Design and Application of High-Density Cold Plasma Devices Based on High Curvature Spiked Tungsten Structured Electrodes

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This paper presents the use of tungsten electrodes with high-curvature-radius spiked structures to replace traditional electrodes in plasma elements, achieving an ultra-high-density, low-pressure cold plasma with a density reaching 1.15 × 10¹² cm⁻³. The fabricated tubular and annular high-density cold plasma elements exhibit very low radar cross-sections, indicating their potential for use in plasma transient antennas. The large-area plasma generated by an array of high-density plasma elements can effectively absorb electromagnetic waves, reducing the radar cross-section of metallic objects and achieving radar stealth. This has significant application value in the field of electronic countermeasures.

Abstract

Advances in radar technology have driven efforts to develop effective countermeasures. Plasma is recognized as a highly effective medium for absorbing electromagnetic waves. Recent research has focused on enhancing plasma element performance. This paper achieved ultra-high-density, low-pressure cold plasma with a density of 1.15 × 10¹² cm⁻³, surpassing similar studies by more than an order of magnitude. Tungsten electrodes with high-curvature spiked structures were invented to replace traditional iron–nickel alloy electrodes, increasing plasma density by 88.2% under the same conditions. Lightweight and cost-effective tubular and annular ultra-high-density, low-pressure cold plasma devices were developed, demonstrating exceptional performance in electromagnetic wave absorption, plasma transient antennas, and radar stealth technology. The influence of plasma on electromagnetic waves and its numerical relationship were analyzed. By measuring the radar cross-section (RCS), the reduction in radar detection rates was quantified. The results show that the ultra-high-density cold plasma devices exhibit very low intrinsic RCS values, suitable for plasma antenna applications. The array of plasma elements generates a large-area high-density low-pressure cold plasma. This plasma effectively reduces the radar cross-section (RCS) of metallic equipment in the S and C bands and shows attenuation in the X band. These effects highlight the superior characteristics of plasma technology in electronic warfare. This exploratory research lays the groundwork for further defense applications.

1. Introduction

Radar is the cornerstone of modern technology, allowing us to determine the spatial location of targets from great distances through the use of electromagnetic waves. As radar technology advances, so does the development of effective countermeasures, such as wave absorption technology [1,2]. Correspondingly, plasma is drawing increasing attention as a new type of wave absorbing material [3,4].

The plasma element is a medium that is able to displace ions and electrons. When an electromagnetic wave interacts with the plasma element, it gives energy to the particles, but only a small fraction of that energy is returned [5]. Some of the missing energy during this process may be converted into heat by scattering or resonant acceleration that occur between the electromagnetic wave and the plasma, and dissipate thereafter [6]. The possibility of being detected by radar can therefore be effectively reduced by the mechanisms such as the reflection, refraction and absorption of electromagnetic waves by the plasma elements [7]. By reducing an aircraft’s radar cross-section (RCS), plasma can significantly enhance radar stealth capabilities, resulting in shorter detection distances, larger blind spots, and reduced warning times.

Plasma density and temperature are key factors affecting the absorption performance of plasma elements [8]. Increasing the plasma density can facilitate the attenuation of the electromagnetic waves in plasma elements and then achieve stealth against the radar across the entire band. Increasing the plasma temperature, which results in an increased plasma collision frequency, can also help accelerate the attenuation of radar electromagnetic waves within a certain range. Therefore, the dynamic adjustment of plasma density and temperature are required in the face of different types of radar systems. Namely, the design of the plasma generator is a crucial aspect of plasma absorption technology.

There are two main types of plasma generators currently available: the atmospheric generator and the low-pressure plasma generator. The former has an open structure, while the latter has a closed one. While both types have their own strengths in various applications, for electromagnetic absorption technology, the low-pressure plasma generator is preferred for the following reasons:

• Volume and size. Atmospheric plasma generators are typically large and made of steel, making them difficult to use on aircraft due to their weight and size. In contrast, the low-pressure generator is much simpler and lighter, using wave-transparent materials like glass to construct the cavity.
• Energy consumption. The main discharge mode of atmospheric plasma elements is arc discharge, which requires a high current of tens of amps, resulting in high energy consumption. The low-pressure plasma generator, on the other hand, uses glow discharge as its main discharge mode, which consumes less energy due to the low gas pressure inside its cavity.
• Plasma maintenance. The full surface coverage of a layer of plasma can achieve the best electromagnetic absorption. However, the atmospheric plasma element can easily disturb the plasma generated on a high-speed flying vehicle. Conversely, the low-pressure plasma generator has the plasma generated within a closed cavity, ensuring a long-lasting effect [9].

Given these advantages, low-pressure plasma generators show greater potential for plasma absorption technology compared to atmospheric generators. Consequently, substantial efforts have been dedicated to enhancing their plasma absorption performance.

