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A general methodology is presented for evaluating the dielectrophoretic velocity of a freely suspended spherical colloid in an electrolyte solutes under the action of a nonuniform electric field and for a Debye layer of arbitrary thickness. The nonlinear induced charge electrophoretic problem is first considered. General analytic expressions are derived for the mobility of an uncharged particle in the form of products between adjacent modes of the ambient electric field demonstrating a symmetry-breaking-type phenomena. It is shown that the mobility of a conducting (i.e., ideally polarizable) spherical particle vanishes for a quadratic electric field in the limiting case of a thin Debye layer. For an infinitely thick Debye layer it attains asymptotically a positive finite value. Yet, there is another value of a finite Debye length for which the mobility changes sign. This interesting nonintuitive effect may have implications to separation of particles by size. The linear case of a uniformly charged colloid...

The short wavelength limit of the magnetron instability of a relativistic sharp boundary electron sheath is examined. For short wavelengths the mode is localized to the sheath edge. This localization leads to a simple relationship (essentially a Lorentz transformation) between the relativistic and nonrelativistic growth rates. This relationship involves only equilibrium quantities evaluated at the sheath edge and explains previously noted trends that have been observed numerically.

Experimental tests of an E×B plasma sweeper, designed to control the plasma density near the mouth of a phased waveguide array, are described.

A computer simulation study of the excitation of lower hybrid waves by external sources and the associated plasma heating is presented. A plasma slab with a nonuniform density profile is modeled with a two and one‐half dimensional electrostatic particle code. Both a finite‐length electrostatic antenna and a single wave exciter are considered. The frequency is chosen so that a wave conversion layer exists in the plasma. It is found that a narrow sheath is formed at the plasma edge and the dominant effect is surface electron heating within that region. Ponderomotive force effects as well as the nonlinear generation of harmonics and subharmonics also occur. A low amplitude lower hybrid wave is observed to be excited by the sources and propatates to the wave conversion layer where it is absorbed.

The acceleration of ions by two isothermal species of electrons, thermal and suprathermal, in a laser‐fusion plasma is investigated. The disassembly of an initially stationary plasma slab, including charge separation effects, is described. Before the rarefaction wave has penetrated appreciably into the slab, an interior Debye sheath which separates the suprathermal and thermal electrons, as well as an exterior sheath at the ion‐vacuum interface is found. As the rarefaction approaches the center of the slab, the dynamics is modified due to the conservation of species number and total energy. The energetics of the long‐time evolution is described by a quasi‐neutral similarity solution appropriate to finite two‐electron species systems.

Flux loss during field reversal on the TRX‐1 field‐reversed θ pinch is found to be much less than predicted by the inertial model of Green and Newton. This can be explained by a pressure bearing, conducting sheath which naturally forms at the wall and limits the flux loss. A one‐dimensional (r‐t) magnetohydrodynamic (MHD) numerical model has been used to study the formation and effectiveness of the sheath. The calculations are in excellent agreement with experimental measurements over a wide range of operating parameters. The results indicate that good flux trapping can be achieved through the field reversal phase of FRC formation with much slower external field reversal rates than in current experiments.

The plasma‐sheath equation for a collisionless plasma with arbitrary ion temperature in plane geometry is formulated. Outside the sheath, this equation is approximated by the plasma equation, for which an analytic solution for the electrostatic potential is obtained. In addition, the ion distribution function, the wall potential, and the ion energy and particle flux into the sheath are explicitly calculated. The plasma‐sheath equation is also solved numerically with no approximation of the Debye length. The numerical results compare well with the analytical results when the Debye length is small.

A simple model for the current history of plasma focus experiments is presented. The presence of a leak current which does not pass through the plasma sheath is allowed. Results are found to compare quite well with those of much more sophisticated two‐dimensional magnetohydrodynamic calculations. For the Frascati experiment, which has detailed current measurements, computed results do not agree with experimentally derived values. A reasonable match for the total current in the Frascati experiment can be found by lowering the leak current. Both total and leak current can be matched if a mass loss from the run‐down region is allowed.

