bluuebunny/crossref_metadata_2025 huggingface dataset:
Kinetic Theory of the Sharp Leading Edge Problem in Supersonic Flow
Authors: Huang A. B. , Hartley D. L.
Published: February 2004

The sharp leading edge problem is studied within the framework of the kinetic theory of gases. The Boltzmann equation with the Bhatnagar-Gross-Krook model is used as the governing equation. The method of discrete ordinates developed by Huang is applied. The local distribution functions for the entire flow field have been calculated for the case of supersonic flow, M∞ = 1.5; thus, the complete flow field has been generated for various plate temperature values. The calculated results offer considerable insight into the behavior of a rarefied gas flow as it traverses the complete spectrum of flow regimes from near-free molecular to continuum, and present a meaningful connection between the near-free molecule solution at the leading edge and the extended continuum theories in the interaction regimes. Comparison with the existing theories and experimental data show reasonably good agreement in all flow properties. For higher Mach numbers, however, a higher-order quadrature is necessary. It is felt that the only limitation of the present solution is that of large computer storage requirements.
Stationary Nonlinear Waves in a Stratified Fluid with Respect to a Rotating Cylindrical System
Authors: Shen M. C.
Published: February 2004

Nonlinear periodic waves in a stratified fluid stationary with respect to a rotating cylindrical system are studied. The case to be considered is that of an incompressible, inviscid fluid with free surface rotating about a rigid circular cylinder and pulled toward the axis of the cylinder by a constant body force. Critical angular speeds, near which such periodic waves are possible, are determined by the eigenvalues of an eigenvalue problem, and the equation governing the wave profiles is then obtained by a compatibility condition. With slight modification, the method developed is applied to other cases of interest.
Stability of Transient Natural Convection
Authors: Gunness Robert C. , Gebhart Benjamin
Published: February 2004

A theoretical analysis was carried out to determine the stability properties of unsteady natural convection. In this analysis a perturbation technique was used in conjunction with a special type unsteady base flow for transient natural convection between two infinite parallel vertical plates. Perturbation analysis yields a sequence of ordinary differential equations to describe the coupled time-dependent disturbance behavior. The equations were solved for a number of values of Grashof and wavenumbers and for a wide range of rate of acceleration and deceleration to determine the unsteady base flow stability characteristics. A growth factor was used to determine the stability properties, and it was found that an accelerating (decelerating) base flow is more (less) stable than a steady base flow when compared at common values of the instantaneous Grashof number. This tendency was found to increase rapidly at first and then to slowly decrease with increasing rate of change of the base flow.
Three-Dimensional Motion of a Liquid Film Induced by Surface-Tension Variation or Gravity
Authors: Yih Chia-Shun
Published: February 2004

Steady flows of a thin layer of viscous liquid on a horizontal plane induced by the nonuniformity of surface tension at its free surface are treated. If the film is very thin, surface-tension effects dominate gravity effects. Under that circumstance and away from vertical boundaries, a binomial of depth h of the liquid layer is a harmonic function of the Cartesian coordinates x and y in a horizontal plane, and the surface tension is a function of h. Near any vertical boundary there is a velocity boundary layer whose thickness is of the order of h. The velocity distribution in this boundary layer is given explicitly. The diffusion of the surface material affecting the surface tension is considered. Steady flows of a liquid film induced by gravity are also discussed. Simple solutions are possible if the film flows over a horizontal plane.
Energy Reversal in Turbulent Flows
Authors: Eskinazi S. , Erian F. F.
Published: February 2004

In turbulent shear flows, it is generally known from the mechanical energy equation that a production term of turbulent energy, normally implying a transfer of energy from the mean motion to the turbulence, contributes through a significant physical process to the permanence or quasisteady state of turbulence in the presence of convective, diffusive, and dissipative influences. It is shown that certain flows with asymmetric mean velocity distribution may display localized areas in which the production term is a loss in the energy balance and consequently of the same sign as the dissipation. For better terminology the phenomenon of negative production is here called energy reversal. The existence of zones of energy reversal also implies a concept of zones of opposing shear. In this localized region, the Reynolds stress and the viscous shear stress oppose each other unlike what is expected in normal boundary layer and pipe flows. A modified relationship, relating the Reynolds stress to the mean viscous stress, taking into account small- and large-scale effects, proposed by Hinze and Béguier is justified on the basis of experimental evidence.
Postulate of Statistical Independence for Decaying Reactants in Homogeneous Turbulence
Authors: O'Brien Edward E.
Published: February 2004

An independence hypothesis is proposed which predicts the evolution of the amplitude of Fourier modes of the concentration fluctuation field for a substance undergoing a second-order single-species isothermal reaction in homogeneous turbulence. The hypothesis is that the time history of such an amplitude is a product of its time history due to reaction and its time history due to turbulent mixing and diffusion. A sufficient condition for the hypothesis to be applicable is that the spectral decay due to reaction alone exhibits wavenumber similarity with a constant length scale. When the initial fluctuation intensity is high enough, the initial decay of the mean concentration (mean-square concentration) as predicted by the hypothesis gives a lower (upper) bound on the actual initial rate of decay. It is also demonstrated by numerical calculation of a particular initial isotropic concentration spectrum in the absence of turbulence that the independence hypothesis and the predictions of a valid closure for this problem differ by no more than an order of magnitude over the entire time history of decay for all possible values of the diffusivity and reaction rate. When turbulence is present, the long time evolution of the mean concentration and the mean-square concentrations as predicted by the hypothesis are in excellent agreement with previous computations employing direct interaction.
Axially Symmetric Expansion of a Monatomic Gas from an Orifice into a Vacuum
Authors: Grundy R. E.
Published: February 2004

