0.033 | 0.7 | 13.9 |
| 30.2 | 0.021 | 0.17 | 5.3 |
| 49.2 | 0.021 | 0.12 | 3.7 |
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