# Current, thrust, and power of a corona discharge plasma thruster at tropospheric altitude

Sylvain Grosse, Nicolas Benard, Éric Moreau

► To cite this version:

Sylvain Grosse, Nicolas Benard, Éric Moreau. Current, thrust, and power of a corona discharge plasma thruster at tropospheric altitude. Journal of Physics D: Applied Physics, 2024, 58 (9), pp.095201. 10.1088/1361-6463/ad9d54. hal-05069371

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Submitted on 15 May 2025

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# Current, thrust, and power of a corona discharge plasma thruster at tropospheric altitude

Sylvain Grosse, Nicolas Benard and Eric Moreau

Université de Poitiers - Institut PPRIME, 11 Boulevard Marie et Pierre Curie, 86073 Poitiers CEDEX 9, France

Corresponding author: eric.moreau@univ-poitiers.fr

## Abstract

Recent developments in electro-aerodynamics (EAD) thrusters that use plasma have demonstrated their abilities for aircraft propulsion, at least for low-velocity drones. Further improvements in the technology bring EAD propulsion closer to full-scale applications. However, certain doubts still exist concerning their behavior in different atmospheric conditions. The study focuses on the effects of altitude on the propulsive performance of a corona discharge thruster in the troposphere. A thruster is placed in a climatic chamber that can vary the temperature and pressure independently, and force and current measurements provide the thrust generation and power consumption of the thruster. First, tests under varying pressure between 500 and 1000 hPa were performed at room temperature. As expected, at constant voltage, they highlight that the power increases almost linearly when the pressure decreases. Conversely, they demonstrated that the thrust decreases with pressure at a constant current. The combined effects result in a loss of effectiveness (i.e. thrust-to-power ratio) when the pressure reduces. Yet, a plateau of maximum effectiveness is achieved between 800 and 1000 hPa. Secondly, the temperature was varied between -20 and +30°C at ground pressure. No significant effect was captured concerning the current and power, and a weak decrease in thrust was measured at higher temperatures. Finally, altitudes between 0 and 6 km were simulated by combining pressure and temperature modifications. Mostly led by the pressure drop, the power decreases linearly when the altitude increases, but the thrust decreases to a plateau between 3 and 6 km. Hence, the effectiveness also decreases with altitude down to a stagnation between 3 and 6 km. The coupled decreases in drag and thrust with altitude engender a small decrease in the maximum achievable freestream velocity of the thruster down to a plateau over 3 km.

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Keywords: plasma propulsion, electroaerodynamics, corona discharge
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# 1. Introduction

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In the past decades, more efforts have been made to electrify all transportation systems. In the case of modern aviation, this trend transpires through the use of electric motors that drive propellers. In 2018, a drone realized at MIT by Xu et al. [1] revived the interest in Electro-AeroDynamic (EAD) propulsion. With a mass of 2.45 kg and a span of 5 m, its flight performance was limited to $4.5 \text{ m} \cdot \text{s}^{-1}$ at a height of nearly 2 m over less than 60 m (indoor flight). This demonstrator proved the feasibility of EAD propulsion of light drone in the air at mean sea level. Plasma thrusters have advantages over typical electric motors with propellers (e.g. no moving parts and sparse emissions). More effort has been dedicated to EAD propulsion since, and it has been estimated that current EAD thrusters need to produce 3 to 10 times as much thrust in order to achieve suitable flight velocities [2]. New developments with more complex multistage configurations show this goal is within reach [3,4]. Now that EAD propelled aircraft are envisioned, more work focuses on the effect of the flight conditions of the said aircraft such as wind speed [5] and atmospheric conditions [6]. First, the underlying principles of EAD propulsion must be introduced.

The most studied single-stage EAD thruster is the wire-to-cylinder Corona Discharge (CD) thruster displayed in the schematic in figure 1. The small radius of curvature at the surface of the wire and the high voltage causes the electric field to strengthen locally around the wire. The electric field exceeds the breakdown of the air, and the air ionizes. Some of the charged particles created in this plasma escape and are forced to drift into the inter-electrode gap due to the electric field between the high-voltage wire and the grounded cylinder. In the inter-electrode region across the electrodes, the electrically charged particles are accelerated by Coulomb forces. Moving towards the collector, they collide with the neutral air molecules and generate an ionic wind. Upon reaching the collector, the electrical charges are neutralized while the accelerated air forms a jet flow.

The wire-to-cylinder thruster has been extensively studied in quiescent air by various authors [7–11]. The current *I* that goes through the thruster scales as Townsend’s law:

$$I = C \cdot V \cdot (V - V_0), \quad (1)$$

where *C* is a constant depending on the gas, the geometry of the electrodes, the polarity of the discharge and the ionic mobility, $V_0$ is the ignition voltage, and $V \ge V_0$ is the voltage applied to the thruster [12]. Townsend’s law works well for glow discharges but underestimates the
consumption of current in the streamer regime [13]. Moreover, it is limited to quiescent conditions, and a more suitable model proposed by Chapman [14] extends Townsend's law to non-zero freestream velocities [5].

The generated thrust $T$ has two components, namely the electric forces produced by the discharge (here called EAD force) $F_{\text{ead}}$ and the total drag of the electrodes $F_{\text{D}}$:

$$T = F_{\text{ead}} - F_{\text{D}}. \qquad (2)$$

Since the wire emitter is very thin compared to the cylindrical collector, the total drag is predominantly caused by the drag of the collector. The electric force is the sum of all the Coulomb forces that act on the charged particles due to the electric field that exists between the electrodes. In quiescent conditions, Stuetzer [15] showed that:

$$F_{\text{ead}} = \frac{I \cdot d}{\mu}, \qquad (3)$$

with $d$ the inter-electrode gap (i.e. edge-to-edge distance between the electrodes) and $\mu$ the ionic mobility. Hence, the EAD force increases linearly with the current. On the other hand, the drag of the electrodes arises from the flow of gas around the solid surfaces. The thrust typically grows linearly with the current in quiescent conditions as well [7,9,11,16–19]. This is caused by the low velocity induced by the discharge (lower to or of the order of $1 \text{ m} \cdot \text{s}^{-1}$ [5,9] depending on the voltage), which yields a low drag compared to the EAD force.

