bluuebunny/crossref_metadata_2025 huggingface dataset:
Heat Transfer in Magnetohydrodynamic Channel Flow
Authors: Eraslan Arsev H. , Eraslan Necdet F.
Published: February 2004

The general mathematical problem of magnetohydrodynamic thermal entrance regions is investigated for a parallel plate channel by including the Hall effect, axial heat conduction, Joule heating, and viscous dissipation. The associated eigenvalue problem is solved by the Galerkin method and the results are presented for the temperature development in a channel under uniform wall temperature conditions. It is concluded that the Hall current has considerable effect on the thermal problem and that the axial heat conduction cannot be neglected for low Peclet numbers.
Sub-Alfvénic Duct Flow with a Nonuniform Magnetic Field
Authors: Peyret Roger
Published: February 2004

The flow of a conducting fluid in a duct in the presence of a magnetic field with a small nonuniformity of the following kind is considered : for x < 0, the field is uniform and parallel to the axis 0x of the duct; for x > 0, the field is nonuniform and the curvature of the magnetic lines is small, of order ε. A perturbation theory is presented for the case of small magnetic Reynolds number Rm and small Alfvén number A. In particular, the flow field is determined to order ε and to zero order in Rm, and the magnetic field to order ε Rm. Downstream, all the perturbations decay algebraically. The upstream perturbations of the flow field initially decay exponentially, with ultimate algebraic decay in the ε Rm-order terms. For the induced magnetic field, the upstream decay is algebraic.
Effects of Viscosity and Electrical Conductivity on the Stability of a Liquid Model of Hard-Core Pinch
Authors: Gokhale M. H.
Published: February 2004

The effects of viscosity and finite electrical conductivity of mercury on the axisymmetric instabilities of a current-carrying annular cylinder of mercury are considered in the context of the experiment of Lehnert and Sjögren. A straightforward numerical method to solve the characteristic value problems is used to determine the real values of growth rates for various values of the wavenumbers and current density ratios, using true as well as hypothetical values of viscosity and electrical conductivity. It is shown that the consideration of neither the viscosity nor the electrical conductivity of mercury is adequate to remove a discrepancy between the experiment and an earlier theory by Jayasimha and Murty. It is shown that other parameters remaining the same, the viscosity of the fluid will have to be 10 times larger, or its electrical conductivity would have to be 107 times higher to reduce the growth rates to nearly half their values in the absence of viscosity and electrical conductivity.
Flow Induced in Fluid-Particle Suspension by an Infinite Rotating Disk
Authors: Zung Laurence B.
Published: February 2004

An exact similarity solution is given for the flow of a fluid-particle suspension over an infinitely large disk rotating at a constant velocity. Numerical solutions of the resulting ordinary differential equations provide velocity distributions for both fluid and solid phases and density distributions for the solid. The boundary-layer thicknesses of the particle cloud and the fluid are found to be approximately equal. In addition to its intrinsic value as a solution to a physical problem, the results provide a convenient basis for judging the accuracy of approximate techniques.
Electrostatic Plasma Oscillations in an Alternating External Electric Field
Authors: Rebhan Eckhard
Published: February 2004

The one-dimensional electrostatic oscillations of a plasma are investigated under the influence of an alternating external electric field. If the motion of ions is ignored, it is shown that there is no influence of the external field on the stability of the plasma, even nonlinearly. The motion of the ions is taken into account by an expansion with respect to the mass ratio α = m−/m+. A dispersion relation for linear plasma oscillations is derived and investigated for different limiting cases. The influence of the external field is shown to be destabilizing on the electron-electron two-stream instability for all frequencies and amplitudes.
Toroidal Theta Pinch Collapse by the Snowplow Model
Authors: Itoh Satoshi , Fujisawa Noboru , Yamamoto Kenzo
Published: February 2004

Accurate equations for the cross section of the toroidal theta pinched plasma column are derived using the snowplow model, and then are solved numerically to study the shift of the column position and the deformation of the cross section during the collapse. The column shifts towards the outer wall and the shape of the cross section changes from the initial circle into a heart as the collapse proceeds. The shift and the deformation, however, are not serious, if the aspect ratio is larger than 10.
Coordinated Measurements of Plasma Density and Cooperative Light Scattering in a Theta-Pinch Plasma
Authors: Daehler Mark , Sawyer G. A. , Thomas K. S.
Published: February 2004

Measurements have been made on the spectral broadening of ruby laser light scattered at a small forward angle by density fluctuations in a theta-pinch plasma, in order to systematically investigate the variations in scattering cross section with reverse bias magnetic field and with time during the first half-cycle of the compression field. Measurements of density under the same plasma conditions were made so that the effects of cross section variations could be separated from density variations. The principal results are: (1) The observed cross section is approximately six times the theoretical cross section for a plasma with the Scylla III temperature and density (no bias magnetic field). The large cross section is attributed to superthermal density fluctuations (turbulence) in the plasma. (2) The scattering cross section for a plasma with a bias field of -800 G is three times larger than for the plasma with no bias field. (3) There is little difference in the scattering cross sections measured at two times during the discharge. (4) The density measurements show a plasma loss rate which increases with increased reverse bias field. (5) There is a strong dependence of scattering on plasma temperature; the hotter the plasma, the smaller the scattering cross section and the broader the spectral width of the scattered light.
Minimum Energy Property of a Bounded One-Dimensional Plasma
Authors: Hohl Frank
Published: February 2004

