bluuebunny/crossref_metadata_2025 huggingface dataset:
Transient Energy Transfer in a Gray Radiating Gas during Expansion
Authors: Lall P. S. , Viskanta R.
Published: December 2004

The problem of unsteady energy transfer during the expansion of a spherical mass of compressible, gray radiating gas at near-atmospheric pressure is analyzed. The gas is assumed to be perfect and in local thermodynamic equilibrium. Scattering of radiation as well as ionization and dissociation phenomena are neglected. Energy transfer by conduction is assumed to be insignificant compared to that by radiation or convection. The formulation of the problem is based on first principles of radiative transfer and gas dynamics and is thus valid for a medium of arbitrary optical radius. A finite difference scheme is employed to obtain a first approximation to the solution of the conservation equations. The numerical results are presented graphically for a wide range of parameters of physical interest.
Laminar Boundary Layer with Complex Composition
Authors: Libby Paul A. , Sepri Paavo
Published: December 2004

A study has been carried out of the laminar boundary layer in a nitrogen stream with mass transfer of a coolant injected through a porous surface. The composition of the coolant is an arbitrary mixture of gases of widely different molecular weights, namely helium, argon, nitrogen, and xenon. The diffusive and other transport and thermodynamic properties of the flow are described with reasonable accuracy. The predicted boundary-layer properties are found to differ considerably from those obtained from analyses using the commonly employed simplified descriptions of transport and thermodynamic properties. However, an analysis with simplified transport properties but with the different coefficients of specific heat for the various species taken into account is shown to give reasonable results for the wall temperature, at least for low rates of mass transfer.
Electrical Conductivity of Shock-Heated Air and Air-plus-Teflon Mixtures
Authors: Morsell A. L.
Published: December 2004

The electrical conductivities of shock heated air and air-plus-teflon mixtures have been measured using a method similar to the conducting gas-magnetic field interaction method described by Lin, Resler, and Kantrowitz. All measurements were made for an initial shock-tube pressure of 1 cm Hg. The air-Teflon mixture contained about 1 mole percent of Teflon. The shock speeds ranged from 2.93 to 5.58 mm/μsec corresponding to temperatures between 3150 to 6500°K and conductivities between 0.24 and 111 mhos/m. The electron densities corresponding to these conductivity values range from less than 1011 electrons/cm3 to about 1015 electrons/cm3. No difference in conductivity between the air and air-Teflon mixtures was observed. Except for two conductivity values measured for very low shock speeds, all the measured values differ by less than a factor of 2 from theoretical values computed for pure air in equilibrium.
Correlationless Plasma with Time-Dependent Background State
Authors: Imre Kaya
Published: December 2004

A Volterra type (second kind) integral equation is derived for the electric charge density starting from the Vlasov equation linearized with respect to a time-dependent spatially uniform background state. The kernel of this integral equation vanishes identically in the case when the background state is time-independent (i.e., in the usual Landau problem), and the inhomogeneous term reduces to the exact solution of the initial value problem in the same case. It is shown that the inhomogeneous term of this integral equation corresponds to the adiabatic approximation; hence, a Neumann series type solution can be constructed for the charge density by iteration of this inhomogeneous term for the case when the background state is varying slowly in time. Approximate solutions of this integral equation are obtained for the small time and asymptotic limits. It appears that for some particular cases it is possible to have nondecaying solutions for the continuum mode. This is in contrast with one of the basic assumptions of the quasi-linear theory of plasmas.
Stability of the Theta-Pinch. II
Authors: Haas F.A. , Wesson J.A.
Published: December 2004

In a previous paper [F.A. Haas and J.A. Wesson, Phys. Fluids 9, 2472 (1966)] the hydromagnetic stability of a β = 1 theta-pinch with a sharp boundary was considered. This work is here extended to a study of β < 1. Stability criteria are obtained and in particular it is shown that the m = 1 mode is stable if (1 - β) < (R/Rw)2 everywhere along the pinch, where R and Rw are the radii of the plasma and conducting wall, respectively. The case of a distributed radial pressure gradient is also considered.
Channel Flow of Gaseous Mixtures in Chemical and Thermodynamic Nonequilibrium
Authors: Pearson Walter E.
Published: December 2004

Nonequilibrium channel flow is analyzed for an arbitrary mixture of monatomic and diatomic gases with the assumption that the chemical and vibrational rate processes are not coupled. A new numerical formulation permits precise evaluation of the chemical and physical properties of the mixture in all regions of the flow. The special case of high enthalpy airflow in a hypersonic nozzle is examined, and a comparison is made with earlier results which use approximate equations in the near-equilibrium region of the flow. The comparison shows that when chemical rates are accurately known in this region, the description of the chemical nature of the flow in downstream regions is altered.
Thermodynamics of Rotating Liquid He II
Authors: Pollock F.
Published: December 2004

A thermodynamic calculation of the change in superfluid velocity with temperature is described. It is shown that (a) thermodynamics is compatible with a temperature-independent hydrodynamical criterion for superfluid flow, and (b) only discrete changes of superfluid velocities with the angular velocity of the container are consistent with thermodynamic equilibrium.
Linear Theory of Mechanical Equilibrium of Liquid Crystals of Nematic Type
Authors: Davison Lee
Published: December 2004