If EAD propulsion is applied to general aviation, it is essential to ascertain the impact of altitude changes on the propulsive performance of EAD thrusters (i.e., on the thrust generation and power consumption). A change in the altitude has several physical considerations regarding the generation of plasma (i.e. ionization), the drift of the charged species in the gap region (i.e. ionic wind) and the losses on solid surfaces due to viscous and pressure drag. As shown by Grosse et al. [5], at freestream velocities lower than $20 \text{ m} \cdot \text{s}^{-1}$, the electric force is constant with the air velocity. Thus, the typical evolution of the drag with the air density and velocity can be applied:

$$F_{\text{D}} = \frac{1}{2} \cdot \rho_{\infty} \cdot S \cdot C_{\text{D}} \cdot u_{\infty}^{2}, \qquad (4)$$

where $\rho_{\infty}$ is the air density, $S$ the reference surface of the electrode (e.g. diameter of the cylinder), $C_{\text{D}}$ its drag coefficient, and $u_{\infty}$ the freestream velocity.
In the study of single stage thrusters, it is common to analyze the current $I^*$, thrust $T^*$ and power $P^*$ per unit span of electrode [8,11,16,20]. This approach is also adopted in the present study; however, for clarity and consistency, the discussion will continue to reference the total current, thrust, and power, rather than their per unit span counterparts.

In the troposphere, the ideal gas law allows the calculation of the density based on the ambient pressure $p_\infty$ and temperature $t_\infty$:

$$p_\infty = \rho_\infty \cdot R \cdot t_\infty, \qquad (5)$$

where $R = 287 \text{ J} \cdot \text{kg}^{-1} \cdot \text{K}^{-1}$ is the specific gas constant of dry air. In the International Standard Atmosphere (ISA) at mean sea level, the pressure, temperature and density are respectively $p_0 = 1013.25 \text{ hPa}$, $t_0 = 15^\circ\text{C}$ and $\rho_0 = 1.23 \text{ kg} \cdot \text{m}^{-3}$. The ISA model is given by ISO 2533:1975 [21]. The ISA model can be found online or in good textbooks such as [21], and allows to calculate the temperature, pressure and density as a function of altitude. Equation (4) thus enables the calculation of the drag in different flight conditions.

Khomich et al. [6] investigated the current, thrust and effectiveness (aka. thrust-to-power ratio) of an array of three parallel wire-to-cylinder thrusters side-by-side (i.e., in parallel) for near-space applications. With a lower pressure, the authors noted a decrease in the ignition voltage $V_0$ with an increase in the current at a given voltage. Yet, this rise was accompanied by a decrease in the thrust at a given current. This resulted in a drop in effectiveness with decreasing pressure at a given consumed power. These results suggest that a greater current flows across the thruster at low pressure, but that it does not lead to greater force generation - as suggested by equation (3) - because of the dependency of the ionic mobility on pressure. The previous study enables the verification of analytical predictions [22] and gives an overview of the propulsive performance of a thruster in several layers of the atmosphere. However, the temperature is not considered and the resolution in pressure (and altitude) is coarse.

Regarding the ionization, the drop in $V_0$ and rise in current at lower pressure were also observed in the field of Ion Mobility Spectrometry (IMS) [23]. Besides, the ionic mobility was observed to increase at lower pressure [24–26]. Thus, the higher mobility at low pressure overcomes the gain in current leading to a decreased thrust as suggested by equation (3). The effect of the temperature on corona discharges is mostly discussed in works focusing on IMS [26–28]. The reduced mobility: $\mu_0 = \mu \cdot (p_\infty/p_0) \cdot (t_0/t_\infty)$ is almost constant with pressure and increases weakly with temperature between 0 and 250°C. These results lead to an ionic mobility that increases with decreasing pressure and with increasing temperature.
Other works have focused on the effect of air pressure on the thrust [29] and mass-flow-rate [30,31] on surface Dielectric Barrier Discharge actuators used for airflow control, and highlight an optimum of mass-flow-rate at around 600 hPa and thrust between 600 and 800 hPa.

As a result, there is limited understanding of the performance of EAD thrusters at varying altitudes. The main work of Khomich et al [6] gives a general trend of the propulsive performance of the thruster up to near space altitude, but the effects of the temperatures are not assessed. Besides, previous work [2,5] suggests that the modern EAD thrusters would be focused for light drones of tens of kilograms flying at 10 to 15 m·s⁻¹. These aircraft would be limited to 1 to 2 hours of flight at low altitude to start. Thus, if EAD thrusters were employed for general aviation, a more finely resolved analysis is needed in the lower atmosphere. The present work aims at answering these questions, by studying the combined effects of pressure and temperature on the propulsive performance of a wire-to-cylinder CD plasma thruster in the troposphere. This study focuses exclusively on the basic configuration of a single-stage thruster, consisting of one emitter and one collector, without considering installation effects, such as interactions with multiple stages [1,3,4] or with the carrying vehicle. The configuration of the thruster is consistent with our previous work [5], and the insights gained are expected to be applicable to more complex geometries and will contribute to the improvement of models like those [2,32]. First, the experimental methods for the current and force measurements and the control of the atmospheric conditions are detailed in section 2. Before analyzing the effects of altitude on thrust generation and power consumption, the individual effects of the pressure and temperature are discussed in sections 3 and 4 respectively. Finally, the impacts of the altitude on the propulsive performance of a wire-to-cylinder thruster are detailed in section 5.
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Schematic of a wire-to-cylinder corona discharge thruster.</figcaption></figure>

## 2. Experimental method

### 2.1 Climatic chamber

A climatic chamber (SAPRATIN) was employed. The chamber internal dimensions are 710 mm in width, 660 mm in height and 770 mm in depth. It can control both pressure and temperature. The front door can be tightened thanks to four threaded shafts with handles located at the four corners of the door. Four access tubes go through the right flank of the chamber to pass cables. All possible gaps between the door or tubes and the main structures of the chamber are sealed with rubber. All the tubes are sealed on their outdoor end by silicon corks.

