Cross-field Electron Transport Research Articles

Observation of strong in-plane perpendicular electric field in a radio frequency plasma with a time-varying magnetic nozzle

The spatiotemporal evolution of the electron temperature and plasma potential in a 200-W radio frequency argon discharge with a time-varying (approximately 60 kHz) magnetic nozzle was measured. Unlike in conventional static magnetic nozzles, the two-dimensional profiles of the electron temperature and plasma potential changed in sync with the applied azimuthal electric field, not with the magnetic field. The temporally resolved electric field vectors demonstrated an enhancement of the perpendicular component, where the direction fairly matched that of electron Eθ×B drift, indicating a space charge separation. This observation suggests that the applied time-varying field actively enhanced cross field electron transport, resulting in a unique potential structure and charged particle acceleration.

Effect of axial and radial components of the magnetic field on the electrostatic resistive instabilities in Hall thruster plasma

A two-fluid model is used to investigate the influence of the axial component of the magnetic field on the growth rate of electrostatic resistive instabilities with cross field electron transport in a Hall thruster. The axial component of the magnetic field plays an important role in instabilities. It provides additional confinement to electrons and ions near the channel axis. Also, it helps to protect the walls from the direct impacts of particles, thereby reducing erosion and extending the operational lifetime of the system. A fourth-order dispersion equation is derived using plasma perturbed densities into Poisson's equation to observe the various effects on the growing waves in plasma. It is observed that the growth rate and the real frequency increase with axial and radial components of the magnetic field, respectively. The order of the real frequency of the wave is found to be 106/s. For the fixed value of the azimuthal wavenumber (ky=500/m), the amplitude of the growth rate of the instability dropped to almost 40% if the axial component of the magnetic field is considered. Similarly, the amplitude of the real frequency increases by almost 74% (at ky=500/m) by incorporating the contribution of the axial component of the magnetic field. In addition, it is also observed that the amplitude of the growth rate increases with low values of radial and axial components of the magnetic field, but it decreases at the higher value of the magnetic field due to the resonance of electron cyclotron frequency with plasma frequency.

Stationary axial model of the Hall thruster plasma discharge: electron azimuthal inertia and far plume effects

One-dimensional axial models of the plasma discharge of a Hall thruster provide a valuable picture of its physical behavior with a small computational effort. Therefore, they are very suitable for quick parametric analyses or as a support tool for analyzing the impact of modeling decisions. This paper extends a well-known drift-diffusion stationary, quasineutral model by adding electron azimuthal inertia (EAI), a nonzero thickness cathode layer, and the far-plume region where electrons demagnetize and cool down. The EAI dominates on the far plume and affects positively to thrust. For a small ion backstreaming current, EAI modifies much the electron velocities and density near the anode, but has no discernible effect on the electron cross-field transport. Electron axial inertia and azimuthal gyrovisosity are estimated. The thick cathode layer connects quasineutrally the near and far plumes but the coupling between these two regions is weak. The far plume region is sensitive to the decay length of the magnetic field, the downstream boundary conditions on the electron currents, and the stray electric currents.

Inertial and anisotropic pressure effects on cross-field electron transport in low-temperature magnetized plasmas

In this paper, a one-dimensional (1D) particle-in-cell Monte Carlo collision (PIC-MCC) model is developed to investigate the effects of anisotropic pressure and inertial terms due to non-Maxwellian velocity distribution functions on cross-field electron transport. The conservation of momentum is evaluated by taking the moments of the first-principles gas-kinetic equation. A steady-state discharge is obtained without any low-frequency ionization oscillations by considering an anomalous electron scattering profile. The results obtained from the 1D PIC-MCC model are compared with fluid models, including the quasi-neutral drift-diffusion (DD), non-neutral DD, and full fluid moment models. The discharge current obtained from the PIC-MCC model is in good agreement with the fluid models. The cross-field electron transport due to the inertial terms, i.e. the gradient of axial and azimuthal drift, is evaluated. Moreover, PIC-MCC simulation results show non-zero, anisotropic, off-diagonal pressure tensor terms due to asymmetric non-Maxwellian electron velocity distribution function, potentially contributing to cross-field electron transport.

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.