Conventional plasma focus devices of different capacitor bank energy (kilojoules to megajoules) show very similar discharge behavior with respect to breakdown, compression, and pinch data. The use of SPEED 1—a plasma focus driven by a fast high impedance bank (voltage 200 kV, initial current rise >5×101 2 A/sec, bank impedance 160 mΩ),—allowed the investigation of a 400 nsec discharge in a parameter range not previously accessible. Considerable improvement of current and neutron efficiency (30 A/J; 106/J) has been achieved as compared with values (≤20 A/J; 2×105/J) of conventional slow devices of equal energy (20 kJ). Exceptional compression dynamics (current derivative spike >101 3 A/sec FWHM 10 nsec) is observed from electric signals. This is due to the current stabilizing effect of the high bank impedance and especially to improved current sheath structure (reduced thickness, enhanced conductivity). Current density and conductivity of the sheath depend on ignition parameters at breakdown (voltage, current rise), the low values of which are possibly responsible for the similarity of the discharge behavior of conventional devices. Conclusions on further improvements are drawn.

The electron surface mode dispersion relation, including Landau damping, is obtained for a vacuum–plasma interface. Unlike previous work, the interface is permitted to have a finite width and no wall boundary conditions are assumed. When the density gradient scale length Ln is large compared with a Debye length k−1D and small compared with a surface mode wavelength 2πk−1, then the mode frequency is ω=(ωp/21/2) (1+kLn/6), and the Landau damping rate is γ =−[6/(2π)1/2]ωp/(kDLn). These expressions are much different than the comparable expressions for a wall‐confined plasma.

An experimental study is presented of the cross‐power spectrum of the random high‐frequency signals received by two small dipole antennas immersed in a stable, isotropic and collisionless plasma. These signals are due to the high‐frequency microfield, i.e., to the random linear electrostatic wave field excited by the thermal motion of the electrons. For a Maxwellian plasma, the cross spectrum exhibits a main resonance peak slightly above the plasma frequency, and from this spectrum the electron density and temperature can be determined. The experiment has been performed in a laboratory plasma near thermal equilibrium. The results are in agreement with the theory, and show that the cross spectrum is very sensitive to any departure of the plasma from thermal equilibrium.

The effect of a magnetic field on the transition layer between a plasma and an absorbing wall is studied. A numerical model is used which simulates the motion of plasma particles in the electric and magnetic fields for a prescribed particle influx at the plasma boundary. Bohm’s condition for the existence of a monotonic profile of the layer is generalized. The transition layer proves to have a double structure comprising a quasineutral magnetic presheath preceding the electrostatic Debye sheath. The magnetic presheath scales with the ion gyroradius at the sound speed and with the angle of the magnetic field. The total electric potential drop between plasma and wall proves to be fairly insensitive to the magnitude and angle of the magnetic field.

Low‐frequency drift waves are considered in a planar sheath of neutral plasma with thickness on the order of the ion gyroradius. An integral eigenmode equation is derived and solved numerically using fast Fourier transforms. The analysis is valid for arbitrary wavenumbers and accounts for shear in the equilibrium magnetic field. It is found that unstable universal drift modes can exist in this strongly localized plasma. In contrast to what has been found previously in connection with weakly inhomogeneous plasmas, it is observed here that shear can have a destabilizing influence. The relevance of this idealized model to experiments is also discussed.

A collisionless electric sheath model between a metal surface and a magnetized plasma is given. The magnetic field is assumed to be uniform and has a small angle of incidence with respect to the surface. It is shown that the ambipolar wall potential is essentially independent of the angle of incidence. The finite Larmor radius and secondary electron effects on the wall potential are derived. The sheath thickness is shown to depend strongly on the surface absorption characteristics.

The influence of collisions or of a cross‐magnetic field on the well known Langmuir–Childs relations is examined.

