Ion Velocity Distribution Function Research Articles

Ion Heating Measurements on the Centerline of a High-Current Hollow Cathode Plume

An experimental investigation into the correlation between ion acoustic turbulence (IAT) and anomalous ion heating in the plume of a 100 A-class hollow cathode is presented. Laser-induced fluorescence is employed to measure the ion velocity distribution function, and a translating ion saturation probe is used to quantify the spatial dependence of the IAT wave energy. It is found that over a range of flow rates and operating currents both the ion temperature and IAT energy increase downstream of the cathode in qualitatively similar ways. Both parameters also are shown to be impacted by operating conditions: the IAT energy and ion temperature decrease at higher flow rates and lower discharge currents. It is shown that the ratio between ion temperature and wave energy is related by a scaling parameter that depends on the background plasma parameters, and this relation is examined in the context of previous analytical work on IAT-induced ion heating.

On the Importance of Spatial and Velocity Resolution in the Hybrid-Vlasov Modeling of Collisionless Shocks

In hybrid-Vlasov plasma modeling, the ion velocity distribution function is propagated using the Vlasov equation while electrons are considered a charge-neutralizing fluid. It is an alternative to particle-in-cell methods, one advantage being the absence of sampling noise in the moments of the distribution. However, the discretization requirements in up to six dimensions (3D position, 3V velocity) make the computational cost of hybrid-Vlasov models higher. This is why hybrid-Vlasov modeling has only recently become more popular and available to model large-scale systems. The hybrid-Vlasov model Vlasiator is the first to have been successfully applied to model the solar-terrestrial interaction. It includes in particular the bow shock and magnetosheath regions, albeit in 2D-3V configurations so far. The purpose of this study is to investigate how Vlasiator parameters affect the modeling of a plasma shock in a 1D-3V simulation. The setup is similar to the Earth's bow shock in previous simulations, so that the present results can be related to existing and future magnetospheric simulations. The parameters investigated are the spatial and velocity resolution, as well as the phase space density threshold, which is the key parameter of the so-called sparse velocity space. The role of the Hall term in Ohm's law is also studied. The evaluation metrics used are the convergence of the final state, the complexity of spatial profiles and ion distributions as well as the position of the shock front. In agreement with previous Vlasiator studies it is not necessary to resolve the ion inertial length and gyroradius in order to obtain kinetic phenomena. While the code remains numerically stable with all combinations of resolutions, it is shown that significantly increasing the resolution in one space but not the other leads to unphysical results. Past a certain level, decreasing the phase space density threshold bears a large computational weight without clear physical improvement in the setup used here. Finally, the inclusion of the Hall term shows only minor effects in this study, mostly because of the 1D configuration and the scales studied, at which the Hall term is not expected to play a major role.

Ion velocity analysis of rotating structures in a magnetic linear plasma device

The MISTRAL device is designed to produce a linear magnetized plasma column. It has been used a few years ago to study a nonlinear low frequency instability exhibiting an azimuthal number m = 2. By changing the experimental configuration of MISTRAL, this work shows experimental results on an m = 1 rotating instability with strongly different behavior. The spatio-temporal evolution of the ion velocity distribution function given by a laser-induced fluorescence diagnostic is measured to infer the radial and azimuthal velocities, ion fluxes, and electric fields. The naive image of a plasma exhibiting a global rotation is again invalidated in this m = 1 mode but in a different way. Contrary to the m = 2 mode, the rotation frequency of the instability is lower than the ion cyclotron frequency and ions exhibit a complex behavior with a radial outward flux inside the unstable arm and azimuthal ion fluxes always directed toward the unstable arm. The azimuthal ion velocity is close to zero inside the ionization region, whereas the radial ion velocity grows linearly with radius. The radial electric field is oriented inward inside the unstable arm and outward outside. An axial velocity perturbation is also present, indicating that contrary to the m = 2 mode, the m = 1 mode is not a flute mode. These results cannot be easily interpreted with existing theories.

