Self-consistent Electric Field Research Articles

Ion dynamics in a magnetized source-collector sheath

A bounded plasma is simulated with a spatially generated source in the presence of an oblique magnetic field. The kinetic particle-in-cell technique has been used to track particles fully kinetically. The plasma facing the surface is considered to be an absorbent for the charged particles. The plasma flow is assumed to be normal with respect to the surface and primarily controlled by the self-consistent internal electric field. The ions are observed to follow interesting dynamical behavior near the collector sheath. The low energetic ions reflect back to the ion source region at certain angles of inclination. The reflection seems to be prominent at a low angle of inclination. The interaction of the magnetic field with the surface in a divertor like scenario of a tokamak is typically at a low angle (∼5°). Even the surface of a space station may be tilted with respect to the earth's magnetic field. The observations made in this paper will find a significant impact in these configurations.

Experimental and numerical study of a dust cloud formation in the stratified positive column of a dc glow discharge in helium

The experimental and theoretical investigations of the formation of dust particle clouds in the stratified positive column of a dc glow discharge in helium were performed. The size and shape of a dust cloud that levitated in the strong electric field of the striations in a vertically oriented discharge tube were measured under different helium pressures. Axial electric field strength was also experimentally estimated. A model for radial distributions of all dusty plasma parameters of the positive column of the dc glow discharge was developed to describe the obtained experimental results. The model is based on the solution of a non-local Boltzmann equation for an electron energy distribution function, drift-diffusion equations for ions and dust particles, and a Poisson equation for a self-consistent radial electric field. The experimental and calculated results show that the size of the dust cloud decreases with the increase in the gas pressure, and the axial electric field strength pressure dependencies have minima. At low gas pressures, the dust particle charge number density increases and exceeds the electron density that strongly influences the plasma parameters.

Interfacial mixing in high-energy-density matter with a multiphysics kinetic model.

We have extended a recently developed multispecies, multitemperature Bhatnagar-Gross-Krook model [Haack et al., J. Stat. Phys. 168, 822 (2017)JSTPBS0022-471510.1007/s10955-017-1824-9], to include multiphysics capabilities that enable modeling of a wider range of physical conditions. In terms of geometry, we have extended from the spatially homogeneous setting to one spatial dimension. In terms of the physics, we have included an atomic ionization model, accurate collision physics across coupling regimes, self-consistent electric fields, and degeneracy in the electronic screening. We apply the model to a warm dense matter scenario in which the ablator-fuel interface of an inertial confinement fusion target is heated, but for larger length and time scales and for much higher temperatures than can be simulated using molecular dynamics. Relative to molecular dynamics, the kinetic model greatly extends the temperature regime and the spatiotemporal scales over which we are able to model. In our numerical results we observe hydrogen from the ablator material jetting into the fuel during the early stages of the implosion and compare the relative size of various diffusion components (Fickean diffusion, electrodiffusion, and barodiffusion) that drive this process. We also examine kinetic effects, such as anisotropic distributions and velocity separation, in order to determine when this problem can be described with a hydrodynamic model.

On the Lagrangian structure of transport equations: The Vlasov–Poisson system

The Vlasov-Poisson system is a classical model in physics used to describe the evolution of particles under their self-consistent electric or gravitational field. The existence of classical solutions is limited to dimensions $d\leq 3$ under strong assumptions on the initial data, while weak solutions are known to exist under milder conditions. However, in the setting of weak solutions it is unclear whether the Eulerian description provided by the equation physically corresponds to a Lagrangian evolution of the particles. In this paper we develop several general tools concerning the Lagrangian structure of transport equations with non-smooth vector fields and we apply these results: (1) to show that weak solutions of Vlasov-Poisson are Lagrangian; (2) to obtain global existence of weak solutions under minimal assumptions on the initial data.

Numerical experiments on charging of a spherical body in a plasma with Maxwellian distributions of charged particles

New results of numerical simulation of collisionless plasma perturbation caused by a sphere absorbing electrons and ions are presented. Consideration is given to nonstationary phenomena accompanying the process of charging as well as to plasma steady state reached at long times. Corresponding asymptotic values of charges of the sphere and trapped-ion cloud around it have been found along with self-consistent electric field pattern depending on parameters of the unperturbed plasma. It is established that contribution of the trapped ions to screening of the charged sphere can be quite significant, so that the screening becomes essentially nonlinear in nature. A simple interconnection between the sphere radius, electron and ion Debye lengths has been revealed as the condition for maximum trapped-ion effect. Kinetic structure of the space charge induced in the plasma is discussed with relation to the specific form of the unperturbed charged particle distribution functions.

