Modeling and simulation of the plasma discharge in a radiofrequency thruster

Mención Internacional en el título de doctorIn the current electric propulsion industry for space applications, two of the main issues are the lifetime limitation of the mature technologies, Hall effect thrusters and gridded ion thrusters, due to the erosion of their electrodes; and the search for alternative propellants due to the scarcity of xenon. Electrodeless thrusters with magnetic nozzles, in particular the helicon plasma thruster and the electron cyclotron resonance thruster, are disruptive electric propulsion concepts that offer prolonged lifetime and tolerance for a wide variety of propellants. These thrusters are still under development, and further research is necessary for them to become competitive in terms of propulsive performances. This thesis is focused on the modeling and simulation of the plasma discharge in electrodeless thrusters with two codes. HYPHEN, a two-dimensional axisymmetric hybrid code, is used for full simulations of the thrusters. This code was extended from Hall effect thrusters to electrodeless thrusters, within the objective of developing a multi-thruster simulation platform valid for many types of electromagnetic thrusters. VLASMAN, a one-dimensional kinetic code, is used for simulations of the plasma expansion along the magnetic nozzles. The hybrid formulation of HYPHEN offers a good trade-off between computational cost and reliability of the results for full simulations, with a particle-in-cell model for heavy species and a fluid model for electrons. The particle model was ready for use from previous works, while the fluid model, with the basis established, was incomplete from the numerical point of view. The fluid model is solved on a magnetic field aligned mesh given the anisotropic character of the strongly magnetized electrons. However, the mesh, for realistic magnetic field topologies, can be highly irregular and the preliminary numerical algorithms were leading to inaccurate results. Thus, in this thesis, the numerical treatment of the fluid model is investigated, and solid numerical algorithms are found allowing to solve even complex magnetic topologies with singular points. Once the electron fluid model is completed, simulations coupled with the particle model are run for the helicon plasma thruster prototype HPT05M. The simulations are focused on the plasma transport assuming a known power deposition map from the helicon antenna. The thruster performances and profiles of plasma magnitudes are studied. The prototype is partially optimized, in terms of some design parameters, but the thrust efficiencies obtained are within the state-of-art. The main limitations for a full optimization beyond the state-of-art are identified and solutions are proposed. Furthermore, HYPHEN was initially developed to simulate xenon and other atomic propellants. In this thesis, as many candidates for alternative propellants usually have more complex chemistry, the code is implemented with the main collisions for diatomic substances. Simulations are run with air as propellant for HPT05M testing successfully the implementation. The results have allowed also to evaluate the air-breathing concept in helicon plasma thrusters. The kinetic formulation of VLASMAN is used for deeper studies of the plasma expansion along the magnetic nozzles. In the expansion, the plasma becomes very rarefied, and more accurate simulations than those from HYPHEN are required. Other one-dimensional steady state models were used in previous works, however they were not able to solve self-consistently a subpopulation of electrons trapped along the expansion. VLASMAN models the mechanisms responsible for the trapping of electrons, the transient and collisional processes. Simulations with VLASMAN are run to study the trapped electrons in terms of the transient history and collisionality. The solution of the subpopulation, and that of the whole plasma, reached in the steady state is found dependent on the transient history. Once the collisions are added, even if rare, the transient history is erased and the steady state solution becomes unique. The amount of trapped electrons is found important on the electron cooling and on the balances of electron momentum and energy. Furthermore, some studies focused on the extraction of results for implementation in macroscopic models are conducted.En la industria actual de la propulsión eléctrica para aplicaciones espaciales, dos de los principales problemas son la limitación de la vida útil de las tecnologías maduras, propulsores de efecto Hall y propulsores iónicos con rejillas, debido a la erosión de sus electrodos; y la búsqueda de propulsantes alternativos debido a la escasez del xenón. Los propulsores sin electrodos con tobera