Ion Velocity Distribution Function Research Articles

RF antenna helicity dependent particle heating in a helicon source

Experiments have demonstrated that ion phenomena, such as the lower hybrid resonance, play an important role in helicon source operation. Damping of the slow branch of the bounded whistler wave at the edge of a helicon source (i.e. the Trivelpiece-Gould mode) has been correlated with the creation of energetic electrons, heating of ions at the plasma edge, and anisotropic ion heating. Here we present ion velocity distribution function measurements, electron density and temperature measurements, and magnetic fluctuation measurements on both sides of an m=|1| helical antenna in a helicon source as a function of the driving frequency, magnetic field strength, and magnetic field orientation relative to the antenna helicity. Significant electron and ion heating (up to two times larger) occurs on the side of the antenna consistent with the launch of the m=+1 mode. The electron and ion heating occurs within one electron skin depth of the plasma edge, where slow wave damping is expected. The source parameters for enhanced particle heating are also consistent with lower hybrid resonance effects, which can only occur for Trivelpiece-Gould wave excitation.

Slow Electron Holes in the Earth's Magnetosheath

AbstractWe present a statistical analysis of electrostatic solitary waves observed aboard Magnetospheric Multiscale spacecraft in the Earth's magnetosheath. Applying single‐spacecraft interferometry to several hundred solitary waves collected in about 2‐minute interval, we show that almost all of them have the electrostatic potential of positive polarity and propagate quasi‐parallel to the local magnetic field with plasma frame velocities of the order of 100 km/s. The solitary waves have typical parallel half‐widths from 10 to 100 m that is between 1 and 10 Debye lengths and typical amplitudes of the electrostatic potential from 10 to 200 mV that is between 0.01% and 1% of local electron temperature. The solitary waves are associated with quasi‐Maxwellian ion velocity distribution functions, and their plasma frame velocities are comparable with ion thermal speed and well below electron thermal speed. We argue that the solitary waves of positive polarity are slow electron holes and estimate the time scale of their acceleration, which occurs due to interaction with ions, to be of the order of one second. The observation of slow electron holes indicates that their lifetime was shorter than the acceleration time scale. We argue that multi‐spacecraft interferometry applied previously to these solitary waves is not applicable because of their too‐short spatial scales. The source of the slow electron holes and the role in electron‐ion energy exchange remain to be established.

Optimization of the collective Thomson scattering diagnostic for the GDT open magnetic trap

The collective Thomson scattering of high-power millimeter-wave radiation on plasma density fluctuations (CTS) is widely used for diagnosing the velocity distribution function of energetic ions in fusion plasma. In this paper, we discuss a non-standard scheme of CTS measurements, which exploits strong refraction of probing and scattered microwave beams when reflecting from the cut-off layer in dense plasma. The scheme may be realized with the existing CTS diagnostic system at the Gas-Dynamic Trap (GDT) facility, a large open magnetic trap operating at Budker Institute (Novosibirsk, Russia). This requires a minor upgrade of the available hardware and essentially increases the range of plasma densities allowed for CTS measurements, as well as its sensitivity and spatial resolution. A detailed study of CTS efficiency for different geometries and plasma conditions at GDT is performed by means of an advanced numerical model that allows for an accurate description of non-Gaussian beam scattering in inhomogeneous plasma. To perform this task, we develop a quasi-optical theory of scattering, which itself may be of general interest.

Ion kinetic effects linked to magnetic field discontinuities in the slow Alfvénic wind observed by Solar Orbiter in the inner heliosphere

Slow solar wind, sharing magnetic and plasma properties typical of fast wind, the so-called slow Alfvénic wind, has been widely observed in the heliosphere. Here, we report an analysis of the turbulent properties of a slow Alfvénic stream observed by Solar Orbiter at 0.64 AU. This solar wind stream is characterized by well distinguishable regions, namely, a main portion, an intermediate region, and a rarefaction region. Each of those intervals have been studied separately, in order to enhance similarities and differences in their turbulence properties. Coherent structures naturally emerge over different time/spatial scales and their characteristics at ion scales have been investigated. The presence of these intermittent events have been found to be closely related to kinetic features in the ion (both proton and alpha particles) velocity distribution functions, suggesting a fundamental role in the kinetic physical processes that mediate the sub-ion turbulence cascade.

