Ion Velocity Distribution Function Research Articles

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.

Collisionless ion modeling in Hall thrusters: Analytical axial velocity distribution function and heat flux closures

The genesis of the ion axial velocity distribution function (VDF) is analyzed for collisionless Hall thruster discharges. An analytical form for the VDF is obtained from the Vlasov equation, by applying the Tonks–Langmuir theory in the thruster channel, under the simplifying assumptions of monoenergetic creation of ions and steady state. The equivalent set of 1D unsteady anisotropic moment equations is derived from the Vlasov equation, and simple phenomenological closures are formulated, assuming a polynomial shape for the ion VDF. The analytical results and the anisotropic moment equations are compared to collisionless particle-in-cell simulations, employing either a zero heat flux (Euler-like equations) or the polynomial-VDF closure for the heat flux. The analytical ion VDF and its moments are then compared to experimental measurements.

Macroscopic and parametric study of a kinetic plasma expansion in a paraxial magnetic nozzle

A kinetic paraxial model of a collisionless plasma stationary expansion in a convergent-divergent magnetic nozzle (MN) is analyzed. Monoenergetic and Maxwellian velocity distribution functions of upstream ions are compared, leading to differences in the expansion only on second and higher-order velocity moments. Individual and collective magnetic mirror effects are analyzed. Collective ones are small on the electron population since only a weak temperature anisotropy develops, but they are significant on the ions all over the nozzle. Momentum and energy equations for ions and electrons are assessed based on the kinetic solution. The ion response is different in the hot and cold limits, with the anisotropic pressure tensor being relevant in the first case. Heat fluxes of parallel and perpendicular energies have a dominant role in the electron energy equations. They do not fulfill a Fourier-type law; they are large even when electrons are near isothermal. A crude electron fluid closure based on a constant diffusion-to-convective thermal energy ratio is shown equivalent to the much invoked polytropic law. Analytical dimensionless parameter laws are derived for the nozzle total electric potential fall and the downstream residual electron temperature. Electron confinement and related current control by a thin Debye sheath and a semi-infinite divergent MN are compared.

Effect of gas temperature on CO2+ ion transport in CO2

The effect of gas temperature on the transport of the CO2+ ion in its parent gas CO2 is studied. For this purpose, a Monte Carlo (MC) solution technique of the ion transport equation developed in the past by the authors, which was formally proven to provide the exact solution of the transport equation, is used. The study is performed first by benchmarking against experimental data and another MC code, using cross sections from literature and then changing the gas temperature. The solution is characterized through its moments such as reduced mobility, coefficients of its expansion in Legendre polynomials and three-dimensional ion velocity distribution function. It is shown that the gas temperature has a significant effect on all these quantities. This finding has important consequences for plasma modeling which are discussed.

The far-field plasma characterization in a 600 W Hall thruster plume by laser-induced fluorescence

Non-intrusive characterization of the singly ionized xenon velocity in Hall thruster plume using laser induced fluorescence (LIF) is critical for constructing a complete picture of plume plasma, deeply understanding the ion dynamics in the plume, and providing validation data for numerical simulation. This work presents LIF measurements of singly ionized xenon axial velocity on a grid ranging from 100 to 300 mm in axial direction and from 0 to 50 mm in radial direction for a 600 W Hall thruster operating at the nominal condition of discharge voltage 300 V and discharge current 2 A, the influence of discharge voltage is investigated as well. The ion velocity distribution function (IVDF) results in the far-field plume demonstrate a profile of bimodal IVDFs, especially prominent at radial distances greater than channel inner radius of 22 mm at axial position of 100 mm, which is quite different from that of the near-field plume where bimodal IVDFs occur in the central core region for the same power Hall thruster when compared to previous LIF measurements of BHT-600 by Hargus (2010 J. Propulsion Power 26 135). Beyond 100 mm, only single-peak IVDFs are measured. The two-dimensional ion velocity vector field indicates the bimodal axial IVDF is merely a geometry effect for the annular discharge channel in the far-field plume. Results about the IVDF, the most probable velocity and the accelerating potential profile along the centerline all indicate that ions are still accelerating at axial distances greater than 100 mm, and the maximum most probable velocity measured at 300 mm downstream of the exit plane is about 19 km s−1. In addition, the most probable velocity of ions along radial direction changes a little except the lower velocity ion populations in the bimodal IVDF cases. The ion temperature at axial distances of 10 and 300 mm oscillates along the radial direction, while the ion temperature first increases, and then decreases for the 200 mm case. Finally, the axial position for the ion peak axial velocity on the thruster centerline is shifted upstream for higher discharge voltages, and the velocity curve is becoming steeper with the discharge voltage before reaching the maximum. This observation can be used as a criterion to optimize the thruster performance.

