Orbital Motion Limited Research Articles

A novel diagnostic for dust particle size in a low-pressure nanodusty plasma based on the decay of the electron density released by laser-induced photodetachment

One of the key parameters in low-pressure nanodusty plasmas is the dust particle size. In this work, we introduce a new method for the determination of the dust particle size in a nanodusty plasma, created in a mixture of argon and hexamethyldisiloxane. To this end, an ultraviolet (λ=266 nm) pulsed laser was used to release plasma-collected electrons from the nanoparticles. Subsequently, the response of the free electron density of the plasma was measured using microwave cavity resonance spectroscopy. Using a stochastic model for particle charging using orbital-motion limited (OML) theory, the predicted charging timescale can be directly compared to the experimentally measured decay timescale of the photo-released electron density. Good agreement was found between the experimentally predicted dust particle size and ex situ scanning electron microscopy (SEM) measurements. Furthermore, the sensitivity of the OML model to its input parameters was assessed. Finally, reversing the method can yield an estimate for the positive ion density based on the dust particle size from SEM.

M-NLP Inference Models Using Simulation and Regression Techniques.

Current inference techniques for processing multi-needle Langmuir probe (m-NLP) data are often based on adaptations of the Orbital Motion-Limited (OML) theory which relies on several simplifying assumptions. Some of these assumptions, however, are typically not well satisfied in actual experimental conditions, thus leading to uncontrolled uncertainties in inferred plasma parameters. In order to remedy this difficulty, three-dimensional kinetic particle in cell simulations are used to construct a synthetic data set, which is used to compare and assess different m-NLP inference techniques. Using a synthetic data set, regression-based models capable of inferring electron density and satellite potentials from 4-tuples of currents collected with fixed-bias needle probes similar to those on the NorSat-1 satellite, are trained and validated. The regression techniques presented show promising results for plasma density inferences with RMS relative errors less than 20%, and satellite potential inferences with RMS errors less than 0.2V for potentials ranging from -6 to -1V. The new inference approaches presented are applied to NorSat-1 data, and compared with existing state-of-the-art inference techniques.

The swarm Langmuir probe ion drift, density and effective mass (SLIDEM) product

Current methods for estimating ion density on Swarm rely on the assumption of 100% O + and no along-track ion velocity flows. These assumptions are routinely violated, particularly on the nightside and during high-latitude and polar cap traversals, compromising the accuracy of the measurements. The use of faceplate current data along with the Langmuir probe ion admittance measurements, and orbital-motion limited (OML) theory, make it possible to relax some of the assumptions inherent in current ESA Swarm density estimates. This further yields along-track ion drift and effective ion mass estimates. This paper describes the theoretical basis for estimating revised ion density, providing a new estimate for effective ion mass, as well as an alternative way of estimating along-track ion drift. The complete Swarm historical data set has been generated and validated using empirical models (International Reference Ionosphere, and an empirical electric field model), as well as ground-spacecraft conjunctions. Case studies and statistical results reveal clear geophysical signatures in the new product of light ions at low- and mid-latitudes and along-track ion drift at high latitudes, and their response to space weather.Graphical

In-situ measurement of dust charge density in nanodusty plasma

A dust grain immersed in a low-pressure gas discharge obtains a permanent negative surface charge due to the high mobility of electrons compared to that of ions. This charge essentially governs all fundamental processes in dusty and complex plasmas involving dust grains, neutrals, (an)ions and electrons and—consequently—virtually all industrial applications of these types of plasmas are affected and steered by it. In this work, we have measured the surface charge by application of laser-induced electron detachment from nanosized dust grains in concert with microwave cavity resonance spectroscopy and laser light extinction. The main result is that the electron release is governed by photodetachment rather than by thermionic emission, and that recharging of the dust grains occurs on timescales that are well in agreement with the orbital-motion-limited (OML) theory. The total surface charge density residing on the dust grains inside the laser volume follows from the saturation of the photodetachment signal, which was used in combination with dust density values derived from extinction measurements to estimate the mean dust charge. The negative dust charge on the 140 nm (average) diameter dust grains in this work is obtained to be in the range of 273 – 2519 elementary charges, of which the lower bound matches well with analytical predictions using the OML theory.

