Effect of a dust component on the rates of elementary processes in low-temperature plasmas

Elementary processes in dusty, beam-driven plasma discharges are studied experimentally and theoretically for the first time. A theoretical model is constructed for a beam-driven plasma containing macroscopic particles. The effect of macroscopic particles on the electron energy distribution function is estimated assuming a Coulomb field for the particles. The resulting rate of electron-ion recombination on the macroscopic particles is compared with the electron loss constant calculated from the electron energy distribution function with an electron absorption constant in the orbital-motion approximation. This approximation, which is valid in the collisionless case, is found to work satisfactorily beyond its range of applicability. The distributions of the charged particles and electric fields created by macroscopic particles in a helium plasma are determined. The experimental data demonstrate the importance of secondary emission by high-energy electrons. Zh. éksp. Teor. Fiz. 115, 2020–2036 (June 1999)     

A stochastic model for the dynamics of a classical spin

A stochastic model for the dynamics of a macroscopic or classical spin based on a classical generalized Lagrangian formalism is proposed. The model can be used to describe the evolution of the magnetic moment of superparamagnetic particles. In this sense, it is a generalization of the model proposed by Brown, allowing for fluctuations on the magnitudes of the magnetic moments of the particles. The corresponding covariant Fokker-Planck equation is also obtained.     

Changes in the Effective Parameters of Averaged Motion in Nonlinear Systems Subject to Noise

We discuss how the effective parameters characterising averaged motion in nonlinear systems are affected by noise (random fluctuations). In this approach to stochastic dynamics, the stochastic system is replaced by its deterministic equivalent but with noise-dependent parameters. We show that it can help to resolve certain paradoxes and that it has a utility extending far beyond its usual application in passing from the microscopic equations of motion to the macroscopic ones. As illustrative examples, we consider the diode-capacitor circuit, a Brownian ratchet, and a generic stochastic resonance system. In the latter two cases we calculate for the first time their effective parameters of averaged motion as functions of noise intensity. We speculate that many other stochastic problems can be treated in a similar way. PACS: 05.10.Gg, 05.40.-a, 05.40.Jc     

Anomalous kinetic energy of a system of dust particles in a gas discharge plasma

The system of equations of motion of dust particles in a near-electrode layer of a gas discharge has been formulated taking into account fluctuations of the charge of a dust particle and the features of the nearelectrode layer of the discharge. The molecular dynamics simulation of the system of dust particles has been carried out. Performing a theoretical analysis of the simulation results, a mechanism of increasing the average kinetic energy of dust particles in the gas discharge plasma has been proposed. According to this mechanism, the heating of the vertical oscillations of dust particles is initiated by induced oscillations generated by fluctuations of the charge of dust particles, and the energy transfer from vertical to horizontal oscillations can be based on the parametric resonance phenomenon. The combination of the parametric and induced resonances makes it possible to explain an anomalously high kinetic energy of dust particles. The estimate of the frequency, amplitude, and kinetic energy of dust particles are close to the respective experimental values.     

Charge Fluctuations in Finite Coulomb Systems

When described in a grand canonical ensemble, a finite Coulomb system exhibits charge fluctuations. These fluctuations are studied in the case of a classical (i.e., non-quantum) system with no macroscopic average charge. Assuming the validity of macroscopic electrostatics gives, on a three-dimensional finite large conductor of volume V, a mean square charge Q ² which goes as V ^1/3. More generally, in a short-circuited capacitor of capacitance C, made of two conductors, the mean square charge on one conductor is Q ²=TC, where T is the temperature and C the capacitance of the capacitor. The case of only one conductor in a grand canonical ensemble is obtained by removing the other conductor to infinity. The general formula is checked in the weak-coupling (Debye–Hückel) limit for a spherical capacitor. For two-dimensional Coulomb systems (with logarithmic interactions), there are exactly solvable models which reveal that, in some cases, macroscopic electrostatics is not applicable even for large conductors. This is when the charge fluctuations involve only a small number of particles. The mean square charge on one two-dimensional system alone, in the grand canonical ensemble, is expected to be, at most, one squared elementary charge.     

Stochastic simulation of variations in the autoignition delay time of premixed methane and air

A mesoscopic stochastic particle model for homogeneous combustion is introduced. The model can be used to investigate the physical fluctuations in a system of coupled chemical reactions with energy (heat) release/consumption. In the mesoscopic model, the size of the homogeneous gas volume is an additional variable, which is eliminated in macroscopic continuum models by the thermodynamic limit N→∞. Thus, continuous homogeneous models are macroscopic models wherein fluctuations are excluded by definition. Fluctuations are known to be of particular importance for systems close to the autoignition limits. The new model is used to investigate the stochastic properties of the autoignition delay time in a homogeneous system with stoichiometric premixed methane and air. Temperature and species concentrations during autoignition of sub-macroscopic volumes, including physically meaningful fluctuations, are presented. It is found that different realizations mainly differ in the time when ignition occurs; besides this the development is similar. The mesoscopic range and the macroscopic limit are identified. Which range a specific system is assigned to is not only a question of the length scale or particle number, but also depends on the complete thermodynamic state. The stochastic algorithm yields the correct results for the macroscopic limit compared to the continuous balance equations. The sensitivity of the results to two different detailed reaction mechanisms (for the same system) is studied and found to be low. We show that when approaching the autoignition limit by decreasing the temperature, the fluctuations in the autoignition delay time increase and an increasing number of realizations will have exceedingly long ignition delay times, meaning they are in practice not autoignitable. With this result the mesoscopic simulations offer an explanation of the transition between autoignitable and non-autoignitable conditions. The calculated distributions were compared with ten repetitions of the same experiment. A mesoscopic distribution that matches the experimental results was found.     

