bluuebunny/crossref_metadata_2025 huggingface dataset:
High-Temperature Transport Properties of Dissociating Hydrogen
Authors: Vanderslice J. T. , Weissman Stanley , Mason E. A. , Fallon R. J.
Published: December 2004

The transport properties of dissociating hydrogen gas have been calculated from 1000°K to 15 000°K with the assumption of no ionization or electronic excitation. The rigorous kinetic-theory formulas, which have recently been modified to take into consideration the multiplicity of interaction curves, were used in the calculations. The transport coefficients at each temperature are tabulated as a function of composition rather than pressure for reasons of compactness and ease of interpolation. The fact that the collision integrals for the H-H interactions are abnormally large compared to those for the H-H2 and H2-H2 interactions causes the transport properties of the mixtures to exhibit somewhat unusual behavior as a function of composition at constant temperature and pressure. Various approximate formulas for the calculation of transport properties of mixtures have been checked against the results of the rigorous calculations. The errors in the viscosity and thermal conductivity are about 10%. For the Prandtl number, however, which involves the ratio of these coefficients, the error is only about 1%.
Radiation by Plasma Oscillations Incident on a Density Discontinuity
Authors: Tidman D. A. , Boyd J. M.
Published: December 2004

The electromagnetic radiation produced by plasma oscillations propagating across a density discontinuity is calculated and the boundary conditions to be applied in this process are discussed in some detail.
Transition from Turbulent to Laminar Pipe Flow
Authors: Sibulkin Merwin
Published: December 2004

An experimental investigation of low-speed pipe flow was conducted for an initially turbulent flow of air. At subcritical Reynolds numbers, as the fluid traveled downstream its velocity profile approached the parabolic distribution corresponding to laminar flow; the rate of transition toward laminar flow being more rapid at lower Reynolds numbers. Concurrent hot-wire-anemometer measurements showed a corresponding dependence on Reynolds number of the rate of decay of the longitudinal velocity fluctuations. These velocity fluctuations were also found to decay more rapidly near the wall and center of the pipe than at intermediate radii. The energy spectrum of the fluctuations was measured along the pipe centerline, and, in terms of the macroscale, these spectra were similar.
Solutions for a Nonlinear Singular Magnetic Flux Diffusion Equation
Authors: Zabusky Norman J.
Published: December 2004

The interdiffusion of a uniform one-dimensional compressible and resistive plasma with a uniform one-dimensional magnetic field is described by a pair of coupled diffusion equations. These equations separate if one assumes a slow diffusion process. The magnetic flux diffusion equation is singular at the interface, as the magnetic field maintains a constant value at the interface. The analytic properties of the solution in the region of the interface is written in terms of the similarity variable z. The current density jy = −dh/dz at the interface is shown to be finite in the adiabatic approximation and singular (as z−½) in the isothermal approximation. The results obtained for h and −dh/dz show that the magnetic field penetration is smaller in the isothermal than it is in the adiabatic case. The interface moves into the magnetic field region so that its displacement from the equilibrium interface is proportional to ci (time)½, where ci is greater in the adiabatic case than in the isothermal case.
Model for Energy Transfer in Isotropic Turbulence
Authors: Kraichnan Robert H. , Spiegel Edward A.
Published: December 2004

An approximate energy-transfer function for isotropic turbulence is proposed on the basis of an analogy with radiative transfer in an inhomogeneous medium. An essential feature of the approximation is replacement of the actual triad interactions of the Fourier modes by interactions between pairs of modes. The interaction of each pair of modes satisfies detailed conservation of energy. Regardless of which mode has the higher wave number, the net transfer of energy is always from the more strongly excited to the more weakly excited mode of a pair. The transfer function gives an inertial range where the spectrum obeys the Kolmogorov law and where energy transfer is by local cascade. The spectrum in the far-dissipation range falls off sufficiently rapidly that all spatial derivatives of the velocity field exist in mean square.
Stability of Steady-State Equilibrium Detonations
Authors: Erpenbeck Jerome J.
Published: December 2004

The hydrodynamic stability of one-dimensional, steady, equilibrium detonation waves is investigated through solution of the initial-value problem for the detonation equations, linearized in perturbations from the steady-state solution. A criterion for stability is then found depending on the sign of the real parts of the zeros of a certain function of the steady flow. Determination of stability for a specific case through this criterion would involve extensive, but entirely feasible, numerical computations. The hydrodynamic stability of states of chemical equilibrium is also proved, this problem being pertinent to equilibrium detonations from both physical and mathematical considerations.
Streaklines in a Perturbed Shear Flow
Authors: Hama Francis R.
Published: December 2004

