Quasi-neutral Approximation Research Articles

Ionization instability by energized electrons in weakly ionized unmagnetized plasmas

A fluid model for an ionization instability in weakly ionized and non magnetized plasmas is presented. The equilibrium state is assumed to exist in a plasma where additional ionizations are produced by an energized electron group Jeb, considered as monoenergetic, with energy exceeding the ionization threshold of the neutral gas. Ionization by thermal electrons and all charge losses are contemplated and the Poisson equation relates the plasma potential fluctuations with electric charge densities. The leading role of elastic collisions between ions and neutral atoms is evidenced and determines the characteristic time and length scales. The instability requires a minimum suprathermal electron current density Jeb within a narrow energy range. According to the magnitude of this current, two different growth modes are possible separated by a bifurcation point. There is aperiodic exponential growth for low wave numbers and an increasing amplitude plasma wave from the bifurcation up to a maximum wave number. This latter feature determines the characteristic length for electric charge fluctuations. The quasineutral approximation recovers the exponential growth modes but fails to predict this maximum wave number for the oscillatory growth rate.

The effect of a space charge on the operation of a high-power semiconductor current interrupter

A theoretical model has been developed that describes operation of a high-power semiconductor current interrupter (SOS diode) with allowance for the space charge formation. According to this model, as well as to the models based on the quasineutral approximation, the process of current breakage in a semiconductor structure of the SOS diode is related to the formation of strong field regions in highly doped parts of the structure. The space charge decreases the role of avalanche multiplication, thus providing for higher switching characteristics of the diode.

Analytic solutions to the Vlasov equations for expanding plasmas.

The renormalization-group approach is applied to derive an exact solution to the self-consistent Vlasov kinetic equations for plasma particles in the quasineutral approximation. The solutions obtained describe three-dimensional adiabatic expansion of a plasma bunch with arbitrary initial velocity distributions of the electrons and ions. The solution found is illustrated by the examples on ion acceleration in a plasma with hot electrons and in a plasma with light impurity ions.

THE VLASOV–POISSON SYSTEM WITH STRONG MAGNETIC FIELD IN QUASINEUTRAL REGIME

Consider the motion of a gas of electrons with a background of ions, subject to the self-consistent electric field and to a constant external magnetic field. As the Debye length and the Larmor radius vanish at the same rate, the asymptotic current density is governed by the 2D1/2 incompressible Euler equation. Establishing limit requires to overcome various difficulties: compactness with respect to the space variable, control of large velocities, oscillations in the time variable. Yet, for particular initial data, the simultaneous gyrokinetic and quasineutral approximation is completely justified.

The influence of a photoinduced volume charge on the weak-radiation-induced interband photoproduction of carriers in semiconductors with impurity recombination centers

Analytical expressions for the average concentrations of photogenerated electrons and holes are obtained outside the framework of the quasineutrality approximation in the case of a strong surface recombination in the presence of a single-level impurity recombination centers. It is shown that the quasineutrality approximation becomes incorrect with decreasing sample size in the direction of irradiation.

Particle dynamics during adiabatic expansion of a plasma bunch

The renormalization-group approach is used to obtain an exact solution to the self-consistent Vlasov kinetic equations for plasma particles in the quasi-neutral approximation. This solution describes the one-dimensional adiabatic expansion of a plasma bunch into a vacuum for arbitrary initial particle velocity distributions. Ion acceleration is studied for two-temperature Maxwellian and super-Gaussian initial electron distributions, which predetermine distinctly different ion spectra. The solution found is used to describe the acceleration of ions of two types. The relative acceleration efficiency of light and heavy ions as a function of atomic weights and number densities is analyzed. The solutions obtained are of practical importance in describing ion acceleration during the interaction of an ultrashort laser pulse with nanoplasma, for example, cluster plasma or plasma produced when thin foils are irradiated by a laser.

The plasma boundary containing fast isotropic electrons: acomparison between kinetic and fluid ion models

The behaviour of a boundary layer containing fast isotropic primaryelectrons has been investigated using a modified Tonks-Langmuir model for theone-dimensional collisionless plasma, both using the full space-charge description and thequasi-neutral approximation. The plasma solutions are compared directly tothose obtained from a fluid model of the same system developed by Schott in 1987(Phys. Fluids 30 1795).In the kinetic ion model a single double-layer structure is observed to formfor all primary electron densities, with a two-stage rise in the boundarypotential approaching the wall. This single double-layer exists at a pointcorresponding to the initiation of oscillatory solutions (periodic doublelayers) in the potential, particle concentrations and space charge in thefluid model. In the quasi-neutral approximation of the kinetic model, forprimary to thermal electron densities above a ratio of about 0.3 thesheath-edge potential jumps from a value close to the voltage equivalent ofthe electron temperature to a value just under the isotropic electron energy.This is in very close agreement with the previously obtained fluidquasi-neutral solutions.