Analytic and numerical methods are used to investigate the dynamics, stability, and approach to equilibrium of a bounded, collisionless one-dimensional plasma with a fixed neutralizing ion background. A class of stationary solutions of the nonlinear Vlasov equation is found which represents minimum energy states. It is found that the quasiequilibrium state which is reached after several plasma periods is close to the Fermi distribution predicted by Lynden-Bell.
Turbulent Mean-Flow Measurements in a Two-Dimensional Supersonic Wake
Authors: Demetriades Anthony
Published: February 2004

Mean-flow measurements have been made in the supersonic wake of a very slender, two-dimensional body at zero incidence and heat transfer rate. Excellent correlation of the lateral distribution of axial velocity is obtained when the lateral distance is divided by the transverse wake scale which is formed from the measured velocity defect. The latter is found to decay as the inverse square root of distance for the entire range of about 1850 virtual model thicknesses mapped; thus, the transverse scale increases as the square root of distance. In the latter half of this range the lateral distribution of static temperature also appears to correlate in the same lateral coordinate, and the temperature defect also decays as the inverse square root of distance. It is demonstrated that these results are accurately predictable from a basic similarity analysis beginning with Townsend's measured velocity decay on the axis; the turbulent Reynolds number of 13.0 agrees closely with Townsend's 12.5. The corresponding Prandtl number found lies in the range from 0.65 to 0.70.
Transport Cross Sections for Screened and Cutoff Coulomb Potentials
Authors: Suchy Kurt
Published: February 2004

The analytic expressions for the transport cross sections of a cutoff Coulomb potential agree with the numerical results of an exponentially screened potential if the cutoff radius is suitably related to the screening Debye-Hückel length and the Landau length.
Dominant Source of Soft X Radiation from Coaxial Discharge Tubes
Authors: Beckner E. H. , Clothiaux E. J. , Smith D. R.
Published: February 2004

A detailed study was made of the spatial and spectral characteristics of x rays produced in a coaxial discharge tube.
Suppression of ∇B Drift in Curved Theta Pinch
Authors: Goldman L. M. , Hurwitz H. , Kilb R. W.
Published: February 2004

Introduction of a conducting ring transverse to the axis of a curved theta pinch and inside the vacuum tube creates an equilibrium position for the plasma on the curved thetapinch axis.
Variational Study of Plasma Oscillations with Diffusion in Velocity Space
Authors: Babloyantz Agnessa
Published: February 2004

It is shown that the local potential method can be applied for the study of plasma oscillations in the presence of linear and nonlinear collision operators.
Transport Properties of Almost-Lorentzian Mixtures
Authors: Sandler Stanley I. , Mason E. A.
Published: February 2004

It is shown that the transport coefficients for an almost-Lorentzian mixture (mβ/mα ≪ 1, nβ/nα < 1) can be computed as a perturbation to the coefficients for a true Lorentzian mixture, which are known exactly. This method of computation is found to be much more efficient than the usual Chapman-Enskog method. Application to partially ionized gases is discussed.
Forced Model Equation for Turbulence
Authors: Jeng Dah-Teng
Published: February 2004

An artificial random force is introduced into Burgers' model equation for turbulence. This forced model equation is solved numerically as an initial-value problem. Both the driving force and initial velocity field are assumed Gaussian and are generated by a white noise process. Many statistical properties of this model for turbulence are studied. By adjusting the external force, the turbulence can reach an equilibrium state. The velocity correlation function and energy spectrum are calculated for the equilibrium turbulence. It is found that the energy spectrum falls off as the inverse second power of the wavenumber. The velocity correlation function is similar to the result obtained in real turbulence experiments. With Gaussian random driving force and Gaussian initial velocity field, it is found that the velocity field remains very nearly Gaussian by comparing the fourth-order velocity correlation with the quasinormal assumption. Although the process remains very nearly Gaussian, it is found that the projection of the process on the initial white noise process becomes smaller and smaller. This is to be expected, since the dynamic system is escaping from the original random base.
Properties of Magnetically Balanced Arcs
Authors: Nicolai Leland M. , Kuethe Arnold M.
Published: February 2004

Experimental results on steady magnetically balanced arcs in supersonic external flows are presented and analyzed, along with investigations elsewhere in subsonic flows, to determine the important similarity parameters. The studies indicate that the steady arc has a central core, impervious to the external flow, within which differential Lorentz forces generate a circulation analogous to that generated by gravity forces in nonuniformly heated gas in a horizontal tube. The conservation equations indicate that a “Lorentz convection parameter,” analogous to the Grashof number in free convection phenomena, is an important similarity parameter over a significant range of arc variables. A “characteristic velocity” for the core circulation is indicated. The similarity parameters that provide the interpolation between the properties of subsonic and supersonic balanced arcs indicate the approximations permissible for a first-order solution to the internal circulation. It is inferred from the results that to a first approximation the thickness of the enthalpy boundary layer varies linearly with the reciprocal of the Reynolds number of the external flow.
Tubular Pinch and Tearing Instability
Authors: Anderson Oscar A. , Kunkel Wulf B.
Published: February 2004

