Anomalous Electron Transport Research Articles

Anomalous cross-field transport in a Hall thruster inferred from direct measurement of instability growth rates.

The contribution of the electron drift instability to anomalous electron transport is experimentally assessed in a Hall effect discharge. The transport is represented by an anomalous collision frequency, which is related through quasilinear theory to the energy and growth rate of the instability. The wave energy is measured directly with ion saturation probes, while estimates of the growth rate are employed based on both linearized theory and direct measurement. The latter measurement is performed with a bispectral analysis method. The wave-driven collision frequency is compared to measurements of the actual collision frequency inferred from a method based on laser-induced fluorescence. It is found that estimates for transport using linearized theory for the growth differ by over an order of magnitude from the actual anomalous collision frequency in the plasma. The wave-driven anomalous collision frequency with measured growth, however, is shown to agree with the electron collision frequency in magnitude and capture aspects of the trends in spatial variation. This result demonstrates experimentally that wave-driven effects ultimately can explain the observed cross-field transport in these devices. The implications of this finding are discussed in the context of the key lengthscales that drive the transport as well as the implications identifying reduced fidelity models that could be used to predict anomalous collision frequency.

Transition from retrograde to prograde drift instabilities in a magnetron microdischarge

Rotating plasma structures, or “spokes,” in magnetized discharges characterized by perpendicular electric and magnetic fields have been seen in a growing number of studies and are believed to be the result of gradient-driven drift instabilities. Under certain conditions, we have shown [Ito and Cappelli, Appl. Phys. Lett. 94, 211501 (2009)] the spoke’s rotation to be opposite to the E × B direction, i.e., retrograde in its expected direction. Recently [Marcovati et al., J. Appl. Phys. 127, 223301 (2020)], we have linked such counter-intuitive rotation to a local inversion of the electric field. Here, we give further experimental evidence for this inversion and attempt to provide an explanation for a relatively distinct transition seen between retrograde and positive (prograde) drift. In the experiments, a partially magnetized plasma forms inside a magnetron device of ≈10 mm radius operated with argon. Discharge current–voltage measurements are acquired for a range of argon fill pressure and inter-electrode spacing. We find two branches of operation—a low current branch of negative resistance, coinciding with the retrograde spoke rotation, and a higher current branch of positive resistance, coincident with prograde spoke rotation. We postulate that at low discharge currents, high magnetic field confinement leads to a large density gradient, causing more electron transport to the anode than that demanded by the external circuit. At higher currents, anomalous axial electron transport (across the magnetic field lines) becomes dominant, eliminating the conditions for field inversion. The current thresholds for the field inversion are found to be sensitive to the argon pressure and inter-electrode spacing.

Observation of Plasma Turbulence in a Hall Thruster Using Microwave Interferometry

To understand anomalous electron transport in a Hall thruster, plasma turbulence inside the acceleration channel was observed using a 76 GHz microwave interferometer. The dependence of the amplitude of the 100–500 kHz turbulence on magnetic flux density, and the relationships between the turbulence and other plasma instabilities and between the turbulence and the discharge current were investigated through spectral density and bicoherence analysis. The amplitude of electron number density fluctuations of the turbulence, integrating the spectral density from 100 to 500 kHz, is , or almost 10% of the time-averaged electron number density. The amplitude of the turbulence decreases with increase in weak magnetic field strength (coil current less than 0.6 A) and then increases with increase in magnetic field strength. The amplitude of the turbulence has a positive relation to the discharge current, leads to anomalous electron transport inside the acceleration channel, and is coupled with ionization instability. In addition, low-frequency perturbations of several hundred hertz were observed, with a positive relation to the turbulence and coupled with both ionization instability and turbulence.

