Discharge and jet characteristics of gliding arc plasma igniter driven by pressure difference

1.   Introduction

Radar stealth technology has always been a research hotspot in the field of anti-detection. The key to radar stealth is primarily to reduce the target's radar cross-section (RCS) to a level that is undetectable by the radar [1, 2]. Generally, the RCS reduction methods rely on modifying the target's geometry and loading the target with the radar-absorbing material (RAM) [3]. Target shaping is not perfect due to its complexity of design and its low efficiency at lower frequencies [1]. Comparatively, loading RAMs on the target's surface is a common method to reduce the RCS. Nevertheless, it is commonly known that traditional RAMs, such as ferrites and carbon-based materials, can only effectively absorb electromagnetic (EM) waves in relatively high-frequency bands [4–7].

To overcome the above shortcomings of the stealth technology, researchers have introduced plasma stealth technology based on the plasma's absorbing capability [8–11]. The collisional plasma can effectively absorb EM waves in a wide frequency band, especially in the low-frequency range. Laroussi [12] studied the interaction of microwaves with atmospheric plasma gas. Vidmar [13] found that plasma generated in air or helium at atmospheric pressure could be an excellent broadband absorber from high frequency to S-band. Koretzky and Kuo [14] demonstrated that plasma torches can effectively attenuate EM waves. However, it is difficult to maintain high electron density in atmospheric pressure plasma owing to the extremely frequent collision between electrons and other heavy particles. Besides, the atmospheric plasma has obvious visible and infrared characteristics and is easily detected by photoelectric equipment. Thus, this atmospheric pressure plasma is not suitable for practical stealth applications.

In contrast, plasma can be easily maintained in a confined cavity with low gas pressure [8, 15]. Yuan et al [2] proposed an enclosed plasma stealth structure, which is a three-layer configuration consisting of a RAM layer, a plasma slab, and a glass slab. Bai et al [3] analyzed the refraction and reflection of the EM waves obliquely incident on the plasma-RAM structure. Chang et al [16, 17] studied EM scattering characteristics of inductively coupled plasma superimposed on a honeycomb absorbing structure. Rahmanzadeh et al [9] analyzed the absorbing properties of broadband absorbers of plasma-graphene structure. Ghayekhloo et al [11] analyzed the absorbing properties of the low-pressure plasma array formed of discharge tubes. It can be found that the flat plasma plate mostly consisted of gas discharge tubes, which are convenient to be deployed on the target. Several studies have revealed that the combination of plasma and RAM has excellent absorbing capability over a wide frequency band. Although many studies have focused on the EM wave absorption by plasma-RAM structure, little has been done concerning the experimental investigation into the effect of the plasma parameters on the EM absorption characteristics. While evaluating the plasma's absorption characteristic, two parameters are indispensable, namely, electron density and collision frequency, which is challenging to select accurate plasma parameters to obtain ideal attenuation [18]. Furthermore, not only their values but also their layouts affect the EM attenuation [19].

In this work, a combined plasma-RAM unit is studied concerning the EM absorption. By adjusting the spatial distribution of plasma, the absorption rate of the plasma-RAM absorber is investigated over the 2–7 GHz microwave band. Two levels of the parameters are involved in this research. In addition, the RCS of the plasma-RAM structure is simulated. This study is valuable to the design of tunable broadband microwave absorbers.

2.   Plasma diagnostics

While studying the interaction of the plasma with the EM wave, one has to mention two fundamental parameters, namely, the electron frequency and the electron neutral collision frequency. These two parameters are indispensable to the design of plasma absorbers [1]. When EM waves interact with the plasma, the plasma parameters are diagnosed by analyzing the results from the microwave transmission experiment and numerical simulation.