The properties of an ion‐acoustic soliton in a weakly inhomogeneous plasma are studied. Unlike previous analyses, the soliton amplitude is not required to be small. The ion generation rate is assumed to be either proportional to the electron density or to be uniform. Assuming that the local soliton width is small compared with the scale length of the plasma inhomogeneity, a perturbation theory is developed which gives the local speed and amplitude of the soliton. For a small amplitude soliton, simple expressions for the local soliton speed, peak soliton potential, and peak soliton ion density are derived. It is shown that both the soliton velocity relative to the ion drift velocity and the peak soliton potential do not vary greatly as the soliton moves from the plasma center toward the sheath. The peak ion density, however, varies over a wider range. These results are shown to agree with those from direct numerical integration of the basic equations.

Collisional plasma layers exist on the electrode surfaces of magnetically insulated gaps. Coupling of the cathode electron sheath with these plasma layers leads to instabilities. These instabilities are of two types: (i) a destabilized negative energy mode on the electron sheath and (ii) a new low‐frequency resistive mode. The growth rates and physical picture of these modes suggest that they might be extremely dangerous in practice, leading to sporadic breakdown of magnetic insulation.

The reflection of continuous sinusoidal waves from a grid is investigated experimentally. It is found that the reflection coefficient has a distinct maximum in contrast to the prediction of the theory. The electron components of the incident and reflected waves are observed to vanish within the quasineutral layer close to the grid where the plasma density rapidly drops. Furthermore it is shown that the reflected wave is a downstream wave that propagates on the ion beam that originates on the other side of the grid.

Emmert et al. [Phys. Fluids 23, 803 (1980)] have modeled the flow of a one‐dimensional collisionless plasma to a material wall by formulating and solving the warm‐ion plasma equation. In contrast to the result of the cold‐ion plasma equation it was found that the electric field at the plasma–sheath boundary was finite. It is first shown that Emmert’s solution satisfies the generalized Bohm criterion, and is thus a valid solution, before discussing the cause of the difference in the results of the two models in calculating the boundary electric field.

Bissell and Johnson [Phys. Fluids 30, 779 (1987)] have calculated the electrostatic potential variation in the sheath and presheath regions of a collisionless plasma in which the source of ions is assumed to be Maxwellian. To do this, they imposed the generalized Bohm criterion as a boundary condition. In this paper the plasma equation is solved numerically without imposing the Bohm criterion as a boundary condition. The results compare well with their results. In addition, the ion distribution function throughout the plasma region is calculated. Because of this particular source model, the ion distribution at the center of the plasma has a spiked non‐Maxwellian shape.

Experimentally observed multiple ion‐acoustic wave excitation in a weak ion beam plasma system is described. An additional anomalous signal was observed to form and propagate hundreds of Debye lengths from the grid in a large quiescent plasma. The existence of this signal is interpreted to be caused by the grid excitation mechanism, and it can be used to ascertain the dimension of the sheath surrounding the grid.

Strong electric potential double layers (eφ/Te≳10) are produced in the University of Iowa’s triple plasma device. The electron beam which results from acceleration by the double layer maintains its identity with little heating until it reaches the end of the chamber. Structure of the double layers is seen to depend upon the characteristics of the free and trapped particle species. A three‐dimensional mapping for double layers is shown. A density criterion model for the stability of double layers is also presented.

During reflection from a sheath, electrons originating in the overdense plasma absorb laser light.

The boundary layer of a weakly ionized rare gas discharge is treated using kinetic theory. A self‐consistent two‐scale analysis is performed and the exact presheath and sheath solutions are constructed for the following model: A plasma consisting of Boltzmann distributed electrons and singly charged atomic ions is in contact with a negative absorbing wall. The ion kinetics is dominated by charge exchange with cold neutrals (T0≪T−). The mean‐free‐path λ is constant and large compared with the electron Debye length λD. This model represents a collision‐dominated counterpart to the well known Tonks–Langmuir model of the collision‐free plasma.