Introduction to the theory and application of a unified Bohm criterion for arbitrary-ion-temperature collision-free plasmas with finite Debye lengths

At present, identifying and characterizing the common plasma–sheath edge (PSE) in the conventional fluid approach leads to intrinsic oversimplifications, while the kinetic one results in unusable over-generalizations. In addition, none of these approaches can be justified in realistic plasmas, i.e., those which are characterized by non-negligible Debye lengths and a well-defined non-negligible ion temperature. In an attempt to resolve this problem, we propose a new formulation of the Bohm criterion [D. Bohm, The Characteristics of Electrical Discharges in Magnetic Fields (McGraw-Hill, New York, 1949)], which is here expressed in terms of fluid, kinetic, and electrostatic-pressure contributions. This “unified” Bohm criterion consists of a set of two equations for calculating the ion directional energy (i.e., the mean directional velocity) and the plasma potential at the common PSE, and is valid for arbitrary ion-to-electron temperature ratios. It turns out to be exact at any point of the quasi-neutral plasma provided that the ion differential polytropic coefficient function (DPCF) of Kuhn et al. [Phys. Plasmas 13, 013503 (2006)] is employed, with the advantage that the DPCF is an easily measurable fluid quantity. Moreover, our unified Bohm criterion holds in plasmas with finite Debye lengths, for which the famous kinetic criterion formulated by Harrison and Thompson [Proc. Phys. Soc. 74, 145 (1959)] fails. Unlike the kinetic criterion in the case of negligible Debye length, the kinetic contribution to the unified Bohm criterion, arising due to the presence of negative and zero velocities in the ion velocity distribution function, can be calculated separately from the fluid term. This kinetic contribution disappears identically at the PSE, yielding strict equality of the ion directional velocity there and the ion sound speed, provided that the latter is formulated in terms of the present definition of DPCFs. The numerical values of these velocities are found for the Tonks–Langmuir collision-free, plane-parallel discharge model [Phys. Rev. 34, 876 (1929)], however, with the ion-source temperature extended here from the original (zero) value to arbitrary high ones. In addition, it turns out, that the charge-density derivative (in the potential “space”) with respect to the potential exhibits two characteristic points, i.e., potentials, namely the points of inflection and maximum of that derivative (in the potential space), which stay “fixed” at their respective potentials independent of the Debye length until it is kept fairly small. Plasma quasi-neutrality appears well satisfied up to the first characteristic point/potential, so we identify that one as the plasma edge (PE). Adopting the convention that the sheath is a region characterized by considerable electrostatic pressure (energy density), we identify the second characteristic point/potential as the sheath edge (SE). Between these points, the charge density increases from zero to a finite value. Thus, the interval between the PE and SE, with the “fixed” width (in the potential “space”) of about one third of the electron temperature, will be named the plasma–sheath transition (PST). Outside the PST, the electrostatic-pressure term and its derivatives turn out to be nearly identical with each other, independent of the particular values of the ion temperature and Debye length. In contrast, an increase in Debye lengths from zero to finite values causes the location of the sonic point/potential (laying inside the PST) to shift from the PE (for vanishing Debye length) towards the SE, while at the same time, the absolute value of the corresponding ion-sound velocity slightly decreases. These shifts turn out to be manageable with employing the mathematical concept of the plasma-to-sheath transition (different from, but related to our natural PST concept), resulting in approximate, but sufficiently reliable semi-analytic expressions, which are functions of the ion temperature and Debye length.

Ion beams in multi-species plasmas

Argon and xenon ion velocity distribution functions are measured in Ar-He, Ar-Xe, and Xe-He expanding helicon plasmas to determine if ion beam velocity is enhanced by the presence of lighter ions. Contrary to observations in mixed gas sheath experiments, we find that adding a lighter ion does not increase the ion beam speed. The predominant effect is a reduction of ion beam velocity consistent with increased drag arising from increased gas pressure under all conditions: constant total gas pressure, equal plasma densities of different ions, and very different plasma densities of different ions. These results suggest that the physics responsible for the acceleration of multiple ion species in simple sheaths is not responsible for the ion acceleration observed in expanding helicon plasmas.

