Ion Velocity Distribution Function Research Articles

Unified solution of the Boltzmann equation for electron and ion velocity distribution functions and transport coefficients in weakly ionized plasmas

We present a framework for the solution of Boltzmann's equation in the swarm limit for arbitrary mass ratio, allowing for solutions of electron or ion transport. An arbitrary basis set can be used in the framework, which is achieved by using appropriate quadratures to obtain the required matrix elements. We demonstrate an implementation using Burnett functions and benchmark the calculations using Monte-Carlo simulations. Even though the convergence in transport quantities is always good, the particle distributions did not always converge, highlighting that simple benchmarks can give misleading confidence in a choice of basis. We postulate a different basis, which avoids a spherical harmonic expansion, which is better suited to strong electric fields or sharp features such as low-energy attachment processes.

3D ion velocity distribution function measurement in an electric thruster using laser induced fluorescence tomography.

Measuring the full ion velocity distribution function (IVDF) by non-intrusive techniques can improve our understanding of the ionization processes and beam dynamics at work in electric thrusters. In this paper, a Laser-Induced Fluorescence (LIF) tomographic reconstruction technique is applied to the measurement of the IVDF in the plume of a miniature Hall effect thruster. A setup is developed to move the laser axis along two rotation axes around the measurement volume. The fluorescence spectra taken from different viewing angles are combined using a tomographic reconstruction algorithm to build the complete 3D (in phase space) time-averaged distribution function. For the first time, this technique is used in the plume of a miniature Hall effect thruster to measure the full distribution function of the xenon ions. Two examples of reconstructions are provided, in front of the thruster nose-cone and in front of the anode channel. The reconstruction reveals the features of the ion beam, in particular on the thruster axis where a toroidal distribution function is observed. These findings are consistent with the thruster shape and operation. This technique, which can be used with other LIF schemes, could be helpful in revealing the details of the ion production regions and the beam dynamics. Using a more powerful laser source, the current implementation of the technique could be improved to reduce the measurement time and also to reconstruct the temporal evolution of the distribution function.

Incident neutron spectra on the first wall and their application to energetic ion diagnostics in beam-injected deuterium–tritium tokamak plasmas

A diagnostic method for small non-Maxwellian tails in fuel-ion velocity distribution functions is proposed; this method uses the anisotropy of neutron emissions, and it is based on the numerical analysis of the incident fast neutron spectrum on the first wall of a fusion device. Neutron energy spectra are investigated for each incident position along the first wall and each angle of incidence assuming an ITER-like deuterium–tritium plasma; it is heated by tangential-neutral-beam injection. Evaluating the incident neutron spectra at all wall positions and angles of incidence enables the selective measurement of non-Gaussian components in the neutron emission spectrum for energetic ion diagnostics; in addition, the optimal detector position and orientation can be determined. At the optimal detector position and orientation, the ratio of non-Gaussian components to the Gaussian peak can be two orders of magnitude greater than the ratio in the neutron emission spectrum. This result can improve the accuracy of energetic ion diagnostics in plasmas when small, anisotropic non-Maxwellian tails are formed in fuel ion velocity distribution functions. We focus on the non-Gaussian components greater than 14 MeV, where the effect of the background noise (i.e., slowing-down neutrons by scattering throughout the machine structure) can be ignored.

Ion velocity distribution function in intrinsic gas plasma under conditions of resonance recharging as a main process. Theory

For the first time, the ion distribution function over energies and directions of the motion for He+ in He and Ar+ in Ar is measured at the arbitrary value of the electric field by the method of the plane onesided probe. The experiment is carried out under conditions when the ion velocity acquired at the mean free path is on the order of and larger than the average thermal velocity of atoms and resonance recharging is the dominating process in plasma. The obtained results make it possible to conclude that, in independent gas discharge plasma, even at moderate fields where E/P = 10–20 V (cm Torr), the ion distribution function can have noticeable anisotropy and can strongly differ from the Maxwellian distribution.

Ion heating and flows in a high power helicon source

We report experimental measurements of ion temperatures and flows in a high power, linear, magnetized, helicon plasma device, the Resonant Antenna Ion Device (RAID). Parallel and perpendicular ion temperatures on the order of 0.6 eV are observed for an rf power of 4 kW, suggesting that higher power helicon sources should attain ion temperatures in excess of 1 eV. The unique RAID antenna design produces broad, uniform plasma density and perpendicular ion temperature radial profiles. Measurements of the azimuthal flow indicate rigid body rotation of the plasma column of a few kHz. When configured with an expanding magnetic field, modest parallel ion flows are observed in the expansion region. The ion flows and temperatures are derived from laser induced fluorescence measurements of the Doppler resolved velocity distribution functions of argon ions.

