Anomalous Collision Frequency Research Articles

Hybrid Modeling of Miniaturized 50 W Annular Hall Thruster

A 50-W-class annular Hall thruster is studied with a hybrid axial–radial two-dimensional model. Ions are described by a kinetic approach, whereas fluid conservation equations are solved for electrons. In such models, additional (anomalous) contributions must be added to the momentum-transfer electron collision frequency to obtain realistic values of the cross-field electron mobility. First, a parametric study is performed, where anomalous transport is described with a simple two-region model based on constant empirical parameters. The simulated global performance is subsequently compared with experimental measurements. Then, laser-induced fluorescence ion velocity measurements are employed to infer a continuous profile of the anomalous electron collision frequency along the channel centerline. The model reproduces the performance, the acceleration structure, the current oscillations, and the doubly charged ion fraction of the laboratory thruster. Measurements of the ion velocity distribution function highlight the presence of a slow ion population in the near plume. The production of the slow ions and their growth for increasing distances from the thruster channel exit is qualitatively reproduced by the model. The results obtained suggest that the generation and dynamics of the observed slow ions can be attributed to the presence of energetic electrons in the plume.

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.

Analytical modeling of the anomalous electron collision frequency in partially magnetized E × B plasmas

An analytical model for the anomalous electron collision frequency is proposed to predict the cross-field mobility of electrons in partially magnetized E × B plasma devices. The proposed model can be implemented through a dimensional analysis based on the electron momentum equations perpendicular to the magnetic field. To test the validity of the proposed method, it is applied to a 1D steady fluid analysis for a Hall thruster. The results show that compared to the Bohm diffusion model, the proposed model can yield more physically appropriate prediction results in terms of axial distributions for the anomalous electron collision frequency and azimuthal electron mean velocity.

Transient non-classical transport in the hollow cathode plume I: measurements of time-varying electron collision frequency

Electrostatic probes are employed to measure the time-variations in electron collision frequency due to a large-scale, low-frequency, plasma instability in a high-current hollow cathode plasma discharge (plume mode oscillation). Time-resolved measurements of ion acoustic turbulence are used to infer the effective collision frequency on the timescale of this underlying wave. Through a direct comparison, it is shown that the observed variation in the electron collision frequency cannot be described by classical collisional processes, i.e. Coulomb and neutral collisions, but rather is well represented by the changes in the anomalous collision frequency due to the turbulence.

Transient non-classical transport in the hollow cathode plume II: evaluation of models for the anomalous collision frequency

The ability of fluid-based closure models to describe the non-classical electron collision frequency in the plume of a hollow cathode is experimentally investigated. Six models—all predicated on the assumption that the non-classical collision frequency can be attributed to ion acoustic turbulence (IAT)—are considered. Experimental measurements of the time-resolved plasma properties in the cathode plume (Georgin M P, Jorns B A and Gallimore A D 2020 PlasmaSources Sci. Technol, 29 105010) are used to evaluate each closure model and compare it to experimental measurements of the effective electron collision frequency. Though more than one of the considered closures can predict the time-average behavior of the plasma in the cathode plume, it is found that only one model accurately predicts the measurements in both space and time for the cathode and operating conditions that were studied. This new highest fidelity model is derived using a single-equation approach based on modeling the average frequency of the IAT as it evolves in space and time. The implications of the success of this model are discussed in the context of the understanding of the dynamics of the IAT in the cathode plume as well as on-going fluid-based modeling efforts related to cathode plumes.