The problem of the steady axially symmetric expansion of a monatomic gas from an orifice into a vacuum is considered. The reservoir conditions are such that the local Knudsen number is initially small. It is noted that the near continuum solution, valid near the orifice, is not uniformly valid far downstream where the local mean free path may be comparable with some characteristic length. A valid solution of Boltzmann's equation, for Maxwell molecules, is deduced for this far field core region. Near the gas-vacuum front, predicted by the equilibrium solution, this expansion procedure also breaks down. It is shown that a further scaling of the variables in Boltzmann's equation, consistent with this limit, can be found and the corresponding moment equations deduced. However, in contrast to the behavior in the core, these equations no longer form a closed set.
Interdiffusion of Gases through Porous Media—Effect of Molecular Interactions
Authors: Breton Jean-Paul
Published: February 2004

The fluxes of a mixture of gases diffusing through a porous medium in the normal diffusion region are derived, with emphasis on the flux ratio at uniform pressure. The Boltzmann equation is solved by the moment method, putting boundary conditions in the solution. Maxwell's method is shown to be inadequate, and it is found that, besides the well-known mass effect, a molecular interaction effect appears in the expression of the flux ratio. Thus, the experimental deviations from the usual law are explained. Then, the flux ratio is experimentally determined for an isobaric N2-C2H4 mixture and found to be in qualitative agreement with theory. Finally the experimental results on the motion of spheres in nonhomogeneous gaseous mixtures are explained for the first time.
Molecular Velocity Distribution Function Measurements in a Normal Shock Wave
Authors: Muntz E. P. , Harnett L. N.
Published: February 2004

Molecular velocity distribution functions have been measured throughout a normal, M = 1.59 helium shock wave that was formed in a low-density wind tunnel. The measurements were obtained by using the electron beam fluorescence technique. Throughout the shock transition, distributions of random velocities were observed from directions both parallel and perpendicular to the flow. Also, direct measurements were made of the density and the flow velocity. The shock wave satisfied the continuity, momentum, and energy equations within the accuracy of the measurements. Parallel and perpendicular temperatures compare favorably to predictions derived from the Navier-Stokes equations. In the upstream portion of the shock the distributions of parallel peculiar molecular velocities predicted according to the Chapman-Enskog first iterate differ significantly from the experimental results, although as mentioned the second moments or temperatures agree with the Navier-Stokes values.
Transient Energy Transfer in a Radiating Gas during Shock Expansion
Authors: Latko R. J. , Viskanta R.
Published: February 2004

The transient energy transfer during expansion of a plane layer of radiating gas bounded by a strong shock is investigated. The inviscid, nonconducting gas is assumed to be perfect and in local thermodynamic equilibrium. A shock fitting procedure is used which completely specifies the motion and position of the shock by an iterative solution of the partial differential equations and the Rankine-Hugoniot shock boundary conditions. For a gray gas, results are presented for parameters of physical interest. Results obtained for transparent, gray, and nongray models are compared.
Simple Equation of State at High Temperatures
Authors: Kim Sungwoon
Published: February 2004

An approximate equation of state which gives good results at high temperatures is obtained for a general intermolecular potential. The method yields the exact second virial coefficient, and the entire equation of state can be obtained with the same amount of computational work as required for the second virial coefficient. The scheme is also applicable to the quantum correction of order h2 to the equation of state.
Electron Distribution Function for a Nonequipartition Plasma in a Strong Electric Field
Authors: Viegas J. R. , Kruger C. H.
Published: February 2004

Solutions to the kinetic equation of a steady, homogeneous plasma of arbitrary degree of ionization subjected to strong electric fields are developed. Nonelastic as well as elastic encounters are included in the analysis. Expressions for the current density, electrical conductivity, and electron temperature of the plasma are also presented. Numerical results are illustrated for the case when the nonelastic effects are neglected. Calculations are presented showing the transition of the isotropic part f0 of the distribution function from a gas-temperature Maxwellian at near equilibrium conditions to an electron-temperature Maxwellian under nonequipartition conditions. It was found that whenever the electron-electron to electron-neutral collision-frequency ratio was much greater than the electron-to-heavy-particle mass ratio, f0 is Maxwellian. When f0 is Maxwellian, the Chapman-Enskog and Spitzer-Härm conductivity expressions developed for the case of weak electric fields are shown to be applicable for strong electric fields providing that in these expressions the electron temperature replaces the gas temperature. An approximate form for f0 suggested by Ginzburg is compared with the exact expression. The accuracy of the use of a Maxwellian rather than the nonequilibrium distribution function in the calculation of the electrical conductivity is assessed.
Nonequilibrium Electrical Conductivity of a Potassium-Seeded Argon Plasma
Authors: Sakao Fujihiko , Sato Hiroshi
Published: February 2004