Parametric investigation of azimuthal instabilities and electron transport in a radial-azimuthal E × B plasma configuration

Partially magnetized low-temperature plasmas (LTP) in an E × B configuration, where the applied magnetic field is perpendicular to the self-consistent electric field, have become increasingly relevant in industrial applications. Hall thrusters, a type of electrostatic plasma propulsion, are one of the main LTP technologies whose advancement is hindered by the not-fully-understood underlying physics of operation, particularly, with respect to the plasma instabilities and the associated electron cross field transport. The development of Hall thrusters with unconventional magnetic field topologies has imposed further questions regarding the instabilities' characteristics and the electrons' dynamics in these modern cross field configurations. Accordingly, we present in this effort a detailed parametric study of the influence of three factors on the plasma processes in the radial-azimuthal coordinates of a Hall thruster, namely, the magnetic field gradient, secondary electron emission, and plasma number density. The studies are carried out using the reduced-order particle-in-cell code developed by the authors. The setup of the radial-azimuthal simulations largely follows a well-defined benchmark case from the literature in which the magnetic field is oriented along the radius, and a constant axial electric field is applied perpendicular to the simulation plane. The salient finding from our investigations is that, in the studied cases corresponding to elevated plasma densities, a long-wavelength azimuthal mode with the frequency of about 1 MHz is developed. Moreover, in the presence of strong magnetic field gradients, this mode results from an inverse energy cascade and induces a significant electron cross field transport as well as a notable heating of the ions.

Radial position effects of externally mounted hollow cathode on a magnetically shielded Hall thruster

A magnetically shielded Hall thruster (MSHT) has a significantly longer service life than a conventional unshielded Hall thruster (USHT) as it shifts the magnetic field of maximum strength from the channel interior to the exterior. In this study, it was experimentally determined that the influence of the radial position of an externally mounted hollow cathode on the performance of an MSHT is quite different from that of a USHT. The measured plasma parameters demonstrate that in addition to the coupling voltage loss and plume divergence loss, the electron cross-field transport loss (not considered previously and introduced by the outward shifting of the magnetic field) is also important to explaining the performance variation in the MSHT. This study refines the coupling theory between the cathode and Hall thruster and provides a valuable reference for determining the radial position of an externally mounted hollow cathode in an MSHT.

Effects of the Wavelength of the Plasma Waves on Cross-Field Electron Transport in Partially Magnetized Plasmas

In this article, the effects of increasing plasma density on the cross-field electron transport driven by kinetic instabilities are investigated. A 2-D collisionless particle-in-cell (PIC) simulation is performed on cases with only singly charged ions and with a mixture of singly and doubly charged ions, at different levels of plasma density. It is observed using the PIC simulations that the level of plasma density affects the plasma waves that are driven by the microinstabilities, including the electron cyclotron drift instability (ECDI) and ion–ion two-stream instability (IITSI). The simulation results suggest that the enhancement of cross-field electron transport is correlated with the excitation of smaller wavelength modes and the increased amplitude of the plasma waves.

The effect of anode axial position on the performance of a miniaturized cylindrical Hall thruster with a cusp-type magnetic field

A 200 W cylindrical Hall thruster with a cusp-type magnetic field was proposed, manifesting convergent plume and high specific impulse. In this paper, a series of ring-shaped anodes are designed and the influence of anode axial position on the performance of CHT with a cusp-type magnetic field is studied. The experimental results indicate that the thruster keeps stable operation at the condition of 140–270 W discharge power. When the anode moves axially towards the upstream cusp field, the thrust enhances from 6.5 mN to 7.6 mN and specific impulse enhances from 1658 s to 1939 s significantly. These improvements of thruster performance should be attributed to the enhancement of current utilization, propellant utilization and acceleration efficiency. According to the analyses on the discharge characteristics, it is revealed that as the anode moves upstream, the electron transport path could be extended, the magnetic field in this extended path could impede electron cross-field transport and facilitate the ionization intensity, yielding to the enhancement of current utilization and propellant utilization efficiency. Moreover, along with this enhancement of upstream ionization at the given anode flow rate, the main ionization region is thought to move upstream and then separate more apparently from the acceleration region, which has been demonstrated by the narrowing of ion energy distribution function shape. This change in acceleration region could decrease the ion energy loss and enhance acceleration efficiency. This work is beneficial for optimizing the electrode structure of thruster and recognize the ionization and acceleration process under the cusp magnetic field.

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.

