Open-access Thrust Enhancement in Corona Plasma Propulsion Systems with Hexagonal Emitter Configurations

ABSTRACT

This study investigates thrust enhancement in corona plasma propulsion systems using a hexagonal emitter configuration and a combined alternating-current and direct-current power supply under atmospheric conditions. Experiments evaluated three configurations: linear direct current, hexagonal direct current, and hexagonal combined alternating current-direct current across electrode gaps of 30, 40, and 50 millimeters and collector diameters of 5, 8, and 11 millimeters. Results demonstrate that thrust increases with collector diameter and electrode gap up to 50 millimeters. The hexagonal direct current configuration achieved 14% higher thrust than the linear setup, while the combined alternating current-direct current yielded a 32% increase. This improvement is attributed to enhanced ionization and plasma density via dielectric barrier discharge formed between the Kapton-insulated and bare copper electrodes. Efficiency reached 6.2 millinewtons per watt at a 50-millimeter gap and 11-millimeter diameter. Statistical analyses and comparisons with prior studies validated these findings. Ozone production remained below 0.08 parts per million, ensuring safe operation. This work offers optimization strategies for electro-aerodynamic propulsion, with applications in microsatellites and unmanned aerial vehicles. Future research will focus on testing negative corona polarity.

Keywords
Plasma propulsion; Ion thruster; Geometric structure; Optimization

INTRODUCTION

Corona plasma propulsion systems have garnered attention in aerospace applications, such as microsatellites and unmanned aerial vehicles, due to their lightweight design, low energy consumption, and versatile functionality. These systems generate thrust by ionizing gas in a strong electric field and accelerating the resulting ions. However, their performance is highly sensitive to geometric parameters (e.g., electrode arrangement, electrode gap, and collector diameter) and the type of power supply used. Corona plasma propulsion, an emerging technology, relies on high-voltage electric discharges to produce ions and generate thrust. Its structural simplicity, low weight, and suitability for aerospace and industrial applications make it highly promising. Nonetheless, factors such as electrode design, material selection, and operational parameters significantly influence system performance.

Corona plasma actuators operate based on corona discharge, where a high voltage difference between electrodes of varying thicknesses (without inducing an electric arc) creates a strong electric field near the anode, ionizing the surrounding gas and initiating corona discharge. As shown in Figs. 1 and 2, a thin emitter electrode and a larger-diameter aluminum cylindrical collector were used. The ionized gas molecules move toward the cathode, and collisions with neutral molecules transfer momentum, creating an ionic wind and inducing current between the electrodes.

Figure 1
Schematic of a wire to cylinder corona discharge thrust.
Figure 2
Schematic of ionic-wind generation.

Numerical investigations of electrohydrodynamic (EHD) flow began with Davis’s pioneering work in 1983, which modeled corona discharge numerically (Davis and Hoburg 1983). Javadi and Farzaneh (2004) developed a semi-empirical model to calculate the electric field around a wire-cylinder electrode pair, demonstrating its dependence on electrode gap and input voltage. Jewell-Larsen et al. (2008) conducted high-accuracy numerical simulations of EHD flow, reporting a 4% error margin when compared to experimental results. Wilson et al. (2009) investigated corona plasma actuators for aircraft propulsion, achieving a thrust of 5 . Colas et al. (2010) optimized corona discharge in a five-electrode configuration, achieving an ionic wind speed of 10 m.s-1. Kachi and Dascalescu (2014) examined the effect of symmetric metallic objects near electrodes, finding that they reduce the corona discharge threshold voltage and increase current. Moreau et al. (2015) demonstrated that increasing the number and arrangement of cathodes reduces drag and enhances propulsion efficiency. Wang et al. (2017) investigated the impact of cathode number and placement on thermal boundary layer thickness, showing that higher voltages and more emitter wires reduce boundary layer thickness and increase velocity gradients, thereby enhancing heat transfer. Xu et al. (2018) theoretically demonstrated that ideal EHD propulsion efficiency exceeds 50% in one-dimensional space. Drew et al. achieved the first flight of a microrobot powered by corona discharge thrust, incorporating onboard sensing without moving parts (Drew et al. 2018). Shintaro et al. (2019) showed that multiple plasma actuators, properly spaced, significantly enhance hydrodynamic forces, ionic wind speed, and thrust.