The diffusion of ions and electron through a uniform neutral gas was treated with complete wall emission‐absorption boundary conditions. Volumetric ionization and recombination processes were ignored. In the limit of the small ratio of Debye length to channel width (e→0), the problem splits into three regions: anode sheath, cathode sheath, and quasi‐neutral region. The solution is obtained in closed form in each of the three regions and matched in the overlap domains. The unusual feature of this problem is that the boundary conditions are coupled to the solution in a transcendental manner requiring iteration in order to achieve a consistent solution. The degree of surface coverage is an important parameter in determining emission and absorption rates. The results show that ion densities are elevated (above quasi‐neutral levels) in the anode and cathode sheaths tending to enhance electron emission. The quasi‐neutral density at each electrode is the geometric mean of the true charged particle densities at the boundary. Electrical current between the electrodes increases linearly, then saturates sharply with increasing voltage between the electrodes.

Simple analytic relations are derived for the floating potential of a solid object in contact with a magnetized plasma as a function of the electron/ion mass ratio, the electron/ion temperature ratio, and the secondary electron emission coefficient. Simple analytic relations are also obtained for the sheath transmission factors, i.e., the particle and energy fluxes to floating and nonfloating surfaces. These analytic formulations, derived from a fluid model treatment of ion flow, are found to give results in close agreement with results derived from more complex analysis based on kinetic theory and numerical models. Tokamak scrape‐off plasmas are often characterized by ion distributions which have finite drift velocities at the point where the ions enter the scrape‐off plasma from the main plasma (via cross‐field diffusion). The Bohm criterion governing the drift velocity of ions as they enter the electrostatic sheath in front of a limiter, divertor plate, or probe is generalized for this case.

A decrease in the frequency of self‐trapped light by as much as a factor of two has been observed in computer simulations of several physical situations. The frequency shift is due to a decrease in the resonant frequency of the plasma cavity as it deepens and expands shortly after the light becomes trapped. Three examples are presented: a model problem in an initially uniform plasma, trapping of laser light in cavities at critical density, and modulational instability and self‐trapping of Raman‐scattered light at quarter‐critical density in a nonuniform, expanding plasma. This effect is essential in the analysis of the evolution and stability of such cavities, and such large frequency changes limit the applicability of models using a nonlinear Schrodinger equation to represent the high‐frequency fields.

In this paper a kinetic theory of the boundary layer of a weakly ionized plasma in contact with a perfectly absorbing wall is presented. The ion kinetics is governed by charge exchange collisions with neutrals of finite temperature; the collision frequency is constant. Based on the assumption that the Debye length is small compared with all other lengths of the system, a self‐consistent two scale (presheath–sheath) analysis is performed. In contrast to Emmert’s analysis [Phys. Fluids 23, 803 (1980)] of the corresponding collision‐free system, the sheath edge shows the usual field singularity. It is shown that in the case where the electron and neutral temperatures are of the same order a large fraction of ions enters the sheath with a multiple of the electron thermal energy.

Few exact solutions for collisional presheaths exist because of the difficulty of simultaneously satisfying both the collisional Boltzmann equation and the Poisson equation. The exact solutions that do exist are for very specialized collision terms such as constant cross‐section charge exchange with cold neutrals. The present paper presents an asymptotic method which is applicable to a variety of collision terms and is applied in particular to constant collision frequency charge exchange with noncold neutrals. Constant collision frequency and constant cross‐section collision with cold neutral results are also presented. The first‐order terms for the presheath potential rise and ion distribution functions are calculated and it is shown that second‐ and higher‐order terms can be calculated using a multiexponential expansion for presheath potential rise. The first‐order cold neutral constant cross‐section results correspond well to the exact solution. The calculated presheath potential rises are of the order...

The electrons of a pure electron plasma may be in thermal equilibrium with each other and still be confined by static magnetic and electric fields. Since the electrons make a significant contribution to the electric field, only certain density profiles are consistent with Poisson’s equation. The class of such distributions for a finite length cylindrical column is investigated. In the limit where the Debye length is small compared with the dimensions of the column, the density is essentially constant out to some surface of revolution and then falls off abruptly. The falloff in density is a universal function when measured along the local normal to the surface of revolution and scaled in terms of the Debye length. The solution for the shape of the surface of revolution is simplified by passage to the limit of zero Debye length.