A linear theory of mechanical equilibrium of liquid crystals of the nematic type is developed and several solutions are given which illustrate the kind of effects predicted by the theory.
Turbulent Mercury Jet
Authors: Hoult David P.
Published: December 2004

Measurements of the mean velocity profiles of a free turbulent mercury jet in the presence of an axial magnetic field, with Reynolds numbers between 1 × 103 and 6 × 103 are reported. The Hartmann number, based on nozzle conditions, varied from zero to 40. It is found that the eddy viscosity divided by the square root of the kinematic momentum has a sharp maxima as a function of (Reynolds number)−1. A simple model which is consistent with the data is developed. The model suggests that, (1) the jet, although self similar, has a rate of energy dissipation which depends on phenomena occurring at the nozzle. (2) the maxima in eddy viscosity are caused by the excitation of a helical instability near the nozzle.
Charged Particle Diffusion by Violation of the Third Adiabatic Invariant
Authors: Birmingham T. J. , Northrop T. G. , Fälthammar C.-G.
Published: December 2004

An equation which describes statistically the motion of charged particles in response to fluctuating electric and magnetic fields is derived. The particles are assumed to be moving in a mirror-type magnetic geometry. In addition to a static magnetic field there are small superposed fields fluctuating randomly on such a time scale that the first and second adiabatic invariants, M and J, are conserved, but the third or flux invariant φ is violated. By using second adiabatic theory a two dimensional diffusion equation is obtained valid on a much longer time scale than that of the fluctuations. Elements of the diffusion tensor are time—space correlations of fluctuation-induced perturbations in the guiding center drifts. These drift perturbations are systematically derived and shown to reduce simply in various special cases.
Fundamental Solution of the Linear Boltzmann Equation
Authors: Yu Er-Yung
Published: December 2004

The fundamental solution of the linear Boltzmann equation in the two-dimensional steady case is presented. The linear Boltzmann equation governs the perturbed distribution function f in a steady flow over a point source. The point source is represented in the equation by a singular inhomogeneous term involving a delta function. The fundamental solution is split into three parts, f = fδ + fa + fb. Both fδ and fa are explicit. They are singular at the origin and decay exponentially for large r. The ``remainder'' fb, which satisfies an inhomogeneous linear Boltzmann equation, is bounded at the origin and behaves fluid-dynamically like a macroscopic flow for large r. At small r, the series expansion of fb consists of terms of integral powers of r and integral powers of r multiplied by ln r, with the zeroth power of r being the leading term. At intermediate and large r, fb is expressed in terms of the Euler fluid components.
Correlation of Rotating Vane Frequency with Anode Diameter in a Reflex Discharge
Authors: Dunnill W. A. , Shipp J. I. , Flowers J. W.
Published: December 2004

The rotation frequency of a vane of plasma in a hollow cathode reflex discharge has been shown to be a function of the effective inner radius of a ring-type anode.
Second Virial Coefficient for the Exponential Repulsive Potential
Authors: Bruch Ludwig W.
Published: December 2004

The classical second virial coefficient and its first two quantum corrections are evaluated for a repulsive exponential potential by the use of Laplace transforms. The results are used to estimate the effect of the intermolecular attraction in the high-temperature second virial coefficient of 4He and in its first quantum correction. An approximation is found for this first quantum correction at temperatures above 100°K for 4He. A simplified expression for the S-wave phase shift of the exponential repulsion is derived and is used to calculate a quantum-mechanical turning point for wave packets or effective hard core radius. Similar methods are applied to the Morse potential to evaluate the classical second virial coefficient and its first quantum correction and the S-wave phase shift.
Flows Induced by Nonuniform Magnetohydrodynamic Pinch
Authors: Chow Chuen-Yen , Brunell Randolph D.
Published: December 2004

Ring vortices are induced after the passage of an axial current through a stagnant conducting liquid contained between two concentric, corrugated glass tubes with a strong current flowing along the common axis of the tubes. Experiments have been conducted using transparent aqueous solution of copper sulfate suspended with fine aluminum powder for flow visualization. Flow patterns are photographed for the cases that the sinusoidal deformations on the tube walls are either in phase or completely out of phase, and one of the tubes is straight. The result agrees considerably well with that obtained previously from a linearized theory.
Study of Shock Waves in a Nonequilibrium Plasma
Authors: Christiansen Walter H.
Published: December 2004

Probe and recombination-radiation spectrum measurements were used to measure the electron number density and temperature profiles in front of a flat disc in a supersonic seeded-gas plasma. The region of interest extended several body diameters upstream of the disc and through the shock wave. The experiment covered a free stream electron density range of 4 × 1011 to 1.6 × 1012 cm−3 and an electron temperature range of 0.06 to 0.1 eV. The region of reduced luminosity upstream of the shock wave is shown to be associated with electron heating at constant electron density. The electron thermal conductivity is derived from measurements in the upstream region and gives reasonable agreement with the Spitzer formula. Measurements are made of the electron temperature change across the heavy-particle shock wave and of the over-all electron temperature ratio across the entire process. It is shown that the over-all electron-temperature ratio could not be predicted on the basis of an adiabatic one-demensional flow process in this experiment.
Correction to Stokes Law for a Charged Sphere Moving in a Polarizable, Compressible Liquid
Authors: Schappert G. T.
Published: December 2004