Eighteen gas discharge tubes were closely arranged on the metal plate, with high voltage ballasts ionizing these gas discharge tubes to generate plasma, as displayed in figure 1, to measure the backscattering attenuation of the plasma array under transverse magnetic (TM) mode. After 5 min of stable discharge of the plasma unit, the peak voltage and current value of each plasma element of the ionization source were measured to be 0.8 kV and 40 mA, respectively. The power supply is the alternating current, the ballast is connected to 220 V voltage, and the frequency of the current output by the ballast is 40 kHz. The gas discharge tube and the ballast are connected in series, one ballast can control two gas discharge tubes, and the specifications of the ballasts and the gas discharge tubes are the same. The ballasts are connected in parallel, so that the output current of each ballast is consistent, to ensure the consistent discharge state of each fluorescent lamp.

Figure  1.  Configuration for the measurement of plasma backscattering attenuation spectrum. (a) Experiment setup, (b) schematic diagram.

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The distance L between the horn antenna and the sample is 5 m to meet the far-field condition of L≥2×D²/λ, where D is the vertical dimension of the object to be tested, which is 0.2 m. The actual plasma units are composed of airtight glass tubes with an outside diameter of 15 mm, and a length of 42 cm, and the thickness of the glass tube is 1 mm, with the dielectric constant of 3.8. The cavity is filled mainly with argon and mercury, and the gas pressure was typically 2–3 Torr. The model of the vector network analyzer (VNA) is ANRITSU 3734D, which can measure the frequency range from 40 MHz to 20 GHz [20]. Setting the time domain threshold can avoid space clutter interference so that the experimental results are more accurate than not. The signal transmitter and receiver source are a pair of broadband horn antennas with an operating range of 2–18 GHz.

The VNA measures the backscattering attenuation spectrum of the plasma array, and the results are exhibited in figure 2. The numerical scattering coefficient of the plasma array is calculated by COMSOL simulation software, and the plasma parameters are estimated for simulating after several analyses to be qualitatively consistent with experimental results. In simulating, the electromagnetic wave frequency domain interface of the COMSOL RF module is used, periodic boundary conditions are set to simulate an infinite plasma array, and user-defined ports are set in the z-direction to simulate plane wave incidence. Therefore, the precise range of the plasma parameters could be deduced. The electron in plasma oscillates harmonically vibration under the excitation of a high voltage power supply, which is called plasma oscillation [21]. Therefore, the Drude model is adopted to approximately represent the EM characteristics of non-magnetized plasma during simulation calculation. The relative permittivity of plasma can be expressed as follows:

Figure  2.  Comparison of simulation and experiment for backscattering attenuation.

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The formula above ${\omega }_{\mathrm{p}}$ is the plasma frequency, ${\nu }_{\mathrm{e}}$ is the electron collision frequency, and $\omega$ is the angular frequency of the incident wave. The plasma frequency can be expressed as follows: ${\omega }_{\mathrm{p}}=\sqrt{n_{\mathrm{e}}{e}^2/m_{\mathrm{e}}{\epsilon }_0},$n_e is the electron density in the plasma, m_e is the electron mass, and e is the charge of the electron.

The experimental and simulation results of the plasma units' backscattering attenuation are indicated in figure 2, and the two results are distinguished by different colors and symbols. The S parameter of the initial state is normalized to zero during simulation and experiment, and the variation tendency of the two curves is approximately consistent. It can be observed that the positions of the attenuation peaks of the two curves are similar, and the decay amplitude will fluctuate slowly with the increase of discharge time, which is caused by the discharge unit's fluctuation of collision frequency and electron density. The corresponding collision frequency can be inferred from the gas pressure in the discharge tube. The air pressure of the low-pressure discharge tube used in this work is 2–3 Torr, due to the limitation of the ballast's power and plasma tube's pressure, and the approximate range of the collision frequency can be obtained by calculation of about 1–3 GHz. According to the simulation results, it can be inferred that the plasma electron density ranges from 1×10¹⁷ to 9×10¹⁷ m^-3, and the corresponding plasma frequency varies from 1.7×10¹⁰ to 5.3×10¹⁰ rad s^-1. The plasma frequency used in the simulation results is 5.18×10¹⁰ rad s^-1, and the collision frequency is 1.256×10¹⁰ rad s^-1. The diagnosis method of plasma parameters by using estimation analysis combined with the microwave transmission method has been fully validated in other literature [11].

