bluuebunny/crossref_metadata_2025 huggingface dataset:
Flow of Elasticoviscous Liquid between Rotating Cylinders with Suction and Injection
Authors: Mishra Shankar Prasad , Roy Jyotirmoy Sinha
Published: February 2004

The steady-state laminar flow of an incompressible elasticoviscous liquid in an annulus with coaxial porous walls, rotating about a common axis is considered. The rate of fluid injection at one wall is taken to be equal to the rate of fluid suction at the other. The flow phenomenon has been characterized by the nondimensional parameters Rc (elastic number), R (cross-flow Reynolds number), m (ratio of the angular velocities of the cylinders), and σ (radii ratio). A small perturbation method has been used to obtain an approximate solution for the velocity field. The perturbation method is in powers of R and, thus, valid for sufficiently small |R|, but general Rc. A perturbation method in powers of Rc has also been used to obtain an approximate solution of the velocity field. This solution should be valid for sufficiently small |Rc| but general R. The effects of the above parameters on the velocity distribution, shear stress at the walls, and the radial pressure variation have been studied.
Euler-Lagrange Relationship for Random Dispersive Waves
Authors: Hoult David P.
Published: February 2004

It is shown that the equations for the motion of a tagged fluid particle in a random wave field define a singular perturbation problem, characterized by a nonuniformity at large times. The uniformly valid asymptotic expansion to this problem, the Euler-Lagrange relationship for random dispersive waves, is obtained. As an application of these general results, an integral representation of the solution is worked out for the case of vertically propagating random acoustic waves in an isothermal atmosphere. It is shown that the nonuniformity of medium leads to a wave generated diffusion process. The time and length scales over which the process is diffusive are determined, and a formula for the diffusion coefficient is presented.
Quantitative Test of the Direct Interaction Hypothesis
Authors: O'Brien Edward E.
Published: February 2004

It is shown that the direct interaction hypothesis, when applied to the problem of isotropic mixing of a reactant undergoing an isothermal second-order reaction, fails to preserve, even approximately, an important invariance. Namely, in the absence of molecular diffusion the decay of single-point statistical functions of the concentration field should be independent of the turbulence.
Compressible Relativistic Flow
Authors: Truitt Robert W.
Published: February 2004

The governing equations of compressible relativistic flow are cast in a form suitable for treating the subsonic, transonic, and supersonic regimes by established aerodynamic techniques. Small disturbance solutions are found which are the relativistic generalizations of the well-known aerodynamic laws for these flows. A comparison of present results with the nonrelativistic solutions for pressure coefficient shows significant compressible-relativistic effects for all three flow regimes. In the supersonic regime, the character of the variation of pressure coefficient with Mach number is quite different for the relativistic and nonrelativistic cases. The ultrarelativistic case is found to represent the limit of the compressible-relativistic effect in the three flow regimes.
Low-Energy Underwater Explosions
Authors: Heuckroth L. E. , Glass I. I.
Published: February 2004

Results are presented concerning a theoretical and experimental investigation of low-energy spherical underwater explosions. The theoretical analysis makes use of the explicity hydrodynamic-shock-tube solution, a simple incompressible bubble theory, and its modification which accounts for the finite signal propagation times and the low compressibility of the water medium. Experimentally, the low-energy blasts are generated by exploding glass spheres pressurized with various gases in a water-filled spherical test chamber under well-defined conditions. The results are primarily recorded by schlieren optical systems and piezo-pressure gauges. The experimental phenomena are shown to be in good quantitative agreement with the theoretical predictions within the physical limitations of the relatively small testing facility and the glass fragments. In particular, for the early stages of the explosions the experimental flow results are well described by the modified bubble theory.
Spatially Homogeneous Solutions of the Boltzmann Equation
Authors: Frohn Arnold
Published: February 2004

The approach towards the equilibrium distribution function is investigated for a monatomic gas having an initial distribution function with strong deviations from a Maxwellian. It is assumed that the distribution function can be approximated by a sum of two characteristic distribution functions whose particle densities are functions of time. These functions are eliminated by the solution of the transfer equation for cx4. The result is compared with the exact solution of the Krook equation. The deviation is 3-15% for the initial distribution functions considered in the present paper. Relaxation constants for a hard-sphere gas are evaluated for two special initial distribution functions. They cover a range roughly 10% lower than the relaxation times obtained with the linearized Boltzmann equation in a recent paper by Kuščer and Williams. For an initial distribution function consisting of a superposition of two Maxwellians with different temperatures the relaxation constant is computed from both the momentum equations for cx4 and cx6. The difference between the results is only 6.5%.
Second-Order Kinetic Theory of Stress for a Dense Gas of Rigid Spheres
Authors: McCoy Benjamin J. , Dahler John S.
Published: February 2004

The Enskog dense gas theory is generalized to arbitrary order in gradients of macroscopic field variables. A constitutive relation for the pressure tensor involving products of velocity gradients is presented in an irreducible tensor formulation. The second-order transport coefficients are evaluated for smooth rigid spheres, and the theory is applied to certain viscometric flows. Expressions are derived for normal stress effects.
Intermolecular Forces: Thermal Diffusion and Diffusion in He-Kr and H2-Kr
Authors: Annis B. K. , Humphreys A. E.
Published: February 2004