Kinetic analysis of the plasma sheath around an electron-emitting object with elliptic cross section.

The structure of the sheath and the current exchange of two-dimensional electron-emitting objects with elliptic cross section immersed at rest in Maxwellian plasmas are investigated with an energy-conserving stationary Vlasov-Poisson solver free of statistical noise. The parameter domains for current collection within the orbital-motion-limited (OML) regime and current emission in space-charge-limited (SCL) conditions were studied by varying the characteristic dimension of the ellipse, its eccentricity, and the emission level. The analysis reveals the correlations between the onset of the non-OML and SCL regimes and the local curvature of the ellipse. As compared to nonemitting ellipses, electron emission broadens the parameter domain for OML current collection for ions and reduces considerably the current drop for non-OML conditions. Under identical plasma environments, elliptic bodies are more prone to operate under non-OML and SCL conditions than cylinders. Their emitted current in SCL conditions can be computed accurately from well-known results for cylinders if appropriate dimensionless variables and an equivalent radius are used. The role of the eccentricity, which acts as an integrability-breaking parameter, on the filamentation of the distribution function of the attracted species is studied.

Parametrization of current–voltage characteristics and operation domains of cylindrical emissive probes in collisionless Maxwellian plasmas at rest

Important progress has recently been made on the Orbital Motion Theory for cylindrical emissive probes immersed at rest in collisionless and Maxwellian plasmas. However, due to the computational cost of its numerical algorithm, only solutions for specific values of the physical parameters were found, thus preventing its direct application to the interpretation of experimental current–voltage characteristics ( curves). In this work, and thanks to an analytical analysis of a Jacobian matrix appearing in the algorithm, the computational cost was reduced by a factor in the order of , where is the number of grid points. This achievement, together with the implementation of parallel programming, allowed to construct a database with more than 18 000 curves for a broad range of physical parameters, including the emission level, the probe radius-to-Debye length, and the ion-to-electron temperature ratios. The boundaries in parameter space of the operational regimes of emissive probes, covering both orbital motion limited (OML) and space charge limited (SCL) transitions were computed. A novel OML/non-OML transition for emissive probes operating at low bias was found. The numerical results were used to propose useful analytical laws for the SCL boundary happening at negative bias, the reduction of the emitted electron current due to SCL effects, and the floating potential of emissive probes. The applications of the results to the modeling of low work function tethers and three experimental methods for measuring the plasma potential, i.e. the separation point, the inflection point, and the floating potential techniques, were discussed. The formation of an inverse sheath for strong emission was investigated.

Fixed Bias Probe Measurement of a Satellite Floating Potential

A simple sensor is described to measure satellite potentials. The proposed instrument consists of two small spherical Langmuir probes biased to different fixed voltages, from which currents are measured. A predictive model is constructed for spacecraft floating potentials by combining the orbital motion limited (OML) approximation for spherical probes, and a multivariate regression algorithm. Construction of the model is based on a training data set obtained from 3-D simulation results, covering a range of plasma parameters of relevance to satellites in low earth orbit (LEO) at midlatitudes. The model skill is then assessed by comparing predictions with potentials in a distinct validation data set. Owing to large satellite orbital speeds, fixed bias probes would provide measurements with higher temporal and spatial resolution than possible with sweep voltage probes.

The Electric Field Detector on Board the China Seismo Electromagnetic Satellite—In-Orbit Results and Validation

The aim of this work is to validate the China Seismo-Electromagnetic Satellite 01 (CSES-01) Electric Field Detector (EFD) measurements through the analysis of the instrument response to various inputs: (a) geomagnetic field variations, (b) plasma density depletions, and (c) electromagnetic signals from natural and artificial sources such as Schumann resonance and VLF (Very Low Frequency) antennas. The knowledge of the geomagnetic induced electric field vs×B (where vs is the satellite speed and B and the local magnetic field), and the plasma variations effect, described by the Orbit Motion Limited (OML) theory, are key parameters to determine the expected theoretical values of the EFD sensors potentials data. Based on the CSES on-board measurements of plasma parameters and geomagnetic field, a direct quantitative validation is presented. In addition, the electromagnetic signals detection capability is checked but only qualitatively confirmed, since the ionospheric complexity does not allow an accurate theoretical computation of waves modulation. The quantitative comparison highlights the very good agreement between observed and theoretical potentials values during average condition. Conversely, in case of strong electric fields, the OML theory shows partial inability in reproducing the actual space plasma conditions resulting in a reduced theoretical values reliability. Finally, both natural and artificial electromagnetic signals are satisfactorily identified showing a reliable sensitivity in different frequency bands.