Calculation of one-dimensional plasma flows with allowance for the kinetics of ion collisions

The influence of kinetic effects on the generation of line X radiation during the spherical implosion of a laser corona plasma with two ion species is studied under the conditions prevailing in experiments with thin-wall spherical targets in the Iskra-5 laser facility of the All-Russia Research Institute of Experimental Physics (Sarov, Russia). Kinetic processes occurring in a multicharged plasma are investigated using a specially devised code for solving one-dimensional Landau equations for a nondegenerate multicomponent plasma by the Monte Carlo method (the KIN-MC code). The code was developed using the quasineutral plasma approximation under the assumption that the electron distribution function is locally equilibrium. The model equations are presented, the scheme of numerical solution is described, and the calculated results are discussed.

Ion acceleration during adiabatic plasma expansion: Renormalization group approach

The renormalization group approach is applied to derive an exact solution to self-consistent Vlasov kinetic equations for plasma particles in the quasineutral approximation. The solution obtained describes the one-dimensional adiabatic expansion into vacuum of a plasma bunch with arbitrary initial velocity distributions of the electrons and ions. The ion acceleration is investigated for both a Maxwellian two-temperature initial electron distribution and a super-Gaussian initial electron distribution.

Comment on “Role of quasineutrality in drift waves” [Phys. Plasmas 8, 368 (2001)

The physics of various low-frequency electrostatic and electromagnetic waves in a nonuniform magnetoplasma is revisited. It is shown that the approach of Saleem and Haque [Phys. Plasmas 8, 368 (2001)] is misleading with regard to the electrostatic limit and the role of the quasineutrality approximation.

Role of quasineutrality in drift waves

The ambiguity in using the quasineutrality approximation to describe the low-frequency plasma perturbations in nonuniform magnetized plasmas is pointed out.

Quasi-Current-Free Approximation in the Electrodynamics of a Hot Current-Carrying Collisionless Plasma

To study slow electromagnetic processes of induction type in a hot collisionless nonmagnetized high-beta plasma near magnetic-reconnection regions, where the influence of eddy electric currents on magnetic-field configuration should be described self-consistently, we develop a kinetic description in the quasi-current-free (QCF) approximation, which includes the quasi-neutral approximation. The QCF approximation is valid for large-scale nonstationary processes if the scale of spatial inhomogeneity of the fields exceeds the scale of the diamagnetic current screening, the anomalous skin scale, and the polarization-screening scale. In this case, the diamagnetic currents are compensated by the conductivity currents. The equations of the QCF approximation for accelerated particles with narrow distribution functions are formulated as the MHD equations. To illustrate the method, we consider a one-dimensional problem on magnetic annihilation. The self-similar solution of this problem describes the relaxation of the current system typical for solar streamers and the tail of the Earth's magnetosphere.

The role of nonequilibrium carriers in linear charge transport (Ohm’s law)

The charge transport in a bipolar semiconductor to a metal wire was studied in a linear approximation with respect to the electric field. It is shown that both electrons and holes in general are nonequilibrium carriers in an arbitrarily weak electric field. Therefore, the consideration of surface and bulk recombination is necessary for the correct description of electrical conductivity. The spatial distributions of quasi-Fermi levels for electrons and holes are obtained in the quasi-neutrality approximation, and the general expression for a bipolar semiconductor conductivity is derived. This conductivity depends strongly not only on the transport of electrons and holes but also on the surface-and bulk-recombination rates. The criteria of low and high rates of recombination are determined; it is shown that a commonly used expression for the conductivity of a bipolar semiconductor is valid only at high rates of surface and/or bulk recombination.

Dynamics of plasma bunches in slowly varying external fields

We use the quasineutrality approximation and the method of moments to analyze a system of kinetic equations that describes the expansion into vacuum of a plasma bunch generally containing several species of charged particles. For a two-component collisionless plasma in slowly varying external potential fields, we obtain a complete description of the dynamics of the matrices of centered second moments of the particle velocity distribution functions. We construct a new class of self-similar solutions of the kinetic equations in which the moments of the distribution functions act as parameters. These solutions are found to be valid for any mass and energy ratios of the constituent particles and generally describe the dynamics of a plasma bunch that is asymmetric in space. For a symmetric bunch we also find an analytical solution corresponding to the presence of eddy electric currents in the plasma, while for an asymmetric bunch we find that interparticle collisions, which give rise to anisotropy in the process of expansion of plasma into vacuum, play an important role. The method developed in the paper is used to study the acceleration and compression of a plasma bunch in time-dependent magnetic fields with a mirror configuration.

Exact Solution of Vlasov Equations for Quasineutral Expansion of Plasma Bunch into Vacuum

In the quasineutral approximation an exact self-similar solution of the three-dimensional Vlasov equations for electrons and ions with self-consistent electric field is obtained. This solution is valid for an arbitrary value of electron-to-ion mass ratio, arbitrary relation between electron and ion thermal energies, and for a large variety of electron velocity distribution functions and initial spatial plasma density distribution. The results obtained can be used as a basic model for studying the problem of expansion of an arbitrary two-component plasma.

