bluuebunny/crossref_metadata_2025 huggingface dataset:
Theory of an Electric-Current-Carrying Discontinuity Driven through Nonconducting Gas by a Lorentz Force
Authors: Gallington Roger W. , Bond Charles E.
Published: February 2004

A physical model is presented for the structure of an electric-current-carrying discontinuity moving into nonconducting gas and leaving nonconducting gas behind. The model assumes a normal shock wave followed by a porous current sheet. A three-fluid analysis (electrons, neutrals, and singly charged ions) is made for the case where the component of magnetic field normal to the plane of the discontinuity is zero. All the dependent variables can be computed as functions of displacement in the streamwise direction, as demonstrated in two specific examples. The model admits finite-strength current sheets as solutions, with the electron and ion density diminishing to zero upstream and downstream of the sheet. As seen moving with the discontinuity, the impressed electric field and the induced electric field are additive on both sides of the discontinuity. This is in contrast to the case for magnetohydrodynamic shock waves, where these two fields cancel on both sides; and to gas-ionizing shock waves, where the two fields cancel on the downstream side. In the frame of reference moving with the discontinuity, the discontinuity dissipates electrical energy and decelerates the gas. A new jump relation is found which may be described as a “sheet Ohm's law.” The fact that one and only one such relation exists, implies that a current-carrying discontinuity moving through nonconducting gas is unstable and cannot be part of a unique flow solution unless the discontinuity moves supersonically with respect to the upstream gas and subsonically with respect to the downstream gas.
Momentum Transfer in Plasma Flows at High Alfvén Mach Numbers
Authors: Friedman Herbert W. , Patrick Richard M.
Published: February 2004

Momentum coupling between two interpenetrating plasmas in the presence of a weak magnetic field has been studied experimentally. A coaxial plasma gun ionizes and accelerates aluminum (0.4 mg to 10 cm/μsec) into a low-pressure background gas which has been preionized by ultraviolet radiation from the gun. A steady magnetic field is applied parallel to the aluminum flow with maximum amplitude such that (1) the ratio of dynamic (aluminum) pressure to magnetic pressure, is of order 103, (2) the ion gyroradius is much larger than over-all flow scale, and (3) the Alfvén Mach number is greater than 10. Under these conditions, the field should have no direct influence on the deceleration rate of the aluminum plasma. Streak camera photographs show little momentum transfer between the two plasmas when no field is applied (verifying collisionless conditions) and almost complete transfer when field is applied. Magnetic field probes show that the applied field has been pushed aside by the aluminum plasma creating a field free bubble region. The scale length of the electron density gradients has been measured with a holographic interferometer indicating momentum transfer lengths less than 1 cm and thus two orders of magnitude less than the ion gyroradius.
Early-Time Model of Laser Plasma Expansion
Authors: Wright Thomas P.
Published: February 2004

A model for the high-beta spherical expansion of a plasma in a background magnetic field and ambient plasma is applied to laser-created plasmas. An analytic solution for the magnetic field configuration during early phases of the expansion is obtained and is found to be stable to small amplitude disturbances propagating in arbitrary directions with respect to the background magnetic field. The electrons are treated as an inertialess fluid throughout the analysis.
Numerical Studies of the Plasma Focus
Authors: Potter D. E.
Published: February 2004

The dynamical formation and structure of the plasma focus has been studied with a two-dimensional numerical fluid model. The extremely high kinetic energy densities obtained in the numerical fluid experiment as the result of adiabatic compression and viscous heating agree well with experiment. Three features in the plasma focus are isolated: an anode cold source, a hot pinch region, and an axial shock. The anomalously long lifetime of the plasma focus is shown to be the result of axial flow, with stabilization of magnetohydrodynamic modes through the ion stress tensor in the intermediate collisionless, collision-dominated regime. Estimates of the neutron yield based on the numerical fluid experiment concur with experimental yields, and are the result of thermally reacting deuterons in the hot pinch region. The plasma parameters of interest determined from the hot pinch region suggest that the ion distribution function will not have a simple Maxwellian form and this in particular may account for the discrepancy with experiment on the anisotropy in space of the neutron yield.
Hydrodynamic Fluctuations
Authors: Kelly G. E. , Lewis M. B.
Published: February 2004

A set of hydrodynamic-like equations describing the actual (fluctuating) variables for a dense system are derived from the Klimontovich equations. The equations have the same structure as the hydrodynamic equations but, in addition, have stochastic driving terms that have their origin in the pressure tensor and heat flux vector. The stochastic terms are evaluated in the dilute gas case.
Fluctuations in an Equilibrium Gas
Authors: Saleeby B. B. , Lewis M. B.
Published: February 2004

Equations for the correlation functions of the number density in μ space are derived, for a neutral gas and a plasma in equilibrium, from the two time Liouville equation. For the neutral gas, after sufficient smoothing has taken place the equation becomes the linearized Boltzmann equation. For the plasma the “collision” term is approximated and the equation solved for the correlation functions in space. The electron-electron function is examined in the limit of zero wavenumber and lowest order in the mass ratios and shows that, due to electron-ion collisions, the resonance is shifted from the collisionless result ωe and has a width proportional to ωe times the plasma parameter.
Density Fluctuations in a Magnetized, Weakly Ionized Plasma
Authors: Chappell W. R. , Williams R. H.
Published: February 2004