Backstreaming ions at a high Mach number interplanetary shock

Context.Solar Orbiter, a mission developed by the European Space Agency, explores in situ plasma across the inner heliosphere while providing remote-sensing observations of the Sun. The mission aims to study the solar wind, but also transient structures such as interplanetary coronal mass ejections and stream interaction regions. These structures often contain a leading shock wave that can differ from other plasma shock waves, such as those around planets. Importantly, the Mach number of these interplanetary shocks is typically low (1–3) compared to planetary bow shocks and most astrophysical shocks. However, our shock survey revealed that on 30 October 2021, Solar Orbiter measured a shock with an Alfvén Mach number above 6, which can be considered high in this context.Aims.Our study examines particle observations for the 30 October 2021 shock. The particles provide clear evidence of ion reflection up to several minutes upstream of the shock. Additionally, the magnetic and electric field observations contain complex electromagnetic structures near the shock, and we aim to investigate how they are connected to ion dynamics. The main goal of this study is to advance our understanding of the complex coupling between particles and the shock structure in high Mach number regimes of interplanetary shocks.Methods.We used observations of magnetic and electric fields, probe-spacecraft potential, and thermal and energetic particles to characterize the structure of the shock front and particle dynamics. Furthermore, ion velocity distribution functions were used to study reflected ions and their coupling to the shock. To determine shock parameters and study waves, we used several methods, including cold plasma theory, singular-value decomposition, minimum variance analysis, and shock Rankine-Hugoniot relations. To support the analysis and interpretation of the experimental data, test-particle analysis, and hybrid particle in-cell simulations were used.Results.The ion velocity distribution functions show clear evidence of particle reflection in the form of backstreaming ions several minutes upstream. The shock structure has complex features at the ramp and whistler precursors. The backstreaming ions may be modulated by the complex shock structure, and the whistler waves are likely driven by gyrating ions in the foot. Supra-thermal ions up to 20 keV were observed, but shock-accelerated particles with energies above this were not.

Plasma Ion Velocity Distribution Function Perturbed by Ion-Acoustic Solitons: Analytical Calculations Based on KDV Equation

Plasma Ion Velocity Distribution Function Perturbed by Ion-Acoustic Solitons: Analytical Calculations Based on KDV Equation

Plasma Ion Velocity Distribution Function Perturbed by Ion-Acoustic Solitons: Analytical Calculations Based on KDV Equation

Using the Korteweg–De Vries equation, for background plasma, the distribution functions perturbed by ion-acoustic solitons are calculated. For describing the perturbed distribution functions, the explicit formula is obtained, which is suitable for practical applications. The results are compared with the analytical calculations and simulation results obtained previously.

Evidence of non-Maxwellian ion velocity distributions in spherical shock-driven implosions.

The ion velocity distribution functions of thermonuclear plasmas generated by spherical laser direct drive implosions are studied using deuterium-tritium (DT) and deuterium-deuterium (DD) fusion neutron energy spectrum measurements. A hydrodynamic Maxwellian plasma model accurately describes measurements made from lower temperature (<10keV), hydrodynamiclike plasmas, but is insufficient to describe measurements made from higher temperature more kineticlike plasmas. The high temperature measurements are more consistent with Vlasov-Fokker-Planck (VFP) simulation results which predict the presence of a bimodal plasma ion velocity distribution near peak neutron production. These measurements provide direct experimental evidence of non-Maxwellian ion velocity distributions in spherical shock driven implosions and provide useful data for benchmarking kinetic VFP simulations.

Observations and Modeling of Unstable Proton and α Particle Velocity Distributions in Sub-Alfvénic Solar Wind at Parker Solar Probe Perihelia