Physics and instabilities of low-temperature E × B plasmas for spacecraft propulsion and other applications

Low-temperature E×B plasmas are used in various applications, such as Hall thrusters for satellite propulsion, ion sources and magnetron discharges for plasma processing, and negative ion sources for neutral beam injection in fusion. The plasmas in these devices are partially magnetized, meaning that the electrons are strongly magnetized while the ions are not. They are subject to various micro- and macro-instabilities that differ significantly from instabilities in fusion plasmas. These instabilities are often triggered by the large difference in electron and ion drift velocities in the E×B direction. The possibility of maintaining a large electric field in the quasineutral plasma of Hall thrusters despite anomalous electron transport, or the presence of strong double layers associated with the azimuthal rotation of plasma structures (“rotating spokes”) in magnetron discharges and Hall thrusters are examples of the very challenging and exciting physics of E×B devices. The turbulence and instabilities present in E×B plasma devices constitute a major obstacle to the quantitative description of these devices and to the development of predictive codes and are the subject of intense research efforts. In this tutorial, we discuss the key aspects of the physics of low-temperature partially magnetized E×B plasmas, as well as recent advances made through simulations, theory, and experiments in our understanding of the various types of instabilities (such as gradient-drift/Simon-Hoh and lower hybrid instabilities, rotating ionization waves, electron cyclotron drift instability, modified two-stream instability, etc.) that occur in these plasmas.

Influence of the axial oscillations on the electron cyclotron drift instability and electron transport in Hall thrusters

A 2D-3V finite-element particle-in-cell model, which is applied to simulate the radial-azimuthal plane near the exit of Hall thrusters, has been presented to investigate the influence of axial oscillation on electron cyclotron drift instability (ECDI) and anomalous cross field electron transports. The simplified theoretical analysis about the ECDI and the anomalous electron transport has been introduced. The uniform and harmonic axial electric fields, which are based on the typical axial oscillations in Hall thrusters, have been considered in the simulations. It is concluded that different constant axial electric fields can influence the properties of instability but cannot significantly change the cross field electron mobility. However, the axial oscillation plays a significant role in the instability, and the electron transports provided that appropriate amplitudes and frequencies are achieved. The equilibrium of the instability is destroyed and reformed with the axial oscillation. The cross field electron transports are enhanced in the range of low amplitudes and frequencies and are suppressed when they are in a high value. In addition, it is observed that the variation of the electron mobility and electron–ion friction force show high consistency with the trend of electron temperature. It is further confirmed that the increase in electron temperature takes responsibility for the enhanced cross field electron transport due to the axial oscillation.

Challenges with the self-consistent implementation of closure models for anomalous electron transport in fluid simulations of Hall thrusters

The performance of closure models for the anomalous electron transport when self-consistently implemented in a fluid model for a Hall effect thruster is investigated. This cross-field transport, which is orders of magnitude higher than classical collisional transport, is represented as an effective collision frequency. The proposed closure models relate this transport coefficient to local fluid properties of the plasma. Before implementation, the models are calibrated against values of the collision frequency inferred empirically from a 9 kW Hall thruster at 300 V and 15 A. It is found that even though closure models match the empirical collision frequency values, they diverge from these values when implemented self-consistently in a Hall thruster code. Possible drivers of this behavior are examined, including the role of non-linearity in the governing equations of the Hall thruster fluid model, artifacts from using time-averaged calibration data, and the non-uniqueness of the empirically-inferred collision frequencies. These results are discussed in the context of their implications for discovering and validating new closures necessary for enabling fully-predictive Hall thruster models.

A theoretical thrust density limit for Hall thrusters

Hall Thrusters typically operate at thrust densities on the order of 10 N/m^2, which appear to be orders of magnitude below the thrust density limits suggested in previous literature. These limits have been considered here and each component of thrust density is analyzed to demonstrate the relative contribution to the total thrust density. Dependencies of the thrust density limits upon the thruster geometry, electron mobility, and the applied magnetic field are revealed and compared with experimental measurements of thrust density. This analysis reveals that with conventional applied magnetic field strengths, Hall thruster thrust density appears to be on the order of 1000 N/m^2. It is shown that this limit can be further increased through higher applied magnetic fields, applied voltage, and suppression of anomalous electron transport. This suggests Hall thrusters can be made much more compact and operated at higher power densities, given improvements to the thermal management and materials.