Forces between unlike molecules are investigated via mutual and thermal diffusion measurements on 4He-85Kr and H2-85Kr. New experimental results are reported, the thermal diffusion measurements covering the temperature range 77 to 760°K. Above 300°K the measurements are in reasonable accord with those of Ghozlan and Kistemaker, but below 300°K there are substantial discrepancies. Evidence is presented which indicates that the previous results at the lowest temperatures, particularly for He-Kr, are incorrect. Present measurements support the adequacy of the common potential parameter combination rules for H2-Kr, but not for He-Kr; in the latter case the potential well depth ε12is apparently smaller than theoretically predicted, a conclusion in accordance with molecular-beam scattering measurements.
Heat Conduction in a Rarefied Gas between Concentric Cylinders
Authors: Su Chih-Lan , Willis D. Roger
Published: February 2004

Heat conduction through a rarefied gas contained between concentric cylinders is studied analytically. Emphasis is placed on the connection with the experimental determination of thermal accommodation coefficients by the low-pressure method. The linearized BGK-model equation is used, based on small relative temperature difference. Two coupled linear integral equations for the perturbed temperature and density are then formulated. An asymptotic analysis is carried out for the case of mean free path much greater than the inner but of the same order as the outer cylinder radius, which corresponds to typical operating conditions for experiments. The lowest-order deviation of the heat flux from its free-molecular value is of O[ln(Kn)/Kn], the same as that obtained by Knudsen iteration. Numerical calculations are performed to find this term. It is found that for a mean free path 20 or more times the inner cylinder radius the relative error introduced by using the free-molecular value for the heat flux is less than 5%, provided that the ratio of the mean free path to the outer cylinder radius is at least 0.2.
Variational Principles for the Heat Flux in a Rarefied Gas between Concentric Cylinders
Authors: Su Chih-Lan
Published: February 2004

In studying the heat conduction in a rarefied monatomic gas between concentric cylinders two coupled linear integral equations are obtained using the linearized BGK-model equation for the molecular velocity distribution function. These integral equations are transformed into a symmetric form. Variational principles are then formulated for the heat flux which hold for all Knudsen numbers.
Initial Ionization Rates and Collision Cross Sections in Shock-Heated Argon
Authors: McLaren T. I. , Hobson R. M.
Published: February 2004

The initial ionizing processes in shock-heated argon are investigated in a low-pressure, 4.5-in.-diam, shock tube using double electrostatic probes to measure the ionization rates. The experimental conditions cover a range of initial pressures of spectroscopically pure argon from 0.2 to 3.0 Torr and temperatures from 7000 to 12 000°K. The maximum impurity level at 1 Torr pressure is less than 7 parts per million. Correction terms are applied to take account of flow nonuniformities in shock tubes operating at low initial pressures. The cross section for excitation, σ*, in the reaction A + A → A* + A is assumed to vary as S1*(E − Ea*) and S1* is measured to be 2.5 × 10×20cm2/eV. The cross section for ionization, σ+, in the reaction A* + A → A+ + A + e is assumed to vary as S+(E − Ea′) and S+ is found to be 5.1 × 10−17cm2/eV. The corresponding rate constants k* and k+ are given for this temperature range.
Electromechanical Costreaming and Counterstreaming Instabilities
Authors: Ketterer Frederick D. , Melcher James R.
Published: February 2004

The dynamics of two highly conducting, finite length streams in relative motion, coupled by a transverse electric or longitudinal magnetic field, are examined in detail. The systems may be mathematically described by two second-order coupled, hyperbolic, partial differential equations. Four classes of flow exist: (I) subcapillary, (II) supercapillary costreaming, (III) supercapillary counterstreaming, and (IV) subcapillary-supercapillary flow. The first three are considered in the present paper. The Bers-Briggs stability criterion is applied to the dispersion relation for the infinitely long system. The eigenvalue problem is formulated for class I and III flows (no eigenvalues exist for class II flow) and the complex eigenfrequencies computed. Electrohydrodynamic experiments on these systems are described and compared with the theory. Physical explanations are given for the observed instabilities.
Expansion of a Resistive Spherical Plasma in a Magnetic Field
Authors: Bernstein Ira B. , Fader Walter J.
Published: February 2004

The expansion of a resistive plasma into an external magnetic field has been treated in the limit in which the magnetic field does not perturb the plasma motion. The use of a class of exact solutions for the purely radial motion of the plasma in the absence of a field permits the reduction of the electromagnetic problem to consideration of a diffusion equation for the magnetic stream function. Explicit solutions are derived for a resistive spherical plasma expanding into a uniform applied magnetic field. Representative numerical results related to laser-produced plasma experiments of Haught and Polk are presented.
Nonlinear Interactions of Positive and Negative Energy Waves
Authors: Aamodt R. E. , Sloan M. L.
Published: February 2004

