Assumption Of Quasi-neutrality Research Articles

Sheath thickness evaluation for collisionless or weakly collisional bounded plasmas

The widely used Child-Langmuir law for sheath thickness evaluation in semi-infinite collisionless plasmas makes the assumptions of quasi-neutrality (n/sub e/=n/sub i/) and zero electric field intensity E=0 at the sheath edge, as well as applying the Bohm criterion for ions entering the sheath. However, through a whole region fluid model, Poisson's equation has been solved numerically for the steady-state solution through the sheath and presheath without these assumptions. With the sheath edge defined, as in the Child-Langmuir law, at the place where the ion velocity is equal to the Bohm velocity, the sheath thickness of a bounded collisionless or weakly collisional plasma has been found with this model in some cases to be much larger than that obtained with the Child-Langmuir Law. The sheath thickness discrepancy is significant under conditions found in low pressure high density plasma (HDP) tools for plasma processing. Results presented indicate that the sheath thickness is very sensitive to the electric field and space charge density at the sheath edge. The electric field and space charge density can be successfully estimated by an intermediate scale matching method, and are used to derive a modified expression for the potential in the sheath that can be solved numerically for sheath thickness. With these results, the matching problem, arising when sheath and plasma are modeled separately, can be overcome.

Low frequency oscillations in a stationary plasma thruster

Stationary plasma thrusters are ion thrusters whose properties make them especially suitable for satellite station keeping or orbit transfer. In these thrusters, a magnetic field transverse to the electron flow towards the anode increases the electron collision frequency and makes possible the generation of a plasma at relatively low gas flow and gas density. The decrease of the plasma conductivity due to the magnetic field induces a large electric field in the plasma which accelerates the quasicollisionless ions whose trajectories are not significantly affected by the magnetic field. The purpose of this article is to clarify, using results from a simple model, the electrical properties of these thrusters and the low frequency oscillation regime which has been observed experimentally. The model is based on the assumption of quasineutrality of the plasma column and on a 1D transient hybrid treatment of electron and ion transport in the device. Electrons are considered as a fluid and ions are described with a collisionless kinetic equation. This model provides reasonable estimates of the plasma properties and is able to give a clear picture of the low frequency oscillations, qualitatively close to the experimental observations.

Expansion of a dusty plasma into a vacuum: effects of charge nonneutrality

The nonlinear expansion of a dusty plasma into a vacuum region investigated without imposing a quasi-neutrality assumption. The nonlinear expansion is obtained using numerical methods. Electrons and positive ions are found to initially escape into the vacuum region creating an electric field that accelerates a small group of massive dust particles into the vacuum ahead of the dust expansion.

Quasineutrality in semiconductors

A general analysis of the semiconductor transport equations is performed in order to establish under which conditions the often used, but rarely verified, quasineutrality assumption of negligible space charge in the so-called ‘‘neutral regions’’ in a semiconductor holds. The small-signal deviation from exact neutrality is calculated for all four nonequilibrium states, that is, injection, accumulation, extraction and exclusion, for one-dimensional current flow in a semi-infinite homogeneous semiconductor. It is shown how the deviation from neutrality depends on the material parameters. Contrary to injection and exclusion, the small-signal deviation from neutrality for accumulation and extraction depends strongly on the current density. A range of current densities for which quasineutrality holds is given. Significant new results are obtained for the intermediate- and large-signal regime. For high-level injection and accumulation in n-type material, quasineutrality is shown to hold whenever small-signal quasineutrality holds at the same material parameters and current density. For high-level extraction, the deviation from neutrality is found to increase compared to the small-signal case. The corresponding current density range for which quasineutrality holds is given. The high-level exclusion case is still an open issue.

