Figure
1.
A principle scheme of the coaxial plasma accelerator.
| Citation: |
Nisar AHMAD, Ping ZHU, Ahmad ALI, Shiyong ZENG. Viscous effects on plasmoid formation from nonlinear resistive tearing growth in a Harris sheet[J]. Plasma Science and Technology, 2022, 24(1): 015103. DOI: 10.1088/2058-6272/ac3563
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In this work, the evolution of a highly unstable m = 1 resistive tearing mode, leading to plasmoid formation in a Harris sheet, is studied in the framework of full MHD model using the Non-Ideal Magnetohydrodynamics with Rotation, Open Discussion simulation. Following the initial nonlinear growth of the primary m = 1 island, the X-point develops into a secondary elongated current sheet that eventually breaks into plasmoids. Two distinctive viscous regimes are found for the plasmoid formation and saturation. In the low viscosity regime (i.e. Pr ≲ 1), the plasmoid width increases sharply with viscosity, whereas in the viscosity dominant regime (i.e. Pr \gtrsim 1), the plasmoid size gradually decreases with viscosity. Such a finding quantifies the role of viscosity in modulating the plasmoid formation process through its effects on the plasma flow and the reconnection itself.
It is well known that during edge localized mode instabilities in magnetic fusion devices, the disruption of the plasma filament and the production of the heat and particle fluxes occur on the wall of the reactors. As a result, the plasma-facing material surface is damaged and dust particles are created. All of these events negatively affect the safety and normal operation of the reactor. As an example, dust ejection into the plasma core volume leads to the contamination of the discharge and may contribute to tritium safety issues [1].
In studies [2–5], the disruption and plasma-wall interaction simulation experiments were performed at the plasma accelerators. As a potential candidate material for the first wall, the graphite was chosen in [2, 3]. The graphite plate was irradiated with the high-energy plasma flux generated in a coaxial plasma accelerator. In work [4] a quasi-stationary pulsed plasma accelerator was used to provide high heat plasma flux, which is expected during operation of an international thermonuclear experimental reactor, and to study the damage of divertor plasma-facing components with a combination of the pulsed and quasi-stationary heat fluxes. In that work the tungsten target was used as a candidate material of the divertor. In work [5] a pulsed coaxial plasma gun was assembled to investigate the dependence plasma flow structure on initial operating working gas pressure at 'continuously filled' regime. In studies [6–8] new design and construction of pulsed plasma accelerators intended for creation of dense pinch plasma focus discharges were presented. Moreover, in this work, the impact of the electrode system on the neutron yield, x-ray radiation in a dense pinch plasma focus was investigated.
As mentioned above, one of the applications of plasma accelerators is the experimental simulation of the plasma filament compression and disruption in magnetic fusion devices and Z-pinches [9, 10]. For these purposes, recently we have modified the coaxial plasma accelerator by installing more capacitive and low-inductive energy storage capacitors and also by using electrical coupling cables with low reactive impedance. In addition, the avoidance of reverse reflected plasma flow from the end of the accelerator is taken into account. It was achieved by using a special plasma-absorbing target installed inside the vacuum chamber. This constructive modification allows obtaining plasma flow with its self-magnetic field and the relatively long body filament. Those changes give the opportunity to experimentally simulate the processes occurring in the plasma filament. The main purpose of this work is to conduct complex plasma diagnostics for studying the physical properties and plasma flow formation dynamics in the channel of modified plasma accelerator. There is a wide spectrum of diagnostic methods for the investigation of the plasma filament and its basic parameters in CPA at extreme conditions (at high temperatures and plasma densities, at high frequency oscillations created in an accelerator by pinch discharges). Of these, some of the frequently used electrical signal measurement-based techniques for plasma diagnostics such as Rogowski coil, Faraday cup, and magnetic probes, were utilized. Furthermore, high-speed imaging techniques, for visual observation of the accelerated plasma, were used.