Kinetic equations are obtained for the phase space cross-correlation functions in a magnetized, weakly ionized plasma. The equations are solved by using the BGK model to represent the collisions with neutrals and an expression is obtained for the electron density cross-correlation function. The expressions obtained are valid for stationary, homogeneous, weakly ionized plasmas in a uniform magnetic field. The expression obtained for the spectral density generalizes the result of Dougherty and Farley to nonequilibrium situations. For the special case of long times and large probe separations, the expression obtained for the cross-correlation function reduces to the diffusion dominated result obtained by Ichimaru. In this limit numerical results are obtained for various collision frequencies and magnetic field strengths.
Computer Simulation of Ion-Acoustic Shocks. The Diaphragm Problem
Authors: Mason R. J.
Published: February 2004

Ion-acoustic shocks in the diaphragm problem are examined with a hybrid particle-in-cell computer simulation scheme that treats ions as particles and electrons as an isothermal fluid. Phase space plots and density profiles are given for flows from initial density jumps 1.2≤R = nI/nII≤15, with initial temperatures 1≤θ = Te/TiII≤60 and for times out to ωpiIIt≤60, where II denotes the original low-density conditions. For R = 1.2, results are in close accord with previous exact linearized solutions. The flows contain nearly antisymmetric compression and expansion regions, with embedded wavelets at θ = 30, Landau damped away for θ≤5. New nonlinear features include (a) an increase of the shock Mach number from 1.00 to 1.48, as R = 1.2→15 at θ = 30, and a constant Mach number ( = 1.20) for R = 3 and variable θ; (b) a precursor ahead of the θ = 30 fron traveling at 1.60 to 1.80 times the front speed for 1.6≤R≤15, (c) wash-out of the wavelets behind the front at large R due to increased Landau damping from heightened Ti; and (d) the intense acceleration of certain region I and II ions into the precursor for low θ(≤10) and large R.
Low-Frequency Waves and Instabilities on the Positive Column in a Magnetic Field. IV. Comparison of Various Theories for Helical Modes Illustrated for He at Low Pressures
Authors: Duncan A. J. , Forrest J. R. , Crawford F. W. , Self S. A.
Published: February 2004

The relations between three theories for helical modes of a positive column in a magnetic field, namely, those of Kadomtsev and Nedospasov, of Johnson and Jerde, and Ewald, Crawford, and Self are examined, and are shown to be different approximations, valid for different orderings of ω, ωci, νi, to a general theory which includes both ion inertia and the effect of the magnetic field on the ions. A discussion is also given of the relation of these theories to the gradient-driven ion acoustic and drift instabilities of an inhomogeneous magnetoplasma in a simple planar model. An experimental study of the positive column in He at low pressures supports the conclusion that there are two distinct instabilities. The first, setting in for low magnetic field and high frequency, corresponds to the ion acoustic instability and is described by the Ewald-Crawford-Self theory. The second, setting in for high magnetic field and low frequency, corresponds to the drift instability, and is reasonably described by the Johnson-Jerde theory except at very low pressures. Their common asymptote is the Kadomtsev-Nedospasov theory, valid only for high pressures.
Low-Frequency Waves and Instabilities on the Positive Column in a Magnetic Field. V. Axisymmetric Ionization Waves
Authors: Duncan A. J. , Forrest J. R.
Published: February 2004

The perturbation theory of the positive column in a magnetic field is extended to the nonisothermal case by allowing for fluctuations in Te and ionization rate, using the electron energy equation. The model assumes a homogeneous plasma, which is a satisfactory approximation for m = 0 modes. The ion-acoustic and electron waves of isothermal theory are modified and, more importantly, a new temperature or ionization wave arises. The latter can be unstable and is the linear form of striations. Measurements are presented of the dispersion characteristics of externally excited m = 0 ionization waves on a He column in the pressure range 38-600 mTorr and field range 0-400 G, which covers the transition from spatially damped to growing waves. Good agreement is obtained between the calculated and measured dispersions.
Plasma Resonance and Standing Longitudinal Electron Waves
Authors: Goldan Paul D. , Yadlowsky Edward J.
Published: February 2004

Using an electron beam probe, the existence of a standing electrostatic wave in the sheath surrounding a planar probe immersed in a plasma when the probe is driven at frequencies near ωp has been demonstrated. The driven probe exhibits two admittance resonances. The larger of these (near 12ωp) is the well documented “resonance probe” resonance. The smaller second resonance at ω≈ωp is associated with the standing wave and its interpretation as a Tonks-Dattner resonance is discussed. The effect of such a standing wave on the usual interpretation of plasma resonance probe data is examined.
Resonant Three-Wave Coupling in a Magnetoplasma
Authors: Gratzl H.
Published: February 2004

The matrix elements in the kinetic wave equation are calculated for three resonantly coupled electrostatic plasma waves of a turbulent spectrum in a magnetic field. The total wave energy is conserved. Applications are Bernstein modes and coupling of electron plasma with ion sound waves.
Parametric Instabilities in Inhomogeneous Plasmas
Authors: Perkins F. W. , Flick J.
Published: February 2004