Streaklines are numerically obtained for a shear flow perturbed by an unamplifying traveling sinusoidal wave. It is shown that, if a dye is injected from near the critical layer, the streaklines have an appearance of amplification and rolling as if to indicate that the flow develops into discrete vortices. The rolling-up of a streakline cannot therefore constitute a positive identification of the presence of discrete vortices. Away from the critical layer, on the other hand, the streakline appear to show an alternating amplification and damping. Apparent wavelength and wave velocity are both incorrect except in the critical layer. Further, any information due to pathlines or obtained by tracing marked particles is equally improper in regard to the wave motion. These results strongly suggest that a great deal of caution must be exercised in interpreting flow phenomena based upon flow-visualization techniques.
Kinetic Equations for Plasmas
Authors: Koga Toyoki
Published: December 2004

The effect of the inner-core field which is induced by a charged particle within the Landau distance and has been neglected in current kinetic theories of plasmas, is investigated from the transport-theory viewpoint. In the equation for a one-particle distribution function, the effect of the outer-core field between the Landau distance and the Debye distance is represented by the friction and diffusion terms of the Fokker-Planck type, while the effect of the inner-core field by the collision term of the Boltzmann type. The magnitudes of these terms are compared with each other. It is shown that the collision term may be larger than the friction and diffusion terms under certain conditions. When the effect of the outer-core field is larger than that of the inner-core field, the assumption of weak interaction is shown not to be valid. The possible nonlinear and non-Markovian behavior of a particle is considered only implicitly. The radiation phenomena are neglected.
Transonic Flow of a Perfectly Conducting Gas with Aligned Magnetic Field
Authors: Tamada Ko
Published: December 2004

The two-dimensional transonic flow of a perfectly conducting, inviscid, compressible fluid past a thin body with aligned magnetic field is studied by developing a small-perturbation theory in the hodograph plane. It is shown that the equations of motion as well as the conditions for possible shock waves can be reduced to those of ordinary flow by a suitable affine-transformation. Thus, von Kármán's transonic similarity law is extended to the present class of magneto-gas-dynamic flow. In this extension, super-Alfvénic flows (flow speed larger than Alfvén wave speed) are found to be similar to the corresponding ordinary flow, while sub-Alfvénic flows are related to the ordinary flow with reversed flow direction. The flow over a half-wedge at Mach number 1 is considered in detail.
Shock-Producing Mechanisms for Exploding Wires
Authors: Bennett F. D.
Published: December 2004

Single-fringe interferograms are presented of 4-mil Cu wires exploded at 20 kV into argon at ambient pressures of 1/8, 1/16, and 1/32 atm. Features discernible include a compressive-head shock wave, arc plasma, a weak plasma wave and the expanding metal wire. On the basis of certain plausible assumptions it is seen that the arc plasma has a temperature of about 2.5 eV; but its leading edge, a region not in thermal equilibrium, has electron temperatures ∼ 102 eV and is the boundary of an electron-driven shock wave.
Coaxial Plasmoid Source of Small Aspect Ratio
Authors: Wetstone David M.
Published: December 2004

An annular source is described which approximates a one-dimensional geometry. Characteristic behavior is given, primarily for one set of operating parameters. A fast-acting valve injects 0.3 cc STP hydrogen, and capacitor firing is timed to permit operation in the ``slug'' mode. Photomultiplier data indicate a luminous front acceleration (for 40 cm) to a muzzle velocity of 103 cm/μsec; position probes yield 74 cm/μsec. The data appear to verify a hydromagnetic acceleration model, based on analog computation for a 0.06-μg slug (which is more than half the gas available in the annulus). The theoretically expected momentum is 6.2 dyn-sec; experiment yields 11.4 dyn-sec. Tentative number density and electron temperature are 3 × 1014/cc and 3.6 eV, respectively, the latter obtained by a double Langmuir probe. The discussion includes efficiency considerations and a brief examination of the ion and electron collisional and gyromagnetic parameters.
Concept of Field Modes and the Behavior of the Magnetohydrodynamic Field
Authors: Clauser Francis H.
Published: December 2004

A method for studying the behavior of fields by splitting their behavior into independent field modes is presented. The method is used to explore the characteristics of steady, two-dimensional, linearized magnetohydrodynamic fields with finite viscosity and resistivity and arbitrary orientation of the magnetic vector relative to the velocity vector.

It is shown that in general boundary layers and wakes cease to exist in magnetohydrodynamics. Their place is taken by diffusing waves which, in reality, are the fields of a set of viscous-resistive sources, vortices, poles and currents whose field lines are strongly oriented along the characteristic wave directions. When the viscosity and resistivity are equal, these waves diffuse in a simple and independent way, but when these quantities are not equal, the diffusing waves generate a new kind of wake which is located, veil-like, in the fan-shaped region between the two wave directions. These wakes are fed from the differential diffusion of the primary waves. In the special case for which the resistivity is much greater than the viscosity, a new type of pseudo boundary layer is shown to exist in the velocity field. When the viscosity is much greater than the resistivity, this pseudo boundary layer occurs in the magnetic field.
Cyclotron Radiation from a Hot Plasma
Authors: Drummond W. E. , Rosenbluth M. N.
Published: December 2004