Nonlinear resonant three-wave interactions are examined for a number of weakly inhomogeneous plasmas with available free energy. It is shown that for some resonant interactions the necessary and sufficient conditions for the existence of unbounded solutions to the interaction equations reduce to simple criteria. For a number of different realizations of electron and ion beams these criteria indicate that the longitudinal modes in these systems lead to large fluctuations even for wavelengths and beam velocities for which the modes are linearly stable.
Nonlinear Propagation of a Moderately Strong Electromagnetic Wave in a Fully Ionized Plasma
Authors: Kaw P. K. , Salat A. R.
Published: February 2004

The nonlinear effects resulting from the propagation of a moderately strong electromagnetic wave in a fully ionized plasma are investigated; a detailed study of the case, when the incident frequency is in the vicinity of the plasma frequency, has been made. The nonlinear contributions to the absorption of the wave and to the reflected components from a plasma-free space interface, have also been obtained. It is shown, in contrast with earlier work, that under some conditions the nonlinear effects can increase the absorption. The generation of harmonic components in the current density and the reflected wave has also been studied.
Ion Acoustic Wave Dispersion in a Highly Ionized Argon Plasma in a Magnetic Field
Authors: Levin Richard R. , Oleson Norman L.
Published: February 2004

Ion acoustic waves have been magnetically excited and optically detected in a highly ionized argon plasma in the presence of a longitudinal magnetic field. The dispersion of the waves has been studied as a function of the exciting frequency between 187 kHz and 352 kHz and with the confining static magnetic field in the range 800-2200 G. A dispersion relation is derived which includes the combined effects of ion drift velocity, ion thermal motion, damping, axial magnetic field, and finite beam geometry as adjustable parameters. Dispersion curves are presented which compare the experimental data to the dispersion relation, the parameters being evaluated by a least-squares fit. The agreement is good.
Macroscopic Quasilinear Theory of the Garden-Hose Instability
Authors: Davidson Ronald C. , Völk Heinrich J.
Published: February 2004

The quasilinear stabilization of the garden-hose instability is discussed from a macroscopic point of view with closure in the fluid model obtained by neglecting the effects of heat flow. In order to keep the problem well-posed mathematically finite Larmor radius corrections to the conventional growth rate are retained, which leads to a natural cutoff in the growth rate for sufficiently large wavenumber.
Penning Discharge in a Strongly Inhomogeneous Magnetic Mirror Field
Authors: Hopfgarten N. , Johansson R. B. , Nilsson B. , Persson H.
Published: February 2004

In a Penning discharge in a magnetic mirror field with an axial mirror ratio Bmax/Bmin = 40, a burning voltage as high as 20 kV with a current of a few amps is observed. Normally, the gas is hydrogen in the pressure range 10−4-10−3 Torr. The classical mean free path is longer than or comparable to the dimensions of the device. From calorimetric measurements on the cathodes, the plasma density and ion energy in the cathode regions are estimated to a few times 1010cm−3 and a few kiloelectron volts, respectively. Magnetic loop measurements in the anode region indicate a plasma energy density in that region of 1012-1013 eV/cm3. Neutral particles, emitted perpendicular to the magnetic field, with energies exceeding 4 keV, are observed with a scintillator. Measurements on a split anode show oscillations in the frequency range 3-20 kHz. The aim of the experiment is to investigate the potential distribution in this type of low-density plasma, in particular the electric field component parallel to the magnetic field, and to determine typical energies of the plasma particles.
Corner Parameters for the Oscillating Disk; Consequences for Liquid Helium II
Authors: Folse R. F. , Hussey R. G.
Published: February 2004

Measurements of the period and logarithmic decrement of oscillating disks indicate that the inertial part of the corner parameter is zero. This result is used to correct the pile of disks measurements of the normal fluid density of liquid helium II.
Explosive-Driven, Spherical Implosion Waves
Authors: Flagg Robert F. , Glass I. I.
Published: February 2004

A method is described for producing explosive-driven, spherical, imploding shock waves. The implosion waves provide a means for conducting physical experiments at extreme pressures and temperatures in the laboratory, in a reusable facility.
Spectra of Water Waves in Channels and around Islands
Authors: Shen M. C. , Meyer R. E. , Keller J. B.
Published: February 2004

Spectra of bounded and unbounded basins are calculated on an asymptotic approximation based on smallness of the seabed slopes. This leads to the geometrical optics theory of surface waves of Keller, which is used to extend the known, exact result for an idealized beach to the prediction of the spectra of a variety of more natural water bodies. Attention is directed to cylindrically symmetrical and two-dimensional topographies corresponding, respectively, to islands and to continental slopes and laboratory channels. Marked differences are found in the character of the spectra for these two types of topography.
Fine Structure of Scalar Fields Mixed by Turbulence. II. Spectral Theory
Authors: Gibson Carl H.
Published: February 2004

