Measuring cell for measuring the surface force exerted by a particle flow

Abstract

According to one aspect, the present description relates to a measurement cell (110) comprising a fixed part (112), a resonator (114) including a longitudinal axis (Δ), and a movable solid part (116) including a face (117) exposed to the particle flux. The solid part is movable relative to the fixed part along a single axis of rotation (Ox) perpendicular to a plane formed by the longitudinal axis of the first resonator and a direction normal to the exposure face. The first resonator has a first end fixed to said fixed part and a second end fixed to said movable solid part. The axis of rotation and the longitudinal axis of the resonator are separated in the direction normal to the exposure face by a predetermined non-zero distance (dp).A first distance (h) between the axis of rotation and a center of mass (Cm) of the moving massive part is strictly less than a second distance (p) between the axis of rotation and a center of pressure (Cp) of the exposure face. FIG. 2A.

Description

Title of the invention: Measuring cell for measuring the surface force exerted by a particle flow technical field

[0001] This description relates to a measuring cell for the surface force exerted by a flow of neutral and / or charged particles. Furthermore, this description relates to a device for measuring the surface force exerted by a particle flow, comprising such a measuring cell and a method for measuring the surface force exerted by a particle flow using such a device. This description relates in particular to the measurement of the surface force exerted by a particle flow in rarefied environments, for example, the qualification of ground-based satellite thrusters in rarefied (low-pressure) environments, including the qualification of electric and cold-gas thrusters. State of the art

[0002] The measurement of the surface force exerted by a flow of neutral and / or charged particles, particularly in a rarefied environment, finds applications, for example, but not limited to, in the qualification of satellite thrusters or in the measurement of plasma pressure in a tokamak for the exploration of plasma physics. A rarefied environment is understood to mean a vacuum or an environment within an enclosure, for example the interior of a chamber, in which the mean free path of the particles is greater than the dimensions of the enclosure.

[0003] In particular, a difficult problem associated with satellite propulsion is the qualification and subsequent validation of the ground performance of the thrusters. The parameters that one seeks to qualify include, in particular, the thrust level (magnitude in Newtons (N) of the force exerted by the flow of particles ejected by the thruster), the specific impulse (in seconds (s)) and the efficiency of the thruster defined by a figure of merit which compares the kinetic energy of the particle flow and the energy injected into the thruster.

[0004] In the present description, we are interested in measuring the surface force exerted by a flow of particles, for example for ground qualification but also in orbit in the case of satellite thrusters.

[0005] In the case of electric propulsion, for example, electrical energy is used to ionize the atoms of the propellant mass and eject the particles (ionized gas) to their ejection velocity. In this example, we are interested in measuring the surface force exerted by a flow of charged particles. In the example of a cold gas thruster that uses a gas stored under high pressure which is released into a nozzle, which allows the thrust exerted to be directed, we seek to measure the surface force exerted by a flow of neutral particles.

[0006] Measuring the surface force exerted by a particle flow in a rarefied environment requires high resolution, i.e., the lowest possible measurable minimum surface force value over large measurement ranges. For example, a resolution better than 10⁷ Pa, or 10⁵ pN·cm², is sought, meaning a minimum measurable surface force value lower than 10⁷ Pa, or 10⁵ pN·cm², over measurement ranges, for example, between 10⁷ Pa and 10² Pa.

[0007] It is known to use thrust balances (or pendulums) in vacuum chambers, particularly for the qualification of electric thrusters for ground-based satellites. Such thrust balances are described, for example, in Packan et al. [Ref. 1]. The pendulum is fixed at one end to the chamber and supports the thruster at the other. It is possible to determine the surface force indirectly by measuring the deflection of the pendulum. However, such thrust balances are bulky and require gravity to operate, which precludes, for example, their use in orbit.

[0008] More recently, studies have been conducted on the development of probes for measuring plasma impact on a target. The displacement of this target or the stresses it experiences allow the surface force of the jet to be determined. Such a measurement is intrusive in that it can modify the properties of the particle jet. Therefore, there is a need for a probe of limited size that is nevertheless capable of performing surface force measurements over measurement ranges from approximately 10⁷ Pa to 10² Pa.

[0009] In the article by Chavers et al. [Ref. 2], a target designed for measuring the thrust of a high-power electric thruster is described. More specifically, the measuring device comprises a 5 cm diameter target held by a 22.8 cm long arm, the arm being supported by a titanium beam to which strain gauges are attached. When the plasma impacts the target, the arm transmits the force to the titanium beam, which deforms. The strain gauges measure the deformation of the beam, from which the plasma thrust can be determined. However, this device has the disadvantage of having a sensitivity proportional to the length of the arm. As a result, the device is relatively large, which, in addition to its size, can induce changes in the plasma's behavior. The system also requires gravity to operate. Therefore, it can only be installed by suspending it from the ceiling of a measuring chamber.

[0010] The device described in Trottenberg et al. [Ref. 3] is also designed to measure the thrust of a propulsion system. The device comprises a 20 mm diameter target held at the end of an 11 cm arm balanced with a weight. When the plasma impacts the target, it is displaced. An active galvanometer compensates for this force to return the pendulum to its initial position. Although smaller than a pendulum or the target described in [Ref. 2], the dimensions of the device described in [Ref. 3] are still significant, and the device has the disadvantages of a pendulum, in which, on the one hand, sensitivity is proportional to the length of the arm, and on the other hand, the system requires gravity to function.

[0011] In this context, the present description describes measurement cells adapted to the measurement of the surface force exerted by a flow of neutral and / or charged particles, compact, and which do not require gravity to operate. Summary of the invention

[0012] In the present description, the term "include" means the same as "include" or "contain", and is inclusive or open and does not exclude other elements not described or represented.

[0013] In addition, in the present description, the term "approximately" or "substantially" is synonymous with (means the same as) has a margin of 10%, for example 5%, below and / or above the respective value.

[0014] According to a first aspect, the present description relates to a measuring cell for measuring the surface force exerted by a flow of particles comprising: - a fixed part configured to be mechanically and electrically connected to a support; - at least one first resonator comprising a longitudinal axis, said first resonator having a first end fixed to said fixed part; - a movable massive part comprising a face exposed to the particle flux, said massive part being such that: - said massive part is mobile relative to the fixed part along a single axis of rotation perpendicular to a plane formed by the longitudinal axis of the first resonator and a direction normal to the exposure face; - the axis of rotation and the longitudinal axis of the first resonator are separated in the direction normal to the exposure face by a predetermined non-zero distance; - the first resonator has a second end attached to said moving solid part; and - a first distance between the axis of rotation and a center of mass of the moving massive part is strictly less than a second distance between the axis of rotation and a center of pressure of the exposure face, the first distance and the second distance being distances projected onto a plane parallel to the exposure face.

[0015] The center of mass of the moving massive part is also called the center of inertia. In the case where the moving massive part is homogeneous in mass (all points have the same weighting), the center of mass coincides with the barycenter of the moving massive part.