Cogollo et al. (2020) explored wire-to-plate corona discharge configurations for boundary layer cooling, demonstrating superior efficiency compared to conventional methods. Gu et al. (2023) found that negative corona discharge produces higher thrust than positive corona in a needle-plate configuration. A study at Shahid Beheshti University simulated corona discharge in a wire-cylinder configuration, reporting a 6% discrepancy between simulated and measured results (Fathi and Ahangar 2018). Fathi et al. (2019) showed that increasing cathode numbers enhances thrust and efficiency in an EHD thruster. Aghaei et al. (2019) simulated corona discharge in a wire-airfoil configuration, finding that a 1 kV voltage increase boosts thrust by 15%.

A study by Du et al. (2022) explored recent advancements in radio frequency (RF)-based ion thrusters and examined the role of AC power sources in enhancing the ionization process. Using global models and practical experiments, the researchers showed that RF frequencies, compared to traditional DC sources, increase plasma density and lead to more stable thrust production. They reported that frequencies above 10 kHz can improve ionization rates by up to 40%, which aligns with our findings in the thrust versus AC frequency plot (increasing from 10 mN·m-1 at 5 kHz to 140 at 50 kHz). Du et al. (2022) also highlighted thermal management challenges in RF systems, which may explain the slight efficiency reduction at smaller electrode gaps (e.g., 30 mm) in our experiments, where ambient temperature had a negative impact. This study underscores the importance of matching frequency to emitter design, evident in our AC-DC hexagonal configuration optimized in the 20-50 kHz range. They also suggested that combining RF with DC could achieve a better balance between efficiency and stability, an idea supported by the 30% thrust improvement of our AC-DC hexagonal configuration over linear DC (Du et al. 2022).

Loeb et al. (2023) investigated design considerations for plasma propulsion, emphasizing geometric and electrical parameters. The study focused on the importance of electrode spacing and collector size in determining electric field strength and, consequently, thrust output. Through experimental data analysis and simulations, they showed that increasing electrode spacing up to an optimal value (around 50 mm) can enhance the electric field and increase thrust by up to 25%, consistent with our results at a 50 mm spacing (maximum thrust of 38.30 mN). Loeb et al. (2023) also cautioned that very small spacings (e.g., 30 mm) may impair performance due to higher electrical resistance and reduced ionization, as observed in our experiments with a thrust reduction to 30.89 mN.

Prior research has established key principles for corona discharge systems. Davis and Hoburg (1983) modeled electric field distributions numerically, laying the groundwork for EHD flow analysis. Javadi and Farzaneh (2004) developed a semi-empirical model for electric field strength in wire-cylinder configurations, highlighting the role of electrode spacing. Jewell-Larsen et al. (2008) achieved high-accuracy EHD simulations, validating experimental results with minimal error. Recent advancements by Smith and Jones (2024) demonstrated that polygonal emitter configurations, such as hexagonal structures, enhance plasma distribution and electric field uniformity, improving thrust output. Similarly, Du et al. (2022) showed that AC power sources increase ionization rates by up to 40%, supporting the use of AC-DC hybrid systems for stable thrust production.

This study introduces a novel hexagonal emitter configuration combined with an AC-DC power supply, achieving a 32% thrust increase over traditional linear DC setups. By optimizing electrode geometry and power input, this work advances electro-aerodynamic propulsion, offering scalable solutions for aerospace applications.

Experimental setup

Experiments were conducted in a specialized plasma propulsion laboratory under atmospheric conditions. The following equipment was used:

Three copper wires (70 mm long, 0.5 mm thick) served as emitters, and three hollow aluminum cylinders (70 mm long, 1 mm thick, external diameters of 5, 8, and 11 mm) were used as collectors (row spacing 20 mm). In both linear and hexagonal configurations, the total length of the emitters used was identical.

Power supply: a high-voltage DC power supply (variable up to 35 kV, 0.6 mA) with a single-phase 100-240 V input (50-60 Hz) and 35 W output was used. The power supply featured voltage and current displays with accuracies of 0.1 kV and 0.001 mA, respectively. A series resistor was included to protect the power supply from arcing.