Magnetized fluid electron model within a two-dimensional hybrid simulation code for electrodeless plasma thrusters

An 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.

Analysis of small scale fluctuations in Hall effect thrusters using virtual Thomson scattering on PIC simulations

Hall effect thrusters are yet not fully understood due to multiple open questions, among which the anomalous electron transport is the most challenging. Particle-In-Cell (PIC) simulations suggested that electron transport is strongly affected by small-scale instabilities which can be investigated experimentally using Collective Thomson Scattering (CTS). In this paper, we perform a virtual CTS diagnostic on PIC data in order to investigate these small scales and to relate simulation and experiments. The virtual diagnostic is performed on the electron density maps from a simplified 2D axial-azimuthal PIC simulation. Analysis along the channel axis showed two dominant modes at 8 and 3 rad mm−1. These modes exhibit ion-acoustic wave features and appear to be selectively affected by the acceleration of the ions when transitioning from the ionization zone to the acceleration zone. A numerical study of the electron density fluctuation rate from the virtual CTS is also performed and the obtained profiles are compared to PIC. This reveals that the virtual CTS integrates both axial and azimuthal fluctuations of the electron density due to the spatial extension of the scattering volume. Moreover, it also highlights the importance of a good estimation of the electron density in the scattering volume for an accurate estimation of the fluctuation rate.

Moiré Physics of One-Dimensional Related Systems and Their Measurement

Currently, the magic-angle graphene has given a tremendous boost to the study of unconventional superconductors. On the other hand, there were still limited experimental studies on superconductivity in one-dimensional (1D) carbon nanotube systems. The study of experimental systems in demonstrating superconductivity was therefore scientifically important. In this review, we have shown strategies toward demonstrating the superconductivity for the single double-wall carbon nanotube (DWCNT). In general, there have been two directions to analyse superconducting properties of one-dimensional materials: (i) strong correlated states (ii) anomalous electron transport operations. We introduced the transmission electron microscope (TEM) and Rayleigh scattering spectroscopy to describe the strong correlation. The theoretical foundations of moiré physics have also been described. Given all the methods, we concluded that the most intuitive way to demonstrate the superconductivity of single double-walled carbon nanotubes is the critical temperature. The sharp drop of the resistance could be directly observed, and the Tc could be obtained from the electrical transport data. In the last section, we also summarized the challenges that need to be addressed in future superconductivity studies of 1D carbon nanotubes.

Characterization of hollow cathode plasma turbulence using coherent Thomson scattering

Turbulence in hollow cathodes used for space propulsion is believed to play an important role in anomalous electron transport and ion heating. In this work, the implementation of coherent Thomson scattering to identify and characterize MHz-frequency ion acoustic turbulence and kHz-frequency oscillations in the plume of a hollow cathode is achieved. In the presence of a background magnetic field of a Hall thruster, a number of unstable modes are observed. A directive ion acoustic mode propagating predominantly within a restricted angle around the magnetic field is found, exhibiting an energy scaling with wavenumber k of the form k−5.2±0.58, which differs from the classic Kadomtsev k−3 scaling for unmagnetized conditions. Bi-directional ion acoustic mode fluctuations propagating over a range of angles with respect to the magnetic field have been measured, possibly signifying the existence of a large-amplitude plasma wave, similar to the Buneman instability. Finally, electron density fluctuations in the kHz-frequency range, a possible consequence of drift-driven instabilities in the plane perpendicular to the magnetic field, have also been identified. These results not only are an indication of the diversity of wave types that exist in hollow cathode plumes but also point to the key role played by the presence of, and the configuration of, the magnetic field in their appearance.

Anomalous transport of electrons in an electric discharge with transverse magnetic field

The experimental data showing the relationship of excitation of microwave oscillations with abnormally transport of electrons across the magnetic field in turbulent plasma are presented. The mechanism of the formation of the discharge current due to scattering of drift electrons in the near-electrode layers of the electric discharges on microwave oscillations has been substantiated. The conditions for the manifestation of the turbulent mechanism of anomalous electron transport through the magnetic barrier at the boundary of the toroidal electric discharge have been studied most fully. The mobility of electrons across a magnetic field is one of the main parameters of electric discharges that use crossed electric and magnetic fields for technological purposes.