[0016] The center of pressure of the exposure face of the moving mass part is the center of application of the resultant pressure forces due to the particle flow, that is, the point on the exposure face where, during operation, the moment of the pressure forces of the flow becomes zero. In practice, in the approximation of a uniform particle flow incident on the exposure face of the moving mass part, the center of pressure is essentially coincident with the geometric center, or barycenter, of the exposure face.

[0017] A measuring cell according to the first aspect allows for the measurement of the surface force exerted by a particle flow on the moving mass, also referred to as the "test mass" in this description. More precisely, a measurement of the force exerted by the particle flow can be obtained by measuring the change in the resonance frequency of the resonator fixed between the fixed part and the test mass when the first resonator is excited to an initial resonance frequency.

[0018] The test mass is subjected to the force exerted by the particle flow, which, thanks to the original arrangement of the measuring cell as described in the first aspect, results in the application of compression or tension on the resonator and, consequently, a change in the resonance frequency. Such a measuring cell is advantageous compared to state-of-the-art measuring devices, not only because its size is reduced, but also because the measurement is performed without the need for gravity. Consequently, in the case of application to a satellite thruster, for example, this allows measurements of the force exerted by the particle flow ejected by the thruster, even when the satellite is in orbit.

[0019] Because the first distance between the axis of rotation and the center of mass of the moving mass part is strictly less than the second distance between the axis of rotation and the center of pressure of the exposure face, the measurement is relatively insensitive to the effects of acceleration. Indeed, in such a configuration, the contribution of thrust is greater than that of acceleration.

[0020] In preferred embodiment examples, the ratio between said first distance and said second distance is less than about 0.1, advantageously less than about 0.01.

[0021] The applicant has shown that the smaller the ratio between the first distance and the second distance, the less sensitive the device is to the effects of acceleration. This results in a measurement with very good resolution.

[0022] In embodiment examples, the first distance is substantially zero, meaning that the center of mass of the moving mass lies in a plane defined by the axis of rotation of the moving mass and by the direction normal to the exposure face. This condition eliminates the effects of acceleration in the direction perpendicular to the exposure face and further improves resolution.

[0023] According to one or more embodiments, the ratio between a third distance, defined between the axis of rotation and the center of mass of the moving mass part, and a fourth distance, defined between the axis of rotation and the axis of the first resonator, is strictly less than 1, advantageously strictly less than approximately 0.1, the third and fourth distances being distances projected onto a plane perpendicular to the exposure face. This condition eliminates the effects of acceleration in the direction parallel to the longitudinal axis of the resonator. Here again, the resolution is improved.

[0024] According to one or more embodiments, the measuring cell is monolithic, or monobloc, meaning that the assembly comprising the fixed part, the moving mass, and the resonator is made in a single piece. For example, the measuring cell is made from a block of quartz. Other materials can be considered for the manufacture of the measuring cell, such as silicon, langatate crystal (LGT), gallium phosphate crystal (GaPO4), or more generally any other piezoelectric material: ferroelectric piezoelectric crystals (LBO, LNO, LTO), zinc oxide (ZnO), gallium nitride (GaN), gallium arsenic (GaAs), etc.

[0025] According to one or more embodiments, the measuring cell comprises two hinges sharing a common axis of rotation, said common axis of rotation forming the single axis of rotation of said moving mass. Two hinges ensure that there is only one pivot around a single axis and thus limit the effects that could result from rotations about other axes and affect the measurement. A sufficient distance between the two hinges is sought, for example, a distance of between approximately 2 mm and approximately 5 mm.

[0026] In exemplary embodiments, a projection of the axis of the first resonator onto a plane parallel to the exposure face and including said common axis of rotation intersects said common axis of rotation at a point located between the two hinges, advantageously at a midpoint located approximately halfway between the two hinges. Such a configuration eliminates the effects of any rotations around an axis perpendicular to the exposure face.

[0027] According to one or more embodiments, a fifth distance, defined between a projection of the center of mass of the moving solid part onto said common axis of rotation and said midpoint, is strictly less than a sixth distance, defined between said midpoint and each of the hinges. The smaller the ratio between said fifth distance and said sixth distance is compared to 1, the more the measurement is free from the effects of possible rotations around an axis perpendicular to the exposure surface, even in the presence of two hinges. The resulting cell is more robust. This results in better resolution. In preferred embodiments, the fifth distance is substantially zero and the projection of the center of mass of the moving solid part onto said common axis of rotation is substantially coincident with said midpoint.

[0028] According to one or more embodiments, the massive movable part comprises a target forming the exposure surface and two wings, said target being connected to the two wings, the two hinges and the second end of the first resonator.

[0029] Such an arrangement of the measuring cell makes it possible, thanks to the presence of the two wings, to shift the center of mass towards the axis of rotation, which makes it possible to limit the effects of acceleration along a direction perpendicular to the exposure face.

[0030] According to one or more embodiments, the movable bulky part comprises two arms connecting the target to each of the two wings, the arms defining an opening. Such an opening limits the impact of particles near or on the resonator, which can, during operation and in the case of charged particles, disrupt the measurement.

[0031] According to one or more embodiments, the fixed part comprises a decoupling frame and an external frame configured to be connected to the support, said decoupling frame having a tuning fork shape connected on one side to the external frame, and on the other side to the two hinges and the first end of the first resonator. Such an arrangement is advantageous in that it can limit the effects resulting from thermal stresses or external vibrations on the resonator.

[0032] According to one or more embodiments, the first resonator comprises at least one vibrating beam, for example, a vibrating beam in bending mode. In some embodiments, the first resonator comprises two vibrating beams arranged in parallel to form a double tuning fork, each beam being connected at its ends respectively to the same first peduncle and the same second peduncle, the first and second peduncles forming respectively the first and second ends of the resonator. A double tuning fork can provide better resolution.

[0033] According to one or more embodiments, at least a portion of the moving solid part comprises a coating of electrically conductive material. The coating, made of an electrically conductive material, is, for example, metal or graphite. In the case of a metal, the coating can be obtained by metallization. In the case of graphite, the coating can be obtained by CVD or PVD deposition (acronyms for "Chemical Vapor Deposition" and "Physical Vapor Deposition," respectively). Metallization or graphite deposition may involve a metallic or graphite coating on all or part of the surface of the moving mass. In other embodiments, the measuring cell may include a metal plate arranged on a portion of the moving mass to achieve metallization. The metal may be one of the following metals (or an alloy of these metals): titanium, tantalum.In the case of a charged particle flux (electric thruster or tokamak, for example), coating the moving bulk component at least partially with an electrically conductive material can facilitate charge collection. Coating the moving bulk component at least partially with an electrically conductive material can also increase thermal conductivity, thereby protecting the resonator by limiting potential thermal gradients. More generally, coating the moving bulk component at least partially with an electrically conductive material, particularly a metal or graphite coating, can limit erosion and consequently increase the lifespan of the measurement cell.