The chamber can decrease the temperature down to -35°C and the pressure down to 250 hPa. The pressure is controlled through a vacuum pomp with humidity filters at the air intake, and the cooling system uses coolant flowing through heat exchangers plus a fan to cool and mix the air inside the test chamber. One of the main outcomes of the present study involves the measurement of a force. However, when the control system of the pressure and temperature is turned on, the low-pressure pump and the internal fan create too much vibration for proper force measurements with the lab scale. When turning off the control of the pressure and temperature, small leakages prevent the pressure and temperature to stay constant. Down to 600 hPa and/or
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178 -15°C shutting down the control for 5 to 10 minutes did not lead to severe variations of the pressure and temperature. However, lower settings of the pressure and temperature were difficult to maintain within ±100 hPa and ±5°C after 5 minutes of shutdown. Thus, the pressure and temperature were measured throughout the study as well as the timing of the different measurements (pressure, temperature, force, and current) to accurately derive the pressure and temperature at the time of the measurements. Before switching off the control of the atmospheric conditions inside the chamber at the start of the tests, we waited for the chamber to stabilize the pressure within ±15 hPa and the temperature within ±2°C of the input values. As explained previously, the input values at the shutdown of the control system had to take the drift of the pressure and temperature during the tests into account. After the completion of the test, any data point exceeding the aforementioned thresholds for the errors were rerun. Consequently, the accuracy of measurements is ±15 hPa for the pressure and ±2°C for the temperature. The internal conductive walls of the chamber are coated with Kapton for protection and to reduce their interaction with the discharge.

192 2.2 Test rig

193 A schematic of the test rig is shown in figure 2(a). To support the lab scale on a horizontal surface, a wooden plate was fitted with four adjustable feet of 60 mm height. This table was placed in the middle of the chamber and a spirit level was used to adjust the feet. The lab scale was placed on the table and inside a Faraday cage.

197 The electrodes are a 100 µm diameter tungsten wire for the emitter and a 6 mm diameter stainless steel cylinder for the collector with an inter-electrode gap of 40 mm. To hold the electrodes, a tower-like structure made of different plastic parts was designed. It can be observed in figure 2(b). A PLA (polylactic acid) plate is placed on the scale and four 250 mm Delrin rods are inserted in the base plate. At the top end of the rods a PLA frame (inside an empty square section of 200 mm × 200 mm) four grooved rods in PLA support the Nylon struts that hold the electrodes at their ends. When needed, Nylon screws tightened the parts. The wire and cylinder were aligned vertically on top of each other with the cylinder on top. Two PVC pipes are screwed vertically to the table to hold the cables. The air-exposed span for the wire and cylinder is 187 mm due to the bending of the plastic parts that hold the mechanical tension in the electrodes. The connections between the cables are all sealed with CEREWAX 4T and 5T insulating waxes to prevent parasitic discharges. A Faraday cage was realized to protect the scale from possible electric interference. The electrodes were placed so that the chamber walls and Faraday cage were at least 200 mm away from both electrodes.
211 2.3 Electric measurements

The high-voltage cable is connected to the wire and the ground cable is connected to the cylinder. Each of the two cables passes through a dedicated tube in the wall of the chamber. PTFE tubes also insulate the cables from the walls. The power cable and RS-232 cable of the scale both go in a third tube through the wall. An Amprobe AM-540-EUR ammeter measures the current at the ground wire outside the chamber. The ammeter has an accuracy of 1.2% ± 0.2 µA. The errors are listed in table 1 for the different values of the current used in the study. An ammeter was chosen due to the simplicity of the measurement technique and its reliability when used for glow discharges [33]. Besides, the frequency response of the AM-540-EUR is 1 kHz. Unstable readings were correlated with the occurrence of unwanted parasitic discharges that were visualized through the glass door of the test chamber. When such parasitic discharges were confirmed by visual inspections and unstable ammeter readings, the current of occurrence was excluded from the study and was not exceeded. In the study, the range of voltages and current stay in the corona glow regime without parasitic discharges.

A positive high-voltage was supplied to the wire by a Spellman SL-1200. The supplied voltage can be read at the device monitor; its accuracy has been verified with a high-voltage probe and is about 1%. Preliminary tests were carried out with ammeters on both the high-voltage and ground wires to verify if there was a leakage of current from the thruster. The placement of the balance was modified and Kapton sheets were taped to the walls of the chamber to reduce the leakage at high voltage. In the study, the voltage range brings the leakage of current down to the accuracy of the ammeters and does not ignite parasitic discharges at room atmospheric conditions. The main limitation in the discharge current was caused by parasitic discharges that ignited on dielectric materials near the tips of the electrodes. Especially, the lower the pressure and temperature, the lower the maximum achievable current. In our experiments, we measured the produced thrust as a function of the mean discharge current. Consequently, to obtain a given current value, the voltage dial was set to a high value (typically 20 kV) and the current was adjusted with the current dial. The power supply was then used as a current generator, and the voltage monitor of the power supply was used to obtain the voltage readings. The ammeter was used to obtain accurate readings in the selected range. When calculating the power consumption for a DC power source $V \times I$, the propagation of error gives an accuracy of ±1.6%. Since the maximum power measurement is around 2.5 W·m⁻¹, the maximum error is ±0.04 W·m⁻¹.
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<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>**Figure 2.** Schematic of the force measurement test rig (a) and picture of the 3D printed frame of the electrodes (b).</figcaption></figure>
<table><caption>**Table 1.** Accuracy of the current measurements.</caption><thead><tr><td>Current (μA·m<sup>-1</sup>)</td><td>Error (± μA·m<sup>-1</sup>)</td></tr></thead><tbody><tr><td>25</td><td>1.4</td></tr><tr><td>50</td><td>1.7</td></tr><tr><td>75</td><td>2.0</td></tr><tr><td>100</td><td>2.3</td></tr><tr><td>125</td><td>2.6</td></tr></tbody></table>

## 2.4 Force measurements

The Denver Instrument SI-603 scale has an accuracy of 2 mg (±0.1 mN·m⁻¹). The measurements were realized at 10 Hz over 30 s for both the tare weights and high-voltage measurements. During the experimental campaign, the standard deviation was usually of the order of 0.2-0.3 mN·m⁻¹. Hence, the confidence interval is ±0.6 mN·m⁻¹ (95% confidence). Because of the noisy environment that is the climatic chamber, after the control systems (pressure and temperature) were switched off, a tare was realized, the high-voltage measurements, and finally another tare. The tare weights were averaged and deducted from the measurements to calculate the thrust.

