bluuebunny/crossref_metadata_2025 huggingface dataset:
Some Transition Patterns in Axisymmetric Boundary Layers
Authors: Hama Francis R.
Published: December 2004

Direct observation of the vortex pattern caused by a ring-shaped trip is made on 1-in. and ½-in. circular cylinders and on a 30° cone in a water tank. Over the cylinders the boundary-layer thickness is approximately equal to the radius of the cylinders. Ring-shaped vortices are shed and deformed into vortex loops in the same manner as on a flat plate. On the cone the ring-shaped vortices are stretched and then inevitably deformed into vortex loops, indicating that a mere stretching is not a sufficient mechanism for the creation of a turbulence spot. A mechanism of the final breakdown from the vortex loop is tentatively proposed.
Collision Integrals for the Exponential Repulsive Potential
Authors: Monchick Louis
Published: December 2004

The exponential potential function, Ae−r/ρ long has been regarded as the true qualitative form of the repulsive intermolecular potential at moderately small internuclear distances (or equivalently, high temperatures). Because of the increasing interest in gases at high temperatures it has become desirable to be able to evaluate the transport properties under these conditions. The calculation of integrals related to the usual collision integrals Ω(l,s) and cross sections Q(l) have been carried out for the exponential repulsive potential. Some high-temperature viscosities have been calculated and compared to the calculated results of Amdur and Mason which are based on an experimental scattering potential.
One-Dimensional Equilibrium Spectra in Isotropic Turbulence
Authors: Reid W. H.
Published: December 2004

The one-dimensional equilibrium spectra in isotropic turbulence are given for the physical transfer theories of Heisenberg, Kovásznay, and Obukhoff. These results are then compared with the experimental measurements of the spectrum of ∂3u1/∂x13 fluctuations. For two of the theories (Heisenberg's and Kovásznay's), reasonable agreement is obtained for kη < 0.04, but for larger values of kη there is considerable divergence between the theoretical and experimental results. The relationship between the equilibrium and similarity spectra are also discussed for these two theories.
Exact Solutions for the One-Dimensional Viscous Flow of a Perfect Gas
Authors: Rosen Gerald
Published: December 2004

Velocity-free equations are derived for the unsteady one-dimensional real fluid flow of a perfect gas. These equations admit a pressure-time symmetry, a stress symmetry, and a displacement symmetry. Fundamental solutions associated with each of the three symmetries are reported.
Edge Effects and the Stability of Plane Couette Flow
Authors: Case K. M.
Published: December 2004

The effects of edges on the stability of a uniform shear flow past one or two parallel plates is investigated in the inviscid limit. It is shown that no instabilities are produced.
Laminar Parallel Stream Mixing with Dissociation and Recombination
Authors: Kovitz A. A. , Hoglund R. F.
Published: December 2004

The boundary layer approximation is used to obtain closed-form solutions for the approach to equilibrium in a constant velocity mixing zone, i.e., the velocity gradients are neglected and only temperature and concentration gradients are considered. The chemical system consists of symmetric diatomic molecules and their atoms. A rate of atom production is assumed that is proportional to the difference between local atom concentration and the atom concentration associated with equilibrium mixing. The limiting cases of frozen flow and equilibrium flow appear as special cases of the general solution. Initial composition before mixing and composition outside the mixing zone need not be in local chemical equilibrium. It is shown that nonequilibrium conditions outside the mixing zone can have a strong influence on the evolution toward equilibrium within the mixing zone.
Diffusion Processes in a Plasma Column in a Longitudinal Magnetic Field
Authors: Hoh F. C. , Lehnert B.
Published: December 2004