Theoretical considerations and previous experimental findings with fast tubular (cylindrical sheet) pinch discharges are reviewed briefly. More recent work with magnetic probes, as well as streak and Kerr cell photography, corroborates that the sheet-current configuration can be sufficiently stable to survive a fair number of pinch oscillations. It is shown, however, that under conditions of high compression the current layer is likely to break up into a set of individual channels because of a resistive instability. The process involves tearing and reconnection of magnetic field lines. Wavelengths and growth rates seem to be in agreement with rough theoretical predictions. The current channels form separate linear pinches, which under certain circumstances disintegrate subsequently by a secondary instability. A generally turbulent behavior results. Tearing is not prevented by superposition of a strong axial magnetic field, again in agreement with theory, although a slight retardation is noted. When deuterium is used in the discharge, neutrons are emitted. Presumably because of the slow rate of reconnection in most of our studies, the neutrons appear mainly during the secondary instability, rather than at the time of tearing. These findings are of interest both to astrophysics and to controlled-fusion research.
Rarefaction Shock Possibility in a van der Waals-Maxwell Fluid
Authors: Kahl G. D. , Mylin D. C.
Published: February 2004

The rarefaction shock is found to be impossible practically in an equilibrium van der Waals-Maxwell fluid, in and across all phase regions, although numerical tables seem to indicate the opposite result. The existence of this type of shock depends explicitly on the constant-volume specific heat, as well as the pressure equation of state. The form of specific heat assumed here includes contributions from translation, rotation, and vibration energies of the molecule; Einstein functions are used to represent the latter. In particular, the vaporizing expansion wave in the saturated liquid phase cannot be discontinuous. Metastable states of supersaturation are not considered. Despite the results for this theoretical model, the necessary conditions for the rarefaction shock are found to be satisfied, in principle, for a small region near the critical point of a real two-phase fluid (steam).
Relaxation Rate Spectrum of the Linearized Boltzmann Equation for Hard Sphere
Authors: Yan C. C.
Published: February 2004

The linearized Boltzmann equation for the hard-sphere gas is analyzed by comparing the eigenvalues of its relaxation rate with those of the corresponding foreign gas equation. An analysis of the latter, carried out by reduction to a second-order differential equation, exists elsewhere. It is shown for the angular indices 0 and 1 that the Boltzmann equation has an infinite set of eigenvalues each of which is smaller than the corresponding eigenvalue of the foreign gas equation. The basic theorem is also valid for the angular index 2. However, as the properties of the foreign gas equation have not yet been established for this case, only tentative conclusions can be drawn. The two equations share the same continuous spectrum; it covers all values larger than a positive minimum. The discrete series found are asymptotic to the minimum.
Neutral Particle Flux Measurements in a Plasma Wind Tunnel
Authors: Patrick R. M. , Pugh E. R. , Jonkman R. M.
Published: February 2004

The neutral particle flux in a plasma wind tunnel has been measured using a BeCu detector and has been found to be less than 1% of the ion density making it very unlikely that neutrals play an important role in the dissipation processes in the collision-free flow.
Quantum-Mechanical Plasma Transport Theory
Authors: Williams R. H. , DeWitt H. E.
Published: February 2004

The quantum-mechanical convergent kinetic equation of Gould and DeWitt is used for the calculation of static transport coefficients through first order in the plasma parameter for a fully ionized, nondengenerate, two-component plasma near thermal equilibrium. The equation is solved with the standard Chapman-Enskog procedure using a three-term Sonine polynomial expansion. Since close collisions and dynamic screening effects are treated correctly, the results contain both logarithmic (dominant) and nonlogarithmic (subdominant) terms evaluated exactly to first order in the plasma parameter. Since close collisions are treated quantum mechanically the transport coefficients obtained are valid for a wide range of temperatures. For the case where only one Sonine polynomial is used in the evaluation of the electrical conductivity, the result obtained here reduces to that of Kivelson and DuBois in the high-temperature limit (kT ≫ Ry) and to that of Gould and DeWitt in the low-temperature, classical limit (kT ≪ Ry). Using more than one Sonine polynomial in the expansion of the distribution function, we obtain for the electrical conductivity σ(χ) = c(χ)σ(1), where χ is the number of terms in the Sonine expansion and σ(1) is the result for one term. In the limit where the Coulomb logarithm is large, c(3) = 1.95 and c(∞) = 1.973, so that our results are accurate to 1 or 2% for a wide range of temperatures (including kT ∼ Ry).
Enhanced Scattering and Anomalous Absorption of Light Due to Decay into Plasma Waves
Authors: Bornatici M. , Cavaliere A. , Engelmann F.
Published: February 2004