Collisionless coupling of a high-β expansion to an ambient, magnetized plasma. II. Experimental fields and measured momentum coupling

The momentum coupled to a magnetized, ambient argon plasma from a high-β, laser-produced carbon plasma is examined in a collisionless, weakly coupled limit. The total electric field was measured by separately examining the induced component associated with the rapidly changing magnetic field of the high-β (kinetic β∼106), expanding plasma and the electrostatic component due to polarization of the expansion. Their temporal and spatial structures are discussed and their effect on the ambient argon plasma (thermal β∼10−2) is confirmed with a laser-induced fluorescence diagnostic, which directly probed the argon ion velocity distribution function. For the given experimental conditions, the electrostatic field is shown to dominate the interaction between the high-β expansion and the ambient plasma. Specifically, the expanding plasma couples energy and momentum into the ambient plasma by pulling ions inward against the flow direction.

Effect of Elastic Collisions on the Ion Distribution Function in Parent Gas Discharge Plasma

An analytical solution is obtained for the Boltzmann kinetic equation for ions in the plasma of its gas with allowance for the processes of resonant charge exchange and elastic ion scattering on the atom. The cross section of differential elastic scattering was assumed to be isotropic in the system of the mass center, and the resonant charge exchange process is independent of the elastic scattering. It is shown that the ion velocity distribution function is determined by two parameters and differs significantly from the Maxwellian one. The allowance for elastic scattering with these assumptions leads to a change in the ion angular distribution and also to a decrease in the average ion energy due to the transfer of part of the ion energy to atoms upon elastic collisions. The calculated values of the drift velocity, the average energy, and the coefficient of transverse diffusion of He+ ions in He, Ar+ ions in Ar are compared with the known experimental data and the results of Monte Carlo calculations; they show good agreement.

Spectroscopic Measurements of the Ion Velocity Distribution at the Base of the Fast Solar Wind

Abstract In situ measurements of the fast solar wind reveal non-thermal distributions of electrons, protons, and minor ions extending from 0.3 au to the heliopause. The physical mechanisms responsible for these non-thermal properties and the location where these properties originate remain open questions. Here, we present spectroscopic evidence, from extreme ultraviolet spectroscopy, that the velocity distribution functions (VDFs) of minor ions are already non-Gaussian at the base of the fast solar wind in a coronal hole, at altitudes of <1.1 R ⊙. Analysis of Fe, Si, and Mg spectral lines reveals a peaked line-shape core and broad wings that can be characterized by a kappa VDF. A kappa distribution fit gives very small kappa indices off-limb of κ ≈ 1.9–2.5, indicating either (a) ion populations far from thermal equilibrium, (b) fluid motions such as non-Gaussian turbulent fluctuations or non-uniform wave motions, or (c) some combination of both. These observations provide important empirical constraints for the source region of the fast solar wind and for the theoretical models of the different acceleration, heating, and energy deposition processes therein. To the best of our knowledge, this is the first time that the ion VDF in the fast solar wind has been probed so close to its source region. The findings are also a timely precursor to the upcoming 2018 launch of the Parker Solar Probe, which will provide the closest in situ measurements of the solar wind at approximately 0.04 au (8.5 solar radii).

On limitations of laser-induced fluorescence diagnostics for xenon ion velocity distribution function measurements in Hall thrusters

Hall thruster operation is characterized by strong breathing oscillations of the discharge current, the plasma density, the temperature, and the electric field. Probe- and laser-induced fluorescence (LIF) diagnostics were used to measure temporal variations of plasma parameters and the xenon ion velocity distribution function (IVDF) in the near-field plasma plume in regimes with moderate (<18%) external modulations of applied DC discharge voltage at the frequency of the breathing mode. It was shown that the LIF signal collapses while the ion density at the same location is finite. The proposed explanation for this surprising result is based on a strong dependence of the excitation cross-section of metastables on the electron temperature. For large amplitudes of oscillations, the electron temperature at the minimum enters the region of very low cross-section (for the excitation of the xenon ions); thus, significantly reducing the production of metastable ions. Because the residence time of ions in the channel is generally shorter than the time scale of breathing oscillations, the density of the excited ions outside the thruster is low and they cannot be detected. In the range of temperature of oscillations, the ionization cross-section of xenon atoms remains sufficiently large to sustain the discharge. This finding suggests that the commonly used LIF diagnostic of xenon IVDF can be subject to large uncertainties in the regimes with significant oscillations of the electron temperature, or other plasma parameters.

