Electron Debye Length Research Articles

Formation of trapped-ion population in the process of charging of an absorbing sphere in a collisionless plasma

Dynamics of charging of an absorbing spherical body is studied by means of a numerical simulation. Upon saturation of the charge of the body and relaxation of transient oscillatory phenomena accompanying the charging, the disturbed plasma passes into a stable steady state. Along with the determination of space-time dependences of electrostatic quantities, the numerical experiment allows to observe the time evolution of electron and ion distributions in phase space. A dense cloud of trapped ions is formed near the spherical body, provided that the ion Debye length is of the order of the radius of the body, and the electron Debye length exceeds appreciably the radius. The trapped ions contribute substantially to the screening of the charged sphere, thereby affecting the structure of the disturbed plasma in the asymptotic steady state at long times.

Magnetized sheath near positively biased wall between two permanent magnetic plates

The characteristics of magnetized electron sheath near a positively biased conducting wall parallel to magnetic field formed between two permanent magnetic plates were experimentally investigated in a double plasma device. The magnetic field strength between the magnetic plates is about 1200 G which is sufficient to magnetize the plasma such that the ion gyroradius is comparable to the electron Debye length. A virtual cathode (or potential dip) structure was found between the electron-rich sheath and bulk plasma. For a given neutral gas pressure, the potential minimum (dip position) remains almost the same for different positive biases on the wall. For a given bias on the wall, however, the electron sheath thickness and the potential drop from the bulk plasma to the dip decrease with the increase of the neutral gas pressure. In addition, the electron sheath and potential dip appear to be wider and deeper in the downstream side of the wall.

A gyrokinetic one-dimensional scrape-off layer model of an edge-localized mode heat pulse

An electrostatic gyrokinetic-based model is applied to simulate parallel plasma transport in the scrape-off layer to a divertor plate. The authors focus on a test problem that has been studied previously, using parameters chosen to model a heat pulse driven by an edge-localized mode in JET. Previous work has used direct particle-in-cell equations with full dynamics, or Vlasov or fluid equations with only parallel dynamics. With the use of the gyrokinetic quasineutrality equation and logical sheath boundary conditions, spatial and temporal resolution requirements are no longer set by the electron Debye length and plasma frequency, respectively. This test problem also helps illustrate some of the physics contained in the Hamiltonian form of the gyrokinetic equations and some of the numerical challenges in developing an edge gyrokinetic code.

Benchmarking sheath subgrid boundary conditions for macroscopic-scale simulations

The formation of sheaths near metallic or dielectric-coated wall materials in contact with a plasma is ubiquitous, often giving rise to physical phenomena (sputtering, secondary electron emission, etc) which influence plasma properties and dynamics both near and far from the material interface. In this paper, we use first-principles PIC simulations of such interfaces to formulate a subgrid sheath boundary condition which encapsulates fundamental aspects of the sheath behavior at the interface. Such a boundary condition, based on the capacitive behavior of the sheath, is shown to be useful in fluid simulations wherein sheath scale lengths are substantially smaller than scale lengths for other relevant physical processes (e.g. radiofrequency wavelengths), in that it enables kinetic processes associated with the presence of the sheath to be numerically modeled without explicit resolution of spatial and temporal sheath scales such as electron Debye length or plasma frequency.

Comprehensive kinetic analysis of the plasma-wall transition layer in a strongly tilted magnetic field

The magnetized plasma-wall transition (MPWT) layer at the presence of the obliquity of the magnetic field to the wall consists of three sub-layers: the Debye sheath (DS), the magnetic pre-sheath (MPS), and the collisional pre-sheath (CPS) with characteristic lengths λD (electron Debye length), ρi (ion gyro-radius), and ℓ (the smallest relevant collision length), respectively. Tokamak plasmas are usually assumed to have the ordering λD≪ρi≪ℓ, when the above-mentioned sub-layers can be distinctly distinguished. In the limits of εDm(λD/ρi)→0 and εmc(ρi/ℓ)→0 (“asymptotic three-scale (A3S) limits”), these sub-layers are precisely defined. Using the smallness of the tilting angle of the magnetic field to the wall, the ion distribution functions are found for three sub-regions in the analytic form. The equations and characteristic length-scales governing the transition (intermediate) regions between the neighboring sub-layers (CPS – MPS and MPS – DS) are derived, allowing to avoid the singularities arising from the εDm→0 and εmc→0 approximations. The MPS entrance and the related kinetic form of the Bohm–Chodura condition are successfully defined for the first time. At the DS entrance, the Bohm condition maintains its usual form. The results encourage further study and understanding of physics of the MPWT layers in the modern plasma facilities.