An intense collimated light beam of frequency ωt incident on a quiescent plasma with plasma frequency ωpe ≪ ωt can couple with electron plasma waves, to enhance their level well above the equilibrium value. As a consequence, the spectrum of the scattered light “reddens,” and a part of the beam energy is transferred to the plasma. For a bandwidth Δω < ωpe of the beam, two basic regimes are important: one where the enhanced fluctuations travel at large angles to the light beam and which is the equivalent at high intensities of the equilibrium collective scattering, and a second, where electromagnetic and plasma waves have phase velocity nearly parallel and of the same order which seems suited for an important absorption of the light. Competing processes such as instability of the scattered light, and decay of plasma waves into ion-acoustic waves, become important in certain ranges of the beam and plasma parameters. All the mentioned processes are investigated in detail in the framework of lowest-order mode coupling using a corrected random-phase approximation. The results indicate that nonlinearly enhanced scattering should be detectable for a beam of laser light passing through a laser-produced plasma, whereas it seems doubtful that the considered mechanism can produce an appreciable anomalous absorption.
Elongational Flow of a Dilute Suspension of Viscoelastic Spheres
Authors: Kaloni P. N. , DeSilva C. N.
Published: February 2004

Steady slow elongational flow of a dilute suspension of viscoelastic spheres is analyzed within the framework of the theory of oriented fluids.
Stationary Equilibrium for the Toroidal Theta Pinch
Authors: Tasso H. , Green B. J. , Zehrfeld H. P.
Published: February 2004

It is already known that static (velocity V ≡ 0), axisymmetric, toroidal equilibria with a purely toroidal magnetic field (toroidal theta-pinch configuration), do not exist. Here, this result is generalized to the case where the effects of inertia are included.
Axial Pressure Gradient in Direct-Current Discharges
Authors: Oskam H. J.
Published: February 2004

The axial pressure gradient in dc discharges due to the previously reported volume force on the neutral particles is calculated both for closed and by-pass systems assuming laminar gas flow.
Observation of Oscillations at the Ion-Ion Hybrid Frequencies
Authors: Haas G. M.
Published: February 2004

An instability in a beam-generated plasma column has resulted in the observation of oscillations at the ion-ion hybrid frequency.
Higher-Order Landau Modes
Authors: Derfler Heinrich , Simonen Thomas C.
Published: February 2004

A systematic account of the infinitely many solutions of Landau's dispersion relation verifies that there is always a least-damped wave provided the wavenumber is real and not zero. This no longer holds when the frequency is real; yet, the mode originally considered by Landau predominates in a limited range. Strong “coupling” is found between this wave and higher-order modes at complex frequencies, or when collisions are taken into account. However this coupling does not give rise to resonances other than at the plasma frequency. Short tables of Landau poles and singular points of the dispersion relation conclude this account.
Low-Frequency Waves and Instabilities on the Positive Column in a Magnetic Field. I. Analysis and Study of Axisymmetric Modes
Authors: Ewald H. N. , Crawford F. W. , Self S. A.
Published: February 2004

An analysis is presented for the normal modes of low-frequency wave propagation on the positive column in an axial magnetic field. Dispersion characteristics are obtained from a hydrodynamic treatment by perturbing a steady-state discharge model which includes generation and ion inertia, and is valid for arbitrary pressure. The resulting complex eigenvalue problem is solved numerically by use of a Fourier-Bessel expansion. In general, two types of waves are found for a given frequency: ion-acoustic waves and electron waves. For the regions of parameter space appropriate to laboratory discharges, the ion-acoustic wave branches are predicted to be heavily damped, expect at low pressures where the computer solutions are in general agreement with available experimental data. The electron wave branches do not show instability for axisymmetric modes (m = 0), but can be unstable for asymmetric modes (m ≠ 0). Stable modes only are considered and it is shown that some hitherto unexplained damped waves, observed experimentally, are identifiable as symmetric electron-wave modes (m = 0).
Nonlinear High-Frequency Plasma Conductivity
Authors: Salat A. , Kaw P. K.
Published: February 2004

Some numerical results for the high-frequency nonlinear conductivity of a fully ionized plasma are presented. Special attention has been given to the case when the frequency ω of the applied electromagnetic field is close to the electron plasma frequency ωp. Apart from its intrinsic theoretical interest, this frequency range is of relevance to the problem of production and heating of plasmas by laser irradiation.
Transient Plasma Sheath—Discovered by Ion-Acoustic Waves
Authors: Alexeff I. , Jones W. D. , Lonngren Karl , Montgomery David
Published: February 2004

For a high negative voltage V0 placed impulsively at the edge of a plasma, a sheath is formed of thickness X = (2eV0)1/2(4πnie2)−1/2 This sheath is observed by extrapolating the position of the leading edge of an ionic sound-wave pulse back to zero time. The ion number density can be obtained from this sheath.
Diffusion of Precursor Ions and Electrons Upstream of a Strong Shock Wave Propagating down a Shock Tube
Authors: Cohen Ira M.
Published: February 2004