Time-of-Flight Characteristics of a Laser Torch during Ablation of a MnSi Target in Argon Atmosphere

The Langmuir-probe technique has been used to study the time-of-flight characteristics of a laser torch during MnSi-target ablation in vacuum and argon atmosphere by pulsed 532-nm laser radiation at 15-ns pulse duration. It is established that the amplitude of the signal of fast particles in the laser torch nonmonotonically depends on the buffer-gas pressure. Mechanisms determining this dependence of laser-torch characteristics on the pressure are considered. The influence of buffer-gas pressure on the ion-velocity distribution function is determined.

Challenges in the determination of the interstellar flow longitude from the pickup ion cutoff

Context. The interstellar flow longitude corresponds to the Sun’s direction of movement relative to the local interstellar medium. Thus, it constitutes a fundamental parameter for our understanding of the heliosphere and, in particular, its interaction with its surroundings, which is currently investigated by the Interstellar Boundary EXplorer (IBEX). One possibility to derive this parameter is based on pickup ions (PUIs) that are former neutral ions that have been ionized in the inner heliosphere. The neutrals enter the heliosphere as an interstellar wind from the direction of the Sun’s movement against the partially ionized interstellar medium. PUIs carry information about the spatial variation of their neutral parent population (density and flow vector field) in their velocity distribution function. From the symmetry of the longitudinal flow velocity distribution, the interstellar flow longitude can be derived.Aim. The aim of this paper is to identify and eliminate systematic errors that are connected to this approach of measuring the interstellar flow longitude; we want to minimize any systematic influences on the result of this analysis and give a reasonable estimate for the uncertainty.Methods. We use He+ data measured by the PLAsma and SupraThermal Ion Composition (PLASTIC) sensor on the Solar TErrestrial RElations Observatory Ahead (STEREO A) spacecraft. We analyze a recent approach, identify sources of systematic errors, and propose solutions to eliminate them. Furthermore, a method is introduced to estimate the error associated with this approach. Additionally, we investigate how the selection of interplanetary magnetic field angles, which is closely connected to the pickup ion velocity distribution function, affects the result for the interstellar flow longitude.Results. We find that the revised analysis used to address part of the expected systematic effects obtains significantly different results than presented in the previous study. In particular, the derived uncertainties are considerably larger. Furthermore, an unexpected systematic trend of the resulting interstellar flow longitude with the selection of interplanetary magnetic field orientation is uncovered.

Determination of Anisotropic Ion Velocity Distribution Function in Intrinsic Gas Plasma. Theory.

The first seven coefficients of the expansion of the energy and angular distribution functions in Legendre polynomials for Hg+ ions in Hg vapor plasma with the parameter E/P ≈ 400 V/(cm Torr) are measured for the first time using a planar one-sided probe. The analytic solution to the Boltzmann kinetic equation for ions in the plasma of their parent gas is obtained in the conditions when the resonant charge exchange is the predominant process, and ions acquire on their mean free path a velocity much higher than the characteristic velocity of thermal motion of atoms. The presence of an ambipolar field of an arbitrary strength is taken into account. It is shown that the ion velocity distribution function is determined by two parameters and differs substantially from the Maxwellian distribution. Comparison of the results of calculation of the drift velocity of He+ ions in He, Ar+ in Ar, and Hg+ in Hg with the available experimental data shows their conformity. The results of the calculation of the ion distribution function correctly describe the experimental data obtained from its measurement. Analysis of the result shows that in spite of the presence of the strong field, the ion velocity distribution functions are isotropic for ion velocities lower than the average thermal velocity of atoms. With increasing ion velocity, the distribution becomes more and more extended in the direction of the electric field.