The interaction between ion transit-time and electron drift instabilities and their effect on anomalous electron transport in Hall thrusters

Recent simulations and experiments have observed a transition from short to long-wavelength azimuthal instabilities that leads to enhanced electron transport in Hall thrusters. Here we make the hypothesis that this phenomenon stems directly from the interaction between the axial ion transit-time instabilities (ITTI), and the azimuthal electron drift instability (EDI). This interaction is studied using 2D axial-azimuthal self-consistent particle-in-cell simulations which include a 1D neutral dynamics solver. It is found that a short to long-wavelength transition only occurs if the breathing-mode and ITTI are captured in the simulation, and two distinct instability regions can be distinguished depending on the local ion Mach number. Upstream of the ion sonic point the EDI exhibits an ion-acoustic behaviour, and the associated instability-enhanced electron transport is well described by a previously developed model based on kinetic theory. Downstream of the ion sonic point however, the ITTI significantly changes the local plasma parameters, and this modifies the EDI while increasing the electron transport.

Application of sparse grid combination techniques to low temperature plasmas Particle-In-Cell simulations. II. Electron drift instability in a Hall thruster

Three-dimensional simulations of partially magnetized plasma are real challenges that actually limit the understanding of the discharge operations such as the role of kinetic instabilities using explicit Particle-In-Cell (PIC) schemes. The transition to high performance computing cannot overcome all the limits inherent to very high plasma densities and thin mesh sizes employed to avoid numerical heating. We have applied a recent method proposed in the literature [L. F. Ricketson and A. J. Cerfon, Plasma Phys. Controlled Fusion 59, 024002 (2017)] to model low temperature plasmas. This new approach, namely, the sparse grid combination technique, offers a gain in computational time by solving the problem on a reduced number of grid cells, hence allowing also the reduction of the total number of macroparticles in the system. We have modeled the example of the two-dimensional electron drift instability, which was extensively studied in the literature to explain the anomalous electron transport in a Hall thruster. Comparisons between standard and sparse grid PIC methods show an encouraging gain in the computational time with an acceptable level of error. This method offers a unique opportunity for future three-dimensional simulations of instabilities in partially magnetized low temperature plasmas.

Non-intrusive tools for electric propulsion diagnostics

This paper reports about the advances in non-intrusive diagnostic systems for ion thruster engines undergoing at Aerospazio Tecnologie. Among the various optical diagnostics developed and applied in electric propulsion, laser-induced fluorescence (LIF) is a powerful, non-intrusive and species selective technique. It is capable to bring knowledge, where other techniques cannot be applied, as for example in the ionization region. Thanks to its selectivity to a given species, LIF can provide valuable information also about the neutrals. Another important topic is the occurrence of regular plasma oscillation in Hall thrusters channel, being correlated in different complex ways with performance of the thruster. In particular, it has been demonstrated that rotating inhomogeneity in the plasma ring (also termed rotating spokes) can be one of the principal mechanisms explaining quantitatively the anomalous electron transport in the discharge channel. Since the electron transport affects directly the efficiency in Hall thrusters, the characterization of plasma oscillation results in a valuable tool to assess the conditions for optimal thruster operation. The ultra-fast imaging technique offers the chance for a non-intrusive optical diagnostics of the plasma oscillation with high spatial and temporal resolution. In this paper, we propose a new approach to this technique to obtain higher frequency resolution and higher contrast by optical filtering. Both techniques are successfully applied as diagnostic tools of Aerospazio 200 W Xenon fed Hall effect thruster.

