Xueguang Ren

Tsveta Miteva

Přemysl Kolorenč

Kirill Gokhberg

Alexander Kuleff

Lorenz S Cederbaum

Alexander Dorn

Observation of fast and slow interatomic Coulombic decay in argon dimers induced by electron-impact ionization

INTRODUCTION

Electron-collision induced processes are of great importance in a variety of applications [1], including plasma physics, astrophysics and atmospheric science, and more recently medical radiation therapy, in which the secondary low-energy electrons produced by primary ionizing radiation can lead to significant damages to biological tissue [2][3][4].

In weakly-bound systems, e.g. in van-der-Waals clusters, due to the presence of the neighboring atoms, new electronic decay channels such as Interatomic Coulombic Decay (ICD) can be opened [5]. Here internal excitation energy of one electronically excited constituent is transferred to a neighbor ionizing it which results in a low-energy electron and a pair of energetic ions. Studies of ICD have attracted a great deal of attention due to its potential role as an efficient source of low-energy electrons. The first successful experiments on ICD have been performed using photoionization of neon clusters [6] and neon dimers [7]. Since then, extensive studies of ICD in van-der-Waals clusters and hydrogen bonded systems have been carried out by photoabsorption experiments (see e.g. [8][9][10][11][12][13][14][15][16][17][18][19][20]). Experiments of ICD induced by energetic particles like ions and electrons have also been performed mostly in rare gas dimers [21][START_REF] Kim | Proc. Natl. Acad. Sci[END_REF][START_REF] Grieves | [END_REF][24][25][26].

For the argon dimer (Ar 2 ), two different interatomic relaxation mechanisms, ICD and radiative charge transfer (RCT), have been identified in recent electron-impact [26] and photoabsorption [20] experiments in which the kinetic energies of all the final-state electrons and ions were measured in coincidence. Both ICD and RCT channels can end up in the repulsive Ar + + Ar + fragmentation channel. In RCT, as shown schematically by the potential energy curve diagram in Fig. 1 (a), an argon atom, which is doubly ionized by electron-impact, receives an electron from a neutral neighbor and emits a photon. The rate of this radiative charge transfer process is rather low at the equilibrium internuclear distance (R eq ) but is strongly increasing for decreasing R. As result nuclear motion in the intermediate state is enabled and the transition preferentially takes place at shorter R.

A recent ab initio calculation by Miteva et al. [27] has predicted two types of ICD channels in Ar 2 referred to as fast and slow ICD, where nuclear dynamics are strongly involved in the slow ICD process. These are shown schematically in Fig. 1 electrons and argon dimer. The potential energy curves were adapted from [27,28] .

Ar-Ar + * (3p -2 ( 1 D)4d 2 S) initial state [20].

In the present work, we aim to identify the fast and slow ICD process in Ar 2 induced by electron-impact ionization. The ICD electron energy and the kinetic energy release (KER)

for Ar + + Ar + fragment ions are measured in the experiment. From the measurements we determine the ICD initial state energies and analyze the projectile energy loss spectra which allow us to identify the fast and slow ICD channels in Ar 2 and, thus, to study in detail the effect of nuclear dynamics on ICD. Ab initio calculations for the fast ICD channel are compared with the experimental data. Our experiments were carried out at the projectile energy of 90 eV which is close to the mean energy for secondary electrons produced by ionizing radiation e.g. in water [2]. Thus, in general the present experiment can simulate the subsequent effects of secondary electrons in weakly-bonded condensed systems.

II. EXPERIMENTAL METHOD

The experiment was performed using a reaction microscope specially designed to perform electron collision experiments [29,30]. Details of the experimental setup were described before [26]. Briefly, a pulsed electron beam is crossed with an argon gas jet produced by supersonic expansion. The gas jet consists of ∼98% Ar, ∼1.5% Ar 2 and ∼0.5% Ar n (n ≥

3). The pulsed electron beam is emitted from an electron gun consisting of a tantalum photocathode which is irradiated by a pulsed ultraviolet laser beam (λ = 266 nm, ∆t < 0.5 ns). Charged collisional products (electrons as well as ions) are extracted by means of a homogeneous electric field 0.9 V/cm and magnetic field (6.9 Gauss) and projected onto two position-and time-sensitive multi-hit detectors. The electron detector is centered on the projectile beam axis about 30 cm behind the target jet.

The solid angle of acceptance for detection of electrons from 2 eV up to the energy of 15 eV is almost 4π. Energies below 2 eV, and for higher energies small forward and backwards angles are excluded due to the presence of a primary beam dump in the center of the electron detector. Above 15 eV the angular acceptance is gradually decreasing until at ∼60 eV all electrons emitted transversal or backwards with respect to the projectile beam direction do not reach the electron detector anymore. On the other hand the faster projectiles are predominantly scattered to forward directions and in the present experiment they are detected within a range of scattering angles between θ = 2 • and 20 • . Therefore, projectile energy loss spectra can be easily recorded. In other cases we compare electron spectra for monomers and dimers which are obtained in the same experimental run and with identical detection efficiency. As result the finite angular acceptance does not affect the conclusions drawn from the data obtained in this work.

Experimental data for argon dimers were obtained using an electron-ion-ion triplecoincidence method where one of the final-state electrons is detected in coincidence with two Ar + ions. For comparison, ionization of the argon monomers was measured simultaneously using the electron-ion double-coincidence method. The momentum vectors of the emitted electrons and ions are determined from the impact positions on the detectors and the corresponding times-of-flight. Ions originating from a Coulomb explosion have rather high momentum which require high electric fields for efficient detection. Therefore, after 400 ns when the electrons have reached the detector the electric field is ramped up to 20 V/cm for extraction of the ions. An important step in the offline data analysis is to separate dimer reactions from random Ar + /Ar + coincidences and from contributions from larger clusters.

Therefore, dimer Coulomb explosions are identified by two energetic Ar + ions with equal but opposite momenta such that their sum momentum is close to zero and their sum kinetic energy is clearly beyond thermal energies in the few eV range. Larger clusters undergoing

Coulomb explosion partially dissociate into ion pairs with a heavier ion like Ar + 2 + Ar + which can be easily separated. Most others dissociating into two Ar + ions and neutrals can be identified if some momentum is carried by the undetected neutrals and, thus, the ions do not show the required momentum sum close to zero. Nevertheless, it is not possible to completely exclude such events in case the neutrals do not obtain significant momentum.

In the measurements, we obtain the kinetic energies for final-state electrons and ions from the ICD and RCT reactions in Ar 2 as presented in Fig. 1 and also in Eqs. ( 1) and ( 2): The total KER spectrum is presented Fig. 2 (a) where the emitted electron energy is integrated from 0 to 60 eV. It shows a double peak structure in which the peak at 3.8 eV is mainly attributed to the fast ICD channel while the slow ICD and RCT channels contribute dominantly to the peak at 5.2 eV. As seen in Fig. 1 (b),(c) and in Eq. ( 1), ICD in Ar 2 relies on the population of satellite states Ar + * (3p -2 nl). In the fast ICD channel the dimer is excited to the lower-lying Ar-Ar + * states with ICD lifetimes shorter than the corresponding vibrational periods [27]. Consequently, nuclear motion is negligible and the system quickly decays at R eq which produces the lower KER peak at about 3.8 eV. For the slow ICD channel the system is excited to the higher-lying Ar-Ar + * states with ICD lifetimes longer than the vibrational periods. Nuclear motion can take place, resulting in ICD preferentially occurring at shorter R and forming the KER peak at about 5.2 eV.

e -+ Ar 2 → Ar -Ar + * (3p -2 nl) + 2e - ICD --→ Ar + + Ar + + e ICD + 2e - (1) e -+ Ar 2 → Ar -Ar ++ (3p -2 ) + 3e - RCT ---→ Ar + + Ar + + hν + 3e - (2)
In Fig. 2 (b), the faster electrons (> 30 eV) are generally identified with the scattered projectiles. One can determine the projectile energy loss (E loss ) by the incident electron energy (E 0 ) minus the energy of the scattered projectile. Fig. 2 (c) shows the E loss spectra for the Ar + + Ar + channels at different KER regions. Also included in Fig. 2 (c decay channels, respectively. This demonstrates that populating lower satellites does not contribute to the high KER peak.