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.

A unified analysis of plasma-sheath transition in the Tonks–Langmuir model with warm ion source

The paper presents a comprehensive kinetic theory of the famous Tonks–Langmuir model of a plane symmetric discharge, taking into account the thermal motion of ion source particles. The ion kinetics is governed by the ionization of neutrals at electron impacts. The plasma consisting of Boltzmann distributed electrons and singly charged ions is in contact with the absorbing negative wall. The derivations are performed in the frame of the “asymptotic two-scale” approximation, when the ionization mean-free path Li is much larger than the electron Debye length λD. In the limit (λD/Li)→0, the plasma-wall transition (PWT) layer can be split into two sublayers: a quasineutral presheath (PS) (with the scale-length Li) and the Debye sheath (DS) (with the scale λD). Such a subdivision of the PWT layer allows to investigate these sublayers separately and simplify the analysis of the influence of the ion source thermal motion (this has been neglected in the major part of publications up to now). The uniform description of the PWT layer as a single unit is complicated by the singular presheath and sheath structure and by a coupling with the eigenvalue problem originating from the plasma balance in the bounded system. The issue is clarified both analytically and numerically by construction of a matched asymptotic expressions. The equation and the length-scale governing the transition between neighboring PS and DS sublayers are derived. The eigenvalue problem combining the wall potential, the wall location, and the ionization mean-free path is discussed.

Effective Coulomb force modeling for spacecraft in Earth orbit plasmas

Coulomb formation flight is a concept that utilizes electrostatic forces to control the separations of close proximity spacecraft. The Coulomb force between charged bodies is a product of their size, separation, potential and interaction with the local plasma environment. A fast and accurate analytic method of capturing the interaction of a charged body in a plasma is shown. The Debye–Hückel analytic model of the electrostatic field about a charged sphere in a plasma is expanded to analytically compute the forces. This model is fitted to numerical simulations with representative geosynchronous and low Earth orbit (GEO and LEO) plasma environments using an effective Debye length. This effective Debye length, which more accurately captures the charge partial shielding, can be up to 7 times larger at GEO, and as great as 100 times larger at LEO. The force between a sphere and point charge is accurately captured with the effective Debye length, as opposed to the electron Debye length solutions that have errors exceeding 50%. One notable finding is that the effective Debye lengths in LEO plasmas about a charged body are increased from centimeters to meters. This is a promising outcome, as the reduced shielding at increased potentials provides sufficient force levels for operating the electrostatically inflated membrane structures concept at these dense plasma altitudes.

Modeling a planar sheath in dust-containing plasmas

One-dimensional fluid model is utilized to describe the sheath at a dust-containing plasma-wall boundary. The model equations are solved on the scale of the electron Debye length. The spatial distributions of electric potential and of the velocities and densities of charged species are calculated in a wide range of control parameters. The dust charge number, electric force, and ion drag force are also investigated. The impacts of Havnes parameter, the electron to ion temperature ratio, the ion collisionality, and the ionization on the spatial distributions of the plasma species and the incident fluxes of the ions to the wall (or to the probe) are investigated. With increase of Havnes parameter, the sheath thickness and the ion flux to the wall are reduced, whereas the ion drift velocity is increased. Enhanced ion thermal motion causes the ion flux to the wall to increase. An increase in ion collisionality with neutrals causes both the sheath thickness and the ion flux to the wall to decrease. With increase of the ionization rate, the sheath thickness is found to decrease and the ion flux collected by a probe increases. The localization of dust particles above the electrode is intensified by the increases in Havnes parameter, the electron to ion temperature ratio, collisionality, and ionization rate.