Earlier results, by Lehnert, on the diffusion processes in the positive column in a longitudinal magnetic field have been confirmed in a new series of measurements over a wide range of data. Experiments with helium, argon, krypton, nitrogen, and hydrogen are described. In the case of helium good agreement is obtained between the collision diffusion theory and the experiment up to a certain critical magnetic field. For stronger fields the potential drop along the column indicates a much higher diffusion rate across the magnetic field than that expected from the binary collision theory. Account is taken, in the theory, of the presence of molecular ions and of charge exchange collisions. Abnormal voltage characteristics indicating an increased diffusion rate above a certain magnetic field strength have also been investigated in argon, krypton, nitrogen, and hydrogen. The transition from the normal to the abnormal branch of the characteristics seems to depend neither on the length of the discharge tube nor on the length of the magnetic field, provided that these lengths exceed some fifty tube diameters. On the other hand, the transition depends upon the gas density, the nature of the gas, the tube radius, and, also slightly, upon the discharge current. The transition is also indicated by an increasing noise level above the transition point. Finally, the product of the magnetic field strength and the tube radius seems to be constant at this point.
Long-Wavelength Beam Instability
Authors: Rosenbluth Marshall N.
Published: December 2004

The kinematics of a self-pinched neutralized relativistic stream is developed in the limit of oscillations whose frequency in the rest frame of the beam is low compared to the betatron frequency of oscillation of the particles of the beam. It is shown that in this limit the beam is able to displace itself more or less rigidly giving rise to the possibility of kink-type instabilities depending on its coupling with the external medium. In particular, the case where the beam passes through a low conductivity plasma is considered here. In this case there is a viscous drag when the beam displaces and pulls its magnetic field through the resistive plasma. This leads to an instability of the beam.
Charge Excitation of Plasma Motion in a Magnetic Field
Authors: Pappert R. A.
Published: December 2004

The wake of a massive point charge traversing a low-density plasma of vanishing ion temperature, in a constant external magnetic field, is investigated by means of linearized Boltzmann theory. The speed of the exciting charge is taken to be less than the root-mean-square thermal speed of the electrons and the electron thermal energy is taken to be much less than the ion energy associated with the ambient flow velocity, that is, the ion flow velocity as seen in a reference frame moving with the external charge. The magnetic field is taken along the direction of motion of the exciting charge. One of the effects of the magnetic field is the production of oscillations of both the charge density and the potential. Over some regions of space the frequency of these oscillations is approximately equal to the ion cyclotron frequency.
Correlated Electrical and Optical Measurements of Exploding Wires
Authors: Bennett F. D. , Burden H. S. , Shear D. D.
Published: December 2004

Description is given of a high-resolution streak camera and of an experimental method whereby streak-camera records and electrical measurements of exploding wires may be accurately correlated in time. Composite data together with derived values of resistance, power, and energy are given for 4 and 5 mil Cu wires at several voltages. These data are compared with the experimental and theoretical results of other workers. The transfer of energy from electrical to fluid-mechanical form is discussed as are problems having to do with formation of the shock waves.
Initiation of Detonation
Authors: Strehlow Roger A. , Cohen Arthur
Published: December 2004

A conventional shock tube modified so as to prevent local early detonation from the diaphragm burst or from wall crevasses was used to study the initiation of detonation behind the reflected shock wave. Three types of initiation behavior were observed, two of which appear to be nicely one dimensional. In all cases stoichiometric hydrogen-oxygen mixtures diluted with argon were used in the tube. In the first case a simple acceleration of the reflected shock occurred when the pressure wave generated by the adiabatic explosion reached the reflected shock. In the second case a typical accelerating wave pattern headed by a shock wave was formed behind the reflected shock while in the third case (which does not appear to be strictly one dimensional) the adiabatic explosion quickly produced a Chapman-Jouguet detonation wave behind the reflected shock wave. A simple qualitative theory for the occurrence of the wave patterns observed is presented and the adiabatic explosion delays are compared to Schott and Kinsey's recent results using a different shock-tube technique.
Wave Propagation in a Partly Ionized Gas
Authors: Tanenbaum B. Samuel , Mintzer David
Published: December 2004

A three-fluid theory (using Maxwell's equations together with a set of coupled hydrodynamic equations for an interacting mixture of electrons, ions, and neutral molecules) is used to examine small-amplitude oscillations in an infinite, homogeneous, partly ionized gas with a uniform external magnetic field. Dispersion relations are obtained when the uniform magnetic field is either parallel or perpendicular to the direction of wave propagation, and the results are interpreted (in the case of negligible collisional damping) by analyzing plots of phase velocity versus frequency. Comparison is made with the simpler one-fluid theories (the magneto-ionic theory, magnetohydrodynamics, and acoustics), as well as with the two-fluid theory for a fully ionized gas. Collisional damping effects are included in all the dispersion relations and are described in detail for the magneto-ionic and magnetohydrodynamic limits.
Structure of a Plane Shock Layer
Authors: Liepmann H. W. , Narasimha R. , Chahine M. T.
Published: December 2004