The threshold ac electric field required for the excitation of the purely growing “oscillating two-stream” and decay instabilities is found to increase when the density-gradient scale length H becomes less than the mean free path. For a plasma with no magnetic field, the threshold field is given by E2/4πnTe≈2(k‖H)−1, where k‖≲(1/4)D−1 is the wavenumber of the instability in the direction orthogonal to the density gradient. (D is the electron Debye length.) Qualitative arguments suggest that this result should hold in the presence of a magnetic field. Recent experimental measurements of the threshold field agree well with these theoretical calculations. The reason for the threshold field increasing is that, in an inhomogeneous plasma, the unstable region has a finite extent spatially and energy (in the form of electron plasma waves) can propagate out of this region, thus creating an energy loss not found in uniform plasmas.
Microinstabilities in Axisymmetric Mirror Machines
Authors: Horton C. W. , Callen J. D. , Rosenbluth M. N.
Published: February 2004

The stability theory of electrostatic modes is formulated for a general axisymmetric magnetic mirror trap. For a low-β plasma with a small average gyroradius, the integral wave equation is derived for general variations in the perturbation and the equilibrium. The single-particle orbits used in the theory are calculated correct to the second order in the gyroradius expansion parameter. In special wave-frequency ranges additional expansions give previously studied forms of the mode equation. Criteria for the occurrence of flutelike modes and localized modes are given and the stability conditions discussed.
Effect of Detrapping on Trapped-Particle Instabilities in Tokamaks
Authors: Jablon C. J. , Rutherford P. H.
Published: February 2004

The effect of weak detrapping of magnetically trapped particles on low-frequency, trapped-particle modes in sheared magnetic configurations is considered; such detrapping can be imposed by oscillation of the magnetic configuration, e.g., by major-radius compression. Detrapping has a dynamical effect analogous to collisions. In particular, it is shown that trapped-particle instabilities in tokamaks can be dynamically stabilized by weak oscillation of the aspect ratio with frequency Ω and relative amplitude λ, thus imitating ion collisions with ion detrapping. In the intermediate regime of the collisional trappedparticle instability, where νi/e≪ω∼ε1/2ω*≪νe/ε, stabilization is found if ω≪Ω<λνe/ε, where ε = r/R. The stabilizing effect (surprisingly of order λ) arises from oscillation of the field strength near its maximum, where detrapping occurs. These results are for simple models of the geometry.
Electron Distribution Measurements in a Hot-Electron, Mirror-Contained Plasma
Authors: Ard W. B. , Hogan W. A. , Stetson R. F.
Published: February 2004

Electron distributions in the afterglow of a hot electron, mirror contained plasma are measured as a function of time by analysis of the bremsstrahlung spectra. The distributions are compared with those derived from a computer model which follows the cooling and scattering of electrons by ions and neutral molecules. It is found that although scattering off neutrals is an important process in cooling the electrons in this plasma, the major loss mechanism is scattering into the loss cone.
Plasma Experiments with a Three-Meter θ Pinch
Authors: Gribble R. F. , Quinn W. E. , Siemon R. E.
Published: February 2004

Measurements are reported on the plasma produced in an 830-kJ theta pinch (scylla IV) with a 3-m compression coil in which the compression field is extended to 120 μsec by means of “crowbar” switches. Double-exposure holographic interferometry, side-on streak photographs, and neutron-emission measurements establish the following comparison with the previous version of the experiment: (1) The plasma confinement time and neutron emission have been extended from 3 to 10 μsec. (2) The scaling of confinement time and plasma temperature from the 1-m device is accounted for by simple end-loss and shock-compression considerations. (3) An m = 1 “wobble”of the plasma column is observed in the present experiment and is interpreted in terms of plasma rotation propagating from the ends at approximately the Alfvén speed.
Spatial Resolution of a Resistance Wire Temperature Sensor
Authors: Wyngaard J. C.
Published: February 2004

Effects of sensor length on measured one-dimensional temperature spectrum and temperature variance dissipation rate are studied. Expressions are evaluated numerically for isotropic turbulence with the Corrsin-Pao three-dimensional temperature spectrum, providing response curves.
A New Class of Equilibrium Configurations of a Plasma Which Fit into a Sphere
Authors: Infeld Eryk
Published: February 2004

A class of equilibrium configurations such that the plasma occupies a sphere connected to an external linear current is described.
Low-Frequency Waves in a Weakly Ionized Plasma under a Weak Magnetic Field
Authors: Sato Noriyoshi , Sugai Hideo
Published: February 2004

Measurements of propagating waves excited by a small coil surrounding a dc discharge tube are reported. The waves excited on the cathode side show forward-wave and backward-wave dispersions for lower and higher frequencies, respectively, as predicted theoretically.
Effect of the Temperature Gradient on the Drift Instabilities in a High-β Collisionless Plasma
Authors: Hung R. J. , Liu V. C.
Published: February 2004