Neutral Ingestion Effects on Plume Properties of a Radio-Frequency Plasma Discharge

To enable comparison of thruster performance across different vacuum facilities, an understanding of the effect of operating pressure on plasma plume properties generated in a helicon ion thruster architecture is required. Plasma property measurements acquired at two different vacuum facility operating pressures are used to determine the effect of neutral ingestion on the operation of a replica of the Madison Helicon Experiment at low power. The ion velocity distribution function, electron temperature, ion number density, and plasma potential are measured along the thruster axis. Plasma plume property measurements made at the “high-pressure condition” ( corrected for argon) are compared to values recorded at the “low-pressure condition” ( corrected for argon) for thruster operation at radio-frequency forward power, 340 G source region magnetic field strength, and argon volumetric flow rate. Operation at the high-pressure condition has 31–79 V lower ion energy, 0.8–6.1 eV lower electron temperature, and higher ion number densities than operation at the low-pressure condition. Changes in collision frequency and ionization balance result from increased neutral ingestion at the higher operating pressure.

Ion velocity distribution function in intrinsic gas plasma under conditions of resonance recharging as a main process. Experiment

Ion velocity distribution function in intrinsic gas plasma under conditions of resonance recharging as a main process. Experiment

Moment fluid equations for ions in weakly ionized plasma.

A one-dimensional fluid model for ions in weakly ionized plasma is proposed. The model differs from the existing ones in two aspects. First, a more accurate approximation of the collision terms in the fluid equations is suggested. For this purpose, the results obtained using the Monte Carlo kinetic model of the ion swarm experiments are considered. Second, the ion energy equation is taken into account. The fluid equations are closed using a simple model of the ion velocity distribution function. The accuracy of the fluid model is examined by comparing with the results of particle-in-cell Monte Carlo simulations. In particular, several test problems are considered using a parallel plate model of the capacitively coupled radio-frequency discharge. It is shown that the results obtained using the proposed fluid model are in good agreement with those obtained from the simulations over a wide range of discharge conditions. An approximation of the ion velocity distribution function for the problem under consideration is also discussed.

Experimental studies of ion flow near the sheath edge in multiple ion species plasma including argon, xenon and neon

The Bohm sheath criterion was studied with laser-induced fluorescence (LIF) in three ion species plasmas using two tunable diode lasers. It was found in the first LIF studies of three ion species plasma (Yip et al 2016 Phys. Plasmas 23 050703) in which krypton was added to a mixture of argon and xenon plasma confined in a multidipole, dc hot filament discharge, that the addition of krypton served to turn off instability enhanced collisional friction (IEF) found in two ion species plasma (Yip et al 2010 Phys. Plasmas). In this study, neon, a less massive atomic gas than argon was added. Argon and xenon ion velocity distribution functions (IVDFs) were measured at the sheath-presheath boundary near a negatively biased boundary plate, and the Ne+ density was systematically increased. We found in both cases that once the added ion density significantly exceeded the density of the other two ions, IVDF measurements consistent with the absence of the instability were obtained, and the measured ion sheath edge speeds tended toward their individual Bohm velocities. For all other relative concentrations, the ions reached the sheath edge neither at their Bohm speeds nor the ion sound speed of the system, consistent, qualitatively, with the action of the IEF.

Ion behavior in low-power magnetically shielded and unshielded Hall thrusters

Magnetically shielded Hall thrusters achieve a longer lifespan than traditional Hall thrusters by reducing wall erosion. The lower erosion rate is attributed to a reduction of the high energy ion population impacting the walls. To investigate this phenomenon, the ion velocity distribution functions are measured with laser induced fluorescence at several points of interest in the magnetically shielded ISCT200-MS and the unshielded ISCT200-US Hall thrusters. The center of the discharge channel is probed to highlight the difference in plasma positioning between the shielded and unshielded thrusters. Erosion phenomena are investigated by taking measurements of the ion velocity distribution near the inner and outer wall as well as above the magnetic poles where some erosion is observed. The resulting distribution functions show a displacement of the acceleration region from inside the channel in the unshielded thruster to downstream of the exit plane in the ISCT200-MS. Near the walls, the unshielded thruster displays both a higher relative ion density as well as a significant fraction of the ions with velocities toward the walls compared to the shielded thruster. Higher proportions of high velocity ions are also observed. Those results are in accordance with the reduced erosion observed. Both shielded and unshielded thrusters have large populations of ions impacting the magnetic poles. The mechanism through which those ions are accelerated toward the magnetic poles has so far not been explained.