Experiments have been made on the electrical conductivity of a nonequilibrium, potassium-seeded argon plasma at atmospheric pressure. The gas is heated uniformly in a vacuum heater up to a temperature of 1700°C. Electric field in the plasma is determined by electrostatic probes as a function of the current density through the plasma, which ranges from 10−5 to 2A/cm2. For small current density, the plasma is in thermal equilibrium and the conductivity is independent of the current density. The average momentum transfer cross section between electron and potassium atoms estimated from the equilibrium conductivity is 2.3 × 10−14 cm2. As the current density is increased the conductivity decreases, reaches a minimum, and then increases. When the current density is not small, the plasma is not in thermal equilibrium and the distribution function of electrons is not Maxwellian. The decrease of the conductivity is explained by considering inelastic collisions between electrons and potassium atoms and the radiation loss from the plasma. The apparent conductivity at large current density is much higher than the equilibrium value, although the uniformity of the current density was not assured.
Magnetohydrodynamic Flow Past Axisymmetric Bodies with Aligned Magnetic Field
Authors: Parbhakar Kanwal J. , Uberoi Mahinder S.
Published: February 2004

The steady axially symmetric flow of an inviscid incompressible fluid of small conductivity, embedded in a strong magnetic field, past fixed bodies is studied as a problem of finite perturbation. The magnetic Reynolds number is assumed small so that the magnetic field is unperturbed. The flow depends on the parameter β which is proportional to the product of conductivity and the square of the magnetic field strength. The flow past a semi-infinite body and a sphere is numerically calculated and the solution indicates that the effect of the body is felt upstream. This upstream influence is convected by the flow and appears as a nondiffusive boundary layer and a wake for the semi-infinite body and the sphere, respectively. The drag and the various boundary layer and wake characteristics decrease with β. The classical Bernoulli function H ( =p + 12 u2) decreases along streamlines and the pressure distribution on the surface of the bodies changes appreciably from the corresponding nonmagnetic value.
Korteweg-de Vries Equation for Nonlinear Hydromagnetic Waves in a Warm Collision-Free Plasma
Authors: Kever H. , Morikawa G. K.
Published: February 2004

As has been shown previously for the case of a cold plasma, the structure and propagation of hydromagnetic waves of finite but small amplitude can be described by the Korteweg-de Vries equation. This equation can be derived from the set of the hydromagnetic equations for a collisionless cold plasma, by applying certain scaling relations between the pertinent field variables. For a cold plasma, the hydromagnetic transport equations are equivalent to the Vlasov equations because the distribution functions of the particle velocities are delta functions. In the case of a warm plasma, the initial distribution functions are Maxwellian. Starting from the Vlasov equations for the electron and ion gas of the plasma, the procedure as applied in the case of a zero temperature plasma leads, under known conditions, to a generalized time-dependent Korteweg-de Vries equation, with coefficients depending on the temperature of either plasma component and on the angle between the direction of wave propagation and the initial magnetic field. Charge separation effects and displacement currents appear to be negligible to lowest order.
Numerical Study of Weakly Unstable Electron Plasma Oscillations
Authors: Armstrong Thomas P. , Montgomery David
Published: February 2004

The initial-value problem for an unstable electron plasma has been solved by numerically integrating the Vlasov equation in one dimension. The situation chosen is the familiar “bump-on-the-tail” situation of quasilinear theory. The solution is followed well beyond the point at which the electrostatic field energy has reached its maximum value. The electric field spectrum is eventually dominated by the single most linearly unstable wavenumber, which lies in the middle of the allowed range of wavenumbers; it undergoes what appear to be the beginnings of gentle long-period oscillations characteristic of trapped-particle periodicities. It is argued that differences from quasilinear predictions may be explained in terms of the level of initial excitations, or “noise,” from which the instability is assumed to proceed.
Plasma Density Measurement by Cavity Perturbation in High Density Plasma
Authors: Lieberman M. A. , Lichtenberg A. J.
Published: February 2004

A TM010, time-resolved, cavity perturbation technique has been used to measure the total number of electrons Ne in a magnetic mirror compression experiment (Te ∼ 75 keV; ne ∼ 1012−1013 cm−3; plasma length ∼ 10 cm; plasma diameter ∼ 0.5 cm; cavity length ∼ 30 cm; cavity diameter ∼ 10 cm). Ne is measured independently of the plasma density profile and in a high plasma density regime (ωp > ω010). High density measurements are possible because the plasma skin depth is greater than the plasma diameter and because the induced charge at the ends of the plasma is small. A swept frequency, raster presentation is used so that the variation of Ne with time can be followed. The measurements show that Ne ∼ 1012−1013 at peak compression, and that Ne decays on a time scale ∼ 4 msec. The cavity measurements were in substantial agreement with synchrotron radiation and light measurements, as well as with simple mirror theory.
Warm-Plasma Stabilization of Resonant Loss-Cone Instabilities
Authors: Dory R. A. , Farr W. M. , Guest G. E. , Callen J. D.
Published: February 2004

