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Publication Enhanced AOCS verification techniques for Euclid's high-pointing performance(Elsevier, 2022-08-30) Navarro Tapia, Diego; Marcos Esteban, Andrés; Veenman, JoostThis paper presents an enhanced Verification and Validation (V&V) framework accompanied by dedicated tools that allows to analytically evaluate pointing error performance of high-pointing accuracy missions in the presence of disturbances and uncertainties. The proposed analysis approach poses the V&V problem in the robust control framework using linear fractional transformation modelling theory (to include model uncertainties) and frequency dependent weighting functions (to capture the spectral properties of the disturbances and the pointing error performance metrics), and is based on the structured singular value approach as well as the integral quadratic constraint (IQC) framework. The validity of this formal approach is exemplified through the verification of the stringent pointing performance of the Euclid mission during the science observation phase. The results show that the proposed enhanced V&V approach is capable of providing certificates for robust stability and performance for all modelled uncertainties.Publication Comparison of Flight FTC Techniques: from standard and structured H∞, to self-scheduling and LPV(Elsevier, 2022-09-27) Marcos Esteban, Andrés; Waitman, Sergio; Sato, Masayuki; European CommissionIn this article several robust control design techniques are compared via their application to the fault tolerant control problem for the lateral/directional motion of JAXA's research aircraft MuPAL-α. The techniques used include: (i) a single, passive-FTC, robust structured H∞ design, (ii) single, active-FTC, robust standard and structured H∞ designs, (iii) manual scheduling schemes from the previous designs, (iv) a self-scheduled structured H∞ design, and (v) a linear parameter varying design. All the designs were implemented in the onboard computer and validated in the so-called Aircraft-In-the-Loop configuration, which entails the operation of the full aircraft in fly-by-wire mode in the hangar. The results show that all the approaches provided acceptable solutions, but with the last two techniques resulting in a more homogeneous performance throughout the fault and command scenarios tested.Publication PIC/fluid/wave Simulation of the Plasma Discharge in an ECR Plasma Thruster(2019-09-15) Sánchez Villar, Álvaro; Zhou, Jiewei; Merino Martínez, Mario; Ahedo Galilea, Eduardo Antonio; European Commission; Ministerio de Economía y Competitividad (España)We present the first self-consistent, complete simulations of the Big-Magnet electron-cyclotron resonance thruster (ECRT) developed by ONERA. The simulation uses a hybrid PIC/ uid model for the plasma transport and a frequency-domain full-wave model for the electromagnetic fields based on an adaptable mesh and a collisional cold plasma dielectric description. Plasma properties and electromagnetic fields are shown for the nominal operating point. Most of the electromagnetic power absorption is due to radial electric fields near the ECR region. The simulation shows that the ECRT plasma discharge contains multiple electromagnetic wave propagation regimes, and the sensitivity of the wavefields on the the plasma profiles.Publication Fluid-kinetic propulsive magnetic nozzle model in the fully magnetized limit(2019-09-15) Nuez, Judit; Merino Martínez, Mario; Ahedo Galilea, Eduardo Antonio; European Commission; Ministerio de Economía y Competitividad (España)A kinetic electron model and a fluid ion model are combined to describe the 2D plasma expansion in an axisymmetric magnetic nozzle in the fully-magnetized, collisionless limit. Electrons can be separated into free, reflected, and doubly-trapped populations, and are seen to develop anisotropy and to cool down in a non-trivial way downstream. A polytropic electron model with same asymptotic electric potential value, 8, misses these kinetic aspects and fails to approximate the behavior of the electric potential and the average electron temperature. These differences are important in determining the performance of the device.Publication Effect of the initial VDFs in magnetic nozzle expansions(2019-09-15) Correyero Plaza, Sara; Merino Martínez, Mario; Ahedo Galilea, Eduardo Antonio; European Commission; Ministerio de Economía y Competitividad (España)This work presents a kinetic study of the plasma response in a fully magnetized plasma expansion. A paraxial, collisionless, steady-state plasma model is used to analyze the effect of expanding in a convergent-divergent nozzle a plasma with different types of VDF at the plasma reservoir. The first part of the paper studies the kinetic features, such as magnetic mirroring and anisotropy for both ions and electrons. The