Universal similarity hypotheses are proposed based on the local straining mechanisms, Kolmogoroff's local isotropy theory, and the mixing theories of Obukhov, Corrsin, and Batchelor. Three sets of similarity coordinates follow from the hypotheses depending on five fundamental parameters of turbulent mixing: ε, the turbulence dissipation rate; χ, the scalar variance dissipation rate; γ, the local strain rate; ν, the kinematic viscosity; and D, the molecular diffusivity of the scalar. Transformations between coordinate systems are shown to depend only on Pr ≡ ν/D as a mapping parameter. A unified spectral array with convergence properties required by the hypotheses is produced when the similarity hypotheses are used to predict the scalar spectrum function Γ. The inertial subrange (Γ ∼ k−5/3, k is the wavenumber) of Obukhov and Corrsin and the large Pr value viscous-convective (Γ ∼ k−1) subrange of Batchelor are reproduced. However, for small Pr values, a new inertial-diffusive subrange arises with Γ ∼ k−3 and cutoff at wavenumber (γ/D)12. Bounds for the universal subrange constants and functional forms for arbitrary Pr values are inferred using Batchelor's diffusive cutoff function, and compared with available experimental measurements.
Lagrangian History Direct Interaction Equations for Isotropic Turbulent Mixing under a Second-Order Chemical Reaction
Authors: O'Brien Edward E.
Published: February 2004

The Lagrangian history direct interaction approximation is applied to isotropic turbulent mixing of a second-order chemical reaction, the resulting closed sets of equations are presented, and an a-bridgement of them is carried out. It is shown that in the limit of a stochastically distributed second-order reaction the equations reduce to those of direct interaction. It is also demonstrated that the approximation preserves an important property of the exact equations; namely, that in the absence of molecular diffusion, the decay of single point statistical functions of the concentration field is independent of the turbulence.
Light Scattering by Dilute Monatomic Gases Using the Burnett Equations
Authors: Foch J.
Published: February 2004

The hydrodynamic theory of light scattering is generalized by using the linearized Burnett equations instead of the linearized Navier-Stokes equations. It is emphasized that this is necessary if one is interested in phenomena which are of second order in lK, with l the mean free path and K the magnitude of the change in optical wave vector. The principal results are expressions for the initial dispersion (K dependence) of the Brillouin shift and Landau-Placzek ratio.
Trimodal Solutions for Shock Structure in a Gas of Spherocylinders
Authors: Haight Charles H. , Lundgren Thomas S.
Published: February 2004

Trimodal solutions are given for the structure of a strong shock in a gas of spherocylindrical molecules. The trimodal theory includes rotational relaxation effects by setting up a kinetic theory for diatomic particles and adding a third equilibrium form to the monatomic bimodal distribution function of Mott-Smith. Spherocylinders are characterized by two parameters. They are associated with (1) the eccentricity of the force field and (2) the ability to transfer energy between the translational and rotational modes. Virial coefficient experiments suggest that a value of one-third for the eccentricity parameter is typical of several gases. Using this value, special emphasis is placed on the effects of the Mach number and the conversion parameter. Verification is provided for the absence of an internal temperature overshoot and for the predicted limitations of the theory. Shock profile and thickness curves are given that are comprehensive enough to be compared with data taken for widely varying Mach numbers and relaxation rates. Thus far, the only data on rotational relaxation are for nitrogen. Comparisons with the trimodal results show that spherocylinders with eccentricities of one-third and conversion parameters of 0.025 would simulate the shock thickness behavior of nitrogen molecules. Profile displacement considerations, however, indicate that eccentricities other than one-third must be investigated to simultaneously satisfy displacement and thickness data.
Interaction of Linear Waves with Oblique Shock Waves
Authors: McKenzie J. F. , Westphal K. O.
Published: February 2004

Formulas are derived for the amplitudes of waves that diverge from a shock as a result of any given incident disturbance. For strong shocks, that is the Mach number (M) is large, in an ideal gas it is shown that the pressure amplitude and the component of the energy flux normal to the shock of a transmitted sound wave are of O (M2 greater than those in the incident sound wave. Furthermore, if the impinging sound wave is incident near the critical angle the ratio of the pressure amplitude of the transmitted sound wave to that of the incident one is of O (M3). On the other hand, if a sound wave is normally incident upon the back of the shock, only about 1% of the acoustic energy flux is reflected in the form of sound waves. It is also shown that incident entropy-vorticity waves can generate intense sound waves behind a strong shock. The dependence of the transmission, reflection, and generation coefficients for sound waves on the Mach number and the angle of incidence is depicted in a series of graphs. The results are applied to the amplification of small disturbances in the solar wind on passage through the bow shock of the earth.
Ionizing Shock Structure in a Monatomic Gas
Authors: Chubb Donald L.
Published: February 2004

The structure of an ionizing shock front in a monatomic gas is described. Both atom-atom and electron-atom collisional ionization are considered. The ionization rates for either of these processes is assumed to be controlled by the rate of excitation from the ground state to the first excited level. In the front part of the shock, called the atom-atom shock, atom collisional dissipative mechanisms (viscosity and thermal conductivity) determine the shock structure. A bimodal Mott-Smith velocity distribution function is assumed for the atoms in this region, which has a thickness of the order of the atom-atom viscosity mean free path. In the rear part of the shock front, called the relaxation zone, the collisional ionization processes determine the structure. For this region, which has a thickness proportional to the electron-atom ionization mean free path, Maxwellian velocity distributions are assumed for the electrons, ions, and atoms. It was found that for Mach numbers of 30 or more the atom-atom shock is of comparable thickness to the relaxation zone and the degree of ionization behind the atom-atom shock is the order of 10−1.
Observed Structure of Spray Detonations
Authors: Ragland K. W. , Dabora E. K. , Nicholls J. A.
Published: February 2004