Dynamics of a hollow cathode discharge in the frequency range of 1–500 kHz

We present results from 2D axisymmetric fluid simulations of the partially-ionized Xe gas in a 25-A cathode discharge, for a range of flow rates (5–20 sccm) in which transition between the so-called spot and plume modes has been observed in laboratory experiments. The simulations for the first time capture very well the characteristic rise of the peak-to-peak amplitude in the keeper voltage oscillations with decreasing flow rate—the so-called ‘plume margin’—thereby allowing for a closer interrogation of the processes that drive them. The oscillations are found to be due to plasma dynamics in the near-plume region that increase in amplitude as the flow rate is reduced. The cathode interior remains largely quiescent and changes in the emitter peak temperature do not exceed 2% across the entire range of flow rates examined. Along the cathode centerline the amplitude of the electron density oscillations peak at a location where the number density of the Xe atoms has diminished to its minimum value and the degree of ionization is close to one. The computed spectra reveal that most of the oscillation power resides in the frequency range of 100–300 kHz. These frequencies are much greater than the local ionization collision frequency ( < 10 kHz), and are associated with wavelengths of several centimeters. Such wavelengths are many orders of magnitude greater than λD. The waves are largely longitudinal with wave vector in the axial direction, and phase velocity ω/k > 10 km s−1, which is more than 6× greater than the ion acoustic speed. Though the computed and measured plume margins are in good agreement the measured spectra show that most of the power resides between ∼60 and 90 kHz, lower than the computed range (100–300 kHz), and exhibits a sharper distribution. It is argued this is due to the presence of a rotational mode in the experiment that is coupled with the longitudinal mode, yielding a complex 3D plasma motion that cannot be captured by the simulations due to the assumption of azimuthal axisymmetry, but that it is indeed the longitudinal plasma motion that drives the transition from spot to plume modes. An anomalous resistivity has been invoked in the simulations that is based on the formulations of Sagdeev and Galeev for the saturation of IAT which is long known to exist in these discharges. Though the simulations do not account for possible anomalous heating of the ions, the idealized model for the electrons is found to be sufficient in capturing the abovementioned dynamics, yielding a multiplication coefficient α of the anomalous collision frequency να = αωpe(Te/Ti)(ue/uTe) that is within a factor of two of the estimated theoretical value.

Topology of the Magnetic Field and Resistivity of a Compact Torus Generated in a Mirrorless Theta Pinch

The mapping of the magnetic field and analysis of the plasma resistivity were used to study the change of magnetic field topology during the formation of a reversed field configuration. Using a theta pinch with straight coil, the formation of the torus was observed during the early time of the plasma radial implosion, in scale comparable to Alfven’s time and shorter than the resistive diffusion. The non-intrusive excluded flux probe also indicated the formation of the torus even in the absence of mirror coils in the system. The plasma at the end region of the coil has distributed in the entire cross section of the tube, slightly peaked at the null field region. The anomalous plasma resistivity at the reconnection site was close to the prediction given by numerical calculation using numerical hybrid code with anomalous collision frequency either calculated using Chodura’s algorithm or evolution of microinstabilities, particularly the lower hybrid drift instability.

Non-invasive time-resolved measurements of anomalous collision frequency in a Hall thruster

The time-resolved cross-field electron anomalous collision frequency in a Hall thruster is inferred from minimally invasive laser-based measurements. This diagnostic is employed to characterize the relationship between the dominant low-frequency “breathing” oscillations and anomalous electron transport mechanisms. The ion Boltzmann equation combined with a generalized Ohm's law is used to infer key quantities including the ionization rate and axial electric field strength which are necessary in computing the total electron cross-field collision frequency. This is accomplished by numerically integrating functions of velocity moments of the ion velocity distribution function measured with laser-induced fluorescence, in conjunction with current density measurements at a spatial boundary. Estimates of neutral density are used to compute the classical collision frequency profile and the difference in the total collision frequency, and this quantity describes the anomalous collision frequency. This technique reveals the anticipated trends in electron transport: few collisions in the acceleration region but a collision frequency approaching the cyclotron frequency farther downstream. The time-resolved transport profiles indicate that the anomalous collision frequency fluctuates by several orders of magnitude during a breathing cycle. At troughs in the discharge current, classical collisions may dominate; at peaks in the discharge current, anomalous collisions dominate. These results show that the breathing mode and electron transport are directly correlated. This finding is discussed with regard to existing numerical models for the breathing mode and interpretations of anomalous electron transport.