To calibrate the systems, preliminary tests were carried out with OIML F2 masses of 1 and 2 g (around 50 and 100 mN·m⁻¹ span) and different small uncalibrated masses of 100 to 300 mg (5 to 15 mN·m⁻¹). In atmospheric conditions and with both electrodes connected to the cables, the scale gave proper measurements with the OIML F2 masses. Moreover, for the smaller uncalibrated masses, the same readings were acquired with the scale with and without the test rig. Thus, the connections and cables do not impact the force measurements.

Tests were carried out when decreasing the pressure at room temperature with the OIML masses. The variations in the measurements did not show a clear trend and were of the order of the confidence interval. Finally, tests were performed when decreasing the temperature at constant atmospheric pressure. This time, the rig was replaced by an equivalent mass for the tare (around 435 g), and the OIML masses were used for the measurements. A linear drift in the gain of the balance was captured (-0.38 %·K⁻¹). In the study, the range of the temperatures is 50°C (30 to -20°C) and the thrust is always less than 30 mN·m⁻¹. Hence, between the maximum and minimum temperatures, the maximum variation due to temperature is 0.57 mN·m⁻¹. This variation is of the order of the confidence interval of the measurement. We can then assume that the temperature and pressure do not affect the force measurements inside the climatic chamber.
## 2.5 Repeatability of the measurements

The experiments comprise several uncontrolled variables. First, the humidity inside the chamber is not measured. Even after being dehumidified through the filter of the intake of the pump, the actual level of humidity of the air inside the chamber is not known. Other unexpected parasitic effects could arise. Consequently, the repeatability of the measurements must be assessed.

The study comprises three experimental campaigns, one for each atmospheric variable which are the pressure, temperature and altitude. Each campaign was realized within a week à different times of the year. For each campaign, we repeated several tests conditions two to three times on different days within the week. For example, data were acquired on three occasions at 900 hPa for all the current values between 25 and 125 µA·m⁻¹ span of the electrodes during the pressure campaign (20 datapoints in total at 900 hPa). Thus, the repeatability can be analyzed over 40 datapoints for the pressure campaign, 20 for the temperature campaign and 30 for the atmosphere campaign. The error between the repeats was computed for every datapoint, and the root-mean-square errors (RMSE) were obtained over all datapoints of each individual experimental campaign. The RMSE of the repeats agreed within ±2% for the power for all test campaigns. For the thrust, the RMSE of the repeats are ±1.6 mN·m⁻¹ for the pressure campaign, ±2.4 mN·m⁻¹ for the temperature campaign, and ±2.6 mN·m⁻¹ for the altitude campaign.

## 3. Pressure effects

As explained in section 2.1, the climatic chamber was able to decrease the pressure down to 250 hPa but the pressure control had to be switched off to perform force measurements. Consequently, the pressure was not controlled during the time taken for the scale signal to stabilize and for the measurements to be acquired (around 5 to 10 minutes). Due to weak pressure leakages, and the lack of control, the lowest pressure that could be obtained for the force measurements is between 450 to 500 hPa. Hence, the pressure tests were realized at room temperature (16°C) with a pressure ranging from 500 hPa to 1000 hPa by steps of 100 hPa. Points were obtained at constant current ranging from 25 to 125 µA·m⁻¹. As indicated previously, the study focuses on the current, power and thrust per unit span, even though the terms “per unit span” are not always repeated.

### 3.1 Current

First, the current can be visualized against the voltage in figure 3(a). At every pressure, the current increases with the voltage in a quadratic manner, as predicted by Townsend's law in equation (1). The computed coefficients of equation (1) are plotted against the pressure in figure
3 309 3(b). As expected, decreasing the pressure leads to a lowering of the ignition voltage $V_0$ (see figure 3(b)). As the current is here limited to 125 µA·m⁻¹, the effects reported by Khomich et al. [6] at higher current are not observed here and the different curves in figure 3 share the same trend. However, figure 3(b) shows that the coefficient C increases almost linearly with dropping pressure. This dependency is not surprising as the coefficient C depends linearly on the mobility [12] and the ionic mobility has been observed to decrease almost linearly as the pressure increases [24,25]. At higher voltage, the curves would hence diverge from each other, as seen in [6]. The limited number of points in figure 3(b) does not allow us to verify non-linear models such as the power laws in [14].

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In the glow regime with a DC power supply, the consumed power per unit span $P^*$ (in W·m⁻¹) corresponds to the product of voltage and current per meter span:

$$P^* = V \cdot I^* . \qquad (6)$$

The power is plotted against the pressure at constant currents in figure 5. At constant current, the power increases linearly with the pressure. Thus, such a thruster is expected to consume less power in altitude. For instance, at 125 µA·m⁻¹, 27% of power (around 0.75 W·m⁻¹) is saved at 500 hPa on the mean sea level value at 1000 hPa.
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Current per unit span against voltage at constant pressure (a) and coefficients of the fitted Townsend's laws as a function of pressure (b).</figcaption></figure>

## 3.2 Thrust

It is common to plot the thrust against the current for corona thrusters, as it is done in figure 6 for the different pressure values. As expected in quiescent conditions, the thrust increases linearly with the current. This trend holds over all the tested pressures. Yet, as the pressure drops, the slope decreases. For example, at 500 hPa, the thrust is only 30 to 40% of the thrust at ground pressure.

This phenomenon is clearer in figure 7, where the thrust is represented against the pressure at a constant current. The thrust increases with pressure in a non-linear manner. As expected, a greater current is always associated with a higher thrust, and apart from a few points of lower accuracy at 500 hPa, the behaviors of the thrust versus pressure curves are consistent across all
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tested currents. At 125 µA·m⁻¹, the thruster generates 22 mN·m⁻¹ of thrust at mean sea level but only 18 mN·m⁻¹ at 800 hPa (18% loss) and 9.5 mN·m⁻¹ at 500 hPa (57% loss).

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Altogether, the results highlight a loss of thrust at constant current (i.e. flow of charged particles across the electrodes) with a drop of pressure.