The emitted slow electrons (< 30 eV) in Fig. 2 (b) originate from both, the direct ionization in the collision and the ICD processes. ICD in rare gas dimers usually manifests itself through the energy-correlation between the ICD electron and the fragment ions. Such a correlation diagonal is not clearly observable in Fig. 2 (b) since it contains strong background from slow electrons produced in the direct ionization process. In order to reveal the ICD signature we subtract the slow ejected electron signal. It is obtained from the measurement of ionized electron energy spectrum of Ar monomers which is simultaneously recorded with Ar 2 . Since ICD is absent for monomers, it can be considered as a reference to determine the continuous electron energy distribution due to the ejection of bound electrons from the target induced by direct electron-impact ionization.

The emitted electron energy spectra for Ar monomers and dimers are presented in Fig. 3 where the results for Ar 2 are integrated over the KER range from 2.5 eV to 4.6 eV (fast ICD) for (a) and from 4.6 eV to 6.5 eV (slow ICD) for (b). Additionally, in Fig. 3 (a) the spectra for Ar monomers are presented both for single ionization (e -/Ar + ) and for double ionization (e -/Ar ++ ). It can be seen that the shapes of the ionized slow electron energy distributions (< 30 eV) are quite similar between Ar + and Ar ++ in the present experiment.

A closer examination shows that the electron energy distribution for dimers in the higher energy region (> 15 eV) is better represented by the monomer double ionization spectrum (e -/Ar ++ ). Therefore, we consider the electron energy spectrum for Ar ++ as a reference to subtract the slow electron contributions due to direct ionization. The spectra for Ar monomers and dimers are normalized to each other in the energy range from 12 eV to 25

eV where the ICD process does not contribute [20,26,27]. As can be clearly seen in the background-subtracted electron energy spectra in Fig. 3 (c) and (d) for dimers (e -/Ar + /Ar + ) the low-energy electron production (< 10 eV) is enhanced due to the presence of the ICD processes.

Since the RCT process relies on double ionization of one atom in a dimer (see Fig. 1 (a))

the number of emitted electrons and the electron energy spectrum is essentially identical as for double ionization of Ar monomers. The subtraction procedure removes not only the background of directly ionized slow electrons from single ionization but also from double ionization and as result no signature of the RCT process is left. Thus, after subtracting the properly scaled monomer spectrum from the total electron energy spectrum of Ar 2 in Fig. 2 (b) the pure ICD electron spectrum is obtained and presented in Fig. 4 literature values of the satellite states energies of Ar measured by electron-impact (E 0 = 500 eV) [31] and photoabsorption (hν = 82 eV) [32] experiments. The peak intensities are free fitting parameters. A total of nine peaks are obtained in Fig. 4 (b). The assignment of the lines and the relative intensities are listed in Table I.

Furthermore, the fast and slow interatomic decay processes can be identified by the measurements of the E ini ICD and the E loss of ICD in Ar 2 . As shown in Fig. 2 (c), the minimum E loss of 35.6 eV and 38.8 eV are obtained for KER ∼ 3.8 eV and ∼ 5.2 eV channels, respectively. This means that we could extract the fast ICD channel (KER ∼ 3.8 eV) by selecting an energy region of ICD initial state E ini ICD from 35.6 eV to 38.8 eV, i.e. in between the two diagonal lines of (1) and (2) in Fig. 4 (a). This belongs to the lower-lying satellite states and corresponds to peaks (1)-(3) in Fig. 4 (b) and Table I. In order to separate the slow decay channel an energy region of 38.8 eV < E ini ICD < 45 eV is selected, i.e. the region in between the two diagonal lines of ( 2) and (4) in Fig. 4 (a), which corresponds to the higher-lying satellite states. The different KER and ICD electron energy spectra for the fast and slow decay processes are obtained and presented in Fig. 5.

As can be seen in Fig. 5 (a) for the fast decay channel the resulting KER spectrum shows essentially a single peak at 3.8 eV. The KER spectrum contains information about the internuclear distances at which ICD takes place and is, therefore, sensitive to the ratio of the electronic decay lifetime to the vibrational period. The peak at KER = 3.8 eV corresponds to the fast decay at R being close to R eq (3.8 Å) with negligible nuclear motion.

The measured electron energy spectrum for the fast ICD channel is presented in Fig. It can be seen in Fig. 5 (a) and (c) that rather good agreement between experiment and calculations is achieved for the fast ICD channel in Ar 2 .

For the slow ICD channel, the KER distribution is presented in Fig. 5 (b) which exhibits a pronounced peak at 5.2 eV and a second peak (or an extended intensity) ranging down to 3.5 eV. Here, the decay occurs with a high probability at R near the inner turning point of the potential energy curve, see in Fig. 1 (c). Due to the population of the higher-lying ICD initial states for this decay channel higher ICD electron energies are observed and presented in Fig. 5 (d) which shows a relatively broad distribution with a tail at the high energy side.

According to the features of KER distribution in the 2D map of Fig. 4 (a) we can further separate the slow ICD process into two groups at E ini ICD = 41.8 eV corresponding to the diagonal line (3) in Fig. 4 (a). One group (S1) belongs to the energy region of 38.8 eV < E ini ICD < 41.8 eV, i.e. peaks ( 4) and ( 5) in Fig. 4 (b) (see also Table I). As can be seen in Fig. 5 (b), the measured KER spectrum for S1 shows two peaks at roughly 3.8 eV and 5.2 eV with relatively higher intensity for the larger KER peak. This result is consistent with the recent measurement of photon induced ICD in Ar 2 by Rist et al. in which the separate KER spectrum is obtained for the Ar-Ar + * (3p -2 ( 1 D)4d 2 S) state [20]. The other group of the slow ICD process (S2) corresponds to a energy region of 41.8 eV < E ini ICD < 45 eV which belongs to a series of satellite states of Ar + * (3p -2 nl) with nl = 5d, 6d, 7d, 8d, etc. [31,32].

The obtained KER spectrum for S2 shows a major peak at roughly 5.4 eV and an extended lower intensity down to 3.5 eV. The differences in the KER spectra between two groups of slow ICD processes are attributed to the different lifetime and nuclear dynamics of the decay channels.

IV. CONCLUSIONS

In conclusion, we have reported on a combined experimental and theoretical study of ICD induced by electron-impact ionization (E 0 = 90 eV) in argon dimers. In the experiment, the kinetic energies of one emitted electron and two Ar + ions are measured in coincidence.

The relatively higher projectile energy compared to our previous study [26] (E 0 = 67 eV) allows for a better separation of predominantly fast scattered projectile and slow secondary electrons. From the measurements we obtain the projectile energy loss spectra, the corre-lation diagram between the kinetic energy of ICD electron and that of the fragment ions, and moreover the energies and the populations of ICD initial states. These results allow us to identify the fast and slow ICD channels and to extract the corresponding KER and ICD electron energy distributions. The fast ICD states produce a lower KER peak at ∼ 3.8 eV corresponding to the decay at R eq . Since these states lie low in energy and their decay is nearly unaffected by nuclear dynamics, they produce a peak at ∼ 2 eV in the ICD electron spectrum. The measured KER and ICD electron energy spectra for the fast ICD channel are well reproduced by the ab initio calculations [27]. By contrast, for the slow decay channel we observe the relatively higher ICD electron energies, and the KER distributions show strong influence of nuclear motion with a second strong peak appearing at KER ∼ 5.2 eV.

Furthermore, we showed that electron-collision induced processes in argon dimers with projectile energy below 100 eV cause an additional enhancement of the low-energy (< 10 eV) electron production. This mechanism could generally be extended to biologically relevant condensed systems. We can control the energy of emitted low-energy electrons by choosing the ICD initial states at which the decay process occurs. This result suggests that the observed decay processes may have a significant influence on the radiation damage of biological tissues.