Statistical analysis of the reflection of incident O+ pickup ions at Mars: MAVEN observations

AbstractAnalyzing ~1.3 year data set of O+ ion velocity distribution functions obtained from the Suprathermal and Thermal Ion Composition instrument on the Mars Atmosphere and Volatile Evolution (MAVEN) spacecraft, we statistically investigate reflections of incident O+ pickup ions (>10 keV) occurring below the Martian bow shock. To quantitatively evaluate importance of the reflection of incident O+ pickup ions, we estimate reflection ratios by calculating average inward and outward O+ ion fluxes above the Martian bow shock. Our result shows that an average reflection ratio is 14.1 ± 6.7%. We also investigate dependences of the reflection ratio on the solar wind, solar EUV flux, and southern hemispheric crustal magnetic field on Mars. We find that the reflection ratio strongly depends on the magnitude of the interplanetary magnetic field (IMF), solar wind dynamic pressure, and gyroradius of O+ pickup ions in the solar wind, rather than the solar EUV flux and the crustal magnetic field. We suggest that the reflection ratio is determined by the magnetic field both in the solar wind and below the bow shock that mainly controls gyroradius of incident O+ pickup ions in these regions. We also find that the reflection ratio increases to 38.9 ± 10.2% as these parameters become extreme conditions (i.e., IMF magnitude >6 nT). Since incident O+ pickup ions are known to be a major source of atmospheric sputtering escape from Mars, our result suggests that ion reflections may have a role to reduce the sputtering escape from Mars under the extreme solar wind condition.

Numerical and semi-analytical treatments of neutral beam current drive in DEMO-FNS

Neutral Beam Current Drive (NBCD) is considered as a highly attractive mechanism for a steady state regime in such contemporary projects as a tokamak based Fusion Neutron Source (FNS) or a DEMO type thermonuclear reactor. In this report numerical calculations of NBCD with a Monte Carlo code NUBEAM are complemented by a semi-analytical treatment of fast ion velocity distribution function. Spectral distributions of fast ions injected with neutral beams to FNS plasma are obtained for DEMO-FNS and a Spherical Tokamak Neutron Source FNS-ST. A detailed comparison of NUBEAM and semi-analytical approaches is presented on the basis of ASTRA transport code provided equilibrium data for different plasma regimes. The applicability of the semi-analytical approach is discussed.

MeV-range velocity-space tomography from gamma-ray and neutron emission spectrometry measurements at JET

We demonstrate the measurement of a 2D MeV-range ion velocity distribution function by velocity-space tomography at JET. Deuterium ions were accelerated into the MeV-range by third harmonic ion cyclotron resonance heating. We made measurements with three neutron emission spectrometers and a high-resolution γ-ray spectrometer detecting the γ-rays released in two reactions. The tomographic inversion based on these five spectra is in excellent agreement with numerical simulations with the ASCOT–RFOF and the SPOT–RFOF codes. The length of the measured fast-ion tail corroborates the prediction that very few particles are accelerated above 2 MeV due to the weak wave-particle interaction at higher energies.

Ion velocity distribution function in intrinsic gas at cryogenic gas temperatures

The influence of elastic scattering on the ion distribution function in the plasma of an intrinsic gas in weak fields has been considered. An analytical expression valid for cryogenic temperatures of atoms has been obtained. The reduced He+–He, Ar+–Ar mobilities as functions of the temperature of atoms in a range of 4–1000 K have been calculated in the approximation of the zero field taking into account elastic collisions; the calculated dependences well agree with the available experimental data. It has been demonstrated that elastic collisions play an important role in the formation of the ion distribution function at low temperatures. The results of measurement of the ion mobility in the limit of the zero field at low temperatures can be used to obtain data on the ratio of elastic scattering and resonance charge exchange cross sections.