The angular dependence of the absorption coefficient of cyclotron radiation is obtained from the Vlasov equation and evaluated numerically, and the total radiation from both slab and cylindrical plasmas is calculated. The critical harmonic m* (below which the radiation is effectively contained) is presented graphically as a function of Te, and the combination βeBL/(1−R). The results for the total radiation are in agreement with the earlier results of Trubnikov and Kudryavtsev. The energy production in a thermonuclear reactor is computed for several different models and compared with the cyclotron radiation loss to find the critical size. The critical size depends on (1/βe)3 and for β = βe + βi = 0.40, the critical size is moderate (less than a meter) for all but the most unfavorable assumptions. For smaller β reflectors must be used to obtain reasonable critical sizes.
Cylinder Drag in the Transition from Continuum to Free-Molecule Flow
Authors: Maslach G. J. , Schaaf S. A.
Published: December 2004

The drag coefficients for cylinders normal to the flow have been determined experimentally at Mach ∼2, Mach ∼4, and Mach ∼6 with Knudsen numbers extending from continuum conditions to free-molecule-flow conditions. The results indicate a smooth transition from inviscid values at low Knudsen numbers to free-molecule-flow predictions for diffuse reflection at high Knudsen number. Small departure theories which are applicable to the ``near free molecule flow'' regime are compared to the experimental data.
Transition Reversal and Tollmien—Schlichting Instability
Authors: Reshotko Eli
Published: December 2004

Transition reversal—the sometimes observed decrease in transition Reynolds number with surface cooling—has been thought to be other than a Tollmien—Schlichting instability phenomenon since it could not be reconciled with the results of the Dunn and Lin calculations of the temperatures required for complete stabilization of supersonic flat plate boundary layers. Recent theoretical developments in the stability of compressible boundary layers to Tollmien—Schlichting waves, however, point out the importance of considering in the analysis the hitherto neglected temperature fluctuations and thermal boundary condition. Accordingly, the temperatures required for complete stabilization of flat plate boundary layers to both two-and three-dimensional disturbances have been recomputed. The new required temperatures are all below the Dunn—Lin values. In the usual diagram of surface temperature vs stream Mach number there are two loops of complete stability. The trends suggested by this diagram tend to substantiate the experimentally observed transition reversal phenomenon. The results are compared with available wind tunnel and flight data.
Rate of Ionization Behind Shock Waves in Air. II. Theoretical Interpretations
Authors: Lin Shao-Chi , Teare J. Derek
Published: December 2004

The problem of spontaneous ionization (i.e., no externally applied electromagnetic fields, nor hard radiation) in the reaction zone behind strong normal shock waves in air has been treated concurrently with the problem of dissociation and vibrational relaxation. Through a comparison of specific ionization rates, one may conclude that up to a shock velocity of 9 km/sec (about 27 times the speed of sound at room temperature), the predominant electron production process would be atom—atom ionizing collisions. This would be followed in an approximately decreasing order of importance by photoionization, electron impact, atom—molecule collisions, and molecule—molecule collisions. The charge exchange reactions, while not contributing directly to the electron production process, were found to have a small but noticeable indirect effect on the resultant electron density distribution at some distance behind the shock due to their continuous shifting of the relative population between atomic and molecular ions (which recombine with the electrons at different rates). The specific rate constants for the atom—atom processes required to interpret all existing experimental results appear to be consistent with a simple extrapolation of the low-temperature rate constants according to the crossing-point model of Bates and Massey for atom—atom ionizing collisions.
Behavior of a Plasma Produced by a Button-Type Source in Presence of a Magnetic Field
Authors: Alidieres M. , Aymar R. , Jourdan Ph. , Koechlin F. , Samain A.
Published: December 2004

In a plasma produced by a hydrogen-loaded titanium electrode gun, the pertinent physical quantities—mass, velocity, angular divergence, ion species, and resistivity—are experimentally determined. This plasma is injected along the axis of the magnetic configuration of a loop coil, and also transverse to the field of two parallel coils. The observed motion of the plasma is described, and explained mainly by macroscopic interaction of the plasma with the field.
Green's Function for the Linearized One-Dimensional Krook Equation with Electric Forces
Authors: Weitzner Harold
Published: December 2004

An integral representation is obtained for the Green's function for the linearized one-dimensional Krook equation with the induced electric field of the medium included. Various asymptotic expansions in time are then obtained. When the plasma frequency is set to zero, slightly modified hydrodynamic modes appear. For nonzero plasma frequency, only plasma oscillations unaffected by the collisions are present. Finally, the initial value problem corresponding to an initial wave packet of approximate wavenumber k is considered. For times long, but not too long, plasma oscillations are present for which the frequency and wavenumber satisfy the usual Landau dispersion relation for small wavenumber. After a sufficiently long time, the solution behaves like the Green's function itself and exhibits Landau damping.
Theory of Forbidden Zones in the Flow of a Magnetized Plasma
Authors: Helmer J. C.
Published: December 2004