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<figure><img src="image_6.png" /></figure>

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<caption>**Figure 4.** Voltage against pressure at constant current.</caption>

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<figure><img src="image_7.png" /></figure>

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<caption>**Figure 5.** Power against pressure at constant current.</caption>
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Thrust against current at constant pressure.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 7.** Thrust against pressure at constant current.</figcaption></figure>

Two phenomena participate in this drop. First, as indicated in section 1, other works [24,25] report a weakly non-linear increase in the ionic mobility when pressure decreases from 1000 hPa down to 600 hPa. According to equations (2) and (3), this leads to a decrease in thrust at constant current. If we neglect the drag of the collector in equations (2, equation (3) allows us to estimate the ionic mobility from the data represented in figure 6, as the slope of the straight corresponds to $\mu/d$. Linear regressions were performed, and the calculated values of the ionic
mobility are graphed against the pressure in figure 8. Our results concur with the measurements of Asano et al. [24] with $2.0 \times 10^{-4} \text{ m}^2 \cdot \text{V}^{-1} \cdot \text{s}^{-1}$ at 1000 hPa and around $3.0 \times 10^{-4} \text{ m}^2 \cdot \text{V}^{-1} \cdot \text{s}^{-1}$ at 700 hPa. Yet, our measurements extend to 500 hPa where the almost linear trend breaks, and the ionic mobility increases up to $5.2 \times 10^{-4} \text{ m}^2 \cdot \text{V}^{-1} \cdot \text{s}^{-1}$.

Furthermore, as explained in section 3.1, a lower voltage is required to achieve a constant current as the pressure diminishes. This results in a weakening of the electric field between the electrodes. Since the EAD force is the sum of the Coulomb forces, it also drops with the lower voltage used at 500 hPa.

It is now necessary to determine the impact of the pressure on the effectiveness (aka. thrust-to-power ratio) of the thruster.

<figure><img src="image_10.png" /><figcaption>**Figure 8.** Ionic mobility against pressure at 16°C.</figcaption></figure>

### 3.3 Effectiveness

The effectiveness $\theta$ is defined as:

$$ \theta = \frac{T}{P} = \frac{T^*}{P^*} . \qquad (7) $$

Due to the accuracies of the thrust (±1.6 mN·m⁻¹) and power (±0.05 W·m⁻¹) measurements, the propagation of error yields an accuracy of 7.7% for the effectiveness. When neglecting the drag force (quiescent conditions) and by using equations (3) and (6), equation (7) leads to:

$$ \theta = \frac{d}{\mu \cdot V} . \qquad (8) $$
Two antagonist effects arise from equation (8). On the one hand, the higher ionic mobility at low pressure decreases the effectiveness, but on the other hand, the lower voltage at constant current increases the effectiveness.

First, the thrust can be visualized against the power at constant pressure in figure 9. For every pressure, an almost linear increase of the thrust along the power can be observed. Besides, from 600 hPa, the slope of the curves is nearly constant, and the effect of the pressure is weak over 800 hPa.

<figure><img src="image_11.png" /><figcaption>**Figure 9.** Thrust against power at constant pressure.</figcaption></figure>

It is common to plot the effectiveness against the thrust as shown in figure 10. Although the decrease of the effectiveness with the thrust is usual [7,10,16,17], the effect of the pressure is visible, especially under 800 hPa with a general decrease of the effectiveness with the pressure. Over 800 hPa up to mean sea level conditions, the effectiveness takes similar values at constant thrust.

To highlight this phenomenon, the effectiveness has been displayed against the pressure at a constant current in figure 11. The higher effectiveness at low current is particularly visible, but mostly, the effectiveness stays almost unchanged between 800 and 1000 hPa.

In conclusion, a lower pressure was observed to increase the current at constant voltage due to a lower ignition voltage and a higher ionic mobility, and to decrease both the power
consumption and thrust generation, but with a weak effect on the effectiveness of the thruster between 1000 hPa (ground) and 800 hPa (around 2 km). The isolated effect of the temperature must now be analyzed as well to segregate the contributions of each factor on the propulsive performance of the thruster in altitude.

<figure><img src="image_12.png" /><figcaption>**Figure 10.** Effectiveness against thrust at constant pressure.</figcaption></figure>

## 4. Temperature effects

Tests were performed at a constant pressure of 1000 hPa (atmospheric pressure) at varying temperatures from -20 to +30°C to determine the effects of the temperature on the discharge. To reduce the humidity inside the chamber before running the tests, a vacuum (around 250 hPa) was held for several minutes before going back to 1000 Pa, several times. This method allowed air to go through the dehumidifying filter of the chamber before coming inside the chamber. Consequently, we prevented droplets from condensing at low temperatures. Due to the weak changes in the ionic mobility detailed in section 1, the temperature is not expected to strongly impact the power or thrust.
<figure><img src="image_13.png" /><figcaption>**Figure 11.** Effectiveness against pressure at constant current.</figcaption></figure>

4.1 Current

First, the evolution of the current with the voltage at constant temperature is shown in figure 12. With the errors of around ±2 µA·m⁻¹ and 1% of the voltage (see section 2.3), it can be estimated that the curves are superimposed. Thus, the current follows a standard quadratic relationship with the voltage (see equation (1)).

The voltage is displayed against the temperature at a constant current in figure 13. A general trend can be observed at every value of the current. All the curves follow a convex shape where the voltage stays nearly constant between 0 and +20°C and then drops by less or around 0.5 kV towards -20°C and +30°C. No explanation has been found for this phenomenon. Nevertheless, it is very weak and does not significantly impact the discharge.

With the insignificant effects of the temperature on the current and voltage, the power consumption can be expected to be almost constant with the temperature. The calculated power has been represented along the temperature at a constant current in figure 14. As predicted, it only increases linearly with the voltage and current but does not depend on the temperature. As a result, for all the tested currents, the power stays almost constant with the temperature.
<figure><img src="image_14.png" /><figcaption>**Figure 12.** Current against voltage at a constant temperature.</figcaption></figure>

## 4.2 Thrust

With a negligible effect on the current and power, it could be expected that the thrust is little impacted by the temperature. The thrust has been drawn against the temperature at a constant current in figure 15. For every current, an increase can be observed with decreasing temperature.

