Orbital Motion Limited Research Articles

Simulation of W dust transport in the KSTAR tokamak, comparison with fast camera data

In this paper, dust transport in tokamak plasmas is studied through both experimental and modeling aspects. Image processing routines allowing dust tracking on CCD camera videos are presented. The DUMPRO (DUst Movie PROcessing) code features a dust detection method and a trajectory reconstruction algorithm. In addition, a dust transport code named DUMBO (DUst Migration in a plasma BOundary) is briefly described. It has been developed at CEA in order to simulate dust grains transport in tokamaks and to evaluate the contribution of dust to the impurity inventory of the plasma. Like other dust transport codes, DUMBO integrates the Orbital Motion Limited (OML) approach for dust/plasma interactions modeling. OML gives direct expressions for plasma ions and electrons currents, forces and heat fluxes on a dust grain. The equation of motion is solved, giving access to the dust trajectory. An attempt of model validation is made through comparison of simulated and measured trajectories on the 2015 KSTAR dust injection experiment, where W dust grains were successfully injected in the plasma using a gun-type injector. The trajectories of the injected particles, estimated using the DUMPRO routines applied on videos from the fast CCD camera in KSTAR, show two distinct general dust behaviors, due to different dust sizes. Simulations were made with DUMBO to match the measurements. Plasma parameters were estimated using different diagnostics during the dust injection experiment plasma discharge. The experimental trajectories show longer lifetimes than the simulated ones. This can be due to the substitution of a boiling/sublimation point to the usual vaporization/sublimation cooling, OML limitations (eventual potential barriers in the vicinity of a dust grain are neglected) and/or to the lack of a vapor shielding model in DUMBO.

Nanoparticle growth by collection of ions: orbital motion limited theory and collision-enhanced collection

The growth of nanoparticles in plasma is modeled for situations where the growth is mainly due to the collection of ions of the growth material. The model is based on the classical orbit motion limited (OML) theory with the addition of a collision-enhanced collection (CEC) of ions. The limits for this type of model are assessed with respect to three processes that are not included: evaporation of the growth material, electron field emission, and thermionic emission of electrons. It is found that both evaporation and thermionic emission can be disregarded below a temperature that depends on the nanoparticle material and on the plasma parameters; for copper in our high-density plasma this limit is about K. Electron field emission can be disregarded above a critical nanoparticle radius, in our case around nm. The model is benchmarked, with good agreement, to the growth of copper nanoparticles from a radius of nm– nm in a pulsed power hollow cathode discharge. Ion collection by collisions contributes with approximately 10% of the total current to particle growth, in spite of the fact that the collision mean free path is four orders of magnitude longer than the nanoparticle radius.

Floating surface potential of spherical dust grains in magnetized plasmas

A particle-in-cell (PIC) simulation study of the charging processes of spherical dust grains in a magnetized plasma environment is presented. Different magnetic field strengths with corresponding electron/ion gyration radii of smaller, the same or larger size than the grain radius and the plasma Debye length are examined. The magnetized plasma is created by overlapping the simulation box with a homogeneous, constant magnetic field. The charging currents are significantly reduced in the presence of a magnetic field, resulting in a more negative grain floating potential. Indeed, the most probable electron gyration radius is always smaller than that of ions in a Maxwellian plasma: however, it is demonstrated that the situation of simultaneous magnetized electron but an unmagnetized ion charging current never exists. The simulation results do not fit with a modified orbital motion limited (OML) theory approach for this situation, since the ion current is significantly reduced due to the increase of the gyration radius in the potential field of the dust grain. For very small gyration radii, the simulation results are in good agreement with a modified OML approach for both magnetized electron and ion charging currents.

Comparison of dust charging between orbital-motion-limited theory and particle-in-cell simulations

The Orbital-Motion-Limited (OML) theory has been modified to predict the dust charge and the results were contrasted with the Whipple approximation [X. Z. Tang and G. L. Delzanno, Phys. Plasmas 21, 123708 (2014)]. To further establish its regime of applicability, in this paper, the OML predictions (for a non-electron-emitting, spherical dust grain at rest in a collisionless, unmagnetized plasma) are compared with particle-in-cell simulations that retain the absorption radius effect. It is found that for large dust grain radius rd relative to the plasma Debye length λD, the revised OML theory remains a very good approximation as, for the parameters considered (rd/λD ≤ 10, equal electron and ion temperatures), it yields the dust charge to within 20% accuracy. This is a substantial improvement over the Whipple approximation. The dust collected currents and energy fluxes, which remain the same in the revised and standard OML theories, are accurate to within 15%–30%.