Past observations show that solar wind (SW) acceleration occurs inside the sub-Alfvénic region, reaching the local Alfvén speed at typical distances ∼10–20 solar radii (R s ). Recently, Parker Solar Probe (PSP) traversed regions of sub-Alfvénic SW near perihelia in encounters E8–E12 for the first time, providing data in these regions. It became evident that the properties of the magnetically dominated SW are considerably different from the super-Alfvénic wind. For example, there are changes in the relative abundances and drift of α particles with respect to protons, as well as in the magnitude of magnetic fluctuations. We use data of the magnetic field from the FIELDS instrument, and construct ion velocity distribution functions (VDFs) from the sub-Alfvénic regions using Solar Probe ANalyzer for Ions data, and run 2.5D and 3D hybrid models of proton-α sub-Alfvénic SW plasma. We investigate the nonlinear evolution of the ion kinetic instabilities in several case studies, and quantify the transfer of energy between the protons, α particles, and the kinetic waves. The models provide the 3D ion VDFs at the various stages of the instability evolution in the SW frame. By combining observational analysis with the modeling results, we gain insights on the evolution of the ion instabilities, the heating and the acceleration processes of the sub-Alfvénic SW plasma, and quantify the exchange of energy between the magnetic and kinetic components. The modeling results suggest that the ion kinetic instabilities are produced locally in the SW, resulting in anisotropic heating of the ions, as observed by PSP.

Kinetics of Cold Ions in Asymmetric Reconnection: Particle‐In‐Cell Simulation

AbstractCold ions from Earth's ionosphere and plasmasphere have frequently been observed at the magnetopause, where they impact reconnection and get energized in the process. The behavior of cold ions in different regions of magnetopause reconnection is not well understood. This study investigates their kinetics in asymmetric reconnection through a 2.5‐D fully kinetic simulation. The simulation starts with cold ions being present only in the magnetosphere. We find that the velocity distribution functions (VDFs) of cold ions in different reconnection regions are composed of two types of particles, distinguished by their ability to penetrate the magnetosheath. One type produces ring‐shaped distributions in the magnetosheath due to meandering motion, while the other generates ring‐shaped distributions in the magnetospheric separatrix as a result of gyromotion. The reconnection electric field Ey has a negative effect on one type and a positive effect on the other. Moreover, the Hall electric field Ez can stepwise accelerate the meandering particles. The cold ion temperature increases significantly in the magnetosheath as compared to its original temperature, the enhancement is a kinetic effect as a result of the ring‐shaped velocity distribution. On the other hand, in the remaining regions, cold ions experience bulk heating, resulting in noticeable temperature elevation. These findings further emphasize the necessity to examine the VDF for an all‐round comprehension of the particle heating mechanism and contribute to a better understanding of cold ion dynamics at the Earth's magnetopause.

Kinetic Equilibrium of Two-dimensional Force-free Current Sheets

Force-free current sheets are local plasma structures with field-aligned electric currents and approximately uniform plasma pressures. Such structures, widely found throughout the heliosphere, are sites for plasma instabilities and magnetic reconnection, the growth rate of which is controlled by the structure’s current-sheet configuration. Despite the fact that many kinetic equilibrium models have been developed for one-dimensional force-free current sheets, their two-dimensional (2D) counterparts, which have a magnetic field component normal to the current sheets, have not received sufficient attention to date. Here, using particle-in-cell simulations, we search for such 2D force-free current sheets through relaxation from an initial, magnetohydrodynamic equilibrium. Kinetic equilibria are established toward the end of our simulations, thus demonstrating the existence of kinetic force-free current sheets. Although the system currents in the late equilibrium state remain field aligned as in the initial configuration, the velocity distribution functions of both ions and electrons systematically evolve from their initial drifting Maxwellians to their final time-stationary Vlasov state. The existence of 2D force-free current sheets at kinetic equilibrium necessitates future work in discovering additional integrals of motion of the system, constructing the kinetic distribution functions, and eventually investigating their stability properties.

A confocal laser-induced fluorescence diagnostic with an annular laser beam

In this work, we report an annular beam confocal laser-induced fluorescence (LIF) configuration, which allows for high spatial resolution measurements of plasma properties in plasma setups and sources with limited optical access. The proposed LIF configuration utilizes the annular laser beam generated by a pair of diffractive axicons. The LIF signal is collected along the main optical axis within the ring region. It is shown experimentally that at a focal distance of 300 mm, a spatial resolution of ∼5.3 mm can be achieved. Using geometric optics estimations, we showed that ∼1 mm resolution at the same focal distance could potentially be achieved by modifying laser beam parameters. This approaches the localization accuracy of conventional LIF collection methods (with crossing laser beam injection and fluorescence collection optical paths). Measurements of the ion velocity distribution function in an argon plasma using both the confocal LIF with an annular laser beam and conventional LIF demonstrate a satisfactory agreement. The proposed LIF setup has potential applications for diagnostics in various plasma processing equipment and plasma sources, such as hollow cathodes, microplasmas, electric propulsion, etc.