In 1956, Arnold Eldredge filed a patent application for an “Object camouflage method and apparatus”, using ionizing clouds to refract or absorb incident radar waves [10]. In 1962, Swarner et al. conducted a study of the RCS measurements of target objects covered with plasma [11]. In 1990, Vidmar found that plasma produced in air or in helium at atmospheric pressure is an excellent absorber of electromagnetic waves. He clearly stated that plasma has an absorbing and reflecting effect on electromagnetic waves, introducing the concept of plasma stealth [9]. In 1993, Laroussi et al. studied the refraction, reflection and absorption of electromagnetic waves by plasma sheaths and reported equations for the estimation of reflected and absorbed power [3]. In 2007, Yang et al. studied the effect of plasma with a non-uniform distribution of electron density on the reflection properties of electromagnetic waves [12]. In 2016, Singh et al. further carried out systematic numerical simulations of the composite stealth properties of plasma and wave absorbing materials in their monograph, and optimized their design as well [13].

In 2015, Zhang et al. used a 3D barrel model to analyze the plasma stealth of aircraft intakes, but this method could only achieve the goal of stealth in the low frequency band [14]. In 2017, Ghayekhloo et al. designed a collisional low-pressure plasma in an arrayed structure and measured the radar cross-section of a covered metallic surface. However, their study mainly focused on the X-band and required a constraint layer to achieve the desired results using this approach [15]. In 2018, Sun et al. conducted electromagnetic wave absorption studies using plasma channels formed by femtosecond lasers, but the results of this study could not be directly applied to vehicle stealth [16].

While these studies have contributed valuable insights, there remain challenges in achieving effective plasma stealth across a broader frequency range and in practical applications. Recognizing these limitations, further innovation is necessary to develop more versatile and efficient plasma stealth solutions.

This paper presents the design of a novel low-pressure plasma generator, which employs original high-curvature-radius spiked tungsten structure electrodes. It also uses an NHWY10K-0.5 high-frequency switching power supply and high-purity argon gas as the working atmosphere, to form a stable glow discharge plasma. The surface structure of the tungsten electrodes, formed through a hydrothermal reaction, featured high-curvature-radius spikes that enhanced field emission characteristics. The generator’s chamber, made from lightweight quartz, was adaptable to various working conditions and was used with a custom-designed Langmuir double probe system for precise plasma density measurements, thereby reducing the cost of plasma generation and diagnostics.

This study compared the plasma density produced by box-type iron–nickel alloy electrodes and tungsten electrodes under different conditions. The experimental results indicated that the plasma density generated by the tungsten electrode elements reached up to 7.79 × 10¹¹ cm⁻³ under low current conditions, which was 88.2% higher than that of traditional plasma elements and capable of withstanding a broader current range. The study also achieved for the first time an ultra-high-density, large-area, low-pressure cold plasma with a density of up to 1.15 × 10¹² cm⁻³, surpassing similar studies by more than an order of magnitude [17,18,19,20,21,22,23,24,25,26,27,28] as shown in

Table 1. Recent density comparison of low-pressure cold plasma studies.

Literature	Generation Method	Power Supply Parameters	Operating Pressure	Year	Plasma Density
This paper	Glow Discharge	950 W, 200 mA	0.5 torr	2024	1.15 × 1012 cm−3
[17]	Inductive Coupling	1500 W	0.1 torr	2023	1.0 × 1011 cm−3
[18]	Microwave Discharge	500–700 W	100 Pa (0.75 torr)	2023	3.4 × 1010 cm−3
[19]	Capacitive Coupling	50–200 W	0.15–0.38 torr	2022	2.2 × 1010 cm−3
[20]	Glow Discharge	300–900 W	2.13 × 10−4 torr	2021	1.6 × 109–3.9 × 1010 cm−3
[21]	Glow Discharge	Not Mentioned	140 Pa (1.05 torr)	2018	5.62 × 1011 cm−3
[22]	Simulation Analysis, Not Mentioned	Not Mentioned	Not Mentioned	2018	Theoretical analysis can reach 6.5 × 1011 cm−3
[23]	Simulation Analysis, Not Mentioned	Not Mentioned	Not Mentioned	2017	1.56 × 109 cm−3
[24]	Capacitive Coupling	252.5 W	0.5–0.9 torr	2017	2.60 × 1010 cm−3
[25]	Microwave Discharge	1000 W	Not Mentioned	2016	Theoretical analysis can reach 1.0 × 1012 cm−3
[26]	Glow Discharge	150–350 mA	1.5 torr	2016	1.0 × 1010 cm−3
[27]	Inductive Coupling	800 W	100 Pa (0.75 torr)	2015	7.61 × 1010 cm−3
[28]	Glow Discharge	Not Mentioned	9 Pa (0.07 torr)	2010	1.4 × 1011 cm−3

.

Regarding the parameters of the input power supply, the cold plasma prepared in this study needs to achieve coverage of the equipment to be concealed in electromagnetic wave-absorbing radar stealth applications. In practical operation, the power used by the input supply is strongly correlated with the total volume of the plasma (corresponding to the total area per unit thickness). If the plasma volume is larger (corresponding to a larger area per unit thickness), the power requirements will be higher. Another advantage of this study is that the generated plasma volume can be controlled by the number of component arrays so that the demand for input power can be adjusted accordingly.