The structure of a plane shock wave is discussed and the expected range of applicability of the Navier-Stokes equations within the shock layer is outlined. The shock profiles are computed using the Bhatnagar-Gross-Krook model of the Boltzmann equation and a uniformly converging iteration scheme starting from the Navier-Stokes solution. It is shown that the Navier-Stokes solution remains a good approximation in the high-pressure region of the shock layer up to approximately the point of maximum stress for all shock strengths. In the low-pressure region, the correct profiles deviate with increasing shock strength from the Navier-Stokes solution. The physical significance of the kinetic model used and the relation of the present study to previous theoretical and experimental work is discussed.
Turbulent Thermal Convection at Arbitrary Prandtl Number
Authors: Kraichnan Robert H.
Published: December 2004

The mixing-length theory of turbulent thermal convection in a gravitationally unstable fluid is extended to yield the dependence of Nusselt number H/H0 on both Prandtl number σ and Rayleigh number Ra. The analysis assumes a layer of Boussinesq fluid contained between infinite, horizontal, perfectly conducting, rigid plates. Also obtained is the dependence of mean temperature deviation T̄(z), rms temperature fluctuation ψ̃(z), and rms velocity upon height z above the bottom plate. The theory gives H/H0 ∝ Ra1/3 (high σ), H/H0 ∝ (σ Ra)1/3 (low σ), and H/H0 ∼ 1 (very low σ). The boundaries of the several σ ranges are determined. At one intermediate Prandtl number only, the behavior of T̄(z) and ψ̃(z) reduces to that previously found by Priestly. At high σ, there is a range of z, outside the molecular conduction region, where T̄(z) ∝ z−1, ψ̃(z) ∝ z−1. The results at very low σ reduce to those of Ledoux, Schwarzschild, and Spiegel. The dynamics are found to be importantly modified at extremely large Ra because of the stirring action of small-scale turbulence generated in shear boundary layers attached to the eddies of largest scale. The consequent corrected asymptotic law of heat transport at fixed σ is H/H0 ∝ [Ra/(In Ra)3]1/2.
Viscous Flow through Porous Media. II. Approximate Three-Point Correlation Function
Authors: Weissberg Harold L. , Prager Stephen
Published: December 2004

Lower bounds were derived earlier [S. Prager, Phys. Fluids 4, 1447 (1961)] for the resistance of a porous medium to the passage of a viscous fluid. The information required for the calculation of such bounds consists of certain two- and three-point correlations S and G. An approximate expression for G in terms of S is presented and used to calculate the resistance of a bed of widely spaced spheres. The result is about 5% above the resistance calculated using the correct G, which in turn is about 25% below the true value of the resistance. Improved lower bounds on the resistance are available, but have not yet been applied because of the complexity of the calculations involved.
Exact Solutions to a Class of Linearized Magnetohydrodynamic Flow Problems
Authors: Levy R. H.
Published: December 2004

A general discussion of the properties of magnetohydrodynamic flows at low conductivity is given, and then attention is restricted to the class satisfying the following conditions: (a) The flow is steady, two-dimensional, inviscid, and only slightly perturbed from uniform conditions. (b) The magnetic field vector is also two-dimensional and lies in the plane of the flow. (c) The distortion of the applied field by the induced currents is negligible. (d) Physical boundaries on the flow are one or two infinite plates parallel to the flow direction. (e) The conductivity of the fluid is a scalar quantity, but may vary in a restricted manner with position.