A fluid model of the edge plasma in low-temperature discharges containing beam electrons

The influence of mono-energetic beam electrons on the behaviour of a plane plasma boundary is investigated assuming that the ion, electron and beam electron components in the pre-sheath act as three coupled fluids. The sheath edge is identified by the singularity in the electric field appearing under the quasi-neutral assumption, and the Bohm criterion is solved for a range of beam and plasma parameters. Collisions between the plasma particles and the neutral species are considered in a regime in which Coulomb interactions are unimportant. The plasma is generated by beam and thermal electron impact ionization of the neutral gas. Under collision-free conditions, sheath-edge potentials and ion energies are found to increase with the ratio of beam to thermal electron density, up to a critical ratio of about 0.3, above which no sheath edge is predicted to exist. Ion - neutral species collisions further raise the Bohm speed; however, the attenuation of the electron beam through scattering and ionization does not appreciably alter the sheath-edge conditions, but changes the width of the boundary layer. The results of this model, which are relevant to industrial plasma discharges containing beam electrons, are compared with those found from other treatments of the beam - plasma boundary.

Simulation of negative resistance and current instabilities in a p-i-n Si diode

Current instabilities in a p-i-n Si diode heavily doped with gold impurities are investigated numerically. In order to clarify the explicit effect of the space charge of impurities on the current instabilities, we re-examine numerically the steady-state solutions for this particular diode without the quasineutrality assumption. The linearized stability analysis shows that the spontaneous self-sustained current oscillations can occur in the low-injection regime, where the DC resistance remains positive.

Minority carrier accumulation at high-low junctions

The semiconductor transport equations have been solved for lifetime semiconductors under the assumption of quasineutrality which is calculated to be valid up to relatively high current densities. The effective diffusion length of minority carriers is shown to be (strongly) current dependent. Of the four nonequilibrium processes, minority carrier accumulation is treated analytically in greater detail, showing current dependent resistance decreases which are confirmed by both numerical solutions of the transport equations and experiments.

Covered electrode HgCdTe photoconductor under high illumination levels

The issue of thermal imaging systems exposed to large photon fluxes is of great practical importance, as it is encountered while observing a scenery which includes ‘‘hot’’ sources. High illumination level phenomena appear when excess carrier density is comparable or larger than majority carrier density in the bulk. This state can be reached quite easily in n‐type HgCdTe detectors due to the moderate doping levels (typically ≤1015 cm−3). A modified expression for the current responsivity is derived, suitable for use at both high and low illumination levels. The quasineutrality assumption is verified; thus the ambipolar equation can be applied to describe high illumination behavior. Photoconductive detectors with and without covered electrodes are measured and analyzed. It is shown that under high illumination levels (1) the dominating recombination mechanism is the phonon assisted Auger process, and (2) the relative photoresponse for a covered electrode structure decreases monotonously with increasing cove...

Effect of ion-neutral collisions on plasma flow in the edge region of stellarators

The paper presents a study of the effect of charge exchange and elastic scattering collisions between ions and neutrals on the plasma flow along the divergent magnetic field lines in the divertor region of a stellarator. In the analysis, which is kinetic, an indirect solution to the kinetic equation for the ions is obtained using a Monte Carlo description for the ion dynamics together with the assumption of Boltzmann electrons and quasi-neutrality. Ion-neutral collisions are studied in a three-dimensional velocity space using a Monte Carlo algorithm. The results show that charge exchange and elastic scattering collisions play a significant role in reducing the drop of the electrostatic potential in the divertor chamber below that obtained from collisionless calculations. This, in turn, reduces the electrostatic barrier, which may be useful in retarding the flow of high Z impurity ions from the target plate towards the confined plasma. The calculations for the ion energy distribution suggest that, owing to ion-neutral collisions, most of the impact energy of ions on the divertor plate is gained while they cross the sheath region of the plate.