Regarding the operating pressure parameters, plasma density generally increases with pressure, showing a trend of first rising and then falling. Section 3.2 analyzes the reasons for this phenomenon from a theoretical perspective. For the plasma prepared in this study, before 0.5 torr, the increase in operating pressure allows electrons to gain higher energy and collision ionization, increasing plasma density. After 0.5 torr, the increase in pressure reduces the mean free path of electrons, thereby reducing their average kinetic energy, and thus the plasma density decreases.

Given the tungsten material’s high melting point and low work function, it is more conducive to achieving the goal of stealth and can effectively avoid the disadvantages seen in similar studies [14,15,16]. Building upon these findings, this paper further investigated the influence of the working gas pressure inside the element on the plasma density, and optimizes the pressure parameters of the plasma element. The final plasma elements developed in this paper can be arranged in arrays to form a large-area, ultra-high-density, low-pressure cold plasma, which is suitable for radar stealth applications.

2. Materials and Methods

The electrode plays a crucial role in the performance of the plasma element. To generate high-density plasma, the electrode must be able to withstand a large current (≥100 mA).

Traditional closed-structure plasma elements usually employ barrel-shaped iron–nickel alloy as the electrode. However, the electron emission performance of iron–nickel alloy is poor. Therefore, it is necessary to add Cs₂O electron powder to the electrode to reduce its work function.

The iron–nickel alloy material, which consists of 40% iron and 60% nickel, is bent into a straight barrel to produce a barrel-shaped electrode. The inner side of the electrode is coated with Cs₂O electron powder and then welded to a metal wire that is embedded in the glass tube. Dumet wire is used at the intersection of the metal wire and glass tube to ensure the tightness and stability of the plasma chamber. To import the argon gas with different gas pressures, the gas delivery tube of the closed plasma chamber is also made of glass. After the gas delivery is completed, the gas transmission pipeline is sealed by high-temperature melting.

Cs₂O is an n-type semiconductor material with a smaller work function (W₂) than that of iron–nickel alloy (W₁), as shown in Figure 1a. In the figure, E₀ is the vacuum energy level, E_f1 is the Fermi energy level of the iron–nickel alloy, E_f2 is the Fermi energy level of Cs₂O, E_c is the conduction band of Cs₂O, E_v is the valence band of Cs₂O, and E_f3 is the Fermi energy level of tungsten.

When Cs₂O is in contact with the metal electrode, they compose a Schottky contact, and the Fermi energy levels of metal E_f1 and Cs₂O E_f2 remain the same due to the pinning effect, as shown in Figure 1b. Thus, the work function of the iron–nickel electrode with Cs₂O decreases from W₁ to W₂, making it easier to generate plasma. For the tungsten electrode, its work function (W₃) is smaller than W₂, making it more suitable for use as a plasma electrode material.

However, when the applied current is high, the plasma chamber generates a lot of heat, which lowers the plasma density and can cause damage to the electrode or the chamber. Moreover, Cs₂O is prone to volatilization under high-temperature conditions, leading to a low working life and the poor continuity of conventional iron–nickel electrodes. Therefore, we developed tungsten electrode plasma elements based on the fabricated iron–nickel electrode elements. Using NHWY10K-0.5 high-frequency switching power supply as the working power source and high-purity argon gas (99.99% by volume) as the working gas, we compared the plasma densities under different currents with a barrel-shaped Fe-Ni electrode and a tungsten electrode.

The structure of the tungsten wire electrode is similar to that of the cartridge iron–nickel electrode, but the iron–nickel part is replaced with a forked structure with a tungsten wire attached.

The forked structure and the tungsten wire electrode can increase the electrode’s surface area. Combined with the high curvature radius spiked structure on the tungsten electrode surface, it further enhances field emission characteristics, improving electron emission efficiency. Additionally, the forked structure facilitates better heat dissipation and adapts to thermal expansion or contraction, reducing the likelihood of mechanical failure or degradation and extending the electrode’s lifespan. For iron–nickel alloy electrodes, since Cs₂O electron powder is added to lower the work function, a relatively uniform barrel-shaped structure is required, making it unsuitable for forked or filament structures. Moreover, iron–nickel has relatively low fatigue resistance, necessitating the use of a barrel-shaped structure to more evenly distribute stress and reduce local stress concentration.

Figure 2a,b show the perspective views of the element structure. Figure 2c shows a tungsten electrode plasma element in operation. Ultimately, these elements can be arranged in arrays to form a large-area, ultra-high-density, low-pressure cold plasma.

Tungsten wire is known as a pyrocondensation metal material, because it becomes thinner as the temperature rises, which limits the increase in the current and enables long-term operation. On the other hand, other thermal expansion metals expand when exposed to high temperatures, resulting in a reduction in resistance and an increase in current, which can lead to burnout. Additionally, the electron emission coefficient of tungsten wire increases significantly at high temperatures, leading to a higher rate of thermionic emission. As the temperature rises, more electrons acquire enough energy to overcome the surface potential barrier and escape, creating a large amount of electron emission [29]. Thermionic emission occurs when the kinetic energy of the electrons within the solid is increased by heating.