Low work-function thermionic emission and orbital-motion-limited ion collection at bare-tether cathodic contact

With a thin coating of low-work-function material, thermionic emission in the cathodic segment of bare tethers might be much greater than orbital-motion-limited (OML) ion collection current. The space charge of the emitted electrons decreases the electric field that accelerates them outwards, and could even reverse it for high enough emission, producing a potential hollow. In this work, at the conditions of high bias and relatively low emission that make the potential monotonic, an asymptotic analysis is carried out, extending the OML ion-collection analysis to investigate the probe response due to electrons emitted by the negatively biased cylindrical probe. At given emission, the space charge effect from emitted electrons increases with decreasing magnitude of negative probe bias. Although emitted electrons present negligible space charge far away from the probe, their effect cannot be neglected in the global analysis for the sheath structure and two thin layers in between sheath and the quasineutral region. The space-charge-limited condition is located. It is found that thermionic emission increases the range of probe radius for OML validity and is greatly more effective than ion collection for cathodic contact of tethers.

Efficient Computation of Current Collection in Bare Electrodynamic Tethers in and beyond OML Regime

AbstractOne key issue in the simulation of bare electrodynamic tethers (EDTs) is the accurate and fast computation of the collected current, an ambient dependent operation necessary to determine the Lorentz force for each time step. This paper introduces a novel semianalytical solution that allows researchers to compute the current distribution along the tether efficient and effectively under orbital-motion-limited (OML) and beyond OML conditions, i.e., if tether radius is greater than a certain ambient dependent threshold. The method reduces the original boundary value problem to a couple of nonlinear equations. If certain dimensionless variables are used, the beyond OML effect just makes the tether characteristic length L* larger and it is decoupled from the current determination problem. A validation of the results and a comparison of the performance in terms of the time consumed is provided, with respect to a previous ad hoc solution and a conventional shooting method.

Secondary electron emission from a charged spherical dust particle due to electron incidence according to OML model

Effect of secondary electron emission (SEE) current to dust charging and influence to forces on a dust particle are studied according to the orbital motion limited (OML) model. As higher electron temperature increases the SEE current, the negative dust charge decreases. As a result, the ion friction force on the dust particle decreases. The critical electron temperatures without the dust charge are 75.1, 70.3 and 55.9eV for graphite and are 31.3, 30.4 and 27.1eV for tungsten to the temperature ratio Ti/Te=0.1, 1.0 and 10.0, respectively. At the critical electron temperature, there is no ion scattering force but the ion absorption force remains finite.

Orbital-motion-limited theory of dust charging and plasma response

The foundational theory for dusty plasmas is the dust charging theory that provides the dust potential and charge arising from the dust interaction with a plasma. The most widely used dust charging theory for negatively charged dust particles is the so-called orbital motion limited (OML) theory, which predicts the dust potential and heat collection accurately for a variety of applications, but was previously found to be incapable of evaluating the dust charge and plasma response in any situation. Here, we report a revised OML formulation that is able to predict the plasma response and hence the dust charge. Numerical solutions of the new OML model show that the widely used Whipple approximation of dust charge-potential relationship agrees with OML theory in the limit of small dust radius compared with plasma Debye length, but incurs large (order-unity) deviation from the OML prediction when the dust size becomes comparable with or larger than plasma Debye length. This latter case is expected for the important application of dust particles in a tokamak plasma.

Charging and heat collection by a positively charged dust grain in a plasma.

Dust particulates immersed in a quasineutral plasma can emit electrons in several important applications. Once electron emission becomes strong enough, the dust enters the positively charged regime where the conventional orbital-motion-limited (OML) theory can break down due to potential-well effects on trapped electrons. A minimal modification of the trapped-passing boundary approximation in the so-called OML(+) approach is shown to accurately predict the dust charge and heat collection flux for a wide range of dust size and temperature.