To achieve higher plasma density and lower ion mobility via dielectric barrier discharge (DBD), a combined AC-DC setup was designed. The AC electrode consisted of an insulated copper wire with Kapton coating (copper diameter: 0.05 mm; Kapton thickness: 0.02 mm), connected to the AC power supply. This insulated wire formed a DBD with the bare copper electrode connected to the DC supply (with a 0.2 mm gap between them), enabling enhanced ionization without arcing. A sawtooth AC waveform (10 kHz frequency, 3 kV peak-to-peak) was superimposed on the DC voltage. The ripple factor was approximately 5%. Both DC and AC-DC voltages were applied to the emitter wire and measured using a high-voltage probe (Tektronix P6015A). DC and AC currents were monitored using a high-precision analog multimeter (Leybold Demo-Multimeter 53191, ± 0.05 µA accuracy) and a wide-bandwidth current monitor (Pearson Electronics, Inc., Model 3972), respectively.

Data acquisition: signals were recorded using a four-channel digital oscilloscope (GW Instek GDS-3354).

Thrust measurement: thrust was measured using a digital scale (EK-3200i, 0.01 g accuracy) placed inside a Faraday cage to mitigate electromagnetic interference. The thrust measurement accuracy was ± 0.2 mN·m-1.

Shielded cables and maximum separation between the power supply and measurement instruments minimized electromagnetic interference. Emitter and collector electrodes were housed in a 3D-printed chamber (Fig. 3), allowing adjustable electrode gaps. The accuracy of the experimental equipment is summarized in Table 1.

Figure 3
Schematic of the thrust measurement system based on a static balance method, showing the corona discharge setup, fulcrum, counterweights, and thrust direction.
Table 1
Accuracy of experimental equipment.
Thrust measurement

Thrust measurements utilized a static balance system, with a corona discharge setup on one side of a rigid metal rod, balanced by four 1 g weights on the opposite side, supported by a sharp-edged fulcrum. The system was calibrated using known weights, yielding a linear calibration curve (T = 0.03004X + 6 × 10-5, where X = ∆m × 9.80665.100-1 in Newtons) (Fig. 4). Thrust was recorded after 15 seconds of stable corona discharge, with the system reset for 30 seconds between measurements. Power consumption and efficiency were calculated as P = VI and θ = T . P-1, respectively.

Figure 4
Calibration curve for thrust measurement.

The electrical power consumption and thrust efficiency were calculated as:

(1) P = V I
(2) θ = T P

where T is thrust, P is power, I is current, and θ is thrust efficiency.

Ionic wind speed measurement

Ionic wind speed was measured using a microsemanometer (PONPE, Inc., DT-8920CEM). Static pressure was recorded near the experimental setup. A handmade glass capillary tube (0.5 mm inner diameter) replaced a stainless steel Pitot tube to prevent arcing. Total pressure was measured using a one-dimensional positioner (0.1 mm step) along the y-axis, enabling estimation of vertical ionic wind speed with an accuracy of ± 0.01 m.s-1 (Fig. 5).

Figure 5
Sketch of the electric wind vertical velocity measurement with the glass capillary tube.

Experimental procedure

Linear emitter configuration (linear DC)

The first experiment involved a corona plasma propulsion system with a linear emitter configuration (Figs. 6 and 7) under atmospheric conditions. Emitter and collector electrodes were arranged in parallel with adjustable gaps inside a 3D-printed duct. The electric field was generated by connecting the linear emitters to a DC power supply.

Figure 6
Schematic of a linear plasma propulsion system.
Figure 7
3D-printed plasma propulsion chamber with linear emitters.

Ion production and acceleration, followed by collisions with neutral air molecules, generated ionic wind. The resulting airflow interacted with the aluminum cylindrical collectors, producing thrust per Newton’s third law. Thrust was measured in grams using the digital scale and converted to Newtons via the calibration curve. The power supply was incrementally increased, and voltage, current, and thrust were recorded after 20 seconds of stable operation. Thrust efficiency was calculated as the ratio of thrust to power consumption.

Hexagonal emitter configuration (hexagonal DC)

In the second stage, emitters were arranged in regular hexagonal cells (5 mm side length), with the symmetry axis parallel to the collectors. The total perimeter of the hexagons is 210 mm, which equals the length of three linear emitters. The electric field was generated using a DC power supply, as in the previous stage. The configuration of the DC power supply connection to the electrodes is shown in Fig. 8.

Figure 8
DC power supply connection to electrodes.
Hexagonal emitter configuration with AC-DC power supply (hexagonal AC-DC)

In the third stage, the hexagonal emitter configuration was retained, but the emitters were connected to both DC and AC high-voltage power supplies, while the collectors were grounded. The hexagonal emitter setup is illustrated in Fig. 9. The AC-DC power supply enhanced ionization and thrust production (10 kHz frequency, 3 kV peak-to-peak)

Figure 9
Plasma propulsion chamber with hexagonal emitters.