This increase in the thrust cannot be explained through changes in the drag. On the one hand, at constant pressure and colder temperatures, the density of air increases (ideal gas law). On the other hand, the lower temperature causes the dynamic viscosity of air to decrease (Sutherland's law). The combined effect is an increase of the Reynolds number at low temperature. At an average induced ionic wind velocity near 0.5 m·s⁻¹ [5] that is here assumed constant, the **Reynolds number** stays in the range 100 to 300 where the drag coefficient of the cylinder in nearly constant at around 1.5 [34]. In this situation, equation (4) predicts a greater drag at low temperature. Consequently, based solely on the drag of the collector, the thrust should decrease in cold temperatures. Since we observed an opposite trend, a different phenomenon is at play.

As reported in section 1, the ionic mobility increases with the temperature. The ionic mobility can be calculated by using equations (2) and (3) with the neglect of the drag. At 125 µA·m⁻¹, the propagation of error results in a 4.4% accuracy for the ionic mobility. Our results fail to capture a clear trend. The average and standard deviation of the ionic mobility are 2.48 ±0.27
455

$m^2 \cdot V^{-1} \cdot s^{-1}$. A linear regression gives a weak increase of around $0.33 \ m^2 \cdot V^{-1} \cdot s^{-1}$ between -20 and +20°C, but this value is very similar to the standard deviation.

456

In conclusion, the temperature at ground pressure does not influence the generation of current and consumed power significantly between -20 and +30°C. However, the thrust decreases with a rise in the temperature. This phenomenon could be explained by the increase of ionic mobility with the temperature, yet we cannot confirm this trend with our data.

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<figure><img src="image_15.png" /></figure>

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<caption>**Figure 13.** Voltage against temperature at constant current.</caption>

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<figure><img src="image_16.png" /></figure>

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<caption>**Figure 14.** Power against temperature at constant current.</caption>
<figure><img src="image_17.png" /><figcaption>**Figure 15.** Thrust against temperature at constant current.</figcaption></figure>

**5. Altitude effects**

The individual impacts of the pressure and temperature have been studied in sections 3 and 4 respectively. It can be expected that the power consumption drops solely due to the loss of pressure in altitude. On the other hand, the lower temperature and lower pressure have antagonistic effects at higher altitudes. First, a range of altitudes that fits the capabilities of the used climatic chamber has been selected.

**5.1 Selected altitudes**

Given the minimal achievable temperature of -20 to -25°C and minimum achievable pressure of 400 to 500 hPa, it is only possible to simulate atmospheric conditions up to about 6 km of altitude in the ISA model.

It was decided to test every kilometer between ground level (0 km) and 5 km. The conditions at these altitudes are given in table 2. However, given the accuracy of the temperature and pressure settings, the desired altitudes were not always properly simulated. To correct the altitude, the density was calculated with the ideal gas law in equation (5) based on the measured values of the pressure and temperature. Then, the corresponding altitude was found in the ISA model based on the value of the density. The calculated altitude has an accuracy of ±0.23 km. Moreover, Sutherland's law was used to calculate the variations in the viscosity of air and determine the Reynolds number of the flow around the cylinder. The evolution of the density
and dynamic and kinematic viscosities against the altitude are presented in table 2. The motivations behind these calculations are discussed in section 5.5. As explained in section 2.5, the analysis of the results must take the higher error of the thrust measurements into account (±2.6 mN·m⁻¹), and only the variations of the thrust with changing altitude are of importance in the study.

<table><caption>**Table 2.** ISA conditions over the selected range of altitudes.</caption><thead><tr><th>Altitude (km)</th><th>Pressure (hPa)</th><th>Temperature (°C)</th><th>Density (kg·m⁻³)</th><th>Dynamic viscosity (× 10⁻⁵ Pa·s)</th><th>Kinematic viscosity (× 10⁻⁵ m²·s⁻¹)</th></tr></thead><tbody><tr><td>0</td><td>1013</td><td>+15.0</td><td>1.225</td><td>1.789</td><td>1.461</td></tr><tr><td>1</td><td>899</td><td>+8.5</td><td>1.112</td><td>1.758</td><td>1.581</td></tr><tr><td>2</td><td>795</td><td>+2.0</td><td>1.007</td><td>1.726</td><td>1.715</td></tr><tr><td>3</td><td>701</td><td>-4.5</td><td>0.909</td><td>1.694</td><td>1.863</td></tr><tr><td>4</td><td>616</td><td>-11.0</td><td>0.819</td><td>1.661</td><td>2.029</td></tr><tr><td>5</td><td>540</td><td>-17.5</td><td>0.736</td><td>1.628</td><td>2.212</td></tr><tr><td>6</td><td>472</td><td>-24.0</td><td>0.660</td><td>1.595</td><td>2.416</td></tr></tbody></table>

## 5.2 Current

Before analyzing the results, it must be highlighted here that the combination of decreasing pressure and temperature strengthened the occurrence of parasitic discharges on dielectrics, but we cannot explain it fully. Experimentally, these unwanted discharges ignited irregularly near the connections of the electrodes with the plastic support. These parasitic discharges caused erratic variations in the current measured by the ammeter. The higher the simulated altitude is, the lower the voltage of ignition of the parasitic discharges. We excluded these data points in the study, resulting in a drop in the maximum achievable current at a higher altitude.

First, the evolution of the current with the voltage at constant pressure can be observed in figure 16. Because the temperature does not affect the current, a decrease in the ignition voltage leads to an increase in the current at a constant voltage, as in figure 3. If Townsend's law can fit the data series below 2 km of altitude, the inaccuracy and low number of points over 3 km do not allow an accurate calculation of the coefficients. Thus, figure 16 does not comprise any mathematical fitting.
This phenomenon is clearer in figure 17 where the voltage to obtain a given value of current is plotted against the altitude. In the figure, the corrected altitude is used instead of the desired altitude. Figure 17 shows an almost linear decrease in the voltage with rising altitude at a constant current. The weak non-linearity of the variation of pressure with the altitude and the linear decrease of the voltage with the decreasing pressure at constant current (figure 3) explain this behavior. Therefore, when plotting the power against the altitude at a constant current figure 18), a linear decrease of the power with rising altitude can also be observed. Again, power consumption is mostly affected by the changes in the pressure, and the trends captured in figure 18 are comparable to the ones observed in figure 5.

With a current and power mostly driven by the pressure, it is now necessary to determine the combined effects of the temperature and pressure on the thrust generation.

