Using electron fluid models to analyze plasma thruster discharges

Fluid 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.This work has been supported by the PROMETEO project, funded by the Comunidad de Madrid, under Grant reference Y2018/NMT-4750 PROMETEO-CM

Low frequency azimuthal stability of the ionization region of the Hall thruster discharge. I. Local analysis

Results based on a local linear stability analysis of the Hall thruster discharge are presented. A one-dimensional azimuthal framework is used including three species: neutrals, singly charged ions, and electrons. A simplified linear model is developed with the aim of deriving analytical expressions to characterize the stability of the ionization region. The results from the local analysis presented here indicate the existence of an instability that gives rise to an azimuthal oscillation in the +E x B direction with a long wavelength. According to the model, the instability seems to appear only in regions where the ionization and the electric field make it possible to have positive gradients of plasma density and ion velocity at the same time. A more complex model is also solved numerically to validate the analytical results. Additionally, parametric variations are carried out with respect to the main parameters of the model to identify the trends of the instability. As the temperature increases and the neutral-to-plasma density ratio decreases, the growth rate of the instability decreases down to a limit where azimuthal perturbations are no longer unstable.Support is being provided by the Air Force Office of Scientific Research, Air Force Material Command, USAF, under Grant No. FA8655-13-1-3033. Additional support comes from Spain’s R&D National Plan (Project No. AYA-2010-16699)

The 2022 Plasma Roadmap: low temperature plasma science and technology

Documento escrito por un elevado número de autores/as, solo se referencia el/la que aparece en primer lugar y los/as autores/as pertenecientes a la UC3M.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.Cristina Canal acknowledges PID2019-103892RB-I00/AEI/10.13039/501100011033 Project (AEI) and the Generalitat de Catalunya for the ICREA Academia Award and SGR2017-1165. The research by Annemie Bogaerts was funded by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (ERC Synergy Grant 810182 SCOPE). Eduardo Ahedo was funded by Spain's Agencia Estatal de Investigación, under Grant No. PID2019-108034RB-I00 (ESPEOS Project)

Low frequency azimuthal stability of the ionization region of the Hall thruster discharge. II. Global analysis

The linear stability of the Hall thruster discharge is analysed against axial-azimuthal perturbations in the low frequency range using a time-dependent 2D code of the discharge. This azimuthal stability analysis is spatially global, as opposed to the more common local stability analyses, already afforded previously (D. Escobar and E. Ahedo, Phys. Plasmas 21(4), 043505 (2014)). The study covers both axial and axial-azimuthal oscillations, known as breathing mode and spoke, respectively. The influence on the spoke instability of different operation parameters such as discharge voltage, mass flow, and thruster size is assessed by means of different parametric variations and compared against experimental results. Additionally, simplified models are used to unveil and characterize the mechanisms driving the spoke. The results indicate that the spoke is linked to azimuthal oscillations of the ionization process and to the Bohm condition in the transition to the anode sheath. Finally, results obtained from local and global stability analyses are compared in order to explain the discrepancies between both methodsSupport to D. Escobar has been provided by the Air Force Office of Scientific Research, Air Force Material Command, USAF, under Grant No. FA8655-13-1-3033. Support to E. Ahedo has come from Spain’s R&D National Plan (Project ESP-2013-41052)

Fully magnetized plasma flow in a magnetic nozzle

A model of the expansion of a plasma in a magnetic nozzle in the full magnetization limit is presented. The fully magnetized and the unmagnetized-ions limits are compared, recovering the whole range of variability in plasma properties, thrust, and plume efficiency, and revealing the differences in the physics of the two cases. The fully magnetized model is the natural limit of the general, 2D, two-fluid model of Ahedo and Merino [Phys. Plasmas 17, 073501 (2010)], and it is proposed as an analytical, conservative estimator of the propulsive figures of merit of partially magnetized plasma expansions in the near region of the magnetic nozzle.This work has been supported by the Spanish R&D National Plan, Grant No. ESP2013-41052-P