A warm Maxwellian plasma can stabilize velocity-space instabilities which might otherwise occur in a hot non-Maxwellian plasma with which it coexists. The relative densities and temperatures of the two species required for stabilization of resonant (ω ≈ lΩi, the ion gyroharmonics) loss-cone modes in a mirror-confined hot-ion plasma are evaluated for a model plasma whose density is spatially uniform but whose velocity-space distribution function simulates the loss-cone effect of mirror confinement. Marginal stability boundaries are given and compared with several simple but inexact criteria. The dominant features of the stability boundaries are explained on the basis of cutoff of propagation of the unstable waves. Temporal growth rates of the absolutely unstable modes are found to decrease significantly with increasing warm-plasma density. The resulting transition from absolute to convective growth is demonstrated for the first two gyroharmonics.
Recombination Instability as an Example of a More General Class of Instabilities
Authors: Kofoed-Hansen O.
Published: February 2004

The recombination instability described by D'Angelo is shown to constitute an example of a more general class of density change instabilities where over-all density changes of gases and plasmas are caused by volumetric processes. A simplified version of the fluid mechanics equations pertaining to this problem is examined both in the linearized case and in the complete nonlinear complexity case.
Destabilization and Quasilinear Evolution of the Ion Flute Mode
Authors: Horton C. W.
Published: February 2004

The regions of instability of the ion flute mode are investigated for a low -β plasma in axisymmetric multipoles. A stability criterion is given including the effects of (1) finite Debye length, (2) small temperature anisotropy, and (3) small temperature gradient. Using quasilinear theory the growth of a spectrum of waves is shown to produce a stabilizing anisotropy. The level of density fluctuations in the saturated state is given for plasmas close to marginal stability.
Transverse Kelvin-Helmholtz Instability in a Rotating Plasma
Authors: Kent Gerald I. , Jen Norman C. , Chen Francis F.
Published: February 2004

In thermally ionized alkali-metal plasmas (Q machines), two types of low-frequency oscillations are found: the usual drift wave localized to the region of large-density gradient, and a higher-frequency wave localized to the region of the radial boundary. The latter “edge” oscillation is shown to be a Kelvin-Helmholtz instability driven by the large shear in plasma rotational velocity at the boundary. An analytic solution of the finite-Larmor-radius dispersion equation for the unstable wave is found by making the simplifying assumption that the rotational velocity jumps discontinuously. The results agree reasonably well with experimental measurements.
Nonlinear Stability of a Beam Plasma System
Authors: Samain A.
Published: February 2004

The evolution of a collisionless beam plasma system initially in a linearly unstable state ε adjoining a marginally unstable state εcr is considered. This instability is a reactive effect, not a resonant particle effect. All phenomena are assumed to be periodic with a definite period along the beam direction. An examination is made to see whether a weak turbulence with an intensity depending on the deviation Δ between ε and εcr and going to 0 with Δ, or on the contrary a turbulence independent of Δ develops in the plasma. To that end a study is made, using a variational method, to see whether a small-amplitude ergodically periodic potential can exist in the plasma as a result of spontaneous evolution. It is found that this is impossible, and it is concluded that a turbulence with an intensity independent of Δ develops in the plasma.
Density and Potential Distribution in a Cylindrical Beam-Generated Plasma
Authors: Ma Chao-Hung , Johnson Curtis C.
Published: February 2004

A static theory of density and potential distribution in a cylindrical beam-generated plasma is presented. The theory requires only minor modifications of the Langmuir-Tonks free-fall theory for a positive column and is based on the assumption that the electron is the principal source of ionization. Both theoretical and experimental results for a singly ionized mercury plasma are given for the case of an electron beam partially filling a cylindrical tube.
Stability of the Resistive Sheet Pinch
Authors: Barston E. M.
Published: February 2004

Necessary and sufficient conditions for exponential stability of equilibria are obtained for the resistive, viscous, incompressible magnetohydrodynamic sheet pinch in a gravitational field. Insulating as well as conducting boundaries are considered. The unperturbed magnetic field B0 (horizontal), resistivity η0, viscosity ν0, and mass density ρ0 are permitted to be arbitrary (neither necessarily constant nor small) functions of the vertical coordinate z consistent with the equilibrium equations. In particular, it is shown that: (1) previous results claiming the existence of an exponentially growing “tearing” mode for a constant η0 equilibrium with zero gravity are incorrect, (2) a nonconstant η0 equilibrium with insulating boundaries cannot be gravitationally stabilized, and (3) a nonconstant η0 equilibrium with g(dρ0/dz) ≡ 0 and B0 nonunidirectional is exponentially unstable to all perturbations (i.e., waves of arbitrary wavelength) with certain directions of propagation.
Study of the Diffusion of High-β Plasma in a Theta Pinch
Authors: Bodin H. A. B. , Newton A. A.
Published: February 2004