Screening in a multicomponent plasma by the example of a wet air plasma

A general theory of screening of a dust-particle charge in a multicomponent plasma is developed based on the asymptotic screening theory. In the asymptotic theory, the balance equations for the number of charged plasma particles in the diffusion-drift approximation supplemented with point sinks of plasma particles on a dust particle and the Poisson equation for the self-consistent electric field potential are solved by the linearization method using the three-dimensional Fourier transform. The coefficients of a secular or a characteristic polynomial, whose zeroes determine screening constants in a multicomponent plasma, were calculated by the Leverrier–Faddeev method, allowing one to find these coefficients for any number of initial balance equations for the number of charged plasma particles. By the example of a wet air plasma produced by an external gas-ionization source, the procedure is considered for constructing the truncated system of balance equations for main plasma ions and screening constants are determined. The influence of the number of main ions on screening constants is considered and the physical meaning of all screening constants is found.

Plasma-wall interactions in the presence of plasma fluctuations—interpretation of line emission from sputtered tungsten in PSI-2

The analysis in this work essentially addresses the general question to what extent the temporal average of a particular quantity which is a highly nonlinear function of fluctuating quantities can be approximated by using the averages of the fluctuating quantities for its evaluation. The concrete case considered is the line emission intensity from sputtered impurities being a function of fluctuating electron density and temperature in a plasma beam of the PSI-2 device. A three-dimensional fluid model is employed to study the impact of plasma fluctuations on the distribution of particles and line emission in PSI-2 discharges and its interpretation in long-term measurements. In the model presented the solution of a vorticity equation to obtain a self-consistent electric field is avoided and a synthetic turbulent velocity field is included instead. This approach is based on a Langevin model including advection and allows numerically efficient parameter scans by controlling amplitude, correlation length and correlation time of plasma fluctuations known from extended 3D simulations and/or experiment. The synthetic turbulence model considered is an extension of established stochastic models used for studies of passive scalar advection and therefore, it is described in detail in a general framework. Numerical examples of PSI-2 applications show that a double log-normal probability density function for the electrons and impurity ions is likely to occur and that this supports the conclusion that very high levels of intermittency are required to find a significant impact on the experimental evaluation method which is based on temporal averages only. Consequently, for typical PSI-2 experiments the method of evaluation based on averaged plasma parameters is justified.

Kinetic approach to condensation: Diatomic gases with dipolar molecules.

We derive a kinetic equation for rarefied diatomic gases whose molecules have a permanent dipole moment. Estimating typical parameters of such gases, we show that quantum effects cannot be neglected when describing the rotation of molecules, which we thus approximate by quantum rotators. The intermolecular potential is assumed to involve an unspecified short-range repulsive component and a long-range dipole-dipole Coulomb interaction. In the kinetic equation derived, the former and the latter give rise, respectively, to the collision integral and a self-consistent electric field generated collectively by the dipoles (as in the Vlasov model of plasma). It turns out that the characteristic period of the molecules' rotation is much shorter than the time scale of the collective electric force and the latter is much shorter than the time scale of the collision integral, which allows us to average the kinetic equation over rotation. In the averaged model, collisions and interaction with the collective field affect only those rotational levels of the molecules that satisfy certain conditions of synchronism. It is then shown that the derived model does not describe condensation; i.e., permanent dipoles of molecules cannot exert the level of intermolecular attraction necessary for condensation. It is argued that an adequate model of condensation must include the temporary dipoles that molecules induce on each other during interaction, and that this model must be quantum, not classical.

Gyrofluid Model of Plasma Expansion in a Diverging Magnetic Field

The gyrofluid equations for electrons and for ions are used to model the acceleration of plasma from a source region of high magnetic field to a region of lower field. The model includes a source term for plasma generation, a self-consistent electric field, nonzero ion temperature, plasma acceleration by the mirror force, and the reduction in density from the diverging flow. The model is applicable to plasma experiments with helicon sources, ion engines for spacecraft, and some plasma processing configurations. The ion flux from the source region is found to be approximately the Bohm flux and the downstream ion flux density scales with the magnetic field. The downstream flow is determined by the conversion of upstream thermal energy in both electrons and ions into kinetic energy in flow speed. For large expansion ratios, the final speed approaches 1.5 times the ion sound speed.