collective effects are analyzed by evaluating the momentum and energy equations based on the kinetic solution. The study of the collisionless heat fluxes allows estimating a simple closure to the fluid equation hierarchy for the electrons. The second part of the paper analyzes the solution with two species of electrons with disparate temperatures at the upstream source. A quasineutral steepened profile is formed, which impacts the plasma properties along the expansion. The collisionless electron cooling, as well as the anisotropy on the divergent side of the nozzle are analyzed by separating the different subpopulations of electrons (free, reflected, or doubly-trapped), of both the thermal and the suprathermal species.Publication Global stability analysis of azimuthal oscillations in Hall thrusters(IEEE, 2014-11-20) Escobar Antón, Diego; Ahedo Galilea, Eduardo AntonioA linearized time-dependent 2-D (axial and azimuthal) fluid model of the Hall thruster discharge is presented. This model is used to carry out a global stability analysis of the plasma response, as opposed to the more common local stability analyses. Experimental results indicate the existence of low-frequency long-wave-length azimuthal oscillations in the direction of the E × B drift, usually referred to as spokes. The present model predicts the presence of such oscillations for typical Hall thruster conditions with a frequency and a growth rate similar to those found in experiments. Moreover, the comparison between the simulated spoke and the simulated breathing mode, a purely axial low-frequency oscillation typical in Hall thrusters, shows similar features in them. Additionally, the contribution of this azimuthal oscillation to electron conductivity is evaluated tentatively by computing the equivalent anomalous diffusion coefficient from the linear oscillations. The results show a possible contribution to anomalous diffusion in the rear part of the thruster.Publication Influence of electron and ion thermodynamics on the magnetic nozzle plasma expansion(IEEE Press, 2015-01) Merino Martínez, Mario; Ahedo Galilea, Eduardo AntonioA two-fluid 2-D model of the supersonic plasma flow in a propulsive magnetic nozzle (MN) is extended to include simple electron and ion thermodynamics to study the effects of electron cooling and ion thermal energy on the expansion. A faster electron cooling rate is seen to reduce plasma jet divergence, increase radial rarefaction, and enhance detachment from the closed magnetic lines. Ion thermal energy is converted to directed kinetic energy by the MN without the mediation of an ambipolar electric field, and alters the electric response of the plasma.Publication Current-Voltage and floating-potential characteristics of cylindrical emissive probes from a full-kinetic model based on the orbital motion theory(IOP Publishing, 2017-09) Chen, Xin; Sánchez Arriaga, Gonzalo; Ministerio de Economía y Competitividad (España)To model the sheath structure around an emissive probe with cylindrical geometry, the Orbital-Motion theory takes advantage of three conserved quantities (distribution function, transverse energy, and angular momentum) to transform the stationary Vlasov-Poisson system into a single integro-differential equation. For a stationary collisionless unmagnetized plasma, this equation describes self-consistently the probe characteristics. By solving such an equation numerically, parametric analyses for the current-voltage (IV) and floating-potential (FP) characteristics can be performed, which show that: (a) for strong emission, the space-charge effects increase with probe radius; (b) the probe can float at a positive potential relative to the plasma; (c) a smaller probe radius is preferred for the FP method to determine the plasma potential; (d) the work function of the emitting material and the plasma-ion properties do not influence the reliability of the floating-potential method. Analytical analysis demonstrates that the inflection point of an IV curve for non-emitting probes occurs at the plasma potential. The flat potential is not a self-consistent solution for emissive probes.Publication Collisional effects in non-stationary plasma expansions along convergent-divergent magnetic nozzles(2018-05) Zhou, Jiewei; Sánchez Arriaga, Gonzalo; Ahedo Galilea, Eduardo Antonio; Martinez-Sánchez, M.; Ramos, Jesús JoséThe electron-electron collisional effect on the nonstationary expansion of a plasma in a convergentdivergent magnetic nozzle is studied. Under paraxial and fully magnetized plasmas approximations, an Eulerian code has been adapted to solve Poisson's equation coupled with the kinetic transport equations for plasma species, i.e. a Vlasov equation for singly-charged ions and a Boltzmann equation with a Bhatnagar-Gross-Kook operator for electrons. The study is focused on weakly collisional