A direct measurement is described of the perpendicular diffusion coefficient in a theta pinch operating in the low-pressure regime with zero bias field. The diffusion was studied by comparing the measured time variation of the radial electron density distribution with computations assuming classical and other resistivities. A coil 8 m long is used in order to delay end effects and measurements confirm theoretical predictions that the plasma in the midplane is uninfluenced by the ends and free of energy losses for about 25 μsec. The plasma temperature was varied from 90 to 160 eV and the values of density and beta on the axis are 3−4 × 1016/cm3 and 0.7, respectively. In the early stages (before 2 μsec) diffusion at approximately the Bohm rate is found, and this is believed to be due to a streaming mechanism. At later times the measured diffusion coefficient is in good agreement with the classical value in all conditions studied, and the experimental error is such that diffusion is unlikely to exceed 110 of the Bohm rate.
Enhanced Bremsstrahlung from Plasmas with Relativistic Electron Tails
Authors: Papadopoulos Konstantinos
Published: February 2004

The bremsstrahlung emitted from thermal plasmas which coexist with a flux of relativistic electrons is calculated. The emission is found to be greatly enhanced at the fundamental and second harmonic of the electron plasma frequency. Some possible astrophysical applications of the theory are discussed.
Space, Time, and Energy Distributions of Neutrons and X Rays from a Focused Plasma Discharge
Authors: Bernstein M. J. , Meskan D. A. , van Paassen H. L. L.
Published: February 2004

The energy spectrum and spatial distribution of neutrons emitted by a plasma focus device were measured with nuclear emulsions and scintillation detectors, and the results are reported. The average energy of the D-D neutrons emitted along the axis was shifted ∼500 keV corresponding to an axial center-of-mass velocity of 2 × 108 cm/secfor the reacting deuterons. An 11% anisotropy in the neutron fluxes measured in the forward and radial directions correlates with an axially streaming plasma which is not isotropic; the reacting deuterons collide predominantly in the radial direction. Time-resolved collimation measurements of the emitted neutrons showed an axial translation of the neutron source corresponding to velocities up to 2 × 108 cm/sec; this correlates with the nonsimultaneous pinching of the noncylindrical plasma along the axis. Plasma densities of ∼ 2 × 1020cm−3 and ion temperatures of 2 keV were consistent with observed neutron yields of 1010 and pulse widths of 60 nsec. X-ray intensity measurements were made for x-ray energies of 7 < Ep < 30 keV and showed an Ep−2 dependence which does not agree with plasma bremsstrahlung, but appears to result from anode bombardment of axially accelerated electrons with energies > 200 keV. The line radiation corresponded to that of fairly cold ions.
Lack of Equilibrium in a Plasma Betatron
Authors: Ferrari L. A.
Published: February 2004

The motion of charged particles in combined betatron and azimuthal magnetic fields is investigated for the case when the radial betatron focusing force vanishes.
Exact Motion of a Charged Particle in an Arbitrary Plane Wave Propagating along a Constant Homogeneous Magnetic Field
Authors: Leer Egil
Published: February 2004

The classical relativistic equations of motion are solved for a charged particle moving in an arbitrary plane electromagnetic wave propagating along a constant homogenous magnetic field. The solutions are expressed by (proper time) evolution tensor factors, operating upon the initial value quantities. The calculations are performed in terms of tensor-component matrices. Elliptically polarized waves are then considered. At resonance frequency an expression for the increase in the kinetic energy is obtained. This expression shows that the kinetic energy increases indefinitely, and that the energy exchange is caused by the field component rotating in the same direction as the particle.
Ion Cyclotron Heating in the Model C Stellarator
Authors: Rothman M. A. , Sinclair R. M. , Brown I. G. , Hosea J. C.
Published: February 2004

A new ion cyclotron resonance heating system has been installed on the Model C stellarator. Use of low-power rf during the entire Ohmic heating pulse shows that the density for optimum coupling is a factor of 1.5-2 greater than that calculated from a simple theory. The variation of coupling with density and plasma radius is found to agree with theory. An anomalous second maximum in the coupling curve is found. At 1 MW power levels, little energy is transmitted around the ∪ bends by ion cyclotron waves, and it is necessary to have magnetic beaches adjacent to the Stix coil. Best heating is obtained with the least amount of magnetic beach. Use of a larger axial field gradient results in rapid loss of density under the Stix coil, with subsequent decrease in coupling and heating. The maximum ion temperature obtained in the ∪ bends is ∼ 550 eV, uniform to within 20%. A model is proposed in which cooling is dominated by particle losses and charge exchange, the particle loss rate being dependent on kTe.
Variational Principle in Magnetohydrodynamics
Authors: Merches Ioan
Published: February 2004

By using a special set of electromagnetic field potentials and an appropriate Lagrangian density, the momentum equation for a compressible, inviscid, infinitely conducting fluid undergoing isentropic motion in an electromagnetic field is obtained.
Thermodynamic Equilibrium of Rotating Superfluids
Authors: Putterman Seth , Uhlenbeck G. E.
Published: February 2004

The thermodynamic equilibrium of rotating liquid He II is investigated on the basis of the macroscopic Landau theory. After reviewing the classical theory of rotating fluids, it is shown that for He II the normal fluid component is in solid body rotation while the superfluid flow can be irrotational except for a set of vortex lines or vortex sheets which must be stationary in a reference frame rotating with the normal fluid. Therefore, an array of quantized vortex lines which rotate with the normal fluid can be considered to be in thermal equilibrium. The number and positions of the lines is determined by thermodynamic stability requirements. The dissipative effects must have the property that they vanish in equilibrium and that they drive the system to the state of equilibrium. It is further shown that the equations proposed by Khalatnikov fulfill these requirements.
Thermal Diffusion Factors for He4-He3 at Low Temperatures
Authors: Weissman Stanley
Published: February 2004