The propagation of a detonation wave in a tube containing a single stream of 2600-μ-diam diethylcyclohexane droplets dispersed in gaseous oxygen has been studied with streak and space resolved photography, special pressure transducers, and thin-film heat-transfer gauges. The detonation wave, which reached a velocity of 4100 ft/sec, consisted of a planar shock front followed by secondary shocks and a gradual decrease in pressure as heat is added. A detailed history of an individual drop within the reaction zone is presented. Under the observed conditions a 2600-μ-drop disintegrates continuously over a period of 500 μsec. Combustion is initiated in the wake of the drops at 65 μsec after the passage of the shock with the reaction zone considered completed in 670 μsec. One-dimensional equations for a two-phase Chapman-Jouguet detonation wave with mass and heat addition within the reaction zone, and momentum and heat transfer out of the reaction zone are derived. Comparison of the experiments with the theoretical prediction yields a reasonable agreement.
Influence of an Axial Magnetic Field on the Steady Linear Ekman Boundary Layer
Authors: Gilman Peter A. , Benton Edward R.
Published: February 2004

A hydromagnetic version of the Ekman boundary layer is developed in a simple form in order to study how the geophysically important Ekman suction velocity is affected by magnetic fields. The problem treated consists of a viscous, incompressible, conducting fluid in the presence of an infinite, flat, insulating boundary which rotates at speed Ω0. Outside the boundary layer, the fluid rotates uniformly with speed Ω1 = Ω0 (1 + ε), and there is a uniform magnetic field aligned with the rotation axis. An expansion in powers of ε, the Rossby number, together with von Kármán similarity, leads to an exact solution which to first order in ε, describes a continuous transition between pure Ekman flow and a rotating analog of Hartmann flow. The magnetic field is found to inhibit Ekman suction; yet, such a boundary layer may still exert a strong influence on the outer flow because of a new feature that replaces the suction, namely an induced axial current outside the boundary layer. This “Hartmann current,” not present in the conventional Hartmann problem, owes its existence to the fluid rotation.
Stability of a Perfectly Conducting Liquid Jet in the Presence of a Magnetic Field
Authors: Chakraborty B. B.
Published: February 2004

The stability of a cylindrical jet of a perfectly conducting, incompressible, and inviscid fluid in the presence of an axial magnetic field is studied for both axisymmetric and asymmetric disturbances. It is found that the jet becomes stable against disturbances of any wavelength when the magnetic field strengths are sufficiently high both inside and outside the jet, so that the Alfvén wave velocities at these places are greater than the undisturbed velocities of the fluid there. When the magnetic field strengths are not sufficiently high, the jet becomes unstable, and the critical wavenumber for those disturbances at which the instability first sets in is calculated in the axisymmetric case with the fluid outside the jet taken to be at rest.
Stabilities of Periodic Waves in a Cold Collision-Free Plasma in a Magnetic Field
Authors: Yeh Tyan
Published: February 2004

The existence of periodic waves propagating at an arbitrary angle to the magnetic field in a plasma is demonstrated by Stokes expansions in amplitude. Stability analysis is then made for such periodic waves with respect to side-band frequency disturbances. It is shown that waves of slow mode are unstable whereas waves of fast mode are stable if the frequency is below the cutoff frequency. The cutoff frequency depends on the propagation angle. For longitudinal propagation, the cutoff frequency is equal to one-fourth of the gyrofrequency of the electron. For transverse propagation, the cutoff frequency is so high that waves of all frequencies are stable.
Collisional Drift Waves—Identification, Stabilization, and Enhanced Plasma Transport
Authors: Hendel H. W. , Chu T. K. , Politzer P. A.
Published: February 2004

Density-gradient-driven collisional drift waves are identified by the dependences of ω and k on density, temperature, magnetic field, and ion mass, and by comparisons with a linear theory which includes resistivity and viscosity. Abrupt stabilization of azimuthal modes is observed when the stabilizing ion diffusion over the transverse wavelength due to the combined effects of ion Larmor radius and ion-ion collisions (viscosity) balances the destabilizing electron-fluid expansion over the parallel wavelength, determined by electron-ion collisions (resistivity). The finite-amplitude (ũ/n0 ≃ 10%) coherent oscillation, involving the entire plasma body, shows a phase difference between density and potential waves (which is predicted by linear theory for growing perturbations). The wave-induced radial transport exceeds classical diffusion, but is below the Bohm value by an order of magnitude. Although observations have been extended to magnetic fields three times those for drift-wave onset, turbulence has not been encountered.
Wave Mixing in a Bounded Magnetoplasma
Authors: Kuhn Lawrence , Leheny R. F. , Marshall T. C.
Published: February 2004