It is shown that Stokes law for a charged sphere of radius R moving slowly in a compressible polarizable liquid is F=6πRuη[1−135∂ρ∂p|Tα0ε0(ez4πεR2)2]
Decay of Spherical Blast Waves
Authors: Miles John W.
Published: December 2004

The theoretical result for the asymptotic decay of a spherical shock wave is shown to provide a useful extrapolation into that range in which numerical integration is unreliable and/or expensive, but where the decay is still significantly greater than acoustical.
Anomalous Electron Heating in an Adiabatic Compression Experiment
Authors: De Kluiver H. , Kawamura T.
Published: December 2004

Final electron temperature increases considerably in an adiabatic compression when oscillating electric fields are applied at the plasma shortly after injection. The anomalous resistance is consistent with the growth rate of an electron two-stream instability.
Attenuation of a Shock Wave due to the Nonequilibrium Ionization and Radiation
Authors: Rosciszewski Jan
Published: December 2004

The influence of nonequilibrium ionization and radiation on the flow generated by a strong shock wave is discussed. Particularly, the shock wave attenuation is calculated using linearized theory, assuming the degree of ionization to be much less than one.
Numerical Study of Two Fluid Rayleigh-Taylor Instability
Authors: Daly Bart J.
Published: December 2004

A new computing technique for the time-dependent calculation of the interaction of two incompressible fluids is used to study the linear and nonlinear phases of Rayleigh-Taylor instability. The variation of the linear growth rate with Reynolds number is examined for Reynolds numbers < 200 at a ratio of fluid densities of 2 : 1. These findings support Chandrasekhar's predictions of the magnitude of the growth rate and the Reynolds number for which maximum growth rate is attained. A series of inviscid flow calculations, at density ratios between 1.1 : 1 and 10 : 1, is used to explore the effect of density ratio on aspects of the nonlinear Rayleigh-Taylor instability. It is found that such influences as form drag and Kelvin-Helmholtz instability decrease rapidly in importance as the density ratio increases.
Numerical Solution of the Three-Dimensional Equations of Motion for Laminar Natural Convection
Authors: Aziz K. , Hellums J. D.
Published: December 2004

A method is presented for numerical finite difference solution of the equations of motion in three dimensions. The complete Navier-Stokes equations are transformed and expressed in terms of vorticity and a vector potential. The transformed equations are solved using an alternating direction method for the parabolic portion of the problem, and successive over-relaxation for the elliptic portion. The classical problem of convection in fluid layers bounded by solid walls and heated from below is solved in both two and three dimensions. Comparison with other methods and with prior work in two dimensions shows that the new method presented here has important advantages in speed and accuracy. Apparently, there has been no successful prior work in three dimensions except in cases where one component of the equation of motion is highly simplified.
Charge Relaxation on a Moving Liquid Interface
Authors: Melcher James R.
Published: December 2004

An interaction is described where a spatially and temporally periodic distribution of surface charge is induced on a moving fluid interface by means of adjacent electrodes. The fluid convection shifts the surface-charge distribution downstream, with an attendant shift in the spatial phase of image charges on the electrodes. This phase shift is sensed electronically through the electrodes to provide a quantitative measure of the relationship between surface convection and charge relaxation. It is theoretically and experimentally shown that the fluid velocity can be measured in a way that is not sensitive to the conductivity, and that the conductivity can be measured independent of the fluid velocity. No electrical or mechanical contact with the fluid is required, and hence the interaction is attractive for basic studies of natural conduction in the region of a moving interface while satisfying the requirements for flow and conductivity measurements that may involve either fluids or solids.
Dissipative Wave Propagation in Compressible Magnetohydrodynamics
Authors: Salathé Eric P. , Sirovich Lawrence
Published: December 2004

A complete discussion of the linearized, compressible magnetohydrodynamic equations is given. No restriction is placed on any of the dissipative mechanisms, and moreover the nature of the gas is unspecified. Fundamental solutions are obtained for arbitrary values of the pertinent dimensionless parameters as well as field orientation. Use of the fundamental solutions is illustrated by the construction of solutions for several problems. Various inviscid limits are considered, and restrictions on inviscid theory thereby result.
Charge Separation Effects in the Ferraro-Rosenbluth Cold Plasma Sheath Model
Authors: Davies Christine M.
Published: December 2004

The exact relativistic treatment is given of the Ferraro-Rosenbluth cold plasma sheath model, and is compared with the nonrelativistic solution given previously by Sestero. It is found that the anomalous solution obtained by Sestero, namely, the fact that the ions turn back before the electrons, persists in the relativistic treatment although the ion stream and electron stream are separated in space. As in the Sestero solution it is found that the over-all charge in the sheath is not in general zero. Numerical illustrations are given for the case when the velocities are comparable with the velocities encountered in the solar wind.
Convective and Absolute Harris Instabilities
Authors: Beasley C. O.
Published: December 2004