Photoionization upstream of strong shock waves produces ion-electron pairs. These charged particles diffuse to the walls of the shock tube where they recombine unless they are first overtaken by the advancing shock. This diffusion problem, governed by the particle flux equations and Poisson's equation for the self-consistent electric field, is considered in the limiting situation when a dimensionless photoionization rate (α) and dimensionless shock speed (νs) are large, and the ratio of ion to electron diffusion coefficients (δ) is small. The α and νs limits separate the region of production by photoionization from regions of charged particle diffusion. The δ limit separates regions of electron diffusion from regions of ion diffusion. The subproblems in these regions are formulated and solutions are obtained when the electrostatic potential at the shock surface is small. The electric current density to the shock tube wall is calculated and the result inverted to express the photoionization rate as a function of current density. The centerline potential is also found and inverted to yield another expression for the photoionization rate.
Surface Effects of Vortices in Helium Films
Authors: Clark R. C.
Published: February 2004

The presence of quantized vortices in helium films causes large fluctuating pressures on the surface. A variational method of general applicability for calculating the surface shape of flow over a vortex is developed, but it is shown that in helium films the surface tension will eliminate the disturbance. A film may be treated locally as a very narrow channel with a moveable rigid wall. If the vortices are of the order of the film thickness apart or less, it is shown that the mean pressure on the surface due to their presence may significantly reduce the film thickness.
Three-Dimensional Boundary Layer with Uniform Mass Transfer
Authors: Libby Paul A.
Published: February 2004

The three-dimensional laminar boundary layer near the windward generator of a cone at an angle of attack subjected to uniform mass transfer, either suction or injection, is studied by means of a series solution. The important wall values which permit application of the results to the prediction of skin-friction, heat transfer, and surface streamline divergence are tabulated for a wide variety of Mach numbers, wall temperature ratios, and values of a parameter related to the angle of attack of the cone. For suction the results are shown to approach a three-dimensional, asymptotic suction boundary layer. For injection indications of “blow off,” and its behavior with the aforementioned parameters are found.
Model Kinetic Equation for Dense Gases and Liquids
Authors: Wisnivesky D.
Published: February 2004

A kinetic theory approach to collision processes in dense gases and liquids is presented. The nonlinear collision operator is constructed in terms of the first few moments of the distribution function and contains both a reversible and an irreversible part under time inversion. The advantage of this model is that the linearized equations can be solved exactly. The kinetic equation is used to discuss various problems in the long-wavelength regime, and it is shown that it reproduces many of the properties of dense systems.
Flow in the Entrance Region of Ducts
Authors: Wiginton C. L. , Wendt R. L.
Published: February 2004

A technique for the solution of an eigenvalue problem arising in entrance region flow is presented along with a simplification of the nonlinear transformation used with such problems. From this, certain other results are obtained.
Plasma Density Measurement by Electromagnetic Wave Propagation at Small Angles to Magnetic Field
Authors: Bachynski M. P. , Gibbs B. W.
Published: February 2004

The propagation of a left-circularly polarized plane wave in a plasma at small angles to the static magnetic field direction shows a sharp “dip” in the wave amplitude when the plasma frequency equals the wave frequency.
Choking of a Subsonic Gas Flow by Thermal Radiation
Authors: Moore Franklin K. , George Yves H.
Published: February 2004

The process of thermal choking of a subsonic flow of a grey, ideal gas by absorption of thermal radiation from an upstream source is analysed. The flow may be considered produced by a shock. Calculations for streamwise variation of flow properties are presented, and, for the radiation-dominant case, an initial transparent process, a final Rosseland process and a matching solution are found analytically. A simple model is given for finding the radiation source temperature required to produce choking.
Stability of a Plane Fluid Interface in the Presence of a Transverse Electrostatic Field
Authors: Raco Roland J. , Peskin Richard L.
Published: February 2004

An equation of motion for the amplitude of the perturbation of the interface of two incompressible fluids is obtained under the specification of small viscosities and small electrical conductivities. This equation describes the motion of a damped harmonic oscillator with the effects of the electric field given as: (1) a forcing function proportional to the displacement, and (2) a forcing function proportional to the time integral of the displacement. A stability analysis of this equation shows how the electrical conductivity, surface charge, frequency of the applied field, viscosity, surface tension, electric permittivity, fluid depth, and density affect the stability of the fluid interface. The destabilizing effect of the surface charge and the stabilizing effect of the viscosity are illustrated for dc and ac applied fields. It is shown that the minimum dc destabilizing voltage can be lower than the value given by Taylor and McEwan, and that instability can result with an ac field that is about 0.2 the strength of the destabilizing dc field.
Edge Effect of a Flush Electrostatic Probe
Authors: Schubert Gerald
Published: February 2004

The edge effect problem for a flush electrostatic probe is modeled by the flow of a weakly ionized compressible gas past a discontinuous wall potential. The basic flow is a Couette flow and the potential jump is applied at the lower wall which is thus divided into positive and negative current collectors. For a sufficiently small applied potential discontinuity the problem may be linearized about a basic state whose characteristics are known numerically. The linear problem retains the full coupling and ellipticity of the nonlinear one. Results are presented for the total current collected by each electrode, the magnitude of the jump in current density at the junction of the electrodes and the dependence of this quantity on Reynolds number, the first-order moments of the current density, and the upstream and downstream length scales for the current collection. For conditions investigated here, these length scales are several channel thicknesses. Thus, the operation of a flush electrostatic probe may be completely dominated by edge effects.
Kinetic Theory of Inhomogeneous Systems
Authors: Price John C.
Published: February 2004