On the deviation from Maxwellian of the ion velocity distribution functions in the turbulent magnetosheath

The deviation from thermodynamic equilibrium of the ion velocity distribution functions (VDFs), as measured by the Magnetospheric Multiscale (MMS) mission in the Earth’s turbulent magnetosheath, is quantitatively investigated. Making use of the unprecedented high-resolution MMS ion data, and together with Vlasov–Maxwell simulations, this analysis aims at investigating the relationship between deviation from Maxwellian equilibrium and typical plasma parameters. Correlations of the non-Maxwellian features with plasma quantities such as electric fields, ion temperature, current density and ion vorticity are found to be similar in magnetosheath data and numerical experiments, with a poor correlation between distortions of ion VDFs and current density, evidence that questions the occurrence of VDF departure from Maxwellian at the current density peaks. Moreover, strong correlation has been observed with the magnitude of the electric field in the turbulent magnetosheath, while a certain degree of correlation has been found in the numerical simulations and during a magnetopause crossing by MMS. This work could help shed light on the influence of electrostatic waves on the distortion of the ion VDFs in space turbulent plasmas.

Cross Sections and Rate Coefficients for O+ Reacting With N2, O2, and NO

AbstractIon‐molecule reaction cross sections between 0.03 and 3 eV can best be inferred from data taken in drift tube mass spectrometers. For the title reactions, the cross sections inferred from drift‐tube measurements in the late 1970s have been accepted as accurate, even though the methods used to infer them made substantial assumptions about the ion velocity distribution functions. Here the Gram‐Charlier method for solving the Boltzmann equation is used to obtain ion distribution functions that are anisotropic, having different average energies parallel and perpendicular to the uniform electrostatic field. The Gram‐Charlier method incorporates skewness, kurtosis, and correlation between the motions parallel and perpendicular to the field. This leads to more accurate ion distribution functions from which more accurate reaction cross sections have been inferred. The results differ by as much as 50% from the generally accepted cross sections that are currently used to model ion‐neutral reactions in the upper atmosphere.

The Impact of Turbulent Solar Wind Fluctuations on Solar Orbiter Plasma Proton Measurements

Abstract Solar Orbiter will observe the Sun and the inner heliosphere to study the connections between solar activity, coronal structure, and the origin of the solar wind. The plasma instruments on board Solar Orbiter will determine the three-dimensional velocity distribution functions of the plasma ions and electrons with high time resolution. The analysis of these distributions will determine the plasma bulk parameters, such as density, velocity, and temperature. This paper examines the effects of short-timescale plasma variations on particle measurements and the estimated bulk parameters of the plasma. For the purpose of this study, we simulate the expected observations of solar wind protons, taking into account the performance of the Proton-Alpha Sensor (PAS) on board Solar Orbiter. We particularly examine the effects of Alfvénic and slow-mode-like fluctuations, commonly observed in the solar wind on timescales of milliseconds to hours, on the observations. We do this by constructing distribution functions from modeled observations and calculate their statistical moments in order to derive plasma bulk parameters. The comparison between the derived parameters with the known input allows us to estimate the expected accuracy of Solar Orbiter proton measurements in the solar wind under typical conditions. We find that the plasma fluctuations due to these turbulence effects have only minor effects on future SWA-PAS observations.