Generation of space-charge waves at ultra-high frequencies by the nonlinear interaction of two microwave signals in a magnetoplasma is described. The experiment was performed using a neon after-glow (p = 2 × 10−2 Torr), which formed a post in a square X-band waveguide. The results of the experiment agree quantitatively with a calculation of the interaction which accounts for its finite geometry. The nonlinear coupling is found to result from a Lorentz force interaction between the electron velocity induced by one incident wave and the time varying magnetic field of the other. A similar calculation and experiment were performed in which one microwave signal was scattered from a driven space-charge wave. The mechanism for this coupling is found to be an ñev type nonlinearity. It is shown that the results of the two first-order interactions can be combined to give a realistic prediction of a second-order process such as “optical mixing.”
Geodesic Acoustic Waves in Hydromagnetic Systems
Authors: Winsor Niels , Johnson John L. , Dawson John M.
Published: February 2004

In toroidal systems with geodesic curvature an electrostatic acoustic mode occurs with plasma motion in the magnetic surfaces, perpendicular to the field. In typical stellarators this mode should dominate ordinary sound waves associated with motion along the field.
Enhanced Bremsstrahlung from Supraluminous, and Subluminous, Waves in an Isotropic, Homogeneous Plasma
Authors: Lerche I.
Published: February 2004

A calculation is presented of the bremsstrahlung radiation from a thermal, Maxwellian electron plasma which may have an isotropic, relativistic, (non-Maxwellian) tail. The calculation assumes homogeneity, isotropy, the absence of any imbedded ambient magnetic fields, and a smeared out distribution of ions which serves to preserve over-all space charge neutrality, but does not take part in any motion. When allowance is made for the fact that no particles resonate with waves whose phase velocity exceeds the speed of light, it is demonstrated that the “character” of the emission changes sharply at ω = ck. Provided the electron temperature is less than about 108 °K, it is shown that the supraluminous (ω > ck) bremsstrahlung from the thermal electrons dominates the subluminous (ω < ck) radiation from the same particles. It is also shown that a few relativistic electrons can act as a “catalyst,” greatly enhancing the subluminous bremsstrahlung but hardly influencing the supraluminous bremsstrahlung. The enhanced emission occurs at, and at twice, the electron plasma frequency. Using numerical values appropriate to the Crab nebula, it is shown that the enhanced subluminous bremsstrahlung can easily dominate the synchrotron radiation and the usual “collisional” bremsstrahlung at, and at twice, the electron plasma frequency. Also the enhanced supraluminous emission due to static “bumps” in the plasma is shown to exceed other conventional radiation processes in the Crab nebula.
Scattering of Charged Particles in a Weakly Unstable Plasma
Authors: Roqué Celso
Published: February 2004

The mean-square deflection of suprathermal test particles from a weakly unstable electron plasma is calculated. The instability is assumed to have been driven by a tenuous beam of energetic electrons. The random phase approximation expression for the spectral density is used and the electric field energy density of the turbulent spectrum is estimated by the quasilinear theory. It is shown that the mean-square scattering angle can be increased by more than an order of magnitude by a suitable beam density or drift velocity. This enhances the potential usefulness of charged-particle scattering as a diagnostic tool for turbulent laboratory plasmas.
Two-Dimensional Equilibrium for High-β Mirror Devices Including Particle Loss
Authors: Freidberg J. P. , Grossmann W.
Published: February 2004

Two-dimensional equilibria for high-β mirror devices are found by solving the Vlasov equation and Ampere's law self-consistently. Particle loss is taken into account self-consistently by allowing particles to exist only outside of the local loss-cone angle. It is found that for a given set of plasma parameters and applied mirror ratio (1) solutions only exist below some critical value of β, and (2) in certain cases the solutions show a nonuniqueness related to the question of stability.
Experimental Studies of a Deep, Negative, Electrostatic Potential Well in Spherical Geometry
Authors: Hirsch Robert L.
Published: February 2004

Steady electron injection produced a stable, negative electrostatic potential well at the center of a hollow, open, 6.35-cm-diam spherical anode. Even though the primary electron source was localized, electron flow became spherically symmetric at anode currents of the order of 10 mA for anode potentials up to 1.0 kV. Well defined and reproducible oscillations were observed over a lower current range. These oscillations ceased and certain collector characteristics abruptly changed at currents which varied as V32, suggesting space charge saturation. An electron beam probe verified the presence of the well and measured its depth. The data showed correlation with a simple model and demonstrated the ease with which such wells can be produced.
Neutrally Stable Disturbances for a Nonplanar, Parallel Flow
Authors: Kelly R. E.
Published: February 2004

The stability of a continuously varying, nonplanar shear flow is considered, and two neutrally stable solutions are presented.
Kinetic Theory of Sound Propagation in a Rarefied Gas
Authors: Toba K.
Published: February 2004

A study of the sound propagation in a rarefied gas is described by the method of generalized orthogonal polynomial expansion.
An Exact Solution for Axially Symmetric Equilibrium Electron Density Distributions
Authors: Sajben Miklos
Published: February 2004

A closed form general solution of Poisson's equation with an eκ forcing term is given containing two arbitrary constants. Specialization of constants to two examples shows that the usual linearization (eκ ≈ 1 + κ) can be grossly misleading.
High-Amplitude Torsional Oscillations of a Disk in a Viscous Fluid
Authors: Folse R. F. , Hussey R. G. , Bosnak J. S.
Published: February 2004