Multiprobe characterization of plasma flows for space propulsion

Plasma engines for space propulsion generate plasma jets (also denominated plasma plumes) having supersonic ion groups with typical speeds in the order of tens of kilometers per second, which lies between electron and ion thermal speeds. Studies of the stationary plasma expansion process using a four-grid retarding field energy analyzer (RFEA), an emissive probe (EP) and a Langmuir probe (LP), all mounted on a three dimensionally (3D) displaced multiprobe structure are discussed. Specifically, the determination of plasma beam properties from the RFEA current-voltage (IV) characteristic curves is presented. The experimental results show the ion energy spectra to be essentially unchanged over 300 mm along the plasma-jet expansion axis of symmetry. The measured ion velocity distribution function (IVDF) results from the superposition of different ion groups and has two dominant populations: A low-energy group constituted of ions from the background plasma is produced by the interaction of the plasma jet with the walls of the vacuum chamber. The fast-ion population is composed of ions from the plasma beam moving at supersonic speeds with respect to the low-energy ions. The decreasing spatial profiles of the plasma-jet current density are compared with those of the low-energy ion group, which are not uniform along the axis of symmetry because of the small contributions from other ion populations with intermediate speeds.

Pressure dependence of an ion beam accelerating structure in an expanding helicon plasma

We present measurements of the parallel ion velocity distribution function and electric field in an expanding helicon source plasma plume as a function of downstream gas pressure and radial and axial positions. The ion beam that appears spontaneously in the plume persists for all downstream pressures investigated, with the largest parallel ion beam velocities obtained for the lowest downstream pressures. However, the change in ion beam velocity exceeds what would be expected simply for a change in the collisionality of the system. Electric field measurements confirm that it is the magnitude of the potential structure responsible for accelerating the ion beam that changes with downstream pressure. Interestingly, the ion density radial profile is hollow close to the end of the plasma source for all pressures, but it is hollow at downstream distances far from the source only at the highest downstream neutral pressures.

Deuterium temperature, drift velocity, and density measurements in non-Maxwellian plasmas at ASDEX Upgrade

We measure the deuterium density, the parallel drift velocity, and parallel and perpendicular temperatures (, ) in non-Maxwellian plasmas at ASDEX Upgrade. This is done by taking moments of the ion velocity distribution function measured by tomographic inversion of five simultaneously acquired spectra of -light. Alternatively, we fit the spectra using a bi-Maxwellian distribution function. The measured kinetic temperatures ( keV, keV) reveal the anisotropy of the plasma and are substantially higher than the measured boron temperature (7 keV). The Maxwellian deuterium temperature computed with TRANSP (6 keV) is not uniquely measurable due to the fast ions. Nevertheless, simulated kinetic temperatures accounting for fast ions based on TRANSP ( keV, keV) are in excellent agreement with the measurements. Similarly, the Maxwellian deuterium drift velocity computed with TRANSP (300 km s−1) is not uniquely measurable, but the simulated kinetic drift velocity accounting for fast ions agrees with the measurements (400 km s−1) and is substantially larger than the measured boron drift velocity (270 km s−1). We further find that ion cyclotron resonance heating elevates and each by 2 keV without evidence for preferential heating in the spectra. Lastly, we derive an expression for the 1D projection of an arbitrarily drifting bi-Maxwellian onto a diagnostic line-of-sight.

Времяпролетные характеристики лазерного факела при абляции мишени MnSi в атмосфере аргона

AbstractThe Langmuir-probe technique has been used to study the time-of-flight characteristics of a laser torch during MnSi-target ablation in vacuum and argon atmosphere by pulsed 532-nm laser radiation at 15-ns pulse duration. It is established that the amplitude of the signal of fast particles in the laser torch nonmonotonically depends on the buffer-gas pressure. Mechanisms determining this dependence of laser-torch characteristics on the pressure are considered. The influence of buffer-gas pressure on the ion-velocity distribution function is determined.