A theory is developed which treats the coupled equations of the various hierarchies as simultaneous equations in time. This scheme proceeds by successive approximations rather than a power series expansion in the small parameter ([nλd3]−1 in a plasma, nr03 in a Boltzmann gas). The theory is suitable for the derivation of equations for nonuniform and force driven systems. Examples are given for a plasma and a Boltzmann gas.
Parametric Excitation and Higher-Order Mode Coupling Effects in Plasmas
Authors: Goldman Robert
Published: February 2004

Parametric excitation [wherein a Langmuir oscillation at (ω k) simultaneously drives an ion-acoustic mode at (ω′, k′), one sideband Langmuir oscillation at (ω − ω′, k − k′), and possibly another at (ω + ω′, k + k′(] is considered. Steady-state solutions are found for these systems in various limits, taking into account contributions which are third order and higher in the mode fields. Connections with experiment are discussed.
Exact Elementary Solutions of the Spectral Equation of Nonstratified Turbulent Shear Flow
Authors: Panchev S.
Published: February 2004

The spectral equation of nonstratified turbulent shear flow in the equilibrium range is solved analytically. A numerical example is computed and presented.
Pulsed Breakdown in Nonuniform Fields
Authors: Epstein Melvin
Published: February 2004

A variational method is described for predicting high-frequency pulsed breakdown of gases having nonuniform properties and/or subjected to spatially nonuniform fields. The method is illustrated by calculating the breakdown criterion for gas contained between two parallel planes.
Formulation of Plasma Wave Echoes as an Initial-Value Problem
Authors: Nishikawa Kyoji
Published: February 2004

Landau's solution for the linearized Vlasov equation describes a plasma wave echo for a certain class of initial perturbations. A criterion for the occurrence of an echo is examined, and new types of higher-order echoes are predicted.
Action of a Variable Stress at the Surface of Water Waves
Authors: Longuet-Higgins M. S.
Published: February 2004

A boundary-layer argument shows that, paradoxically, a variable tangential stress which is greatest at the wave crests and least in the wave troughs produces a thickening of the boundary layer on the rear slopes of the waves and a thinning on the forward slopes. In deep water, a variable tangential stress ⊥ is precisely equivalent to a normal stress i⊥ in quadrature with the tangential stress. The corresponding rate of growth of the waves is calculated.
Microwave-Induced Plasma Shield Propagation in Rare Gases
Authors: Bethke George W. , Ruess Allen D.
Published: February 2004

It has been observed that microwave irradiation of localized weak ionization in heavy rare gases can cause an ionization wave (“plasma shield”) to form and propagate toward the rf source. This ionization wave is preceded by an electron precursor, with the electron density at the ionization wave front increasing very rapidly to a maximum followed by a relatively slow plasma decay. At rf power levels well below normal breakdown, the ionization wave will form and then propagate at velocities from about 2 × 103 cm/sec to 1 × 107 cm/sec. Discontinuous changes of ionization wave velocities with changes in rf power and gas pressure indicate the existence of three different velocity-controlling mechanisms in the gas pressure and rf power ranges investigated. These mechanisms for ionization wave formation and propagation have been investigated in xenon, krypton, and argon gases, and are discussed.
Electromagnetic Echoes in Collisionless Plasmas
Authors: Wong Alfred Y.
Published: February 2004

A new process for generating electromagnetic echoes is proposed which depends upon the velocity distribution and the magnetic interaction enhanced by plasma collective effects.
Nonlinear Theory of the E x B Instability
Authors: Kim John J. , Simon Albert
Published: February 2004

A weakly ionized plasma will go unstable in the presence of a density gradient and parallel electric field, both at right angles to a magnetic field, if the electric field is of the right sign and sufficiently large. The nonlinear limit of the first mode to go unstable when E is increased is determined as a function of Δ [Δ ≡ (E - Ec)/Ec]. A general theory of this small amplitude behavior is used. The mode amplitude, frequency shift, density flattening, electric field change, and anomalous plasma transport are obtained as functions of Δ. It is shown that mode coupling corrections are small, and hence that the quasilinear result is sufficient.
Weak Turbulence Theory of Velocity Space Diffusion in a Magnetic Field
Authors: Manheimer Wallace M.
Published: February 2004

The particle-wave interaction to arbitrary order in perturbation theory is investigated for a weakly turbulent plasma in the presence of a uniform magnetic field. It is found that to every order in perturbation theory, the ensemble average distribution function obeys a diffusion equation in v⊥ vz space. By conservation of energy and momentum between waves and particles, the growth or damping rate to any order may be determined. The damping rate for nonlinear cyclotron damping, the particle energization rate from very low-frequency turbulence, and the growth rate for a nonlinear instability are calculated.
Inviscid Layers in Magnetohydrodynamics
Authors: Buckmaster John
Published: February 2004