Floating potential of large dust grains with electron emission

Electron emission from the surface of solid particles plays an important role in many dusty plasma phenomena and applications. Examples of such cases include fusion plasmas and dusty plasma systems in our solar system. Electron emission complicates the physics of the plasma-dust interaction. One of the most important aspects of the physics of the dust plasma interaction is the calculation of the particle's floating potential. This is the potential a dust particle acquires when it is in contact with a plasma and it plays a very important role for determining its dynamical behaviour. The orbital motion limited (OML) approach is used in most cases in the literature to model the dust charging physics. However, this approach has severe limitations when the size of the particles is larger than the electron Debye length λDe. Addressing this shortcoming for cases without electron emission, a modified version of OML (MOML) was developed for modelling the charging physics of dust grains larger than the electron Debye length. In this work, we will focus on extending MOML in cases where the particles emit electrons. Furthermore, a general method for calculating the floating potential of dust particles with electron emission will be presented for a range of grain sizes.

Comparison of various interpretation methods of the electric probe measurements in inductively coupled Ar and O2 plasmas

In low-pressure inductively coupled argon and oxygen discharges, the plasma density and electron temperature and the electron energy distribution function (EEDF) were obtained by using a cylindrical electric probe. The plasma densities were determined by various methods to interpret the probe current-voltage characteristic curve: the EEDF integration, the electron saturation current, the ion current at the floating potential, and the orbital-motion-limited (OML) ion current. Quite a good agreement exists between the plasma densities determined by various classical methods. Although the probe technique has some limitation in electronegative plasmas, the plasma densities determined from OML theory compare well with those measured by the ion saturation current at the floating potential in the oxygen discharges. In addition, the EEDFs of inductively coupled Ar and oxygen plasmas are observed to be nearly Maxwellian at the pressure range of 1-40 mTorr.

Fast growth of nanoparticles in a hollow cathode plasma through orbit motion limited ion collection

Plasma-based nanoparticle synthesis techniques are attractive in many respects but suffer from a major drawback—low productivity. We demonstrate a technique by which the growth rate of copper nanoparticles has been substantially increased by collection of copper ions. A growth rate as high as 470 nm/s was obtained as compared to a growth rate of less than 3 nm/s in the case of growth by neutrals. The increased trapping of copper is explained as orbital motion limited (OML) collection of ions. Experimentally obtained nanoparticle growth rates are in good agreement with theoretical estimates of the OML ion collection rates.

Discharging of dust particles in the afterglow of plasma with large dust density

The discharging of dust particles in the afterglow of plasma with large dust density is studied. We used measured electron and metastable dependencies to calculate the rate describing collection of electrons by dust particles by solving the electron balance equation. This rate is compared with the rate calculated using the orbital motion limited (OML) theory. It is found that the OML theory may not be applied for description of dust charging at large afterglow times, and the energetic electrons generated in metastable-metastable collisions significantly affect charging of dust particles. The time dependence for dust charge is calculated by two different approaches: first, the "standard" approach is used, which assumes that ion and electron fluxes to the dust particles are different in the afterglow. Second, the dust charge is calculated by assuming that desorption of electrons from dust particles is very fast. Both approaches gave similar results for dust charging. In addition, the effects of secondary emission due to ion-dust and metastable-dust collisions on dust discharging are investigated. The main source of dust charging in the late afterglow of plasma with large dust density are the energetic electrons generated in Ar(m) metastable-metastable collisions.

Analysis of cylindrical Langmuir probe using experiment and different theories

Cylindrical probe data have been analyzed using different theories in order to determine some plasma parameters (electron temperature and electron and ion densities). Langmuir probe data are obtained in a cylindrical DC glow discharge in the positive column plasma at argon gas pressures varied from 0.5 to 6 Torr and at constant discharge current equal to 10 mA. The electron density has calculated from the elec� tron current at the space potential and from Orbital Motion Limited (OML) collisionless theory. Ion density has obtained from the OML analysis of the ion saturation currents. In addition, the electron temperature has measured by three different methods using probe and electrons currents. The electron temperature Te, plasma density ne, and space potential Vs, have been obtained from the measured single cylindrical probe I- V characteristic curves. The radial distribution of the electron temperature and plasma density along the glow discharge are measured and discussed. Using the collisionless theories by Langmuir cylindrical probe and up to several Torr argon gas pressures the differences between the values of electron temperature and electron and ion densities stay within reasonable error limits.