The work novelty is summarized as follows: in comparison with related former researches, this work considers the most important physical properties of plasma flow and the physical processes, such as charge separation (electrons and ions) in plasma flow with FC, compression and disruption of plasma filaments using frames synchronized with magnetic probe signals.
A principle scheme of the coaxial plasma accelerator is shown in figure 1. An experimental setup consists of two concentric (coaxial) copper electrodes: an inner anode and an outer cathode. Anode and cathode are isolated by a dielectric material. The operational principle of experimental setup is based on the acceleration of plasma generated by ionization of gas filling in interelectrode space, when a high-voltage is supplied to the electrodes. The acceleration takes place due to the J × B force acting on plasma. A vacuum arrester was used for the transfer of capacitor-stored energy to the gas between two electrodes. The installation design and its operational principle are described in detail elsewhere [11–14].
The power system of the CPA includes a low-inductive capacitor banks with five parallel- connected capacitors of the KPIMK-8-288 type (288 μF). The total capacitance is 1.44 mF and maximum energy stored on the capacitors at a maximum charging operating voltage of 6 kV is W = 26 kJ.
The current flowing through the electric circuit of the CPA was measured by a Rogowski coil [15] with the ~75 mm diameter loop and L = 27.5 μH inductance.
The magnitudes of magnetic fields generated by pulsed plasma flow in space between two concentric electrodes and at the out of an accelerator were measured using two magnetic probes (No. 1 and No. 2 in figure 1). The dimension and characteristics of each probe are as follows: number of turns n = 7, loop radius r = 1.1 mm, loop cross-sectional area A = 3.8 mm2, time constant τ = L/R = 2.3 ns [16]. The winding ends of magnetic probes were twisted and brought out. Then they were connected to the BNC cable attached to the end of glass tube. The impedance of this cable is 50 Ω. The BNC cable was used to connect the twisted pair terminals of magnetic probes to the oscilloscope through a passive RC integrator circuit (RC = 100 μs).
The formation, dynamics and development of pulsed plasma flow inside the CPA vacuum chamber were captured by the high-speed Phantom VEO710S CMOS camera [17]. The plasma flow velocity was measured by analyzing the obtained images. The frequency and exposure time of the high-speed camera were 280 000 frames s-1 and 3.1 μs respectively.
The Faraday cup with 160 μm orifice [18] was used to measure the electron and ion currents, energy and densities of charged particles of plasma flow.
All signals were recorded on the digital storage oscilloscope LeCroy WaveJet 354 A, 500 MHz/4-channel. Also, Berkeley Nucleonics pulse generator (model 577) with an external synchronizing plasma-created signal was used to trigger the scope and CMOS camera in the external trigger mode.
All the experiments were carried out at voltages varied between 2 and 6 kV and at a plasma-forming gas pressures varied between 0.03 and 11 Torr. Two types of gases such as hydrogen, residual air were used as a plasma source. An electrical discharge was initiated by a high-voltage vacuum gap with a residual pressure of ~10-2 Torr.
This section presents the results of plasma diagnostics using the methods described above: (i) Rogowski coil, (ii) magnetic probe and Faraday cup, (iii) high-speed CMOS camera.
For controlling the operation of plasma accelerators, it is important to know the value of the current flowing through its driving circuit. In this regard, the typical current oscillograms and I–V characteristic of the CPA, obtained for the two types of working gas, shown in figures 2(a) and (b). These discharge current oscillograms are in well agreement with the oscillograms presented in other studies [19, 20] and represent a rapidly damping waveform. This indicates a low inductance of the system and demonstrates the fact of effective transfer of the energy stored in the capacitors. The use of air as the working gas for plasma generation is most convenient for conducting preliminary experiments.