A particle-in-cell simulation of dust charging and shielding in lowpressure glow discharges

The transport of particles (“dust”) in low pressure electrical glow discharges is being studied in regard to its role in contaminating silicon wafers during plasma etching and deposition. Particles (10 s nm-μm) negatively charge in glow discharges and, to first order, appear to be massively large negative ions around which sheaths develop. The forces on particles in plasmas include electrostatic (drift of charged particles in electric fields) and viscous ion drag. The latter force is momentum transfer from ions to particles by either collisions or orbital motion. This force critically depends on the charge on the particle and the shape of the sheath surrounding the particle. In this work, we report on a pseudoparticle-in-cell (PIC) simulation of the transport of electrons and ions in the vicinity of dust particles in low pressure glow discharges. The simulation produces the electrical charge on the dust particle, the sheath structure around the dust particle and the orbital dynamics of the ions. A companion molecular dynamics simulation uses these parameters to produce ion-dust and electron-dust particle cross sections for momentum transfer and collection. Results will be discussed for charge, sheath thickness, cross sections and viscous ion drag forces on dust particles as a function of radius and plasma parameters     

Dynamics of neutralized charged particle beams in external magnetic and self fields

The dynamics of charged particle beams under the influence of their self-magnetic field and an external magnetic field is examined on the basis of equations for the trajectory of a boundary particle. A study is made of the change in the dynamics of fast particles due to the influence of the electric field of the partially neutralized space charge of the beam, the stationary electric field, and the field of the oscillations in the quasineutral beam plasma. Changes in the total beam energy caused by the self-electric field and in the longitudinal velocity owing to the self-magnetic field are taken into account. Zh. Tekh. Fiz. 68, 106–109 (August 1998)     

Diffusive Hydrodynamic Limits for Systems of Interacting Diffusions with Finite Range Random Interaction

We consider a system of interacting diffusive particles with finite range random interaction. The variables can be interpreted as charges at sites indexed by a periodic multidimensional lattice. The equilibrium states of the system are canonical Gibbs measures with finite range random interaction. Under the diffusive scaling of lattice spacing and time, we derive a deterministic nonlinear diffusion equation for the time evolution of the macroscopic charge density. This limit is almost sure with respect to the random environment. Received: 3 October 1996 / Accepted: 13 February 1997     

Fluctuations of the charge on a dust grain in a plasma

A dust grain in a plasma acquires an electric charge by collecting electron and ion currents. These currents consist of discrete charges, causing the charge to fluctuate around an equilibrium value 〈Q〉. Electrons and ions are collected at random intervals and in a random sequence, with probabilities that depend on the grain's potential. We developed a model for these probabilities and implemented it in a numerical simulation of the collection of individual ions and electrons, yielding a time series Q(t) for the grain's charge. Electron emission from the grain is not included, although it could be added easily to our method. We obtained the power spectrum and the RMS fluctuation level, as well as the distribution function of the charge. Most of the power in the spectrum lies at frequencies much lower than 1/τ, the inverse charging time. The RMS fractional fluctuation level varies as 0.5 |〈N〉|^-1/2, where 〈N〉=〈Q〉/e is the average number of electron charges on the grain. This inverse square-root scaling means that fluctuations are most important for small grains. We also show that very small grains can experience fluctuations to neutral and positive polarities, even in the absence of electron emission     

Specifications of dust-ion-acoustic shock waves affected by dust charge variation in four-component dissipative quantum plasma

ABSTRACT

Nonlinear propagation of dust-ion-acoustic shock waves in an unmagnetized, collisionless four-component quantum plasma containing electrons, positrons, ions and negatively charged dust grains affected by dust charge variations and viscosity of ions is studied using quantum hydrodynamic model. Considering dust charge variation give rise to calculating of charging currents of the plasma particles. These currents have been calculated with orbit limited motion theory and using Fermi-distribution functions or Boltzmann–Maxwell distribution depending on quantum or classical particles, respectively. The basic characteristics of quantum dust-ion-acoustic shock waves are investigated by deriving Korteweg–de Vries–Burgers equation under the reductive perturbation method. Depending on the relative values of the dispersive and dissipative coefficients, oscillatory and monotonic shock waves can propagate in the plasma model. The effect of chemical potential and density of dust particles on the shock wave’s height and thickness is investigated. In addition, the critical value of H (H_c) is calculated and it is shown that for R?>?0 compressive shock waves and for R?<?0 rarefactive ones can exist. The present study is applicable to researchers on quantum nonlinear structures in dense astrophysical objects and ultra-small micro- and nano-electronic devices.     