With these assumptions, the perturbations to the flow are calculated exactly for arbitrary magnetic fields for the cases in which the undisturbed flow is either incompressible or supersonic. Illustrative examples for simple magnetic fields are evaluated; for some of these examples the subsonic case is also treated. Another particular example is used to show the effect of spatially varying conductivity on the flow. The limits of the applicability of these results are discussed, and general conclusions regarding the nature of the flow perturbation are drawn.
Modification for Magnetohydrodynamic Shock Structure without Collisions
Authors: Morawetz Cathleen S.
Published: December 2004

It is shown that the steady-state shock structure given earlier [C. S. Morawetz, Phys. Fluids 4, 988 (1961)] is valid only for zero-temperature electrons. However, certain modifications of the asymptotic development of the electrons permit one to show that the same shock form will appear if the electrons have a relative thermal speed of the order ε−ν, where ε2 is the mass ratio and ν satisfies ½ < ν < 1. This corresponds to a ratio of electron to ion temperature of the order ε2(1−ν).
Fall of Small Particles through the Upper Atmosphere: An Analytic Treatment
Authors: Granzow Kenneth D.
Published: December 2004

A time-dependent solution of the equation describing the fall of small particles through an infinite exponential atmosphere ∂c∂t−∂∂x(K1ρ∂c∂x+K2ρc)=0, where ρ=ρ0e−x/λ,is found for an arbitrary initial distribution of particles. Qualitative characteristics of the solution including the agreement between this analytic solution and the numerical solutions of Banister and Davis are discussed.
Variational Properties of a Viscous Liquid at a Nonuniform Temperature
Authors: Glansdorff P. , Prigogine I. , Hays D. F.
Published: December 2004

A formulation of the theorem of minimum entropy production is developed to include the case in which mechanical irreversibility due to viscous forces occurs. We have thus obtained a generalization of the dissipation function of Lord Rayleigh as well as a generalization of Helmholtz' theorem, which states that the dissipation function is a minimum in the stationary state. This generalization refers to the slow movement of a viscous incompressible fluid at nonuniform temperature.
Influence of Viscosity, Fluid conductivity, and Wall Conductivity in the Magnetohydrodynamic Rayleigh Problems
Authors: Bryson Arthur E. , Rościszewski Jan
Published: December 2004

A semi-infinite mass of incompressible, viscous, electrically conducting fluid is bounded by an infinite plane wall with a constant-strength magnetic field perpendicular to the wall. Either the wall motion is changed indicially parallel to its surface or a constant current is discharged parallel to the surface. The fluid motion and induced magnetic field are discussed for the ratio of kinematic viscosity to magnetic diffusivity ε small compared to one and equal to one. For ε « 1, it is shown that for the indicial motion of a perfect conductor or for a current discharge there exists a thin viscous boundary layer at the wall; the diffusing Alfvén wave region extends outside this layer.
Kinetic Equation for a Completely Ionized Gas
Authors: Guernsey Ralph L.
Published: December 2004

Previous derivations of the kinetic equation for a completely ionized gas have proceeded under the following assumptions: (a) the system is spatially uniform, and (b) sufficient time has elapsed so that the higher distribution functions depend on time only through the one-particle distribution. A kinetic equation is derived which is not subject to these restrictions, and is valid for any system not too far from equilibrium.
Flame Propagation in Tubes
Authors: Maxworthy Tony
Published: December 2004

An idealized theory of flame propagation is formulated to explain the effects of tube diameter, mixture composition, and direction of motion in a gravity field on the flame shape and ``speed of uniform motion'' of a flame front propagating through a stationary air-fuel mixture contained in a long tube. The effect of local flame curvature on flame speed and viscous effects within the fluid are considered, for it is believed that both play major roles in the production of a steady flame of finite amplitude. Ideally it is possible to match the present theory (valid far from a real wall) to a theory that accounts for the flame shape of the ``quenched'' portion of the flame close to the wall. This matching is only discussed qualitatively.
Magnetohydrodynamic Nozzle Flow with Three Transitions
Authors: Chu C. K.
Published: December 2004

The flow of an infinitely conducting inviscid gas in the presence of a magnetic field everywhere parallel to the velocity is considered. Such a flow starting from rest and expanding to supersonic velocities has three transitions, across each of which the flow differential equations change type: from elliptic to hyperbolic, or vice versa. The flow velocities at the three transitions are, respectively, the sound speed c, the Alfvén-wave speed a, and the speed ca/(c2 + a2)1/2. A class of those flows is approximately constructed by solving the flow differential equations, with the flow velocity, etc., prescribed on an axis of symmetry. The solution is in the form of a formal power series in a neighborhood of the axis. The resulting streamlines give possible symmetric nozzle contours. Some mathematical investigations are made to determine the acceptable form of the data to be given on the axis. Numerical examples giving nozzle shapes are included and compared with similar nozzles for nonconducting gases. The procedure described is an extension of that of Friedrichs for ordinary gas nozzles.
Irreversible Processes in Liquids and the Density Matrix: Monatomic Molecules
Authors: Nettleton R. E.
Published: December 2004