In this work, with a 5 kV charging voltage and 60 mTorr gas pressure, we could reach the maximum current values of 80 kA for the air and 65 kA for the hydrogen, respectively. From obtained I–V characteristics of the CPA (figure 2(b)) one can see that the maximum current linearly increases with increasing the charging voltage supplied to the capacitor banks. We explain this by the insignificant contribution of the pulsed plasma active resistance and the absence of current skipping. In this case, it can be considered that the maximum current Imax flowing through the CPA driving circuit is proportional to the applied voltage U. A relevant I–V characteristic can be also found in [21].
Also, the dependence of the discharge current on the hydrogen gas pressure was obtained in this work (figure 3(a)). This graph shows that the current initially increases to its absolute value, and then it gradually decreases with increasing the pressure of hydrogen in the vacuum chamber. We explain this result by increasing the inductance and inductive resistance of the CPA circuit, which occurs while forming long-lived plasma filaments. The absolute value of the discharge current was measured at pressure of 1.2 Torr. A relevant dependence was also presented in studies [22, 23]. The dependence of the plasma filament's self-magnetic field on the hydrogen pressure was shown in figure 3(b). As can be seen in figure 3(b), the magnitude of the magnetic field decreased more than twofold with tenfold increasing gas pressure. At higher gas pressures of 2–4 Torr, the magnetic field magnitude almost did not change.
Thus, the experimentally confirmed optimal gas pressure in the CPA is about 200 mTorr, because at this pressure it allowed us to achieve the maximum value of the plasma filament's self-magnetic field. In this regard, the experiments were performed at pressures at which the maximum plasma compression (Z-pinch) was achieved. Consequently, these provide us for steady focusing of the plasma flux to the axis of the vacuum chamber.
It can be seen from the obtained results shown in figure 3, that the absolute values of the magnetic field and the discharge current are observed at various gas pressures in the vacuum chamber. Therefore, a small change in the discharge current leads to a significant change in the plasma filament's self-magnetic field.
The typical images of the formation of plasma flow in hydrogen gas, obtained in one pulse shot at voltages of 4 kV and gas pressure of 2 Torr, through the quartz viewing side window of the vacuum chamber, are shown in figure 4(b). It should also be noted that the time evolution of the images matches with the time dependence of the magnetic probe signal shown in figure 4(a) (the CMOS camera was synchronized with the discharge in the experiment). The typical magnetic probe signals as in figure 4(a) were presented in [24].
Figure 4(b) shows the plasma flux formation and acceleration frames recorded by using a high-speed camera. The camera frequency, resolution and exposure time are 280 000 frames s-1, 256 × 64, 3.1 μs. These frames were registered in a single pulse, but at different time moments. In figure 4(b), plasma acceleration direction is from the left to the right. The time moment of the vacuum arc discharge ignition between the coaxial cylindrical electrodes was fixed as the initial reference point. A high-current arc discharge produces strong self-induced magnetic field. Thus, plasma is accelerated toward the cathode tip by electromagnetic forces. As can be seen in figure 4(b)I, the head of the accelerated plasma flux was registered at a time of 17.8 μs. At the same time, as can be seen from the oscillograms, the magnetic probe No. 1, placed between inner and outer electrodes registered the magnitude of the magnetic fields with an absolute value of the order of ~0.3 T, while the magnetic probe No. 2 did not register this field. The magnetic probe No. 2 was shielded by a ferromagnetic material with a 1 mm side slit. Respectively, it was sensitive only to the magnetic field created by the plasma flux current, flowing via the area where the magnetic probe No. 2 is located. Then, in the subsequent frame, at t = 21.4 μs, the visible region of the high-speed camera is completely filled with bright plasma, and plasma flow with a duration of more than ~70 μs is formed (figure 4(b)II). At this time moment, plasma flow passes the vacuum chamber cross section, where the magnetic probe No. 2 is mounted, and the voltage is gradually induced at its winding ends. Thus, the magnetic field first increases to a maximum value of ~0.6 T, and then decreases. The magnetic field fluctuations are observed in the CPA at relatively high gas pressures, but they have a tendency to decay as the pressure increases. In this case, it can be assumed that instability occurs in the CPA due to the anomalous plasma resistance, and subfilament-type structures are formed. Therefore, the voltage decreasing from its absolute value on the probe No. 2 and its fluctuation are explained with the plasma flux compression and disruption with its self-magnetic field. Thus, in one pulse, the plasma filament is disrupted into multiple sub-filaments. These indicate the creation of an inhomogeneous plasma fluxes. The estimated from two consecutive frames first sub-filament duration and directional velocity are ~70 μs, ~25.5 km s-1 (figure 4(b)I). The following sub-filament was recorded after 96.4 μs (figure 4(b)III). The frame shown in figure 4(b)IV (140–160 μs) corresponds to the third peak of the magnetic probe signal No. 2 with amplitude of 0.1 T (figure 4(a)).