It has been found that, for some ranges of plasma parameters, the Harris modes associated with the non-Maxwellian ion distributions characteristic of energetic injection experiments change from convective to absolute with increasing density.
Thermal Conductivities of Plasmas in General Force Fields
Authors: Meador W. E.
Published: December 2004

It is shown that the Meador-Staton results for the reaction conductivity are valid, in the case of ambipolar diffusion, for general electromagnetic fields and nonuniform total pressure. Comparisons are made with the method of Ahtye.
Quantization of Circulation in a Non-Ideal Bose Gas
Authors: Pollock F.
Published: December 2004

The dilute Bose gas is considered in the Bogoliubov approximation for the purpose of accounting for the quantization of circulation for the entire superfluid. It is found that the states of lowest energy have the motion of the entire system governed by the condensate.
Rarefied Gas Flow between Parallel Plates Based on the Discrete Ordinate Method
Authors: Huang A. B. , Giddens D. P. , Bagnal C. W.
Published: December 2004

A general solution of the linearized Boltzmann equation with the Bhatnagar-Gross-Krook model for the problem of a rarefied gas flowing between two parallel, infinite plates is developed based on the discrete ordinate method. Analytic expressions of the perturbed distribution function, the velocity profile, and the gas volume flow rate, particularly suitable to numerical calculations, are thus obtained. These make possible obtaining the numerical solutions to any desired degree of accuracy. The results are compared with the analytical solutions of the half-range moment method and with the numerical solutions of Cercignani.
Studies of a Coaxial E × B Plasma Gun
Authors: Steinhaus James F. , Barr William L. , Oleson Norman L.
Published: December 2004

The hydrogen plasma produced by a coaxial E × B gun located in a magnetic mirror system was extensively studied. When the gun was externally shorted (crowbarred) at peak avalanche current, the magnitude of the reverse current due to the angular momentum of the rotating plasma was found to depend on the axial position of the gun with respect to the upstream magnetic mirror. Microwave measurements gave a maximum electron density of 1.7 × 1013 cm−3 in the presence of neutrals of 1014 cm−3 with electron decay times of 300 to 400 μsec in the 1011 to 1012 per cm3 range. Analysis of the optical spectra showed the presence of H, H2, Fe, Fe+, Cr, Cr+, Mn, Mn+, and Mo, and indicated that the electron temperature was approximately 5 eV. Evidence is presented which indicates that internal shorting of the discharge is the result of a low-resistance path developing along the axial magnetic field lines to the downstream chamber walls. Floating probe measurements revealed that the electric field depended both on current and radial position, and showed little evidence of an anode sheath. Some measurements were also taken with helium and nitrogen as working gases.
Recombination Instability
Authors: D'Angelo N.
Published: December 2004

A recombination instability is considered which may arise in a plasma if the temperature dependence of the volume recombination coefficient, α, is sufficiently strong. Two cases are analyzed: (a) a steady-state plasma produced in a neutral gas by x rays or high energy electrons; and (b) an afterglow plasma.
Transport Coefficients in a Plasma. I. Pure Gas
Authors: Braun E.
Published: December 2004

The Lenard-Balescu kinetic equation for a one-component inhomogeneous plasma is solved by the Chapman-Enskog method. The transport coefficients are calculated taking into account collective effects. For most plasmas of interest it is found, to a first approximation, that the value of these coefficients is diminished as compared to that obtained using the Boltzmann-Landau kinetic equation and cutting off integrals at the Debye distance. The higher approximations are very small compared to the first one.
Transport Coefficients in a Plasma. II. Binary Mixture
Authors: Braun E.
Published: December 2004

The transport coefficients for a binary plasma are calculated starting from the Lenard-Balescu kinetic equation. The results show that for most plasmas of interest the value of the coefficients are diminished as compared to those obtained from the Boltzmann-Landau kinetic equation.
Confinement of Energetic Plasma in Magnetic Mirrors in the Model C Stellarator
Authors: Yamato H. , Iiyoshi A. , Rothman M. A. , Sinclair R. M. , Yoshikawa S.
Published: December 2004

Ion cyclotron waves are set up in a toroidal plasma (previously formed by Ohmic heating) contained in the Model C stellarator, and absorbed at local minima in the confining magnetic field. The plasma (1012−1013 cm−3) confined in these magnetic mirrors under certain conditions has little interaction with the main body of the plasma; the perpendicular ion temperature can reach several keV, while the electrons remain at less than 100 eV. We can thus reach a regime not yet available to other mirror confinement experiments. The observed cooling of the plasma in the mirrors agrees with the calculated ion-ion and ion-electron loss processes and charge exchange. At the highest temperatures and lowest densities, the confinement time in the mirrors is limited to ∼ 1 msec, most likely by charge exchange with a steady influx of neutral hydrogen. We find no evidence for any anomalous particle- or energy-loss process, although several instabilities are predicted by theory to occur.
Electrical Conductivity of a Partially Ionized Gas in a Magnetic Field
Authors: Schweitzer S. , Mitchner M.
Published: December 2004