Plasma structure and electron cross-field transport induced by azimuthal manipulation of the radial magnetic field in a Hall thruster E × B discharge

Plasma structure and electron cross field in the z–θ plane of a Hall thruster E×B plasma under an azimuthally inhomogeneous magnetic field are studied by both experimental and numerical approaches. The work is intended to identify a primary role of electron dynamics on the structure formation by manipulating only the strongly magnetized electrons. The plasma potential distribution shows an axial–azimuthal variation; a low magnetic field region results in spatial potential saturation further downstream. The plasma density structure shows a 1D-like azimuthal variation with less axial deformation. A dense region is observed near the location of ∇B>0, where electrons are expected to undergo the ∇B and curvature drift toward the anode where neutrals are introduced. The potential structure is in close correlation to the Hall parameter distribution, indicating that electron dynamics plays a primary role in plasma structure formation, and via multiple consecutive stepwise physical steps, it eventually affects the density structure formation. In the z–θ space, the cross-field transport by E×B and diamagnetic drifts dominantly determines the electron flow and increases the overall axial electron mobility due to the azimuthal inhomogeneity. It is shown that most of the current is carried by the largest structure, but as the macroscopic structure fades out downstream, small structures grow and share the current. By considering the conservation laws, we show that a relation between azimuthal distributions of physical properties is formed to conserve the axial flux by a balance of specific forces, a balance between the resistive force and the magnetic force in the near-anode region and a balance between the electric/pressure force and the magnetic force in the acceleration and plume region, which differs from the Boltzmann relation satisfied in the radial dimension. Based on this principle, with a simplified test case having a uniform plasma density distribution, we show an analytic relation between azimuthal distributions of the magnetic field and the plasma potential and confirm the relation by a 2D hybrid simulation.

Mitigation of breathing oscillations and focusing of the plume in a segmented electrode wall-less Hall thruster

In the absence of the channel walls bounding the plasma, a wall-less Hall thruster is a promising configuration with a potentially longer lifetime and easier scalability than conventional Hall thrusters. Because the ion acceleration takes place in the fringing magnetic field with a strong axial component, the operation of a typical wall-less thruster is characterized by a large beam divergence of the plasma flow, which reduces the thrust. In this work, the addition of a biased segmented electrode to the wall-less thruster is shown to significantly narrow the plasma plume and suppress large amplitude breathing oscillations of the discharge current commonly associated with ionization instability. Both effects result in improvements to the thruster performance. Physical mechanisms responsible for these effects are unclear, but they are apparently associated with the reduction of the electron cross field transport to the anode and a transition in the breathing mode frequency.

Effects of multiply charged ions on microturbulence-driven electron transport in partially magnetized plasmas

Nonlinear interaction between kinetic instabilities in partially magnetized plasmas in the presence of multiply charged ion streams is investigated using kinetic simulations. It was observed by Hara and Tsikata [Phys. Rev. E 102, 023202 (2020)] that the axial ion–ion two-stream instability due to singly and doubly charged ion streams, coupled with the azimuthal electron cyclotron drift instability (ECDI), enhances cross-field electron transport. In the present study, it is observed that the addition of triply charged ions (as a third ion species) contributes to damping of the excited modes, leading to a reduction in the cross-field electron transport. The net instability-driven electron transport is shown to be a function not only of the azimuthal modes, such as the ECDI, but of the multiple ion species that dictate the development of additional plasma waves. It is found that trapping of the higher ion charge states within the plasma waves results in broadening of the ion velocity distribution functions.

Evolution of electron cross-field transport induced by an equilibrium azimuthal electric field in an E × B Hall thruster discharge under an azimuthally inhomogeneous neutral supply

The electron cross-field transport by the induced azimuthal electric field in a Hall thruster exhibits the mobility scaled by $1/B$. This study investigates parameters affecting this transport over a Hall thruster's distinct regions, such as the ionization, acceleration, and plume region. The main focus is on the nonzero equilibrium azimuthal electric field induced by an azimuthally inhomogeneous neutral supply. A fast Fourier transform analysis of the plasma structure reveals that the wavenumber $k$ of the azimuthal plasma structure increases from $k=2$, which is the input condition, to $k=4$ in the plume region, and that the total axial flux caused by the azimuthal electric field is mainly induced from the structures of the dominant Fourier components. The azimuthal phase relation between plasma potential and density is formed to maximize the axial electron flux at the plume region and starts varying along with other plasma properties as electrons flow toward the acceleration region. The spatial evolution of the effective axial mobility coefficient is extracted, and its regional characteristics are discussed.