plasma plumes, which have a collisional time scale larger than the transit time in the nozzle of typical electrons. A kinetic analysis shows that phasespace regions of isolated, doubly-trapped electrons that are nearly empty in the collisionless case are progressively populated due to the electron-electron collisions. Such a higher density of trapped electrons modifies the profile of the electrostatic potential, which keeps almost unaltered the density of free electrons and decreases the density of the reflected ones. As compared with the collisionless case, the collisions decrease the length of the downstream sheath and the parallel electron temperature while increasing the normal one. Therefore the steady plasma state is more isotropic. The simulations show that collisions erase the time history of the system and, unlike the collisionless case, the steady state is unique.Publication Advances in wave-plasma modelling in ECR thrusters(2018-05) Sánchez Villar, Álvaro; Merino Martínez, MarioThis paper presents the development status of the simulation tool THaMES (Time-Harmonic Maxwell Equations Solver) that aims to reproduce the electromagnetic (EM) wave propagation inside an ECR plasma thruster to study the ECR resonance absorption and wave propagation. THaMES allows the use of a planar domain filled with arbitrary cold magnetized inhomogeneous plasmas, specifying parameters such as the electron plasma density, the applied magnetic field or the effective collisional rate. The simulation relies on MFEM discretization library.Publication Ion acceleration in the magnetic nozzle of an ECR thruster: comparison of experimental measurements with a quasi 1D kinetic model(2018-05) Correyero Plaza, Sara; Jarrige, Julien; Packan, Denis; Ahedo Galilea, Eduardo AntonioThis paper presents experimental results on the magnetic nozzle of the 50 W Electron Cyclotron Resonance (ECR) thruster of ONERA, consisting of a 27 mm diameter ECR cavity and a fully divergent magnetic nozzle, created by a Neodymium permanent magnet. The diagnostics installed are a cylindrical Langmuir probe to measure plasma potential, plasma density and electron temperature, and a Laser Induced Fluorescence set-up to measure the mean ion kinetic energy. Both the ion velocity and plasma potential profiles seem to be independent of the mass flow rate when normalized with the electron temperature estimated at the sonic transition of the plasma flow. This sonic transition appears to be slightly shifted downwards of the thruster exit. Results are compared with a supersonic collisionless kinetic 1D model where electron dynamics account for magnetic mirror effects and potential barriers, while ions are treated as a fluid cold species.Publication Innovative electric propulsion trends, concurrent mission design and enabling technologies for a bold CubeSat Lunar Positioning System(2017) Wijnen, Mick; Correyero Plaza, Sara; Agüera López, Nereida; Pérez Grande, DanielCubeSats have become exceedingly versatile satellite platforms over the last decade. However they are still limited by a lack of efficient propulsive means. A novel electric thruster based on Electron Cyclotron Resonance heating and Magnetic Nozzle acceleration may provide a suitable yet simple solution. This device, while currently providing 1000s Isp and 1 mN of thrust at 30W of power, may enable Lunar CubeSat missions from GEO using on-board propulsion. An example mission to provide GPS on the lunar surface using 3U CubeSats in a 60°:24/4/1 Walker constellation with a semi-major axis of 4000 km is proposed; a preliminary assessment of this mission, together with the satellite architecture and cost, is performed. Concurrent trajectory design for very-low-energy transfers is used to demonstrate the feasibility of the mission and its in uence on the space-craft design.Publication One-dimensional direct Vlasov simulations of non-stationary plasma expansion in magnetic nozzle(2017) Sánchez Arriaga, Gonzalo; Zhou, Jiewei; Ahedo Galilea, Eduardo Antonio; Martínez-Sánchez, Manuel; Ramos, Jesús José; European Commission; Ministerio de Economía y Competitividad (España)The one-dimensional (paraxial approximation) transient expansion into vacuum of a collisionless electron-ion plasma guided by a magnetic nozzle is studied numerically. The simulation box, initially empty, has zero boundary conditions for the gyrocenter distribution functions of electrons and ions fe and fi, except at the entry of the nozzle, where particles with a positive axial velocity follow a Maxwellian. The time evolutions of fe and fi are computed with a parallelized direct Vlasov code, which solves a non-stationary guiding center equation for fully magnetized plasmas and discretizes the distribution functions in phase space. The latter involves the (conserved) magnetic moment, and the axial coordinate and