3.   Plasma-RAM absorbing properties

The plasma spatial distribution can be altered by manipulating each discharge unit's On/Off state or changing its voltage. This work proposes a new EM wave absorbing component that combines the double-layer plasma unit and the RAM. The plasma cylinder array is assumed to be infinitely distributed on a perfect electrical conductor (PEC) which is covered with traditional RAM. A schematic diagram of its structure is displayed in figure 3(a). Plasma with different electron densities can be obtained by adjusting the voltage of the rectifier. The effect of spatial plasma distribution on radar absorption is analyzed by simulation. Figure 3(a) indicates that the different combined distributions of plasma units with the two plasma frequencies are arranged respectively. N_e1 and N_e2 represent the corresponding electron density, where the electron collision frequency is fixed at 1.256×10¹⁰ rad s^-1 for convenience of analysis. According to the simulation results in figure 2, the plasma frequency in the gas discharge tube is 1.8×10¹⁰ rad s^-1 and 5.18×10¹⁰ rad s^-1 when the rectifier is loaded voltage with 140 V and 220 V, respectively. Adjusting the voltage can change the electron density, thereby changing the plasma frequency. Several simulation results reveal that the designed plasma structure can effectively absorb low-frequency EM waves when the plasma frequency is distributed alternately high and low. Figure 3(a) lists five different plasma distribution situations, where N_e1 (1.8×10¹⁰ rad s^-1) corresponds to a plasma with low electron density, and N_e2 (5.18×10¹⁰ rad s^-1) corresponds to a plasma with high electron density. The absorbance of the five different distribution patterns is shown in figure 3(b).

Figure  3.  Absorption of electromagnetic waves by different plasma distribution. (a) Five plasma distribution modes, (b) absorbance corresponding to five modes and only RAM.

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Figure 3(b) exhibits that the plasma layer has a unique advantage when distributed according to Mode 1. It has a significant absorption capability for the EM waves in the S and C frequency bands, with an absorption rate that can reach over 90%, which cannot be achieved by other distribution modes. In addition, the absorption efficiency at 9.5–11.5 GHz and 15–18 GHz also exceeds 90%, which can realize excellent absorption stealth for multi-bands. The different plasma distribution modes present various characteristics of absorption in the X and Ku frequency bands, which is due to the combined interaction of the plasma and the RAM. In order to further analyze the absorption performance of the plasma-RAM structure in different frequency bands, the structure's distribution of electric field values and energy flow density at different frequency points are listed below. Figure 4 presents the distribution of electric field values at 2.6 GHz, 6.7 GHz, 10.5 GHz, and 16.5 GHz, and figure 5 gives the distribution of power flow density at the corresponding frequency points.

Figure  4.  The electric field distributions at each frequency point. (a) 2.6 GHz, (b) 6.6 GHz, (c) 10.5 GHz, (d) 16.5 GHz.

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Figure  5.  Power flow density distribution at each frequency point. (a) 2.6 GHz, (b) 6.6 GHz, (c) 10.5 GHz, (d) 16.5 GHz.

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It is widely known that when the frequency of the EM wave is higher than that of plasma, the EM wave cannot propagate within the plasma in specific frequency bands, which are called photonic bandgaps. When the frequency of the EM wave is lower than that of plasma, the EM wave cannot transmit inside the plasma, which is called the plasma cut-off frequency [22]. Generally, ${\omega }_{\mathrm{p}}/2\pi$(Hz) is regarded as the plasma cut-off frequency, and the EM wave below the plasma cut-off frequency will be reflected and cannot enter the plasma. When the EM wave coupling enters plasma arrays with a large area, the inhomogeneous plasma layer can increase the possibility of absorbing broadband EM waves. The distribution of the plasma units arranged as Modes 2–5 in figure 3 is relatively homogeneous and presents lower absorption efficiency within 2–8 GHz band compared with Mode 1. Hence, the uneven distribution of thin plasma units can enable more EM waves to be coupled into the plasma layer, which can increase the possibility of multiple scattering of EM waves, dissipate EM energy and improve the absorptivity to EM waves.