The equations of inviscid magnetohydrodynamics, appropriate when the induced magnetic field can be neglected, are studied when the interaction parameter N is very large. The limit equations, in which the nonlinear inertia terms do not appear, cannot fully describe general inviscid flow situations suggesting the existence of inviscid boundary layers in which the missing terms must be reinstated. Similarity solutions are obtained for two kinds of layers, one perpendicular to the magnetic field and the other parallel to the magnetic field. The parallel layers are backward jets and constitute our most important result. The existence of the perpendicular layers, which look like reversed shock layers, may have implications for flow in ducts with discontinuous area changes.
Precursors Ahead of Shock Waves: I. Electron Diffusion
Authors: Weymann Helmut D.
Published: February 2004

Experimental investigations of precursors ahead of pressure-driven shock waves in argon lead to the conclusion that for the existing conditions electron diffusion is the dominant cause of the precursors. A theoretical analysis of the electron temperature and density is presented.
Interaction of Magnetoacoustic and Entropy Waves with Normal Magnetohydrodynamic Shock Waves
Authors: Westphal K. O. , McKenzie J. F.
Published: February 2004

Equations are obtained from which the amplitudes of magnetoacoustic and entropy waves diverging from a normal magnetohydrodynamic shock as a result of an incident disturbance of the same kind can be computed, where we assume that the magnetic field is parallel to the flow. The solutions of these equations are then used to construct the ratios of the amplitudes of the transmitted to the incident waves. Also, the ratios of energy fluxes associated with the incident and transmitted waves are obtained in terms of the solutions of the governing equations. The formulas are applied to an example.
Property of Large-Amplitude Steady Electrostatic Waves
Authors: Valeo E. J. , Oberman C. , Kruskal M. D.
Published: February 2004

It is shown that the large-amplitude electrostatic waves of Bernstein, Greene, and Kruskal cannot be constructed from distribution functions which are monotonically decreasing functions of the particle energy.
Parametric Amplification in Plasmas with Negative Energy Waves
Authors: Goldman R. , Davidson R. , Hasegawa A.
Published: February 2004

Parametric amplification is considered for systems including negative energy waves. The results may differ qualitatively from those found without negative energy waves. In particular, it is possible to excite anti-Stokes' modes in the absence of Stokes' modes.
Parametric Excitation in a Plasma Slab
Authors: Goldman Robert
Published: February 2004

The theory of parametric excitation involving Langmuir and ion-acoustic waves for a homogeneous, plasma slab with specular reflection of particles at the slab walls is treated. Optimum thresholds are determined for one or two traveling waves incident on the plasma. In terms of electric fields within the plasma they are asymptotically the same as those previously calculated for infinite geometry; in terms of electric fields outside the plasma they may be much smaller. Two nonoptimum cases are also investigated. The first involves two incident traveling waves either of which by itself would produce an optimum threshold. The second consists of a single incident traveling wave which excites an infinite number of pump modes of the same size (in an asymptotic sense) within the plasma.
Waves and Instabilities in a Finite Plasma
Authors: Cheng C. C. , Harris E. G.
Published: February 2004

A dispersion relation is derived for electrostatic waves in a plasma confined between planes which perfectly reflect the particles but have no effect on the fields. A uniform magnetic field perpendicular to the planes is assumed. Both classical and quantum-mechanical derivations are given. In the quantum-mechanical derivation some terms appear which do not appear in the classical derivation. These terms are due to finite de Broglie wavelength of the particles. The classical dispersion relation is applied to the investigation of volume and surface plasma oscillations and volume and surface ion sound waves in an unmagnetized plasma and to volume waves in magnetized plasmas. Volume waves are characterized by a discrete set of parallel wavenumbers. The damping or growth of volume waves is nearly the same as that of a corresponding infinite plasma wave. The damping of surface waves is quite different.
Self-Consistent Kinetic Model for Two-Dimensional Cusped and Minimum-B Type Equilibria
Authors: Sestero A. , Giupponi P.
Published: February 2004

Plane quadrupolar cusp containment is studied in terms of the Vlasov equation for ions and electrons. The treatment applies both with and without a constant magnetic field component normal to the considered plane (respectively, minimum-B type and pure-cusp type confinement.) Under certain assumptions, the problem reduces to an elliptic nonlinear partial differential equation of the second order with Dirichlet boundary conditions, which is investigated numerically using standard relaxation methods. Solutions are found with cusp width as small as the electron Larmor radius; if the field lines are short-circuited, however, the smallest cusp width is of the order of the ion Larmor radius. The plasma outflow through the cusps is also computed, and the results are discussed.
Stability of Orbits in Combined Betatron and Azimuthal Magnetic Fields
Authors: Ferrari Lawrence A. , Zucker Martin S.
Published: February 2004