Measurements have been made of the logarithmic decrement and period of disks of radius 3-8.5 cm performing torsional oscillations at amplitudes in the range 0.01-1.6 rad in fluids of kinematic viscosity 0.29-3.06 centistokes. Both the logarithmic decrement and period were observed to depend on the amplitude of oscillation in qualitative agreement with a thory due to Rosenblat which predicts amplitude effects due to secondary flow. The amplitude effects were smaller than predicted and were dependent on the radius of the disk but were relatively insensitive to kinematic viscosity, disk thickness, or distance to the outer boundary. Below 0.2 rad the period was constant within 0.001% and below 0.3 rad the logarithmic decrement was constant within 0.3%; empirical correlations are presented for the data at higher amplitudes.
Kinetic Theory of Weak Shock Generation by an Impulsively Started Piston
Authors: Mason Rodney J.
Published: February 2004

The impulsive piston problem is examined for an early period before nonlinear effects acquire significance. It is assumed that the velocity of the piston is well below the mean thermal speed, that specular reflection occurs at its surface, and that the linearized isothermal Bhatnagar-Gross-Krook equation governs the gas dynamics. With the aid of Fourier and Laplace transforms an exact solution to this equation and also asymptotic solutions for times short and long as compared to a mean free time are derived. At the earliest times a “relative steepening” of the density profile near the isothermal sound speed is observed. Much later a Navier-Stokes shock-type profile is achieved, but, in addition, a careful analysis predicts the presence of a “transient Knudsen layer” near the piston joined smoothly to an extremely weak “kinetic precursor disturbance” far ahead of the shock. Discussion is given to the influence of the chosen kinetic model equation and boundary condition on these results.
Kinetic Equations for Polyatomic Gases: The 17-Moment Approximation
Authors: McCormack Francis J.
Published: February 2004

A set of kinetic equations for polyatomic gases is obained by extending the 13-moment approximation of Grad to solve the inelastic Boltzmann equation of Wang Chang, Uhlenbeck, and de Boer. It is expected that the resulting 17-moment approximation (the four additional moments are the internal temperature and the internal heat flux vector) will be applicable to a wider class of physical problems than the “normal”-type Chapman-Enskog solutions to the inelastic Boltzmann equation. In particular, the kinetic equations should prove quite useful in the study of shock structure and sound propagation in polyatomic gases. As examples, the 17-moment approximation is applied to near equilibrium and relaxation type flows; and all the essential features of the Wang Chang et al. analysis are recovered, such as those involving temperature equilibration, volume viscosity, and the extension of the Navier-Stokes equations to polyatomic gases. In addition, corrections to the Navier-Stokes equations are derived involving terms which are second order in the transport coefficients. Possible generalizations and extensions of the 17-moment approximation are also discussed.
Knudsen Flow through a Porous Medium
Authors: Strieder W. C. , Prager Stephen
Published: February 2004

Rigorous bounds on the permeability of a porous medium to Knudsen flow are formulated by applying the variational procedure of DeMarcus. The bounds are expressed in terms of certain averages characterizing the random-pore geometry. Explicit calculations are given for a model pore structure generated from randomly overlapped spheres.
Thermal Conductivity of Polyatomic Gases
Authors: Sandler Stanley I.
Published: February 2004

Approximate formulas for computing the thermal conductivity of a polyatomic gas developed by Eucken, Hirschfelder, Mason and Monchick, and Saxena are compared with experimental data and the results of calculations for models of polyatomic molecules. It is found that due to the scatter in the experimental results, comparison with the model calculations is the most severe test of the approximate formulas. On this basis, the Mason and Monchick formulas are found to be the most accurate. A modification of the Mason-Monchick computational scheme is considered, and it is found that this modification leads to results which are in even better agreement with both the model calculations and laboratory data.
Strength of the Frozen Shock in Steady One-Dimensional Flow of Relaxing Gases
Authors: Böhme G.
Published: February 2004

For two important classes of inviscid and relaxing gases, namely for real gases with several internal degrees of freedom and for diatomic dissociating gases, the frozen shock in steady one-dimensional compression flow is always weaker than the equilibrium shock.
Compressible Turbulent Magnetohydrodynamic Boundary Layers
Authors: Argyropoulos G. S. , Demetriades S. T. , Lackner K.
Published: February 2004

A closed analytical model for compressible magnetohydrodynamic boundary layers is formulated by using transport equations for the turbulent fluctuations of species mass density, velocity, and temperature, and thus avoiding a priori relations between turbulent fluxes and mean flow quantities. The equations for both the mean and the fluctuating motion are simplified according to the boundary-layer approximation, and closure of the system is achieved by the introduction of “universal turbulence structure parameters” that only relate turbulent correlations among themselves. This model accounts for convection and diffusion of turbulent fluxes as well as for the effect of turbulence suppression by applied magnetic fields. It is shown that if convection, diffusion, and electromagnetic effects were omitted in the equations of fluctuating motion, the latter would reduce to algebraic forms defining the concepts of mixing length, turbulent Prandtl number, and turbulent Schmidt number in terms of turbulence structure parameters.
Flow in a Magnetic Shock Tube with Unsteady Magnetic Field
Authors: Yasuhara Michiru
Published: February 2004