Meanwhile, the surface of the tungsten electrode underwent hydrothermal treatment, resulting in the creation of irregular, rough surface features. This process involved immersing the tungsten electrode in a solution containing tungsten ions, which reacted hydrothermally with hydrazine hydrate, forming irregular spike-like structures on the electrode. This treatment enhances the field emission characteristics of the electrode by leveraging the surface inhomogeneity to strengthen the partial electric field. Consequently, this improves the electrode’s breakdown capability and reduces the turn-on field. The surface morphology of the electrode after hydrothermal treatment will be presented in Section 3.1.

Plasma diagnosis refers to the use of various experimental techniques to determine plasma parameters. Commonly used plasma diagnostic techniques include the probe method, microwave method, and spectroscopic method. Among these, the probe method is considered one of the most effective diagnostic methods.

The Langmuir dual-probe system used in this paper has several advantages, including:

• The dual-probe system collects current without exceeding the ion saturation current, thus preventing the probe from burning while collecting electron current in high-density plasma.
• The dual-probe structure is simple, and the probe system is easy to operate.

Since the dumet wire and the glass tube have similar thermal expansion coefficients, a 0.2 mm diameter dumet wire was selected as the probe for the Langmuir dual-probe system. In this way, the chamber will not be damaged when the diagnostic system is matched to the plasma chamber in a heat-treated manner, and a stable plasma can be maintained. Figure 3 shows a sketch of the Langmuir dual-probe system structure.

3. Results and Discussion

3.1. Surface Morphology of the Tungsten Electrode after Hydrothermal Treatment

Figure 4a displays the spike surface structures on the tungsten electrode surface as observed under AFM. The surface morphology of the tungsten electrode after hydrothermal treatment shows these irregular, rough features. Figure 4b provides the height measurement of these spike surface structures.

The basic regularity of field ionization can be obtained from the Flower–Nordheim formula:

$$J=\left(\frac{A{E}_0^2}{\mathsf{\Phi }}\right)exp\left(-\frac{B{\mathsf{\Phi }}^{\frac{3}{2}}}{E_0}\right)$$

(1)

$$E_0=\beta \left(\frac{E}{d}\right)$$

(2)

where J denotes the field emission current density, A and B are constants, Φ is the metal surface work function, β is the electric field enhancement factor related to the metal surface morphology, E is the applied voltage, and d denotes the spacing of the spike surface structures. It can be seen that a reasonable improvement of the electrode can effectively improve the process of discharge and reduce the difficulty of ionization.

3.2. Effect of Electrode and Working Gas Pressure on Plasma Density

Both electrodes were applied to the low-pressure plasma elements, with argon as the working gas and a high-frequency switchable power supply as the driver. The devices with different electrodes were tested under the operating current at 100 mA, 150 mA and 200 mA. The relationship between plasma density and argon gas pressure is shown in Figure 5.

From Figure 5a,b, it can be observed that with the increase in the argon gas pressure in the tube under the high-frequency DC pulse drive of 100 mA and 150 mA, the plasma density under both electrodes exhibits a trend of increasing first, and then decreasing. For both the electrodes, the maximal plasma density appears at the gas pressure of 0.5 torr. In low-pressure environments below 0.5 torr, the plasma density increases as the pressure gradually rises. This occurs because at low pressures, electrons can accumulate sufficient kinetic energy under the influence of the electric field, leading to collisions and the ionization of gas molecules. As the pressure continues to rise, the frequency of collisions between gas molecules also increases, further boosting plasma density. However, when the pressure exceeds the critical point of 0.5 torr, the frequent collisions between gas molecules and the reduced mean free path of electrons due to higher pressure cause the electrons to no longer gain enough energy in the electric field to sustain the continuous ionization of gas molecules. This results in a decrease in plasma density.

As shown in Figure 5, under 100 mA current, the Fe-Ni electrode element has the maximum values of $4.14\times {10}^{11}{\mathrm{c}\mathrm{m}}^{-3}$, and the W electrode element has the maximum values of $7.79\times {10}^{11}{\mathrm{c}\mathrm{m}}^{-3}$. The improvement is 88.2%. For 150 mA current, the maximum plasma density of the Fe-Ni electrode element is $8.21\times {10}^{11}{\mathrm{c}\mathrm{m}}^{-3}$ and that of the W electrode element is $9.47\times {10}^{11}{\mathrm{c}\mathrm{m}}^{-3}$. The improvement is 15.3%. It is worthwhile noticing that the plasma density increases with the increase in current, which is consistent with the plasma density calculation formula:

$$n\left(x\right)=(\frac{j}{q{D}_a}x+n_0)e^{-\frac{qE}{kT}x}$$

(3)

where n is electron concentration, j is drift current, q is electronic power, D_a is bipolar diffusion coefficient, and E is electric field strength.

In Figure 5c, under a high-frequency DC pulse drive of 200 mA, the Fe-Ni electrode only shows the plasma density of $1.36\times {10}^{11}{\mathrm{c}\mathrm{m}}^{-3}$ at 0.5 torr, which is lower than the plasma density at 100 mA. In addition, the plasma density does not follow the same trend that changes with the gas pressure inside the element. This phenomenon can be attributed to the damage of the Fe-Ni electrode at 200 mA, which caused the plasma element to fail to work properly. Notably, for the W electrode, when the gas pressure inside the tube is 0.5 torr, the plasma density can reach a maximum value of 11.5 × 10¹² cm⁻³, which is more than an order of magnitude higher than those reported in similar cold plasma studies.