Finite Larmor radius and end effects are included in a treatment of the low‐β interchange instability. Higher order modes are shown to be destabilized by incomplete line‐tying through an external plasma.

The amount of electron emission required to partially line‐tie the m=1 flute mode is measured on an axisymmetric mirror‐confined plasma. The results are consistent with an ideal magnetohydrodynamic (MHD) calculation with a sheath dissipation term added. The minimum electron emission required is approximately the ion saturation current. The sheath impedance is also calculated for the case when the electron emission exceeds the threshold required for the formation of a virtual sheath.

Waves such as drift waves and lower hybrid oscillations in a plasma are sensitive to the degree to which charge neutrality can be maintained by electron flow along the magnetic field. When the plasma is bounded axially, the sheath conditions on the end plates determine the parallel wavelength. It is found that the nature of the bounded modes depends on whether the motion of electrons is resistive or inertial. If it is resistive, the sheath matching conditions can be satisfied by standing waves with the proper wavelength. If it is inertial, pure standing waves are not possible; there must also be a variation of phase along B. Application is made to two‐ion hybrid waves in connection with isotope separation.

A method is proposed for treating linear longitudinal perturbations in one‐dimensional collisionless plasma diodes with a uniform plasma region and thin electrode sheaths. The method is comprehensive in that it allows for very general equilibrium, initial, boundary, and external‐circuit conditions. Upon Laplace‐transforming the Vlasov and Poisson equations in both space and time, appropriate evaluation of all pertinent relations leads to a set of 2+2nσ(nσ is the number of particle species) coupled integral equations in x and v for the following quantities (which are the time Laplace transforms of the respective physical perturbations): je(ω) (external‐circuit current density), E(x,ω) (electrostatic field), fσl(v>0,ω), and fσr(v

Radio‐frequency plugging and heating of a magnetized sheet plasma has been studied both experimentally and theoretically. It is confirmed that a sheath resonance related to ion motion occurs at a frequency intermediate between the ion cyclotron frequency and the lower hybrid frequency, and an anti‐resonance occurs at the lower hybrid frequency. The rf electric field in the plasma, which produces a ponderomotive force on the ions, is strongest at the sheath resonance, and is used for the nonadiabatic rf plugging of the magnetized sheet plasma in a mirror field. The ion heating process is explained by Joule heating due to the rf electric field.

The reflection coefficient R for linear monochromatic ion acoustic waves incident on the transonic layer and sheath from the plasma interior is calculated. The treatment differs from previous analyses in that (1) the exact zero‐order ion density and velocity profiles for a planar, bounded plasma are used, and the zero‐order charge separation is not neglected, and (2) the first‐order quantities near the transonic layer are considered in detail, including first‐order charge separation, whereby it is found that no coupling to the beam modes exists, and that the functional form of the first‐order solution is completely determined. It is shown that the upper bound for ‖R‖ is (1)/(3) . The largest reflection occurs for frequencies which are small compared with the ionization frequency, and generally decreases with increasing frequency. By Fourier superposition, the reflection of a pulse is computed. For a narrow incident pulse, the reflected pulse is greatly distorted and is small compared with the incident pulse. For a broad pulse, the reflected pulse is similar in shape to the incident pulse, and has a magnitude which is approximately (1)/(3) of the incident pulse.

A promising resistive magnetohydrodynamic candidate for the underlying cause of turbulence in the edge of a tokamak plasma is the rippling instability. In this paper a computational model for these modes in the cylindrical tokamak approximation was developed and the linear growth and single‐helicity quasi‐linear saturation phases of the rippling modes for parameters appropriate to the edge of a tokamak plasma were explored. Large parallel heat conduction does not stabilize these modes; it only reduces their growth rate by a factor sacling as K−4/3∥. Nonlinearly, individual rippling modes are found to saturate by quasi‐linear flattening of the resistivity profile. The saturated amplitude of the modes scales as m−1, and the radial extent of these modes grows linearly with time due to radial Ẽ×B0 convection. This evolution is found to be terminated by parallel heat conduction.