Collective focusing of an intense pulsed ion beam

Under the assumptions of quasineutrality and small perturbation to the applied solenoidal magnetic field, collective focusing of a neutralized, intense pulsed ion beam injected into a solenoidal magnetic field region is demonstrated. The focal point was observed to occur within the solenoidal magnetic field and was at a location in between the single-particle electron and ion focal points. The focused beam current density was an order of magnitude above the 20 A/cm2 of the incident beam. The experimental results were found to be in good agreement with a theoretical model developed under the above assumptions. The presence of background plasma or a conducting liner was observed to remove the collective focusing, confirming the physical picture of the theoretical model.

Magnetized Positive Column between Coaxial Cylinders

Steady state analysis is carried out for plasma between coaxial cylinders in presence of an externally applied uniform axial magnetic field under the assumption of quasi-neutrality of electric charge and neglect of sheaths at the walls. The radial distributions of plasma density and electric potential are given as functions of the ratio of inner and outer radii of the two cylinders. For any given value of this ratio and gap size, an equivalent radius of a cylindrical plasma is given that has the same temperature and electric field for the same gas under the same physical conditions as the coaxial plasma. The equivalent radius may be used to determine the temperature and axial electric field of a cylindrical plasma of the same gas under the same physical conditions are known from theory or experiments.

Hydrodynamic derivation of double layers (DL) and electric fields in plasmas

The hitherto successful hydrodynamic plasma theory needed the simplifying assumption of quasi-neutrality. Earlier known ambipolar fields in plasma surfaces were considered as exceptions and Alfvén's model of a complementary description by plasma currents was criticized. Fields in plasmas were derived from the kinetic theory of turbulence. Following a model for the nonlinear force of laser–plasma interaction, we needed a general description of the plasma without space charge neutrality which succeeded numerically and analytically. High electric fields due to inhomogeneities inside plasmas were derived explaining for the first time quantitatively the reduction of thermal conduction in laser-fusion, the measured inverted double layers including a new type of resonance process, the MeV α-upshift by nonlinear-force driven caviton fields and the radial fields in tokamaks which cause plasma rotation.

Stability of a magnetized positive column between coaxial cylinders

Theoretical analysis for the stability of a diffusion dominated positive column between coaxial cylinders in the presence of an axial magnetic field is carried out under the assumptions of quasi-neutrality of charges and no sheath at the walls. Self-consistent infinitesimal perturbations of plasma density and electric potential, which satisfy the linearized governing equations to the same degree of approximation are used to derive the dispersion relation. The perturbations associated with aximuthal modes m ≤ 0 are stable for any gap size and plasma parameters. The stability of non-axisymmetric perturbations is studied for different gaps. It is found that the presence of inner cylinders increases the stability of a magnetized positive column and m = 2 defines the region of stability when the ratio of the radii of the inner and outer cylinders is less than 0·5. In the case of narrow gaps, higher and higher modes are excited. The minimum non-dimensional axial electric field at which the magnetized positive column between coaxial cylinders becomes unstable for different gaps is also determined.

Magnetosonic Solitary Waves in Hot Plasmas

In this paper, a magnetosonic solitary wave in hot plasma is considered both analytically and numerically, taking account of the charge separation. The two-direction one-dimension Maxwell-two-fluid equations are obtained. It is shown that there exist solitary wave solutions of these equations when , where C is the-wave velocity. The distributions of density and of magnetic intensity both have the shape of single peak. The effect of the magnetic field is to depress the amplitudes and to widen the widths of the solitary waves; and when B0→0 the magnetosonic solitary wave turn to sonic solitary wave. It is found that for large C the charge separation may be remarkable, so the assumption of quasineutrality is incorrect.

Excess concentration, electron and hole currents in an epitaxial emitter

Algorithms for calculating the emitter hole and electron currents in the case of an n + n − epitaxial emitter have been published by Yu [2] and Rofail et al. [3]. Both algorithms are restricted to a small ratio of hole to electron current whereas Yu's algorithm is further restricted by the assumption of a constant electric field in the epilayer. In the present paper an algorithm is presented in which both restrictions have been removed and which is valid from low through high injection. The assumption of quasineutrality in the epilayer, which is used in the present algorithm, is veryfied using Adlers criterium [4]. Calculation results are presented for a structure treated by Poorter [1] and a comparison is made with his results.