The theories of Alfvén and Karlson on the two-dimensional flow of a magnetized plasma are discussed. An analog mathematical model is introduced to clarify the various features of Karlson's exact theory of forbidden zones. It is shown that the boundary of the forbidden zone is a contour of constant magnetic field strength. Karlson's theory is generalized to include an arbitrary energy distribution in the plasma, and it is shown that the size of the forbidden zone is not unique. The physical processes which give rise to charge separation and the creation of high electric fields in the plasma are examined in detail, and an elementary derivation of the appropriate Poisson's equation is given.
Detonation Wave Structure near the Hot Boundary
Authors: Koumoutsos N. G. , Kovitz A. A.
Published: December 2004

The solutions of Wood and Adamson for steady state detonation wave structure are discussed with particular attention given to the hot boundary where combustion is complete. Unimolecular, irreversible reaction kinetics, with an ignition temperature, and small rate parameter are assumed. An alternate solution based on Wood's analysis is presented which agrees with Wood's and Adamson's results when the hot boundary Mach number is less than unity. The solution presented here does not agree with that of Wood when the hot boundary Mach number is unity. We find that u ∼ 1 + const (log x)−1 as x → 0 when the hot boundary Mach number is unity. u is the reduced velocity; x is the mass concentration of combustible.
Application of the Two-Particle Distribution Function to Estimate the Collisional Damping of Plasma Oscillations
Authors: Burgers J. M.
Published: December 2004

An approximate, linearized equation for the pair correlation function, containing a Debye potential instead of the Coulomb potential, is used to derive by direct integration a solution for the pair correlation function for the case of long-wavelength plasma oscillations in a fully ionized gas without a magnetic field. The correlation function is then applied to describe the effect of collisions in a linearized Boltzmann equation for the single-particle distribution function, which again is integrated directly. By substituting the integral of the single-particle function over the velocity space (so as to obtain the number density of the particles) into Poisson's equation for the electric field, a dispersion equation is constructed for the oscillations. From this dispersion equation the damping of the oscillations can be found. The result combines the Landau damping with the collisional damping.

The purpose of the paper is to show what can be done with direct integration in coordinate space, without introducing Fourier and Laplace transforms and without integrations in a complex plane. Only the most interesting terms have been considered. The results obtained are not essentially different from those derived by means of other methods.
On Equilibrium of a Current-Carrying Toroidal Plasma. II. Experiments with the Model C Stellarator
Authors: Sinclair Rolf M. , Yoshikawa Shoichi , Harries Wynford L. , Kessler John O.
Published: December 2004

A series of experiments with the Model C stellarator showed that a previously detected asymmetry in the device could be removed by applying such a magnetic field BT, transverse to the main confining magnetic field, that an inherent lack of closure of the flux lines of the confining field was removed. The symmetrized stellarator was then used to demonstrate that an equilibrium (discussed theoretically elsewhere) could be achieved in the plasma by applying a uniform magnetic field transverse to the plane of the stellarator. With current IOH flowing toroidally in the plasma, the tendency for the toroid to expand, due to the hoop force and the U-bend drift, is counterbalanced by the IOH × BT force. The observed transverse field required for equilibrium is in good agreement with the value predicted theoretically. Improvement at equilibrium of such plasma parameters as electron temperature, particle confinement time, and energy replacement time is demonstrated.
Numerical Evaluation of the Slip Coefficient
Authors: Albertoni Sergio , Cercignani Carlo , Gotusso Laura
Published: December 2004

The slip coefficient is evaluated by a numerical quadrature using the exact analytical formula, which is obtained from the Gross-Bhatnagar-Krook model. The obtained value z=1.1466(5)l, which is exact to the fourth decimal figure, is compared with the previous results.
Calculation of the Detonation Properties of Condensed Explosives
Authors: Fickett Wildon
Published: December 2004

The Chapman-Jouguet detonation velocity and thermodynamic state variables are calculated for a representative set of CHON explosives, using the Lennard-Jones and Devonshire cell theory equation of state together with a modified conformal solution treatment of the mixture problem, and allowing for chemical equilibrium among nine product species. Although fair agreement with experiment can be obtained by adjusting a single parameter of the pair potentials, the results are little better than those obtainable with much simpler theories.
Energy Transfer in Isotropic Turbulence
Authors: Uberoi Mahinder S.
Published: December 2004

Energy transfer from large to small eddies at three stations in turbulence behind a square mesh is determined by measuring the rates of change and viscous dissipation of the spectrum and the results are compared with a theoretical prediction. Large eddies for which viscous dissipation is negligible satisfy a similarity relation which agrees with the fact that the total energy decays as some negative power of time. Small eddies which are in approximate statistical equilibrium satisfy local similarity according to Kolmogoroff. Various terms in the vorticity equation are also determined and the quantities representative of small scale motion are universal constants when expressed in terms of Kolmogoroff parameters.
Flow Fields of Flame Propagating in Channels Based on the Source Sheet Approximation
Authors: Uberoi Mahinder S.
Published: December 2004