[0034] According to a second aspect, the present description relates to a device for measuring the surface force exerted by a particle flow, comprising: - a support; - at least one first measuring cell according to the first aspect, said fixed part being mechanically and electrically connected to said support; - an electronic circuit configured to excite the first resonator of said at least a first measuring cell at an initial resonant frequency and to measure, when the device is subjected to the particle flux, a measurement resonant frequency; - a processing unit configured to determine, from a difference between the measurement resonance frequency and the initial resonance frequency, the surface force exerted by the particle flow.

[0035] According to one or more embodiments, the device according to the second aspect comprises a second measuring cell, enabling differential measurements and increased resolution. The second cell is, for example, substantially similar to the first measuring cell and comprises, for example, a fixed part mechanically connected to the support, a resonator, and a movable solid part. The fixed part, the resonator, and the movable solid part of the second measuring cell are substantially identical, respectively, to the fixed part and the resonator. and to the moving mass of the first measuring cell. However, the positions of the resonator and the axis of rotation along the direction normal to the exposure face are reversed between the first and second measuring cells, such that when the exposure face of each measuring cell is exposed to the particle flow, one resonator undergoes compression while the other undergoes extension. The processing unit is then configured, for example, to further determine the difference between the measurement resonance frequency measured by the first measuring cell and the measurement resonance frequency measured by the second measuring cell in order to determine the surface force exerted by the particle flow.Such a differential measurement eliminates quadratic terms in the relationship between the resonator's resonance frequency and the surface force exerted by the particle flux. This differential measurement also eliminates potential thermal drift and any effect of acceleration along an axis perpendicular to a plane comprising the normal to the exposure face and the axis of rotation of the moving mass.

[0036] Such a differential measurement can also be carried out with a single measuring cell comprising two resonators.

[0037] Thus, in some embodiments, the measurement cell includes a second resonator, substantially identical to the first resonator. The projections of the first and second resonators onto a plane perpendicular to the axis of rotation lie on either side of a projection of said axis of rotation onto said plane, such that when the exposure face is exposed to the particle flux, one resonator undergoes compression while the other undergoes extension. Again, with such an arrangement, it is possible to perform a differential measurement that will cancel out perturbations common to both cells, such as drift induced by heat fluxes or vibrations.

[0038] The description relates according to a third aspect to a satellite comprising a thruster with means for ejecting a flow of neutral and / or charged particles and a device for measuring the force exerted by said flow of particles according to the second aspect, the support of the measuring device being mechanically and electrically connected to a body of the stellite by means of an arm.

[0039] According to a fourth aspect, the description relates to an enclosure with a rarefied environment configured for the qualification of a flow of neutral and / or charged particles. The enclosure includes a device for measuring the force exerted by a particle flow according to the second aspect, the support of the measuring device being mechanically and electrically connected to a body of the enclosure, for example by means of an arm, the measuring device being configured to measure the particle flow.

[0040] For example, the enclosure is a rarefied environment chamber configured for the qualification of a satellite thruster comprising means for ejecting a stream of neutral and / or charged particles. The measuring device is then configured to measure the particle stream ejected by the thruster.

[0041] The description relates according to a fifth aspect to a method of measuring the surface force exerted by a flow of particles by means of a device according to the second aspect.

[0042] In exemplary embodiments, the process comprises: - excitation of the first resonator and measurement of an initial resonance frequency of the resonator, without particle flux; - the reception of the particle flux by the exposure face of the measuring cell and the measurement of a measurement resonance frequency of the resonator resulting from the force applied by the particle flux on said exposure face; - the determination, from a difference between the measurement resonance frequency and the initial resonance frequency, of the surface force of the particle flux.

[0043] For example, the method according to the fifth aspect allows the measurement of the surface force exerted by a stream of particles ejected by a satellite thruster. The initial resonant frequency of the resonator is measured, for example, when the thruster is switched off and then switched on, to measure the resonant frequency resulting from the force applied by the stream of particles ejected by the thruster to the exposure face of the measuring cell.

[0044] According to one or more embodiments, the measurement of the surface force exerted by said particle flow is carried out when the propellant is on a satellite in orbit.

[0045] According to one or more embodiments, the measurement of the surface force exerted by said particle flow is carried out when the propellant is in an enclosure with a rarefied ground environment, for example a vacuum chamber.

[0046] According to one or more embodiments, the measurement method comprises: - the successive application of several potential differences between a region comprising a coating of electrically conductive material of the moving mass part and an opposing metal plate, the application of each potential difference resulting in an electrostatic force applied to the moving mass part; - for each potential difference, the measurement of a measurement resonance frequency resulting from said electrostatic force and the determination of the difference between the measurement resonance frequency and the initial resonance frequency.

[0047] These steps allow for calibration of the measuring device. The applied electrostatic force can then be determined as a function of the voltage. Knowing the measurement resonance frequency (since measured), we obtain the calibration curve of the difference between the measurement resonance frequency and the initial resonance frequency as a function of the force applied on the moving massive part. Brief description of the figures

[0048] Other advantages and features of the invention will become apparent from the description, illustrated by the following figures:

[0049] [Fig. 1], represents a diagram of a device for measuring the surface force exerted by a flow of particles, according to an example of an embodiment;

[0050] [Fig.2A], represents a diagram of a measuring cell according to an example of realization, according to a first view;

[0051] [Fig.2B], represents a diagram of the measuring cell illustrated in [Fig.2A], according to a second view;

[0052] [Fig. 3A], represents a diagram of a resonator of a measuring cell, according to a example of implementation, the resonator being formed from a beam in tension;

[0053] [Fig. 3B], represents a diagram of a resonator arrangement as illustrated on the [Fig.3A], according to an example of implementation;

[0054] [Fig.3C], represents a diagram of a resonator of a measuring cell, according another example of implementation, the resonator being formed of a double beam in tension;

[0055] [Fig.4A], represents a diagram of a measuring device according to an example of implementation, the device comprising two measuring cells arranged for differential measurement;

[0056] [Fig. 4B] represents a diagram of an example of a measuring cell in a device according to the present description, the measuring cell comprises two resonators arranged for differential measurement;

[0057] [Fig.5], represents a diagram of a measuring cell, as well as a device for calibrating the cell, according to an example of an embodiment;

[0058] [Fig. 6A], represents a diagram of a monolithic measuring cell according to a example of implementation, according to a first view;

[0059] [Fig. 6B], represents a diagram of the measuring cell illustrated in [Fig. 6A], according to a second view;

[0060] [Fig.6C], represents a diagram of the measuring cell illustrated in [Fig.6A], according to a third view;

[0061] [Fig.7A], represents a diagram of a monolithic measuring cell such as illustrated on [Fig.6A], arranged on a support, according to an example of realization and according to a first view;

[0062] [Fig.7B] represents a diagram of the measuring cell illustrated in [Fig.7A], according to a second view.