Predictive, data-driven model for the anomalous electron collision frequency in a Hall effect thruster

Symbolic regression is applied to find a data-driven model for the anomalous cross-field electron transport in a Hall effect thruster. This model is formulated in terms of an anomalous electron collision frequency that is related to the cross-field electron transport through a generalized Ohm’s law. Empirically determined estimates of this anomalous collision frequency as a function of local plasma parameters from three 1–6 kW class Hall effect thrusters form the training dataset for this investigation. A commercially-available, evolutionary genetic algorithm is applied to regress this dataset and identify models for the anomalous collision frequency that are expressed as symbolic functions of the local plasma properties. It is found that these data-driven models not only fit the training dataset but that they can predict anomalous collision frequency values for a test dataset taken from a fourth thruster not used in the initial regression. Five existing models for the anomalous collision frequency derived from first-principles are applied to the same training and test datasets used for the data-driven model. The estimates of the anomalous collision frequency as a function of local plasma parameters from the data-driven models are shown to exhibit improved quantitative agreement with both datasets compared to the analytical models. These findings are discussed in terms of the physical insight they yield for identifying dominant physical processes that govern electron transport as well as the practical application of using this technique for creating predictive Hall thruster models.

The importance of the cathode plume and its interactions with the ion beam in numerical simulations of Hall thrusters

Numerical simulations with a 2-D axisymmetric multi-fluid plasma code illustrate the significance of the near-plume interactions in investigations of the anomalous electron transport in Hall thrusters. In our simulations, the transport of electrons is modeled using an anomalous collision frequency, νanom, yielding νanom ≈ ωce (i.e., the electron cyclotron frequency) in the near-plume region. We first show that restricting the anomalous collision frequency in this region to only within the ion beam, where the current density of ions is large, does not alter the plasma discharge in the Hall thruster as long as the interaction between the beam and the cathode plume is captured properly. These simulations suggest that electron transport occurs largely inside the beam. A second finding is on the significance of accounting for the ion acoustic turbulence (IAT), now known to occur in the vicinity of the cathode exit. We have included in our simulations a model of the IAT-driven anomalous collision frequency based on Sagdeev's model for saturation of the ion-acoustic instability. This implementation has allowed us to achieve excellent agreement with experimental measurements in the near plume of the H6 Hall thruster. Low frequency plasma oscillations similar in both magnitude and frequency to those found in the H6 thruster are recovered in our simulations when the model for the anomalous collision frequency in the cathode plume is included.

Numerical Simulations of the Partially Ionized Gas in a 100-A LaB&lt;sub&gt;6&lt;/sub&gt; Hollow Cathode

Numerical simulations of a hollow cathode with a lanthanum hexaboride (LaB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> ) emitter operating at 100 A have been performed using the 2-D Orificed Cathode (OrCa2D) code. Results for a variety of plasma properties are presented and compared with laboratory measurements. The large size of the device permits peak electron number densities in the cathode interior that are lower than those established in the NASA Solar Electric Propulsion Technology Application Readiness (NSTAR) hollow cathode, which operates at a 7.3× lower discharge current and 3.2× lower mass flow rate. The maximum electron current density also is lower in the LaB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> cathode, by 4.2×, due to the larger orifice size. Simulations and direct measurements show that at 12 sccm of xenon flow the peak emitter temperature is in the range of 1630°C-1666°C. It is also found that the conditions for the excitement of current-driven streaming instabilities and ion-acoustic turbulence (IAT) are satisfied in this cathode, similarly to what was found in the past in its smaller counterparts like the NSTAR cathode. Based on numerical simulations, it has long been argued that these instabilities may be responsible for the anomalously large ion energies that have been measured in these discharges as well as for the enhancement of the plasma resistivity. Direct measurements of the turbulent spectra and confirmation of the presence of IAT in this cathode have now been completed. Interpolation of the measured anomalous collision frequency based on slightly different operating conditions than the one in the numerical simulations suggests good agreement with the computed values.

Ion acoustic turbulence in a 100-A LaB₆ hollow cathode.