Plasma detachment in a propulsive magnetic nozzle via ion demagnetization

Plasma detachment in propulsive magnetic nozzles is shown to be a robust phenomenon caused by the inability of the internal electric fields to bend most of the supersonic ions along the magnetic streamtubes. As a result, the plasma momentum is effectively ejected to produce thrust, and only a marginal fraction of the beam mass flows back. Detachment takes place even if quasineutrality holds everywhere and electrons are fully magnetized, and is intimately linked to the formation of local electric currents. The divergence angle of the 95%-mass flow tube is used as a quantitative detachment performance figure.This work has been sponsored by the Air Force Office of Scientific Research, USAF (FA8655-12-1-2043) and Spain R & D National Plan (AYA-2010-61699

Effect of the plasma-induced magnetic field on a magnetic nozzle

A two-fluid, two-dimensional model of the plasma expansion in a divergent magnetic nozzle is used to investigate the effect of the plasma-induced magnetic field on the acceleration and divergence of the plasma jet self-consistently. The induced field is diamagnetic and opposes the applied one, increasing the divergence of the magnetic nozzle and weakening its strength. This has a direct impact on the propulsive performance of the device, the demagnetization and detachment of the plasma, and can lead to the appearance of zero-field points and separatrix surfaces downstream. In contrast, the azimuthal induced field, albeit non-zero, is small in all cases of practical interest.Initial work was sponsored by the Air Force Office of Scientific Research, Air Force Material Command, USAF (FA8655-12-1-2043). Additional support was provided by Spanish R&D National Plan (grant number ESP2013-41052-P)

Axial-azimuthal, high-frequency modes from global linear-stability model of a Hall thruster

Axial-azimuthal instabilities of a Hall-thruster plasma discharge are investigated using fluid model and a linear global stability approach, appropriate to the large axial inhomogeneity of the equilibrium solution. Electron pressure and electron inertia are considered in both the equilibrium and perturbed solutions. Fourier transform in time and azimuth are taken and the dispersion relation, for the resultant Sturm&-Liouville problem governing the axial behavior of the modes, is numerically obtained. The analysis, focused in mid-to-high frequencies and large wavenumbers identifies two main instability types. The dominant mode develops in the near plume at 1-5 MHz and azimuthal mode numbers ∼10–50, has a weak ion response and seems to be triggered by negative gradients of the magnetic field. The subdominant mode develops near the anode at 10-300 kHz and azimuthal mode numbers ∼1–10, and seems of the rotating-spoke type. Both instabilities are well characterized by investigating their oblique propagation, the influence of design and operation parameters, and the effects of anode–cathode electric connection, electron inertia, and temperature perturbations. The possible impact of these instabilities on electron cross-field transport is estimated through a quasilinear approach, which yields a spatially-rippled turbulent force.This research was funded by the Comunidad de Madrid (Spain), under PROMETEO-CM project, with Grant No.Y2018/NMT-4750. Enrique Bello-Benítez is supported by Spain’s Ministerio de Ciencia, Innovaci´on y Universidades, under Grant FPU18/03686

Global stability analysis of azimuthal oscillations in Hall thrusters

Proceeding of: 33rd International Electric Propulsion Conference (IEPC 2013)A 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.This work was supported in part by Spain's Research and Development National Plan under Project AYA-2010-61699 and in part by the Air Force Office of Scientific Research, Air Force Material Command, U.S. Air Force, under Grant FA8655-13-1-3033

Contactless steering of a plasma jet with a 3D magnetic nozzle

A 3D, steerable magnetic nozzle (MN) is presented that enables contactless thrust vector control of a plasma jet without any moving parts. The concept represents a substantial simplification over current plasma thruster gimbaled platforms, and requires only a small modification in thrusters that already have a MN. The characteristics of the plasma expansion in the 3D magnetic field and the deflection performance of the device are characterized with a fully magnetized plasma model, suggesting that thrust deflections of 5 degrees - 10 degrees are readily achievable.This work has been supported by the Spanish R&D National Plan under grant number ESP2016-75887-P