A volume source sheet plus a uniform flow is used to represent the flow field of a flame propagating in a channel. The unknown flame shape is determined by the requirement that the velocity normal and relative to it, i. e., the local flame speed is constant. The ratio of the propagation speed of the flame as a whole to the local flame speed appears as the important parameter. Five flow fields for the values 1.05, 1.20, 1.50, 2.00, and 4.00 of the parameter are computed. These give generally correct flame shapes and flow fields. The detailed results of the analysis are compared with two observed flow fields. Subject to the inherent limitations of the theory, the comparison is favorable.
Nonlinear Landau Damping of Oscillations in a Bounded Plasma
Authors: Montgomery David
Published: December 2004

A previously developed perturbation-theory-to-all-orders formalism is applied to the oscillations of a ``collisionless'' electron plasma which is bounded by perfectly reflecting walls. The long-time damping rate is the same for the nth order electric field as for the first order. This result generally does not apply to the unbounded plasma.
Nonlinear Stationary Waves in Relativistic Plasmas
Authors: Wang H. S. C.
Published: December 2004

Theory of nonlinear stationary longitudinal waves in relativistic plasmas is treated by solving a relativistic Boltzmann equation without the conventional approximation of linearization. It is proved here that in plasmas of physically reasonable electron velocity distributions, stationary waves of arbitrary amplitude can be propagated and obey a dispersion equation. If the velocity of propagation V is less than the velocity of light c, the amplitude of these waves will generally be limited; if the velocity of wave propagation is greater than c, however, there is no amplitude limitation. The nonlinearity in the Boltzmann equation causes a decrease of frequency of oscillation for a given wave velocity in addition to the distortion in waveform from pure sinusoidal waves. Detailed solutions for plasmas with Maxwellian electron velocity distribution and relativistic electron beams are given. In the former case, a dispersion equation including nonlinear effect is derived through a series expansion to an order higher than that used in the linearized theory. In the latter, a complete analytic solution in terms of elliptical integrals is given. In both cases dispersion characteristics for several parameters are computed and plotted. The agreement between these nonlinear dispersion equations in the limit of vanishing amplitudes and those of the linearized theory published in literature is indicated.
Plasma Oscillations and Landau Damping
Authors: Weitzner Harold
Published: December 2004

The problem of the plane wave oscillation of a one-dimensional plasma is considered. It is shown that for stable plasmas with unperturbed distribution functions in a general class which includes Maxwellians as a special case, the electric field does not damp exponentially fast, as predicted by Landau. Instead, the electric field tends to zero as some reciprocal power of time, where the exact power depends on the smoothness of the initial data. To obtain a more conventional result it is assumed that all distribution functions vanish for particle speed greater than some constant, as they must relativistically. Then for wavenumber less than a certain constant the plasma oscillations do have an undamped part corresponding to a conventional normal mode with a phase speed greater than the fastest particle speed. For wavenumbers larger than that constant the oscillations tend to zero as some reciprocal power of time.
Some New Results on the Quasi-Linear Theory of Plasma Instabilities
Authors: Frieman E. , Bodner S. , Rutherford P.
Published: December 2004

The quasi-linear theory of plasma oscillations developed by Drummond and Pines, and Vedenov, Velikhov, and Sagdeev is examined in detail using the Bogoliubov-Krylov technique of nonlinear mechanics. For the particular case treated, the mode coupling terms which were neglected in earlier work are of the same order of magnitude as those kept. The asymptotic time development of the system is also discussed in detail.
Some Exact Solutions of Magnetohydrodynamics
Authors: Uberoi Mahinder S.
Published: December 2004

Four examples of the exact solutions of two-dimensional magnetohydrodynamics of incompressible inviscid fluid are given. Two are valid for infinite conductivity and the other two for finite conductivity.
Generation of Secondary Motions in the Field of a Vortex
Authors: Weske J. R. , Rankin T. M.
Published: December 2004

The investigation is concerned with motions in the region of the core of a vortex which exhibit peripheral vorticity. From theoretical reasoning it appears that development of such motions is favored as a zonal maximum of axially vorticity components is produced, e.g., by divergence of the vortex core. Several experiments devised to verify theoretical conclusions furnish evidence that concentrations of vorticity periodic about the perimeter actually do occur as expected.
Entropy Changes in Nonequilibrium Flows
Authors: Eschenroeder Alan Q.
Published: December 2004

The entropy increases arising from chemical nonequilibrium in inviscid flows are investigated by the use of an analytical model. After the validity of the model is examined, the irreversibilities in nonequilibrium expansions are studied. The basic approach to the problem is an analytical study of limiting behavior of the entropy integral followed by numerical evaluation of this integral over finite limits. Small perturbation analyses are employed for investigating near-equilibrium and near-frozen flow in order to justify truncation of the entropy integral for some cases. The conditions necessary for the existence of freezing and for the existence of entropy bounds are established for large expansions. The results of exact numerical solutions for nonequilibrium nozzle flows are compared with those from isothermal approximations for upper bounds on entropy increments. Irreversibilities are also evaluated for relaxation flows in a constant-area duct, a shock-wave reaction zone, and a venturi for a previously frozen flow. It is observed that the entropy rise in the freezing process is practically negligible compared with the total entropy for a wide range of conditions characterizing flows of technical interest. The constant-area relaxation and venturi relaxation flows also show small entropy rises. The shock wave and its accompanying relaxation zone lead to substantial irreversibilities. The entropy rise in the expansion cases is small permitting constant entropy approximations which may be utilized in numerical computation.
Laminar Jet Mixing in Radiation Gasdynamics
Authors: Pai S. I.
Published: December 2004