3.3. Effect of Electrodes on the Light Intensity of Plasma Elements

For low-pressure plasma generators, when a high-frequency DC pulse is used to make the working gas discharge inside the element, the atoms will be then excited by the transferred energy. The excited atoms can lose energy in various ways, one of which is through radiative decay, where the atom releases a photon to transfer energy. The number of photons determines the intensity of the light and is also proportional to the concentration of the plasma. Therefore, the density of the plasma can be qualitatively determined by the intensity of its luminosity [30].

Figure 6 shows the light intensity of the low-pressure plasma generator measured with both electrodes at the argon gas pressure of 0.5 torr.

As can be seen, the light intensity of the W electrode is greater than that of the Fe-Ni electrode over the entire range of current, and the light intensity keeps increasing with the increase in current. In comparison, the light intensity of the Fe-Ni electrode decreases when the current exceeds about 150 mA, which verifies that the working condition of Fe-Ni electrode should be below 150 mA, as discussed earlier in Figure 5c.

This result demonstrates that the W electrode plasma element produces a higher density of plasma under the same conditions, works more reliably, and can withstand a wider range of currents, and the Fe-Ni electrode produced in this paper can work properly within the range of 150 mA.

3.4. Changes of Electrode Morphologies before and after Discharge

To investigate the performance of the W electrode and Fe-Ni electrode under higher currents, scanning electron microscopy (SEM) was used to analyze the morphology of the two electrodes after 200 mA discharge. The results are shown in Figure 7, which presents the SEM images of the two electrodes after undergoing 10,000 cycles.

Prior to discharge, the tungsten electrode had well-distributed spike surface structures after hydrothermal treatment, and no defects were observed (Figure 7a). After discharge, only minor changes were observed on the surface of the electrode (Figure 7b). These changes were attributed to the slight agglomeration of tungsten under high current. This small difference indicates that the tungsten electrode is capable of withstanding a current of 200 mA.

The morphological characteristics of the Fe-Ni alloy electrode before and after discharge are illustrated in Figure 7c,d. Prior to discharge, the electrode surface was uniformly coated with the Cs₂O electron powder coating; however, after discharge, the coating became lumpy and cracks appeared on the surface of the electrode.

Among several commonly used metals, tungsten (W) has the highest melting point and the largest emission constant. Even if its surface is slightly damaged, tungsten can continue to act as the cathode and maintain the discharge. Therefore, as the current increases, the W electrode will not be damaged and the plasma density remains increased.

However, for Fe-Ni electrodes, when the Cs₂O electron powder coating is damaged, the base metal will not be able to maintain the discharge as a cathode. This is because the Si-containing nickel metal is doped with iron in this electrode. If it is used as a cathode directly, the iron will be distributed on the surface of the base metal, which will significantly reduce the emissivity of the electrode. Therefore, an excessive current will destroy the oxide coating and damage the Fe-Ni electrode. As a result, the plasma density generated will decrease and no longer change with the current.

3.5. Advantages of Tungsten Electrode

There are three advantages of tungsten electrode elements that enable higher plasma densities and a wider tolerance range:

• The tungsten electrode has a high melting point. The melting point of tungsten is 3410 °C, while the melting point of iron–nickel alloys is between 1430 °C and 1480 °C. This high melting point enables the tungsten electrode to withstand higher currents, effectively increasing the plasma density.
• Tungsten electrodes have a low work function value. Its work function is 4.5 eV, which is lower than that of most metallic materials used for electrodes. This low work function means that less energy is required to move electrons from inside the tungsten electrode to its surface, making it more conducive to improve the performance of the plasma element.
• As shown in

  Table 2. Thermal conductivity and specific heat capacity of metallic materials.

  Metallic Materials	Thermal Conductivity (W/m·K)	Specific Heat Capacity (kJ/kg·K)
  W	173	0.13
  Fe	80	0.45
  Ni	8	0.46

  , tungsten has a higher thermal conductivity and lower specific heat capacity than iron and nickel, which means that tungsten electrodes have a shorter thermal hysteresis and can reach a sufficient temperature in a shorter period of time to bring the element into operation.

3.6. The Propagation of Electromagnetic Waves in Plasma

Plasma is a collection of charged particles composed of free electrons, ions, and neutral particles. When electromagnetic waves enter the plasma, the electric and magnetic fields of the waves act on the free electrons in the plasma, causing them to accelerate. This acceleration is not only the basis for the propagation of electromagnetic waves in plasma but also a direct manifestation of the plasma’s response to electromagnetic waves. Additionally, within the plasma, the free electrons, influenced by the electromagnetic waves, generate new electromagnetic waves as their acceleration changes. This occurs because the accelerated motion of any charged particle can produce electromagnetic radiation. Thus, the free electrons in the plasma not only respond to the incoming electromagnetic waves but also generate electromagnetic waves through their motion, creating an interactive process.