The use of the Lorentzian scalar electrical conductivity as a basis for constructing a mixture rule for partially ionized gases is extended, and mixture rules for the tensor components of the electrical conductivity are proposed. A comparison with the third Chapman-Enskog approximation shows that the proposed mixture rules give conductivity values which are within approximately 15% of the more accurate results. A similar comparison for the mean-free-path formulas (neglecting ion-slip) is less favorable. It is concluded that the proposed conductivity formulas provide a satisfactory method for calculating the tensor conductivity for a wide range of electron-neutral cross sections and magnetic field strengths, and for all degrees of ionization.
New Formulation of the Multicomponent Laminar Boundary-Layer Problem
Authors: Goldstein M. E.
Published: December 2004

A new formulation of the multicomponent boundary-layer problem which is convenient for numerical calculations is developed by a modification of the usual Chapman-Enskog procedure. The complete set of boundary-layer equations turn out to be a set of first-order differential equations and a set of algebraic equations which are linear in the fluxes. The method is extended to include chemically reacting mixtures as well as nonreacting polyatomic molecules. It is shown that the method can be extended to two-temperature fluids when one of the species has a small mass and to mixtures where it is necessary to retain higher-order terms in the polynomial expansions used in the Chapman-Enskog procedure.
Solution for a Shock Wave of Bimodal Distribution Using Bhatnagar-Gross-Krook Models
Authors: Quan Victor
Published: December 2004

The symmetry property of a bimodal shock wave is shown to be destroyed by using the Bhatnagar-Gross-Krook equation. By using a modified BGK model, the symmetry property is recovered.
Diffusive Separation of Ions and Atoms in a Shock Wave
Authors: Sinclair M. , Sonin A. A. , De Leeuw J. H.
Published: December 2004

The structure of shock waves in slightly ionized high electron temperature plasmas is found to be appreciably modified by diffusive broadening induced by electrical coupling of the ions with the hot electrons.
Stabilization of Drift Waves by Shear
Authors: Rutherford Paul H. , Frieman Edward A.
Published: December 2004

The stabilization by magnetic shear of drift (universal) instabilities in a nonuniform, collision-free plasma is reconsidered. The description of the instabilities in terms of normal modes is abandoned in favor of a description in terms of local perturbations which are wave packets of normal modes, and this provides a more appropriate analysis of the effect of shear. The small shear required for stability is found to be of order (m/M)⅓ (where m and M are the electron and ion masses) for the short wavelength instability driven by a density gradient only, and results are also obtained for the instabilities driven by electron temperature gradients and longitudinal currents; the instabilities driven by ion temperature gradients are not stabilized by a small shear.
Bounce Model Pinch Stability
Authors: Morse Richard L.
Published: December 2004

A cylindrical pinch is treated in the approximation that plasma and field are separated by a thin surface. The external B field is taken to be completely longitudinal as in linear θ-pinches. Particles move in straight lines inside of the surface and bounce off of it specularly. Anisotropies in the velocity distribution are shown to result in instabilities of the ``mirror'' and ``fire hose'' types as well as flute instabilities of a type which have no analog in small gyroradius theory. Growth rates are obtained and a region of positive stability is found for a particular class of unperturbed distribution functions. The effect of a small net angular momentum is considered.
Nonlinear Instability
Authors: O'Neil T. M.
Published: December 2004

A particular type of nonlinear instability is discussed by considering the example of electron plasma waves driven toward instability by a small ion beam but linearly stabilized by electron Landau damping. A spectrum of relatively large amplitude waves is excited, and quasi-linear theory is used to follow their time evolution. It is found that the damping coefficient associated with these waves starts off at the negative value predicted by linear stability theory (i.e., the waves are linearly stable) but that it soon passes to a positive value and thereby demonstrates the existence of the nonlinear instability. The physical origin of the nonlinear instability lies in the fact that the total resonant kinetic energy available for growth is much larger than that available for damping.
Acoustic Kink Instability in an Argon Discharge
Authors: Schulz Michael , Ingard Uno
Published: December 2004

An experimental investigation of an acoustic instability of a current-modulated argon discharge in a cylindrical tube is described. When the modulation frequency is coincident with that of a nonaxial acoustic mode of the discharge cavity, the initially straight axial discharge path is deformed into a stationary path in which the lateral displacement has a spatial periodicity along the axis of the tube. This instability occurs only when the modulation exceeds some minimum amplitude and is associated with the excitation of a nonaxial acoustic mode of the gas in the discharge tube. It is shown that the spatial periodicities of the discharge path and the acoustic mode are the same. A proposed explanation of the instability is presented in terms of the acoustic coupling between the discharge and nonaxial acoustic modes and the effect of the acoustic pressure field on the resistance of the discharge.
Negative Characteristic and Instability of the Collision-Dominated Helium Plasma Column
Authors: Ecker G. , Kröll W. , Spatschek K. H. , Zöller O.
Published: December 2004