Positron sound waves and nonlinear Landau damping of intense transverse EM waves in an isotropic EPI plasma

AbstractRelativistically hot electron–positron–ion (EPI) plasmas in the presence of relativistic intense electromagnetic (EM) radiation that are not in thermal equilibrium are studied by following a modified plasma particle distribution function. By means of a kinetic description, soliton solution is obtained for a small amplitude EM wave, whereas for large amplitude EM waves a cusp soliton solution is obtained. A general expression of positron density oscillations is obtained for long wavelength in comparison with the Debye length of electrons, and is discussed for special cases. Dispersion relations for a new type of longitudinal waves with slow damping is formulated as a consequence of resonant wave–particle interaction, and the necessary conditions for the existence of positron sound waves are obtained. Furthermore, for ultrarelativistic electrons and non-relativistic positrons, quasi positron sound waves dispersion relation in the intermediate wave range is obtained. It is shown that the modulation of amplitude of relativistic EM waves leads to instability for the rare plasma. Finally, we have obtained the relativistic kinetic nonlinear Schrödinger equation (KNLS) with local and non-local nonlinearities. The KNLS equation depicts nonlinear Landau damping rates for intense EM waves, and these damping rates are also examined.

Effects of temperature and electron collision frequency on the elastic electron–ion collisions in a collisional plasma

AbstractThe effects of dynamic temperature and electron–electron collisions on the elastic electron–ion collision are investigated in a collisional plasma. The second-order eikonal analysis and the velocity-dependent screening length are employed to derive the eikonal phase shift and eikonal cross section as functions of collision energy, electron collision frequency, Debye length, impact parameter, and thermal energy. It is interesting to find out that the electron–electron collision effect would be vanished; however, the dynamic temperature effect is included in the first-order approximation. We have found that the dynamic temperature effect strongly enhances the eikonal phase shift as well as the eikonal cross section for electron–ion collision since the dynamic screening increases the effective shielding distance. In addition, the detailed characteristic behavior of the dynamic screening function is also discussed.

Hot-electron generation by “cavitating” Langmuir turbulence in the nonlinear stage of the two-plasmon–decay instability

The kinetic reduced-description particle-in-cell simulation technique has been applied to study the nonlinear stage of two-plasmon–decay (TPD) instability in an inhomogeneous plasma driven by crossed laser beams. The TPD instability is found to be a prolific generator of “cavitating” Langmuir turbulence. Langmuir “cavitons”—localized longitudinal electric fields, oscillating near the local electron plasma frequency, trapped in ponderomotive density depressions—collapse to dimensions of a few electron Debye lengths, where the electric field energy is collisionlessly transferred to electron kinetic energy. The resulting hot electrons can attain instantaneous temperatures up to 100 keV with net suprathermal heat flux out of the system of up to a few percent of the input laser energy. Scaling laws for this hot-electron generation by TPD, in regimes motivated by recent experiments on the Omega laser, were presented recently by Vu et al. (H. X. Vu, D. F. DuBois, D. A. Russell, and J. F. Myatt, Phys. Plasmas 19, 102703 (2012)). This paper concentrates on the microscopic mechanisms for hot-electron generation. The spatial distribution of the maxima of the electric field envelope modulus is found to be very spiky, with the distribution of electric field envelope maxima obeying Gaussian statistics. The cavitons are produced in density-depletion trenches produced by the combined ponderomotive interference of the crossed laser beams and the ponderomotive beats of the primary backward-going TPD Langmuir waves (LWs) resulting from the crossed beams. The Langmuir turbulence is strongest in the electron-density region near 0.241× the laser's critical density, where the forward LWs from the crossed-beam TPD are degenerate. Nucleation of cavitons is assisted by the modulation of the electron density in the trenches, which in turn is caused by the beating of the common forward-going LW and the pair of backward-going LWs. The autocorrelation function of the LW envelope field provides a near-universal shape for intense cavitons—in the neighborhood of the local field maxima. The hot-electron temperature is found to be approximately a linear function of the “caviton temperature” determined from the Gaussian distribution of caviton maxima. These diagnostics provide strong evidence for the importance of Langmuir caviton collapse in the generation of hot electrons by TPD. Extended Zakharov model predictions for TPD exhibit the same qualitative phenomena.

