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Publication Leakiness of Pinned Neighboring Surface Nanobubbles Induced by Strong Gas-Surfice Interaction(American Chemical Society, 2018-03-27) Maheshwari, Shantanu; Van Der Hoef, Martin; Rodríguez Rodríguez, Francisco Javier; Lohse, DetlefThe stability of two neighboring surface nanobubbles on a chemically heterogeneous surface is studied by molecular dynamics (MD) simulations of binary mixtures consisting of Lennard-Jones (LJ) particles. A diffusion equation-based stability analysis suggests that two nanobubbles sitting next to each other remain stable, provided the contact line is pinned, and that their radii of curvature are equal. However, many experimental observations seem to suggest some long-term kind of ripening or shrinking of the surface nanobubbles. In our MD simulations we find that the growth/dissolution of the nanobubbles can occur due to the transfer of gas particles from one nanobubble to another along the solid substrate. That is, if the interaction between the gas and the solid is strong enough, the solid-liquid interface can allow for the existence of a "tunnel" which connects the liquid-gas interfaces of the two nanobubbles to destabilize the system. The crucial role of the gas-solid interaction energy is a nanoscopic element that hitherto has not been considered in any macroscopic theory of surface nanobubbles and may help to explain experimental observations of the long-term ripening.Publication Impact of propellant temperature on the emission regime of an externally wetted electrospray system using time-of-flight mass spectrometry(Elsevier, 2023-12) Villegas Prados, David; Cruz, Javier; Wijnen, Mick; Correyero Plaza, Sara; Fajardo Peña, Pablo; Navarro Cavallé, Jaume; Comunidad de MadridElectrospray thrusters operate in different regimes depending on the ejected particles: pure ionic regime, characterized by the presence of only solvated ions; droplet regime; and mixed regime, where both ion and droplets are emitted. The electrospray emission regime is driven by the physical properties of the liquid, the flow rate to the emission site, and the electric field applied. Because of the temperature dependence of the ionic liquid, the emission regime and hence the propulsive performance are sensitive to the liquid temperature. Additionally, in externally wetted electrospray emitters, where the flow rate is passively controlled by viscous forces, temperature plays a crucial role as it drives the hydraulic impedance of the emitter due to the variation of the liquid's viscosity, and therefore the emitter flow rate. The research described in this work is focused on the effect of the propellant temperature on the emission regime of externally wetted emitters. By means of a time-of-flight mass spectrometer the plume composition has been analyzed under different conditions of applied voltage and operating temperature, finding that voltage increases the relative amount of ion species and temperature increases the relative amount of droplets.Publication Commentary: On helicon thrusters: Will they ever fly?(Frontiers, 2020-08-20) Takahashi, Kazunori; Charles, Christine; Boswell, Rod W.; Takao, Yoshinori; Fruchtman, Amnon; Navarro Cavallé, Jaume; Merino Martínez, MarioPublication Simulations of driven breathing modes of a magnetically shielded Hall thruster(IOP Science, 2023-07) Perales Díaz, Jesús; Domínguez Vázquez, Adrián; Fajardo Peña, Pablo; Ahedo Galilea, Eduardo Antonio; European Commission; Agencia Estatal de Investigación (España)The operation of a 5 kW-class magnetically shielded Hall effect thruster with sinusoidal modulation of the discharge voltage is investigated through simulations with a 2D axisymmetric hybrid (particle-in-cell/fluid) code. The dynamic response of the thruster for different modulation amplitudes and frequencies is presented and discussed. The analysis of partial efficiencies contributing to thrust efficiency allows identifying counteracting effects limiting net gains in performance figures. Voltage modulation enhances the amplitude of plasma oscillations and can effectively control their frequency when the modulation frequency is close to that of the natural breathing mode (BM) of the thruster. The 2D plasma solution reveals that the dynamics of the ionization cycle are governed by the electron temperature response, enabling a driven BM at the modulation frequency. For modulation frequencies far from the natural BM one, voltage modulation fails to control the plasma production via the electron temperature, and the natural BM of the thruster is recovered. High order dynamic mode decomposition applied to the 2D plasma solution permits analyzing the complex spatio-temporal behavior of the plasma discharge oscillations, revealing the main characteristics of natural and externally driven modes.Publication Kinetic electron cooling in magnetic nozzles: experiments and modeling(IOP Science, 2023-07) Kim, June Young; Chung, Kyoung-Jae; Takahashi, Kazunori; Merino Martínez, Mario; Ahedo Galilea, Eduardo Antonio; European Commission; Agencia Estatal de Investigación (España)As long-distance space travel requires propulsion systems with greater operational flexibility and lifetimes, there is a growing interest in electrodeless plasma thrusters that offer the opportunity for improved scalability, larger throttleability, running on different