[0063] [Fig.8] represents a diagram of a satellite equipped with a measurement device the surface force exerted by a particle flow according to the present description, configured for the measurement of the surface force exerted by the particle flow ejected by the satellite's thruster.

[0064] [Fig.9] represents a diagram of an enclosure for the ground qualification of a satellite propulsion, by means of a device for measuring the surface force exerted by a flow of particles according to the present description.

[0065] The accompanying figures are schematic and not necessarily to scale; their primary purpose is to illustrate the principles of the invention. From one figure (fig.) to another, identical elements (or parts of elements) are identified, where possible, by the same reference numerals. Detailed description of the invention

[0066] Fig. 1 represents a diagram of a device for measuring 100 the surface force exerted by a flow of particles 10, according to an example of an embodiment.

[0067] The measuring device 100 in this example comprises a measuring cell 110 fixed to a support (not shown). The measuring cell includes, in particular, a resonator 114 and a movable mass 116, also referred to as the test mass in this description, which will be described in more detail later. The test mass 116 comprises a particle flux exposure face 117 and is movable about a single axis of rotation (not shown in [Fig. 1]). An electronic circuit 120 is configured to excite the resonator at an initial resonant frequency fr0. The test mass and the resonator are arranged such that, during operation, when the device is subjected to a surface force Fp exerted by a particle flux 10 incident on the exposure face 117, the test mass undergoes a rotation that results in a tensile force T (or a compressive force) on the resonator.This results in a change in the resonant frequency of the resonator. The electronic circuit 120 then measures the changed resonant frequency of the resonator, called the measurement resonant frequency and denoted fm in this description. The measuring device 100 further includes a processing unit 130 configured to determine, from the difference between the measurement resonant frequency and the initial resonant frequency, the magnitude Fp of the surface force Fp exerted by the particle flow.

[0068] The electronic circuit 120 includes, for example and in a known manner, an electronic oscillator 122 configured to apply a voltage Vf to coupling electrodes (not shown) arranged on the resonator, such as to excite the The resonator is at its initial resonant frequency f. The resonator is, for example, a vibrating beam in tension mechanically excited by the piezoelectric effect, as will be described in more detail later. The electronic circuit 120 also includes an amplifier 124 configured to increase the power of the electrical signal generated by the vibrating beam and a frequency meter 126 for measuring the frequency of the amplified signal.

[0069] The processing unit 130 may comprise one or more physical entities and may be assembled in one or more computers. Where reference is made in this description to calculation or processing steps for the implementation of process steps, it is understood that each calculation or processing step may be implemented by software, hardware, firmware, microcode, or any suitable combination of these technologies. When software is used, each calculation or processing step may be implemented by computer program instructions or software code. These instructions may be stored or transmitted to a storage medium readable by the processing unit and / or executed by the processing unit in order to implement these calculation or processing steps.

[0070] Figures 2A and 2B show two views of an example of a measuring cell 110 of a measuring device according to this description. The cell is illustrated schematically to explain its operation.

[0071] The measuring cell 110 comprises a fixed part 112 mechanically connected to a support of the device (not shown in the figures). The measuring cell further comprises at least one first resonator 114 comprising a longitudinal axis A and a movable mass 116, or test mass. The first resonator 114 has a first end fixed to the fixed part 112 and a second end fixed to the movable mass (point B). The movable mass 116 comprises a face 117 exposed to the particle flow. The massive mobile part 116 is mobile relative to the fixed part 112 along a single axis of rotation Ox perpendicular to a plane formed by the longitudinal axis A of the first resonator and a direction n normal to the exposure face 117. As illustrated in [Fig.2A], the axis of rotation Ox and the longitudinal axis A of the first resonator 114 are separated in the direction n normal to the exposure face by a predetermined non-zero distance dp..

[0072] As illustrated in [Fig. 2B], the measuring cell may comprise two hinges 118 having a common axis of rotation, said common axis of rotation forming the single axis of rotation Ox of said moving mass part. Thus, the test mass is connected to the fixed part by the two hinges. This configuration leaves the test mass 116 with only one degree of freedom: rotation about the common axis of rotation Ox. Thus, the normal force on the exposure surface 117 The force exerted by the particle flow on the test mass is transmitted to the resonator 114. In the example in [Fig. 2A], the resonator 114 is arranged on the front face of the measuring cell (approximately in the plane of the exposure surface), while the test mass is connected to the fixed part by the two hinges arranged on the rear face (approximately in a plane on the face opposite the exposure surface). This results in a tensile force T applied to the resonator, while the test mass experiences a tensile force -T applied at point B. In other embodiments, the resonator 114 can be arranged on the rear face of the measuring cell (face opposite the exposure surface), while the test mass is connected to the fixed part by the two hinges arranged on the front face (exposure surface). This will result in a compressive force applied to the resonator.

[0073] Advantageously, a projection of the axis A of the first resonator onto a plane parallel to the exposure face and including said common rotation axis Ox intersects said common rotation axis at a midpoint O located approximately halfway between the two hinges (see [Fig. 2B]). This arrangement eliminates effects resulting from possible rotations about an axis orthogonal to the exposure face (axis Oz).

[0074] The resonator 114 is, for example, a vibrating beam operating in bending, in a plane parallel to the exposure face. Electrodes arranged on the beam allow, in a known manner, the resonator to be coupled to the oscillating electrical circuit 120 ([Fig. 1]) and the beam to be mechanically excited (by piezoelectric effect) at its resonant frequency. The vibrating beam is, for example, excited in a fundamental bending mode, that is, it vibrates in the plane of the cell (xOy plane). Resonators are described in more detail below with reference to [Fig. 3A] to [Fig. 3C]. The dimensions of the resonator determine its natural vibration frequency. The natural vibration frequency can vary according to the compressive or tensile forces acting longitudinally on the resonator. The electronic circuit is configured to determine the vibration frequency of the vibrating beam when it is subjected to such forces.From the measurement of the variation in vibration frequency, the force exerted by the particle flux can be quantified as described below. By convention, the notations in bold in this description represent vectors.