Non-Maxwellian velocity distribution functions for Coulombic systems out of equilibrium.

The velocity distribution function (VDF) of ions in the solar wind, as observed by spacecraft at 1 AU and elsewhere in the heliosphere, exhibits a consistent trend: at low energies in the solar wind frame, the distribution is largely Maxwellian-the core; at higher but still modest energies in the solar wind frame, the distribution follows a power law (f ∝ v -γ , where f is the VDF, v is the speed in the solar wind frame, and γ is an arbitrary spectral index parameter)-the tail-with a spectral index of γ ≈ 5 being extremely common. Several theories have been proposed to explain this common index. Among these theories is that the tail is a natural consequence of an ensemble of particles obeying Coulomb's law (Randol & Christian 2014, 2016). In this study, we derive a general analytical formula for the distribution of electric fields, and find that it always exhibits a power law tail with a spectral index of exactly 9/2, or 4.5, due to the spatial power law index of Coulomb's law. We then show how the VDF is a convolution of the distribution of electric fields with a pre-existing VDF, and that for small values of time after being created, the ion VDF always exhibits a γ = 9/2 power law, wherein the probability of the tail relative to the core depends on particle density, n, and inversely on the pre-existing VDF thermal speed, v th . Finally, we compare our results with previous works, and find good agreement but with important distinctions.

Optimization of the Collective Thomson scattering diagnostic for future operation

Collective Thomson scattering (CTS) is a microwave diagnostic allowing measurements of a number of plasma parameters such as the bulk ion temperature, the plasma composition, drift velocities and fast ion velocity distribution function. A CTS system has been successfully installed and commissioned on the Wendelstein 7-X (W7-X) stellarator. The measured spectra are analyzed by the means of the CTS forward model eCTS and the Minerva scientific framework enabling the use of Bayesian inference of relevant plasma parameters. Here we discuss the options for further optimization of the CTS diagnostic and focus on two topics of importance for the inference of bulk ion temperature values from CTS spectra: influence of impurities on the CTS spectra and the width of the notch filters that are employed to protect the receiver from high-power radiation. In addition to that we discuss the possibility of effective charge measurements by CTS. We explore the existence of an optimal notch filter width.

Evolution of Relative Drifts in the Expanding Solar Wind: Helios Observations

Ion velocity distribution functions (VDFs) measured in-situ in the solar wind show often large deviations from a simple Maxwellian distribution. Even a main part of the proton VDF (proton core) situated around the global maximum maintains a bi-Maxwellian character. Moreover, skewness, related to a non-thermal tail or proton beam, is often observed. In addition to these two proton populations, various heavy ion species are present and their VDFs also exhibit the mentioned non-thermal features. In the proton core frame, minor components including ion beams drift along the interplanetary magnetic field and their average differential velocities decrease with an increasing distance from the Sun. We present reprocessing of the VDFs measured by the Helios spacecraft with a motivation to discuss evolutions of relative drifts between three dominant components – the proton core, proton beam, and $\upalpha $ -particle core at different distances from the Sun. Our processing is based on assumptions that partial VDFs of all these components can be approximated by a bi-Maxwellian distribution. We compare results of this novel procedure with those from previous computation results and introduce basic characteristics of the VDF components in both slow and fast solar wind streams. Finally, we investigate the correlated variations of the velocity ratios on the ion components and magnetic field orientations occurring independently on the radial distance from the Sun.