Exact solution of the problem of quasineutral expansion into vacuum of a localized collisionless plasma with cold ions

An analytical solution of the Vlasov equation for the electrons and the hydrodynamic equations for the ions in a self-consistent electric field is constructed in the quasineutral approximation. This solution is valid for a finite electron-to-ion mass ratio. It permits describing the expansion into vacuum of a collisionless plasma with cold ions and arbitrary initial electron velocity distribution, forming a plasmoid that is bounded and, in the general case, spherically asymmetric in space.

Quasi-neutral Vlasov stability

The Vlasov stability principle of Schindler–Pfirsch–Wobig operates with an implicitly defined functional V(a) = W(a, φ[a]), where W(a, φ) is given explicitly, but φ[a] is the solution of a perturbed Poisson equation that relates the perturbation of the electric potential, φ, to that of the flux function, a. Furthermore, in W the stationary and perturbed quantities are interwoven in a complicated manner. Here, using an operator formalism, we separate stationary and perturbed quantities. Then, in the quasi-neutral approximation, we construct the general solution φqn[a] of the quasi-neutrality condition and arrive at an explicit formula for Vqn(a).

A 3-D Darwin–EM Hybrid PIC Code for Ion Ring Studies

A new, 3-D electromagnetic (EM), hybrid, particle-in-cell (PIC) code, FLAME has been constructed to study low-frequency, large orbit plasmas in realistic cylindrical configurations. The stability and equilibrium of strong ion rings in magnetized plasmas are the first issues suitable for its application. In FLAME the EM-field is governed by Maxwell's equations in the quasi-neutral Darwin approximation (with displacement current neglected), the ion components are represented by discrete macro-particles, and the plasma electrons are modeled as a massless cold fluid. All physical quantities are expanded into finite Fourier series in the azimuthal (θ) direction. The discretization in the poloidal (r,z) plane is done by a finite-difference staggered grid method. The electron fluid equations include a finite scalar resistivity and macro-particles experience slowing-down collisions. A substantial reduction of computation time is achieved by enabling separate time advances of background and beam particle species in the time-averaged fields. FLAME has been optimized to run on parallel, MIMD systems, and has an object-oriented (C++) structure. The results of normal mode tests intended to verify the code ability to correctly model plasma phenomena are presented. We also investigate in 3-D the injection of a powerful annular ion beam into a plasma immersed in a magnetic cusp followed by an axially ramped applied magnetic field. A nonaxisymmetric perturbation is applied to the magnetic field and its effect on ion ring formation is analysed.

Comment on "Modeling of metal electrodeposits: Analytical solutions"

When the equations of ionic motion for electrodeposition in a one-dimensional cell filled with a dilute binary electrolyte are solved under fixed-boundary conditions, a diffusion-limited current, independent of applied potential, is obtained. This result is well expected in the framework of the quasineutrality approximation. In this framework, the assumption by Huang and Hibbert [Phys. Rev. E. 52, 5065 (1995)] of an electrical-migration term in the evolution equation for the concentration is incorrect. However, a term of the same form, though smaller, may appear either from the concentration dependence of the mobilities or from an electro-osmotic effect if the electrolyte is embedded in a gel or a porous medium. \textcopyright{} 1996 The American Physical Society.

Structural properties of the one-dimensional drift-diffusion models for semiconductors

This paper is devoted to the analysis of the one-dimensional current and voltage drift-diffusion models for arbitrary types of semiconductor devices and under the assumption of vanishing generation recombination. We show in the course of this paper, that these models satisfy structural properties, which are due to the particular form of the coupling of the involved systems. These structural properties allow us to prove an existence and uniqueness result for the solutions of the current driven model together with monotonicity properties with respect to the total current I I , of the electron and hole current densities and of the electric field at the contacts. We also prove analytic dependence of the solutions on I I . These results allow us to establish several qualitative properties of the current voltage characteristic. In particular, we give the nature of the (possible) bifurcation points of this curve, we show that the voltage function is an analytic function of the total current and we characterize the asymptotic behavior of the currents for large voltages. As a consequence, we show that the currents never saturate as the voltage goes to ± ∞ \pm \infty , contrary to what was predicted by numerical simulations by M. S. Mock (Compel. 1 (1982), pp. 165–174). We also analyze the drift-diffusion models under the assumption of quasi-neutral approximation. We show, in particular, that the reduced current driven model has at most one solution, but that it does not always have a solution. Then, we compare the full and the reduced voltage driven models and we show that, in general, the quasi-neutral approximation is not accurate for large voltages, even if no saturation phenomenon occurs. Finally, we prove a local existence and uniqueness result for the current driven model in the case of small generation recombination terms.