On radar cross section reduction effect by filamentary discharge in a dielectric barrier discharge

The Radar Cross Section Reduction (RCSR) is a significant technology area in modern warfare as it directly impacts the survivability of an aircraft. Radar Cross Section (RCS) signifies the size of the target correlated with the observability of the object by radar.^1–3 RCS is determined based on external features, such as frequency, and electromagnetic features, such as the rate of flection of the electromagnetic wave of the target,⁴ which essentially measures the power scattered in a specific direction when the incident wave illuminates the target.

Several technologies have been developed for RCSR. The simplest methods involve Radar Absorbing Material (RAM)⁵ and Radar Absorbing Structure (RAS).⁶ Initially, research focused on using materials less reflective than metals and altering the shapes of RCSR-vulnerable areas, such as wings. These approaches yielded significant RCSR. However, these methods raised concerns about increasing the weight of the aircraft or altering its shape, potentially affecting its performance.

Recent advancements have led to the development of various technologies for RCSR, including artificial magnetic conductors (AMCs),⁷ frequency selective surfaces (FSSs), metamaterial structures, and the plasma based technology. AMC structures scatter incident energy in specific directions, significantly reducing reflection. FSS involves the repetitive arrangement of arbitrary-shaped metallic structures on dielectric substrates or apertures on metallic plates. FSS essentially acts as a filter that either transmits or reflects electromagnetic waves in the chosen frequency band. Such structures facilitate RCSR at the designed frequency band.^8,9 FSS demonstrates attenuation effects for various angles of incidence.¹⁰ Metamaterials utilize a substrate design to create a phase difference in reflected waves, leading to cancellation.^11–13 

Recently, plasma technology has been actively developed. There has been various research conducted on etching in semiconductor fabrication,^14,15 and plasma stealth technology.^3,16,17 Plasma refers to ionized gas with plasma and possesses high potential for stealth applications concerning electromagnetic waves. If a plasma cloud is formed around an aircraft, it scatters and absorbs EM waves without reflection. Absorption occurs when energy from EM waves is transferred to the charged particles of plasma and again to the neutral atoms via elastic/inelastic collisions.¹⁸ Scattering occurs due to changes in refractive index when EM waves travel through plasma.¹⁹ Plasma is lightweight and capable of reducing EM waves across a broad frequency range while being selectively turned on and off. However, it also has several drawbacks. First, generating plasma requires high power, increasing the overall weight of the aircraft due to power sources. Second, it forms a visible plasma trail, contradicting the very purpose of RCSR.²⁰ 

To address these issues, Dielectric Barrier Discharge (DBD) plasma sources in the form of simple unit cells have been developed.^{3,16,17,21,22,23} These sources offer the advantage of discharge at relatively low voltages under relatively high pressures due to the dielectric layer, making them widely used in various fields, such as life sciences and plasma medicine.²⁴ For RCSR, research involving electrode patterns resembling FSS for simultaneous use with plasma has been extensively conducted. Despite these efforts, drawbacks persist in using plasma for RCSR, as it needs extremely high plasma density^3,22,23,25 in a conventional source level. It is primarily related to the high-power requirement and thermal damage risk.^26–28 

DBD plasmas exhibit both filament and diffusion modes, and these modes tend to change based on factors such as flow rate or other conditions.²⁹ Previous studies have mostly explored the diffusion mode, leaving discussions on the reduction effects of RCS unaddressed in the case of filament modes. In the filament mode, current density concentrates in a small volume of filament, resulting in a lower average density across the entire substrate, mitigating the risk of thermal damage and achieving sufficient RCSR effects.

In this paper, we evaluated the RCSR characteristics during filamentary discharge in a DBD source. Initially, we have confirmed the filamentary discharges in the DBD source, which has already been confirmed to have enough RCSR effect.^3,22,23 Simulations were conducted assuming filaments with small volume and high density. In accordance with the experimental data, a distinct RCSR effect is confirmed. The RCSR characteristics are changed by the physical properties of the filaments, with a maximum up to 15 dB, which corresponds to the experimental results.