magnéticas, en particular el propulsor Helicón y el propulsor cicloelectrónico, son conceptos de propulsión eléctrica disruptivos que ofrecen una vida útil prolongada y tolerancia a una amplia variedad de propulsantes. Estos propulsores aún están en desarrollo y se necesita más investigación para que sean competitivos en términos de actuaciones propulsivas. Esta tesis se centra en el modelado y simulación de la descarga de plasma en propulsores sin electrodos con dos códigos. HYPHEN, un código híbrido axisimétrico bidimensional, se usa para simulaciones completas de los propulsores. Este código es extendido de los propulsores de efecto Hall a los propulsores sin electrodos, bajo el objetivo de desarrollar una plataforma de simulación multipropulsor válido para muchos tipos de propulsores electromagnéticos. VLASMAN, un código cinético unidimensional, se usa para simulaciones de la expansión del plasma a lo largo de las toberas magnéticas. La formulación híbrida de HYPHEN ofrece un buen punto intermedio entre el coste computacional y la fiabilidad de los resultados para simulaciones completas, con un modelo de partículas para especies pesadas y un modelo fluido para electrones. El modelo de partículas estaba ya listo para su uso de trabajos anteriores, mientras que el modelo fluido, con la base establecida, estaba incompleto desde el punto de vista numérico. El modelo fluido se resuelve en una malla alineada con el campo magnético dado el carácter anisotrópico de los electrones fuertemente magnetizados. Sin embargo, la malla, para topologías de campos magnéticos realistas, puede ser muy irregular y los algoritmos numéricos preliminares llevaban a resultados inexactos. En esta tesis, se investiga el tratamiento numérico del modelo fluido y se encuentran algoritmos numéricos sólidos que permiten resolver incluso topologías magnéticas complejas con puntos singulares. Una vez que se completa el modelo fluido, se llevan a cabo simulaciones junto con el modelo de partículas para el prototipo de propulsor Helicón HPT05M. Las simulaciones se centran en el transporte de plasma asumiendo un mapa conocido de deposición de potencia de la antena Helicón. Se estudian las actuaciones del propulsor y perfiles de las magnitudes del plasma. El prototipo se optimiza parcialmente, en términos de algunos parámetros de diseño, pero las eficiencias de empuje obtenidas están dentro del estado de arte. Se identifican las principales limitaciones para una optimización total más allá del estado de arte y se proponen soluciones. Además, HYPHEN se desarrolló inicialmente para simular xenón y otros propulsantes atómicos. En esta tesis, como muchos candidatos a propulsantes alternativos suelen tener una química más compleja, el código se implementa con las principales colisiones de sustancias diatómicas. Simulaciones se llevan a cabo con aire como propulsante para el HPT05M testeando con éxito la implementación. Los resultados también han permitido evaluar el concepto de air-breathing en los propulsores Helicón. La formulación cinética de VLASMAN se utiliza para estudiar con mayor profundidad la expansión del plasma a lo largo de las toberas magnéticas. En la expansión, el plasma se vuelve muy enrarecido y se requieren simulaciones más precisas que las de HYPHEN. En trabajos anteriores se utilizaron otros modelos unidimensionales estacionarios, sin embargo, no pudieron resolver de manera autoconsistente una subpoblación de electrones atrapados a lo largo de la expansión. VLASMAN modela los mecanismos responsables del atrapado de electrones: los procesos transitorios y colisionales. Simulaciones con VLASMAN se llevan a cabo para estudiar los electrones atrapados en términos del transitorio y colisionalidad. La solución de la subpoblación, y la de todo el plasma, alcanzada en el estacionario depende del transitorio. Una vez que se incluyen las colisiones, incluso si son poco frequentes, se borra el transitorio y la solución estacionaria colapsa en una única. Se descubre que la cantidad de electrones atrapados es importante en el enfriamiento y en el balance de momento y energía de los electrones. Además, se realizan algunos estudios enfocados a la extracción de resultados para su implementación en modelos macroscópicos.This thesis received funding mainly from Airbus Defense and Space, contract number CW240050. The last year of thesis was supported by the HIPATIA project of HORIZON 2020 (European Commission), grant number GA870542.Programa de Doctorado en Mecánica de Fluidos por la Universidad Carlos III de Madrid; la Universidad de Jaén; la Universidad de Zaragoza; la Universidad Nacional de Educación a Distancia; la Universidad Politécnica de Madrid y la Universidad Rovira i VirgiliPresidente: Ricardo Albertoni.- Secretario: José Miguel Reynolds Barredo.- Vocal: Justin Littl