Density inhomogeneities and Rashba spin-orbit coupling interplay in oxide interfaces

There is steadily increasing evidence that the two-dimensional electron gas (2DEG) formed at the interface of some insulating oxides like LaAlO3/SrTiO3 and LaTiO3/SrTiO3 is strongly inhomogeneous. The inhomogeneous distribution of electron density is accompanied by an inhomogeneous distribution of the (self-consistent) electric field confining the electrons at the interface. In turn this inhomogeneous transverse electric field induces an inhomogeneous Rashba spin-orbit coupling (RSOC). After an introductory summary on two mechanisms possibly giving rise to an electronic phase separation accounting for the above inhomogeneity, we introduce a phenomenological model to describe the density-dependent RSOC and its consequences. Besides being itself a possible source of inhomogeneity or charge-density waves, the density-dependent RSOC gives rise to interesting physical effects like the occurrence of inhomogeneous spin-current distributions and inhomogeneous quantum-Hall states with chiral “edge” states taking place in the bulk of the 2DEG. The inhomogeneous RSOC can also be exploited for spintronic devices since it can be used to produce a disorder-robust spin Hall effect.

Dynamics of a charged gas suspension with an initial spatially nonuniform distribution of the average dispersed phase density during the transition to the equilibrium state

Results of calculations are presented for the transition of a charged gas suspension from the initial nonequilibrium state with a spatially nonuniform distribution of the average density to a state with a uniform distribution of the average density and charge in a bounded volume. A numerical solution is obtained for the system of equations describing the motion of a polydisperse multirate and multitemperature gas suspension, the particles of which carry an electric discharge and create a self-consistent electric field.

Asymptotic stability of the rarefaction wave for the compressible quantum Navier–Stokes–Poisson equations

In this study, we consider the large time behavior of the solution to the one-dimensional isentropic compressible quantum Navier–Stokes–Poisson equations. The system describes a compressible particle fluid under quantum effects with the potential function of the self-consistent electric field. We show that if the initial data are close to a constant state with asymptotic values at far fields selected such that the Riemann problem on the corresponding Euler system admits a rarefaction wave with a strength that is not necessarily small, then the solution exists for all time and it tends to the rarefaction wave as t→+∞. The proof is based on the energy method by considering the effect of the self-consistent electric field and quantum potential in the viscous compressible fluid. In addition, we compare the quantum compressible Navier–Stokes–Poisson equations and the corresponding compressible Navier–Stokes–Poisson equations based on the large-time behavior of these two classes of models.

The exact solution of one-dimensional nonrelativistic Vlasov equation: Antitropic electron beams and Landau damping

The exact stationary solution of one-dimensional non-relativistic Vlasov equation is obtained in the article. It is shown that in the energy exchange with the self-consistent longitudinal electric field, both wave trapped charged particles and the passing ones take part. It is proved that the trapped electron distribution is fundamentally different from distribution functions described by other authors, which used the Bernstein, Greene, and Kruskal method. So, the correct distribution function is characterized by its sudden change at the equality of wave and electrons' velocity but not on the edges of the potential well. This jump occurs for any arbitrary small value of wave potential. It was also found that the energy density of fast electrons trapped by the wave is less than the energy density of slow trapped electrons. This leads to the fact that the energy of the self-consistent electric field may both increase and decrease due to the nonlinear Landau damping. The conditions under which a similar effect can be observed are defined. Also for the first time, it is shown that the self-generated strong electric field always produces antitropic electron beams.

Analysis of the Transmission “Window” Formation in the Electrooptical Switch of Laser Pulses With Plasma Electrodes

A process of plasma electrodes and optical transmission “window” formation in electrooptical switch (Pockels cell) of high-power laser radiation pulses is studied experimentally and analyzed numerically. A 2-D computer model of a gas discharge, forming the electrodes and allowing for the charged particles transport and reactions kinetics in self-consistent electric field is developed. A time dependence of the optical transmission in various points of the cross section of the cell operating in the two-pulse mode is computed. In the cell center, the calculated dependence is consistent with the optical transmission oscilloscope trace.