<figure><img src="image_18.png" /><figcaption>**Figure 16.** Current against voltage at constant altitude.</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>**Figure 17.** Voltage against altitude at constant current.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Figure 18.** Power against altitude at constant current.</figcaption></figure>

### 5.3 Thrust

The thrust versus altitude at constant current is represented in figure 19. The decrease in thrust is very strong at the beginning, between 0 and 1 km of altitude, then this decrease becomes weaker and weaker as the altitude increases, until it reaches a plateau from about 5
km. This decrease is due to the opposing effects of pressure and temperature, but the pressure effect prevails. On the one hand, when the altitude increases, the temperature decreases, and the thrust slightly increases (figure 15). On the other hand, when the pressure decreases, the thrust strongly drops (figure 7) because the ion mobility increases (figure 3).

For instance, when the altitude rises from zero to 6 km, the pressure decreases from about 1000 hPa down to 500 hPa, corresponding to a decrease of thrust from about 10 mN·m⁻¹ to 4 mN·m⁻¹ when the current is equal to 50 µA·m⁻¹ (figure 7). For the same altitude increase, the temperature drops from +15°C down to -22°C, corresponding to an increase in thrust from 8 mN·m⁻¹ to 10 mN·m⁻¹ (figure 15). These observations apply to all the tested currents. To analyze the effect of pressure, it is more informative to evaluate the relative decrease in thrust when pressure drops from 1000 hPa to 500 hPa, expressed as a percentage of the thrust at 1000 hPa. Figure 7 shows that this relative decrease in thrust remains constant at about 60%. In contrast, when the temperature decreases from +15°C to -22°C, the thrust consistently increases by approximately 2 to 3 mN·m⁻¹ in figure 15. Therefore, the loss of thrust due to the pressure drop outweighs the gain from the temperature decrease for thrust levels above 3 to 5 mN·m⁻¹ at sea level (0 km altitude).

## 5.4 Effectiveness

Based on equation (8), it is difficult to predict the evolution of the effectiveness with altitude. On the one hand, the voltage at constant current decreases with altitude (figure 17) and the mobility is both raised by the lower pressure and decreased with the lower temperature. The effectiveness is drawn against the altitude at a constant current in figure 20.

As for the thrust, a decrease in effectiveness can be observed below 3 km of altitude at all the currents. Over 25 µA·m⁻¹ and 3 km, the effectiveness stagnates at around 10 mN·W⁻¹. Furthermore, the current plays little role in the effectiveness. From 50 µA·m⁻¹, the effectiveness follows the same trend within the error of the measurements. At 75 and 100 µA·m⁻¹, the effectiveness drops from around 15 mN·W⁻¹ down to 10 mN·W⁻¹ at 3 km of altitude. Thus, the altitude causes the effectiveness to decrease compared to ground conditions. Yet, from 3 km, the effectiveness becomes stable.

This indicates that the thrust and power both decrease due to the lower pressure but that the thrust decreases to a greater extent below 3 km, leading to a steeper reduction of the effectiveness. From 3 km, the dampening effect of the lower temperature allows the thrust to decrease at a similar rate than the power. As a result, the effectiveness is almost constant above 3 km.
<figure><img src="image_21.png" /><figcaption>**Figure 19.** Thrust against altitude at constant current.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>**Figure 20.** Effectiveness against altitude at constant current.</figcaption></figure>

### 5.5 Effect of moving air

Up to this point, the drag of the electrodes has been neglected due to the low velocity of the 571 ionic wind induced by the thruster. However, during flight at high altitudes, the drag decreases 572
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573 due to the lower air density (see equation 4). Depending on the decreases of the EAD and drag forces, a higher altitude could be beneficial (see equation (2)).

575 As reported by Grosse et al. [5] for corona thrusters, the main limitation is the drag of the electrodes. Moreover, it was also shown that the EAD force and drag force are independent below 15 m·s⁻¹ [5] in a co-flow configuration (air flowing from the wire towards the cylinder). Using equations (2) to (5), it is thus possible to estimate the maximal freestream velocity that balances the EAD and drag force for the chosen thruster (i.e. a freestream velocity for which the thrust is zero). This velocity hence corresponds to the maximum achievable velocity in an ideal situation in a co-flow situation, without considering the drag of other components of the carrying vehicle. Moreover, the drag force is not only impacted by the density but also by the drag coefficient of the cylinder, which itself depends on the Reynolds number $R_e$:

$$R_e = \frac{u_\infty \cdot D}{\nu}, \qquad (9)$$

584 where D is the diameter of the cylinder (6 mm) and the kinematic viscosity of air. The evolution of the viscosity with the altitude can be observed in table 2 based on Sutherland's and ideal gas laws in the ISA model.

587 To give more accurate estimates, an Euler method has been coded. For each of the points in figure 19, starting from a low initial freestream velocity, the Reynolds number is calculated at the corresponding altitude. Then, the drag coefficient is extracted from the typical drag coefficient versus the Reynolds number curve for the cylinder (for example, the compiled data in [34]). With an air density and a drag coefficient calculated at the altitude, the drag force can be calculated using equation (4). The EAD force is here approximated by the thrust in quiescent conditions in figure 19. The error criterion $\epsilon$ used in the computation is:

$$\epsilon = \left| \frac{F_{\text{ead}} - F_{\text{D}}}{F_{\text{ead}}} \right| . \qquad (10)$$

594 A while loop is run by incrementing the freestream velocity by steps of 10⁻³ m·s⁻¹ until the error criterion becomes lower than 0.1%. Given the accuracy of the measurements, the derived velocity has an accuracy of 4.8%.

597 The maximum freestream velocity is represented along the altitude at a constant current in figure 21. The error in the velocity has been obtained with the propagation of error and amounts to 0.15 m·s⁻¹. It comes with no surprise that the maximum achievable velocity rises with the current at constant altitude since a higher current is linked to a greater thrust. At 125 µA·m⁻¹, the maximum freestream velocity is almost constant at around 2.9 m·s⁻¹ up to 2.5 km of altitude.
At a lower current, the freestream velocity reduces up to 2 to 3 km and then stabilizes within the uncertainty. Below 3 km, these results indicate that the altitude primarily reduces the available EAD force compared to the drag. Thus, the predicted thrust in flight drops and the achievable freestream velocity as well. From 3 km, the drag force reduces more significantly with the altitude, and the achievable freestream velocity shows weak variations. For all currents below 125 µA·m⁻¹, figure 21 suggests a loss of around 0.5 m·s⁻¹ between ground conditions and 3 km of altitude.