A density matrixρ̄ is introduced to describe a macroscopically small subvolume of an infinite, pure, monatomic liquid. It is assumed that the effect of molecular interactions across the wall bounding the subvolume may be represented by a random force which is a functional of the density matrix itself. The form of the functional is determined by expanding bothρ̄ and the random force potential as linear sums of a set of scalar, vector, and tensor variables, for which the time rates of change are calculated from the Von Neumann equation. It is shown that the system should relax in two stages to the local equilibrium whose decay is described by the Navier-Stokes equations and that the inertial effects which are important in the initial stage are described by the parameters in the imaginary part ofρ̄. From the low-frequency limiting forms of the pressure, heat flux, and rate equations, general expressions for the transport coefficients are written down.
Green's Function for the Linearized Vlasov Equation
Authors: Weitzner Harold
Published: December 2004

The Vlasov equation is considered without magnetic fields, linearized about a state with no electric fields or space and time variation. Integral representations for the Green's functions are presented for systems of one, two, and three dimensions. For the one-dimensional stable case, two asymptotic expansions of the electric field for large time are presented. Similar expansions are given for a specific example of a one-dimensional unstable plasma. In two and three dimensions, asymptotic expansions are exhibited for arbitrary plasmas having cylindrical or spherical symmetry.
Observation of Plasma Rotation Produced by an Electrodeless Plasma Gun
Authors: Wells Daniel R. , Schmidt George
Published: December 2004

Rotation of plasma produced by a conical θ-pinch coil fired down the axis of a longitudinal magnetic field is investigated. It is found that rotation is observed whenever the magnetic field in the θ-pinch coil is permitted to change sign and is absent whenever it is crowbarred. Rotational velocity agrees with the measured Er/Bz values within experimental error. Possible explanations of the origin of the rotation are discussed.
Cavitation Bubble Collapse in Water with Finite Density behind the Interface
Authors: Holt Maurice , Schwartz Nathan J.
Published: December 2004

The collapse of an empty cavity in water has been treated by Hunter, using a similarity solution. Conditions for similarity require that the value of the density of water at the cavity boundary is zero, although the value corresponding to zero pressure given by the Tait equation of state is nonzero. To satisfy the correct boundary conditions on the cavity surface, Hunter's similarity solution is perturbed to take account of first-order changes in the wall density. The perturbation equations have critical points coinciding with or close to the corresponding singularities of the similarity equations. Regular integral curves passing through all these points can be determined uniquely. Near the cavity wall these can be represented by expansions in powers of the similarity variable. Near the singular characteristic, however, the corresponding expansions must be found in terms of a modified variable, determined by Lighthill's technique. The corrected velocity of the cavity wall can be determined solely in terms of series expansions there.
Origin of the Driving Force in Electromagnetic Shock Tubes
Authors: Fowler Richard G.
Published: December 2004

An explanation is offered for the failure observed by Cloupeau of ordinary shock theory in the electromagnetic shock tube.
Magnetogasdynamic Flows with Shock Waves
Authors: Geffen Nima
Published: December 2004

A consistent small-perturbation theory for the aligned-fields, steady, magnetogasdynamic two-dimensional and axisymmetric flow of an inviscid conductor in the sonic, Alfvénic, and hypercritical regimes is developed, and approximate shock relations derived by a simple method. This results in nonlinear relatively simple systems of equations and shock relations for mixed flows around bodies in the transition regimes. It is found that transonic magnetogasdynamic problems can be reduced to gasdynamic ones; each gasdynamic transonic flow around a given body implies an infinite number of magnetogasdynamic patterns around the same body for all values of Alfvén numbers different from zero and one, and each of these, in turn, yields another family of flows around similar bodies, according to a modified von Kármán similarity rule. The hypercritical and transonic systems are mathematically similar and obey the same similarity rule. An explicit correspondence between specific transonic and hypercritical flows does not exist, but transonic arguments and methods can be used to infer qualitative properties of hypercritical flows and to obtain exact solutions of hypercritical flow patterns.
Axial Component of Mutual Friction in Uniformly Rotating Liquid Helium
Authors: Snyder H. A.
Published: December 2004