The effect of temperature gradient on the drift instabilities in an inhomogeneous high-β plasma is discussed. The analysis shows that in the presence of a temperature-gradient, ion-acoustic, and Alfvénic instabilities can be developed.
Stabilization of Instabilities by Mode Coupling
Authors: Flynn Robert W. , Manheimer Wallace M.
Published: February 2004

The nonlinear interaction between unstable and damped ion acoustic waves is investigated numerically. Energy couples to damped waves, stabilizing the system. The manner of stabilization depends strongly on the functional dependence of the growth (or damping) rate on wavenumber.
Saturation of Spatial Plasma Wave Echoes
Authors: Guillemot M. , Olivain J. , Perceval F. , Quémeneur A. , Matthieussent G.
Published: February 2004

The amplitude of spatial plasma wave echoes has been studied as a function of (i) the amplitude of the primary waves and (ii) the distance between the emitters. Saturation effects as well as the dissymmetric role played by the emitters have been observed and compared with theory.
Radiation of Hydromagnetic Waves from a Tangential Velocity Discontinuity
Authors: Duhau S. , Gratton F. , Gratton J.
Published: February 2004

An outgoing group velocity criterion is used to determine the regions of existence of radiation modes for a tangential velocity discontinuity in a collisionless hydromagnetic régime. It is shown how previously published results must be corrected.
Turbulent Layer in an Ideal Two-Dimensional Fluid
Authors: Kadomtsev B. B. , Kostomarov D. P.
Published: February 2004

The problem of the turbulent layer arising in the two-dimensional ideal fluid is considered. The sharp initial velocity discontinuity was replaced by a row of 100 point vortices whose evolution in time was found by numerical methods. The average velocity profile and velocity fluctuations are given. The picture is very similar to the ordinary turbulent layer in spite of the potential character of the ideal fluid motion outside the discontinuity.
Linearized Variational Analysis of Single-Species, One-Dimensional Vlasov Plasmas
Authors: Lewis H. Ralph
Published: February 2004

Analysis of linearized Vlasov plasmas by means of Hamilton's variational principle is illustrated by application to the initial-value problem for a neutralized, single-species plasma in one-spatial dimension with periodic boundary conditions. For any degree of approximation and for arbitrary equilibrium velocity distributions, the problem is reduced to the solution of a system of ordinary differential equations in time with constant coefficients and time-dependent driving terms; an exact particular solution has been found. The equations are discussed, including the relation of the equations to Eulerian treatments of the problem, and the use of the equations to obtain numerical results. Numerical examples have been worked out for a Maxwellian equilibrium distribution function, equilibrium distribution functions that are sums of two Maxwellian distributions, and for nonanalytic equilibrium distribution functions that are represented by cubic spline functions. Comparisons are made between numerical results from the variational method and precise solutions of the exact plasma dispersion relation.
Sharp-Boundary Model of a High-Pressure Tokamak
Authors: Haas F. A.
Published: February 2004

A simple sharp-boundary model for a high-pressure tokamak is described. Its relationship to the recent work of Greene, Johnson, and Weimer is demonstrated.
Mode Conversion in an Inhomogeneous Plasma
Authors: Moore B. N. , Oakes M. E.
Published: February 2004

An expression for the mode conversion efficiency is derived for waves propagating in an inhomogeneous plasma. Special consideration is given to the effects of finite wave vector parallel to a static magnetic field. It is shown that damping results in a reduction of the efficiency in the immediate neighborhood of the conversion layer. This reduction is partially offset by an increase in efficiency with increased density gradient. Efficiences for plasmas found in tokomaks are presented.
Toroidal Equilibrium for a High-β Theta-Pinch Plasma
Authors: Berge Gerhard
Published: February 2004

The effect of superimposing a time-oscillating l = 1 helical mode on a static straight theta pinch is investigated. The stability obtained for the m = 1 mode can be used to support the toroidal force which is introduced ad hoc. Conditions for obtaining toroidal equilibrium by this technique are obtained. The theory is within the framework of ideal magnetohydrodynamics.
Contrastreaming Instability in a One-Dimensional Finite-Length System
Authors: Lin A. T. , Rowe J. E.
Published: February 2004

Two independent and oppositely directed electron beams with equal densities and speeds are considered to interpenetrate one another in a finite-length system with a stationary neutralizing ion background. The nonlinear development of the resulting electrostatic waves is followed both in time and space by numerical simulation. The results include the time-dependent behavior of the particle trajectories governed by the equation W = 12mv2−| qφ0(t) | coskmaxz. In the cold beam case a hysteresis-like loop in phase space is observed to develop in the transition from the laminar to a turbulent state. The vortices formed in velocity space are found to be absorbed at the right-hand boundary of the finite-length system and coalesce into one another for all warm beam cases. The total electric field energy saturates at approximately 16% of the total system energy. This result is three times greater than for a one-dimensional system with periodic boundary conditions.
Nonlinear Evolution of the Dory-Guest-Harris Instability
Authors: Joyce Glenn , Knorr Georg
Published: February 2004