propellants and limited device erosion. The majority of electrodeless designs rely on a magnetic nozzle (MN) for the acceleration of the plasma, which has the advantage of utilizing the expanding electrons to neutralize the ion beam without the additional installation of a cathode. The plasma expansion in the MN is nearly collisionless, and a fluid description of electrons requires a non-trivial closure relation. Kinetic electron effects and in particular electron cooling play a crucial role in various physical phenomena, such as energy balance, ion acceleration, and particle detachment. Based on experimental and theoretical studies conducted in recognition of this importance, the fundamental physics of the electron-cooling mechanism revealed in MNs and magnetically expanding plasmas is reviewed. In particular, recent approaches from the kinetic point of view are discussed, and our perspective on the future challenges of electron cooling and the relevant physical subject of MN is presented.Publication Time-dependent axial fluid model of the Hall thruster discharge and its plume(IOP Science, 2023-10-12) Poli, Davide; Bello-Benítez, Enrique; Fajardo Peña, Pablo; Ahedo Galilea, Eduardo Antonio; Comunidad de Madrid; Agencia Estatal de Investigación (España)One-dimensional axial models of a Hall thruster give a good qualitative picture of the main physical phenomena in the discharge with small computational effort. Time-dependent models, in particular, are widely used for the analysis of low-frequency axial oscillations (i.e. the breathing mode). The standard time-dependent three-fluid model found in the literature is here enhanced by extending the physical domain beyond the cathodic surface into the far plume, and improving the modeling of some physical phenomena. A suite of five models is presented in this work with an increasing complexity of added physics; the most complete version accounting for ion and neutral energy evolution equations along with the partial inclusion of electron inertia. The added physics has a non negligible impact on both the dynamics of the breathing mode and the time-averaged response of the plasma. In particular, it is found that the onset of the instability is sensitive to both the level of modeled physics and the operational parameters. In some cases, the strong breathing mode oscillations can result in a weak plasma attachment to the anode, leading to the collapse of the normal anode sheath and to the subsequent failure of the model.Publication Machine-learning flow control with few sensor feedback and measurement noise(AIP, 2022-04-21) Castellanos García de Blas, Rodrigo; Cornejo Maceda, G.Y.; de la Fuente, I.; Noack, B.R.; Ianiro, Andrea; Discetti, StefanoA comparative assessment of machine-learning (ML) methods for active flow control is performed. The chosen benchmark problem is the drag reduction of a two-dimensional Kármán vortex street past a circular cylinder at a low Reynolds number (Re = 100). The flow is manipulated with two blowing/suction actuators on the upper and lower side of a cylinder. The feedback employs several velocity sensors. Two probe configurations are evaluated: 5 and 11 velocity probes located at different points around the cylinder and in the wake. The control laws are optimized with Deep Reinforcement Learning (DRL) and Linear Genetic Programming Control (LGPC). By interacting with the unsteady wake, both methods successfully stabilize the vortex alley and effectively reduce drag while using small mass flow rates for the actuation. DRL has shown higher robustness with respect to different initial conditions and to noise contamination of the sensor data; on the other hand, LGPC is able to identify compact and interpretable control laws, which only use a subset of sensors, thus allowing for the reduction of the system complexity with reasonably good results. Our study points at directions of future machine-learning control combining desirable features of different approaches.Publication Plume characterization of a waveguide ECR thruster(AIP Publishing, 2023-03-21) Inchingolo, M. R.; Merino Martínez, Mario; Navarro Cavallé, Jaume; Comunidad de Madrid; Ministerio de Ciencia e Innovación (España)A circular waveguide electron cyclotron resonance plasma thruster prototype driven by microwaves at 5.8 GHz (80-300 W) is characterized. The magnetic field is generated by a combination of Sm-CoYXG32 magnets and an electromagnet, which enables the tuning of the resonance position and magnetic nozzle shape. The main plasma plume properties are analyzed by using electrostatic probes when the mass flow rate (Xenon), microwave power, electromagnet current, and propellant injector design are varied. An estimation of the propulsive performance of the device is also presented. Results show that a single radial injector hole is not sufficient for a symmetric ion current profile and that magnetic nozzle shape and strength tuning can significantly affect the divergence angle and thruster floating potential. A utilization efficiency of up to 70% and electron temperatures of up to 16 eV have been measured.Publication Comparison of a hybrid model and experimental measurements for a dielectric-coated coaxial ECR thruster(IOP Science, 2023-01) Sánchez Villar, Álvaro; Boni, Federico; Désangles, Victor; Jarrige, Julien; Packan, Denis; Ahedo Galilea, Eduardo Antonio; Merino Martínez, Mario; European