For helium II in uniform rotation, the component of mutual friction along the rotational axis Bz has been studied. The attenuation of second sound transverse to the axis of rotation (characterized by the parameter B) has been compared with the attenuation in the direction of the axis (measured by Bz). It is shown: that B/Bz > 500 over a large range of temperature and frequency; that Bz is not very reproducible; that Bz is dependent on the second sound amplitude; and that Bz is not linear in Ω, the rate of rotation. Within the temperature and frequency range covered by Hall and Vinen the present data on B agree with the results of these authors. Near the λ point, B increases rapidly. The anomalous dependence of B on Ω near 2.0°K as reported by Hall and Vinen is not observed. Some preliminary measurements of the parameter B′ are mentioned.
Errors and Stability of the Entry Problem Equations in Laminar Magnetohydrodynamic Flow
Authors: Shohet J. L.
Published: December 2004

The finite difference equations utilized to solve the entry problem in laminar magnetohydrodynamic flow are analyzed according to the Lax stability theory to determine the restrictious on velocity and mesh sizes required to permit a stable and convergent system when it is utilized on a computation device.
Reflection and Refraction of Magneto-Acoustic Waves at an Interface
Authors: Pridmore-Brown D. C.
Published: December 2004

The reflection and refraction of plane magnetohydrodynamic waves at an interface separating two different media is studied for various orientations of the external magnetic field. It is pointed out that by making use of trace velocity plots it is a simple matter to determine the nature and disposition of the reflected and refracted waves which are generated by an incident wave of any given species.
Electrical Conductivities of Seeded Flame Plasmas in Strong Electric Fields
Authors: Lapp M. , Rich J. A.
Published: December 2004

The effect of an applied electric field on the electrical conductivity of potassium-seeded acetylene-air and hydrogen-oxygen flame plasmas at atmospheric pressure has been explored experimentally. These flames, of interest for magnetohydrodynamic studies, were produced on a Meker-type burner designed to give a seeded cylindrical core surrounded by an unseeded shield flame. The flow system, unconfined by walls, was particularly advantageous for conductivity measurements. The voltage gradient was determined by means of a floating double probe. The effective flame diameter, seed partial pressure and gas temperature were determined spectroscopically. Good agreement between measured and calculated conductivities was obtained for low current densities. The enhancement of the conductivity observed for increasing current density can be accounted for on the basis of Joule heating of the gas in the case of C2H2/air/K. No simple explanation for the enhancement in the case of H2/O2/K has been found.
Ionized Gases at Low Density in Axially Symmetric Magnetic Fields
Authors: Henrich Louis R.
Published: December 2004

The Boltzmann equation is used to derive the expression for the current in ionized gases at low density in an axially symmetric nonuniform field. The gas is assumed to be in a steady state and collisionless. Using this method, the usual expression for the total drift current is obtained without the necessity of using first-order orbit theory. When the integration is made over the whole region of charged particles, the diamagnetic terms clearly will not contribute to the total current.
High-Frequency Plasma Conductivity in a Magnetic Field
Authors: Oberman Carl , Shure Fred
Published: December 2004

The rigorous expression for the classical high-frequency conductivity of a fully ionized plasma was obtained earlier through a joint solution, in the plasma limit, of the first two members of the B-B-G-K-Y hierarchy when both are able to change on the same time scale. [C. Oberman, A. Ron, and J. Dawson, Phys. Fluids 5, 1514 (1962)]. That treatment is now extended to include the presence of a uniform magnetic field. Through the use of a Fourier-Bessel transformation, the equation for the pair correlation function is rendered formally identical to that of the no magnetic field case.
Hydromagnetic Wave Propagation near Ion Cyclotron Resonance
Authors: Boley Forrest I. , Wilcox John M. , DeSilva Alan W. , Forman Peter R. , Hamilton Gordon W. , Watson-Munro C. N.
Published: December 2004