The temporal fluctuations in the near plume of a 100-A LaB(6) hollow cathode are experimentally investigated. A probe array is employed to measure the amplitude and dispersion of axial modes in the plume, and these properties are examined parametrically as a function of cathode operating conditions. The onset of ion acoustic turbulence is observed at high current and is characterized by a power spectrum that exhibits a cutoff at low frequency and an inverse dependence on frequency at high values. The amplitude of the turbulence is found to decrease with flow rate but to depend nonmonotonically on discharge current. Estimates of the anomalous collision frequency based on experimental measurements indicate that the ion acoustic turbulence collision frequency can exceed the classical rate at high discharge current densities by nearly two orders of magnitude.

Observation of ion heating during stimulated Buneman instability in a temporally growing plasma

Observations and conclusive measurements of ion heating during stimulated Buneman instability (BI) are reported in a temporally growing plasma, created by short-pulse electromagnetic waves. The instability lasts for during the pulse on time and arises when the applied electric-field amplitude supersedes the threshold critical electric field for free acceleration. During the initial period of plasma development after the launch of the pulsed waves, the maximum growth of BI is registered at . The analysis of time-resolved measurements of electron and ion energy distributions indicates an anomalous collision frequency and a hot ion energy tail that persists for more than 700 ns. The energy from the instability is responsible for bringing about the intense and rapid ionization observed upon its termination.

Superdiffusion revisited in view of collisionless reconnection

Abstract. The concept of diffusion in collisionless space plasmas like those near the magnetopause and in the geomagnetic tail during reconnection is reexamined making use of the division of particle orbits into waiting orbits and break-outs into ballistic motion lying at the bottom, for instance, of Lévy flights. The rms average displacement in this case increases with time, describing superdiffusion, though faster than classical, is still a weak process, being however strong enough to support fast reconnection. Referring to two kinds of numerical particle-in-cell simulations we determine the anomalous diffusion coefficient, the anomalous collision frequency on which the diffusion process is based, and construct a relation between the diffusion coefficients and the resistive scale. The anomalous collision frequency from electron pseudo-viscosity in reconnection turns out to be of the order of the lower-hybrid frequency with the latter providing a lower limit, thus making similar assumptions physically meaningful. Tentative though not completely justified use of the κ distribution yields κ &amp;amp;approx; 6 in the reconnection diffusion region and, for the anomalous diffusion coefficient, the order of several times Bohm diffusivity.

Resistivity in the dynamic current sheath of a field reversed configuration

The resistivity of a field reversed configuration in a theta-pinch with slow rising current was investigated during the turbulent phase from the moment of field reversal until end of plasma radial implosion. This transport coefficient was obtained in a hydrogen plasma by local measurements with magnetic probe and compared to numerical calculations with Chodura resistivity and evolution of lower hybrid drift instability. The values of resistivity are higher than those predicted by classical binary collision. During early phase of confinement, the doubly layer structure of current sheath in the low electric field machine was theoretically well reproduced with anomalous collision frequency calculated with Chodura resistivity that provides appropriate conditions for onset of lower hybrid drift instability and the regular evolution of pinch. The plasma dynamic, radial profiles of magnetic field during the radial compression and resistivity values were equally close to those observed by the measurements.

Reconciliation of rocket‐based magnetic field measurements in the equatorial electrojet with classical collision theory

We provide an explanation for a long‐standing (more than 35 years) discrepancy between theory and rocket experiments concerning the peak height of the electrojet current and the magnitude of magnetic field perturbation. The arbitrary correction of the electron‐neutral collision frequency by a factor of 4, which has been used to explain these problems, is not necessary if the field line–integrated conductivities are used. Recent research using ground‐based magnetometers and CHAMP have also used this constant connection to classical collision theory. These methods arbitrarily change the electron‐neutral collision frequency. A field line–integrated theoretical study of the electrojet by G. Haerendel and J. V. Eccles, implemented in this paper, explains the height of the electrojet using classical collision frequency. Furthermore, we argue that since the correction factor is independent of the driving electric field, it is unlikely that anomalous electron collision frequency due to a nonlinear plasma instability (gradient drift) is involved.