Secondary Electron Emission from a Negatively Charged Spherical Dust Particle by Electron Incidence

Secondary electron emission (SEE) from a spherical metallic dust particle by electron incidence was analyzed according to the OML (Orbit Motion Limited) model. As the observed dust speed in fusion plasmas (< 100m/s) is much slower than electron thermal speed, its effect to the SEE current is negligibly small. It is clarified that there is a window of electron temperature, where the ratio of the SEE current to the absorbed electron current exceeds unity; for graphite 80 eV < Te < 326 eV and the maximum of the ratio ∼ 1.10 at Te ∼ 165 eV, for tungsten 32 eV < Te, the maximum ∼ 2.47 at Te ∼ 358 eV. These excesses come from the inverse proportion of the incident angle to the dust particle.

The Electron Sheath Around an Emissive Wire in Vacuum

An orbit-motion-limited (OML) theory is developed for the electron sheath and the virtual cathode that forms around an emissive wire in vacuum. The electron cloud above the wire surface is assumed to be described by a 2-D Maxwellian distribution function. A comparison is made with a 1-D theory having only radial velocities for the electrons. The OML theory gives a greater electron density and a more negative virtual cathode because of differences between the 1-D and 2-D distribution functions. Expressions are derived for the current from the cathode to the anode.

Calibration of Langmuir probes against microwaves and plasma oscillation probes

The use of Langmuir probes for measuring plasma density is subject to uncertainty because the theories commonly used to interpret the data give widely differing results. This is especially troublesome in partially ionized plasmas used, for instance, in the semiconductor industry, since no existing theory adequately treats the case when there are a few collisions between ions and neutral atoms. In this work, plasma densities measured by microwave interferometry and plasma-oscillation probes are compared with those from probe data analyzed with Langmuir's orbital motion limited (OML) theory, the Allen–Boyd–Reynolds (ABR) theory and the Bernstein–Rabinowitz–Laframboise (BRL) theory. It is found that ABR underestimates and BRL overestimates the density, the problems being the neglect of ion orbiting in ABR and the effect of ion-neutral collisions in BRL. The best theory is either OML or the geometric mean between the ABR and BRL results. For thicker probes, other methods are suggested.

Relativistic current collection by a cylindrical Langmuir probe

The current I to a cylindrical Langmuir probe with a bias Φp satisfying β≡eΦp/mec2∼O(1) is discussed. The probe is considered at rest in an unmagnetized plasma composed of electrons and ions with temperatures kTe∼kTi≪mec2. For small enough radius, the probe collects the relativistic orbital-motion-limited (OML) current IOML, which is shown to be larger than the non-relativistic result; the OML current is proportional to β1/2 and β3/2 in the limits β≪1 and β≫1, respectively. Unlike the non-relativistic case, the electron density can exceed the unperturbed density value. An asymptotic theory allowed to compute the maximum radius of the probe to collect OML current, the sheath radius for probe radius well below maximum and how the ratio I/IOML drops below unity when the maximum radius is exceeded. A numerical algorithm that solves the Vlasov-Poisson system was implemented and density and potential profiles presented. The results and their implications in a possible mission to Jupiter with electrodynamic bare tethers are discussed.

Floating potential of large dust grains in a collisionless flowing plasma

Dust immersed in plasma quickly charges to a potential where the ion and electron currents to its surface balance; this is the floating potential. In order to accurately determine dust behavior, the floating potential must be known. The charging of dust grains that are small with respect to electron Debye length (λ(D)) may be adequately approximated using the orbital-motion-limited (OML) approach. A modified version of OML is presented for large dust grains in both stationary and flowing plasmas. This modified OML is compared with simulation and found to be in good agreement. The modified OML is applied to large grains charging under tokamak conditions and found to have an appreciable effect on the drag force.

Dust Charging and Dynamics in Tokamaks

Fundamental characteristics of charging of a dust particle and its dynamics in SOL/divertor plasma in tokamaks are studied. According to the OML (orbit motion limited) theory, the charging process is extremely faster, with a charging time of nanoseconds, than the dynamics process of the dust particle in SOL/divertor plasma, with a characteristic time of milliseconds, which means that the local charge state can be taken as the equilibrium charge state. It was clarified that the equilibrium charge Zd,eq can be determined in the form of Zd,eq/RdTe, which is a function of both the normalized relative speed of plasma ion flow with respect to the velocity of the dust particle and the plasma temperature ratio. After the investigation of dominant forces acting on dust particles, the friction forces due to the plasma ion absorption and ion Coulomb scattering are found of the same order for the case of low relative speed. The critical radius of a dust particle, for which the gravity is larger than the friction forces due to plasma ions, is obtained.