  (b) and (c), respectively, and will be discussed below in detail. The recent photoabsorption experiment in Ar 2 by Rist et al. examined and confirmed the effect of nuclear dynamics on ICD for the single

FIG. 1 .

 1 FIG. 1. Illustration of RCT (a), fast ICD (b) and slow ICD (c) processes in collisions between

Fig. 2 (

 2 Fig. 2 (b) shows the correlation diagram between the kinetic energy of one emitted electron and the KER for a pair of Ar + ions detected in coincidence. The electron spectrum includes scattered projectiles, directly ionized electrons and low-energy ICD electrons (< 10 eV), as described in Eqs. (1) and (2).

  FIG. 2. (a) Total KER distribution for Ar + + Ar + fragment ions; (b) Measured correlation map between emitted electron energy and KER; (c) Projectile energy loss spectra for the double ionization of Ar monomer (Ar ++ ) and for the Ar + + Ar + fragmentation channels of Ar 2 at different KER regions.

FIG. 3 .

 3 FIG. 3.Top row: the ionized electron energy spectra for Ar monomer and dimer measured in e -/Ar + (dash-dotted line) and e -/Ar ++ (solid line) double-coincidence for monomer and in e -/Ar + /Ar + triple-coincidence (open circles) for dimer. All spectra for monomers and dimers were normalized to each other in the energy range from 12 eV to 25 eV; Bottom row: the backgroundsubtracted spectra obtained by subtracting the spectra of Ar (e -/Ar ++ ) from Ar 2 (e -/Ar + /Ar + ).The data are summed over the KER range from 2.5 eV to 4.6 eV (left column) and from 4.6 eV to 6.5 eV (right column).

9 FIG. 4 .

 94 FIG. 4. (a) Correlation map between ICD electron energy and KER; (b) Measured ICD initial state energy spectrum. The dashed lines are fitted Gaussian peaks corresponding to different states and the solid lines are the sum of the fits.

  5 (c) which shows a peak at E ICD ∼ 2 eV. The obtained KER and ICD electron energy spectra for the fast ICD processes are compared with the results of ab initio calculations by Miteva et al.[27]. The calculated KER and ICD electron energy spectra for the ( 1 S)4s 2 S, ( 1 D)3d 2 D and ( 1 D)3d 2 S states are considered with the relative ratio of 1:15:8 to simulate the fast decay processes in Ar 2 . Here, the intensity ratio is taken from the fitting procedure in Fig.4(b).

  FIG. 5. Measured KER (top row) and ICD electron energy (bottom row) spectra for the separate fast (left column) and slow ICD (right column) processes. The curves are ab initio calculations for the fast ICD processes.

TABLE I .

 I ICD initial state intensities of Ar-Ar + * (3p -2 nl) extracted from Fig. 4 (b).

	Peak	Measured	Intensity	State
		E ini ICD (eV)		assignment
	1	36.5	1.0	3p -2 ( 1 S)4s 2 S
	2	37.2	15.0	3p -2 ( 1 D)4p 2 P
				3p -2 ( 1 D)3d 2 D
	3	38.6	8.0	3p -2 ( 1 D)3d 2 S
	4	39.6	9.0	3p -2 ( 1 S)4p 2 P
				3p -2 ( 3 P)4d 2 D
	5	41.2	11.0	3p -2 ( 1 D)4d 2 S
	6	42.6	7.2	3p -2 ( 1 D)5d 2 S
	7	43.4	2.0	3p -2 ( 1 D)6d 2 S
	8	44.0	1.2	3p -2 ( 1 D)7d, 8d 2 S
	9	45.0	1.5	Rydberg series

ACKNOWLEDGMENTS X. R. is grateful for support from DFG Project No. RE 2966/3-1. T. M. acknowledges financial support by the Research Executive Agency (REA) under the European Union's Horizon 2020 research and innovation program Grant agreement No. 705515. K.G. gratefully acknowledges the financial help of the Deutsche Forschungsgemeinschaft (FOR 1789).


Direct thrust measurements of an Electron Cyclotron

I. Introduction

LECTRODELESS plasma thrusters are an alternative technology to the well-known Gridded Ion Engines and Hall Thrusters. The advantage of the concept is the quasi-neutrality of the plasma that is expelled: there is no need for a neutralization cathode, which is one of the most fragile components in ion and hall thrusters, and which are very sensitive to impurities in the propellant. This leads to a potentially higher reliability, longer lifetime, and lower development and recurring costs for electrodeless thrusters. But the complexity of the underlying physics involved is so far limiting the development of this technology. One of the main difficulties is to model with enough precision all the mechanisms occurring simultaneously in the thruster such as ionization and plasma acceleration.

The main electrodeless technologies that are currently being developed are the Helicon Plasma Thruster (HPT), the Electron Cyclotron Resonance (ECR) plasma thruster, and the Variable Specific Impulse Magnetoplasma Rocket (VASIMR) which is a combination of a Helicon and an ICR (Ion Cyclotron Resonance) plasma [START_REF] Charles | Plasmas for Spacecraft Propulsion[END_REF]. HPT and ECR thrusters use radio-frequency electromagnetic waves as power sources to heat electrons and an electron-driven magnetic nozzle to accelerate the plasma out of the chamber, whereas VASIMR relies on ion heating in an ICR source and ion acceleration in a magnetic nozzle. The HPT uses the wave-plasma coupling obtained by the propagation of Helicon waves (low frequency whistler waves [START_REF] Chen | Physics of Helicon Discharges[END_REF]) in cold magnetized plasma. On the other hand, the ECR plasma thruster uses the resonant absorption [START_REF] Geller | Electron Cyclotron Resonance Ion Sources and ECR Plasmas[END_REF] of microwave power (frequency of several GHz) by the electrons in a magnetized plasma in order to produce and maintain the discharge. For both technologies, the E mechanisms that occur in the magnetic nozzle, i.e. ion acceleration and plasma detachment, are not fully understood and are still active fields of research [START_REF] Arefiev | Ambipolar Acceleration of Ions in a Magnetic Nozzle[END_REF].

ECR plasma thrusters have been studied since the 60s [START_REF] Kosmahl | Plasma Acceleration with Microwaves near Cyclotron Resonance[END_REF]. In the middle of the 90s, Sercel performed a study on an ECR engine where the microwaves are launched in the plasma source from a cylindrical waveguide [START_REF] Sercel | Electron-Cyclotron-Resonance (ECR) Plasma Acceleration[END_REF]. Stallard and Hooper, also studied these technologies and developed a prototype based on a bi-helical antenna [START_REF] Stallard | Plasma Confinement in the Whistler Wave Plasma Thruster[END_REF][START_REF] Stallard | Whistler-Driven, Electron-Cyclotron-Resonance-Heated Thruster: Experimental Status[END_REF]. The interest into these technologies was hampered by the low efficiency of the microwave generators available at the time, and the poor vacuum conditions of the experiments (often much larger than 5 10  mbar), due to the high power and to the high mass-flow rate. Indeed it is now known that an electric thruster must be operated in a good vacuum (less than -5

10 mbar) to show good performances [9,10].

Since 2010, the ECR plasma thruster technology is re-investigated and a new coaxial design has been proposed [START_REF] Onera | [END_REF]. At the current development stage, the power range (< 50 W) and the thrust range (100 µN to 1 mN) are compatible with the rising nanosat market, whose requirements are not well covered by commercially available technologies.