Plasma can be considered a special type of dielectric that can conduct current and respond to electromagnetic waves. Under the influence of electromagnetic waves, the current formed by the motion of electrons in the plasma interacts with the incoming electromagnetic waves, affecting their propagation characteristics, such as speed, direction, reflection, refraction, and absorption. The interaction between plasma and electromagnetic waves adheres to Maxwell’s equations:

$$\left\{\begin{array}{c}\nabla \times \stackrel{⃑}{E}=-j{\mu }_0\omega \stackrel{⃑}{H}\\ \nabla \times \stackrel{⃑}{H}=j{\mathsf{\epsilon }}_0{\mathsf{\epsilon }}_r\omega \stackrel{⃑}{E}\\ \nabla ·{\mathsf{\epsilon }}_0{\mathsf{\epsilon }}_r\stackrel{⃑}{E}=0\\ \nabla ·\stackrel{⃑}{H}=0\end{array}\right.$$

(4)

where $\stackrel{⃑}{E}$ represents the electric field strength, μ₀ represents the vacuum permeability, $\stackrel{⃑}{H}$ represents the magnetic field strength, ε₀ represents the vacuum permittivity, and ε_r represents the relative permittivity of the plasma; the following equations apply:

$${\epsilon }_r=1-\frac{{\omega }_p^2}{\omega \left(\omega -jv\right)}=1-\frac{{\omega }_p^2}{{\omega }^2+v^2}-j\frac{v}{\omega }\frac{{\omega }_p^2}{{\omega }^2+v^2}$$

(5)

where v represents the collision frequency of the plasma, and ${\omega }_p$ represents the plasma frequency. For electromagnetic waves, the following applies:

$$\stackrel{⃑}{E}=\stackrel{⃑}{E_0}{e}^{j(\omega t-\stackrel{⃑}{k}·\stackrel{⃑}{r})}$$

(6)

where $\stackrel{⃑}{k}$ represents the propagation vector of the electromagnetic wave; the Maxwell’s equations are given by:

$$\left\{\begin{array}{c}\stackrel{⃑}{k}\times \stackrel{⃑}{E}={\mu }_0\omega \stackrel{⃑}{H}\\ \stackrel{⃑}{k}\times \stackrel{⃑}{H}=-{\mathsf{\epsilon }}_0{\mathsf{\epsilon }}_r\omega \stackrel{⃑}{E}\\ \stackrel{⃑}{k}·{\mathsf{\epsilon }}_0{\mathsf{\epsilon }}_r\stackrel{⃑}{E}=0\\ \stackrel{⃑}{k}·\stackrel{⃑}{H}=0\end{array}\right.$$

(7)

From this, it can be derived that:

$$(\stackrel{⃑}{k}·\stackrel{⃑}{E})\stackrel{⃑}{k}-({\stackrel{⃑}{k})}^2\stackrel{⃑}{E}=-{\epsilon }_r{\left(\frac{\omega }{c}\right)}^2\stackrel{⃑}{E}$$

(8)

For the attenuation constant α and the phase constant β of electromagnetic waves in plasma, the following equations apply:

$$\stackrel{⃑}{k}=(-j\alpha +\beta )\stackrel{⃑}{l}$$

(9)

where $\stackrel{⃑}{l}$ is the unit vector in the direction of electromagnetic wave propagation. Thus, the electromagnetic wave can be described as:

$$\stackrel{⃑}{E}=\stackrel{⃑}{E_0}{e}^{(j\omega t-\alpha \stackrel{⃑}{l}·\stackrel{⃑}{r}-j\beta \stackrel{⃑}{l}·\stackrel{⃑}{r})}$$

(10)

Furthermore, since

$$\stackrel{⃑}{k}·{\mathsf{\epsilon }}_0{\mathsf{\epsilon }}_r\stackrel{⃑}{E}=0$$

(11)

It can be derived that:

$${\left(-j\alpha +\beta \right)}^2\stackrel{⃑}{E}={\left(\frac{\omega }{c}\right)}^2(1-\frac{{\omega }_p^2}{{\omega }^2+v^2}-j(j\frac{v}{\omega }\frac{{\omega }_p^2}{{\omega }^2+v^2}))\stackrel{⃑}{E}$$

(12)

$$\left\{\begin{array}{c}\alpha =\left(\frac{\omega }{c}\right)\sqrt{-\frac{1}{2} \left(1-\frac{{\omega }_p^2}{{\omega }^2+v^2}\right)+\frac{1}{2}\sqrt{{\left(1-\frac{{\omega }_p^2}{{\omega }^2+v^2}\right)}^2+(-j\frac{v}{\omega }\frac{{\omega }_p^2}{{\omega }^2+v^2})}}\\ \beta =\left(\frac{\omega }{c}\right)\sqrt{\frac{1}{2} \left(1-\frac{{\omega }_p^2}{{\omega }^2+v^2}\right)+\frac{1}{2}\sqrt{{\left(1-\frac{{\omega }_p^2}{{\omega }^2+v^2}\right)}^2+(-j\frac{v}{\omega }\frac{{\omega }_p^2}{{\omega }^2+v^2})}}\end{array}\right.$$

(13)

In the equation, α serves as the attenuation constant and can be used to represent the collision absorption effect of plasma on electromagnetic waves. When electromagnetic waves, such as radar signals, propagate into the plasma, the charged particles within the plasma (primarily free electrons and ions) are accelerated under the influence of the electromagnetic field, thereby gaining the energy transmitted by the electromagnetic waves and undergoing changes in motion and position. During this process, the particles will return a portion of the energy to the external environment in the form of electromagnetic waves. Another portion of the electromagnetic wave energy is absorbed and converted into heat during interactions with the plasma, such as scattering. This energy conversion process leads to a reduction in the propagation intensity of the electromagnetic waves within the plasma, resulting in the energy loss of the electromagnetic waves.