[0075] The impact of the particle flow (10, [Fig. 1]) on the exposure face 117 of the test mass 116 creates a moment about the Ox axis. The moment is a function of the distance p between the center of application Cp of the resultant pressure forces due to the particle flow (or center of pressure) and the Ox axis, the distance p being a distance projected onto a plane parallel to the exposure face. In practice, the center

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[0088] The pressure Cp can be substantially confused with the geometric center, or barycenter, of the exposure face 117. As illustrated in Fig. 2A, the force (in Newtons) exerted by the particle flux Fp = - Fpz is exerted at the pressure center Cp at a distance dpz + py from the center O, where dp is the distance between the axis of rotation Ox and the axis A of the first resonator 114, said distance being a distance projected onto a plane Oxz perpendicular to the exposure face 117. The MO(FP) moment of the force Fp applied at Cp, with respect to the Ox axis, is thus: [Math.l] M0(Fp) = -pFpX There is also a moment Mo(-T) of the tensile force -T applied at point B by the resonator to the test mass, with respect to the Ox axis: [Math.2] Mo{-T)-dpTx In a quasi-static approximation, the sum of the moments of the forces applied to the test mass with respect to the Ox axis is zero: [Math.3] MO(-T)+MO{FP) =0 j ~ dp^p We denote — JL the amplification factor. P dp More generally, as will be described in more detail later, the test mass can also be subjected to accelerations along the y and z axes, due to vibrations. The geometry of the measurement cell can be optimized to reduce these effects. The extensional force on the resonator modifies its vibration frequency such that: [Math.4] fr < P » = A) + S ^ P + + Where P is the thrust (or surface force Fp / A, where A is the surface area of ​​the exposure face), fr is the vibration frequency of the resonator when a pressure force is exerted by the particle flow on the test mass, is the vibration frequency of the unconstrained resonator, Sp i is the linear pressure sensitivity, and Spz is the quadratic sensitivity. This equation does not take into account nonlinear frequency variations beyond the second order, which are assumed to be negligible. The last term represents the frequency variation due to possible perturbations.

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[0092] Indeed, when measuring the force exerted by the particle flow, the cell can be subjected to stresses resulting from the measurement environment. These stresses can result from vibrations, particularly from the vacuum pumps of the chamber housing the measurement cell, from heating caused by the particle flow, or from electrical loading resulting, for example, from a flow of charged particles that can generate forces. Thus, when the cell is not exposed to the particle flux, the resonator's vibration frequency is f. Exposing the measuring cell to the particle flux causes a change in the vibration frequency, which becomes f(P). The frequency difference fr(P) ~ fr0 allows us to determine the surface force exerted by the particle flux, Fpl A. The measurement device described here has the advantage of allowing measurement regardless of the gravitational field. Indeed, regardless of the orientation of the measuring cell, if it does not move during the measurement, the effect of gravity is canceled in the term fr(P). Such a device also allows measurements to be made in microgravity, and particularly in space, for example, in the case of satellite thrusters in orbit. Figure 3A shows a schematic diagram of a resonator for a measuring cell, according to an example embodiment. In this example, the resonator 114 is formed by a vibrating beam with dimensions of length L (y-direction) and widths l and e (respectively in the x and z directions). The width e along the z-axis is called the non-vibrating width of the beam, and the width l along the x-axis is called the vibrating width. As illustrated in Figure 3B, the vibrating beam is mounted in tension between the fixed part 112 and the test mass 116. It is connected to the fixed part 112 at one end and to the test mass at the other. For a vibrating beam 114 such as illustrated in Fig. 3A, the linear pressure sensitivity Spy can be determined, for example by using the Rayleigh method, and taking into account the amplification factor -JL; [Math.5] ^,1 - 1.49x10 e2MEp x to pA

[0093]

[0094] The linear pressure sensitivity Sp y is expressed in Hz / (pN.cm2), l and e are the dimensions of the beam respectively in the x and z directions, E is the Young's modulus of the material from which the beam is formed, and p is the density of the material, A is the surface area of ​​the exposure face 117. The sensitivity of the measuring cell can thus be modified by adjusting various parameters. First, the choice of material allows for modification of the modulus of Young's energy (E) and its density (p). Sensitivity is, however, inversely proportional to the square root of the material properties, and the choice of material therefore has a moderate influence on sensitivity. The geometry of the test mass also affects sensitivity. The cell's sensitivity is indeed proportional to the surface area (A) of the particles on the test mass. It is also proportional to the amplification factor, that is, the distance between the surface area and the axis of rotation (Ox). Finally, sensitivity depends on the geometry of the vibrating beam.

[0095] The smaller the non-vibrating width (e) and the vibrating width (l), the higher the cell's sensitivity. These dimensions thus have a significant impact on sensitivity, which is inversely proportional to the square of the vibrating width. The thinner the beam, the greater the sensitivity.However, the reduction in vibrating and non-vibrating widths is limited by the manufacturing technique and the mechanical strength of the material. A beam that is too thin risks being destroyed during its manufacture, handling, and use. The applicant has shown that optimized dimensions for the vibrating beam are between approximately 1 micron and approximately 1 mm for the beam's cross-section and between approximately 0.1 mm and approximately 10 mm for the beam's length.

[0096] Other resonators may be used in a measuring cell of a device according to this description.

[0097] Fig. 3C thus represents a diagram of a resonator of a measuring cell formed of a double beam in tension.

[0098] Instead of a vibrating beam ([Fig. 3B]), a double tuning fork can be used ([Fig. 3C]). The resonator then comprises two vibrating beams 321, 322, each attached by a pedestal 311, 312. The pedestal 311 is connected to the fixed part 112 by a fastener 301, and the pedestal 312 is connected to the test mass 116 by a fastener 302. When the beams vibrate, they create waves in opposite phase, which cancel each other out in the two pedestals. This prevents waves from propagating in the fixed part 112 (or in the test mass 116), which would constitute a source of energy loss for the device.

[0099] As appears in equation [Math 4], the sensitivity of the measuring cell to the force exerted by the particle flow also implies a sensitivity to other parasitic forces.

[0100] For example, parasitic forces may result from vibrations of the measuring cell which cause dynamic acceleration.

[0101] The point of application of an acceleration experienced by the measuring cell is located at the center of mass Cm of the test mass (Fig. 2A, Fig. 2B), at a distance hy + dgz from the Ox axis of rotation of the test mass, where h is the distance between the center of mass Cm and the Ox axis, the distance h being a distance projected onto a parallel plane to the exposure face, and dg is the distance between the axis of rotation Ox and the center of mass Cm, said distance being a distance projected onto a plane Oxz perpendicular to the face.

[0102] The acceleration r = L^x+ rvj + Rz experienced by the measuring cell creates a force F = MF applied to the center of mass, where M is the mass of the test mass.

[0103] The moment of the force F, applied to the center of mass Cm, with respect to the Ox axis, is: [°104] M0(F)=(hFz-dgFy)x

[0105] The moments around the y and z axes are nuisance since the Ox axis is the only axis of rotation of the test mass.

[0106] In the equation above, it is assumed that the component Fx of the force F does not cause a frequency variation. This assumes that the distance dmp between a projection of the center of mass Cm of the moving mass onto the common axis of rotation of the hinges (see [Fig. 2B]) and the midpoint O between the hinges is very small compared to a distance dpc between said midpoint and each of the hinges. In other words, the projection of the center of mass Cm of the test mass onto the common axis of rotation is essentially coincident with the midpoint O.

[0107] Assuming the test mass is fixed, then the fundamental principle of dynamics indicates that the sum of the moments of the forces applied to the center of mass with respect to point O is zero:

[0108] [Math.6] M0(-T)+M0(F)=^ 101091 ^= <r z -4r,.)