When the EM wave is incident normally to the plasma-RAM absorber, the low-frequency EM wave propagates in the plasma with low electron density. As presented in figure 4(a), the plasma units with an electron density of N_e1 generate an intense coupling effect with the EM wave at 2.6 GHz. With the increase of EM wave frequency, more EM energy can be coupled into the plasma with high electron density. As shown in figure 4(b), the coupling effect between a 6.6 GHz EM wave and plasma with an electron density of N_e2 is more intense. In contrast, the EM waves in the X and Ku frequency bands can pass through the plasma layer and be absorbed by RAM. Figures 4(c) and (d) display the reaction of EM waves and RAM, as well as the induced electric field in RAM, which indicates that such RAM has good absorption performance for high-frequency EM waves. The distribution of power flow density is illustrated in figure 5. It can be noticed from figures 5(a) and (b) that the EM energy in the X and Ku frequency bands is mainly concentrated on the upper surface of the plasma units. With the increases in the incident EM waves frequency, the EM energy is mainly concentrated in the gap outside the plasma units. That means multiple scattering of the EM waves between the gas discharge tube and RAM, and the EM energy is gradually dissipated in this process.

RAM has the advantages of simple manufacture, light in weight, and easy coating on the surface of objects. Therefore, RAM is convenient for large-scale applications in radar stealth. Generally speaking, the RAM can be divided into non-magnetic dielectric absorbing materials and magnetic ferrite absorbing materials according to the different loss mechanisms. There are significant differences in the EM parameters of the two kinds of RAMs, and the absorption bands are also quite different. The following figure 6 content describes the comparison of the EM properties of the magnetic RAM and the non-magnetic RAM [23–25]. In this work, non-magnetic dielectric absorbing materials are selected as the research carrier, and the whole work is based on the non-magnetic RAM.

Figure  6.  Electromagnetic characteristics of magnetic and non-magnetic RAM. (a) Electromagnetic parameters of RAM, (b) electromagnetic absorption characteristics of RAM.

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A vector network analyzer (VNA) was applied to determine the relative permeability and permittivity in the frequency range of 2–18 GHz for the calculation of reflection loss. Figure 6(a) shows the electromagnetic parameters including permittivity and permeability of the RAM. The electromagnetic parameters are measured by the coaxial line method in the Nicolson–Ross–Weir (NRW) theory [23–25]. A sample containing 40 wt% of the obtained composites was pressed into a ring with an outer diameter of 7 mm, an inner diameter of 3 mm, and a thickness of 2 mm for microwave measurement in which paraffin wax was used as the binder. The sample is placed in a coaxial fixture, and the coaxial fixture is connected to the vector grid. Based on the NRW theory [23–25], the precise electromagnetic parameters of the RAM can be obtained as shown in figure 6(a). The electromagnetic parameters are brought into COMSOL software, and the frequency domain solver of the RF module can be used to simulate the absorption properties of a 2 mm thickness absorbing material in the corresponding frequency band, as shown in figure 6(b).

It is known that relative complex permittivity (ε_r=ε_r' - jε_r") and complex permeability (μ_r=μ_r' - jμ_r") dominate the properties of EM absorption materials. According to the previous study [23, 24], the real part of permittivity (ε_r') values of magnetic RAM and non-magnetic RAM exhibit distinct frequency dispersion behaviors, where their ε_r' values gradually decrease from 13.3 and 8.9 at 2.0 GHz to 11.2 and 6.3 at 18.0 GHz, respectively (figure 6(a1)). The imaginary part of permittivity (ε_r") of magnetic RAM declines from 6.0 to 3.2 and presents a more apparent concave profile with a minimum of 3.6 at 12.0 GHz. In contrast, the ε_r" of non-magnetic RAM keeps approximately constant in the 2–18 GHz frequency range (figure 6(a2)). Figure 6(a3) displays the real part of permeability (μ_r') and imaginary part of permeability (μ_r") values of non-magnetic RAM at about 1 and 0, respectively. On the contrary, magnetic RAM benefits from the magnetic metal particle and exhibits variational μ_r values (figure 6(a4)). Corresponding studies have presented that non-magnetic RAM indicates superior EM absorption ability in the high-frequency range, and magnetic RAM possesses evident EM attenuation behavior at low frequency.