Figure 1 shows the design of the DBD source for RCSR. The source is already confirmed to have a distinct RCSR effect in previous studies.^3,22 The DBD source consists of a powered electrode, a dielectric barrier, and a ground electrode with side rim parts. The powered electrode is a cross-dipole type FSS with an X-band of 10 GHz. Under the powered electrode, a dielectric barrier made of RO4350B with a thickness of 0.254 mm and a dielectric constant of 3.66 is used. Both the electrodes and dielectric are covered by the side rim made of FR-4 dielectric with a thickness of 4.572 mm.

Figure 2(a) shows the experimental settings for the filament measurement. The DBD source is placed in the desiccator under 0.3 atm air conditions assuming real operation of a jet plane. 10 kV, 1 kHz sine wave power is applied to make a discharge. The filaments in the source are observed using a high-speed camera (Fastcam SA-Z, Photron).

Figure 2(b) shows a diagram measuring the voltage and current of a DBD source with RCS reduction capability. For high voltage probes, P6015A (Tektronix, Beaverton, OR, USA) was used, and for current probes, 6595 (Pearson, Palo Alto, CA, USA) was used. The voltage was measured between the power line of the DBD source and the ground line to check the voltage applied to the source. In other words, we can see that the voltage in question is the voltage applied to the source. In the case of current, the current was checked on the power line.

We utilize CST Microwave Studio Suite, a commercial 3-dimensional electromagnetic (EM) wave simulation commonly used for various applications such as design of antennas and a waveguides in radio-frequency or microwave,^30,31 and measurement of RCS.³² A DBD source and the filamentary plasma discharge based on the real source are modeled, and RCS is calculated. The filament setting for the DBD source used in the simulation is depicted as shown in Fig. 3. The DBD source comprises fundamental elements, such as the FSS substrate, dielectric material, dielectric barrier, and ground plane. Previous studies have established the use of the FSS substrate as an electrode for plasma discharge.^3,22 The thicknesses of the FSS electrode and target electrode were not considered in the simulations. We have adopted the shape of filaments, which is measured in experiments using a high speed camera. However, in the simulation, the filaments were reproduced as uniform square columns, whereas the real filaments are expected to be cylindrical columns in shape. In our model, the horizontal and vertical lengths of the filaments are 1 mm, while the height is 4.572 mm, aiming to replicate the filaments generated in the actual constructed DBD source. The FSS electrode consists of a repeated pattern of a specific shape, which in this paper is in the form of a cross. The position of the filaments is consistent across each cell. The filaments are connected to the target plate, and there is a dielectric layer connecting from the back of the FSS electrode. The simulation involved directing a linear plane wave toward the front of the DBD plasma generator to measure Radar Cross Section Reduction (RCSR) within the 6–13 GHz range.

Figure 4 shows the V–I graph of the DBD source. Basically, the voltage and current behaviors show that of a common DBD source. The irregular current peaks indirectly show the filamentary discharge, which mainly takes place in the positive/negative rising time of the voltage signals.³ We have confirmed the filamentary discharge by observing the discharge using a high speed camera.

The area where high current peaks occur closely corresponds to the region where a large number of filaments are generated. This indicates that high-density filament currents flow, resulting in high current peaks.

The voltage graph shows a sinusoidal shape at 8.0 kV, which becomes sharper as the voltage increases. This sharp trend is consistent with findings from previous studies.³ 

In the current graph, it was observed that the region where high current peaks occur varies depending on the voltage magnitude. This indicates a decrease in the time taken for filament discharge as the voltage increases.

Figure 5 shows the image of the filamentary discharge in the DBD source measured by the camera. Under our condition, the discharge entirely consists of several column shaped filaments. Once a filament is formed, it moves slowly and dissipates. The estimated size (thickness) of the filament is about 1 mm, and the estimated distribution is about 20 filaments per cell. In the time domain, the generation of filaments is coincident with current signals, which again proves the filamentary discharge in the DBD source.

Using the basic characteristics of the filament in Fig. 5, we have performed the computational simulation.