Previous works on ECR plasma thruster led to a better understanding of the technology [START_REF] Lafleur | Electron Dynamics and Ion Acceleration in Expanding-Plasma Thrusters[END_REF][START_REF] Jarrige | Characterization of a Coaxial ECR Plasma Thruster[END_REF]. An analytical discharge model of a helicon source [START_REF] Lafleur | Helicon plasma thruster discharge model[END_REF] has been adapted to the ECR thruster, and has helped to understand the physical mechanisms at play [START_REF] Cannat | Optimization of a Coaxial Electron Cyclotron Resonance Plasma Thruster with an Analytical Model[END_REF]. Experimental parametric studies have shown that the thruster performances are very sensitive to the operating conditions; the mass-flow rate, the injected power and the magnetic field magnitude have a significant effect on the ion energy and the mass efficiency. It has also been shown that the ion energy to electron temperature ratio, e i T E / , is constant for a given magnetic field magnitude (about 4-5). This enables the use, in certain conditions, of a polytropic expansion law to model electron cooling and ion acceleration in the magnetic nozzle [START_REF] Little | Electron Cooling in a Magnetically Expanding Plasma[END_REF][START_REF] Zhan | Thermodynamic Study on Plasma Expansion along a Divergent Magnetic Field[END_REF]. More recently, electron temperatures up to 35 eV have been measured in the source using a diamagnetic loop diagnostic, and the electron cooling has been observed in the expansion region [START_REF] Correyero | Measurement of Anisotropic Plasma Properties along the Magnetic Nozzle Expansion of an Electron Cyclotron Resonance Thruster[END_REF].

The thruster efficiency has been measured at 16% with a thrust level of 1 mN using electrostatic probe measurements [START_REF] Jarrige | Measurement of Ion Acceleration in the Magnetic Nozzle of an ECR Plasma Thruster[END_REF][START_REF] Cannat | Experimental Geometry Investigation of a Coaxial ECR Plasma Thruster[END_REF]. However, the interpretation of these measurements are difficult in magnetic nozzle plumes because of the high ion energy, the high electron temperatures, the large magnetic field (several hundreds of Gauss), which can lead to a dramatic error on the estimation of the performances. On the other hand, thrust balances, when properly designed and used, are a reliable and fast method to measure thrust, allowing complete parametric studies.

Moreover, thrust balances are the industry standard [START_REF] Polk | Recommended Practice for Thrust Measurement in Electric Propulsion Testing[END_REF].

In this paper the ECR plasma thruster is tested on a pendulum thrust balance that has been previously developed for a helicon thruster [START_REF] Pavarin | Thruster Development Set-up for the Helicon Plasma Hydrazine Combined Micro Research Project (HPH.com)[END_REF] at ONERA's facility. A similar thrust stand was selected by ESA and CNES to characterize cold gas micronewton thrusters for scientific mission such as GAIA, LISA-PATHFINDER, MICROSCOPE and EUCLID [START_REF] Jarrige | Thrust Measurements of the Gaia Mission Flight-Model Cold Gas Thruster[END_REF].

In the last few years several direct thrust measurements have been performed on HPT. Takahashi and Lafleur have used a double pendulum balance with a laser displacement sensor [START_REF] Takahashi | Direct Thrust Measurement of a Permanent Magnet Helicon Double Layer Thruster[END_REF][START_REF] Lafleur | Direct Thrust Measurement and Modeling of Radio-Frequency Expanding Plasma Thruster[END_REF]. They were able to measure thrusts up to 4 mN for powers up to 700 W. Nakamura used a torsional thrust balance with a laser displacement sensor, reaching 650 µN at 400 W [START_REF] Nakamura | Direct Measurement of Electromagnetic Thrust of Electrodeless Helicon Plasma Thruster Using Magnetic Nozzle[END_REF]. In this last work, they were able to discriminate the origin (magnetic or thermal, more detail in the next section) of the thrust. This paper presents the first direct thrust measurements of an ECR plasma thruster with a magnetic nozzle.

Section II presents the ECR thruster technology, along with the thrust balance and the measurement procedure. A parametric study on mass flow-rate and power and the effect of insulating/conducting walls are shown in section III.

Finally, the direct thrust measurements are compared with electrostatic plume diagnostics in section IV.

II. Apparatus and Methods

A. Description of the thruster technology and prototypes

The principle of the ECR plasma thruster is described in detail in [START_REF] Onera | [END_REF] and [START_REF] Jarrige | Characterization of a Coaxial ECR Plasma Thruster[END_REF]. The thruster consists of a 27 mm diameter and 15 mm long semi-open coaxial plasma source (Fig. 1) in which a propulsive gas is injected and microwave power is fed. The source is immersed in a magnetic field created either by a coil or a permanent magnet.

In the regions where the cyclotron frequency, which depends on the applied magnetic field, matches the frequency of the injected microwaves (e.g. 875 G for a microwave frequency of 2.45 GHz), the free electrons from the plasma are heated by the electron cyclotron resonance effect, and absorb the microwave power. The electron temperature is increased up to a few tens of eV [START_REF] Correyero | Measurement of Anisotropic Plasma Properties along the Magnetic Nozzle Expansion of an Electron Cyclotron Resonance Thruster[END_REF], and the electrons ionize the propellant gas by inelastic collisions. The energetic electrons are expelled at the open side of the cavity (exhaust) by two main processes: plasma expansion (driven by the electron pressure) and diamagnetic effects in the divergent magnetic field [START_REF] Lafleur | Direct Thrust Measurement and Modeling of Radio-Frequency Expanding Plasma Thruster[END_REF][START_REF] Correyero | Plume Properties Measurement of an Electron Cyclotron Resonance Accelerator[END_REF][START_REF] Takahashi | Effect of Magnetic and Physical Nozzles on Plasma Thruster Performance[END_REF][START_REF] Ahedo | On Plasma Detachment in Propulsive Magnetic Nozzles[END_REF][START_REF] Ahedo | Two-Dimensional Supersonic Plasma Acceleration in a Magnetic Nozzle[END_REF][START_REF] Longmier | Ambipolar Ion Acceleration in an Expanding Magnetic Nozzle[END_REF]. The difference of mobility between the ions and the electrons creates an ambipolar electric field that maintains the quasi-neutrality of the current-free plasma beam and accelerates the ions. Finally, the electrons detach themselves from the magnetic field lines in the far field in order to produce a net momentum gain. Plasma detachment is still an open question and several mechanisms have been proposed [START_REF] Ahedo | On Plasma Detachment in Propulsive Magnetic Nozzles[END_REF]. The results presented in this paper were obtained with a permanent magnet prototype of the ECR thruster (Fig. 2). The coil version that has been extensively characterized in the previous papers [START_REF] Cannat | Optimization of a Coaxial Electron Cyclotron Resonance Plasma Thruster with an Analytical Model[END_REF] is not appropriate for a direct measurement on a thrust balance due to the weight of the magnetic circuit and the stiffness of the cables used to The ECR zone, i.e. the zone where the magnetic field magnitude is around

) ( 4 . 357 ) ( GHz f G B ECR  
(colored zone in Fig. 3), can be moved inside the cavity by adjusting the distance between the source and the magnet. All the results presented in this paper are obtained with the ECR zone between 0.5 and 1 mm from the backplate.

The thruster is electrically isolated from the facility ground with a DC-Block, so the plume is current-free. The thruster source is floating at the thruster potential, which depends on the electron temperature in the source and is directly proportional to the ion mean energy, as shown in [START_REF] Lafleur | Electron Dynamics and Ion Acceleration in Expanding-Plasma Thrusters[END_REF].

The inner conductor (the antenna) is a 1.7 mm cylinder made of nonmagnetic stainless steel. All the other metallic parts of the thruster are made of aluminum alloy. In some experiments (see Section III.C), the inner part of the external cylinder is covered by polyimide tape in order to electrically insulate the thruster from the plasma. For this new prototype, an experimental investigation on the influence of the parameters has been performed in order to find the optimal operating conditions.

The ECR-PM-V1 prototype is typically operated with microwave input powers in the range 20-60 W, and with xenon mass-flow rates in the range 0.05-0.2 mg/s.

The microwave generator is a combination of a commercial signal generator (Kuhne KUSG245) and an amplifier (KUPA 2325E). It can deliver power from 0 W to 100 W, with an adjustable frequency from 2.3 GHz to 2.6 GHz. The mass flow rate is controlled with a Bronkhorst "EL-FLOW" regulator (1 mg/s full range) calibrated for xenon.