In a cylindrically symmetric magnetic field the requirement for a stable betatron orbit is that there be a minimum in the vector potential component Aθ, i.e., the induction electric field strength. The problem of stability when an azimuthal or Bθ field is added to the betatron field is considered. It is shown that when Bθ is present there must be an extremum in Aθ for stable motion. This criteria includes the pure betatron field as a special case so that the Schmidt beam current formula still applies. Schmidt's result is extended to include resistive as well as runaway currents, and its application to the various plasma betatron experiments is discussed.
Direct Current Conductivity in a Mercury Discharge
Authors: Anastassiades A. J. , Valamontes S. E.
Published: February 2004

The effect on the direct-current conductivity, and electron temperature of ion-acoustic oscillations in a mercury discharge was studied experimentally. The waves were spontaneously excited in the discharge.
Nonlinear Theory of Inviscid Taylor Instability Near the Cutoff Wavenumber
Authors: Kiang Robert L.
Published: February 2004

Uniform solutions for the nonlinear oscillation part of the Taylor instability problem are obtained. Two matchable solutions are needed to describe the problem fully—one for wavenumbers sufficiently larger than the cutoff (outer solution), and one for wavenumbers near the cutoff (inner solution). A nonlinear cutoff is obtained only after the inner solution is obtained. Singular perturbation methods are used for both the outer and the inner problems.
Second-Order Constitutive Relations for Polyatomic Fluids
Authors: McCoy Benjamin J. , Dahler John S.
Published: February 2004

The Burnett dilute gas second-order theory of the heat flux and pressure tensor is generalized to the rigid polyatomic models, viz., the rough sphere, the loaded sphere, and the spherocylinder. The general Chapman-Enskog method is developed for these rotators. The constitutive equations are expressed in terms of the irreducible tensors associated with gradients of velocity, temperature, and density. Tables and graphs of transport coefficients are presented to show the effect of internal molecular structure. The Wang Chang theory of weak shock waves and the theory of sound wave propagation are extended to dilute polyatomic gases. The transport coefficients for rough spheres and loaded spheres are used to estimate shock thicknesses and damping and velocity propagation coefficients.
Calculations of Gas Conductivity in Magnetohydrodynamic Shock Producing Devices
Authors: Hoffman Alan L.
Published: February 2004

The simple scalar conductivity based on electron collisions with other particles is shown to be the governing parameter in determining current sheet diffusion and energy dissipation in magnetohydrodynamic shock producing devices. Simple methods are developed for calculating this scalar conductivity based on previous similarity solutions and experimental measurements of current sheet growth. These methods are shown to be applicable to inverse pinch experiments described in an accompanying paper, where the gas velocity in regions of the current sheet is constant. The position of the shock, through its influence on the gas velocity, is shown to exert a dominant influence on the current sheet diffusion.
Plasma Wave Echo Excited by Two Cyclotron Waves
Authors: Kamimura Tetsuo , Hasegawa Akira
Published: February 2004

It is shown that two cyclotron waves excited with a time interval τ between them, in a collisionless plasma, lead to a longitudinal plasma wave echo. The echo appears at the same time as in the case of excitation by two plasma waves.
Temperature Gradient Instabilities in Axisymmetric Systems
Authors: Liu Chuan Sheng
Published: February 2004

The temperature gradient effect on the stability of a plasma in the “maximum-J configuration” is studied and two possible instabilities due to temperature gradient are found in the axisymmetric system.
Ion Cyclotron Instabilities in Short Mirror Machine Plasmas
Authors: Cordey J. G.
Published: February 2004

An appropriate finite geometry theoretical model of a magnetic mirror machine is examined for ion cyclotron instabilities. The normal modes of the finite model are shown to be unstable even in the presence of large magnetic field gradients. The effect upon the ion cyclotron instability of particle mirroring is discussed. Electron Landau damping is shown to be stabilizing for these modes, but low mirror ratio machines will require high electron temperatures to stabilize instabilities at frequencies near the high harmonics of ωci.
Simple Model for a Rotating Neutral Planetary Exosphere
Authors: Hagenbuch K. M. , Hartle R. E.
Published: February 2004

The model neutral exosphere of Öpik and Singer for a nonrotating planet is generalized by permitting the corresponding barosphere to rotate uniformly at an angular velocity which may or may not be equal to that of the planet. For this case the velocity-distribution function, satisfying the collisionless Boltzmann equation, is constructed. Then, the density is determined from the distribution and compared with the corresponding result for a nonrotating planet obtained by Öpik and Singer. In addition, the radial and azimuthal fluxes are derived. Based on the result for the azimuthal flux, the point at which exospheric corotation can be said to have broken down is indicated for several conditions. It is shown that in all cases, for a given radius, the density at the equator exceeds the density at the pole. For example, a model terrestrial neutral exosphere of hydrogen, helium, and oxygen has density ratios between the pole and the equator of 0.984, 0.869, and 0.530, respectively, at r = 2R.
Exact Solution of Kinetics of a Model Classical Fluid
Authors: Percus J. K.
Published: February 2004

The hydrodynamic limit of the Enskog equation for one-dimensional hard cores is solved in general, and for the special cases of sound and shock propagation. This equation is shown to be the limit of the exact microscopic kinetics, which is also solved exactly.