The propagation of ion acoustic waves toward a plasma sheath is considered, using a fluid model which allows charge separation. It is assumed that wavelengths are sufficiently short to apply the WKB approximation and that amplitudes remain sufficiently small to use the linear approximation. Under these approximations, ion acoustic waves are not reflected from a plasma sheath, and in general are somewhat damped, although they may undergo weak growth deep in the sheath.

A distribution function is presented that may be used to study the effects of finite temperature on the equilibrium and stability properties of magnetically insulated electron flows. This distribution function has the useful property that it generates the thoroughly studied class of constant Q=ω2p/Ω2 equilibria in its zero‐temperature limit. Analytic solutions are given for the general, constant Q, zero‐temperature equilibria.

By adjusting the electrostatic potential on the end plates of a mirror plasma, the plasma’s magnetohydrodynamic (MHD) stability can be altered. Furthermore, the plasma’s MHD response to low‐frequency modulation of the end plates can be used to pump unwanted ions that collect in a thermal barrier. Here, precise boundary conditions are derived for the MHD equations of motion to model an end plate separated from the plasma by a sheath.

The collective behavior of an intense, pulsed, space‐charge‐neutral proton beam (100 kV, 3 A/cm2, 0.8 msec) incident upon a transversely oriented magnetic field of 0–6 kG has been determined experimentally. At 6 kG, a floating potential probe shows longitudinal polarization creating a positive sheath (virtual anode) within the field boundary having a peak electrostatic potential equal to the ion accelerating potential. The sheath thickness is approximately v/wpi, where v is the beam velocity and wpi is the ion plasma frequency. Oscillations in the sheath potential at wpi were observed as predicted by previous computer simulations. Ions were observed to be accelerated out of the sheath in all directions. Transverse polarization of the beam as predicted by Schmidt’s polarization drift model was not observed although the plasma dielectric constant was approximately 102.

Two aspects of double sheaths (nonneutral regions) in plasmas are studied via analytic models. First, the motion of the structure through the plasma is analyzed by considering the force balance among the various species. A general proof is presented which shows the net acceleration of the sheath is zero in the absence of dissipative processes. A specific example is given which shows that a pressure difference between the two sides of the sheath results in the enhancement of the beam current into the low pressure side rather than acceleration of the sheath. The effect of beam‐plasma interactions is also discussed. The second part of the analysis is the derivation of separate (though nearly identical) density criteria for sheath nucleation and sheath maintenance in equilibrium. These are compared with experimental results of Lutsenko, Sereda, and Kontsevoi and reasonable agreement is obtained.

The formation of an electrical potential difference between hot and cold plasmas is studied by means of a particle simulation. It is found that a double layer structure is formed on the hot‐plasma side of the contact surface between the cold and hot plasmas. The potential difference is given approximately by φDL∼Teh/2e, where Teh and e are the hot‐electron temperature and the electronic charge, respectively. The double layer is accompanied by a negative potential dip on the low potential side (cold plasma) of the double layer, the depth of which is φdip∼2Tec/e, where Tec is the cold‐electron temperature. Interestingly, however, the positive potential difference and the negative potential dip are created independently.

Steady plasma flow is analyzed for the case where a positive‐ or negative‐ion beam penetrates and ionizes background gas (or vapor). The work of previous authors is extended to treat nonuniform beam densities that fall to low values at the transverse plasma boundary, and to include gas densities that are nonuniform along the beam axis. These nonuniformities give a two‐dimensional plasma flow problem that is analyzed using a fluid model. The effect of unusually low gas density on the plasma flow is discussed; for negative‐ion beams, the electron density becomes much smaller than the beam density and space‐charge neutralization is maintained by a reduction in plasma flow. When there is a large local gas density, as in a gas cell, the resulting high electron density is also localized to the same region by the nature of the flow.