All the results presented in this paper are obtained with a microwave frequency of 2.45GHz. The experiments are performed in the 4 m long and 1 m in diameter, B61 vacuum chamber at ONERA Palaiseau center. The secondary pumping is ensured by a "Pfeiffer TPH2200" turbo-molecular pump (1 000 l/s for xenon) and a cryogenic system (7 000 l/s for xenon). The base pressure is about 10 -7 mbar. The pressure is measured by a MKS999 Quattro vacuum transducer and is typically about

B. Balance Principle

The pendulum thrust balance is a vertical pendulum balance with a quasi-frictionless pivot. The thruster is mounted at the end of the arm (Fig. 4).

Fig. 4 Schematic of the thrust balance.

When the thruster is operated, the produced thrust creates a torque on the arm. At the steady state, the torques of the thrust and of the arm weight cancel each other (Fig. 5). One can obtain an expression for the thrust, using the equation of the equilibrium of the torques:

) sin( T G L L Mg T  (1)

Fig. 5 Principle of the pendulum balance.

The absolute value of the thrust is directly proportional to the sine of the angle. Two different types of sensors are placed on the pendulum: a Honeywell QA 700 accelerometer, which is used to assess the initial verticality of the arm (without thrust), and a FOGALE MC900 capacitive sensor, which is used to measure the displacement because of its higher signal-to-noise ratio.

In order to adjust the horizontality for the initial tuning of the balance, another accelerometer is placed on the static part of the balance.

One can estimate the order of magnitude of the tilt angle from the eq. ( 1). Taking T=1 mN, M=1 kg (mass of the thruster and the pendulum arm) and 𝐿 𝑇 = 3𝐿 𝐺 , the angle would be 𝜃 = 0.02° (∼ 0.1 mm of displacement). The capacitive sensor must then have a resolution high enough to detect the small displacement of the arm. Experiments with a similar balance [START_REF] Jarrige | Measurement of Ion Acceleration in the Magnetic Nozzle of an ECR Plasma Thruster[END_REF] have shown that non-linearity and hysteresis effects can appear when the arm is moving, due to the pivot or cables attached. The balance has been modified with a PID loop to be operated in "null mode", where the arm is kept vertical while the thrust is applied. The same method has recently been used by Kakami [START_REF] Kakami | A Method for Evaluating the Thrust of a Space Propulsion Device with Wide Range Time Variations Using a Disturbance Observer[END_REF].

C. PID control system

A PID (Proportional, Integrator, Derivator) control system (shown in Fig. 6) is added in order to keep the balance arm at its equilibrium position. The signal from the capacitive sensor is fed to the analog PID controller (SRS SIM960). The output signal (correction of the controller) is sent to a planar coil actuator that is placed near a permanent magnet which is attached on the arm. When the voltage from the PID is applied to the coil, the resulting magnetic field interacts with the permanent magnet and produces a force that can move the arm or, in the present case, prevent it to move.

The output voltage from the PID controller is theoretically proportional to the torque applied on the arm. With a proper calibration, the PID output signal can be used as a thrust signal. The parameters of the PID controller (proportional gain 𝐾 𝑝 , derivative coefficient 𝐾 𝑑 and integral coefficient 𝐾 𝑖 ) have been adjusted in order to obtain a reasonable time response, while limiting the overshoot, the number of oscillations and the static error. The setpoint of the controller is set at 0 V (capacitive sensor), corresponding to the value at rest. The response of the PID control to a step of thrust is shown in Fig. 7. A signal generator (in Fig. 6) plugged on a SRS SIM980 "Summing Amplifier" is used to apply a step signal to the actuator (Coil) in order to simulate a step of thrust. With the settings used for the PID controller, the time response of the regulation is about 5 s, which is short enough for the post-processing. The PID signal on Fig. 7 is post-processed with a centered (0.4 Hz) moving average, which is a non-causal low-pass filter. This is why the post-processed PID signal starts rising slightly before the step of simulated thrust. The post-processing methods of the signals are more detailed in section E.

D. Thrust Calibration

The PID output signal obtained during the acquisition is converted into an absolute thrust value through a calibration method, where small masses are successively deposited on a calibration arm with a vacuum-rated translation stage. The purpose of this operation is to obtain the value of the calibration coefficient and to verify the linearity of the balance response over the whole thrust range (see [START_REF] Jarrige | Thrust Measurements of the Gaia Mission Flight-Model Cold Gas Thruster[END_REF]).

The weights of the calibration masses, g m i , are measured precisely using a Mettler Toledo balance with an accuracy of 0.01 mg. The torque equation for the calibration can be written as:

) ( O g m L L T i c i i   (2)
where L i is the mass position on the calibration arm and L C is the arm length (0.394 ± 2 × 10 -3 m).

The length of the balance arm (L c ), the positions of the calibration masses (L i ) and their weight are known. So, the theoretical value of the "equivalent" thrust (the torque) produced by the calibration masses is determined with a good accuracy using eq. ( 2). The PID signal is measured for each deposited mass, and the calibration factor i  can be deduced (ratio of the PID step signal to the "equivalent" thrust):

i i i T V   (3)
Table 1 lists the different masses, their positions on the calibration arm and the cumulated equivalent thrust yielded. This span of equivalent thrust covers the range of thrust expected with the current version of the ECR thruster. The calibration factor is indeed constant over the thrust range. Then, the mean factor 𝛾 =< 𝛾 𝑖 > will be taken to convert thrust measurements. In this case, the mean calibration factor would be around 2 mV/µN for all the thrust levels. Balance calibration is performed before every series of thrust measurement. It should be noted that the dayto-day repeatability of the calibration coefficient is very good, which strengthens the validity of the method.

E. Signal Acquisition

During the acquisition, the signals of forward power, reflected power, Faraday probe current and PID output (𝑉 𝑃𝐼𝐷 ) are recorded by a National Instrument NIPCI-6281 (16 channel 18 bits, 500 kHz) acquisition board.

Anti-aliasing low-pass Butterworth type filters (SRS SIM965) with a 24 dB/octave slope are used for all channels. The cutoff frequency is set at 20 Hz for the capacitive sensor and at 1 Hz for the other channels. The data acquisition is done at 40 Hz sampling frequency.

The forward and reflected powers are used to calculate the power transmitted in the plasma. They are measured "in-line" with a Werlatone C6187 dual coupler and diode detectors (JFW 50D-052) that are calibrated using a power sensor (Ladybug 478A).

F. Thrust measurement procedure and post-processing Fig. 9 shows a typical acquisition of the PID output signal during a thrust measurement of the ECR thruster. The first peak corresponds to the thruster ignition. The thrust amplitude is quite high because of the injection of a larger mass flow rate during a short period. The operating conditions (mass flowrate and power) are then adjusted, and the properties of the thruster are monitored during its stabilization.

Once the thruster has reached a steady-state regime (after ∼1 minute) the microwave power is turned off. The thrust value is obtained by measuring the step of PID voltage at the plasma extinction. After extinction the thruster is still fed with xenon, and a cold gas thrust is applied to the thruster. The thrust values that are presented in this paper are not corrected for this residual force. Without plasma, the specific impulse in cold gas mode has been measured around 20 s. The fraction of cold gas thrust represents between 2% and 5% of the measured thrust in the mass flowrate range tested here.

Fig. 9 Typical thrust signal during a thrust measurement acquisition.

One of the main requirements to perform a thrust measurement is that the thermal drift on the sensors must be low enough so that the step amplitude can be measured. The dielectric losses in the microwave cables and the charged particles flux on the walls of the plasma source induce a heating of the balance arm and a thermal dilation of the materials. The center of equilibrium of the pendulum is then moved, which produces the drift seen on the thrust signal. No significant effect of the temperature on the calibration coefficient was noticed for this balance. As can be seen in Fig. 9, the thrust step is easily detected despite the thermal drift.

The signals are post-processed in order to have a precise and systematic way to analyze the results. The procedure is as follows: first, a moving average of the data on 100 points (i.e. a bandwidth of 0.4 Hz for an acquisition frequency of 40 Hz) is applied; forward and reflected powers are then combined together to obtain the power transmitted to the thruster; finally, the step of PID signal is converted into thrust using the calibration factor.