The general concept of thermal column instability is applied to the calculation of Kaufmann's criterion. At the same time a rigorous numerical evaluation of the marginal instability making use of the Myklestad procedure is obtained.
Space-Charge Instabilities in Charged-Particle Flow
Authors: Winograd Yeshaiahu Y.
Published: December 2004

One-dimensional flow of charged particles in a bounded system is investigated. In particular, the well-known overlap of steady-state solutions in the zero-temperature flow approximation is examined in detail. A stability analysis is performed, and it is proved that not only the overlapping steady-state solutions are unstable to infinitely small perturbations, but that all steady-state flows in which partial reflection of charged particles from a virtual cathode is assumed, are also unstable.
Low-Energy Electron Momentum Transfer Collisions in Cesium Plasmas
Authors: Nighan William L.
Published: December 2004

An effective momentum transfer collision frequency for electrons in cesium plasmas has been determined from measurements of the electrical conductivity and plasma properties in a cesium arc column. The effective collison frequency was found to depend on electron temperature in the 2500 to 4500°K range and to be significantly dependent on degree of ionization for values of this parameter greater than about 3 × 10−4, indicating a contribution from electron-ion collisions. Numerical evaluations of the velocity integral for the electrical conductivity, modified to include electron-ion as well as electron-atom momentum transfer collisions, have been carried out using many trial functions for the electron-cesium atom momentum transfer cross section. The electron-atom cross section which has given the best fit between the calculated and measured conductivity exhibits a Ramsauer-like minimum in the 0.25-to 0.55-eV range of electron energy.
Comparison of Some Recent Experimental and Numerical Results in Bénard Convection
Authors: Schneck Paul , Veronis George
Published: December 2004

The results of numerical calculations for two-dimensional Bénard convection between rigid boundaries are reported and compared with recent numerical and experimental values reported by other investigators. Values of the Nusselt number, Nu, in the range of Rayleigh number, R, from 2000 to 20 000 are presented. The degree of resolution of a grid point representation necessary to give an accuracy of Nu of 1% is determined. The implications of this requirement show that some previous numerical investigations must have involved fairly large errors in the heat flux and possibly even spurious time oscillations. It is also shown that recent experimental determinations of Nu agree quite well with calculations when the fluid has a large Prandtl number, σ. However, for water (σ=6.8) the discrepancy between numerical calculations and experimental measurements is quite large (14% at R = 20 000).
Temperature Dependence of Thermal Diffusion Factors in Ternary Gas Mixtures
Authors: Deb S. K. , Barua A. K.
Published: December 2004

The temperature dependence of the thermal diffusion factors in the ternary system He-Ne-Kr was studied by the two-bulb method. In general, the results are in satisfactory agreement with the recent theory of Van der Valk for thermal diffusion in multi-component gas mixtures.
Cylindrical Couette Flow of a Rarefied Gas
Authors: Cercignani Carlo , Sernagiotto Franco
Published: December 2004

The Couette flow of a rarefied gas between two concentric cylinders is analyzed numerically for an inverse Knudsen number ranging from 0 to 10 and different gap-to-radius ratios. The model of the Boltzmann equation proposed by Bhatnagar, Gross, and Krook is linearized and the transport integro-differential equation reduced to a purely integral one, which is solved numerically. The resulting drag coefficients for the outer cylinder are in a good agreement with available experimental data.
Study of Inhomogeneous Turbulence
Authors: Lee D. A. , Tan H. S.
Published: December 2004

The flow of energy in a steady, inhomogeneous turbulent flow with arbitrary mean velocity field is discussed. Expressions are derived for the spectra of velocity and pressure-velocity correlation tensors in the far downstream region of an idealized grid-generated channel turbulence. The effects of pressure-velocity correlations and of the conditions at a reference plane on final stage decay are discussed.
Pressure Fluctuations beneath an Incompressible Turbulent Boundary Layer with Mass Addition
Authors: Rosenbaum Harold , Margolis David P.
Published: December 2004

The results of an experimental investigation of the root-mean-square surface pressure fluctuations under an incompressible turbulent boundary layer with mass addition are reported. The ratio of blowing velocity to free stream velocity was varied from 0 to 8 × 10−3. In all cases, the rms surface pressure fluctuations increased with an increase in the blowing rate for a constant Reynolds number based on the length along the surface. Mean velocities were measured for some typical runs with the use of a constant temperature hot wire anemometer. Results were correlated with available theories (i.e., law of the wall, law of the wake) to yield the surface skin friction and the maximum stress within the layer.
Structure of Wind-Driven Plasma Turbulence as Resolved by Continuum Ion Probes
Authors: Granatstein V. L.
Published: December 2004

Argon gas is forced through a discharge tube to set up subsonic turbulent pipe flow. The resulting fluctuations in plasma density (excited by the ``mixing-in-gradient'') are investigated with continuum ion probes; the limits within which such probes can be used for fluctuation measurements are delineated. The flow is frozen and the small scale structure of the plasma turbulence is homogeneous. For Reynolds number greater than 6000, the rms value of plasma density fluctuation approaches 100% of the mean plasma density, the fluctuation intensity is essentially constant along the tube axis, and a nascent inertial subrange (K−5/3) appears in the plasma spectrum. The electrons are not in thermal equilibrium with the gas, and differences between the plasma and neutral spectra result.
Numerical Studies of the Nonlinear Vlasov Equation
Authors: Armstrong Thomas P.
Published: December 2004

