Ion Debye Length Research Articles

Polarization of Dusty “Quasiatoms” in Low-Density Plasma

A model of the polarization of dust particles with trapped ions in an external electric field is presented. It is based on the self-consistent solution of the integral balance equation for trapped ion density and Poisson equation for the electric potential. It is shown that, in a low collisional regime, trapped ions form a spread shell with a maximum located at some distance from thecharged dust particle proportional to the ion Debye length. The estimated polarizability of dusty "quasiatoms" is very high anddepends on the strength of the external electric field due to the field ionization of trapped ions. With increase in the electricfield, the dusty "quasiatom" loses their trapped ions from far orbits due to the field ionization. The radius of the dusty "quasiatom" ionic shell becomes smaller, and the coefficient of polarizability decreases.

Particle simulation of a magnetized plasma sheath with the magnetic field parallel to the wall

The plasma sheath in a magnetic field parallel to the wall is studied by particle in cell simulations. The simulation results show that the spatial structure of the sheath is determined by the ion Debye length, instead of the ion Larmor radius or the electron Debye length. The characteristic time of the magnetized plasma sheath formation is the ion cyclotron time.

Plasma sheath properties in a magnetic field parallel to the wall

Particle in cell simulations were carried out with a plasma bounded by two absorbing walls and a magnetic field applied parallel to them. Both the sheath extent and the potential drop in it were derived from simulations for different plasma parameters, such as the electron and ion temperature Ti, particle density, and ion mass. Both of them exhibit a power law dependent on the Larmor to plasma ion pulsation ratio Ωi. For increasing values of the magnetic field, the potential drop within the sheath decreases from a few Ti/e down to zero, where e stands for the electron charge. The space charge extent increases with Ωi and saturates to 2.15 ion Larmor radius. A simple model of sheath formation in such a magnetic field configuration is presented. Assuming strongly magnetized electrons, and neglecting collisions and ionizations, a new typical length is evidenced, which depends on the ratio Ωi. The charge separation sheath width is theoretically found to increase from a combination of the electron gyroradius and the ion Debye length for low Ωi ratios up to several ion gyroradii for strongly magnetized ions. Both the calculated sheath extent and plasma potential show a fair agreement with the numerical simulations.

Dusty plasma in the region of the lunar terminator

Dusty plasma in the region of the lunar terminator is considered. It is shown that, in this region, a structure resembling a plasma sheath forms near the lunar surface. This sheath creates a potential barrier, due to which electrons over the illuminated part of the Moon are confined by electrostatic forces. The width of the sheath-like structure is on the order of the ion Debye length. In this structure, significant (about several hundred V/m) electric fields arise, which lift charged micron-size dust grains to heights of several tens of centimeters. The suggested effect may be used to explain the glow observed by the Surveyor spacecraft over the lunar terminator.

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.

Formation of a Trapped-Ion Cloud Around a Dust Particle in Low-Density Plasma

A self-consistent model for trapped-ion-cloud formation around a dust particle immersed in low-temperature low-density plasma is presented. The model is based on the solution of an integral balance equation for trapped-ion density, the free ion and electron densities, and the Poisson equation for electric potential distribution. It is shown that, in a weakly collisional regime in plasma, trapped ions form a spread “shell” with the maximum located at some distance from the negatively charged core (dust particle) proportional to an ion Debye length. The estimated polarizability of such dusty “quasi atoms” in an external electric field is very high, and their induced dipole moments can be responsible for the alignment of dust particles, the formation of chain and multilayer structures, and the coagulation of dust grains.

Analysis of the Ion Distribution at a Charged Solid−Liquid Interface Using X-ray Standing Waves

Functionalized solid-liquid interfaces were analyzed by X-ray standing waves (XSW) combined with streaming current measurements to study surface charges, interfacial potential, and ion distributions. Thin films of aqueous solution containing Br(-) anions and Fe(3+) cations at a concentration of 10 mg/L were prepared on functionalized silicon wafers. Functionalization of Si surfaces was accomplished by aminosilane groups shifting the interfacial potential toward positive values. The ion distribution was measured with nanometer resolution, which allows distinguishing between absorbed and mobile ions at the surface and in the diffusive layer, respectively. For Br(-), different degrees of ion attraction were measured for the pH values 5.7 and 2.8. The ion Debye length values of the diffuse layer were 4 and 2 nm, respectively.