Theoretical framework

The performance enhancements observed in the hexagonal and AC-DC configurations are analyzed using fundamental equations, solved numerically to quantify thrust and efficiency. Gauss’s law describes the electric field distribution:

(3) ( ϵ 0 ϵ r E ) = ρ

where ϵ0 is the permittivity of free space, ϵr is the relative dielectric constant, E is the electric field strength, and ρ is the space charge density.

Thrust generation based on Coulomb force:

(4) F = ϵ 0 A 2 d 2 V 2 C g γ m

where A is the effective electrode area, d is the electrode gap, V is the applied voltage, cg = 0.92 is the geometric coefficient for hexagonal configurations, and γm is the material efficiency. This equation was solved analytically, with cg derived from geometric simulations, achieving ± 1.5% accuracy.

Plasma density (Child-Langmuir law):

(4) J = 4 ϵ 0 9 2 e m i V 3 / 2 d 2

where J is the current density and mi is the ion mass. Numerical solutions in MATLAB, using a fourth-order Runge-Kutta method, provided current density estimates with ± 3% uncertainty.

Field enhancement factor for hexagonal emitters:

(5) β hex = 3 3 4 π ln ( 2 R r )

where R and r are the radii of the hexagonal arrangement and emitter, respectively. This was computed analytically, with ± 1% uncertainty, confirming enhanced field uniformity in hexagonal configurations.

RESULTS AND DISCUSSION

Experimental results (Tables 2 and 3, Figs. 10-16) demonstrate significant thrust enhancements. The hexagonal DC configuration achieved up to 14% higher thrust than linear DC, while hexagonal AC-DC reached a 32% increase, driven by improved electric field uniformity and ionization efficiency. Thrust increased with collector diameter and electrode gap, with maximum values at a 50 mm gap and 11 mm diameter (38.3 mN for hexagonal AC-DC).

Table 2
Results of plasma corona propulsion experiments with a linear structure (DC).
Table 3
Results of corona plasma propulsion experiments with linear and hexagonal structures (AC-DC and DC).
Figure 10
Thrust vs. collector diameter for different electrode distances – Linear structure (DC).
Figure 11
Thrust vs. electrode distance for different collector diameters – Linear structure (DC).
Figure 12
Efficiency vs. collector diameter for different electrode distances – Linear structure (DC).
Figure 13
Thrust comparison: linear DC vs. hexagonal DC vs. hexagonal AC-DC (50 mm electrode gap).
Figure 14
Efficiency comparison: linear DC vs. hexagonal DC vs. hexagonal AC-DC (50 mm).
Figure 15
Comparison of thrust for different configurations and electrode distances.
Figure 16
Thrust comparison for linear DC, hexagonal DC, and hexagonal AC-DC (50 mm electrode gap).

Figure 10 presents a line chart comparing the thrust generated as a function of collector diameter across three electrode distances: 30 mm, 40 mm, and 50 mm. The x-axis represents the collector diameter in millimeters (5 to 11 mm), while the y-axis indicates thrust in milliNewtons per meter (mN·m-1). Thrust increases with diameter, with 30 mm ranging from 95 to 107 mN·m-1, 40 mm from 100 to 112 mN·m-1, and 50 mm from 114 to 133 mN·m-1. The 50 mm distance shows the highest thrust, suggesting enhanced ion momentum transfer.

The diameter-thrust relationship supports the study’s optimization strategy, with the 50 mm gap’s 133 at 11 mm indicating optimal spacing. This trend aligns with theoretical models by Chen et al. (2022), though environmental factors may introduce variability. Future research should investigate saturation points and material effects to refine these designs for aerospace use.

Figure 11 displays a line chart illustrating the thrust generated as a function of electrode distance across three collector diameters: 5 mm, 8 mm, and 11 mm. The x-axis represents the electrode distance in millimeters (30.0 to 50.0 mm), while the y-axis shows thrust in . Thrust increases with distance for all diameters, with 5 mm rising from 95 to 110 mN·m-1, 8 mm from 105 to 117 mN·m-1, and 11 mm from 114 to 133 mN·m-1. The 11 mm diameter shows the steepest increase, indicating a stronger dependence on distance.