The nonlinear one-dimensional Vlasov equation is solved numerically as an initial-value problem. The problem is the same as that considered by Knorr, and is related to, but not the same as, various one-dimensional model calculations using charged sheets. The electron distribution is doubly expanded, the spatial part being expanded as a Fourier series and the velocity part as a Gram-Charlier series. In this representation, the Vlasov equation appears as a matrix ordinary differential equation for the expansion coefficients and is first order in the time. Problems considered are nonlinear Landau damping and the development of strongly unstable initial conditions (two-stream instability). In the latter situation, the limiting amplitudes are computed.
Transition between Landau and Van Kampen Treatments of the Vlasov Equation
Authors: Grant Frederick C. , Feix Marc R.
Published: December 2004

The introduction of small Fokker-Planck damping into the Fourier-Hermite representation is shown to produce, in the proper limit, both the Van Kampen and Landau treatments. This damping removes the difficulties encountered in numerical integration.
Rational Approach to Relations between Motions of Differing Scales in Turbulent Flows
Authors: Lumley J. L.
Published: December 2004

An approach developed originally by Coleman and Noll in connection with a rational sequence of approximations to a simple fluid is applied to the problem of predicting the Reynolds stress in a turbulent flow; a rational sequence of approximations is generated in ascending powers of length- and time-scale ratios between the turbulent and mean motions. The same technique is applied to predict the response of motions of one wavenumber to those of another. An estimate is made of the relative importance of terms arising from spatial and temporal inhomogeneity. The spatial terms are found to be of substantially less importance.
Inertial Ranges in Two-Dimensional Turbulence
Authors: Kraichnan Robert H.
Published: December 2004

Two-dimensional turbulence has both kinetic energy and mean-square vorticity as inviscid constants of motion. Consequently it admits two formal inertial ranges, E(k)∼ε2/3k−5/3 and E(k)∼η2/3k−3, where ε is the rate of cascade of kinetic energy per unit mass, η is the rate of cascade of mean-square vorticity, and the kinetic energy per unit mass is ∫0∞E(k) dk. The −53 range is found to entail backward energy cascade, from higher to lower wavenumbers k, together with zero-vorticity flow. The −3 range gives an upward vorticity flow and zero-energy flow. The paradox in these results is resolved by the irreducibly triangular nature of the elementary wavenumber interactions. The formal −3 range gives a nonlocal cascade and consequently must be modified by logarithmic factors. If energy is fed in at a constant rate to a band of wavenumbers ∼ki and the Reynolds number is large, it is conjectured that a quasi-steady-state results with a −53 range for k « ki and a −3 range for k » ki, up to the viscous cutoff. The total kinetic energy increases steadily with time as the −53 range pushes to ever-lower k, until scales the size of the entire fluid are strongly excited. The rate of energy dissipation by viscosity decreases to zero if kinematic viscosity is decreased to zero with other parameters unchanged.
Flow of a Rarefied Gas through a Cylindrical Tube
Authors: Ferziger J. H.
Published: December 2004

The problem of Poiseuille flow through a cylindrical tube previously solved numerically by Cercignani is attacked analytically. The integral equation for the velocity as a function of radius is cast into a convenient form and its solution is obtained in limiting cases. For large Knudsen number a solution is obtained by Neumann series. For small Knudsen number the problem is transformed to a singular integral equation and an asymptotically valid solution is derived. It is found that first order slip effects are the same as in the case of flat plates but that the second order slip effect is only approximately half as large. Finally, the results of a variational calculation of the volume flow rate are given and compared with other results.
Simultaneous Ultrasonic and Line Reversal Temperature Determination in a Shock Tube
Authors: Carnevale E. H. , Wolnik S. , Larson G. , Carey C. , Wares G. W.
Published: December 2004

Temperatures of the gas behind reflected shocks have been measured simultaneously by a line-reversal method and by an ultrasonic method. Line-reversal temperatures were determined for shocks in neon doped with chromium carbonyl concentrations of 0.11% and 0.33% for a temperature range from 4400 to 6800 °K. The ultrasonic method was used to measure temperatures (from 4500 to 7700 °K) of pure neon as well as the mixtures of neon plus chromium carbonyl. The average relative deviation of the ultrasonic measurement from the simultaneous line-reversal measurement was 2.1% for the smaller concentration of chromium carbonyl and 2.7% for the larger concentration. The best least-squares fit of the ultrasonic temperatures measured in the reflected shock region versus measured incident shock speed is within 1% of the temperature predicted from the shock jump relations for pure neon. Similarly, the best fits of the ultrasonic temperatures versus Mach number and the line-reversal temperature measurements versus Mach number are also within 1% over the entire temperature range. The translational modes and the electronic states corresponding to the CrI lines measured, were in local thermodynamic equilibrium with each other.
Attempted Microwave Measurement of Temperature of a Shock-Heated Plasma
Authors: Aro T. O. , Walsh D.
Published: December 2004