The thermal diffusion factor for 50% He4-He3 gaseous mixtures has been measured from room temperature to about 55°K. The experiments were done using a two-bulb type apparatus and in some cases the method of successive separations. From room temperature to about 80°K the present data agree well with earlier investigations. Below 80°K the agreement is only qualitative. The present data compare well with values based on quantum theoretical calculations using the Morse-VDD potential but do not agree with values based on the Lennard-Jones 12-6 potential.
Linear Stress Distribution and the Turbulent Boundary-Layer Equations of Motion
Authors: McDonald Henry
Published: February 2004

In the Stratford-Townsend model of a strongly retarded two-dimensional incompressible turbulent boundary layer, the velocity profile in the wall region, often termed the modified law of the wall, is obtained from an extended mixing length hypothesis together with the assumption of a linear total stress distribution normal to the wall. Here, the equations of motion are solved using a similarity assumption and a linear stress distribution. It is found that for certain flows Townsend's modified law of the wall is quite compatible with the similarity solution. In addition, it emerges from the present analysis that, under certain circumstances, a linear velocity profile satisfies the conditions arising from inserting a linear stress distribution into the equations of motion even better than Townsend's profiles, at least in the region not too close to the wall. It is found that a simple observed change from the conventional assumption of a mixing length varying linearly with distance from the wall allows this linear velocity profile to be predicted and, when the profile is compared with measurements, good agreement is obtained.
Flow Separation on a Vibrating Circular Cylinder
Authors: Mei V. C. , Currie I. G.
Published: February 2004

The location of the boundary-layer separation point on a circular cylinder has been investigated experimentally for a stationary cylinder and for a cylinder which is performing vortex-excited oscillations. The results for the stationary cylinder are in close agreement with published data. For the vibrating cylinder, the range of angular displacement of the separation point was found to depend upon the vibration amplitude and frequency, and the peak displacement occurred at a different frequency from that which gave the peak cylinder amplitude. As the frequency of the wake motion increases beyond that which gives that maximum range in the location of the separation point, the range of the motion of the separation point decreases. For given cylinder and wake frequencies, the higher the cylinder amplitude, the greater the motion of the wake. The phase shift of the actual wake was found to be close to 180 deg behind that of an ideal wake which aligns itself behind the relative velocity vector of the flow. The phase shift was found to be independent of cyclinder amplitude.
Free Convection from a Heated Vertical Plate in a Direct-Current Electric Field
Authors: Turnbull Robert J.
Published: February 2004

A theoretical study is made of the convection near a heated vertical plate in a dc electric field. Electrical forces are produced by a bulk charge density in an electric field. This charge density occurs because the temperature gradients produce gradients in conductivity in a fluid with Ohmic electrical properties. To find the effect of the electrical forces, a set of boundary-layer equations is developed and then integrated over the boundary layer. This integration produces ordinary differential equations when profiles are assumed for the temperature, velocity, and electric field. These profiles each have the same boundary-layer thickness. Both numerical and analytical solutions are found for these equations. The analytical solutions are for special cases and approximate the numerical solutions. The results are approximate expressions for the temperature, velocity, electric field, and heat transfer from the plate.
Thermally Induced Electroconvection
Authors: Wong J. , Melcher J. R.
Published: February 2004

The combined effects of a thermal gradient and a dc electric field upon a poorly conducting fluid are used to induce steady convection. A vertically directed temperature gradient is used to establish an electrical conductivity gradient over the rectangular cross section of a liquid-filled channel. Then a static potential, which varies either linearly or periodically along the channel, is imposed on electrodes that form the channel top. A similar potential, spatially shifted in the longitudinal (horizontal) direction, is applied at the bottom of the channel. These electrodes make physical and electrical contact with the fluid, which typically has a mean electrical conductivity of 10−10 mho/m. Because of the conductivity gradient, the vertical component of the resulting electric field induces free charges in the bulk, and these charges are then pulled in the horizontal direction by the longitudinal component of the electric field. An analytical model is used to predict the distribution of potential, electric stress, and velocity. It is assumed that effects of convection on the charge distribution can be ignored (electric Reynolds number small). An experiment is described in which the periodic potential distribution is closed on itself in a re-entrant channel to achieve fully developed flow. Experiment and theory compare favorably with discrepancies largely attributable to finite electric Reynolds number effects.
Viscous Instability of an Incompressible Full Jet
Authors: Ko Sung-Hwan , Lessen Martin
Published: February 2004

The instability with respect to infinitesimal, antisymmetrical disturbances of a viscous, laminar, plane jet is investigated for an incompressible fluid. The minimum critical Reynolds number is found to be 4.03 when the unperturbed flow is assumed to be parallel and 12.4 when some corrections for nonparallelism are made. In the actual jet flow it does not appear that a small two-dimensional disturbance in itself leads to transition, because as it propagates downstream the disturbance leaves the unstable region in the α-R plane, and then proceeds to damp out.
Sound and Shock Waves in Liquids Containing Bubbles
Authors: Crespo A.
Published: February 2004