For real applications, the shape of the collector should be optimized, for example, by using airfoils [1,5]. In this case, the effect of the altitude on the drag coefficient would be different, especially with the interaction with the ionic wind on the upper and lower surfaces of the airfoil [5]. Besides, the altitude could affect the thrust differently with this new shape of collector.

<figure><img src="image_23.png" /><figcaption>**Figure 21.** Maximum achievable flight velocity against altitude.</figcaption></figure>

## 6. Discussion and conclusion

In the present work, the propulsive performance of a wire-to-cylinder corona discharge thruster has been experimentally investigated at different altitudes in the lower atmosphere. Three experimental campaigns were conducted in a climatic chamber: one at constant temperature with varying pressure, another at constant pressure with varying temperature, and
the third with simultaneous changes in both pressure and temperature to simulate different tropospheric altitudes between 0 and 6 km. Force and current measurements were performed to determine the thrust generation and power consumption of the thruster in altitude. In the previous sections, we focused the study on the individual effects of the three atmospheric parameters on the thrust and power. A conclusion could only be drawn for the absolute propulsive abilities of the used thruster if the data between the three experimental campaigns agree. In that respect, the data obtained at mean-sea level (1000 hPa, 15°C, 0 km) can be compared. The power measurements agree within ±2% between campaigns, however we observed a constant loss of -2.3 mN·m⁻¹ between the pressure and temperature campaigns and a constant gain of +4.7 mN·m⁻¹ between the pressure and altitude campaigns. Therefore, it is impossible for us to derive consistent thrust values across campaigns. Because of the good accuracy and repeatability of each individual experimental campaign (section 2.5), this study offers valuable insights into the effects of the three atmospheric variables on the generation of thrust but cannot provide a definitive assessment of the thruster's overall propulsive abilities.

First, the effect of the pressure was investigated at constant temperature. Our results concur with previous findings with a drop in the ignition voltage and an increase of the ionic mobility at low pressure. The current at constant voltage decreases at lower pressure, but Townsend's law stays valid in the investigated ranges of pressures (500 to 1000 hPa) and currents (25 to 150 µA·m⁻¹). Thus, the power consumption reduces almost linearly with the pressure. Nevertheless, a decrease in thrust at a constant current results from the higher ionic mobility at low pressure. The coupled effects render the thruster less effective at lower pressure with a drop in the thrust-to-power ratio (i.e. effectiveness). It is worth noting our results indicate a plateau of effectiveness between 800 and 1000 hPa.

Second, the temperature was varied from +30 to -20°C at constant pressure. We have not captured any noticeable effect on the current, and all our data series approximatively fall on a common curve with the voltage. This curve agrees with Townsend's law and the resulting power consumption is nearly constant with the temperature. The thrust was found to decrease at higher temperatures. This could be explained by a small increase in the ionic mobility with the temperature. Although this effect has been reported in other studies, our data do not allow us to correlate our observations with the reported phenomenon with certainty.

Finally, the combined effects of the temperature and pressure were assessed between 0 and 6 km of altitude. With the weak effects of the temperature and the strong effects of the pressure, similar conclusions arise concerning the altitude. The ignition voltage decreases at higher altitudes, with a drop in the current at a constant voltage. Therefore, the power consumption
1
2
3 655 decreases linearly with rising altitude. On the other hand, the thrust generation reduces as the
4
5 656 altitude increases. In our case, a plateau is reached between 3 and 6 km. This behavior could
6
7 657 result from the antagonistic interaction of the low temperature and pressure on the ionic
8
9 658 mobility. The previous phenomena cause the effectiveness to decrease with rising altitude, but
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11 659 a plateau is reached at 3 km.

12 660 Although the results suggest a less effective EAD thruster at higher altitudes, the effect of
13
14 661 the low density on the drag of the electrodes and of the carrying vehicle must also be considered.
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16 662 For this purpose, we estimated the maximum freestream velocity that the thruster could achieve
17
18 663 in altitude. It corresponds to the balance of the EAD force and drag force of the thruster in
19
20 664 moving air in a co-flow configuration. Our calculations suggest that the maximum achievable
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22 665 velocity decreases slightly up to 3 km, but that a plateau also exists for this parameter at higher
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24 666 altitudes.

25
26 667 The present study was limited to a single-stage wire-to-cylinder thruster. As the technology
27
28 668 advances toward full-scale application, future work will need to address more complex
29
30 669 scenarios, including interactions between installation effects, the impact of flight velocity,
31
32 670 variations in other environmental conditions, and the interactions between multiple stages.
33
34 671 These efforts are crucial to ensure the technology's readiness for practical deployment.

35
36 672 Acknowledgments
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38

39
40 673 This project is funded by the French public agency Agence National de Recherche under
41
42 674 reference ANR PROPULSION (ANR-20-ASTC-0029).
43
44 675 ORCID IDs
45
46 676 Sylvain Grosse https://orcid.org/0000-0002-0365-1357
47 677 Nicolas Benard https://orcid.org/0000-0001-8822-8525
48
49 678 Eric Moreau https://orcid.org/0000-0002-8492-5494
50
51 679 References
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60 685 [3] Gomez-Vega N and Barrett S R H 2024 Order-of-Magnitude Improvement in
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PRODUCED BY SUB-MILLIMETER CORONA DISCHARGE 2018 Solid-State,

Actuators, and Microsystems Workshop Technical Digest 2018 Solid-State, Actuators,

and Microsystems Workshop (Hilton Head, South Carolina, USA: Transducer Research

Foundation) pp 67–70

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[31] Benard N, Balcon N and Moreau E 2008 Electric Wind Produced by a Single Dielectric

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Lasers Conference (Seattle, Washington: American Institute of Aeronautics and

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Astronautics)

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[33] Defoort É 2020 *Écoulement électro-aérodynamique d'un aérosol de gouttelettes d'eau*

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dans un réacteur de type pointe-plaque en vue de la récupération de composés

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chimiques PhD Thesis (Poitiers, France: Université de Poitiers)
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