Ion dynamic characterization using phase-resolved laser-induced fluorescence spectroscopy in a Hall effect thruster.

Significant information on the dynamics of the plasma constituents in Hall effect thrusters can be obtained using minimally intrusive techniques, such as laser-induced fluorescence (LIF) diagnostics. Indeed, LIF provides an excellent tool to determine the ion velocity distribution function with high spatial resolution. Even in a steady-state operation, recording time-resolved maps of the velocity distribution is relevant due to persisting time-dependent features of the thruster discharge. One of the preeminent phenomena that render the ion velocity distribution to be time dependent is commonly attributed to the breathing mode, characterized by pronounced oscillations in the discharge current. The goal of this work is to propose a new technique for plasma dynamic studies based on LIF spectroscopy with phase-resolution during the breathing period. For this purpose, the Hilbert transform is used to define the instantaneous phase of oscillation of the thruster current. Ion velocity distribution modification over assigned phases of oscillation is measured simultaneously and in real-time thanks to a fully numerical analysis of the data.

1D profile measurement of ion velocity distribution with glass-tube-pair type Doppler probe array

We developed a glass-tube-pair type Doppler probe array for ion velocity distribution function measurement with high spatial and time resolution. By four mirrors and four optical fibers fixed in two parallel glass tubes, the light from ions in each measurement area (3.2 × 2.5 × 1.0 cm3) between tubes is collected in three different directions, and the fibers are led to a Czerny–Turner spectrometer and finally to an ICCD camera (the exposure time of 2 μs) for Doppler spectra measurements with high time resolution. Since the Doppler spectrum profile in each viewing line represents the distribution of the ion velocity component in the line, we can reconstruct 2D velocity distribution by the measured spectra in three viewing lines with tomography techniques. We tested the accuracy of some reconstruction methods from spectra to velocity distribution in numerical simulation and chose the iterative method as the best one. By use of this new diagnostic, we successfully measured the radial profile of ion velocity distribution during magnetic reconnection of merging spherical tokamak plasmas and revealed that their ions have anisotropic velocity distributions.

Ion velocity distribution functions across a plasma meniscus

Here, we present laser-induced fluorescence measurements of an ion beam extraction angle and speed through a plasma-vacuum boundary as a function of plasma source parameters and bias potential applied to a wafer simulacrum outside the plasma. Ion temperature, velocity, and relative density are calculated from the measured ion velocity distribution function and are compared to a particle-in-cell model of the system. The measurements demonstrate that beam steering is feasible by varying plasma source density and extraction bias voltage. The focal point of the extracted beam, resulting from the plasma meniscus at the plasma-vacuum interface, depends on source density and extraction bias in a manner consistent with computational predictions.

Unidirectional transport of ions and perturbation of plasma distribution functions by ion-acoustic solitons: Numerical simulation and analytical solution

New features of motion of background plasma ions in the presence of ion-acoustic solitons are analyzed by using a hydrodynamic model. Based on the ergodic hypothesis, ion velocity distribution functions are obtained analytically for the first time. It is shown that the initial Maxwellian distribution of ions takes a “beam-like” form in the region of plasmas occupied by solitons. Main parameters of the distribution functions of the background plasma corresponding to solitons of different amplitudes are determined. An important case of soliton trains motion, which often observed in experiments, as well as some other experimental aspects are also considered.

On the interpretation of kinetic effects from ionization in fluid models and its impact on filamentary transport

In regions where a plasma is not fully ionized, such as the edge and scrape-off layer (SOL) regions in a tokamak, the charged particles may be subject to strong sources from interactions with neutral atoms and molecules. Such sources, e.g., from electron impact ionization, can introduce kinetic effects, as the ionized particles may have flow velocity and temperature different from that of the main species. If treated in the conventional fluid picture, this kinetic effect emerges as a frictional heating term. In this paper, the physics of this term is discussed, both for un-magnetized and magnetized plasmas. The fluid source terms are mapped back to the kinetic sources to provide a consistent picture for future model comparison. In the limits of low and high ratios between the rates of thermalization and ionization, a multi-ion species drift-fluid model is applied to assess the impact of this kinetic effect on SOL drift-plane plasma transport. This is done by modeling a seeded blob where the ions follow either a single- or double-Maxwellian velocity distribution function (VDF). It is found that the robustness of the magnetized plasma VDF in the drift-plane and the limited effect on the vorticity source ensure that the impact of kinetic effects on the perpendicular blob evolution is small, even in the limit of high ionization to thermalization rate ratio, where kinetic effects to the ion VDF are significant.