Vertical stratification of excited molecules by self-consistent electric field in the lower stratosphere

Vertical stratification of excited molecules by self-consistent electric field in the lower stratosphere

Peculiarities of the formation of a thin current sheet in the Earth’s magnetosphere

We investigate the process of the self-consistent formation of a thin current sheet with a thickness close to the ion Larmor gyroradius in the presence of decreasing magnetic field’s normal component B n . This behavior is typical of the current sheet of the Earth’s magnetospheric tail during geomagnetic substorms. It has been shown that, in a numerical model of the current sheet, based on the particle-in-cell method, the appearance of self-consistent electric field component E y in the current sheet vicinity can lead to its significant thinning and, eventually, to the formation of a multiscale configuration with a thin current sheet (TCS) in the central region supported by transient particles. The structure of the resulting equilibrium is determined by the initial parameters of the model and by the particle dynamics during the sheet thinning. Under certain conditions, the particle drift in the crossed electric and magnetic fields leads to a significant portion of ions becoming trapped near the neutral sheet and, in this way, to the formation of a wider configuration with an embedded thin current sheet. The population of trapped particles produces diamagnetic negative currents that manifest in the form of negative wings at the periphery of the sheet. Correspondingly, in the direction perpendicular to the sheet, a nonmonotonic coordinate dependence of the magnetic field appears. The mechanisms of the evolution of the current sheet in the Earth’s magnetotail and the formation of a multiscale structure are discussed.

Effects of relativistic electrons and spatial non-uniformities of density on periodic absolute parametric instability in a plasma waveguide

The effects of relativistic electrons and spatial plasma nonuniformity of density on periodic absolute parametric instability (API) of electrostatic waves in a relativistic 1−D nonuniform magnetoactive plasma are investigated in a cylindrical geometry. We use the separation method to solve the two-fluid plasma equations, which describe the system. The method used enables us to determine the frequencies and growth rates of unstable modes and the self-consistent electric field. Plasma electrons are considered to have a relativistic velocity. Increment has found in the buildup of the oscillations, and it is shown that the spatial nonuniformity of the plasma exerts a stabilizing effect on the parametric instability. It is shown that the growth rate of the API in relativistic plasma is reduced compared to nonrelativistic plasma. Independent of the geometry of the problem (plane and cylinder), the results of the API in a relativistic plasma waveguide are still valid.The proposal approach (Ȝseparation methodȝ) is significantly simpler that the method ordinarily employed in the theory of parametric resonance in nonuniform plasma. Therefore, it is of special interest to apply the separation method to solution of different problems involving parametric excitation of electrostatic waves in bounded nonuniform plasma.

Steady states of a diode with counterstreaming electron and positron beams

Steady states of a plasma layer with counterstreaming beams of oppositely charged particles moving without collisions in a self-consistent electric field are analyzed. The study is aimed at clarifying the mechanism of generation and reconstruction of pulsar radiation. Such a layer also models the processes occurring in Knudsen plasma diodes with counterstreaming electron and ion beams. The steady-state solutions are exhaustively classified. The existence of several solutions at the same external parameters is established.

Soliton-induced electric currents in plasma

This is a theoretical study of the nonequilibrium motion of charged particles in an electric field of solitons. We show that the self-consistent electric field of ion-acoustic and electron-acoustic solitons is characterized by one-way transfer of charged particles at a distance of several Debye radii. The dependence of relevant local currents on the amplitude of solitons is determined. We consider the practically important case of a moving cascade consisting of many solitons and show that the induced currents have a significant constant component. The kinetic energy acquired by charged particles in the soliton field is calculated. The temporal resolution required for the recording of soliton-induced currents is estimated. The calculations presented here can be used to interpret the results of experiments conducted to study solitons in the space plasma.

The stability of stationary solution for outflow problem on the navier-stokes-poisson system

In this article, we are concerned with the stability of stationary solution for outflow problem on the Navier-Stokes-Poisson system. We obtain the unique existence and the asymptotic stability of stationary solution. Moreover, the convergence rate of solution towards stationary solution is obtained. Precisely, if an initial perturbation decays with the algebraic or the exponential rate in space, the solution converges to the corresponding stationary solution as time tends to infinity with the algebraic or the exponential rate in time. The proof is based on the weighted energy method by taking into account the effect of the self-consistent electric field on the viscous compressible fluid.