Improved analysis techniques for cylindrical and spherical double probes

A versatile double Langmuir probe technique has been developed by incorporating analytical fits to Laframboise's numerical results for ion current collection by biased electrodes of various sizes relative to the local electron Debye length. Application of these fits to the double probe circuit has produced a set of coupled equations that express the potential of each electrode relative to the plasma potential as well as the resulting probe current as a function of applied probe voltage. These equations can be readily solved via standard numerical techniques in order to determine electron temperature and plasma density from probe current and voltage measurements. Because this method self-consistently accounts for the effects of sheath expansion, it can be readily applied to plasmas with a wide range of densities and low ion temperature (T(i)/T(e) ≪ 1) without requiring probe dimensions to be asymptotically large or small with respect to the electron Debye length. The presented approach has been successfully applied to experimental measurements obtained in the plume of a low-power Hall thruster, which produced a quasineutral, flowing xenon plasma during operation at 200 W on xenon. The measured plasma densities and electron temperatures were in the range of 1 × 10(12)-1 × 10(17) m(-3) and 0.5-5.0 eV, respectively. The estimated measurement uncertainty is +6%∕-34% in density and +∕-30% in electron temperature.

The effects of the polytropic coefficient on plasma sheath in two cases isothermal and adiabatic ion thermal flow

Recently it has been shown that for finite and small values of the electron Debye length, the ion polytropic coefficient is approached to some constant value in the plasma sheath region by decreasing the plasma density. In this paper, using a plasma multi fluid model, the effect of ion polytropic coefficient γ i on the plasma sheath structure have been examined. The numerical calculations of the basic equation of the model show that the polytropic coefficient strongly affects on the plasma sheath characteristics. The results show that by transition from an isothermal flow (γ i =1) to an adiabatic flow (γ i =3), the net current to the wall and the electric potential distribution increase and the sheath width decreases in a thermal plasma sheath.

On the unconstrained expansion of a spherical plasma cloud turning collisionless: case of a cloud generated by a nanometre dust grain impact on an uncharged target in space

Nano and micrometre sized dust particles travelling through the heliosphere at several hundreds of km s−1 have been repeatedly detected by interplanetary spacecraft. When such fast moving dust particles hit a solid target in space, an expanding plasma cloud is formed through the vaporization and ionization of the dust particles itself and part of the target material at and near the impact point. Immediately after the impact the small and dense cloud is dominated by collisions and the expansion can be described by fluid equations. However, once the cloud has reached μm dimensions, the plasma may turn collisionless and a kinetic description is required to describe the subsequent expansion. In this paper we explore the late and possibly collisionless spherically symmetric unconstrained expansion of a single ionized ion–electron plasma using N-body simulations. Given the strong uncertainties concerning the early hydrodynamic expansion, we assume that at the time of the transition to the collisionless regime the cloud density and temperature are spatially uniform. We also neglect the role of the ambient plasma. This is a reasonable assumption as long as the cloud density is substantially higher than the ambient plasma density. In the case of clouds generated by fast interplanetary dust grains hitting a solid target, some 107 electrons and ions are liberated and the in vacuum approximation is acceptable up to meter order cloud dimensions. As such a cloud can be estimated to become collisionless when its radius has reached μm order dimensions, both the collisionless approximation and the in vacuum approximation are expected to hold during a long lasting phase as the cloud grows by a factor 106. With these assumptions, we find that the transition from the collisional to the collisionless regime could occur when the electron Debye length λD within the cloud is much smaller than the cloud radius R0, i.e. Λ ≡ λD/R0 ≪ 1. This implies a quasi-neutral expansion regime where the radial electron and ion density profiles are equal through most of the cloud except at the cloud–vacuum interface. The consequence of Λ being much smaller than unity implies that the electrostatic fields within a cloud generated by a dust impact on a neutral target is ∼100 times weaker than in the case of grains hitting a spacecraft, where the positive potential of the target is strong enough to strip-off all the electrons from the expanding cloud leading to a ‘Coulomb explosion’ like regime (e.g. Peano et al 2007 Phys. Plasmas \\bf 14 056704).

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.

Determination of the levitation limits of dust particles within the sheath in complex plasma experiments

Experiments are performed in which dust particles are levitated at varying heights above the powered electrode in a radio frequency plasma discharge by changing the discharge power. The trajectories of particles dropped from the top of the discharge chamber are used to reconstruct the vertical electric force acting on the particles. The resulting data, together with the results from a self-consistent fluid model, are used to determine the lower levitation limit for dust particles in the discharge and the approximate height above the lower electrode where quasineutrality is attained, locating the sheath edge. These results are then compared with current sheath models. It is also shown that particles levitated within a few electron Debye lengths of the sheath edge are located outside the linearly increasing portion of the electric field.