A Lagrangian model for laser-induced fluorescence and its application to measurements of plasma ion temperature and electrostatic waves

Extensive information can be obtained on wave-particle interactions and wave fields by a direct measurement of perturbed ion distribution functions using laser-induced fluorescence (LIF). For practical purposes, LIF is frequently performed on metastable states that are produced from neutral gas particles and ions in other electronic states. If the laser intensity is increased to obtain a better LIF signal, then optical pumping can produce systematic effects depending on the collision rates which control metastable population and lifetime. We numerically simulate the ion velocity distribution measurement and wave-detection process using a Lagrangian model for the LIF signal for the case where metastables are produced directly from neutrals. This case requires more strict precautions and is important for discharges with energetic primary electrons and a high density of neutrals. Some of the results also apply to metastables produced from pre-existing ions. The simulations show that optical pumping broadening affects the ion velocity distribution function f0(v) and its first-order perturbation f1(v,t) when the laser intensity is increased above a certain level. The results also suggest that ion temperature measurements are only accurate when the metastable ions can live longer than the ion-ion collision mean free time. For the purposes of wave detection, the wave period has to be significantly shorter than the lifetime of metastable ions for a direct interpretation. It is more generally true that metastable ions may be viewed as test-particles. As long as an appropriate model is available, LIF can be extended to a range of environments.

Spatial structure of ion beams in an expanding plasma

We report spatially resolved perpendicular and parallel, to the magnetic field, ion velocity distribution function (IVDF) measurements in an expanding argon helicon plasma. The parallel IVDFs, obtained through laser induced fluorescence (LIF), show an ion beam with v ≈ 8000 m/s flowing downstream and confined to the center of the discharge. The ion beam is measurable for tens of centimeters along the expansion axis before the LIF signal fades, likely a result of metastable quenching of the beam ions. The parallel ion beam velocity slows in agreement with expectations for the measured parallel electric field. The perpendicular IVDFs show an ion population with a radially outward flow that increases with distance from the plasma axis. Structures aligned to the expanding magnetic field appear in the DC electric field, the electron temperature, and the plasma density in the plasma plume. These measurements demonstrate that at least two-dimensional and perhaps fully three-dimensional models are needed to accurately describe the spontaneous acceleration of ion beams in expanding plasmas.

IEDF distortion and resolution considerations for RFEA operation at high voltages

Retarding field energy analyzers (RFEA) have been used extensively to measure the ion flux energy distribution function of plasmas. For consistency, the ion flux energy distribution function is referred to as the ion energy distribution function (IEDf) even though it more accurately represents the one-dimensional ion velocity distribution function. In the past, these devices have operated at voltages less than 1 kV. Higher operating voltages (>2 kV) are currently desired. For an RFEA to operate at these voltages, design changes are necessary that impact the energy resolution and cause space charge build-up. To investigate the effect the design changes have for a high voltage RFEA, electromagnetic simulations and particle-in-cell (PIC) simulations were used to analyze the electric field between the grids, the potential drop in the grid holes, and space charge build-up between the grids. Non-unique optimized dimensions for the RFEA increased the electric field uniformity. The optimization minimizes the electric field from distorting the IV curve or adversely affecting the energy resolution. It was found that a larger grid gap distance and smaller grid hole diameter decreases the potential drop in the grid holes improving energy resolution. IV curves from the PIC simulation were used to obtain space charge distorted IEDfs. The point at which space charge distorts the IV curve is dependent on the grid gap distance and incoming flux. Space charge build-up was found to only affect low energy ions which manifested by cutting off the low energy portion of the IEDf. To fix space charge distortions, the flux into the probe can be limited or it may be possible to account for the distortion when calculating the IEDf.

Ring-averaged ion velocity distribution function probe for laboratory magnetized plasma experiment.

Ring-averaged velocity distribution function of ions at a fixed guiding center position is a fundamental quantity in the gyrokinetic plasma physics. We have developed a diagnostic tool for the ring averaged velocity distribution function of ions for laboratory plasma experiments, which is named as the ring-averaged ion distribution function probe (RIDFP). The RIDFP is a set of ion collectors for different velocities. It is designed to be immersed in magnetized plasmas and achieves momentum selection of incoming ions by the selection of the ion Larmor radii. To nullify the influence of the sheath potential surrounding the RIDFP on the orbits of the incoming ions, the electrostatic potential of the RIDFP body is automatically adjusted to coincide with the space potential of the target plasma with the use of an emissive probe and a voltage follower. The developed RIDFP successfully measured the equilibrium ring-averaged velocity distribution function of a laboratory magnetized plasma, which was in accordance with the Maxwellian distribution having an ion temperature of 0.2 eV.