G. Electrostatic diagnostics

Another method to evaluate the thruster performances is to calculate the thrust from electrostatic probes measurements.

The thrust 𝑇 can be estimated from the angular profile of the ion current density 𝐽 𝑖 and from the mean ion velocity i v at centerline (assuming that the velocity is uniform over the angular profile, which has been shown in [START_REF] Jarrige | Characterization of a Coaxial ECR Plasma Thruster[END_REF]). Both measurements are performed with a gridded Faraday probe that is described in [START_REF] Lafleur | Electron Dynamics and Ion Acceleration in Expanding-Plasma Thrusters[END_REF]. The expression of the thrust is:

   2 / 2 / 2 ) cos( ) sin( 2 ) (        d v D J e M T i i i (4)
where 𝑀 𝑖 is the ion mass, 𝑒 the elementary charge, 𝐷 the distance between the probe and the axis, and 𝜑 is the angle of rotation of the probe (see Fig. 10).

Eq.( 4) is valid only if the plasma beam is axisymmetric (the probe can move only in a plane) and for singly ionized ions (multi-ionized ions are neglected).

Fig. 10 Schematic of the Faraday probe diagnostic.

A rotation stage makes the Faraday probe rotate around the ECR thruster in order to perform the angular scans (Fig. 10). The probe is placed 26.5 cm (± 0.5 cm) away from the thruster for all the measurements presented here.

The probe consists of a collector and a grid with a collection aperture diameter of 6 mm ± 0.5 mm and a transparency of 70% ± 10%. For the measurement of ion current density (Fig. 11 top), the collector is biased negatively and the current is taken in the ion saturation zone of the IV curve (typically at -300 V). The grid is floating in order to avoid sheath expansion issues. No noticeable differences are observed when the grid is grounded). The collected ion current is measured with a Keithley picoammeter or with a shunt resistor. As can be seen on Fig. 12, the angular profile of ion current density has two distinctive characteristics. First, the profile is not peaked on centerline: two symmetric peaks are observed at -5° and +5°. This could be due to non-homogeneities of the neutral gas injection (the gas is injected through the two holes in the backplate), which creates variations of plasma density in the source and in the plume. Second, there is a residual ion current at 90°. This could be due to the presence of ambient plasma produced by ionizing collisions of neutrals with electrons from the plume.

The mean ion velocity in eq. 4 can be calculated from the mean ion energy:

i i i M E v 2 
The mean ion velocity is measured using the Langmuir characteristics of the Faraday probe [START_REF] Lafleur | Electron Dynamics and Ion Acceleration in Expanding-Plasma Thrusters[END_REF][START_REF] Lafleur | Electrostatic Probe Diagnostics for Electric Propulsion Systems[END_REF]. The mean ion energy is deduced from the first derivative of the current (Fig. 11 bottom). With a single grid probe, this method is not able to determine the full ion energy distribution function with a good accuracy because of the disturbing presence of electrons from the beam and secondary electrons produced at the surface of the grid. However the mean ion energy calculated with this method is trustworthy and has been verified by comparison with a commercial ion energy analyzer. This method enables measuring the total ion energy (which is the sum of ion kinetic energy and ion potential energy) at the probe location with an error of approximatively 3%. Assuming the conservation of total ion energy in the magnetic nozzle, the measured energy value is the kinetic energy that ions would have in a region where the plasma potential is close to zero (i.e. in the far plume). Depending on the real potential drop in the magnetic nozzle, the mean ion velocity can be overestimated.

III. Thrust measurement results

The standard performance indicators for the thruster technologies are reminded here. First, the total efficiency is given by:

P Q T m T 2 2   , ( 5
)
the specific impulse can be expressed as:

g Q T I m SP  , (6)
and the Thrust To Power Ratio is: TTPR=T/P.

𝑄 𝑚 is the input massflow, and 𝑔 = 9.8089 𝑚/𝑠 2 the gravitation force acceleration. In the following, the thrust 𝑇 and these indicators will be used to characterize the performances of the thruster. For all performance indicators that are used in his article, 𝑃 is the microwave power deposited in the plasma, (taking into account the losses in the microwave line between the coupler and the plasma source).

A. Uncertainties of the direct thrust measurement. The measurement uncertainties have been calculated by error propagation of the elementary error sources. The uncertainty on the power deposited in the plasma comes from the measurement of diode detector voltage (which depends on the power level), from the attenuation value in the microwave line, and from the directivity of the coupler that induces a non-linear behavior.

The uncertainty over the thrust 𝑇 is expressed as:

2 2 2 2 2 ) ( T L L L L Vi V mN T i i T T PID                                                   
Concerning uncertainties of the others quantities deduced from the thrust, one has the uncertainty over the specific impulse

SP I : 2 2 2                            m m SP SP Q Q T T I I ,
the uncertainty over the TTPR:

2 2 2                        P P T
T TTPR TTPR , and the uncertainty over the total efficiency

T  : 2 2 2 2 2                                    P P Q Q T T m m T T   .
The relative uncertainties are given with respect to the thrust 𝑇 on Fig. 12.

Fig. 12 Theoretical relative uncertainties of the performance parameters with respect to the thrust

In what follows, all the uncertainties will be visible as error bars on the figures.

B. Parametric study with conducting walls

The Fig. 13 shows the performances of ECR-PM-V1 thruster for different operating conditions. The thrust and the efficiency are presented with respect to the absorbed microwave power for four different xenon mass flowrates: 0.06, 0.08, 0.1 and 0.15 mg/s. At 0.08 mg/s, when the microwave power is increased from 26 W to 50 W, the measured thrust increases from 560 to 680 µN, while the thruster efficiency drops from 7.7% to 5.5%. Generally, the thrust increases with absorbed power and mass flow rate, with a maximum thrust of 960 µN measured at 0.15 mg/s and 51 W. On the other hand, the total efficiency shows no clear trends: for 0.06 mg/s, 0.08 mg/s, and 0.1 mg/s, 𝜂 𝑇 decreases with power, whereas efficiency seems to have an optimum at 0.125 mg/s, and is steadily increased with power at 0.15 mg/s.

Fig. 13 Evolution of thrust (top) and total efficiency (bottom) with the power for five different mass-flow rates.

A convenient way to analyze these results is to plot the performances versus the ratio of the mass flow rate to the absorbed power Q m /P. Fig. 14 presents the 𝐼 𝑆𝑃 as a function of Q m /P ratio for data obtained with the thruster configuration shown on Fig. 13. The specific impulse steadily drops from 1000 s for low Q m /P to 400 s at 6 µg/J.

One can notice the linear trend of the data in this range of mass flow rate and power. This behavior enables to adjust the specific impulse of the thruster by tuning the operating condition. Even if the underlying physics is not fully understood, some informations can be pulled out from this observation. The most important of them is the behavior of the other quantities (𝑇, TTPR, and 𝜂 𝑇 ) with respect to the operating conditions.

In the linearity range (between 1 and 6 µg/J) the 𝐼 𝑆𝑃 can be written as: [START_REF] Stallard | Plasma Confinement in the Whistler Wave Plasma Thruster[END_REF] with 𝑄 𝑚 the mass flow rate, 𝑃 the absorbed power, 𝛼 and 𝛽 positive contants.

     P Q I m SP
One can deduce expressions for the Thrust To Power Ratio (TTPR) and for the total efficiency(𝜂 𝑇 ):

               P Q g P Q g TTPR m m   2 (8)                              P Q P Q P Q g m m m T 2 2 3 2 2 2 2     (9)
It means that the performance indicators only depends on one parameter, Q m /P, for a given thruster configuration in this range of power and mass flow rate (20-50 W, 0.06 -0.15 mg/s). The thruster efficiency reach its maximum value when the first derivative of eq. ( 9) vanishes, giving: The red curve stands for the efficiency calculated from the I sp fit (Fig. 14) and is computed in the linear range of the data (up to 6 µg/J). In this range, TTPR increases up to Q m /P = 𝛽/2𝛼 ∼ 4 𝜇𝑔/𝐽 where a value around 25 𝜇𝑁/𝑊 is reached. Concerning the total efficiency (Fig. 15 bottom), a maximum value is clearly visible around 8.5% for Q m /P ∼ 3 𝜇𝑔/𝐽. It should be noticed that slightly higher TTPR can be obtained for higher Q m /P (i.e. above the linearity range of the I sp ). However the thruster efficiency decreases in these conditions (less than 5%).