It has previously been shown for nonrelativistic voltages (i.e., much less than 500 kV) that a quasilaminar, cold‐fluid, magnetically insulated equilibrium does not exist on coaxial cylindrical lines for which (1) the magnetic field is azimuthal, (2) electron emission at the cathode is space‐ charge‐limited, and (3) the cathode lies within the anode. Since it is expected to encounter this configuration frequently in practice, and because such lines typically operate at voltages above 500 kV, the previous analysis has been extended to take account of relativistic and sheath diamagnetic effects. Despite their inclusion it is found that the nonexistence of this type of equilibrium state continues to hold at the higher voltage levels.

A model describing the structure of a plane and stationary ionizing current sheath taking into account radiation transport is presented. Five fluid magnetohydrodynamic equations together with radiative transfer equations for continuous radiation (free–free and free–bound) are solved numerically in terms of the pressure of the neutral gas and the value of the pushing magnetic field behind the current sheath, with the assumption that the system becomes opaque for line radiation. Solutions are given for values of the parameters typical of plasma focus device operation [in Methods of Experimental Physics, edited by R. H. Louberg and H. R. Grien (Academic, New York, 1971), Vol. 9B, p. 187]. At a fixed value of the magnetic field, drastic changes in the opacity and in the intensity of the emerging radiant flux are found when varying the neutral gas pressure. In particular, radiative losses can be very high, reaching about 30% of the available power in a frame of reference moving with the current sheath.

The effect of an annular, line‐tied blanket, on the curvature‐driven flute in a magnetic mirror is considered. The blanket is assumed to be line tied to a thermoionically emitting annular end plate. Reduction of the flute growth rate is computed as function of Larmor radius, blanket radius, and axial plasma conductance through either an external plasma or mirror sheath. It is found that significant reduction in growth rate can be achieved.

In a plasma containing more than one ion species, the frequencies of the ion–ion hybrid resonances can be a sensitive measure of the densities of the minor species, but only if the frequency shifts caused by electron motions are small, as experimental observations suggest. By calculating the eigenfrequencies for ion–ion hybrid waves taking into account collisions, Landau damping, electron inertia, electromagnetic effects, and density gradients, it is found that the frequency shifts are not negligible unless k∥ is extremely small. Treatment of the sheath boundary conditions at the ends of a plasma column shows that the effective value of k∥ can indeed be sufficiently small, and that the uncorrected resonance frequency is surprisingly accurate over a wide parameter range. Data from an Ar–Xe discharge demonstrate the usefulness of this technique for measuring impurity concentrations.

The time‐dependent interaction between solid objects and the unmagnetized plasmas in which they are immersed is investigated. To this end over 1900 high‐resolution, one‐dimensional particle‐in‐cell simulations of the plasmas surrounding cylindrical and planar objects are statistically analyzed. Numerical shot noise produces an electron‐plasma‐frequency ringing in the simulations, the amplitude of which is related to the plasma temperature and to the numerical system temperature. Whenever the potential of an object is rapidly biased, the surrounding plasma rings with a large amplitude at the electron‐plasma frequency. During this ringing, a depletion layer forms around the object on ion‐acoustic time scales. Positively charged objects discharge via plasma currents in about τpe /4 and negatively charged objects discharge in about τpi . Owing to charge separations in the plasmas, for the first few ion‐plasma periods after a perturbation, the potential of an object is not directly related to the charge on it....

Experiments on both stationary and propagating double layers and a related analytical model are described. Stationary double layers with eΔφ/kTe≳1 were produced in a multiple plasma device, in which an electron drift current was present. An investigation of the plasma parameters for the stable double layer condition is described. The particle distribution in the stable double layer establishes a potential profile, which creates electron and ion beams that excite plasma instabilities. The measured characteristics of the instabilities are consistent with the existence of the double layer. Propagating double layers are formed when the initial electron drift current is large. The slopes of the transition region increase as they propagate. A physical model for the formation of a double layer in the experimental device is described. This model explains the formation of the low potential region on the basis of the space charge. This space charge is created by the electron drift current. The model also accounts f...