As a portion of the electromagnetic wave energy is converted into heat within the plasma, the electromagnetic waves attenuate as they traverse the plasma, with their intensity decreasing as the propagation distance increases. This process has significant applications in fields such as radar stealth and electromagnetic interference suppression.

3.7. Numerical Relationship of Plasma’s Influence on Electromagnetic Waves

In the interaction between plasma and electromagnetic waves, the WKB method can be used for numerical simulation. The WKB method is an important tool for solving problems in mathematical physics, suitable for obtaining approximate solutions of linear differential equations with spatially varying coefficients.

During the propagation and interaction of electromagnetic waves in plasma, the characteristics of the plasma significantly affect the electromagnetic waves, including refraction, absorption, and other effects, such as Faraday rotation caused by magnetized plasma. From the perspective of wave absorption, in plasma, due to the constant movement and collisions of its particles (such as electrons and ions), the propagation of electromagnetic waves undergoes two main stages: firstly, upon encountering the plasma, refraction occurs, altering their path; secondly, the electromagnetic waves are absorbed by the plasma, resulting in a gradual decrease in energy.

The absorption of electromagnetic waves by plasma is mainly achieved through two basic mechanisms: anomalous absorption and normal absorption. Anomalous absorption occurs during the interaction between electromagnetic waves and plasma, causing collective oscillations of electrons and ions in the plasma, thereby reducing the energy of the electromagnetic waves. Normal absorption occurs when electrons absorb energy under the influence of the electromagnetic field, converting the energy of the electromagnetic waves into their kinetic energy, and transferring it through collisions with neutral particles or ions. Normal absorption is the primary pathway for the attenuation of electromagnetic wave energy and is a key point in the study of plasma stealth technology.

For non-magnetized plasma, the dielectric constant is given by:

$${\epsilon }_p={{\epsilon }_0{\epsilon }_r=\epsilon }_0(1-\frac{{\omega }_p^2}{{\omega }^2+v^2}-j\frac{v}{\omega }\frac{{\omega }_p^2}{{\omega }^2+v^2})$$

(14)

Further, according to the wave propagation equation of electromagnetic waves:

$${\mathcal{\nabla }}^2\stackrel{⃑}{E_r}+k_r^2\stackrel{⃑}{E_r}=0$$

(15)

For the propagation of electromagnetic waves in an isotropic plasma, the WKB method can be used to obtain the solution as follows:

$$\stackrel{⃑}{E_z}=e^{-j{\int }_0^{z}k(z^{\prime })d{z}^{\prime }}\stackrel{⃑}{E_0}$$

(16)

If the electromagnetic wave is incident from z = 0 and reflects at z₀ (where the energy is P₀) and is absorbed again, the energy of the electromagnetic wave when it exits the plasma is:

$$P\left(z_0\right)={e^{-4Im\left({\int }_0^{z}k\left(z\right)dz\right)}P}_0$$

(17)

Thus, the expression for the two-way energy attenuation of electromagnetic waves propagating in plasma can be derived as:

$$Att=\left|10lg\frac{P_{z_0}}{P_0}\right|=\left|17.37Im({\int }_0^{z}k\left(z\right)dz)\right|$$

(18)

3.8. Tubular and Annular Plasma Elements’ Intrinsic Radar Countermeasure Capability

In the radar cross-section (RCS) testing experiments, to evaluate the potential of ultra-high-density cold plasma elements as transient antennas, it is necessary to measure their intrinsic wave-absorbing performance and the effect of plasma density on the RCS value. Therefore, the RCS results for two types of plasma elements were tested: a single tubular plasma element and an annular plasma element, as shown in Figure 8a,b.

In testing the radar cross-section (RCS) performance of high-density cold plasma elements, horizontally polarized (HH) transmit–receive antennas were used. The tests covered three different bands—S, C, X—to ensure a comprehensive evaluation of the stealth performance of the plasma elements across key frequencies. For each band, the wave-absorbing capability of both tubular and annular high-density plasma elements was measured under seven plasma density states: inactive (0 cm⁻³), 5.46 × 10¹¹ cm⁻³, 9.11 × 10¹¹ cm⁻³, 11.24 × 10¹¹ cm⁻³, 11.68 × 10¹¹ cm⁻³, 12.11 × 10¹¹ cm⁻³, and 12.54 × 10¹¹ cm⁻³. The results are shown in Figure 9.