The propagation of infinitesimal sound waves in a liquid containing gas bubbles is considered. Relative motion of gas bubbles and liquid is explicitly allowed for, and it is shown that a significant error in the speed of waves may arise if the relative motion and fluctuations of mass fraction are neglected. The structure of steady shock waves is also derived.
Numerical Integration of the Equations Governing the One-Dimensional Flow of a Chemically Reactive Gas
Authors: Bailey H. E.
Published: February 2004

The concept of parasitic eigenvalues in the numerical solution of sets of ordinary differential equations is introduced. The use of an implicit method is proposed for the solution of sets of differential equations containing such parasitic eigenvalues. These ideas are then applied to the integration of the equations which govern the one-dimensional flow of a chemically reactive gas. In particular, results are presented for the flow downstream of a normal shock wave and for the flow in a converging-diverging nozzle. The conditions are delineated under which the more complicated computations required by the implicit method appear justified.
Thermal Transpiration in a Cylindrical Tube
Authors: Loyalka S. K.
Published: February 2004

Thermal transpiration in a cylindrical tube is studied by using the Bhatnagar-Gross-Krook model and methods previously used by Ferziger and Cercignani and Sernagiotto in solving the Poiseuille flow problem. It appears that recent results of Sone and Yamamoto are in slight error. Finally, in analogy with the recent work of Mason and co-workers on the dusty gas model, a relation for ftr, the translational Eucken factor, is developed.
Hydromagnetic Free Convection from a Horizontal Infinite Strip Facing Downward
Authors: Singh S. N. , Cremers C. J.
Published: February 2004

The problem for the laminar free convection from a horizontal isothermal infinite strip facing downward is studied by the momentum-integral method within the boundary-layer approximations when a vertical magnetic field is imposed on the plate. The solutions are presented in an integral form for the case when the induced magnetic field is negligible. The detailed calculations for Pr = 0.025 and 1 are compared with those of the nonmagnetic case. It is found that the boundary-layer thickness increases and the Nusselt number decreases with the increase of the magnetic field.
Drag of a Sphere of Arbitrary Conductivity in a Current-Carrying Fluid
Authors: Chow Chuen-Yen , Halat John A.
Published: February 2004

It has been found analytically that an aligned electric current increases the drag of a sphere moving in an incompressible fluid if the sphere is less conducting than the fluid, and decreases the drag if it is more conducting.
Stability of the Dense Plasma Focus
Authors: Mather Joseph W. , Bottoms Paul J. , Carpenter James P. , Williams Arthur H. , Ware Kenneth D.
Published: February 2004

The influence of small dc axial magnetic fields upon the stability of the focused plasma column is shown in the light of soft x rays. The material damage to the center electrode and the intense x-ray emission at the electrode face as a result of electron bombardment is considerably reduced. Although the final heating of the ions and electrons is inhibited as expected due to a trapped magnetic field, the spatial stability of the focused column offers a greater possibility for scaling to higher energies.
Measurements of the Longitudinal Pressure Gradient in Direct-Current Discharges
Authors: Bergman R. S. , Chanin L. M.
Published: February 2004

Measurements have been made of the longitudinal pressure gradient in dc discharges in helium, neon, and argon. Studies have been conducted at current densities ∼ 1 A/cm2, over a pressure range of approximately two orders of magnitude with an accuracy of ± 5μ. Present results when compared at high pressures with calculations based on theory indicate good agreement with Leiby and Oskam's theory by comparison with previous theories of the effect. The studies also indicate an anomalous behavior of the gradient at higher discharge currents in neon and argon.
Saturation Currents to Langmuir Probes in a Collision-Dominated Plasma with Uniform Magnetic Field
Authors: Cohen Ira M.
Published: February 2004

Electrostatic probe theory for a slightly ionized, collision-dominated plasma is extended, in the sense of problem formulation, to allow for the presence of a uniform magnetic field. Provided that the Debye length is very much smaller than a probe dimension, ion and electron currents to the probe saturate, respectively, at large negative and positive probe bias with respect to the plasma potential. It is shown that it is not necessary to go through a lengthy asymptotic analysis to compute the saturation currents. Ion and electron saturation currents to ellipsoids of revolution inclined at an arbitrary angle to the magnetic field are given in compact form in terms of common elliptic functions.
Drift-Wave Fluctuations and Anomalous Diffusion in a Fully Ionized Cesium Plasma
Authors: Walsh J. , Schlesinger S. P. , Josephy K. , Marshall T. C.
Published: February 2004

An experimentally determined diffusion coefficient is related to the amplitude of a continuum spectrum of drift-wave-like fluctuations. It is found that the diffusion coefficient depends upon the amplitude of the fluctuation in a way which is consistent with the nonlinear diffusion theory of Dupree; that is, D⊥ ∼ 〈δn2〉 for small amplitude and ∼ 〈δn2〉1/2 for large amplitude. An elementary model which predicts the relative fluctuation amplitude 〈δn2〉/n02 and the autocorrelation time of the continuum spectrum of driftlike waves is also presented and shown to be in agreement with both the properties of the observed spectrum and the results of the diffusion measurements.
Charge Separation Effects in the Chapman-Ferraro-Rosenbluth Cold Plasma Sheath Model
Authors: Murphy Brian L.
Published: February 2004