The nonlinear evolution of the Dory-Guest-Harris type instability is investigated by numerical integration of the Vlasov equation in one spatial and two velocity dimensions. Two methods are used: a particle simulation and the Fourier-Hermite transform. The two methods are compared for f0(v⊥) = (2π5!)−1×(υ⊥/2)10 exp (−υ⊥2/2) for k values which are unstable. A method of predicting the limiting amplitude of the electric field is presented for the case in which one mode dominates the system.
Computer Study of Convection of Weakly Ionized Plasma in a Nonuniform Magnetic Field
Authors: Shiau Jeng-Nan
Published: February 2004

A weakly ionized plasma in a strong and nonuniform magnetic field exhibits an instability analogous to the flute instability in a fully ionized plasma. The instability sets in at a critical magnetic field. To study the final state of the plasma after the onset of the instability, the plasma equations are integrated numerically assuming a certain initial spectrum of small disturbances. In the regime studied, numerical results indicate a final steadily oscillating state consisting of a single finite amplitude mode together with a time-independent modification of the original equilibrium. These results agree with the analytic results obtained by Simon in the slightly supercritical regime. As the magnetic field is increased further, the wavelength of the final oscillation becomes nonunique. There exists a subinterval in the unstable wave band. Final stable oscillation with a wavelength in this subinterval can be established if the initial disturbance has a sufficiently strong component at the particular wavelength.
The Z Pinch as a Spectroscopic Source and the Influence of Shock-Piston Separation
Authors: Roberts D. E.
Published: February 2004

An experimental study has been made of the peak compression phase of the linear (Z) pinch in argon as a spectroscopic source. The initial pressure of argon was varied from 0.05 to 1 Torr and the condenser bank energy from 0.12 to 3.1 kJ. Over this range of conditions measurements of the plasma refractive index yielded quantitative values of electron density in the range 1016−2×1018 cm−3. The electron temperature was found to be between 2 and 3 eV. It was found that complete local thermal equilibrium could not be attained with low energy inputs, irrespective of the initial filling pressure, but that for a bank energy ≳2 kJ local thermal equilibrium should be a good approximation. At high pressures the pinching of the discharge was found to be inhibited so that the axial electron density peaked at some critical pressure. A model based on current penetration into the shock piston region was able to explain the behavior of the observed radial distribution of electron density at different pressures as well as the scaling properties of the critical pressure. Other measurements pertaining to this phenomenon are also examined. Finally, it was found that a large degree of shock-piston separation occurred at high filling pressures but not at low pressures contrary to the “skin depth criterion.”
Experiments with Two-Dimensional, Rectilinear, Convective Rolls at Supercritical Conditions
Authors: Hart J. E.
Published: February 2004

By slightly slanting the normal parallel plate convection apparatus neatly aligned, two-dimensional convective rolls can be obtained. The results can be compared with numerical computations.
Velocity Spectrum of Locally Isotropic Turbulence in the Inertial and Dissipation Ranges
Authors: Lin Jung-Tai
Published: February 2004

A closure approximation is postulated for the energy transfer mechanism of locally isotropic turbulence by relating the energy transfer flux to the energy spectrum. The one-dimensional energy spectrum is compared with the measurements reported by Grant, Stewart, and Moilliet, and by Gibson.
An Attenuation-Free Shock Tube
Authors: Dumitrescu Lucian Z.
Published: February 2004

Shock wave attenuation and its effects on the uniformity of the reflected-shock “hot” region may be compensated for by suitable shaping of the driver chamber.
Velocity Distribution of the Ions Producing Neutrons in a Plasma Focus
Authors: Conrads H. , Cloth P. , Demmeler M. , Hecker R.
Published: February 2004

There is evidence for a noncollision dominated velocity distribution (average energy of at least 20 keV) of the ions producing the neutrons in a dense plasma focus. For a group of ions moving in the axial direction the average energy is at least 0.3 MeV.
Kinetic Theory Analysis of Temperature Jump in a Polyatomic Gas
Authors: Lin J. T. , Willis D. R.
Published: February 2004

A kinetic theory analysis of the temperature jump at the wall and the temperature distribution near the wall in polyatomic gases has been made. The collision term in the Boltzmann equation is represented by a classical (BGK-type) polyatomic model. The problem is linearized by considering small temperature and density variations over their respective mean values, which leads to three simultaneous singular linear integral equations. For the solution of the problem, a direct numerical method is used. The integral equations are reduced to a set of simultaneous linear equations for discrete values of the dependent variables by approximating the integrals with suitable quadrature formulas. This analysis shows that the temperature jump can be expressed as ΔT = (1/Pr)λ(dT/dy′)∞χ(l, β, αt, αi) , where l denotes the effective number of internal degrees of freedom, and αt and αi are the thermal accommodation coefficients for the translational and internal energy transfers, respectively. The parameter β is inversely proportional to N, the number of collisions to achieve equilibrium between the translational and internal modes of molecular motion. The results show that the temperature jump coefficient is, to good approximation, the same as that for the monatomic case only if αi = αt = α. In this case ΔT = [(2.0−0.83α)/α][2γ/(γ+1)](λ/Pr) (dT/dy′)∞.
Radiative Cooling of Shock-Heated Air in an Explosively Driven Shock Tube
Authors: Cooper David M. , Borucki William J. , Chien Kuei-Yuan
Published: February 2004