Commission; Ministerio de Ciencia e Innovación (España)Electrostatic probe and thrust balance measurements of a coaxial electron-cyclotron-resonance plasma thruster with magnetic nozzle are compared against numerical simulations of the device that solve self-consistently the plasma transport problem with a hybrid particle-in-cell/fluid approach and the microwave electromagnetic fields using mixed finite elements. A simple phenomenological anomalous transport model similar to those used in Hall thruster modeling is applied. Reasonable average relative errors are reported on the ion current density (8.7%) and plasma density (12.8%) profiles along the plume. Good agreement is found in terms of relative errors on thruster performance parameters as the 90%-current divergence angle (0%–3%), utilization efficiency (3%–10%), peak ion energy (9%–15%), and energy efficiency (2%–17%). The comparison suggests that enhanced cross-field diffusion is present in the plasma. Differences in the experimental and numerical behavior of electron temperature point to the areas of the model that could be improved. These include the electron heat flux closure relation, which must correctly account for the axial electron cooling observed.Publication Using electron fluid models to analyze plasma thruster discharges(Springer, 2023-12) Ahedo Galilea, Eduardo Antonio; Comunidad de MadridFluid models of the slow-dynamics of magnetized, weakly-collisional electrons lead to build computationally-affordable, long-time simulations of plasma discharges in Hall-effect and electrodeless plasma thrusters. This paper discusses the main assumptions and techniques used in 1D to 3D electron fluid models, and some examples illustrate their capabilities. Critical aspects of these fluid models are the expressions for the pressure tensor, the heat flux vector, the plasma-wall fluxes, and the high-frequency-averaged electron transport and heating caused by plasma waves, generated either by turbulence or external irradiation. The different orders of magnitude of the three scalar momentum equations characterize the electron anisotropic transport. Central points of the discussion are: the role of electron inertia, magnetically-aligned meshes versus Cartesian-type ones, the use of a thermalized potential and the infinite mobility limit, the existence of convective-type heat fluxes, and the modeling of the Debye sheath, and wall fluxes. Plasma plume models present their own peculiarities, related to anomalous parallel cooling and heat flux closures, the matching of finite plume domains with quiescent infinity, and solving fully collisionless expansions. Solutions of two 1D electron kinetic models are used to derive kinetically-consistent fluid models and compare them with more conventional ones.Publication Laser-induced fluorescence spectroscopy on xenon atoms and ions inthe magnetic nozzle of a Helicon plasma thruster(IOP Publising, 2022-09-15) E. Vinci, Alflo; Mazouffre, Stéphane; Gómez, Víctor; Fajardo Peña, Pablo; Navarro Cavallé, Jaume; European CommissionThe dynamics of xenon atoms and ions expanding in the magnetic nozzle (MN) of a helicon plasma thruster is studied by means of near-infrared laser-induced fluorescence spectroscopy on resonant and metastable states. Fluorescence spectra are measured for several operating conditions inside and outside the thruster discharge chamber. In the near-field plume, the relatively intense magnetic field induces Zeeman effect on the probed optical transitions. Hence, modeling of the atomic lineshapes is addressed to accurately compute the Doppler shift and infer the velocity. The first direct measurements of the neutral flow in a MN reveal that atoms are accelerated to supersonic velocities behind the thruster exit. The ions acceleration region extends several centimeters downstream the exit plane. Larger axial ion speeds are attained when the thruster operates at lower mass flow rates and higher levels of input power.Publication Kinetic plasma dynamics in a radial model of a Hall thuster with a curved magnetic field(Elsevier, 2022-11-03) Marín-Cebrián, Alberto; Domínguez Vázquez, Adrián; Fajardo Peña, Pablo; Ahedo Galilea, Eduardo Antonio; Comunidad de Madrid; Agencia Estatal de Investigación (España)A 1D particle-in-cell model of a Hall thruster discharge is used to analyze the effect of a curved magnetic topology in the radial plasma response and the plasma fluxes to dielectric walls. The kinetic solution shows a significant replenishment of the velocity distribution function tail and temperature isotropization for both negative (i.e. anode pointing) and positive curvatures. The new radial magnetic force is electron confining or expanding for, respectively, negative and positive curvatures, and this modifies significantly the electric and pressure radial forces. As a consequence, the plasma density near the wall and the degree of radial ion defocusing are affected: they are highly reduced for negative curvatures, the case of higher interest. For positive curvatures, the kinetic solution shows that the radial ion flow becomes supersonic within the plasma bulk, away from the Debye sheaths. An ancillary quasineutral fluid model is presented to explain this feature and other aspects of the kinetic solution. Some kinetic studies on additional phenomena complete the work.Publication Computation of bifurcation margins based on