      3 2 27 2 3 g P Q MAX m          (10)
The fact that the performances depend on only one parameter (Q m /P) for a given thruster configuration presents several advantages. First, it enables to change the thrust while keeping a maximum efficiency: the mass flow rate and the power can be increased in order to keep Q m /P constant. Moreover, the mass-flow to power ratio Q m /P can be varied in order to select the thruster operation mode: if the available power is the main limit, one can adjust the ratio to optimize the TTPR; if the total mass of propulsive gas is the main limit, a larger 𝐼 𝑠𝑝 can be obtained by reducing the ratio. And as a compromise for both the gas and power consumptions, the total efficiency can be adjusted according to eq. ( 10).

C. Insulating walls

In the following experiments, the inner surface of the source cylinder was covered with an insulating material (a thin layer of Kapton polyimide) to study the effect of the wall properties on the thruster performances. Fig. 16 compares the thrust and efficiency with and without dielectric layer for a mass flow rate of 0.1 mg/s of xenon. The measured thrust is raised by about 20% with non-conducting walls in the source. In the meantime, the thruster efficiency is increased from 7% to 10.5% at 40 W, i.e. an improvement of 40% of the performances. The experimental data with metallic and dielectric walls are expressed as a function of Q m /P ratio in Fig. 17.

One can notice the linear behavior for both cases but with different values for 𝛼 and 𝛽. However, the ratio 𝛽/𝛼 is very similar (9.7 𝜇𝑔/𝐽 vs 10.2 𝜇𝑔/𝐽), which means that the optimum operating condition given by eq. ( 10) is almost the same in both cases. Further experiments have shown that the total ion beam current is increased in the presence of insulating walls while the mean ion energy remains constant (not shown here).

This behavior means that either the ionization rate is higher or the plasma confinement is increased in the plasma source with insulated walls. Two phenomena could explain this effect: Secondary electron emission (SEE) and Simon short circuits. First, the additional dielectric polyimide layer has a different SEE yield than the original aluminum structure. The electron balance in the plasma is then changed, leading to a variation of the ionization rate, of the potential drop in the plasma sheath near the walls, and finally of the charged particle flux on the walls of the source [START_REF] Hobbs | Heat Flow through a Langmuir Sheath in the Presence of Electron Emission[END_REF]. Second, it is known that the conducting properties of the walls can modify the ion diffusion, allowing cross-field diffusion [START_REF] Drentje | Simon Short Circuit Effect in ECRIS[END_REF]. This could affect the plasma confinement and consequently the ion production efficiency.

Finally the combination of these two phenomena could modify the axial distribution of ion bombardment on the walls and therefore the global emission flux of secondary electrons.

IV. Comparisons with electrostatic diagnostics

A comparison is made here between the two methods used to measure the performances of the ECR-PM-V1 The error bars included in Fig. 18, which correspond to the uncertainties of the probe measurement, have been determined according to the recommended practice for the use of Faraday probes [START_REF] Brown | Recommended Practice for Use of Faraday Probes in Electric Propulsion Testing[END_REF]. They have been calculated using eq. ( 4), taking in account the uncertainty on the distance 𝐷 of the probe from the thruster; on the collector diameter; on the grid transparency; on the alignment with thrust axis; and on the ion energy. The current leakage in the measurement circuit and the error on the probe angle are negligible. The effect of secondary electron emission and the possible sheath expansion beyond the grid have not been taken into account.

For all microwave power levels, the thrust that is directly measured with the balance is about 20% higher than the estimation from the probes measurements. This leads to greater values of efficiency obtained with the balance.

The maximum measured thrust is around 800 µN with the balance and 650 µN with the probe at approximatively 50 W. Nevertheless, both methods show the same trends. In particular, the linear behavior of the 𝐼 𝑆𝑃 with respect to the mass-flow to power ratio Q m /P has also been confirmed with the probe measurements.

Although the thrust value inferred from probe measurements is less reliable than the thrust value directly measured with the balance, the probe results give more insight into the performance of the thruster.

Fig. 19 shows the efficiencies of the thruster (mass utilization, energy, divergence and total) with respect to the Q m /P ratio. Different trends are observed. The total efficiency 𝜂 𝑇 is maximum for similar operating conditions (∼ 3 𝜇𝑔/𝐽) with the direct and indirect method. The divergence efficiency 𝜂 𝐷 is almost constant in the whole range (around 80%), which means that power and mass-flow rate have no influence on the angular distribution of ion current in the plume. The energetic efficiency 𝜂 𝑒 increases between 1 and 3 𝜇𝑔/𝐽 and remains constant around 20% above this value. On the opposite, the mass efficiency 𝜂 𝑚 is maximum from 1 to 3 𝜇𝑔/𝐽 (around 40%) and tends to decrease for higher Q m /P.

The variations of the detailed efficiencies can enlighten some physical mechanisms in the source.

Fig. 19 The four different types of efficiencies against the mass-flow to power ratio for the same data set.

High Q m /P correspond to low reduced electric field (𝐸/𝑁). The electron temperature is then lower, and the ionization is less efficient leading to a lower mass efficiency. On the other hand, low mass-flow to power ratio leads to higher electron temperature and a better ionization of the propellant gas, which could explain the trend of 𝜂 𝑚 However, electron losses on the walls also increase with the temperature. With a floating source, this finally leads to higher ion losses on the walls and a decrease of the energy efficiency. The formation of multiply charged ions could also play a role in the energy efficiency.

It is noteworthy that the total efficiency of the ECR thruster is here limited by the energy efficiency 𝜂 𝑒 . The main power losses in electrodeless plasma thrusters are the propellant ionization and the plasma losses on the radial and back walls of the source. The plasma losses depend on the electron temperature and on the magnetic confinement of the source. An analytical model of a helicon discharge has shown that the performances could be significantly improved by increasing the magnetic field [START_REF] Lafleur | Helicon plasma thruster discharge model[END_REF]. This is a possible way of improving the ECR thruster.

The differences between the direct (balance) and the indirect (probe) measurements could have multiple sources and are probably not only due to the uncertainty. First, it could be a wrong assumption in the method used to compute the thrust such as the axisymmetry of the beam for example. Also, it was observed that the Faraday probe significantly perturbs the thruster. The direct thrust measurements on the balance are indeed affected by the presence of the probe. When the Faraday probe is in front of the thruster (𝜑 = 0 °), the measured thrust is typically 10% lower than when the probe is at 𝜑 = 90°, so the efficiency is about 20% lower. However, this effect by itself is not sufficient to explain the relative gap between the direct and indirect thrust measurements. The effect of the probe on the thruster is not understood yet, but the diagnostic is clearly intrusive for the ECR thruster. Note that in all the direct measurements presented in the paper were performed with the probe at 𝜑= 90°.

Finally, charge exchange collisions with the background neutrals and with the plume neutrals could be an issue for the characterization of electric thrusters because it could affect the ion current distribution and the mean ion energy. However, in the conditions of our experiments (background pressure of 5 × 10 -6 to 10 -5 mbar), the mean free path for charge exchange collision with neutrals from the background has been estimated to be in the range 5 m to 20 m with ions between 50 and 300 eV, using the cross sections that can be found in the literature [START_REF] Miller | Xenon charge exchange cross sections for electrostatic thruster models[END_REF]. This value is one to two orders of magnitude higher than the distance between the probe and the thruster, so charge exchanges with background neutrals can be neglected. There is still the possibility of charge exchange collisions with nonionized xenon that exit the thruster. However, normalized angular profiles of ion current density have been compared for different mass-flow rates and no differences have been observed. Therefore the charge exchange collisions with plume neutrals have no significant effect on probe measurements.