Results are presented of an experimental program to measure the effect of radiative cooling on the enthalpy distribution behind incident shock waves traveling in air. The shock velocity was nominally 16 km/sec and the preshock ambient pressure was varied from 0.4 to 1.6 Torr. Shock-tube diameters of 4.7 and 9.4 cm were used to investigate the effects of varying optical depths. Radiative cooling rates were determined from spatially resolved measurements of the profile of the Hα line and from absolute measurements of the continuum radiation. The measured enthalpy profiles are in good agreement with the theoretical predictions of Chien and Compton which account for both nongrey and multidimensional aspects of the radiative transport in the shock tube.
Numerical Solution of the Navier-Stokes Equations for Flows in the Disk-Cylinder System
Authors: Pao Hsien-Ping
Published: February 2004

A numerical computation of a viscous incompressible fluid confined in a circular cylindrical chamber has been carried out, where the top disk is rotating with a constant angular velocity, and the bottom disk and side wall are held fixed. Using the full Navier-Stokes equations, steady secondary flows were calculated for various Reynolds numbers (Re = Ωb2/ν) up to a maximum value of 400. It is found that, for the Reynolds numbers below 10, the governing equations are essentially linear and the numerical solution agrees very well with the analytic solution. For higher Reynolds numbers, the flow near the boundary is intensified. The detailed flow patterns are compared with previous work of a single disk and two infinite disks. The volume flow rate of the secondary flow due to the centrifugal action and the frictional moment of the disk were also calculated.
Experimental Study of Strong Transverse Ionizing Shock Waves
Authors: Moriette Pierre R.
Published: February 2004

Experiments are described in which transverse ionizing shock speeds up to 4×108 cm/sec were measured in gaseous hydrogen. Measurements of the magnetic shock structure, shock thickness, and magnetic field jump are described and compared with theoretical predictions. The ion temperature near the device wall was measured by a charge exchange particle detector. A separation distance of about 30 cm between the shock wave and the magnetic piston was measured.
Precursor Ionization Fronts Ahead of Expanding Laser-Plasmas
Authors: Koopman David W.
Published: February 2004

Fast ionization fronts have been experimentally observed to propagate ahead of a laser-produced plasma expanding into low-density background gas. The ionizing wave has a velocity of 0.3-3×108 cm/sec and a thickness of 1-10 cm both quantities increasing with radius of propagation. Langmuir probe and microwave diagnostics indicate that the wave augments the initial photoionization density by a factor of ∼3; potential fluctuations exist within the wave which can accelerate electrons to energies above the ionization threshold. Equations describing a collisional ionizing electron wave are solved in an approximate manner to yield relations which agree with many features of the measured phenomena.
Magnetohydrodynamics of a Drop
Authors: Narain Jai Prakash , Uberoi Mahinder S.
Published: February 2004

The nature of deformation and drag on a spherical drop of viscous, conducting and incompressible fluid under axisymmetric current distribution in a conducting, viscous, incompressible fluid of infinite extent is considered. The drop fluid and the ambient fluid phases are non-reacting and non-diffusive in nature. In low magnetic Reynolds' number approximation, the effects of space charge, either on the total force density or on the distribution of conduction currents are neglected. In the absence of any free induced currents, the drop deformation to oblate or prolate spheroidal shape in Stokes' approximation is primarily determined by the difference in conductivities and permeabilities of two fluid phases. The drag remains the same as that on a spherical drop in a noncurrent carrying fluid because of axisymmetric current distribution. In Oseen's approximation, the drop deformation to oblate spheroidal shape is aided by inertia of flow for large values of drop to ambient fluid density ratio, whereas inertia retards the deformation to prolate spheroidal shape. The drag on the drop increases (or decreases) from its zero-current carrying ambient fluid counterpart depending on difference in conductivities of two fluid phases. The terminal velocity remains unaffected by currents in Stokes' approximation, but it increases or decreases from its zero-current carrying ambient fluid counterpart value in Oseen's approximation depending on whether drop has higher or lower conductivity than the ambient fluid. The drag and terminal velocity remains unaffected by the permeability of the drop fluid in these approximations. In higher order, the drop tends to a spherical cap shape since the electromagnetic effects are extremely small in this order.
Magnetohydrodynamic Equilibrium of an Elliptical Plasma Cylinder
Authors: Gajewski Ryszard
Published: February 2004

Magnetohydrodynamic equilibrium of an elliptical plasma cylinder is studied for two different current distributions, with longitudinal current either distributed uniformly over the cross section, or confined to the surface only. Magnetic surfaces are found analytically in the vacuum around the plasma. They are elongated along the major axis, and bound by a separatrix.
Two-Fluid Theory of the Positive Column of a Gas Discharge
Authors: Ingold J. H.
Published: February 2004

The transition from inertia-limited flow to mobility-limited flow of ions to the walls of the positive column of a planar gas discharge is analyzed from a hydrodynamic point of view. The analysis is based on the assumption that the electrons and ions in the positive column behave as inviscid fluids with different temperatures. The resultant formulation is valid for gas pressures from the free-fall limit to the continuum limit, including the high-field sheaths at the walls as well as the almost field-free plasma at the center of the discharge. Numerical results for the characteristic value, wall field, wall potential, and ion energy at the wall are given for many different pressures and central Debye lengths, and it is shown that the results are identical to those of Allis and Rose in the continuum limit and very close to those of Self in the free-fall limit.
Ionizing Potential Waves and High-Voltage Breakdown Streamers
Authors: Albright N. W. , Tidman D. A.
Published: February 2004