Non-neutral Langmuir solitons

It is shown that for finite amplitude Langmuir solitons the quasi-neutrality assumption breaks down. For moving solitons, deviations from quasi-neutrality are in general as important as ion nonlinearities. Even for standing solitions, the quasi-neutrality assumption fails when the ions are hot. By perturbation analysis, the correct non-neutral solutions are presented. Physical implications are discussed.

Free expansion of a plasma with two electron temperatures

A theory for the free expansion of a plasma with two electron temperatures is presented. It is shown that in the case of a laser-produced plasma expansion the ions separate into a fast and a slow component, and that the number of fast ions is particularly sensitive to the hot to cold electron temperature ratio. If the electron temperature ratio is ≳ 10 then the quasi-neutral self-similar solution breaks down. The regions in the rarefaction expansion where the quasi-neutrality assumption fails are discussed.

A multidimensional quasineutral plasma simulation model

A multidimensional hybrid simulation model has been developed for use in studying plasma phenomena on extended time and distance scales. The model makes fundamental use of the small Debye length or quasineutrality assumption. The ions are modeled by particle-in-cell techniques, while the electrons are considered a collision-dominated fluid. Some electron inertial effects are retained. The fields are calculated in the nonradiative Darwin limit. The quasineutral counterpart of Poisson's equation is obtained by first summing the electron and ion momentum equations and then taking the quasineutral limit. The resulting elliptic equation correctly includes those electrostatic potentials which occur in sheath or ambipolar phenomena while neglecting the short-range electrostatic fields which give rise to plasma oscillations. This model has been implemented in a two-dimensional code QN2. A lower hybrid drift unstable equilibrium with parameters accessible to both hybrid and full-particle simulation has been selected as a test of the code and a demonstration of the model. Initial results indicate quite good agreement between the two simulation methods in linear growth rate and wave number.

Nonquasineutral theory of ion-acoustic resonances in bounded nonuniform plasmas and comparison with experiments

A theory is developed of ion-acoustic resonances in inhomogeneous plasmas of the positive column type using a fluid plasma description. Poisson's equation is properly taken into account, instead of applying the usual assumption of wave quasineutrality. The order of the differential equation describing the wave is thereby increased by two and the singularity that previously occurred as a result of the presence of a sheath region is thereby removed. It is shown that ion-acoustic resonances are confined within the plasma core, the effective boundary not being the wall, but the region in the plasma where the macroscopic ion flow velocity attains the Bohm velocity (KTe/mi)(1/2). The theoretical predictions are substantiated by a number of experiments taken from the literature and supplemented by a series of new experiments. The theory sheds new light on the problem of wave reflection from a negatively polarized wall and the damping of ion-acoustic waves propagating in inhomogeneous plasmas.

Numerical analysis of a forward-biased step-junction P-L-N diode

Exact numerical steady-state solutions are presented for a forward-biased step-junction one-dimensional p+-n-n+rectifier over a current range of 10-2to 104A/cm2The versatility of the numerical approach is demonstrated by the inclusion in the physical model of injection-dependent carrier lifetimes due to Auger recombination or injection-dependent mobilities due to electron-hole scattering. The solutions obtained are compared to those given by conventional analytical treatments at low and high injection levels. Among the major results established are the validity of the Boltzmann's relations and of the quasi-neutrality assumption at all injection levels of interest. It is shown that at the upper end of the current range, a complete analytical solution for the whole device is intractable. However, partial analytical solutions are available for the quasi-neutral regions, and these have enabled us to obtain a better understanding of some of the numerical solutions. Examples are the early onset of non-linearity effects in the n+region because the minority carrier current there is small compared to the total current, and the shift in the minimum of the base carrier distribution towards the n-p+junction as the injection efficiency from the p+region into the base decreases with increasing forward bias.