[0110] Similar to [Math 5], the acceleration sensitivity can be expressed in Hz / g as a function of the amplification factor Σ with i=z or y such that ace dp ^acc~ dp [YES] [Math.7] 1.49 ss , ^acc “

[0112] The sensitivity depends on the dimensions of the beam (non-vibrating width e and vibrating width Z), the properties of the material (Young's modulus E and density ρ), and the mass M of the test mass. With the beam dimensions and material fixed, the acceleration sensitivities are proportional to:

[0113] [Math. 8] ' $ = 0 Sf-T™

[0114] Because in a measuring cell according to the present description, h is less than p, the ratio A is less than the amplification factor — A and the contribution «p "P dp The acceleration in the measurement is thus less than that of the thrust. Furthermore, it is possible to choose the geometry of the test mass of the measuring cell in such a way as to minimize S^. To achieve this, the test mass of the measuring cell can be designed so that h is very small compared to dp, for example, h approximately equal to 0.

[0115] Furthermore, it is possible to choose the geometry of the test mass of the measuring cell so as to minimize Sj- For this, the test mass of the measuring cell can be designed so that dg is strictly less than dp, advantageously less than 0.1 dp For example, in the case where the axis of rotation is the common axis of rotation of two hinges 118, the hinges can be arranged not on the rear face of the test mass but in the middle of the thickness of the test mass, to make the distance dg tend towards 0.

[0116] Parasitic forces can also result from the deposition of electrical charges on the test mass when measuring a surface force exerted by a flow of charged particles. The depositor has shown that a coating of electrically conductive material on the test mass allows these charges to be dissipated. Such a coating can also increase the lifetime of the measuring cell. As will be explained with reference to [Fig. 5], such a coating, for example metallic, can also be used as an electrode in a calibration procedure for the measuring device.

[0117] Measurement drifts of the surface force exerted by the particle flow can also result from temperature increases that cause thermal expansion. The presence of a metallic coating on the test mass can reduce the temperature gradients at the ends of the resonator and thus reduce thermal drifts.

[0118] As shown in equation [Math 4], the frequency variations depend on a quadratic term of the surface force exerted by the particles on the test mass. To improve measurement accuracy, this quadratic term can be limited by a differential measurement between two sensors.

[0119] Fig. 4A represents a diagram of a measuring device according to an example embodiment, the device comprising two measuring cells 110A, 110B arranged for differential measurement.

[0120] The first measuring cell 110A is similar to the measuring cell described in relation to [Fig. 2A] and [Fig. 2B] and comprises a fixed part 112A mechanically connected to the device support (not shown), a resonator 114A, and a movable mass or test mass 116A with an exposure face 117A. The test mass rotates about a single axis OAx, for example, the common axis of rotation of hinges 118A. CmA denotes the center of mass and CPA the center of pressure. During operation, the exposure face 117A experiences a surface force FpA exerted by the particle flow. This results in a tensile (or extensional) force TA on the resonator 114A at the point BA where the resonator connects to the test mass. We denote MTA the parasitic force exerted at the center of mass CmA and resulting from an acceleration along y, for example due to vibrations.

[0121] The second measuring cell 110B comprises a fixed part 112B mechanically connected to the support, a resonator 114B, and a movable mass or proof mass 116B with an exposure face 117B. The fixed part, the resonator, and the movable mass of the second measuring cell are substantially identical, respectively, to the fixed part, the resonator, and the movable mass of the first measuring cell. In particular, the proof mass 116B rotates about a single axis OBx, for example, the common axis of rotation of hinges 118B. The center of mass is denoted CmB and the center of pressure is denoted CPB.

[0122] Compared to the first measurement cell, only the position of the resonator 114B relative to the axis of rotation is reversed. In other words, the distances, along the direction n normal to the exposure face, between the resonator and the axis of rotation are substantially identical in both cells, but the positions of the resonator and the axis of rotation are reversed between the first measurement cell and the second measurement cell, such that when the exposure face of each of the measurement cells is exposed to the particle flow, one resonator undergoes compression while the other resonator undergoes extension.

[0123] Thus, in operation, when the exposure face 117B is subjected to a surface force FpB exerted by the particle flow, a compressive force TB results on the resonator 114B at the point where the resonator connects to the test mass Bb. MTB denotes the parasitic force exerted at the center of mass CmB and resulting from an acceleration along the y-axis, for example due to vibrations.

[0124] Thus, in the example shown in [Fig. 4A], the resonator 114A of the first measuring cell, for example a vibrating beam, undergoes compression under the effect of a surface force exerted by a particle flow on the exposure face 117A, while the resonator 114B of the second measurement cell, for example a vibrating beam, undergoes extension. This results in opposing frequency variations of resonators 114A and 114B.

[0125] In such a device, the fundamental frequencies of the two resonators are the same, as is any remaining thermal drift f, where 0 is the temperature. Since only the sensitivity to acceleration along y is non-zero, then, if the two cells are close to each other, the accelerations along this axis are similar, and the contributions fy to the resonator frequency of each resonator that derives from this acceleration are also identical. Thus, the frequency (p) of resonator 114A of the first measuring cell 110A and the frequency ys(pj) of resonator 114B of the first measuring cell 110B can be written as:

[0126] [Math.9] / >) = 4) + V x P 2 + f tk (6)+ fr^ ^-S^P + S^P* +fth(8) +facc

[0127] ^A4(P)= /

[0128] The frequency difference A / (P) between the two resonators then allows for a measurement of the surface force exerted by the particle flux by canceling the effects of residual vibration and thermal drift. This results in improved measurement accuracy.

[0129] In the example of [Fig.4A], the measuring device includes two measuring cells to perform a differential measurement.

[0130] A differential measurement can also be obtained with a single measuring cell comprising two resonators.

[0131] Fig. 4B thus represents a diagram of an example of a measuring cell in a device according to the present description, the measuring cell comprising two resonators arranged for differential measurement.

[0132] In this example embodiment, the measuring cell 110 includes a second resonator 114B, substantially identical to the first resonator 114A, the projections of the first resonator and the second resonator in a plane perpendicular to the axis of rotation being located on either side of a projection of the axis of rotation Ox onto said plane, such that when the exposure face 117 is exposed to the particle flux, one resonator (in this example the first resonator 114A) undergoes an extension (tension TA) while the other resonator (in this example the second resonator 114B) undergoes a compression T B.

[0133] In this example, the frequency difference A / (Fp) between the two resonators allows, as in the previous example, for a measurement of the surface force exerted by the particle flux by canceling the effects of residual vibration as well as thermal drifts.

[0134] Advantageously, a calibration of the measuring device is carried out before the implementation of the device.

[0135] Several calibration methods can be implemented. For example, it is possible to exert known forces applied by contact on the exposure face.

[0136] A preferred calibration solution is electrostatic calibration.

[0137] Figure 5 shows a schematic of a measuring cell 110 of a measuring device according to this description, and a device 510 for calibrating the cell, according to one embodiment. The calibration device 510 includes means 514 for applying a potential difference between a metallized region of the measuring cell forming a first electrode 119 and a metal plate forming a second electrode 512, located at a distance d from the first electrode. The first electrode 119 is, for example, made of tantalum or titanium.