Macroparticle Reflection from a Biased Substrtate in Plasma Ion Implantation Systems

Generation of metal plasma in vacuum arc discharge is always accompanied by a production of macroparticles (MPs). The MP contamination in coatings is the most important technological problem in plasma immersion ion implantation (PIII). For the case of PIII with long pulse duration, the results of theoretical study of MP charging and dynamics in the plasma sheath are presented. To describe the MP charging in the sheath the sheath model is combined with orbital motion limited (OML) theory. The MP charging in the sheath is studied with taking into account emission processes from MP surface as well as kinetic electron emission (KEE) from the high voltage substrate. The charge and dynamics of MP are governed by local parameters of counter fluxes of ions and secondary electrons from the substrate. The MP charge depends on the MP local position within the sheath. The dominant role in MP charging is shown to be played by KEE from the substrate, which is an important feature of PIII. KEE from the substrate changes the potential profile within the sheath, the sheath thickness, and current balance on MP surface. MP charge is obtained to be negative because it is caused by higher current density of secondary electrons from the substrate than that of ions. The latter is possible for KEE yield larger than a unit. The substrate biasing influences both the release of secondary electrons from the substrate under ion impact and their acceleration in the sheath. The increasing of negative substrate bias is demonstrated to result in the increasing of absolute value of negative MP charge, and, thereby, the increasing of electrostatic reflection of MP from the substrate. The negative substrate biasing is shown to be the effective alternative method to reduce MP contaminations in coatings without applying any magnetic filters.

Impact of Miniaturized Fixed-Bias Multineedle Langmuir Probes on CubeSats

Kinetic simulation results are presented to study the response of multineedle Langmuir probes of the type used on many satellites. Simulations of isolated probes are used to parameterize the current collected as a function of voltage for a set of densities and temperatures relevant to the Earth’s ionosphere. These simulations also serve to assess the validity of analytic results obtained from the orbital motion limited (OML) theory used in recent studies. Computed probe characteristics are then fitted with empirical scaling laws and used to account for electron current collected by needle probes on a typical triple CubeSat. These fits are then used to determine the impact of the probes and guards on the spacecraft floating potential for a nominal configuration of bias voltages, over the plasma parameters of interest. In order for the probes to work as intended, they must operate at a positive potential with respect to the ambient plasma. However, the results show that for the cases considered, the spacecraft floating potential is so low that the probe with the lowest voltage becomes negative. Possible solutions are examined and proposed to ensure that all probes remain at a positive voltage with respect to surrounding plasma.

Measurement of Thermal Effects in the Dust Acoustic Wave

Over the past 25 years, the dust acoustic wave has been a subject of intense study and the impact that thermal effects have on the dispersion relation has been a subject of investigation. Recently, a theory of dust correlations and the effect that these correlations have on the propagation of compressional modes has been developed that incorporates the effects of the confinement of the dust cloud in a finite volume within the larger plasma volume. This paper applies this model to a systemic study of the dispersion relation over a wide range of experimental conditions in a radio frequency (RF) discharge plasma. It is found the dust thermal pressure is larger than the dust electrostatic pressure and that both pressures are the square of the dust charge calculated using the orbit-motion-limited (OML) theory. It is also observed that the dust temperature and thermal pressure decreases with increasing neutral gas pressure.

Electronegativity Measurements and Analysis for CO2 and CO in DC Plasma Discharge

Electronegativity of CO 2 and CO in dc plasma discharge was investigated employing the Allan-Boyd-Reynolds (ABR), the current balance (CB), the orbital motion limited (OML), and the floating potential (FP) methods by taking advantage of the positive ion number density using the recorded I-V curves. Electron energy distribution functions were evaluated, and electron number density and temperature were obtained. Electron temperature and number density were also obtained for both gases, employing the exponentially rising electron current. Results obtained for positive and negative ions were found to be compatible for ABR, CB, and OML for each gas with the FP method to be more than one order of magnitude higher for both gases. Electronegativity of the CO 2 and CO was deduced using the measured data for electron and negative ion number densities, with the FP method at about one order of magnitude higher than those for the remaining methods.