velocity of the particles. The gyrocenter distribution functions of the electrons and the ions, aected by the axial components of the electrostatic electric eld and the gradient of the magnetic eld strength, are coupled through Poisson equation in the code. The evolution of macroscopic quantities, like particle density and electrostatic potential proles, are discussed. Relevant kinetic features, such as the evolution of the ions towards a mono-energetic distribution function and the evolution of the plasma temperature proles, are analyzed. The electron trapping, which the stationary models cannot determined self-consistently, and the transient trapping mechanism are captured by the code. This allows an assessment of the impact of the population of trapped electrons and a detailed analysis of their distribution function in terms of axial position, velocity and magnetic moment. Extensions of the code to two-dimensional congurations with axisymmetric geometry, but still fully magnetized plasmas, are discussed.Publication The "MINOTOR" H2020 project for ECR thruster development(2017) Packan, Denis; Elias, Paul-Quentin; Jarrige, Julien; Merino Martínez, Mario; Sánchez Villar, Álvaro; Ahedo Galilea, Eduardo Antonio; Peyresoubes, G.; Holste, K.; Klar, P.; Bekemans, M.; Scalais, T.; Bourguignon, E.; Zurbach, S.; Mares, M.; Hoque, A.; Favier, P.; European CommissionElectric propulsion has been identified by European actors as a strategic technology for improving competitiveness in different space areas such as in-space operations and transportation. The European Commission has set up the "In-space Electrical Propulsion and Station-Keeping" Strategic Research Cluster (SRC) in the "Horizon 2020" funding framework with the goal of enabling major advances in Electric Propulsion for in-space operations and transportation. In this framework, the MINOTOR project was funded to mature a potentially disruptive cathodeless electric propulsion technology, the Electron Cyclotron Resonance (ECR) thruster. In recent years, the consortium leader ONERA has built up a large experience on ECR technology for electric propulsion, and the MINOTOR project will bring the expertise from three industrial partners (TMI, TAS-B and SAFRAN) and two university partners (UC3M and JLU) to take the next step.Publication Wave propagation and absorption in ECR plasma thrusters(2017) Merino Martínez, Mario; Sánchez Villar, Álvaro; Ahedo Galilea, Eduardo Antonio; Bonoli, Paul; Lee, Jungpyo; Ram, Abhay; Wright, John; Ministerio de Economía y Competitividad (España)The physical mechanisms involved in the generation, propagation and absorption of microwaves in electron-cyclotron-resonance plasma thrusters, and their relevance in the operation of these devices, are discussed. The features of the electromagnetic waves and electron motion near the resonance region are analyzed with a one-dimensional model. The characteristics of the two-dimensional wave-plasma problem are examined, and a trade-off of different numerical models is presented as a first step toward the development of an ECR wave-plasma interaction simulation code.Publication Investigation on the ion velocity distribution in the magnetic nozzle of an ECR plasma thruster using LIF measurements(2017) Jarrige, Julien; Correyero Plaza, Sara; Elias, Paul-Quentin; Packan, Denis; European CommissionLaser-induced fluorescence (LIF) is a non-intrusive technique that can provide useful information on ion production and acceleration in electric propulsion system. In this paper, spatially resolved LIF measurements of Xe+ are performed in the plume of an electron cyclotron resonance plasma thruster. The mapping of ion velocity distribution function in the magnetic nozzle shows that the ions are accelerated over a distance greater than 12 cm. A mean axial velocity up to 16 km/s has been obtained at 1 sccm and 26 W. The acceleration of ions is compared for different xenon flowrates.Publication Measurement of anisotropic plasma properties along the magnetic nozzle expansion of an electron cyclotron resonance thruster(2017) Correyero Plaza, Sara; Jarrige, Julien; Packan, Denis; Ahedo Galilea, Eduardo Antonio; European CommissionThis work presents experimental measurements along the magnetized plume of the ECR thruster developed by ONERA. Langmuir probes are used to determine the electron energy probability function (eepf) at different axial positions, revealing the non-local character of the distributions. The second part of the paper details a combined diagnostics of non-intrusive diamagnetic loop measurements and laser induced fluorescence to estimate the perpendicular electron temperature inside the plasma source. Averaged perpendicular electron pressure, plasma density, ion velocity at the exit plane and perpendicular electron temperature are determined as functions of the mass flow rate.