Through specific measurements and analysis, it can be observed that the tubular plasma elements exhibit significant interference and absorption effects on electromagnetic waves in the S and C bands. This finding is particularly important for the application of plasma in radar stealth technology and the subsequent use of plasma elements in radar countermeasure antennas. Specifically, when handling horizontally polarized (HH) electromagnetic signals, the elements themselves achieve a minimum RCS of −63 dBsm, indicating excellent radar countermeasure performance. As the plasma density increases, the RCS values show an overall downward trend, demonstrating that the activation of plasma and the increase in its density effectively reduce the reflection intensity of electromagnetic signals in this polarization direction. In the S band, the RCS can be reduced by up to 15.12 dBsm. At higher frequencies in the X band, the impact of plasma density changes on electromagnetic waves is relatively smaller due to the shorter wavelength of X-band electromagnetic waves.

For annular plasma elements, an increase in plasma density in the S band results in a significant reduction in the RCS value of the elements. The results in the C band are even more pronounced; the RCS value in the inactive state is relatively low, and with an increase in plasma density, the RCS value decreases significantly. Particularly in the range of 5.46 × 10¹¹ cm⁻³ to 11.24 × 10¹¹ cm⁻³, the radar countermeasure capability of the elements improves markedly, reducing the RCS by approximately 10 dBsm overall. This indicates that annular plasma elements have better stealth potential in the C band, making them suitable for specialized plasma stealth antenna applications. In the X band, the wave-absorbing capability of the plasma elements is weaker compared to the S and C bands, but there is still an improvement in absorption performance with an increase in plasma density. This suggests that these elements have significant wave-absorbing capabilities and potential as plasma antennas.

The results show that both tubular and annular plasma elements possess excellent radar countermeasure performance. For HH-polarized radar signals in the S and C bands, the RCS value decreases further with an increase in plasma density. This indicates that these two types of high-density plasma elements have excellent potential as radar countermeasure antennas.

3.9. Effect of Density on the Absorption Capacity of Plasma Elements for Electromagnetic Waves

The absorption capability of plasma elements for different wavelength bands was investigated at different densities. To measure the specific shielding effect of the plasma, an array of tubular plasma elements was arranged, with a sheet of aluminum foil placed closely behind them to simulate the metallic equipment intended for stealth. This setup allowed for a more accurate assessment of the wave-absorbing stealth technology of large-area, ultra-high-density cold plasma. The plasma elements were placed in an electromagnetic test microwave darkroom and their RCS performance was tested in the S and C bands with both HH and VV antenna polarities. The RCS test results are presented in Figure 10.

From the measurement results, the large-area ultra-high-density cold plasma generated by the plasma tube array exhibited significant absorption effects on electromagnetic waves in the S and C bands. For instance, for a 3.1 GHz radar signal, the RCS was reduced from 25.18 m² to 8.41 m². In the X band, the plasma tube array also showed wave-absorbing capability, although the absorption effect was not as pronounced as in the lower frequency bands. When comparing the absorption efficiency for electromagnetic wave signals of different polarization directions, the data indicated that the plasma tube array’s absorption capacity was superior in the horizontally polarized (HH) direction compared to the vertically polarized (VV) direction. Furthermore, as the plasma density increases, the wave absorption capacity also increases. This suggests that the W-electrode plasma element designed in this paper will exhibit better performance and higher quality in terms of electromagnetic absorption due to its high-density advantage.

4. Conclusions

This study presents the development of tungsten electrodes with high-curvature-radius spiked structures, replacing traditional iron–nickel alloy electrodes in plasma elements. The new electrodes achieved an ultra-high-density, low-pressure cold plasma with a density of 1.15 × 10¹² cm⁻³, surpassing similar studies by an order of magnitude. Lightweight and cost-effective tubular and annular cold plasma elements were also developed, showing an 88.2% increase in plasma density under the same conditions. These elements have the potential to serve as plasma countermeasure antennas and can form large-area, high-density plasma by combining multiple element arrays, demonstrating excellent performance in electromagnetic wave absorption.

The tungsten electrodes, treated hydrothermally to form spiked structures, enhanced field emission characteristics and reliability compared to conventional iron–nickel alloy electrodes. At 100 mA, the tungsten electrodes achieved a plasma density of 7.79 × 10¹¹ cm⁻³ (88.2% improvement), and at 150 mA, a density of 9.47 × 10¹¹ cm⁻³ (15.3% improvement). Even at 200 mA, the tungsten electrodes maintained a high plasma density of 1.15 × 10¹² cm⁻³, while the iron–nickel electrodes showed damage and a drop in plasma density.

The study also investigated the impact of plasma on radar electromagnetic waves. The experimental results showed that both tubular and annular plasma elements exhibit excellent radar countermeasure performance. For HH-polarized radar signals in the S and C bands, the RCS value decreased with increasing plasma density, indicating that these high-density plasma elements have excellent potential as radar countermeasure antennas. The experimental data of the RCS values of high-density cold plasma element arrays and their underlying metal films demonstrated that large-area, ultra-high-density cold plasma is highly effective in reducing radar detection capability in the S and C bands. For instance, for a 3.1 GHz radar signal, the RCS value was reduced from 25.18 m² to 8.41 m². Attenuation was also observed in the X band, proving the superior characteristics of plasma technology in electronic countermeasures.

This research lays a foundation for further defense applications, showcasing the superior characteristics of high-density cold plasma technology in electronic warfare.