[0138] Placing a metal electrode on the test mass and a metal plate opposite it creates an electrostatic force FEs when there is a potential difference between the two electrodes. The electrostatic force causes the test mass to move around its axis of rotation, for example, the common axis of the hinges 118, which creates a stress on the resonator 114. The force applied to the test mass is:

[0139] [Math. 10] “ld2

[0140] With Anie the surface of the calibration electrode 119 on the test mass, eo the permittivity of free space and V the potential difference applied between the two electrodes.

[0141] By reproducing the measurement for several values ​​of potential differences, a calibration can be performed.

[0142] A calibration such as the one described above has the advantage of being contactless with the measuring cell and easily implemented, since it is sufficient to place a metal plate under the test mass. Thus, this calibration can be performed in situ, or between two measurements.

[0143] Figs. 6A, 6B and 6C represent diagrams of a monolithic measuring cell 110 according to an example embodiment, according to different views.

[0144] The measuring cell 110 is monolithic in that the fixed part, the massive moving part, or test mass, and the resonator 114, for example a vibrating beam, are made from a single block of material, for example quartz.

[0145] In this example, the movable mass part 116 is movable about two hinges 618. The proof mass comprises a target forming the exposure surface 117 and two wings 612, the target being connected on one side to the two wings 612 and on the other side to the two hinges 618 and to one end of the resonator 114. Such an arrangement of the movable mass part makes it possible to distribute the mass so that the center of mass is close to the axis of the hinges 618.

[0146] Furthermore, in this example, the fixed part 112 comprises a decoupling frame 630 and an outer frame 620 configured to be connected to the support (not shown). The decoupling frame has a tuning fork shape and is connected on one side to the outer frame and on the other side to the hinges 618 and to a second end of the resonator 114.

[0147] As illustrated in [Fig. 6B], the target may include two weight-relieving pockets 617 on its rear face. This makes it possible to limit the mass of the target and the stresses applied to the hinges 618 and the vibrating beam 614, while ensuring a large contact area with the particles, good mechanical strength of the target, and distancing of parasitic resonance modes from the operating mode of the vibrating beam.

[0148] In exemplary embodiments, the target 617 is connected to the hinges 618 by two arms 610 such as to create an opening 615 between the target and the beam 114. This optional opening 615 prevents particle collisions near the vibrating beam. The arms 610 are connected to wings 612, which position the center of mass of the test mass as close as possible to the axis of the hinges in the xy plane. The parameter h ([Fig. 2A]) is thus substantially zero. A third arm at the base of the test mass connects the wings 612 to the hinges 618 and to the beam 114. This geometry of the test mass is advantageous because it eliminates the effects of parasitic accelerations (vibrations) on both the x and z axes.

[0149] The fixed part 112 includes the decoupling frame 630 and the external frame 620. The external frame 620 has a mechanical function of holding the test mass, the vibrating beam 114 and the decoupling frame 630. It also allows the test mass to be held during manufacturing and its physical protection.

[0150] The outer frame 620 includes connectors 640 (see [Fig. 6B], [Fig. 6C]), configured to ensure physical contact with the support (not shown), formed, for example, by a base. The connectors 640 also allow electrical contact with the electronic circuit (120, [Fig. 1]). The connectors 640 are advantageously made of a material having thermal behavior close to that of the measuring cell material, for example, Kovar® (iron-nickel-chromium-cobalt alloy). They are bonded to the outer frame, for example, with conductive adhesive.

[0151] The decoupling frame 630 forms a thermal and mechanical filter, protecting the beam 114 and the test mass 116 from the effects of the external environment. In this example, the decoupling frame is shaped like a tuning fork, connected to the outer frame by an end piece 631. The arms of the tuning fork are connected to hinges 618. The vibrating beam is fixed between a central portion of the tuning fork and the third arm of the outer frame, in an area of ​​minimal thermal stress. The thinness of the tuning fork arms allows them to deform and prevents the transmission of forces.

[0152] The applicant has demonstrated very satisfactory performance with monolithic measuring cells as illustrated in [Fig. 6A], [Fig. 6B], [Fig. 6C]. The cells are, for example, made of quartz. The external dimensions of the measuring cell are, for example, between approximately 10 mm and approximately 30 mm, with a thickness between approximately 100 microns and approximately 500 microns at the edges, for example approximately 500 microns, the thickness being less than 50 microns at the hinges and the beam.

[0153] With such a geometry of the measuring cell, the applicant obtained a linear sensitivity of 0.6 Hz / (pN.cm-2) or 60 Hz / Pa for a vibration frequency of 60 kHz.

[0154] The measuring cell produced is particularly compact and is insensitive to gravity.

[0155] Fig. 7A and Fig. 7B represent diagrams according to two views of a monolithic measuring cell 110 as illustrated in Fig. 6A, arranged on a support 201, according to an example embodiment.

[0156] In this example, the support 201 is a base in the form of an electronic board connected to the measuring cell by connectors 640. This arrangement allows the electronics required for vibration to be located as close as possible to the measuring cell. The board 201 may also include electrostatic calibration means, for example, in the form of two plates positioned opposite the wings (see also [Fig. 5]).

[0157] The measuring device may also include, in exemplary embodiments, a plate having dimensions similar to those of the electronic card 201 and placed in front of the cell in such a way that substantially only the target of the test mass is exposed to the particle flow.

[0158] Such a measuring device can then be placed in any position because it is insensitive to gravity.

[0159] Figure 8 shows a schematic of a satellite 800 comprising a body 810 equipped with a thruster and solar panels 820. As illustrated in Figure 8, the satellite in this example is equipped with a surface force measurement device. exerted by a particle stream as described herein. The measuring device comprises a measuring cell 110, for example of the type described with reference to the preceding figures. The fixed part of the measuring cell is connected to a support which is itself attached to an arm 850 mechanically and electrically connected to the satellite body 810. The measuring device is configured to measure the surface force exerted by the particle stream 10 ejected by the satellite's thruster. The electronic circuit and processing unit of the measuring device can be located remotely or arranged near the measuring cell.

[0160] Figure 9 shows a diagram of an enclosure 900 with a rarefied environment, for example a vacuum chamber, configured for the qualification of a satellite thruster 910 comprising means for ejecting a stream of neutral and / or charged particles. The enclosure includes a device for measuring the force exerted by the particle stream 10 ejected by the thruster. The measuring device includes a measuring cell 110, for example of the type described with reference to the preceding figures. The fixed part of the measuring cell is connected to a support which is itself fixed to an arm 950 connected, for example, to a rotating platform. The electronic circuit and the processing unit of the measuring device can be located remotely or arranged near the measuring cell.