The structure of ionizing potential waves driven by a strong electric field in a dense gas is discussed. Negative breakdown waves are found to propagate with a velocity proportional to the electric field normal to the wavefront. This causes a curved ionizing potential wavefront to focus down into a filamentary structure, and may provide the reason why breakdown in dense gases propagates in the form of a narrow leader streamer instead of a broad wavefront.
Lorentz Plasma in a Strong Magnetic Field
Authors: Radin S.
Published: February 2004

The electron distribution function has been calculated for a Lorentz plasma in a strong arbitrarily oriented magnetic field and in a weak electric field, temperature gradient, and flow velocity gradient. The magnetic field is strong enough to significantly affect the collision process, but it is not so strong that it completely dominates the plasma. Using the electron distribution function, corrections to the usual thermoelectric transport coefficients and viscosities have been calculated. The corrections are zero, to this order in the magnetic field, for the electrical and thermal conductivities and the thermoelectric coefficients and are typically on the order of 1% or less for the longitudinal, transverse, and Hall viscosities.
Inertial Effects in Motion Driven by Hydrodynamic Fluctuations
Authors: Nelkin Mark
Published: February 2004

The motion of a bounding surface in a fluid is considered stochastically in the presence of a volume source of thermal fluctuations. The two problems studied are the Brownian motion of a sphere and the thermally excited displacement of a free surface. The stochastic equation of motion for the velocity of the Brownian particle, and for the displacement of the surface, is written as a generalized Langevin equation. The systematic and random forces are identified with the solutions to explicitly defined boundary value problems. It is shown that a fluctuation-dissipation theorem applies. Recent papers which calculate time correlation functions for these problems from the systematic force alone are thus shown to be consistent with the physical origin of the source of fluctuations. The physical similarity of the two problems studied is emphasized. The long time t−3/2 behavior of the velocity correlation function for a Brownian particle is closely related to the modified propagation of surface waves predicted recently by Bouchiat and Meunier. Experimental evidence for the latter phenomenon is discussed briefly.
Surface Waves on Water with Depths Less than the Boundary-Layer Thickness
Authors: Walbridge N. L.
Published: February 2004

Equations are derived for the complex wavenumber for plane surface waves in liquids of low viscosity with depths from one-fifth to two-thirds of the boundary-layer thickness. For capillary waves, the values of the real wavenumber and of the spatial absorption coefficient are approximately proportional to (νσ)1/4, where ν is the kinematic coefficient of viscosity and σ is the real angular frequency. Numerical calculations agree with experimental values for a frequency of 20 Hz and a depth of one-half of the water boundary-layer thickness δ. For gravity waves with depths of about 14δ, the value of the real wavenumber equals that of the spatial absorption coefficient. Each is proportional to (νδ)1/2 but the coefficient is quite different from that of the main term for the absorption coefficient at intermediate depths.
Shallow Water Waves on a Viscous Fluid—The Undular Bore
Authors: Johnson R. S.
Published: February 2004

A theory is presented for the surface profile above a fully developed Poiseuille channel flow. Small disturbances to this flow are examined, and it is shown that if the (channel depth)/(wavelength) ratio is small (shallow waves), and the Reynolds number large enough, these disturbances initially travel at the classical dynamic (Burns) wave speeds. However, by introducing appropriate far-field coordinates it follows that the disturbance eventually travels at a different wave speed—the kinematic wave speed. To confirm this, the dynamic waves are shown to decay by using standard boundary layer techniques. This general result (of decay) agrees with previous one-dimensional theories. The profile close to the kinematic wave front is examined and shown to satisfy an equation of the form ηT + ηηX + ηXXX = ΔηXX, where η(X, T) is the surface profile. This equation is called the Korteweg-de Vries-Burgers equation. The form of the steady solution of this equation exhibits all the characteristics of the undular bore. A bound on Δ agrees with stability requirements found by other authors using different methods.
Laminar Flow in Tubes with Constriction
Authors: Chow Joseph C. F. , Soda Kunihisa
Published: February 2004

To understand the abnormal flow conditions caused by the presence of stenoses in arteries, an analytical solution is obtained for the steady laminar flow of an incompressible Newtonian fluid in an axisymmetric conduit with irregular surface where the spread of the surface roughness is large compared with the mean radius of the conduit. Numerical results are presented for the streamlines, the distributions of velocity, vorticity, and pressure, the energy dissipation, and the separation and reattachment points for conduits with sinusoidal wall variations. The analysis is also applicable to a locally constricted conduit, provided the separation zone does not extend into the straight wall portion of the conduit.
Thermal Diffusion and Convective Stability. II. An Analysis of the Convected Fluxes
Authors: Velarde M. G. , Schechter R. S.
Published: February 2004