The absorption properties of the two RAMs are shown in figure 6(b). The non-magnetic RAM shows excellent absorption behavior in the Ku frequency band, while the magnetic RAM presents more outstanding in the 10.5–13.25 GHz band. The absorption performance of both materials for low-frequency EM waves is significantly decreased since the plasma-RAM structure can absorb the EM energy in the low-frequency band, so it can be inferred that the plasma makes the major contribution to the absorption of this. Different kinds of RAMs combined with the plasma layer designed in this work will possess different absorption effects. Figure 7 depicts the absorbing characteristics of the plasma layer placed on different substrates. There are three different substrates: the PEC without coated RAM, the PEC coated with magnetic RAM, and the PEC coated with non-magnetic RAM. Figure 7 reveals that the plasma layer intensely absorbs EM energy in the frequency band of 2–7 GHz, which is not related to whether the PEC is coated with RAM or not. The RAM plays a significant role in absorbing EM energy above 7 GHz, and the corresponding pure plasma layer displays the limited absorption ability to high-frequency EM waves. RAM not only exhibits good absorption characteristics in its intrinsic absorption band but also expands the absorption band and improves the absorption efficiency after coupling with plasma. Thus the multi-band EM absorption can be achieved by transforming the RAM or changing the spatial distribution of the plasma.

Figure  7.  Wave absorption properties of plasma combined with different absorbing materials.

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The spatial distribution of the plasma is further discussed based on the non-magnetic RAM already coated on the PEC surface. The microwave absorption characteristics of the single-layer and double-layer plasma array are discussed. The distance between single-layer plasma and the substrate (the PEC coated with non-magnetic RAM) is divided into two situations, the plasma layer near the PEC and away from the PEC, as depicted in figure 8, with the distance from the substrate being 0 mm and 13 mm, respectively. The electron density in the plasma layer is still arranged in an alternating high and low distribution. The three plasma distribution situations have a pronounced resonance absorption peak near 10.25 GHz, as shown in figure 8. Through simulation calculation and the results in figure 3(b), it can be concluded that the unexcited gas discharge tube structure determines the resonance absorption near 10.25 GHz. The single-layer plasma array near the substrate has a wider absorbing band than that away from the substrate and exhibits a stronger absorbing performance in X-band, which is inconsistent with the conclusion in [11]. The reason may be the uneven distribution of plasma and the introduction of RAM in the designed structure, which changes the scattering path of the EM waves and increases the pathway for EM energy loss. The monolayer plasma arrays near the substrate can achieve over 90% absorption of EM energy in the X and Ku frequency bands. In contrast, monolayer plasma that away from the substrate, which facilitates the effective transmission of EM waves in the 6–8 GHz band. On the other hand, the tunable band-pass frequency range can be realized by adjusting the spatial distribution of plasma on the equipment's surface, and radar stealth can be achieved without affecting the regular operation of the equipment.

Figure  8.  Absorbing properties of single-layer and double-layer plasma arrays.

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In order to verify the actual backscattering attenuation of EM waves by the plasma distribution proposed in the article, a corresponding test setup was built in the laboratory, as displayed in figure 9(b). The plasma absorber is placed on the aluminum plate substrate coated with non-magnetic RAM using the experiment system displayed in figure 1(b). The size of the aluminum plate is 20 cm × 20 cm. By varying the voltage of the ballast, the plasma element has the corresponding plasma frequency to satisfy the pattern of alternating electron density distribution. The backscattering attenuation spectrum of the plasma-RAM absorber is obtained by the vector network analyzer.

Figure  9.  Plasma-RAM composite absorber model and experimental setup. (a) Schematic diagram, (b) experiment setup.

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As presented in figure 10, the variation trend of the simulated and experimental data is roughly similar, and the positions of the attenuation peaks are also approximately the same. It is noteworthy that the experimental data exhibit more fluctuations, which may be caused by the unstable discharge state in the plasma tube. In addition, the exposed wires and connectors will inevitably scatter EM waves, which increases the EM waves' resonance space and scattering paths.