Two-dimensional hybrid model of gradient drift instability and enhanced electron transport in a Hall thruster

An axial–azimuthal two-dimensional Hall thruster discharge model was developed for analyzing gradient drift instability (GDI) and cross field electron transport enhancement induced solely by the GDI. A hybrid particle-fluid model was used for the partially ionized plasma, where the inertialess electron fluid in the quasineutral plasma was assumed. A nonoscillatory numerical method was proposed for the potential solver in the electron fluid model to avoid numerical instability and analyze the physics of GDI accurately. A simulation is performed for a 1 kW-class anode-layer-type Hall thruster, and the flow field with plasma instability is presented. Plasma instability with vortex-like structures is observed in the acceleration and plume regions. The generated plasma instability enhances the cross field electron transport in the axial direction around the channel exit and in the plume region. Grid convergence is confirmed regarding the effect of electron transport enhancement, which indicates that cross field electron transport enhancement is based on the plasma instability. Furthermore, the comparison between the simulation results and linear perturbation analyses demonstrates that the simulated plasma instability reflects the theory of GDI. Thus, it is concluded that the hybrid model is useful for the analyses of GDI, and the GDI can enhance the cross field electron transport in Hall thrusters.

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 100–300 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.

Cross-field electron diffusion due to the coupling of drift-driven microinstabilities.

In this paper, the nonlinear interaction between kinetic instabilities driven by multiple ion beams and magnetized electrons is investigated. Electron diffusion across magnetic field lines is enhanced by the coupling of plasma instabilities. A two-dimensional collisionless particle-in-cell simulation is performed accounting for singly and doubly charged ions in a cross-field configuration. Consistent with prior linear kinetic theory analysis and observations from coherent Thomson scattering experiments, the present simulations identify an ion-ion two-stream instability due to multiply charged ions (flowing in the direction parallel to the applied electric field) which coexists with the electron cyclotron drift instability (propagating perpendicular to the applied electric field and parallel to the E×B drift). Small-scale fluctuations due to the coupling of these naturally driven kinetic modes are found to be a mechanism that can enhance cross-field electron transport and contribute to the broadening of the ion velocity distribution functions.

Wave-driven non-classical electron transport in a low temperature magnetically expanding plasma

The presence of instabilities in a low density, low temperature plasma expanding through an axially symmetric magnetic nozzle is investigated in the context of non-classical electron cross field transport. Electrostatic probes are used to characterize the background plasma properties and instabilities. The measurements show a primarily azimuthally propagating mode with a broad, incoherent power spectrum that appears linear at low frequencies. It is demonstrated that the observed dispersion is consistent with the lower hybrid drift instability. The energy and linear growth rate of this wave are related through quasilinear theory to an effective electron collision frequency that is shown to be dominant over classical collisions.

Cross-field chaotic transport of electrons by E × B electron drift instability in Hall thruster

A model calculation is presented to characterize the anomalous cross field transport of electrons in a Hall thruster geometry. The anomalous nature of the transport is attributed to the chaotic dynamics of the electrons arising from their interaction with fluctuating unstable electrostatic fields of the electron cyclotron drift instability that is endemic in these devices. The electrons energy gain from those background waves leads to a significant increase in their temperature along the perpendicular direction T⊥/T∥∼4 and an enhanced cross field electron transport along the thruster axial direction. It is shown that the wave-particle interaction induces a mean velocity of the electrons along the axial direction, which is of the same order of magnitude as seen in experimental observations.

Mode transitions in nonlinear evolution of the electron drift instability in a 2D annular E × B system

Nonlinear development of electron drift instability is studied using 2D3V azimuthal-radial Particle-in-Cell simulations of an annular Hall thruster channel of 10 cm diameter. The full 2π azimuthal domain of the annular cross section is simulated with reflecting boundary conditions at the radial boundaries. It is shown that the instability, which starts as a short length scale linear instability, undergoes a sequence of nonlinear transitions into longer wavelength modes. The transitions in the mode wavelengths are accompanied by related transitions of the magnitude of anomalous axial current. In the nonlinear stages, there is evidence of azimuthal trapping and dragging of ions by the propagating wave resulting in saturation of instability. It is demonstrated that the size of the azimuthal domain influences mode dynamics and, thereby, the anomalous cross field electron transport.