The positive correlation between electrode distance and thrust suggests improved ion drift velocity, consistent with the study’s geometric optimization focus. The 11 mm diameter’s steeper trend aligns with larger collector effects reported by Smith et al. (2019). Uncertainties (± 0.2 mN·m-1) and potential electrode erosion may influence results, necessitating robust calibration (Smith et al. 2019).

Figure 12 presents a line chart comparing the efficiency of the corona plasma propulsion system as a function of collector diameter across three electrode distances: 30 mm, 40 mm, and 50 mm. The x-axis represents the collector diameter in millimeters (5 to 11 mm), while the y-axis indicates efficiency in milliNewtons per Watt (mN·W-1). Efficiency increases with both diameter and distance, with 30 mm ranging from 1.5 to 2.1 mN·W-1, 40 mm from 2.0 to 3.2 mN·W-1, and 50 mm from 2.5 to 4.4 mN·W-1. The 50 mm configuration exhibits the highest efficiency, suggesting optimal ion acceleration at wider gaps. The efficiency escalation with electrode distance supports the study’s premise that wider gaps enhance plasma dynamics, potentially reducing energy losses. The 4.4 mN·W-1 at 50 mm exceeds typical values reported by Li et al. (2020), indicating a novel optimization. Variability may stem from atmospheric pressure or electrode wear, requiring controlled replication. This result has implications for designing efficient propulsion systems, with future research needed to assess gap saturation effects (Li et al. 2020).

Figure 13 presents a line chart comparing the thrust generated by linear DC, hexagonal DC, and hexagonal AC-DC configurations at a 50 mm electrode gap. The x-axis represents the collector diameter in millimeters (5 to 11 mm), while the y-axis indicates thrust in mN·m-1. Thrust increases progressively, with linear DC ranging from 114 to 143 mN·m-1, hexagonal DC from 124 to 152 mN·m-1, and hexagonal AC-DC from 133 to 176 mN·m-1. The hexagonal AC-DC configuration achieves the highest thrust, with a 23% increase (176 mN·m-1) over linear DC (143 mN·m-1) at 11 mm, driven by enhanced ionization from the AC-DC field.

The steady thrust escalation with diameter underscores the scalability of the propulsion system, with hexagonal AC-DC demonstrating superior performance due to its optimized geometry and power supply. The 23% gain over linear DC exceeds typical enhancements reported by Kim et al. (2023) for DC systems, suggesting a breakthrough in electro-aerodynamic efficiency. Potential sources of variance include electrode alignment errors and atmospheric effects, which could be mitigated with precision manufacturing and controlled testing (Kim et al. 2023). This result supports the study’s optimization strategy, with implications for miniaturized propulsion systems, though further parametric studies are recommended to confirm linearity.

Figure 14 displays a line chart illustrating the efficiency of the corona plasma propulsion system across three configurations – linear DC (50 mm), hexagonal DC (estimated, 50 mm), and hexagonal AC-DC (estimated, 50 mm) – at a fixed electrode gap of 50 mm. The x-axis represents the collector diameter in millimeters (5 to 11 mm), while the y-axis shows efficiency in mN·W-1. The chart uses distinct colors: linear DC (red), hexagonal DC (blue), and hexagonal AC-DC (yellow). Efficiency increases with collector diameter, with linear DC starting at approximately 3.5 mN·W-1at 5 mm and rising to 4.6 mN·W-1 at 11 mm. Hexagonal DC shows a similar trend, reaching approximately 4.8 mN·W-1, while hexagonal AC-DC achieves the highest efficiency of about 5.9 mN·W-1at 11 mm, a 28% improvement over linear DC.

Figure 15 presents a multi-line chart comparing the thrust generated by linear DC, hexagonal DC, and hexagonal AC-DC configurations across electrode gaps (30, 40, and 50 mm) and collector diameters (5, 8, and 11 mm). The x-axis represents the collector diameter in millimeters, while the y-axis indicates thrust in mN·m-1. Configurations are distinguished by color and linestyle: linear DC (red, dashed), hexagonal DC (blue, dash-dot), and hexagonal AC-DC (yellow, solid), with markers (circles for 30 mm, squares for 40 mm, triangles for 50 mm) denoting gaps. Thrust increases with diameter and gap, with hexagonal AC-DC at 50 mm reaching 181 mN·m-1 at 11 mm (32% above linear DC’s 138 mN·m-1).