robust control concepts(Society for Industrial & Applied Mathematics (SIAM), 2020-08-25) Iannelli, Andrea; Lowenberg, Mark; Marcos Esteban, AndrésThis article proposes a framework which allows the study of stability robustness of equilibria of a nonlinear system in the face of parametric uncertainties from the point of view of bifurcation theory. In this context, a branch of equilibria is stable if bifurcations (i.e., qualitative changes of the steady-state solutions) do not occur as one or more bifurcation parameters are varied. The work focuses specifically on Hopf bifurcations, where a stable branch of equilibria meets a branch of periodic solutions. It is of practical interest to evaluate how the presence of uncertain parameters in the system alters the result of analyses performed with respect to a nominal vector field. Note that in this article bifurcation parameters have a different meaning than uncertain parameters. To answer the question, the concept of robust bifurcation margins is proposed based on the idea of describing the uncertain system in a Linear Fractional Transformation fashion. The robust bifurcation margins can be interpreted as nonlinear analogues of the structural singular value, or µ, which provides robust stability margins for linear time invariant systems. Their computation is formulated as a nonlinear program aided by a continuation-based multistart strategy to mitigate the issue of local minima. Application of the framework is demonstrated on two case studies from the power system and aerospace literature.Publication Worst-case disturbances for time-varying systems with application to flexible aircraft(American Institute of Aeronautics and Astronautics (AIAA), 2019-06-01) Iannelli, Andrea; Seiler, Peter; Marcos Esteban, Andrés; European CommissionThe aim of this Paper is to propose a method for constructing worst-case disturbances to analyze the performance of linear time-varying systems on a finite time horizon. This is primarily motivated by the goal of analyzing flexible aircraft, which are more realistically described as time-varying systems, but the same framework can be applied to other fields in which this feature is relevant. The performance is defined by means of a generic quadratic cost function, and the main result consists of a numerical algorithm to compute the worst-case signal verifying that a given performance objective is not achieved. The developed algorithm employs the solution to a Riccati differential equation associated with the cost function. Theoretically, the signal can also be obtained by simulating the related Hamiltonian dynamics, but this does not represent a numerically reliable strategy, as commented in the Paper. The applicability of the approach is demonstrated with a case study consisting of a flexible aircraft subject to gust during a flight-test maneuver.Publication Region of attraction analysis with Integral Quadratic Constraints(ELSEVIER BV, 2019-11) Iannelli, Andrea; Seiler, Peter; Marcos Esteban, Andrés; European CommissionA general framework is presented to estimate the Region of Attraction of attracting equilibrium points. The system is described by a feedback connection of a nonlinear (polynomial) system and a bounded operator. The input/output behavior of the operator is characterized using an Integral Quadratic Constraint. This allows to analyze generic problems including, for example, hard-nonlinearities and different classes of uncertainties, adding to the state of practice in the field which is typically limited to polynomial vector fields. The IQC description is also nonrestrictive, with the main result given for both hard and soft factorizations. Optimization algorithms based on Sum of Squares techniques are then proposed, with the aim to enlarge the inner estimates of the ROA. Numerical examples are provided to show the applicability of the approaches. These include a saturated plant where bounds on the states are exploited to refine the sector description, and a case study with parametric uncertainties for which the conservativeness of the results is reduced by using soft IQCs.Publication Robust estimations of the Region of Attraction using invariant sets(ELSEVIER BV, 2019-05) Iannelli, Andrea; Marcos Esteban, Andrés; Lowenberg, Mark; European CommissionThe Region of Attraction of an equilibrium point is the set of initial conditions whose trajectories converge to it asymptotically. This article, building on a recent work on positively invariant sets, deals with inner estimates of the ROA of polynomial nonlinear dynamics. The problem is solved numerically by means of Sum Of Squares relaxations, which allow set containment conditions to be enforced. Numerical issues related to the ensuing optimization are discussed and strategies to tackle them are proposed. These range from the adoption of different iterative methods to the reduction of the polynomial variables involved in the optimization. The main contribution of the work is an algorithm to perform the ROA calculation for systems subject to modeling uncertainties, and its applicability is showcased with two case studies of increasing complexity. Results, for both nominal and uncertain systems, are compared with a standard algorithm from the literature based on Lyapunov function level sets. They confirm the advantages in adopting the invariant sets approach, and show that as the size of the