Figures 5(a) and (b) show the measured values of the magnetic field at a distance of 23.5 cm from the tip of the cathode and in space between the electrodes as a function of the charging voltage supplied to the capacitor banks. One can see that the value of the magnetic field in both cases increases proportionally with the voltage. Furthermore, the values of the magnetic field are on average 30% higher when the pure hydrogen is used as the plasma-forming gas than in case of the residual air. The physical interpretation of this phenomenon has not yet been revealed.
As can be seen from the oscillogram in figure 6(b), the increase in pressure up to 11 Torr leads to a decrease in amplitude of the No. 2 magnetic probes signal. Note that probe No. 2 was positioned at a 23.5 cm distance from the cathode tip, due to the fact that at this position the vacuum chamber-viewing window is located. Therefore, this distance is the most convenient and closest for observation by the high-speed camera. Moreover, the signal from the magnetic probe in interelectrode space repeats the current fluctuation in the accelerator circuit in comparison with figure 5(a) obtained at p = 60 mTorr. This indicates that, when the gas pressure is high, the resistance of the medium becomes larger, and as a result, the flow rate decreases, the primary plasma sub-filament is concentrated in interelectrode space. We also assume that this is due to an increase in mass of the plasma bullet, which can also affect the acceleration of plasma flow. One can see from figure 6(b), at higher pressures in the vacuum chamber, both positive and negative peaks appear in the oscillogram of the magnetic field.
This fact shows the separation of plasma charges. The charge separation in plasma flow during the accelerating along the axis of the vacuum chamber can be observed in the FC signal also. When the FC collector voltage is zero, two peaks of opposite polarity are observed on the oscillogram (see figure 7). This happens when the collector of a FC is bombarded first by the electron and then by the ion beams, due to the center of a mass shift in space. We assume that this is firstly related to the principle of plasma flow acceleration in this type of accelerators and, secondly, to the collision processes between the particles: generally between directed ions and thermal neutrals. When the pressure of the gas in the vacuum chamber increases, the number of neutral particles increases too, resulting in an increased frequency of collisions of plasma charges with neutral particles. So, when neutrals collide frequently with ions, the ions begin to be slowed down. During this, the electrons have enough time to separate from the ions at a certain distance along the axis of acceleration.
The plasma accelerators are known as potential sources of a wide variety of radiation such as electrons, ions, neutrons and x-rays, which has great interest for different applications. It is very important to investigate the ion beams and its general characteristics, such as energy, density, and uniformity for material processing, surface modification, ion implantation etc. In this regard, in this work we fabricated and employed FC for measuring the density of ions in plasma flux. In the experiment, FC was mounted in the path of the plasma flux. The resulting current of accelerated plasma particles absorbed by the collector was measured using an oscilloscope. The typical oscillogram at zero voltage on the collector, as well as at a potential of ±40 V is shown in figure 7 as an example.