Theoretical investigation of thermophysical properties in two-temperature argon-helium thermal plasma

The thermophysical properties of argon-helium thermal plasma have been studied in the temperature range from 5000 to 40 000 K at atmospheric pressure in local thermodynamic equilibrium and non-local thermodynamic equilibrium conditions. Two cases of thermal plasma considered are (i) ground state plasma in which all the atoms and ions are assumed to be in the ground state and (ii) excited state plasma in which atoms and ions are distributed over various possible excited states. The influence of electronic excitation and non-equilibrium parameter θ = Te/Th on thermodynamic properties (composition, degree of ionization, Debye length, enthalpy, and total specific heat) and transport properties (electrical conductivity, electron thermal conductivity, and thermal diffusion ratio) have been studied. Within the framework of Chapman-Enskog method, the higher-order contributions to transport coefficient and their convergence are studied. The influence of different molar compositions of argon-helium plasma mixture on convergence of higher-orders is investigated. Furthermore, the effect of different definitions of Debye length has also been examined for electrical conductivity and it is observed that electrical conductivity with the definition of Debye length (in which only electrons participate in screening) is less than that of the another definition (in which both the electrons and ions participate in screening) and this deviation increases with electron temperature. Finally, the effect of lowering of ionization energy is examined on electron number density, Debye length, and higher-order contribution to electrical conductivity. It is observed that the lowering of the ionization energy affects the electron transport-properties and consequently their higher-order contributions depending upon the value of the non-equilibrium parameter θ.

Vlasov modelling of parallel transport in a tokamak scrape-off layer

A one-dimensional Vlasov–Poisson model is used to describe the parallel transport in a tokamak scrape-off layer. Thanks to a recently developed ‘asymptotic-preserving’ numerical scheme, it is possible to lift numerical constraints on the time step and grid spacing, which are no longer limited by, respectively, the electron plasma period and Debye length. The Vlasov approach provides a good velocity-space resolution even in regions of low density. The model is applied to the study of parallel transport during edge-localized modes, with particular emphasis on the particles and energy fluxes on the divertor plates. The numerical results are compared with analytical estimates based on a free-streaming model, with good general agreement. An interesting feature is the observation of an early electron energy flux, due to suprathermal electrons escaping the ions' attraction. In contrast, the long-time evolution is essentially quasi-neutral and dominated by the ion dynamics.

Characteristics of the dust–plasma interaction near Enceladus’ South Pole

We present RPWS Langmuir probe data from the third Enceladus flyby (E3) showing the presence of dusty plasma near Enceladus’ South Pole. There is a sharp rise in both the electron and ion number densities when the spacecraft traverses through Enceladus plume. The ion density near Enceladus is found to increase abruptly from about 10 2 cm −3 before the closest approach to 10 5 cm −3 just 30 s after the closest approach, an amount two orders of magnitude higher than the electron density. Assuming that the inconsistency between the electron and ion number densities is due to the presence of dust particles that are collecting the missing electron charges, we present dusty plasma characteristics down to sub-micron particle sizes. By assuming a differential dust number density for a range in dust sizes and by making use of Langmuir probe data, the dust densities for certain lower limits in dust size distribution were estimated. In order to achieve the dust densities of micrometer and larger sized grains comparable to the ones reported in the literature, we show that the power law size distribution must hold down to at least 0.03 μm such that the total differential number density is dominated by the smallest sub-micron sized grains. The total dust number density in Enceladus’ plume is of the order of 10 2 cm −3 reducing to 1 cm −3 in the E-ring. The dust density for micrometer and larger sized grains is estimated to be about 10 −4 cm −3 in the plume while it is about 10 −6–10 −7 cm −3 in the E-ring. Dust charge for micron sized grains is estimated to be about eight thousand electron charges reducing to below one hundred electron charges for 0.03 μm sized grains. The effective dusty plasma Debye length is estimated and compared with inter-grain distance as well as the electron Debye length. The maximum dust charging time of 1.4 h is found for 0.03 μm sized grains just 1 min before the closest approach. The charging time decreases substantially in the plume where it is only a fraction of a second for 1 μm sized grains, 1 s for 0.1 μm sized grains and about 10 s for 0.03 μm sized grains.