Time-dependent expansion of a weakly-collisional plasma beam in a paraxial magnetic nozzle

This research was funded by the Comunidad de Madrid(Spain), under PROMETEO-CM project, with Grant No.Y2018/NMT-4750. GS-A was supported by the Ministerio deEconomía y Competitividad (Spain) with Grant No. RYC-2014-15357.The transient and steady-state expansion of a weakly-collisional plasma beam in a paraxial magnetic nozzle is studied with a kinetic Boltzmann&-Poisson model. Only intraspecies collisions involving electrons are considered and these are modeled with a Bhatnagar&-Gross&-Krook operator. Simulations show that occasional collisions progressively populate the phase-space region of isolated trapped electrons until a steady state is reached, which is independent of transient history. The steady state is characterized by a partial occupancy of that region increasing with the collisionality rate but far away from the full occupancy postulated by an alternative steady-state kinetic model. The changes on the amount of trapped electrons with the collisionality rate explain, in turn, the changes on the spatial profiles of main plasma magnitudes. Conclusions on the momentum and energy balances of ions and electrons agree, in terms of general trends, with those of the steady-state kinetic model. In the downstream region of the expansion, ions and electrons lose all their perpendicular energy but they still keep part of their parallel thermal energy. Electron heat fluxes of parallel energy are not negligible and are approximately proportional to enthalpy fluxes

Analysis of a cusped helicon plasma thruster discharge

A compact helicon plasma thruster that features a cusp in its internal magnetic field is analyzed with experiments and simulations. A compensated Langmuir probe and a Faraday cup are used in the former, while a hybrid PIC/fluid transport model combined with a frequency-domain electromagnetic field model are used in the latter. Measurements serve to tune the anomalous transport parameters of the model and overall show the same trends as the numerical results, including a secondary peak of electron temperature downstream in the magnetic nozzle, where electron cyclotron resonance conditions for the 13.56 MHz excitation frequency are met. The cusp plays a central role in determining the plasma losses to the walls and the profile of electron temperature, which in turn defines the excitation and ionization losses. While losses to the rear wall are reduced, losses to the lateral wall are increased, which, together with the low production efficiency, limit the performance of the device. Shorter chamber lengths and optimization of antenna and cusp location are suggested as potential ways to improve performance

Erratum: Numerical treatment of a magnetized electron fluid model within an electromagnetic plasma thruster simulation code (2019 Plasma Sources Sci. Technol. 28 115004)

Original article: Plasma Sources Science and Technology, (Nov. 2019), 28(11), 115004. https://doi.org/10.1088/1361-6595/ab4bd3Publicad

Coupled plasma transport and electromagnetic wave simulation of an ECR thruster

An electron-cyclotron resonance thruster (ECRT) prototype is simulated numerically, using two coupled models: a hybrid particle-in-cell/fluid model for the integration of the plasma transport and a frequency-domain full-wave finite-element model for the computation of the fast electromagnetic (EM) fields. The quasi-stationary plasma response, fast EM fields, power deposition, particle and energy fluxes to the walls, and thruster performance figures at the nominal operating point are discussed, showing good agreement with the available experimental data. The ECRT plasma discharge contains multiple EM field propagation/evanescence regimes that depend on the plasma density and applied magnetic field that determine the flow and absorption of power in the device. The power absorption is found to be mainly driven by radial fast electric fields at the electron-cyclotron resonance region, and specifically close to the inner rod. Large cross-field electron temperature gradients are observed, with maxima close to the inner rod. This, in turn, results in large localized particle and energy fluxes to this component.The research leading to these results has been funded by the European Union H2020 program under grant agreement 730028 (Project MINOTOR). Part of A Sánchez-Villar funding came from Spain's Ministry of Science, Innovation and Universities FPU scholarship program with Grant FPU17/06352

Numerical treatment of a magnetized electron fluid model within an electromagnetic plasma thruster simulation code