At zero voltage on the oscillogram one can observe peaks of negative and positive polarity, which is associated with the flux of electrons and ions with a time difference (70–75 μs), and indicates the separation of charge fluxes in plasma. After furthermore analysis of this result, we concluded, that for such a long period of time charge separation is not probable. Because time difference estimation is approximate and is obtained only on the waveform at zero voltage. It should be noted, that charge separation occurs, but only in a short time interval. Therefore, the ion beam current can be appeared earlier than the estimated time. We cannot see this from the FC oscillograms, obtained at zero collector potential, because the ion current can be very low and it can also be dampened by the electron current. The charge fluxes separation in plasma flow occurs in 5 μs, which is evaluated by applying a certain value of negative and positive potential to the collector. As the collector potential increases, for example, positive potential (+40 V), electrons will be attracted and ions will be rejected. In that case, the amplitude of the negative polarity current will increase on the oscillogram. When the potential is negative (–40 V), the amplitude of the current of positive polarity, i.e. ions, increases. The electron and ion currents do not flow to the collector simultaneously at the same collector voltages, as seen in figure 7. The time difference between two current signals is 5 μs. This can be explained by the fact that the collector adsorbs electrons and ions which are separated in space.
Thus, the dependence of electron beam current on the collector voltage was obtained. The obtained I–V characteristic will be the same as that of the single planar probe, therefore for calculations of the electron temperature, we will use the expression (1), derived from the theory and assumption of the single probe that the particle energy distribution must be Maxwellian
| (1) |
where e—lectrical charge, k—Boltzmann's constant,
The thermal velocity of ions is required to know to calculate their density. This can be estimated using Bohm criterion as follows:
| (2) |
where
| (3) |
where
In our case, we assume that the plasma particle velocity distribution is Maxwellian, since the directional velocity of plasma flow calculated by the high-speed camera is 2.5 × 104 m s-1, which is much less than the thermal velocity of electrons. The temperature of the electrons in this work was estimated from the slope of the Faraday cup I–V characteristic plotted on a logarithmic scale and obtained by averaging the currents measured in five repeated pulses at the same collector voltage. The averaging was performed, due to the operation of the experimental setup in the pulse mode. Thus, the calculated electron temperatures for the two types of the plasma-forming gases: air and hydrogen were 40 eV. However, as can be seen in figures 8(a) and (b), in our case, the I–V characteristic of the CPA deviates strongly from the exponential one. This can be explained by the fact that experimentally it is very difficult to obtain a real I–V characteristic, since plasma flows, generated in the plasma accelerator, are inhomogeneous. In addition, it is necessary to take into account the pulsed mode of operation of the accelerator, which limits the measurements in a large range and quantity. Usually, measurement errors with electric probes do not exceed 25% [25]. In our case, the estimate of the error contribution to this is no more than 10%, which is due to the operation in the pulsed mode and the small number of repetitive measurements. Consequently, considering this contribution, we can judge that the total measurement error is 35%.
The calculations of the electron temperature and ion density for two types of plasma-forming gases are shown in table 1. These results were compared with other works [15, 26] and are in good agreement.
| Hydrogen | Air | |||
| 40 | 3.2 × 1021 | 40 | 16 × 1021 | |
DownLoad:
CSV
From the results of calculations, the following conclusion can be done. The temperature of electrons in plasma flow for hydrogen and residual air is practically the same. The density of ions in plasma flow, generated in residual gas is higher than that in hydrogen, which is possibly associated with multiple ionization at a higher gas breakdown voltage.
Plasma flows, generated in high-current pulsed systems, are themselves complex objects of investigation due to the non-homogeneity of the fields and currents created by accelerating plasma. Therefore, the complex plasma diagnostics allowed us to establish representation of the formation of plasma flows in the CPA channel. In particular, it allowed us to observe such phenomena as the plasma filament disruption, the charge (electrons and ions) separation in plasma flow, even with a limited number of measurement points. These phenomena were investigated depending on the external conditions of experiments also. As a result, the optimal parameters of the experimental setup were determined: working gas pressure of 200 mTorr, capacitor bank charge voltage of 5 kV.