Electron cross-field transport in a miniaturized cylindrical Hall thruster

Conventional annular Hall thrusters become inefficient when scaled to low power. Cylindrical Hall thrusters, which have lower surface-to-volume ratio, are more promising for scaling down. They presently exhibit performance comparable with conventional annular Hall thrusters. The present paper gives a review of the experimental and numerical investigations of electron cross-field transport in the 2.6-cm miniaturized cylindrical Hall thruster (100-W power level). We show that, in order to explain the discharge current observed for the typical operating conditions, the electron anomalous collision frequency /spl nu//sub B/ has to be on the order of the Bohm value, /spl nu//sub B/ /spl ap/ /spl omega//sub c//16. The contribution of electron-wall collisions to cross-field transport is found to be insignificant. The optimal regimes of thruster operation at low background pressure (below 10/sup -5/ torr) in the vacuum tank appear to be different from those at higher pressure (/spl sim/10/sup -4/ torr).

Spatial and temporal variations of small-scale plasma turbulence parameters in the equatorial electrojet: HF and VHF radar observational results

Abstract. The spatial and temporal variations of various parameters associated with plasma wave turbulence in the equatorial electrojet (EEJ) at the magnetic equatorial location of Trivandrum (8.5° N, 77° E; dip 0.5° N) are studied for the first time, using co-located HF (18MHz) and VHF (54.95MHz) coherent backscatter radar observations (daytime) in the altitude region of 95-110km, mostly on magnetically quiet days. The derived turbulence parameters are the mean electron density irregularity strength (δn/n), anomalous electron collision frequency (νe*) and the corrected east-west electron drift velocity (Vey). The validity of the derived parameters is confirmed using radar data at two different frequencies and comparing with in-situ measurements. The behaviour of δn/n in relation to the backscattered power during weak and strong EEJ conditions is also examined to understand the growth and evolution of turbulence in the electrojet.

Electron cross-field transport in a low power cylindrical Hall thruster

Conventional annular Hall thrusters become inefficient when scaled to low power. Cylindrical Hall thrusters, which have lower surface-to-volume ratio, are therefore more promising for scaling down. They presently exhibit performance comparable with conventional annular Hall thrusters. Electron cross-field transport in a 2.6 cm miniaturized cylindrical Hall thruster (100 W power level) has been studied through the analysis of experimental data and Monte Carlo simulations of electron dynamics in the thruster channel. The numerical model takes into account elastic and inelastic electron collisions with atoms, electron-wall collisions, including secondary electron emission, and Bohm diffusion. It is shown that in order to explain the observed discharge current, the electron anomalous collision frequency νB has to be on the order of the Bohm value, νB≈ωc/16. The contribution of electron-wall collisions to cross-field transport is found to be insignificant.

Closure of multi-fluid and kinetic equations for cyclotron-resonant interactions of solar wind ions with Alfvén waves

Abstract. Based on quasilinear theory, a closure scheme for anisotropic multi-component fluid equations is developed for the wave-particle interactions of ions with electromagnetic Alfvén and ion-cyclotron waves propagating along the mean magnetic field. Acceleration and heating rates are calculated. They may be used in the multi-fluid momentum and energy equations as anomalous transport terms. The corresponding evolution equation for the average wave spectrum is established, and the effective growth/damping rate for the spectrum is calculated. Given a simple power-law spectrum, an anomalous collision frequency can be derived which depends on the slope and average intensity of the spectrum, and on the gyrofrequency and the differential motion (with respect to the wave frame) of the actual ion species considered. The wave-particle interaction terms attain simple forms resembling the ones for collisional friction and temperature anisotropy relaxation (due to pitch angle scattering) with collision rates that are proportional to the gyrofrequency but diminished substantially by the relative wave energy or the fluctuation level with respect the background field. In addition, a set of quasilinear diffusion equations is derived for the reduced (with respect to the perpendicular velocity component) velocity distribution functions (VDFs), as they occur in the wave dispersion equation and the related dielectric function for parallel propagation. These reduced VDFs allow one to describe adequately the most prominent observed features, such as an ion beam and temperature anisotropy, in association with the resonant interactions of the particles with the waves on a kinetic level, yet have the advantage of being only dependent upon the parallel velocity component.