As the plasma density increases, the RCSR effect becomes stronger. At the plasma frequency of 978 GHz, the corresponding plasma density is 3.06 × 10¹⁴/cm³, which is similar to that of filamentary discharge in a common DBD source regarding the pressure. Under this condition, the filamentary discharge shows the RCSR effect over 15 dB at maximum, and it corresponds to the experimental results.²² Without plasma, no RCSR effects are observed. Moreover, RCS minimum frequency slightly increases with the plasma frequency. These behaviors consistently show that plasma mainly contributes to RCSR.

To verify the detailed effect of filamentary discharge, RCSR in different characteristics of filaments is analyzed. Figure 7(a) shows RCSR according to the number of filaments. As the number of filaments increases, RCSR increases. The degree to which the number of filaments affects RCSR becomes stronger when the number of filaments is large. In particular, when the number of filaments increases from 16 to 25, the RCSR effect increases significantly. In situations where the number of filaments is small, the effective area appears to be too small to provide sufficient effect on RCSR. The size of the filament also affects RCSR. We have simulated RCS changing length of each side (thickness) of a filament. Figure 7(b) shows RCSR according to the thickness of the filament. Again, as the filament thickness increases, RCSR effects get stronger. Different from the filament number, the effect of filament thickness on RCSR is almost linear. In these two parametric studies, we can find that the effective area of filamentary discharge significantly affects the RCSR effects.

In Fig. 8(a), we have compared the influence of the number and the thickness of filaments on RCSR. Each color shows the value of RCS under a certain condition. Since the boundaries of each color are almost vertical, the effect of the number of filaments on RCSR is dominant compared to the thickness of the filaments regardless of the plasma frequency. It means that for the same effective area, the larger number of filaments is more advantageous to RCSR than the thicker ones as in Fig. 8(b). In the viewpoint of the wave, as the target frequency of RCSR is about 9 GHz, the size variation of a filament is almost negligible to the input wavelength, which is in the centimeter range. Therefore, the effect of filament size on RCSR is weaker than the number effect of the filaments. Based on these results, we can conclude that discharges with a greater number of filaments are preferred in RCSR plasmas.

The RCSR effect by filamentary discharge in DBD plasma is studied. At first, the filamentary discharges in a DBD source are observed. The basic characteristics of the filaments are measured. From those properties, we have studied the RCSR effect using the computational simulation. Over 15 dB of RCSR effect is observed, which corresponds to the previous experimental results in filamentary discharges with low average density. As the discharge area shrinks to the filamentary area, the current density is concentrated and the plasma density can increase to the level that makes a distinct RCSR effect. In the parametric study, the RCSR effect can be increased by higher plasma density, a higher number of filaments, and thicker filament thickness. Meanwhile, both the size and the number density of the filaments affect the RCSR effect, and the number of filaments is the critical property in RCSR. Therefore, to enhance RCSR, discharge systems with a greater number of filaments are recommended.

This study has proposed basic parametric data for the RCSR effect of filamentary discharge. Considering the timescale of the measured RCS, we have assumed that the plasma and the filaments are uniformly distributed in this work. For the detailed spatiotemporal effect of the filaments and their physical modeling of RCSR, further studies are required.

This work was supported by the Agency for Defense Development grant funded by the Korean Government (Grant No. UD220003JD).

The authors have no conflicts to disclose.

Minsu Choi (최민수): Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). Shin-Jae You (유신재): Software (equal); Supervision (equal); Validation (equal); Visualization (equal). Jinwoo Jung (정진우): Conceptualization (supporting); Data curation (equal). Changseok Cho (조창석): Conceptualization (supporting); Data curation (equal). Yongshik Lee (이용식): Software (equal); Supervision (supporting); Validation (equal). Cheonyoung Kim (김천영): Funding acquisition (equal). Jungje Ha (하정제): Funding acquisition (equal). Hyunsoo Lee (이현수): Funding acquisition (equal). Youbin Seol (설유빈): Data curation (equal); Formal analysis (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article.