[0161] Although described through a number of exemplary embodiments, the devices and methods for measuring the surface force exerted by a particle flow according to this description include various variants, modifications, and improvements that will be obvious to those skilled in the art, it being understood that these various variants, modifications, and improvements form part of the scope of the invention as defined by the following claims. References

[0162] [Ref. 1] Denis Packan et al. “Thrust Measurements with the ONERA Micronewton Balance” Paper IEPC-2007-118 at the 30th International Electric Propulsion Conference, Florence, Italy, 17-20 September 2007.

[0163] [Ref. 2] DG Chavers and FR Chang-Diaz, “Momentum flux measuring instrument for neutral and charged particle flows” Rev. Sci. Instrum., vol. 73, no. 10, pp. 3500-3507, Oct. 2002, doi: 10.1063 / 1.1505107.

[0164] [Réf. 3] A. Spethmann, T. Trottenberg, and H. Kersten, “Spatially Resolved Momentum Flux Measurements for Thruster Plume Diagnostics” presented at the IEPC, 2013.

Claims

Demands

1. A measuring cell (110) for measuring the surface force exerted by a particle flow comprising: - a fixed part (112) configured to be mechanically and electrically connected to a support; - at least one first resonator (114, 114A) comprising a longitudinal axis (A), said first resonator having a first end fixed to said fixed part; - a movable solid part (116) comprising a face exposed (117) to the particle flow, said solid part being such that: - said solid part is movable relative to the fixed part along a single axis of rotation (Ox) perpendicular to a plane formed by the longitudinal axis of the first resonator and a direction (n) normal to the face of exposure; - the axis of rotation (Ox) and the longitudinal axis of the first resonator are separated in the direction (n) normal to the face of exposure by a predetermined non-zero distance (dp);and - the first resonator has a second end (B) attached to said moving mass part; - a first distance (h) between the axis of rotation (Ox) and a center of mass (Cm) of the moving mass part is strictly less than a second distance (p) between the axis of rotation (Ox) and a center of pressure (Cp) of the exposure face (117), the first distance and the second distance being distances projected onto a plane (Oxy) parallel to the exposure face, the measuring cell (110) being characterized in that the ratio between said first distance (h) and said second distance (p) is less than about 0.1.;

2. Measuring cell according to claim 1, wherein the ratio between said first distance (h) and said second distance (p) is less than about 0.

01.

3. A measuring cell according to any one of the preceding claims, wherein a ratio between a third distance (dg) between the axis of rotation (Ox) and the center of mass (Cm) of the moving massive part and a fourth distance (dp) between the axis of rotation (Ox) and the axis (A) of the first resonator is strictly less than 1, advantageously strictly less than about 0.1, the third distance and the fourth distance being distances projected onto a plane (Oxz) perpendicular to the exposure face.

4. Measuring cell according to any one of the preceding claims, wherein the measuring cell is monolithic.

5. Measuring cell according to any one of the preceding claims, wherein: - the measuring cell comprises two hinges including a common axis of rotation; - said common axis of rotation forms the unique axis of rotation (Ox) of said movable solid part.

6. Measuring cell according to claim 5, wherein a projection of the axis (A) of the first resonator in a plane parallel to the exposure face and comprising said common rotation axis (Ox) intersects said common rotation axis at a midpoint located substantially halfway between the two hinges.

7. Measuring cell according to claim 6, wherein a distance (dmp) between a projection of the center of mass (Cm) of the massive moving part on said common axis of rotation and said midpoint is strictly less than a distance (dpc) between said midpoint and each of the hinges.

8. Measurement cell according to any one of claims 5 to 7, wherein: - the movable solid part (116) comprises a target forming the exposure surface (117) and two wings (612), said target being connected to the two wings, to the two said hinges and to the second end of the first resonator; - the fixed part comprises a decoupling frame (630) and an external frame (620) configured to be connected to the support, said decoupling frame having a tuning fork shape connected on one side to the external frame, and on the other side to the two said hinges and to the first end of the first resonator.

9. Measuring cell according to any one of the preceding claims, wherein the first resonator comprises at least one vibrating beam in bending mode.

10. Measuring cell according to any one of the preceding claims, wherein at least a part of the moving mass part (116) has a coating of electrically conductive material.

11. A device for measuring (100) the surface force exerted by a particle flow (10), comprising: - a support (201); - at least one first measuring cell (110, 110A) according to any one of the preceding claims, said fixed part (112) being mechanically and electrically connected to said support; - an electronic circuit (120) configured to excite the first resonator of said at least one first measuring cell at an initial resonant frequency and to measure, when the device is subjected to the particle flow, a measurement resonant frequency; - a processing unit (130) configured to determine, from a difference between the measurement resonant frequency and the initial resonant frequency, the surface force exerted by the particle flow.

12. A measuring device according to claim 11 comprising a second measuring cell (110B), in which: - the second measuring cell comprising a fixed part (112) mechanically connected to the support, a resonator (114B) and a movable solid part (116B), said fixed part, said resonator and said movable solid part of the second measuring cell being substantially identical respectively to the fixed part, the resonator and the movable solid part of the first measuring cell; - the positions of the resonator and the axis of rotation along the direction (n) normal to the exposure face are reversed between the first measuring cell and the second measuring cell, such that when the exposure face of each of the measuring cells is exposed to the particle flow, one resonator undergoes compression while the other resonator undergoes extension;- the processing unit (130) is configured to further determine a difference between the measurement resonance frequency measured by means of the first measurement cell and the measurement resonance frequency measured by means of the second measurement cell in order to determine the surface force exerted by the particle flow.;

13. Satellite (800) comprising a thruster with means for ejecting a stream of neutral and / or charged particles (10) and a device for measuring the force exerted by said particle stream according to any one of claims 11 or 12, the support for the device measurement being mechanically and electrically connected to a body (810) of the satellite by means of an arm (850).

14. Enclosure (900) with rarefied environment configured for the qualification of a flux of neutral and / or charged particles, the enclosure comprising a device for measuring the force exerted by a particle flux according to any one of claims 11 or 12, the support of the measuring device being mechanically and electrically connected to a body of the enclosure, the measuring device being configured to measure the particle flux (10).

15. A method for measuring the surface force exerted by a particle flow using a device according to any one of claims 11 or 12, the method comprising: - exciting the first resonator and measuring an initial resonance frequency of the resonator (fr0), without particle flow; - receiving the particle flow through the exposure face of the measuring cell and measuring a measurement resonance frequency of the resonator (fr(P)+fr0) resulting from the force applied by the particle flow on said exposure face; - determining, from a difference between the measurement resonance frequency and the initial resonance frequency, the surface force of the particle flow.

16. A measurement method according to claim 15 comprising an additional calibration step, said calibration step comprising: - the successive application of several potential differences between a region having a coating of electrically conductive material of the moving mass part (116) and an opposing metal plate, the application of each potential difference resulting in an electrostatic force applied to the moving mass part; - for each potential difference, the measurement of a measurement resonance frequency resulting from said electrostatic force and the determination of the difference between the measurement resonance frequency and the initial resonance frequency.

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