system and the number of uncertainty increase, the proposed heuristics ameliorate the commented numerical issues.Publication An extension of the structured singular value to nonlinear systems with application to robust flutter analysis(Springer Science and Business Media LLC, 2020-09-09) Iannelli, Andrea; Lowenberg, Mark; Marcos Esteban, Andrés; European CommissionThe paper discusses an extension of μ (or structured singular value), a well-established technique from robust control for the study of linear systems subject to structured uncertainty, to nonlinear polynomial problems. Robustness is a multifaceted concept in the nonlinear context, and in this work the point of view of bifurcation theory is assumed. The latter is concerned with the study of qualitative changes of the steady-state solutions of a nonlinear system, so-called bifurcations. The practical goal motivating the work is to assess the effect of modeling uncertainties on flutter, a dynamic instability prompted by an adverse coupling between aerodynamic, elastic, and inertial forces, when considering the system as nonlinear. Specifically, the onset of flutter in nonlinear systems is generally associated with limit cycle oscillations emanating from a Hopf bifurcation point. Leveraging μ and its complementary modeling paradigm, namely linear fractional transformation, this work proposes an approach to compute margins to the occurrence of Hopf bifurcations for uncertain nonlinear systems. An application to the typical section case study with linear unsteady aerodynamic and hardening nonlinearities in the structural parameters will be presented to demonstrate the applicability of the approach.Publication Plasma-wave interaction in helicon plasmas near the lower hybrid frequency(IOP Publising, 2022-07) Zhao, Yide; Bai, Jinwei; Cao, Yong; Wu, Siyu; Ahedo Galilea, Eduardo Antonio; Merino Martínez, Mario; Tian, Bin; Agencia Estatal de Investigación (España)We study the characteristics of plasma-wave interaction in helicon plasmas near the lower hybrid frequency. The (0D) dispersion relation is derived to analyze the properties of the wave propagation and a 1D cylindrical plasma-wave interaction model is established to investigate the power deposition and to implement the parametric analysis. It is concluded that the lower hybrid resonance is the main mechanism of the power deposition in helicon plasmas when the RF frequency is near the lower hybrid frequency and the power deposition mainly concentrates on a very thin layer near the boundary. Therefore, it causes that the plasma resistance has a large local peak near the lower hybrid frequency and the variation of the plasma density and the parallel wavenumber lead to the frequency shifting of the local peaks. It is found that the magnetic field is still proportional to the plasma density for the local maximum plasma resistance and the slope changes due to the transition.Publication The 2022 Plasma Roadmap: low temperature plasma science and technology(IOP Publising, 2022-07-05) Adamovich, I.; Ahedo Galilea, Eduardo Antonio; European Commission; Agencia Estatal de Investigación (España)The 2022 Roadmap is the next update in the series of Plasma Roadmaps published by Journal of Physics D with the intent to identify important outstanding challenges in the field of low-temperature plasma (LTP) physics and technology. The format of the Roadmap is the same as the previous Roadmaps representing the visions of 41 leading experts representing 21 countries and five continents in the various sub-fields of LTP science and technology. In recognition of the evolution in the field, several new topics have been introduced or given more prominence. These new topics and emphasis highlight increased interests in plasma-enabled additive manufacturing, soft materials, electrification of chemical conversions, plasma propulsion, extreme plasma regimes, plasmas in hypersonics and data-driven plasma science.Publication Magnetized fluid electron model within a two-dimensional hybrid simulation code for electrodeless plasma thrusters(IOP Publising, 2022-04-28) Zhou, Jiewei; Domínguez Vázquez, Adrián; Fajardo Peña, Pablo; Ahedo Galilea, Eduardo Antonio; European CommissionAn axisymmetric fluid model for weakly-collisional, magnetized electrons is introduced and coupled to a particle-in-cell model for heavy species to simulate electrodeless plasma thrusters. The numerical treatment of the model is based on a semi-implicit time scheme, and specific algorithms for solving on a magnetic field aligned mesh. Simulation results of the plasma transport are obtained for a virtual electrodeless thruster. The particle and energy fluxes of electrons are discussed. A first phenomenological model is included for the anomalous cross-field electron transport, and a second one for the anomalous parallel-field electron cooling in the plume. The balances of the plasma properties reveal that wall losses are the crucial reason for the poor thrust efficiency of these thrusters. The magnetic thrust inside the source could be negative and largely depending on the location of the magnetic throat, which is found uncoupled from the location of the plasma beam sonic surface. Furthermore, a sensitivity analysis of the results against the simulated plume extension shows that finite plumes imply an incomplete electron expansion, which leads to underestimating the performances.