Measurements of ion velocity and wave propagation in a hollow cathode plume

The mechanism responsible for the production of energetic ions in the plume of hollow cathodes for electric propulsion is still an open issue. These ions are of concern to cathode and thruster lifetime, particularly for cathodes operating at high (>20 A) discharge currents. Recent theoretical and experimental investigations suggest that there is a correlation between ion energy gain and ion acoustic turbulence. In this paper we present measurements of the evolution of the ion velocity distribution function in the near plume of a 100 A-class hollow cathode, operated in a regime in which the dominant mode is ion acoustic turbulence. Ion flow and thermal properties were related to measurements of the background plasma, fluctuation spectra, and dispersion relations obtained from an array of Langmuir probes. We found ions to flow outward from the cathode and accelerate downstream, to supersonic speeds, approximately aligned with the acoustic wave group velocity vectors. The directions of the ion flow and wave propagation were similar for a range of discharge currents and mass flow rates in the jet region of the plume. One operating condition showed a significant temperature increase, also in the direction of acoustic wave propagation, corresponding to the highest wave energy condition. These results are interpreted in the context of ion acoustic turbulence as a contributing mechanism for ion energy gain.

Presheath-sheath coupling for kinetic trajectory simulation of a magnetized plasma sheath

The coupling of presheath-sheath parameters is extended for the study of magnetized plasma sheath using the kinetic trajectory simulation (KTS) method, in which the final self-consistent states are obtained iteratively by solving the kinetic equations. In our case, it is assumed that the ion and electron velocity distribution functions are cut-off Maxwellians at the sheath entrance. The results show that the cut-off and Maxwellian maximum velocities have equal magnitudes at the sheath entrance and at wall. The presheath electron temperature has a considerable effect on the self-consistent potential profile which affects the Child sheath thickness. The latter increases from 3.8320 μm to 5.4190 μm when the presheath electron temperature increases from 10 eV to 20 eV. It is found that the number of ions reaching wall is higher than that of the electrons and hence the space charge density has its maximum value there. Furthermore, the temperature of ions in the sheath region increases with the increase in presheath ion temperature. Moreover, the cut-off distribution causes our simulation result to deviate from the theoretical result found for the Boltzmann distribution by about 3%. The coupling scheme presented here provides a basis for smooth transition of plasma parameters at the presheath-sheath interface. The proper understanding of the magnetized plasma-wall transition plays a vital role for further exploring the plasma sheath characteristics which has useful applications in fusion and industrial plasma devices.

Analysis of the Angular Distribution of Emission of Neutrons Generated with the Ponderomotive Mechanism of Ion Heating by High-Power Short Laser Pulse Acting on a (CD2)n Target

Experiments on the angular distribution of DD neutrons generated in nuclear reactions upon irradiation of a (CD2)n target have been performed in the “Neodymium” laser facility. Apart from the main pulse, prepulses were observed in the experiment. Measurements have shown that neutrons have an isotropic angular distribution. Experimental results have been analyzed using hydrodynamic calculations accounting for the ponderomotive force. The ion heating mechanism in a shock wave emerging under the action of the ponderomotive pressure of the main pulse in the supercritical region of the plasma has been considered. It is shown that neutrons are generated mainly in the supercritical plasma heated by the ion heat wave. The time of plasma cooling due to hydrodynamic spreading turns out to be much longer than the isotropization time of the ion velocity distribution function due to Coulomb collisions. In these conditions, the neutron angular distribution must be isotropic.

On the Ion Drift in Cold Gas

The problem of ion drift in such a strong electric field that the ion drift velocity significantly exceeds the thermal velocity of atoms is considered. In the case where the ion mass is identical to the gas particle mass, scattering is isotropic in the center-of-mass system and the ion scattering cross section is independent of the collision velocity (hard sphere model). The ion velocity distribution function is calculated by the Monte Carlo method, its characteristics and diffusion coefficient are determined. A comparison with known numerical and analytical solutions is performed. It is found that average characteristics (drift velocity, longitudinal and transverse temperatures) are in very good agreement with the values obtained from integral relations for the two-temperature Maxwellian distribution; however, the ion velocity distribution itself differs significantly from the shifted two-temperature Maxwellian distribution.