Measurements of electric charge and screening length of microparticles in a plasma sheath

An experiment is described in which microparticles are levitated within a rf sheath above a conducting plate in argon plasma. The microparticles forming a two-dimensional crystal structure are considered to possess Debye screening Coulomb potential ϕ(r)=(Q/4πε0r)exp(−r/λ), where Q is the electric charge, r is distance, and λ is the screening length. When the crystal structure is slanted with an angle θ, a particle experiences a force Mg sin θ, where M is the mass of the particle and g is acceleration due to gravity, which must be equal to the Debye screened Coulomb force from other particles. By changing θ, relations for λ(Q) are measured. The screening length λ and Q are determined uniquely from the crossing points of several relations. The electric charge Q is also estimated from a floating potential measured with a probe. The measured λ is nearly equal to an ion Debye length.

A linearized Fokker–Planck study of ion-eigenmodes in an unmagnetized pair-ion-electron plasma

Two kinds of ion-eigenmodes in an unmagnetized pair-ion-electron plasma, pair-ion-acoustic waves (PIAWs) and ion-Langmuir waves (ILWs), are investigated with Fokker–Planck description. The linearized negative- and positive-ion Fokker–Planck equations and linearized electron Vlasov equation are solved numerically as an eigenvalue problem. The frequencies and damping rates of PIAWs and ILWs are presented as a function of kλ, kλD, Te∕T, n−∕n+, where k is the wave number, λ is the mean-free path of the positive ion, λD is the positive ion Debye length, Te and T are electron and ion temperature, and n−∕n+ is the ratio of negative ion density to positive ion density. It is found that the dispersion relations of PIAWs and ILWs are sensitive to the strength of ion-ion collisions. As kλ increases, it is shown that PIAWs evolve into ILWs smoothly at small negative ion concentration. For large n−∕n+, PIAWs and ILWs, respectively, exist in a strong-collisional and rare-collisional region, and coexist in the intermediate regime at about kλ∼1. For comparison, hydrodynamic description and Vlasov description are also discussed. When the Landau damping is negligible, the two-fluid hydrodynamic description can give good results for ILWs if the friction forces between the negative and positive ions are included.

Dispersion of Dust Acoustic Modes and Perturbations of Plasma Flux Balance

AbstractPrevious considerations of dust acoustic waves is demonstrated to be inconsistent ‐ the required equilibrium state for perturbations was not defined since balance of plasma fluxes was neglecting. The self‐consistent treatment shows that plasma flux perturbations are accompanying any collective waves propagating in dusty plasmas and can play an important role in wave dispersion, wave damping and can create instabilities. This is illustrated by the derivation of dispersion relation for dust acoustic modes taking into account the plasma flux balances and plasma flux perturbations by waves. The result of this approach shows that the dust acoustic waves with linear dependence of wave frequency on the wave number exist only in restricted range of the wave numbers. Only for wave numbers larger than some critical wave number for low frequency modes the frequency can be have approximately a linear dependence on wave number and can be called as dust acoustic wave but the phase velocity of these waves is different from that which can be obtained neglecting the flux balance and depends on grain charge variations which are determined by the balance of fluxes. The presence of plasma fluxes previously neglected is the main typical feature of dusty plasmas. The dispersion relation in the range of small wave numbers is found to be mainly determined by the change of the plasma fluxes and is quite different from that of dust acoustic type, namely it is found to have the same form as the well known dispersion relation for the gravitational instability. This result proves in general way the existence of the collective grain attractions of negatively charged grains for for large distances between them and for any source of ionization. The attraction of grains found from dispersion relation of the dust acoustic branch coincides with that found previously for pair grain interactions using some models for the ionization source. For the existing experiments the effective Jeans length for such attraction is estimated to be about 8 – 10 times larger than the ion Debye length and the effective gravitational constant for the grain attraction is estimated to be several orders of magnitude larger than the usual gravitational constant. The grain attraction at large inter‐grain distances described by the gravitationlike grain instability is considered as the simplest explanation for observed dust cloud clustering, formation of dust structures including the plasma crystals. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Electron density perturbations by electrostatic wavesand their effect on plasma waves in a dusty plasma