The boundary layer between a cold streaming plasma and a perpendicular magnetic field is treated for the case where significant charge separation effects occur and the electrons but not the ions are relativistic. This case is characterized by 1 ≲ γ ≪ M/2m, where γ = Mu2/2mc2 is the ratio of the initial ion streaming energy to the electron rest energy. Only the over-all charge neutral boundary layer in which the electrons turn in the magnetic field before the ions is considered. It is found that the length scale of the magnetic field before the electron turning point is the plasma skin depth c/ωpe as in the boundary layer with γ ≪ 1, but that the electron number density diverges near the turning point with a length scale at least u/c smaller. For large γ the fraction of the ion streaming energy gained by the electrons as kinetic energy is approximately (2/γ2)1/2, and the ions are found to penetrate a distance somewhat less than (2/3)(u/ωpi) beyond the electrons.
Nonlinear Theory of Ion Acoustic Waves with Landau Damping
Authors: Ott E. , Sudan R. N.
Published: February 2004

The following macroscopic equation is shown to govern the time development of a nonlinear ion acoustic wave: ∂n∂τ + α2n ∂n∂ξ + α3 ∂3n∂ξ3 + α1(8π)1/2 P  ∫ −∞+∞ ∂n∂ξ′ dξ′ξ − ξ′ = 0, where n, ξ, and τ are normalized wave amplitude, space, and time coordinates, and α1, α2, α3 are parameters which depend on the relative strengths of Landau damping, nonlinearity, and dispersion. The first three terms constitute the Korteweg-deVries equation, and the last term represents the effect of Landau damping. The equation conserves the number of particles but the wave energy can be shown to decay always. It is demonstrated that an initial waveform may either steepen or not depending on the relative size of the nonlinearity as compared to Landau damping. It is also shown that the Landau damping term causes the amplitude of a solitary wave to decay with time as (τ+τ0)−2.
Nonlinear Flute Instabilities Inherent in Two-Component Plasmas
Authors: Manheimer Wallace M.
Published: February 2004

It is shown that a cold plasma in a weak magnetic field coexisting with a low density of energetic electrons is linearly and nonlinearly unstable if the distribution of energetic electrons is of the loss cone type, or is spherically symmetric in velocity space but nearly monoenergetic. Growth rates for linear and nonlinear instabilities are calculated and compared. It is shown that nonlinear growth rates may dominate for very low wave energy.
Bounded, Resonantly Sustained High-Frequency Plasmas in a Magnetic Field and Densities High above Critical Density
Authors: Messiaen A. M. , Vandenplas P. E.
Published: February 2004

It is shown that the wave properties of a magnetized plasma column, i.e., of a bounded magnetized plasma, at low incident high-frequency power determine the behavior of the column at high hf power. At high hf power, the energy absorbed is sufficient to sustain the plasma in one of its linear (i.e., low-power) resonant states. The plasma can either be sustained in one of its cold plasma resonant states or in its hot plasma resonant states. A partially quantitative theoretical picture can be drawn and maxima of the density as a function of B0 (static magnetic induction) exactly predicted. In this manner densities high above critical density (ωe > ω; ω is the angular frequency of hf field; ωe is the electron plasma frequency) can be obtained in the neighborhood of the lower cyclotron harmonics and along the upper branch of the cold plasma resonances. Ejection of plasma outside the interaction region between plasma and wave is observed. This ejection gives rise to plasma “tongues” with density maxima not correlated to the density of plasma in the interaction region. Low-frequency instabilities and the generation of harmonics are also investigated.
Numerical Simulation of Warm Two-Beam Plasma
Authors: Morse R. L. , Nielson C. W.
Published: February 2004

One-dimensional numerical simulation of plasmas consisting of two unequal warm beams has shown flattening of the small beam and, in most cases, a strong single mode structure at about the wavelength of largest linear growth rate, accompanied by an eddylike arrangement of trapped particles in phase space. The total electrostatic field energy first increases at the linear growth rate and then, after saturating abruptly, decreases at about the same rate to an intermediate level where a much slower decay begins.
Nonlinear Development of an Electron Plasma Wave in a Cylindrical Waveguide
Authors: Manheimer Wallace M.
Published: February 2004

It is shown that in a cylindrical waveguide, a long-wavelength electron plasma wave steepens exactly as does a nonlinear sound wave. Possible applications to experiments are discussed.
Experiments and Observations on Polarized Plasma Injection
Authors: Barney Gerald O.
Published: February 2004

The injection of a plasma stream into a transverse magnetic field by polarization and E × B drift is considered in terms of a simple model. An estimate of the peak flux density that the plasma can enter is discussed. An expression for the magnitude of the diamagnetism associated with the particle velocity distribution is indicated. Experiments on the motion of a plasma stream through regions of shorted (or tied) field lines show that a sheath forms on the shorting electrode and that the plasma can penetrate through the shorted lines because the discharge current is limited to the ion saturation current. An expression for the stopping distance is derived.