Correction to this article published in: Plasma Sources Science and Technology, (Jan. 2020), 29(1), 019601. https://doi.org/10.1088/1361-6595/ab5df3Plasma discharges in electromagnetic thrusters often operate with weakly-collisional, magnetized electrons. Macroscopic models of electrons provide affordable simulation times but require to be solved in magnetically aligned meshes so that large numerical diffusion does not ruin the solution. This work discusses suitable numerical schemes to solve the axisymmetric equations for the electric current continuity and the tensorial Ohm's law in such meshes, when bounded by the thruster cylindrical or annular chamber. A finite volume method is appropriate for the current continuity equation, even when meshes present singular magnetic points. Finite differences and weighted least squares methods are compared for the Ohm's law. The last method is more prone to producing numerical diffusion and should be used only in the boundary cells and requires a special formulation in the boundary faces. In addition, the use of the thermalized potential is suggested for an accurate computation of parallel electron current densities for very high conductivity. The numerical algorithms are tested in a hybrid (particle/fluid) simulation code of a helicon plasma thruster, for different magnetic fields, mesh refinement, and plume lengths. The different contributions to the electric current density are assessed and the formation and relevance of longitudinal electric current loops are discussed.The work of J Zhou has been supported mainly by Airbus DS (CW240050) at Toulouse, France. The contributions of D Pérez-Grande and P Fajardo were supported mainly by the National Research and Development Program of Spain (partially with FEDER funds) under grant number ESP2016-75887-P. The work of E Ahedo was supported mainly by the PROMETEO-CM project, funded by the Comunidad de Madrid, under Grant Y2018/NMT-4750 (including FEDER and FSE funds).Publicad

Kinetic features and non-stationary electron trapping in paraxial magnetic nozzles

The paraxial expansion of a collisionless plasma jet into vacuum, guided by a magnetic nozzle, is studied with an Eulerian and non-stationary Vlasov&-Poisson solver. Parametric analyzes varying the magnetic field expansion rate, the size of the simulation box, and the electrostatic potential fall are presented. After choosing the potential fall leading to a zero net current beam, the steady states of the simulations exhibit a quasi-neutral region followed by a downstream sheath. The latter, an unavoidable consequence of the finite size of the computational domain, does not affect the quasineutral region if the box size is chosen appropriately. The steady state presents a strong decay of the perpendicular temperature of the electrons, whose profile versus the inverse of the magnetic field does not depend on the expansion rate within the quasi-neutral region. As a consequence, the electron distribution function is highly anisotropic downstream. The simulations revealed that the ions reach a higher velocity during the transient than in the steady state and their distribution functions are not far from mono-energetic. The density percentage of the population of electrons trapped during the transient, which is computed self-consistently by the code, is up to 25% of the total electron density in the quasi-neutral region. It is demonstrated that the exact amount depends on the history of the system and the steady state is not unique. Nevertheless, the amount of trapped electrons is smaller than the one assumed heuristically by kinetic stationary theories.G.S-A was supported by the Ministerio de Economía y Competitividad of Spain (Grant RYC-2014-15357). J.Z. was supported by Airbus DS (Grant CW240050). J.R. and M.M-S stays at UC3M for this research were supported by a UC3M-Santander Chair of Excellence and by National R&D Plan (Grant ESP2016-75887), respectively. E.A. was supported by the MINOTOR project, that received funding from the European Unions Horizon 2020 research and innovation programme, under grant agreement 730028

One-dimensional direct Vlasov simulations of non-stationary plasma expansion in magnetic nozzle

Proceeding of: 35th International Electric Propulsion Conference (IEPC)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.G.S-A was supported by the Ministerio de Economía y Competitividad of Spain (Grant RYC-2014-15357). J.Z. was supported by Airbus DS (Grant CW240050). J.R. and M.M-S stays at UC3M for this research were supported by a UC3M-Santander Chair of Excellence and by National R&D Plan (Grant ESP2016-75887), respectively. E.A. was supported by the MINOTOR project, that received funding from the European Union's Horizon 2020 research and innovation programme, under grant agreement 730028

The large area detector onboard the eXTP mission

The Large Area Detector (LAD) is the high-throughput, spectral-timing instrument onboard the eXTP mission, a flagship mission of the Chinese Academy of Sciences and the China National Space Administration, with a large European participation coordinated by Italy and Spain. The eXTP mission is currently performing its phase B study, with a target launch at the end-2027. The eXTP scientific payload includes four instruments (SFA, PFA, LAD and WFM) offering unprecedented simultaneous wide-band X-ray timing and polarimetry sensitivity. The LAD instrument is based on the design originally proposed for the LOFT mission. It envisages a deployed 3.2 m2 effective area in the 2-30 keV energy range, achieved through the technology of the large-area Silicon Drift Detectors - offering a spectral resolution of up to 200 eV FWHM at 6 keV - and of capillary plate collimators - limiting the field of view to about 1 degree. In this paper we will provide an overview of the LAD instrument design, its current status of development and anticipated performance