Interaction of high-frequency electrostatic waves and a staticelectron density perturbation is considered in a dusty plasmaincluding the effect of dusty charging. The static electrondensity perturbation is created by the low-frequencyponderomotive force in the parameter regime of a dusty plasmawhere the electron Debye length and temperature are much greaterthan the ion Debye length and temperature, respectively. Theelectron momentum damping rate (νe) due to the high-frequencycharging process of the dust grains can be much greateror much smaller than the electron plasma frequency or wavefrequency (ω) under consideration, depending upon theparameters of the dusty plasma.When ω>>νe, the nonlinear high-frequency wave coupledwith the electron density perturbation is described by anonlinear Schrödinger equation, which bears a modulationallyunstable envelope. When ω<<νe, the high-frequencyelectrostatic wave reduces to a dust charge relaxation mode andthe coupled nonlinear wave equation yields a solution of envelopeshocks.

Parametric interaction of electrostatic waves in a dustyplasma

The nonlinear coupling of a low-frequency electron quasi-mode and ahigh-frequency electrostatic wave through a high-frequency electromagneticpump is considered in a dusty plasma, which includes the effect of dustcharging. The electron quasi-mode occurs in a dusty plasma whose electronDebye length and electron temperature are much greater than, respectively,the ion Debye length and the ion temperature. The nonlinear dispersionrelation has a structure that is much simpler than the nonlinear dispersionrelation for the parametric instability in dust-free plasmas. Only a purelygrowing instability can be excited, and the threshold and growth rate areobtained.

Phase transitions of dense systems of charged ‘‘dust’’ grains in plasmas

The behavior of ‘‘dust’’ grains (particulates) in microelectronics process plasmas has been studied using N-body simulations. Grains are assumed to be negatively charged and interact through a screened Coulomb potential Φ(r). The dimensionless parameters κ=a/λ and Γ=Φ(a)/kBT characterize the thermodynamics of the particulate system, where λ is the ion Debye length, a=(3/4πnD)1/3 is the mean intergrain distance, and nD and T are the dust density and temperature. The simulations exhibit a transition between ‘‘fluid’’ and ‘‘solid’’ phases at a critical value Γc that depends on κ and weakly on the system history (i.e., whether it ‘‘melts’’ from an ordered state or ‘‘freezes’’ from a random one).

Computer Simulation and Analysis for the Spherical and Cylindrical Ion-Acoustic Solitons

The behavior of the spherical and cylindrical ion-acoustic solitons are studied by the computer simulation using a fluid model as well as the theoretical analysis. The simulated results agree well with those obtained by approximately solving the modified Boussinesq equation. A small residue of the high or low density is formed for the inward or outward propagation, respectively, after the spherical and cylindrical ion-acoustic solitons propagate. Moreover, the electron plasma and ion-acoustic waves are emitted from the solitons as they propagate inwards or outwards. The amplitude of the soliton such as the ion density does not grow infinitely for the finite ion temperature even when the soliton concentrates at the center. This is because the half width of the maximum amplitude is limitted by the ion Debye length.

Spherical electric probe in a continuum gas

The problem of a spherical electric probe in a continuum gas without chemical reactions is re-examined when the dimensionless probe potential omega p is large and comparable to rho p, the ratio of probe radius to the ion Debye length. An asymptotic scheme for omega p to infinity shows that the ion-sheath region near the probe and the quasi-neutral region further away are separated by a single transition region which must be carefully matched to them. The properties of the transition equation are investigated in some detail, and numerical results are obtained determining the second-order (ion) current to the probe. Universal curves are given for the first- and second-order currents when the electron temperature equals the ion temperature.