Figure  10.  Backscattering attenuation spectrum of a plasma-RAM composite absorber.

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4.   RCS of plasma-RAM structure

In practical applications, the target's characteristics are often detected by radar. The RCS is a physical quantity that measures the echo intensity generated by the target under the irradiation of radar waves. The RCS is the ratio of the scattered energy to the incident energy, which can be calculated as ${\sigma }_{3\mathrm{D}}=\underset{r\to \infty }{\lim }4\pi r^2{\left|P_{\mathrm{scattered}}^i\right|}^2/{\left|P_{\mathrm{incident}}^i\right|}^2$ or ${\sigma }_{2\mathrm{D}}=\underset{r\to \infty }{\lim }2\pi r{\left|P_{\mathrm{scattered}}^i\right|}^2/{\left|P_{\mathrm{incident}}^i\right|}^2,$ where r is the distance from the target to the detection point, ${\sigma }_{3\mathrm{D}}$ and ${\sigma }_{2\mathrm{D}}$ correspond to the RCS of a three-dimensional and two-dimensional target scatterer, respectively.

The RCS of the proposed plasma-RAM absorber is simulated by using the simulation software COMSOL. Firstly, the RCS of the EM wave vertically incident metal plate is simulated. The results are presented in figure 11, which indicates that the RCS of the metal plate increases with the increase of the incident wave frequency. After coating the plasma-RAM absorber on the metal plate, the RCS of the composite absorber exhibits oscillation, which is similar to the changing tendency of the backscattering attenuation in figure 10. Comparing the two results can reveal the difference in RCS reduction of the plasma-RAM absorber for different frequencies. The plasma-RAM absorber demonstrates superior RCS reduction capability, which can reduce the RCS by 20 dB around the frequency points of 7 GHz, 10 GHz, 14 GHz, and 17 GHz.

Figure  11.  Target RCS versus frequency.

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In addition, the target's RCS exhibits different degrees of attenuation with varying incident degrees of the detection wave. Figure 12 depicts the omnidirectional angle RCS of the 7 GHz incident EM wave, where the incident pitch angle $\theta =90°,$ and the azimuth angle $\phi$ change from -180° to 180°. $\phi =\mathrm{0}°$ indicates that the incident wave radiates vertically to the target. According to figure 12, when the 7 GHz detection wave changes from vertical incidence to ±55°, the RCS decreases by more than 10 dB. The RCS attenuation capability of the absorber is decreased when the incident angle exceeds ±55°. Here, the thickness of the metal plate is only 5 mm, but in practice, the thickness of the target is far more than 5 mm. In addition, how the plasma-RAM absorber maintains low RCS when exposed to wide azimuth angle incident waves will be another research focus. Therefore, it is undeniable that the designed structure has a robust EM absorption capacity at wide incident angles.

Figure  12.  Omnidirectional RCS of the plasma-RAM absorber.

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5.   Conclusion

This study demonstrates a radar stealth structure composed of a plasma array and RAM. The absorption and RCS reduction performance of this stealth structure in the 2–18 GHz frequency band are analyzed. The plasma parameters are obtained by analyzing the results from the microwave transmission experiment and numerical simulation. The absorption efficiency of electromagnetic waves by plasmas of various spatial distributions is analyzed by simulation and experiment. The results show that the plasma array composed of tubes with alternating high and low electron density can absorb up to 90% of the EM energy in the S and C frequency bands. Based on this structure, the effect on the absorption performance of the type of RAMs and the distance from the plasma array to the substrate is further discussed. The plasma-RAM stealth structure can achieve an RCS reduction of more than 10 dB for broad frequency bands and wide incident angles. Meanwhile, this structure is easy to deploy on the surface of the equipment. Furthermore, the radar stealth ability of the structure is tunable by changing the plasma layout and the type of the RAM. This research provides a new approach to the synergistic stealth of targets and has a particular reference value for engineering applications.