Thrust measurements and mesothermal plasma plume of the Alternative Low Power Hybrid Ion Engine (alphie)

The high specific impulse Alternative Low Power Ion Engine (alphie) is a gridded plasma thruster different from conventional (Kaufman) ion engines. In this disruptive concept, the ionization of the propellant neutral gas and the neutralization of ion outflow is achieved with only one cathode located in front and outside of the thruster. Electrons and ions move under the self-consistent field created by the DC voltage applied to its two planar grids together with the currents of charges flowing through them, unlike to conventional ion engines, where only ions move through its ion optics system. The stationary mesothermal flow of ions and electrons in the plasma plume is characterized with a retarded field energy analyzer in conjunction with Langmuir and emissive probes. The ion velocity distribution functions and the electron energy spectra for different operating conditions of the alphie thruster are discussed. The observed high ion temperatures are explained by the collisional interaction between the fast ionizing electrons and the neutral atoms that increases their average kinetic energy. Finally, the alphie delivers 0.8-3.5 mN throttleable thrusts giving specific impulses in the range of 14000-20000 s with estimated thruster efficiencies between 8% and 40%.

InSitu Signature of Cyclotron Resonant Heating in the Solar Wind.

The dissipation of magnetized turbulence is an important paradigm for describing heating and energy transfer in astrophysical environments such as the solar corona and wind; however, the specific collisionless processes behind dissipation and heating remain relatively unconstrained by measurements. Remote sensing observations have suggested the presence of strong temperature anisotropy in the solar corona consistent with cyclotron resonant heating. In the solar wind, insitu magnetic field measurements reveal the presence of cyclotron waves, while measured ion velocity distribution functions have hinted at the active presence of cyclotron resonance. Here, we present Parker Solar Probe observations that connect the presence of ion-cyclotron waves directly to signatures of resonant damping in observed proton-velocity distributions using the framework of quasilinear theory. We show that the quasilinear evolution of the observed distribution functions should absorb the observed cyclotron wave population with a heating rate of 10^{-14}  W/m^{3}, indicating significant heating of the solar wind.

Formations of anode double layer and ion beam in bipolar-pulse HiPIMS (BP-HiPIMS)

As an emerging ion acceleration plasma source, the bipolar-pulse high power impulse magnetron sputtering (BP-HiPIMS) discharge provides an effective approach to improve deposited ion energy and tailor the film properties for a large range of applications. The ion acceleration mechanism in BP-HiPIMS discharge is very vital but still unclear now. In the present work, the ion acceleration mechanism is systematically investigated via the experimental measurements, particle-in-cell/Monte Carlo collision (PIC-MCC) simulation, and theoretical model together. In the experiment part, the floating potential V f and the ion velocity distribution function (IVDF) have been measured via the Langmuir probe and the retarding field energy analyser (RFEA) respectively. The measurements show that the V f at the downstream drops from +80 V to ∼+40 V after applying the positive pulse for ∼75 μs, suggesting the formation of the double layer. Correspondingly, the IVDF changes from the unimodal Maxwellian distribution to the bimodal distribution, suggesting the existence of the ion beam. The PIC-MCC simulation results clearly show the development process of the double layer and ion beam. A theoretical model is introduced to explore the complex plasma dynamics in the experiment and simulation. The theoretical results illustrate that (i) the sheath in front of the target surface prefers an ion sheath rather than an electron sheath, (ii) the stable position of the double layer boundary is in the magnetic null point, (iii) the potential drop across the boundary is influenced by the gas pressure p. These important theoretical results are well consistent with the measurements and simulation. In addition, the oscillation of the double layer boundary and the instabilities of the ions are briefly discussed by combining the previous works.