Kinetic effects on neutron generation in moderately collisional interpenetrating plasma flows

Collisional kinetic modifications of ion distributions in interpenetrating flows are investigated by irradiating two opposing targets, either CD/CD or CD/CH, on the National Ignition Facility. In the CD/CD case, neutron time-of-flight diagnostics are successfully used to infer the ion temperature, 5–6 keV, and velocity, 500 km/s per flow, of the flows using a multi-fluid approximation of beam-beam nuclear fusion. These values are found to be in agreement with simulations and other diagnostics. However, for CD/CH, the multi-fluid assumption breaks down, as fusion is quasi-thermonuclear in this case and thus more dependent on the details of the ion velocity distribution. Using kinetic-ion, hydrodynamic-electron, and hybrid particle-in-cell modeling, this is found to be partially due to a skewed deviation from a Maxwellian in the ion velocity distribution function resulting from ion-ion collisions. This skew causes a downshift in the mean neutron velocity that partially resolves the observation in the CD/CH case. We note that the discrepancy is not completely resolved via collisional effects alone and may be a signature of collisionless electromagnetic interactions such as the Weibel-filamentation 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.

First MMS Observation of Energetic Particles Trapped in High‐Latitude Magnetic Field Depressions

AbstractWe present a case study of the Magnetospheric Multiscale (MMS) observations of the Southern Hemispheric dayside magnetospheric boundaries under southward interplanetary magnetic field direction with strong By component. During this event MMS encountered several magnetic field depressions characterized by enhanced plasma beta and high fluxes of high‐energy electrons and ions at the dusk sector of the southern cusp region that resemble previous Cluster and Polar observations of cusp diamagnetic cavities. Based on the expected maximum magnetic shear model and magnetohydrodynamic simulations, we show that for the present event the diamagnetic cavity‐like structures were formed in an unusual location. Analysis of the composition measurements of ion velocity distribution functions and magnetohydrodynamics simulations show clear evidence of the creation of a new kind of magnetic bottle structures by component reconnection occurring at lower latitudes. We propose that the high‐energy particles trapped in these cavities can sometimes end up in the loss cone and leak out, providing a likely explanation for recent high‐energy particle leakage events observed in the magnetosheath.

Effect of radio-frequency substrate bias on ion properties and sputtering behavior of 2 MHz magnetron sputtering

The effect of radio-frequency substrate bias on ion properties and sputtering behavior of 2 MHz magnetron discharge was investigated. The ion velocity distribution function (IVDF), the maximum ion energy and ion flux density were measured at the substrate by a retarding field energy analyzer. The sputtering behavior was investigated by the electric characteristics of target and bias discharges using voltage–current probe technique. It was found that the substrate bias led to the decrease of sputtering power, voltage and current with the amplitude <7.5%. The substrate bias also led to the broadening of IVDFs and the increase of ion flux density, made the energy divergent of ions impacting the substrate. This effect was further enhanced by increasing bias power and reducing discharge pressure.

Laser-induced fluorescence measurements of acceleration zone scaling in the 12.5 kW HERMeS Hall thruster

We present laser-induced fluorescence measurements of acceleration zone scaling with discharge voltage (Vd), magnetic field strength (B), and facility background pressure (PBG) in NASA’s 12.5 kW Hall Effect Rocket with Magnetic Shielding. At fixed discharge current, the plasma potential profiles at discharge voltages from 300 to 600 V approximately overlapped in the region with plasma potential less than 300 V; ion acceleration began further upstream at higher Vd because the region with a steep potential gradient was broader. The radial divergence of mean ion velocity vectors in the outer half of the channel and near plume increased with decreasing Vd. At fixed Vd, the acceleration zone was located further upstream at higher B and at higher PBG. Bimodal ion velocity distribution functions (IVDFs) were measured along the channel centerline in the acceleration zone at high discharge voltages; this effect was attributed to time-averaging over movement of the acceleration zone during large-amplitude discharge current oscillations. At lower discharge voltages, the broadening of the IVDFs in the near plume could not be fully explained by ionization within the acceleration region. These results have implications for understanding front pole erosion, which can be an important wear mechanism over the long lifetimes of magnetically shielded thrusters, and they provide baseline data for validating first principles models of cross-field electron transport.