The stability of a horizontal, two-component fluid layer subjected to a positive vertical temperature gradient (heating from above) is investigated taking advantage of the fact that the time scales for thermal relaxation and concentration relaxation are widely separated. Based on this hypothesis a buoyancy driven instability owing to the separation by thermal diffusion is found even when the density gradient favors stability. This is in agreement with the previous findings of Schechter, Prigogine, and Hamm thus verifying that the difference in time scales is the essential feature giving rise to this unexpected instability. A convective state in which rolls are assumed to be stable is then studied by solving the nonlinear problem. The analysis shows that the contribution of the convective heat flux to the total heat flux vanishes to the approximation studied here, but that the convective mass flux is an important part of the total. Thus, the separation by thermal diffusion tends to be destroyed by the instability.
Modes of a Submerged Jet
Authors: Nakaya C. , Hasegawa E.
Published: February 2004

An asymptotic expansion is presented for investigating the modes of a submerged jet. It is shown in the second approximation that the submerged jet has various types of flow in quite a wide range of its momentum flux.
Stability of Coaxial Rotating Jet and Vortex of Different Densities
Authors: Uberoi Mahinder S. , Chow Chuen-Yen , Narain Jai Prakash
Published: February 2004

Stability of a rotating axisymmetric jet surrounded by a potential vortex to infinitesimal disturbances in the inviscid incompressible fluid approximation is considered. The jet and the vortex may have different densities. The dispersion relation for angular frequency covers a wide range of configurations. A rotating or nonrotating jet in a medium at rest is unstable for all density ratios. A vortex enclosing a stagnant core is stable for axisymmetric disturbances for all densities. A vortex with a rotating core without axial velocity is unstable if the jet fluid density is greater than the vortex fluid density. The jet vortex system is destabilized by the slightest amount of axial velocity; increasing jet fluid density has a destabilizing effect. A vortex around a rotating or nonrotating jet of any density suppresses some of the large scale instabilities. In general, axial velocity of the jet, its rotation, and increase in its density have a destabilizing effect. The surface tension between the two fluids has a stabilizing effect for small scale disturbances.
Kinetic Theory of Turbulent Flow
Authors: Yen James T.
Published: February 2004

A new and analytical approach is proposed for resolving the closure problem and for achieving the desired analytical treatment of turbulent flow. The kinetic theory is utilized and the molecular distribution function in the time-averaged-flow-velocity frame is approximated. This new distribution is explicitly related to turbulence. It can be considered as a further approximation of the usual Chapman-Enskog and Grad distributions, since the turbulent energy number is small even in strong turbulence; thus, the theory is valid for strong turbulence. Only one-point correlations and perfect gases are studied. Navier-Stokes equations are kept intact, but new moment equations obtained directly from the Boltzmann equation in the above frame will be employed to approximate and to replace the Navier-Stokes moments. In particular, the Reynolds stress equation is exactly imbedded within and fully recovered via the new total stress equation. Fourth- and higher-order velocity correlations are analytically eliminated via the approximation of the molecular distribution. For low-speed compressible flow, 40 component-equations for 40 unknowns are obtained. A closed hierarchy of equations governing the turbulent correlations is analytically derived for the first time, without any phenomenological hypotheses. For high-speed flows, more moments are required. Detailed analyses are needed to ascertain whether a unique and closed hierarchy can be found for such flows.
Diffusion Flame in Homologous Turbulent Shear Flows
Authors: Chung Paul M.
Published: February 2004

The simplified statistical theory developed previously is employed to analyze the equilibrium and near-equilibrium combustion of initially unmixed reactants. It is found that the flame zone in the limit of large Damkohler numbers is very thick and is of the order of the local integral scale of turbulence. This is in contrast to the existing phenomenological theories which predict the infinitesimally thin flame sheet, in the same limit, as it is with the laminar diffusion flame. Qualitative agreements with the available experimental results are shown. It is found that singularities exist at the edges of the flame which are removed as Damkohler number is reduced. Also, it is found that the heat transfer may take place against the local mean temperature gradient in certain regions within the flame.
Effects of Upstream Unsteadiness on Hypersonic Flow past a Wedge
Authors: Hui W. H.
Published: February 2004

The effects of upstream unsteadiness on the hypersonic flow past a stationary wedge are examined. The amplitude of the oscillatory flow in the free stream is assumed small and a perturbation method is used. The problem is reduced to that of a functional-differential equation for which a solution is found. The result for the unsteady pressure is obtained in a form which clearly shows the interaction of the Mach waves with the moving bow shock. The phase-lag angle between the unsteady pressure at the body surface and the oscillation in the free stream is shown to be strongly affected by the waves reflected from the bow shock.
Kinetic Equations for a Chemically Reacting Plasma
Authors: Baum Howard R. , Fang Ta-Ming
Published: February 2004

Kinetic model equations describing the evolution of a chemically reacting plasma are proposed. Inelastic collision terms which account for the ionization and recombination processes are added to the Krook elastic collision model. These chemical reactions are assumed to result from electron-impact processes. Macroscopic multifluid equations are obtained by taking several velocity moments of the kinetic equation for each species of the plasma and applying a modification of the Chapman-Enskog procedure.