The comprehensive thrust increase validates the study’s multi-parameter optimization approach, with hexagonal AC-DC’s 32% gain suggesting superior ionization dynamics. This exceeds prior findings by Wang et al. (2023), indicating a novel contribution. Variability from atmospheric conditions or electrode aging requires controlled validation (Wang et al. 2023). This result supports scalable propulsion designs, with future studies needed to explore gap and diameter limits.

Figure 16 presents a bar chart comparing the thrust generated by the corona plasma propulsion system across three configurations – linear DC, hexagonal DC, and hexagonal AC-DC – at a fixed electrode gap of 50 mm under atmospheric conditions. The x-axis denotes the collector diameter in millimeters (5, 8, and 11 mm), while the y-axis represents thrust in mN·m-1, normalized to the 21 cm emitter length. The chart employs distinct colors to differentiate configurations: linear DC (red), hexagonal DC (blue), and hexagonal AC-DC (yellow). Thrust values increase with collector diameter, with linear DC ranging from 119 mN·m-1 at 5 mm to 138 mN·m-1 at 11 mm, hexagonal DC from 129 mN·m-1 to 157 mN·m-1, and hexagonal AC-DC from 143 mN·m-1 to 181 mN·m-1. The hexagonal AC-DC configuration exhibits the highest thrust, achieving a 31% increase (181 mN·m-1) over linear DC (138 mN·m-1) at 11 mm, while hexagonal DC shows a 14% improvement (157 mN·m-1). This enhancement is attributable to the hexagonal geometry’s improved electric field distribution and the AC-DC power supply’s enhanced ionization efficiency.

The hexagonal emitter configuration increases the local electric field uniformity and field enhancement factor (), promoting a more homogeneous space-charge distribution along the emitter perimeter. In addition, the superimposed AC excitation generates a localized DBD between the insulated AC electrode and the DC-connected bare emitter, which increases electron density and sustains ion production. This mechanism enhances ion mobility and reduces ion recombination losses, leading to higher thrust and efficiency, consistent with previously reported AC-assisted EHD propulsion studies (Wang et al. 2023).

The observed thrust increments align with the study’s hypothesis that geometric and power supply modifications optimize corona discharge performance. The 32% thrust gain with hexagonal AC-DC suggests a synergistic effect, where the alternating current component likely increases effective ion mobility by periodically modulating the electric field, which enhances charge transport and suppresses space-charge saturation near the emitter, complementing the hexagonal arrangement’s uniform field. Compared to prior studies (e.g., Thompson et al. [2020]), which reported modest gains with DC configurations, this result indicates a significant advancement. However, potential limitations include measurement uncertainties (± 0.2 mN·m-1) and environmental factors (e.g., humidity), which may influence repeatability. Future experiments could explore intermediate diameters or varying AC-DC ratios to refine these findings, enhancing their applicability to micro-satellite propulsion systems (Thompson et al. 2020).

Ozone and safety

Ozone production measured < 0.08 ppm using the Aeroqual Series 500 analyzer, below OSHA limits. The hexagonal configuration reduced ozone by 18% due to uniform distribution.

CONCLUSION

This study introduces a novel hexagonal emitter configuration with an AC-DC power supply, achieving a 32% thrust increase and 28% efficiency improvement over traditional linear DC setups in corona plasma propulsion systems. These advancements, driven by enhanced plasma density and field uniformity, outperform prior benchmarks, such as Smith and Jones (2024), and offer scalable solutions for microsatellites and unmanned aerial vehicles. Future research will explore electrode material optimization, system scalability, and long-term stability under diverse environmental conditions.

ACKNOWLEDGMENTS

The authors would like to express their sincere gratitude to Dr. Seyed Hossein Sadati for his valuable support and insightful guidance throughout the various stages of this research.

  • DECLARATION OF USE OF ARTIFICIAL INTELLIGENCE TOOLS
    The materials used in the research are cited in the article where applicable. No artificial intelligence (AI)-generated content or AI applications were used in the generation of the research data, analysis, or results. Any assistance from AI tools was limited to language editing and drafting support, and not to the scientific content of the manuscript.
  • FUNDING
    Not applicable.
  • Peer Review History
    Single Blind Peer Review.

DATA AVAILABILITY STATEMENT

All data sets were generated or analyzed in the current study.

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Publication Dates

  • Publication in this collection
    20 July 2026
  • Date of issue
    2026

History

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