The interaction of finite‐width reconnection exhaust jets with a dipolar magnetic field configuration

AbstractThe structure and properties of earthward propagating exhaust jets produced by a magnetic reconnection source region localized in the out‐of‐plane direction are investigated with 3‐D particle‐in‐cell simulations that incorporate a realistic plasma sheet configuration in which a dipole magnetic field region is connected to an asymptotic tail equilibrium with finite Bz. The jet is found to separate initially into two segments of width ∼10–15di each (di is the ion inertia length). The dawnward segment moves ahead of the duskward one and continues to intensify, while the latter is buffeted by the return flows generated by the former and stagnates. The leading front develops the characteristic structure of a sharp Bz increase and density drop on a 1–2di scale. The current associated with this Bz increase is carried mainly by the electrons, and the jet front is the site of a Region 1 sense field‐aligned current system. The ions develop a moderate temperature anisotropy with Ti||>Ti⊥ ahead of the front, while the electron temperature remains isotropic. The ion heating behind the front is quasi‐adiabatic, while the nonthermal electron tail is enhanced out to the limit of the simulation spectrum (∼15Eth). The ion velocity distribution function behind the front exhibits a strong parallel phase space enhancement at speeds ∼0.5VA associated with the earthward flow, while closer to the dipole region there is a drop out in parallel phase space at speeds of ∼1.5–2.5VA. The electron distribution is isotropic with an enhanced central plateau extending out to ∼4VA.

Ion velocity distribution functions in argon and helium discharges: detailed comparison of numerical simulation results and experimental data

Using the Monte Carlo collision method, we have performed simulations of ion velocity distribution functions (IVDF) taking into account both elastic collisions and charge exchange collisions of ions with atoms in uniform electric fields for argon and helium background gases. The simulation results are verified by comparison with the experiment data of the ion mobilities and the ion transverse diffusion coefficients in argon and helium. The recently published experimental data for the first seven coefficients of the Legendre polynomial expansion of the ion energy and angular distribution functions are used to validate simulation results for IVDF. Good agreement between measured and simulated IVDFs shows that the developed simulation model can be used for accurate calculations of IVDFs.

Simulations of ion velocity distribution functions taking into account both elastic and charge exchange collisions

Based on accurate representation of the He+–He angular differential scattering cross sections consisting of both elastic and charge exchange collisions, we performed detailed numerical simulations of the ion velocity distribution functions (IVDF) by Monte Carlo collision method (MCC). The results of simulations are validated by comparison with the experimental data of the ion mobility and the transverse diffusion. The IVDF simulation study shows that due to significant effect of scattering in elastic collisions IVDF cannot be separated into product of two independent IVDFs in the transverse and parallel to the electric field directions.

Ion flow and sheath structure near positively biased electrodes

What effect does a dielectric material surrounding a small positively biased electrode have on the ion flow and sheath structure near the electrode? Measurements of the ion velocity distribution function and plasma potential near positively biased electrodes were made using laser-induced fluorescence and an emissive probe. The results were compared with 2D particle-in-cell simulations. Both measurements and simulations showed that when the positive electrode was surrounded by the dielectric material, ions were accelerated toward the electrode to approximately 0.5 times the ion sound speed before being deflected radially by the electron sheath potential barrier of the electrode. The axial potential profile in this case contained a virtual cathode. In comparison, when the dielectric material was removed from around the electrode, both the ion flow and virtual cathode depth near the electrode were dramatically reduced. These measurements suggest that the ion presheath from the dielectric material surrounding the electrode may enclose the electron sheath of the electrode, resulting in a virtual cathode that substantially influences the ion flow profile in the region.

Dependence of helium ion diffusion and drift characteristics in own gas on its temperature

The low-temperature gas discharge has a number of features which can appear in experimentswith dusty plasma. For example, at cryogenic temperatures of gas-discharge tube walls, the strong anisotropy of the velocity distribution function of ions takes place, which in turn can cause a significant change in dust structure properties. The dependences of the helium ion drift characteristics in a dc uniform electric field on the atomic temperature of own gas is analyzed.

Development of core ion temperature gradients and edge sheared flows in a helicon plasma device investigated by laser induced fluorescence measurements

We report experimental observation of ion heating and subsequent development of a prominent ion temperature gradient in the core of a linear magnetized plasma device, and the controlled shear de-correlation experiment. Simultaneously, we also observe the development of strong sheared flows at the edge of the device. Both the ion temperature and the azimuthal velocity profiles are quite flat at low magnetic fields. As the magnetic field is increased, the core ion temperature increases, producing centrally peaked ion temperature profiles and therefore strong radial gradients in the ion temperature. Similarly, we observe the development of large azimuthal flows at the edge, with increasing magnetic field, leading to strong radially sheared plasma flows. The ion velocities and temperatures are derived from laser induced fluorescence measurements of Doppler resolved velocity distribution functions of argon ions. These features are consistent with the previous observations of simultaneously existing radially separated multiple plasma instabilities that exhibit complex plasma dynamics in a very simple plasma system. The ion temperature gradients in the core and the radially sheared azimuthal velocities at the edge point to mechanisms that can drive the multiple plasma instabilities, that were reported earlier.