The fundamental equations of a laminar jet mixing region with thermal radiation are first derived, including both radiation stresses and radiation heat flux. Then the cases of both small and finite mean free path of radiation are analyzed. Two important radiation parameters, the radiation pressure number and the radiation flux number, are introduced and discussed. The radiation effects are to reduce the maximum temperature in the mixing region and to increase the spread of the thermal mixing region. Explicit formulae to calculate these effects are given.
Equilibrium of a Toroidal Plasma with a Conducting Aperture Limiter
Authors: Yoshikawa Shoichi , Harries Wynford L. , Sinclair Rolf M.
Published: December 2004

A conducting limiter brings about equilibrium of a toroidal plasma by anchoring magnetic field lines. Charge separation arising from the curvature effect can be short circuited by the limiter. This way of achieving equilibrium is not possible if the charge separation current exceeds the maximum ion saturation current to the limiter. Experiments with the Model C stellarator are consistent with this model. An observed instability is related to the loss of equilibrium due to the excess charge separation current.
Some Stable Plasma Equilibria in Combined Mirror-Cusp Fields
Authors: Taylor J. B.
Published: December 2004

The problem of equilibrium and stability of plasma confined in certain magnetic fields of combined mirror-cusp form is discussed. These fields have the properties that they are nowhere zero and everywhere increase toward the periphery. Attention is drawn to the importance of the existence of closed surfaces of constant |B|—the magnetic isobars. The conditions for plasma equilibrium are derived and interpreted; then by exploiting the existence of closed magnetic isobars certain low-β confined equilibria are constructed. These equilibria are shown to be stable according to the fluid (double adiabatic) energy principle and according to the small Larmor radius limit theory. A direct proof of stability against motions which preserve the magnetic moment is given. These equilibria have the property that there is no current along lines of force so that they are also immune to several drift instabilities.
Analysis of a Self-Sustained Thermally Driven Nonlinear Vibration
Authors: Chu Boa-Teh
Published: December 2004

A pipe closed at both ends contains a pressure-sensitive plane heat source at its midsection. The heat release rate is assumed to be proportional to the pressure fluctuation at the heater. When the feedback coefficient ε is positive, the system is unstable and a self-excited oscillation grows exponentially in time until shock waves are formed in the system. The ensuing self-sustained nonlinear periodic vibration is calculated for the case ε « 1. It is shown that the pressure-time curve at a fixed point in the pipe has the form of a sawtooth function, while the velocity-time curve has the form of a square wavefunction. To the order of ε, the frequency of the self-sustained vibration is equal to the resonance frequency of the system. The shock waves propagate with constant strength and the shock loci in the xt space are calculated. The effects produced by a time lag in heat source's response are discussed.
Velocity Profile Development in the Entrance Region of a Right Circular Cylinder with Slip at the Walls
Authors: Hanks Richard W.
Published: December 2004

The equations of continuity and motion are solved for the velocity and pressure fields in the inlet region of a straight right circular cylinder for the flow of a gas at intermediate pressure levels such that it ``slips'' at the tube walls. Curves are presented showing the effects of distance from the inlet face of the tube, Reynolds number, and pressure level on the excess pressure drop and the velocity profiles. A table containing the first fifteen eigenvalues of the velocity equations for several pressure levels is presented.
Laminar Entry Problem in Porous Tubes
Authors: Hornbeck Robert W. , Rouleau Wilfred T. , Osterle Fletcher
Published: December 2004

The inlet region for laminar flow in porous pipes with small injection or suction is analyzed numerically. Finite difference methods are developed and solutions obtained for the equations of fluid motion with two different wall boundary conditions: constant injection or suction velocity through the wall, and velocity through the wall proportional to local pressure. Solutions are found for both uniform and parabolic axial velocity profiles at the pipe inlet. The results are found to be in good agreement with the solution of Weissberg for the conditions of constant suction velocity and a parabolic inlet velocity profile. Hydrodynamic entrance lengths are found and are compared for uniform and parabolic inlet profiles in the presence of constant injection or suction.
Structure of Shock Fronts in Argon and Nitrogen
Authors: Linzer M. , Hornig D. F.
Published: December 2004