Intrinsic dust transport in ASDEX upgrade studied by fast imaging

Fast video data recorded from 2008 to 2012 in full-tungsten ASDEX Upgrade have been analyzed with the TRACE algorithm developed to automatically detect and track dust particles. The purpose of the work presented in this paper is to complete earlier study of the influence of various discharge conditions on dust rates with an investigation of dust motion under most remarkable conditions. The 3D trajectories of intrinsic dust particles have been confronted to simulations carried out with the DUCAD (Dust Characterization And Dynamics) code, based on the Orbital Motion Limited (OML) approach for dust/plasma interaction modelling. The motion of micrometric spherical dust grains is found to be largely dominated by inertia in the considered experimental conditions. The influence of Vertical Displacement Events (VDEs) and of various heating scenarios on dust areas of formation and trajectories is investigated. It is found that VDEs inject dust originating from the PFCs which are heated by contact with the plasma, upward VDEs having a stronger impact on dust rates and transport than downward VDEs. The use of Neutral Beam Injection (NBI) significantly enhances dust production and transport coming from sectors where injectors are installed. On the contrary, Ion Cyclotron Resonance Heating significantly reduces dust rates and transport in the whole plasma volume.

Chemical model for positively charged dust particles

A chemical model of electron-dust plasmas consisting of electrons and dust particles is systematically developed. An insight is exploited that a single dust particle forms a potential well for electrons, whose depth is determined by the work function of the dust material. The whole electron fluid, initially concentrated inside the dust particles, is somehow reallocated between the bulk of the dust matter and the ambient space available, which is then interpreted as thermionic emission. An expression is employed for the Helmholtz free energy of the system, which includes the ideal and excess parts to thoroughly deal with interactions between the dusty plasma constituents. Numerical calculations of dust particle charge are performed in quite a broad domain of plasma parameters, and a straightforward comparison is made with the orbital motion limited (OML) approximation to demonstrate that the proposed calculation scheme predicts higher positive charge values of dust grains. It is also proved that the OML approximation exactly corresponds to the ideal-gas model when interactions between plasma particles are entirely neglected.

Dust charging current in non equilibrium dusty plasma in the context of Kaniadakis generalization

A first theoretical work for a κ−generalization, electron and ion charging currents are presented. Dust charging theory that provides the dust potential and charge arising from the dust interaction with a plasma is the foundational theory for dusty plasmas. Because of its simplicity, the most widely used dust charging theory for negatively charged dust particles is the so-called orbital motion limited (OML) theory, is briefly presented. The theoretical expressions of the charge current in the case of electrons and ions have been established for the first time also, numerical investigation is presented to examine the effects of the Kaniadakis statistics in dust charging processes.

Electron collection and thermionic emission from a spherical dust grain in the space-charge limited regime

The collection and emission of electrons from a spherical body in the Space-Charge Limited (SCL) regime are investigated. When a Virtual Cathode (VC) in the potential profile around the body is present, the barrier in the effective potential energy of electrons is assumed to be located near the position of the minimum of the VC potential, for both collected and emitted electrons. This assumption is confirmed to be reasonable in the case of a double Yukawa potential profile and allows the SCL cross-section for electron collection and the emitted electron’s trapped-passing boundary to be written in a simple way. An expression for the collection current for Maxwellian electrons is derived and is shown to recover the classical Orbital Motion Limited (OML) theory when the VC vanishes. Using the same assumptions, an expression for the thermionic emission current in the SCL regime is also obtained and comparisons with the OML+ theory are made. Finally, an expression for the dust electric charge in the SCL regime is derived and shown to give drastically different results when compared to the commonly used formula (obtained from a Yukawa potential profile). Consequences in the framework of dust in tokamak plasmas are discussed.