Flow in a magnetic annular shock tube is analyzed, in which both the driving and applied magnetic fields vary with time. First, one-dimensional flow is solved by the hypersonic similarity method for the case in which both fields are proportional to a power of time. Second, the local similarity approximation is described to treat more general case in which the fields are smooth functions of time. Third, a purely numerical integration using Lax's finite difference method is carried out for a flow with a sinusoidal driving magnetic field, in which a typical nonsimilar nature of the solution appears in some parts as well as locally similar ones in other parts of the flow. Next, some experiments on a magnetic annular shock tube using air as the working gas, are described with special interest paid to the effect of unsteady azimuthal magnetic field on the flow, and comparisons with theoretical predictions are reported.
Discharge Structure and Stability of a Nonequilibrium Plasma in a Magnetohydrodynamic Channel
Authors: Zauderer Bert
Published: February 2004

An experimental investigation was performed of the discharge structure in a nonequilibrium plasma flowing at supersonic velocities through a linear, magnetohydrodynamic channel. Optical observations showed that the luminosity of the discharge was concentrated in streamers. The streamers were transverse to the gas velocity, they originated in the entrance region of the channel, and they propagated downstream at the local gas velocity. In addition, in the channel entrance region, where the axial electron density gradient and the convective effect were at a maximum, high-luminosity gas layers were observed on the electrode walls. These observations suggested that the discharge structure is determined by the following sequence of events occurring at the electrodes in the channel entrance region: electrical ignition of the gas, convective extinguishing, and subsequent reignition. Although streamer formation is also predicted by the theory of ionization instabilities in magnetoplasmas, other characteristics of the discharge were in disagreement with the theory. A major difference was the absence in the present experiments of plasma turbulence at large Hall parameters.
Vorticity Generated behind Shock Waves in Conducting Gases
Authors: Ram Rishi , Upadhyaya K. S.
Published: February 2004

It was shown by Kanwal that the vorticity generated behind shock waves in conducting gases is no longer derivable from purely dynamical relations as in nonconducting gases and the energy equation is essentially needed in the process. A proof, independent of the form of the equation of state and based on the momentum equation alone, is presented for the derivation of vorticity generated behind shock waves in conducting gases under two cases: (i) when the magnetic field is tangential to the shock surface, and (ii) when the magnetic field is normal to it.
Interfacial Relaxation Overstability in a Tangential Electric Field
Authors: Melcher James R. , Schwarz Wilfred J.
Published: February 2004

It is well known that electromechanical polarization surface waves propagate along the lines of electric field intensity imposed tangential to the interface between perfectly insulating fluids. These waves have a stiffening effect on electrohydrodynamic equilibria that is analogous to that of the Alfvén surface waves on hydromagnetic equilibria. An investigation is presented of the dynamical effects of charge relaxation on these waves. A self-consistent model represents the relaxation in terms of an Ohmic conduction process in the bulk of the fluids, with surface shears induced by the free interfacial charges placed in dynamic equilibrium by viscous stresses. The dominant effect of the charge relaxation is to produce overstability. Experiments are described where this instability appears as a spontaneous oscillation of the interface with wavenumbers directed along the lines of electric field intensity. Detailed analytical results are given for liquid-gas and liquid-liquid interfaces. The field required to produce incipient instability and the propagation direction of the observed instability are satisfactorily predicted. It is found that in this liquid-vapor case, relatively simple explicit expressions can be given for the incipient instability conditions. A discussion is given of the significance of this work for the dielectrophoretic orientation of liquids in the zero-gravity environments of space.
Hydromagnetic Waves in a Nonuniform Hydrogen Plasma
Authors: Cross R. C. , Lehane J. A.
Published: February 2004

The propagation of azimuthally symmetric Alfvén waves in a cylindrical hydrogen plasma with a nonuniform density distribution is investigated theoretically and experimentally. Dispersion relations are derived for the case of a fully ionized plasma with a radial density gradient and are shown to describe some of the experimental features which are not predicted by a uniform plasma theory. Experimental results are presented for both torsional and compressional Alfvén waves propagating in one and the same plasma. It is shown that the torsional Alfvén wave propagates at a radially varying speed which agrees well with the local Alfvén speed deduced from the local particle density. Compressional Alfvén waves are shown to be planar and at high frequencies to be confined largely to the center of the plasma column due to a refraction of the wave produced by the density gradient. The use of uniform plasma theory to obtain estimates of plasma parameters from the study of compressional waves leads to values different from those obtained from the study of torsional waves. This difference is explained in terms of the radial density gradient in the plasma.
Quasilinear Theory of Hydromagnetic Waves in Collisionless Plasma
Authors: Barnes Aaron
Published: February 2004

A quasilinear theory of hydromagnetic waves in nonrelativistic collisionless plasma (with no superthermal “tail”) is derived. It is shown that the time evolution of the space-averaged velocity distribution function of each species is described by a diffusion equation in velocity space, and that this “diffusion” can be split into resonant and nonresonant parts. The resonant diffusion determines the heating of the (finite-β) plasma by damping hydromagnetic waves; such heating enhances electron and ion kinetic temperatures parallel to the average magnetic field, and does not affect transverse temperatures. Quasilinear quenching of the hose instability is discussed as an example.