The optical reflectivity method was used to investigate the structure of shock fronts in argon from Mach 1.70 to Mach 4.85 and in nitrogen from Mach 2.01 to Mach 3.72. Experimental data were obtained at two wavelengths and over a wide range of initial pressures. The reflectivities, corrected empirically for shock curvature, were fitted to a bimodal profile to yield a maximum-slope density thickness. The reciprocal of the thickness in argon (expressed in terms of the Maxwellian mean free path in the undisturbed gas) rises rapidly to a maximum of approximately 0.31 at about Mach 3.5 and decreases gradually thereafter. Above Mach 3 the thickness is about 50% greater than calculated from the Navier-Stokes equations, using a realistic viscosity-temperature relationship. There is excellent agreement, especially at the higher shock strengths, with recent bimodal calculations carried out by Muckenfuss, using realistic intermolecular potentials. In nitrogen, the shocks are thinner than in argon and appear to attain a minimum value of 2.5 initial mean free paths at about Mach 3.7. Rotational relaxation appears to be as rapid in the strong shocks as previously observed in weak shocks; it appears to be completed within the shock front. The experimental density thicknesses are approximately 50% greater than those calculated from the Navier-Stokes equations, using the experimental shear viscosity μ and a bulk viscosity of 2μ/3. The agreement with these Navier-Stokes solutions is about as good as those in argon.
Electric Field along a Magnetic Line of Force in a Low-Density Plasma
Authors: Persson Hans
Published: December 2004

Stationary states of a collisionless plasma in a narrow axially symmetric magnetic mirror field are considered. It is shown that if the electric field vanishes identically along the magnetic field, then the angular distributions of ion and electron velocities must agree at each point. In a general case, when this condition on the distributions is not fulfilled, there is an electric field parallel with the magnetic field.
Exact Solution of the Collisionless Plasma-Sheath Equation
Authors: Self S. A.
Published: December 2004

The plasma-sheath problem for the low-pressure discharge in plane geometry is treated exactly, that is, with no arbitrary division into plasma and sheath regions. Numerical solutions are presented for various values of the parameter α, which is of the order of the ratio of the Debye length to the discharge width for 10−3 ≤ α ≤ 10−1; and for three assumptions regarding the ion generation rate, namely generation uniform, proportional to electron density, and proportional to the square of electron density.

For the higher values of α, corresponding to weak laboratory discharges, there is a smooth transition from a quasi-neutral plasma region to a thick sheath. At the smaller values of α, the conventional model of a quasi-neutral plasma region passing rather abruptly into a narrow sheath region is substantiated. In all cases, accurate values for the potential profile throughout the plasma and sheath regions are given and compared with the separate asymptotic plasma and sheath solutions for α = 0. The ion current density, wall potential, space-charge density, mean ion energy, and sheath thickness are discussed.
Dynamics of Vapor Bubbles in Spherically Symmetric Temperature Fields of General Variation
Authors: Skinner L. A. , Bankoff S. G.
Published: December 2004

During the growth of a spherical vapor bubble in a superheated liquid the inertial and surface tension effects rapidly become negligible, so that most of the growth occurs in an asymptotic stage characterized by an essentially constant bubble pressure. The asymptotic bubble behavior in initially nonuniform temperature fields is studied. An explicit formula for the bubble radius relation for a general spherically symmetric initial condition is derived. Application is made to the problem of nucleate boiling on a heated surface, where two dimensionless parameters are found to be important. Bubble radius vs time curves are determined and presented graphically for typical values of these parameters. Plots of maximum bubble radius, the time at which the maximum occurs and the average growth velocity are given for the case of subcooled boiling.
A Transformation for Free-Surface Flow in Porous Media
Authors: Yih Chia-Shun
Published: December 2004

Two methods for solving two-dimensional free-surface flows in porous media are presented. Both are based on the fact that the free surface can be transformed into a straight line. The first method utilizes the principle of images, whereas in the second method the Schwarz-Christoffel transformation is used. The solution for free-surface flow into a sink is given to illustrate the first method. The solution of the problem of water wedging is given to illustrate the second method.
Weak-Coupling Version of Bogoliubov's Kinetic Theory of Gases
Authors: Stecki J.
Published: December 2004

The version of Bogoliubov's theory of irreversible phenomena in gases, in which the coupling constant is used as an expansion parameter, is generalized to all orders.
Emission of Radio Noise by Plasmas
Authors: Boyd T. J. M.
Published: December 2004

The generation of radio noise by plasma oscillations is studied, making use of the collisionless Boltzmann equation to describe the electron component of the plasma. A second-order perturbation calculation is performed to determine the power spectrum for radiation at the second harmonic of the plasma frequency in a hot plasma in which there is no external magnetic field and the ions are of uniform density.
Sheet-Current Plasma Model for Ion-Cyclotron Waves
Authors: Hasegawa Akira , Birdsall Charles K.
Published: December 2004