As a result of the complex diagnostics, the parameters of the external electrical circuit of the CPA and the energetic, dynamic characteristics of the plasma filament were obtained. From the results obtained, it was revealed that the current curves represent rapidly damped aperiodic oscillations with a small number of half-periods. Such a condition is advantageous and indicates the low value of inductive resistance of the circuit, including connecting wires, capacitors and vacuum arrester. One can conclude from this that the stored energy is effectively transported into the discharge. Also, it was found that the current depends linearly on the voltage supplied to the capacitor banks, which is explained by the high conductivity and the low resistance of the plasma filament. In the experiment, the absolute current values of 80 and 65 kA for hydrogen and air plasma-forming gases were obtained at a maximum voltage of 5 kV and working gas pressure of 60 mTorr. With increasing gas pressure, it was found that the current amplitudes decrease from the maximum value, which is explained by an increase in inductance associated with the formation of long-lived plasma filaments. Based on the results obtained by the high-speed CMOS camera, the plasma filament disruption was also observed in the experiments, which explains a quasiperiodic ejection of plasma from space between the cathode and anode. The peaks observed in the oscillograms of the magnetic probe also indicate this phenomenon. The electron temperature and ion density in plasma flow were measured by using FC. It is shown that in the dynamic plasma, even when the collector potential is zero, currents are generated at the collector, which is explained by bombarding of the collector surface by charged particles. Therefore, in the calculations, the parasitic currents are extracted from the major currents measured at various collector bias voltages. As a result, we eliminated the influence of background currents on the error of the measurement. At the conclusion of this work, we achieved the following purposes: a physical representation of plasma flow formation in the CPA channel as a function of working gas pressure and the capacitor bank charging voltage has been established; the optimal experimental conditions were determined at which the maximum plasma filament compression can be obtained; charge fluxes separation in space relative to the common center of mass with a time difference of ~5 μs was observed by using FC; the oscillograms of magnetic probes signals and plasma flow acceleration frames simultaneously confirm plasma filament disruption. Especially it is noticeable at high pressures, which is related with an increase in the medium resistance and collision frequency of ions with neutrals. In the future, we will use these results, the new insights we have gained, and proven diagnostic methods in our fusion research work. In particular, to further modify and investigate the processes of plasma flow interaction with materials that are candidates for the fusion reactor's first-wall, and to improve the experimental setup for producing homogeneous plasma flows with the best energetic parameters.
This research was supported by the National Magnetic Confinement Fusion Science Program of China (No. 2019YFE03050004), National Natural Science Foundation of China (Nos. 11 775 221 and 51 821 005), U.S. DOE (Nos. DE-FG02-86ER53218 and DESC0018001), and the Fundamental Research Funds for the Central Universities at Huazhong University of Science and Technology (No. 2019kfyXJJS193). We are grateful for the support from NIMROD team. This research used the computing resources from the Supercomputing Center of University of Science and Technology of China. The author Nisar Ahmad acknowledges the support from the Chinese Government Scholarship.
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| 1. | Chen, Q., Liu, L., Qin, C. et al. Development of an automatic decoupling system for ICRH antenna straps in EAST. Fusion Engineering and Design, 2025. DOI:10.1016/j.fusengdes.2025.114847 |
| 2. | Zhu, G., Li, Q., Sun, X. et al. Particle simulations on propagation and resonance of lower hybrid wave launched by phased array antenna in linear devices. Plasma Science and Technology, 2022, 24(7): 075102. DOI:10.1088/2058-6272/ac5f80 |
| 3. | Liu, L.N., Wang, L., Yuan, S. et al. Impedance matching system using triple liquid stub tuners for high-power ion cyclotron resonance heating in EAST tokamak. Review of Scientific Instruments, 2022, 93(4): 043506. DOI:10.1063/5.0076421 |
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| Hydrogen | Air | |||
| 40 | 3.2 × 1021 | 40 | 16 × 1021 | |
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