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically T _g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T _g/T). The glass cross-over temperature T_g related to correlations among solitons is equal to the average energy barrier and scales like T _g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap. Received 12 December 2001     

Statistical models for spatial patterns of heavy particles in turbulence

The dynamics of heavy particles suspended in turbulent flows is of fundamental importance for a wide range of questions in astrophysics, atmospheric physics, oceanography, and technology. Laboratory experiments and numerical simulations have demonstrated that heavy particles respond in intricate ways to turbulent fluctuations of the carrying fluid: non-interacting particles may cluster together and form spatial patterns even though the fluid is incompressible, and the relative speeds of nearby particles can fluctuate strongly. Both phenomena depend sensitively on the parameters of the system. This parameter dependence is difficult to model from first principles since turbulence plays an essential role. Laboratory experiments are also very difficult, precisely since they must refer to a turbulent environment. But in recent years it has become clear that important aspects of the dynamics of heavy particles in turbulence can be understood in terms of statistical models where the turbulent fluctuations are approximated by Gaussian random functions with appropriate correlation functions. In this review, we summarise how such statistical-model calculations have led to a detailed understanding of the factors that determine heavy-particle dynamics in turbulence. We concentrate on spatial clustering of heavy particles in turbulence. This is an important question because spatial clustering affects the collision rate between the particles and thus the long-term fate of the system.     

Two-dimensional mesoscopic dusty plasma clusters: Structure and phase transitions

A two-dimensional mesoscopic cluster of “dusty plasma” particles, which can be interpreted as a system of microparticles in an rf gas discharge, is investigated. The ground-state configurations and corresponding eigenfrequencies and eigenvectors are found for clusters of N=22–40 particles in a harmonic confining potential. It is shown that a change in the Debye screening length R of the particle charge in the plasma can cause structural transformations of the ground state of the system, manifested as first-order or second-order phase transitions with respect to the parameter R. The disorder (“melting”) of the clusters is analyzed in detail by Monte Carlo simulation and molecular dynamics. By varying the characteristic range of particle interaction in a cluster, it is possible to modulate its thermodynamic properties and the character of the phase transitions, thereby causing a controlled transition of the system into the fully ordered, orientationally disordered, or fully disordered state. The possibility of dusty plasma clusters coexisting in different states is discussed. Zh. éksp. Teor. Fiz. 116, 1300–1312 (October 1999)     

A full wave model of high-harmonic EMIC wave propagation in sheared magnetic fields

ABSTRACT

A new dispersion relation, with finite Larmor orbit effects, for oblique propagating electromagnetic ion cyclotron (EMIC) waves in a magnetized plasma medium, is derived including the magnetic shear effect. The approximate, yet accurate, dispersion relation is used to implement the ray tracing model. A parabolic magnetic field is considered to model the geomagnetic field in the magnetosphere. Energetic protons are also considered as resonant particles. The propagation characteristics of EMIC waves in the vicinity of the ion cyclotron resonances are investigated in some detail. The results reveal adiabatic oscillating motion for wave and magnetic field fluctuations where high harmonics limit the wave damping and confines the magnetic fluctuations. For inward propagating EMIC waves we find (1) turning points which depend on the wave launch position, and (2) wave trapped areas playing a role in quasi-coherent wave-particle interaction in agreement with the observational and theoretical studies. This wave trapping is an effective process for particle acceleration in the context of space plasmas.     

Random resistor network model of minimal conductivity in graphene

Transport in undoped graphene is related to percolating current patterns in the networks of n- and p-type regions reflecting the strong bipolar charge density fluctuations. Finite transparency of the p-n junctions is vital in establishing the macroscopic conductivity. We propose a random resistor network model to analyze scaling dependencies of the conductance on the doping and disorder, the quantum magnetoresistance and the corresponding dephasing rate.     

Jeans-Buneman instability in a dusty plasma

A self consistent formulation of the Jeans instability of a dusty plasma with proper inclusion of charge dynamics is described. It is shown that charge fluctuations significantly affect the Jeans as well as the Buneman mode. For plasma particles (electrons and ions) in local thermal equilibrium, the Jeans lengthλ _J is given byλ _J≈λ _g F(R, ε, β/η), whereλ _g is the Debye length of the charged grains,R is the square of the ratio of the Jeans to the plasma frequency of the grains,ε is the square of the ratio of the Debye length of the grains and the plasma particles andβ/η is the ratio of the attachment to the decay frequency of the electronic charges to the grain surface. The functional form ofF is given in the text. Numerical investigation of the Jeans-Buneman mode for a two and three component plasma shows that the Jeans mode dominates atkλ _D≪1 (wherek is the wave number andλ _D is the Debye length of plasma particles), whereas atkλ _D≫1 only the Buneman mode operates. Charge fluctuations reduce the area of overlap of the two modes. Furthermore, in the absence of gravity, there exists a new, charge fluctuation induced unstable mode in a streaming dusty plasma. Astrophysical applications of the results are discussed.