An approximate plasma model, using current sheets, is introduced and initial results are presented. The primary utility is to obtain the nonlinear behavior of ion-cyclotron waves. Linear analysis is used to develop the bicircular particle motion, to show the coupling of the ion-cyclotron resonance for finite T⊥, to show Landau cyclotron damping for finite T∥. The sheet model is developed in terms of vector potential A and sheet current density Js for k parallel to the steady field B0. There are transverse fields only, with sheet motion along three coordinates. The electrons are assumed to be hot, forming a neutralizing background. The model accuracy tests show a reasonable duplication of cold plasma ion waves. The first computer experiment shows wave damping for T∥ ≫ T⊥ at the rate expected from linear analysis, and with T∥ decreasing, T⊥ increasing. The second computer experiment shows wave growth for T⊥ ≫ T∥, at the rate expected, and with T⊥ decreasing and T∥ increasing. The third computer experiment was to find the limit in T⊥ for interaction with an electron stream for ω ∼ ωci; the nonlinear limit found is equal transverse energies, whereas linear analysis shows an me/mi smaller value. This result is encouraging for using this method for ion heating.
Boundary-Layer Similarity Solutions for Rotating Flows with and without Magnetic Interaction
Authors: King W. S. , Lewellen W. S.
Published: December 2004

The laminar boundary layer produced by the rotating flow of a viscous incompressible fluid over a stationary infinite disk is considered. The external velocity is assumed to be tangential and to vary as some power of the radius, i.e., v∞ ∼ rn. The case in which the fluid is electrically conducting and interacting with a magnetic field aligned with the axis of the disk is also considered. Boundary-layer similarity equations, containing the parameter n and a magnetic interaction parameter are derived. Solutions for n between plus one (solid-body rotation) and minus one (the potential vortex) are investigated.
Studies of a Coaxial Plasma Gun
Authors: Dattner A. , Eninger J.
Published: December 2004

An experimental study of the acceleration of plasma between two coaxial electrodes is described. A high current radial discharge is obtained that is highly reproducible and axisymmetric. Particular attention has been given to the study of current distribution in the plasma. It has been found that the current layer has a complicated conical structure exhibiting closed current loops in the plasma. No pressure wave propagating in front of the current layer has been observed.
Bounded Current Sheets
Authors: Mawardi O. K.
Published: December 2004

An adiabatic two-fluid model is used to discuss generalized solutions for the structure of a plane bounded current sheet in a plasma. The current sheet is advancing in a region with no magnetic field. Numerical results for time-independent solutions are given for different values of the ratio of the velocity of the sheet to the Alfvén velocity referred to the magnetic field at a large distance behind the sheet.
Kinetic Theory of Dense Gases. III. The Generalized Enskog Equation
Authors: Hoffman David K. , Curtiss C. F.
Published: December 2004

The theory of transport phenomena in a gas is considered from a statistical mechanical viewpoint. The formalism is based on the Liouville equation for the time evolution of an ensemble of systems and the Bogoliubov-Born-Green-Kirkwood-Yvon equations which are integrals of the Liouville equation. The BBGKY hierarchy is truncated by a factorization principle which is a generalization of the molecular chaos assumption. For purely repulsive potentials, the set of equations obtained by truncating at f(3) is shown to give rise to the three-body interaction term obtained by Hollinger and Curtiss and by a different argument by Bogoliubov. The two coupled equations obtained by truncating the BBGKY hierarchy at f(3) are considered in detail. An approximation to these equations leads to a Boltzmann equation which is a soft potential generalization of the Enskog dense gas equation for rigid spheres. This Boltzmann equation includes both collisional transfer and three body collision effects.
Note on the Stability of an Elasticoviscous Liquid in Couette Flow
Authors: Datta Subhendu K.
Published: December 2004

The stability of a non-Newtonian inelastic viscous liquid moving between two rotating coaxial circular cylinders was considered by Graebel. Recently Thomas and Walters have considered the same problem for an elasticoviscous liquid with memory, which they call liquid of the type B′. In this note this problem is considered for an incompressible second-order liquid. For the particular case when the outer cylinder is at rest a particularly simple solution is given which brings out the dependence of the critical Taylor number on the viscoelastic parameter quite distinctly. It is also shown that for particular values of the viscoelastic parameters one obtains the equations considered by Graebel and Thomas and Walters.
Oscillations of a Turbulent Flow
Authors: Betchov R. , Criminale W. O.
Published: December 2004

A turbulent boundary layer is assimilated to a laminar layer of large and variable viscosity. This viscosity represents the eddy viscosity. A stability analysis is performed for small perturbations by the use of a digital computer. It is found that a typical turbulent layer is stable, even if the eddy viscosity vanishes at the wall. However, if the mean velocity profile has a weak inflection near the outer edge, instabilities do occur. Various observations of the intermittent part of the layer suggest the existence of such inflections and lead to acceptable values of the wavelengths and phase velocities. It is also found that the laminar sublayer has a negligible effect on this type of oscillation.
Kinetic Theory of Radiation in a Plasma
Authors: Aamodt R. E. , Eldridge O. C. , Rostoker N.
Published: December 2004

A kinetic theory of a fully ionized plasma with the transverse electromagnetic field expanded in vacuum normal modes is developed. The Bogoliubov, Born, Green, Kirkwood, and Yvon hierarchy of equations is terminated using only an expansion in the plasma discreteness parameters e, m, and 1/n. The renormalization of the vacuum field on a fast time scale is discussed for an infinite homogeneous plasma, and a superposition principle for dressed test particles is derived.