OML evaluation of the dust grain charge under quasineutrality conditions

Interaction potentials of electrons and ions with dust particles are developed to consistently treat plasma electrodynamics. It is assumed for the sake for simplicity that the material, the dust particles are made of, is a perfect conductor, and, then, the linear density-response formalism in the random phase approximation is used to take into account finite dimensions of grains. Additionally, the number density of protons is kept fixed such that the negative electric charge is allocated between the free electrons and the dust particles to assure the whole quasineutrality of the system. On the ground of the developed interaction potentials the electric charge of the dust particles is then calculated within the orbital motion limited (OML) approximation, which stems from the ballistic trajectories of the plasma particles at the charging process. It is rather clear that to advocate such a technique the mean free paths of the plasma particles must be much greater than the dimension of the dust grain. It is well known that under OML assumptions the conservation laws of energy and angular momentum are sufficient to determine the absorption cross sections of electrons and ions by the dust particle. The resultant absorption cross sections are then integrated over the velocity distribution distribution function to evaluate the fluxes of plasma particles on the grain surface, and the electric charge of the dust particle is stabilized when those fluxes are finally equalized.

Dust charging and levitating in a sheath of plasma containing energetic particles**Project supported by the National Natural Science Foundation of China (Grant No. 11475223), the National Magnetic Confinement Fusion Science Program of China (Grant No. 2015GB101003), and the JSPS-NRF-NSFC A3 Foresight Program in the field of Plasma Physics (Grant Nos. 11261140328 and 2012K2A2A6000443).

The structure of the sheath in the presence of energetic particles is investigated in the multi-fluid framework. Based on the orbital motion limited (OML) theory, the dust grain charging inside the sheath of plasma containing energetic particles is examined for the carbon wall, and then the effect of the energetic particles on the stationary dust particle inside the sheath is discussed through the trapping potential energy. It is found that with the increase of energetic ion concentration or energy, the size of dust staying in levitation equilibrium decreases and the levitating position is much closer to the wall. In the case of deuterium ions as energetic ions, the bigger dust particle can be trapped by the sheath than in the case of hydrogen ions as energetic ions. When the energetic electron component is present, the levitating position of dust particle in the sheath depends strongly on the energetic electron. The levitating dust particle is closer to the wall as the energetic electron energy or concentration is increased. In addition, with the increase of temperature of thermal background ion, the size of dust particle trapped by the sheath decreases and the levitating positions of dust particles with the same size radius inside the sheath move toward the wall. Our results can be helpful in investigating the property of the sheath where the energetic particle component is present.

Orbital motion theory and operational regimes for cylindrical emissive probes

A full-kinetic model based on the orbital-motion theory for cylindrical emissive probes (EPs) is presented. The conservation of the distribution function, the energy, and the angular momentum for cylindrical probes immersed in collisionless and stationary plasmas is used to write the Vlasov-Poisson system as a single integro-differential equation. It describes self-consistently the electrostatic potential profile and, consequently, the current-voltage (I-V) probe characteristics. Its numerical solutions are used to identify different EP operational regimes, including orbital-motion-limited (OML)/non-OML current collection and monotonic/non-monotonic potential, in the parametric domain of probe bias and emission level. The most important features of the potential and density profiles are presented and compared with common approximations in the literature. Conventional methods to measure plasma potential with EPs are briefly revisited. A direct application of the model is to estimate plasma parameters by fitting I-V measurements to the theoretical results.

Simulation of dust grain charging under tokamak plasma conditions

Dust grains in fusion devices may be radioactive, contain toxic substances, and may penetrate into the core plasma resulting in the termination of plasma discharges. Therefore, it is important to study the charging mechanisms of dust grains under tokamak's plasma conditions. In this paper, the charging processes of carbon dust grains in fusion plasmas are investigated using the developed dust simulation (DS) code. The Orbital Motion Limited (OML) theory, which is a common tool when solving dust-charging problems, is used to study the charging of dust grains due to the collection of plasma ions and electrons. The secondary electron emission (SEE) and thermionic electron emission (TEE) are also considered in the developed model. The surface temperature of dust grains (Td) is estimated for different plasma parameters. Floating potentials have been validated against the data available from the dust simulation code package DUSTT. It is shown that the dust grains are negatively charged for relatively low plasma temperatures below 10eV and plasma densities below 1019m−3. For higher plasma temperature and density, however, the charge on dust grains may become positive. The charging time depends not only on the grain's size, but also on the plasma temperature.