The ‘SXR—Pit’ paradox as an indicator of electron transport in tokamaks

A phenomenon is analyzed, which is observed at some laboratory-scale tokamaks and seems to be unexplained: a strong drop in the soft x-ray radiation (SXR) after it passed through the ‘thick’ Be foils (the pit in the SXR spectrum). This phenomenon becomes more pronounced as the foil thickness increases and the plasma electron density decreases. The explanation for this phenomenon is proposed, which involves the assumption that the Maxwellian electron velocity distribution becomes ‘depleted’ in the range of velocities that are 3–5 times higher than the thermal one. The anomalous electron heat transport along the weakly perturbed toroidal magnetic field of the tokamak (the ‘magnetic flutter’ model) seems to be the most probable reason for this depletion. Thus, the ‘SXR—Pit’ can be a new tool for studying the physical nature of the anomalous electron transport in tokamaks.

Anomalous Electron Transport in Hall Thrusters: Electric Field Fluctuation Measurement

Anomalous Electron Transport in Hall Thrusters: Electric Field Fluctuation Measurement

A comparison between kinetic theory and particle-in-cell simulations of anomalous electron transport in E×B plasma discharges

Understanding anomalous electron transport in E×B discharges remains a key challenge in the development of self-consistent models of these systems. It has been shown that short-wavelength, high-frequency instabilities in the azimuthal E×B direction may be responsible for increased electron transport due to an enhanced electron-ion friction force. Although a theoretical model based on quasi-linear kinetic theory has previously been proposed to describe this friction force, it has so far only undergone limited validation testing. Here, we rigorously assess this theoretical model by comparison with the friction force self-consistently obtained from 2D axial-azimuthal particle-in-cell simulations. The simulation geometry is based on a recently established benchmark configuration for E×B discharges, and a broad parametric study is performed by varying the magnetic field strength, the discharge current density, and the presence of different neutral collisional processes. Overall, the theory is found to be in very good agreement with the simulation results for all cases studied, verifying the underlying physical mechanisms leading to enhanced electron transport. We demonstrate, however, that the friction force depends sensitively on the shape of the electron velocity distribution function, thus posing significant challenges to fully self-consistent, first principles modeling of anomalous transport in fluid simulations.

Anomalous Electron Transport in One-Dimensional Electron Cyclotron Drift Turbulence

The transverse electron current due to the crossed electric and magnetic fields results in the robust instability driven by the electron $${\mathbf{E}} \times {\mathbf{B}}$$ drift. In the regime of interest for electric propulsion applications, this instability leads to the excitation of quasicoherent nonlinear wave resulting in the anomalous electron transport. We investigate the nonlinear stage of the instability and resulting anomalous electron current using nonlinear Particle-in-Cell simulations. It is found that the anomalous current is proportional to the applied electric field thus demonstrating constant anomalous mobility. Moreover, the scaling of the current density follows the dependence of the dominant resonance wavelength on the electric and magnetic field strength thus clearly demonstrating the cyclotron nature of the instability.

Experimental characterization of ID-Hall, a double stage Hall thruster with an inductive ionization stage

We present experimental results on the characterization of ID-Hall, a double stage Hall thruster with an inductively coupled magnetized ionization stage. This first experimental prototype of ID-Hall operates in a low power regime, typically below 400 W. The purpose of this work is not only to study the properties of ID-Hall and provide directions for optimization but also, and more generally, to study the relevance of the double stage concept with respect to important physical issues such as current oscillations and anomalous electron transport. We present experimental measurements of the current–voltage characteristics, extracted ion beam current (Faraday cup measurements), and ion energy and angular distribution functions (RPA measurements) in single and double stage regimes of operation, as a function of DC voltage and RF power. The results demonstrate that ions can be extracted from the inductive RF ionization stage even under conditions where the applied DC voltage is not sufficient to ionize the gas flow, i.e., ID-Hall can indeed operate in a double stage regime. At intermediate voltages, the overshoot observed in the current–voltage characteristics of single stage thrusters disappears in double stage operation, indicating a decrease in anomalous electron transport. Time-resolved and time-averaged ion energy distribution measurements show a coupling between ion energy, breathing mode oscillations, and the magnetic configuration of ID-Hall.