V. Conclusion

In this paper, the first direct thrust measurements on an ECR plasma thruster have been performed. A pendulum thrust balance is used in the null mode with a PID controller. The maximum measured thrust is about 1 mN with a microwave power of 53 W and a xenon mass flowrate of 0.1 mg/s. The best thruster efficiency with the current version of permanent magnet thruster is about 11% at 39 W and 0.1 mg/s (with dielectric walls). The specific impulse can be as high as 1050s.

It was observed that the 𝐼 𝑆𝑃 follows a linear law with respect to the mass-flow rate to power ratio (Q m /P) for a given thruster geometry and magnetic topology. Consequently, the total efficiency (𝜂 𝑇 ) only depends on Q m /P and can be maximized. Moreover, the operating conditions can be adjusted to favor the thrust level, the specific impulse, or the total efficiency. A further study would be required to better understand this behavior.

An important result is the significant improvement obtained when adding a dielectric layer on the metallic source walls. This leads to an increase of 25% of the thrust value. The phenomenon is either due to a change of the secondary electron emission rate or to different ion diffusion in the plasma due to electrical properties of the vessel walls.

Finally, the comparisons between direct and indirect measurements suggest that electrostatic probes systematically underestimate the thrust by about 20%, and hence the total efficiency by about 40%. This could come, at least partially, from the intrusive aspect of the Faraday probe that disturbs the thruster functioning.

All the results presented in this paper are obtained with the ECR-PM-V1 permanent magnet model of the ECR plasma thruster, which appears to be less efficient than the coil version presented in previous papers (4.5% versus 16% of total efficiency [START_REF] Cannat | Optimization of a Coaxial Electron Cyclotron Resonance Plasma Thruster with an Analytical Model[END_REF] when both are measured with probes). One of the reasons could be the topology of the magnetic field: the magnetic nozzle is more divergent in coil version than in the permanent magnet one. Therefore an improvement of the efficiency by a factor of 4 could be expected with an optimization of the magnetic field topology. In the future, different source geometries will be tested, and the effect of the divergence of the magnetic nozzle will be investigated, in order to optimize the design and to further improve the performances.

2 

 2 Resonance plasma thruster are performed with a thrust balance. The thruster performances are deduced, and the influence of power and mass-flow rate is studied. The measured thrust is around 1mN for 50 W of microwave power input and 0.1 mg/s of xenon, corresponding to 1000 s of specific impulse and 11% of total efficiency. It is found that the thrust is increased by 25% when the walls of the plasma source are covered with a dielectric layer. Comparisons are made between the direct thrust measurements and the indirect thrust measurements obtained with electrostatic probes in the plasma beam. pivot and the center of mass of the arm of the balance, m L T = distance between the pivot and the center of thrust on the arm of the balance, m  = angle between the arm of the balance and the fixed part calibration mass i on the calibration arm, m L c = distance between the pivot and the calibration arm on the arm of the balance, m = rotation angle of the Faraday probe e = 1.6 10 -19 C, elementary charge D = rotation radius of the Faraday probe,

Fig. 1

 1 Fig. 1 Picture of the ECR-PM-V1 Thruster operating with xenon in the B09 vacuum chamber at ONERA Palaiseau.

  Fig.2). The propellant is injected through two holes (2 mm in diameter) in a dielectric (boron nitride) back plate.

Fig. 2

 2 Fig. 2 Schematic of the ECR-PM-V1 thruster (not in scale).

Fig. 3

 3 Fig. 3 Magnetic field topology of the ECR-PM-V1 Thruster. The colored zone is the ECR zone. The lengths are in centimeters.

  thruster is operated at 0.1 mg/s.

Fig. 6

 6 Fig. 6 Logic diagram of the PID control system with the capacitive sensor as an input and the planar coil as the actuator for the output.

Fig. 7

 7 Fig. 7 Example of the PID response to a simulate thrust step. The 100 points adjacent-averaged smooth is superimposed to the thrust step applied.

Fig. 8

 8 Fig. 8 Example of balance calibrationwith the five masses. PID signal (top) and corresponding calibration factor i  (bottom).

Fig. 11

 11 Fig. 11 On the top, typical angular profile of the ion current density. On the bottom, example of the first derivative of the ion current with respect to the bias voltage on the collector of the Faraday probe.

Fig. 14

 14 Fig. 14 Specific Impulse (𝑰 𝑺𝑷 ) with respect to the mass-flow rate to power ratio. The experimental data are fitted with a linear regression below 6 µg/J.

Fig. 15

 15 Fig. 15 Thrust to power ratio (top) and total efficiency (bottom) with their empirical curve deduced from 𝑰 𝑺𝑷 linear fit. In the current configuration, the values for 𝛼 and 𝛽 obtained with a linear fit on the Fig. 14 are 103.04 and 1001.4, respectively. Experimental data of the TTPR (top) and thruster efficiency (bottom) versus Q m /P are shown on Fig. 15. The red curve stands for the efficiency calculated from the I sp fit (Fig. 14) and is computed in the linear

Fig. 16

 16 Fig. 16 Comparison of measured thrust (top) and total efficiency (bottom) between metallic walls and dielectric walls configurations at 0.1 mg/s.

Fig. 17

 17 Fig. 17 Comparison of the Specific Impulse (𝑰 𝑺𝑷 ) versus mass-flow rate to power ratio for metallic and dielectric walls.

.

  thruster with conducting walls: direct measurement with the balance and indirect measurement with the electrostatic probe (i.e. Faraday probe). The global performance indicators (𝑇 and 𝜂 𝑇 ), and the detailed efficiencies (mass efficiency 𝜂 𝑚 , energy efficiency 𝜂 𝑒 and divergence efficiency 𝜂 𝐷 ) are shown and discussed. The detailed efficiencies are deduced from Faraday probe measurements. One can remind the formula of the total efficiency: 𝜂 𝑇 = 𝜂 𝐷 2 𝜂 𝑒 𝜂 𝑚 , with 𝑃 is the microwave power deposited into the thruster (taken into account the losses in the cables and the impedance matching of the plasma).

Fig. 18

 18 Fig. 18 shows a comparison of the thrust (top) and of the total efficiency (bottom) obtained with direct thrust measurements and with electrostatic probe measurements. Experiments are performed at 0.1 mg/s for different values of power.

Fig. 18

 18 Fig. 18 Comparison of thrust measurements (top) and thruster efficiencies (bottom) between direct (balance) and indirect (Faraday probe) measurements.

Table 1 Calibration masses and their position on the calibration arm

 1

	Masses (mg)	Position (mm)	Eq thrust (𝝁𝑵)
	197.5	27.5	135.23
	228.64	32.5	320.25
	313.4	42.5	651.88
	335.12	47.5	1048.22
	336.75	52.5	1488.41

Fig. 8 (top) shows a typical acquisition of the output PID signal during a mass deposition. The uncertainty bars come from the error budget explained in Table 2 (section III-A).

Table 2

 2 lists the uncertainties of the different quantities useful for the determination of the performance indicators (𝑇, 𝐼 𝑠𝑝 , 𝜂 𝑇 , TTPR).

Table 2 Uncertainty budget for the direct thrust measurement with the pendulum balance

 2

	Quantity 𝑋 𝑖	Meaning	Uncertainty Δ𝑋 𝑖
	𝑉 𝑃𝐼𝐷 (𝑉)	PID step signal	20 × 10 -3
	𝑉 𝑖 (𝑉)	PID calibration signal	30 × 10 -3
	𝐿 𝑇 (𝑚)	Balance arm length	2 × 10 -3
	𝐿 𝑖 (𝑚)	Calibration arm length until slit 𝑖	5 × 10 -4
	𝑚 𝑖 (𝑘𝑔) 𝑔 (𝑚/𝑠 2 )	Calibration mass Gravity acceleration constant	10 -8 < 10 -4
	𝑄 𝑚 (𝑆𝐶𝐶𝑀)	Mass-flow rate	0.01 + 0.005 𝑄 𝑚
	𝑃 (𝑊)	MW power	0.04 𝑃

Funding Sources

This work was partially made in the framework of project MINOTOR that has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 730028.