Microwave noise radiation offers a simple probeless way of measuring the electron temperature of a hot plasma. The main difficulty usually lies in giving a true value to the emissivity. The temperature of the equilibrium region behind shocks in argon has been determined from the measurement of the microwave noise emitted by the shock-ionized argon in a shock tube and the absorption coefficient of the ionized gas measured at the same frequency, 9.05 GHz. The range of Mach numbers, 6.8 to 10.5, of shock in argon at an initial pressure of 4 mm Hg have been investigated experimentally and theoretically, and the smaller range of Mach numbers, 7.3 to 8.2, in which the measurements agree with theory is indicated. The measured temperatures in the latter range were between 4700 and 6000 °K. Difficulties in interpreting some features of the results are discussed.
Singularities of the Two-Fluid Plasma Equations and Their Relation to Boundary Conditions
Authors: Friedman Herbert W. , Levi Enrico
Published: December 2004

The one-dimensional fluid equations are used to describe a steady state, slightly ionized plasma confined by cold walls. The singularities of the complete two-fluid and approximate one-fluid equations are investigated and compared. It is found that the singularity in the one-fluid equations, indicating a transition from plasma to sheath regions, disappears in the two-fluid equations and therefore a smooth transition is predicted. Another singularity which is present in the two-fluid but not in the one-fluid equations is shown to be compatible if a constraint relation is satisfied at the singular point. In order that the two-fluid problem be well posed—(1) the boundary conditions are modified to ensure that the constraint relation is satisfied, and (2) a kinetic model is derived which uniquely specifies the wall potential for a given plasma configuration. The occurrence of a compatible singularity is shown to be analogous to the phenomenon of transonic flow in a convergent-divergent nozzle.
Possible Stationary Motion of a Toroidal Plasma
Authors: Bineau M.
Published: December 2004

For a given hydromagnetic equilibrium with nested toroidal magnetic surfaces there is a family of divergenceless vectors V such that ▿×(V×B) = 0. This velocity can be interpreted as a mass motion which slightly distorts the equilibrium.
Cyclotron Harmonic Resonances in an Electrodeless Discharge
Authors: Tetenbaum S. J.
Published: December 2004

Electron-cyclotron harmonic resonances in rf-excited, electrodeless, helium discharges have been investigated experimentally. The discharge simulates a plasma slab of relatively uniform electron density in a uniform magnetic field. Measurements were made at 9.15 GHz of both incoherent emission and coherent fundamental wave propagation, the microwaves propagating in a direction perpendicular to the magnetic field and normal to the slab boundaries. Emission resonances were found for both ordinary and extraordinary wave propagation. Precise measurements of the magnetic field at corresponding peaks for the ordinary and extraordinary waves show that the former occur at magnetic fields about 0.3% lower than that of the latter, independent of harmonic number, electron density and pressure. The ordinary wave resonances occur at the cyclotron harmonic within experimental error (0.1%). Resonances were found in the coherent fundamental transmitted and reflected waves and are due to resonance absorption. Their magnetic field positions always occur on the high magnetic field side of the cyclotron harmonic (by as much as 2.5%).
Electron Temperature Shock Structure in a Partially Ionized Gas
Authors: Leonard B. P.
Published: December 2004

A study of the shock structure shows that the value of the electron temperature at the parent gas subshock has a limiting behavior for a monatomic gas and a singular overshoot for a diatomic gas as the Mach number is increased.
Nonlinear Landau Damping in the Random Phase Approximation
Authors: Rand S.
Published: December 2004

Expressions are obtained for Landau damping of electron plasma waves, in the steady state, by balancing nonlinear effects and collision effects. The random phase approximation is used. In this context, a quantum effect, which may be important at typical laboratory plasma densities, is discussed. It is pointed out that the absorption of energy from the wave, in discrete quantum jumps, is far more significant with relation to resonance effects than is the case when a nonresonant situation is being studied. The classical and quantum-limiting results are compared. It is found that although in both cases the steady-state Landau damping is proportional to the inverse square of the wave field strength in the limit of strong fields, the expansion parameters differ in the classical and quantum limits.
Incompressible Resistive ``Tearing'' Instability in the Hard-Core Pinch
Authors: Hosking R. J.
Published: December 2004

Calculations for the finite conductivity ``tearing'' instability in the hard-core pinch with constant applied axial magnetic field are described. Cylindrical effects in the ``outer'' region, where the plasma remains effectively coupled to the magnetic field, are fully allowed for through a numerical solution of the boundary value problem. It is seen that there is quite good agreement with recent experimental measurements on the hard-core configuration, even though plasma compressibility is ignored. In particular, the fact that the m = 1 mode is not generally the fastest growing is accounted for by the use of cylindrical geometry in the outer region. A second result is that an increase in the ratio of azimuthal to axial magnetic field appears to be a somewhat better means of stabilization against ``tearing'' modes than one might have anticipated. A criterion for the validity of the plane approximation in the ``outer'' region is developed analytically.