A torsional hydromagnetic wave is induced by application of an oscillatory radial electric field to one end of a cylindrical deuterium plasma located in a magnetic mirror field. The wave propagates in the axial direction to the center of the device, where a resonance occurs between the hydromagnetic wave frequency and the local ion cyclotron frequency. Wave magnetic-field measurements indicate that transfer of power from the 1-MW, 8.3-Mc oscillator to the hydromagnetic wave is about 65% efficient, and that more than 90% of the wave energy is transferred out of the wave at the resonance region.
Magnetohydrodynamically Supported Hypersonic Shock Layer
Authors: Levy R. H. , Petschek H. E.
Published: December 2004

The two-dimensional problem of the interaction of a hypersonic flow with the field of a current carrying wire is analyzed. The electrical conductivity behind the normal shock is taken to have an arbitrary finite value, while the free stream conductivity is zero. It is found that the magnetohydro-dynamically supported shock wave follows the magnetic field lines closely and that the hot flow is confined to a narrow region behind the shock at all values of conductivity. For low conductivities the shock position is determined by setting the interaction parameter based on the velocity behind the normal shock and a distance of ε times the shock radius equal to ⅓[1 + (2ε)½] where ε(≪1) is the density ratio across the shock. The high conductivity case is reached when the magnetic Reynolds number, based on the above parameters, exceeds unity. The shock position is then determined by equating the dynamic and magnetic pressures. The thickness of the current sheet in this case is of the order of the shock radius divided by Rm½ε−¾. For low conductivities the case of a wire embedded in a solid cylinder has also been considered, and it is shown that the heat transfer is reduced sharply when the shock wave is lifted off of the surface of the cylinder.
Existence of Detonations for Large Values of the Rate Parameter
Authors: Wood W. W.
Published: December 2004

Recent investigations of idealized Navier-Stokes detonation structure have left unresolved the existence and nature of flow solutions in the case of very fast reactions. By formulating the problem explicitly in terms of a specified initial state and a specified hot boundary mass velocity wP (relative to the unreacted explosive), it is shown that suitable ``steady'' flows exist in all cases, providing that a rarefaction wave or a slower moving shock wave is allowed to follow the detonation front.

An initial-state parameter Γ0, involving the reaction-rate ``pre-exponential factor'' and the thermal conductivity, is defined, as well as an associated critical value Γu(CJ), which depends on the heat capacity ratio, and the enthalpy and activation energy of the reaction. If Γ0 < Γu(CJ), then for small wP the predicted flow is the Chapman-Jouguet (CJ) detonation followed by a rarefaction. As wP is increased through the CJ mass velocity wC J, the flow changes continuously to increasingly overdriven detonations. If Γ0 > Γu(CJ), then for small wP the predicted flow is a weak detonation whose velocity D depends on Γ0, followed by a rarefaction. As wP is increased through the corresponding weak detonation mass velocity w(Γ0), the flow becomes the same weak detonation followed by a slower moving shock wave. With continued increase of wP this shock velocity increases until, at a certain value of wP, it becomes equal to the weak detonation velocity. At still larger wP, the flow changes continuously into an overdriven strong detonation.

Both unimolecular and bimolecular kinetics are considered. So-called ``reasonable'' values of the unimolecular parameters lead to the possibility of the flows involving weak detonations, but as noted by Hirschfelder, Curtiss, et al., the conditions are then such as to require a quasi-unimolecular mechanism to become bimolecular, due for example to depletion of the activated state. When bimolecular kinetics are considered, reasonable parameter values appear to exclude the weak detonation flows.
Nonuniform Expansion of a Piston Into an Ionized Medium with a Weak Magnetic Field
Authors: Ness Nathan , Fanucci Jerome B. , Kijewski Louis J.
Published: December 2004

The nonuniform expansion of a rigid, perfectly conducting piston into an infinitely conducting fluid wherein there exists a weak uniform magnetic field is considered. A solution for the state of the plasma and the magnetic field between the piston and the magnetohydrodynamic shock is obtained by a small perturbation method; the dependent variables are expressed in double expansions about a zero order (hydrodynamic) solution. The solution is valid for pistons (either cylindrical or spherical) whose expansion velocity is expressible by a small perturbation on a constant velocity. The development includes second order terms; however, numerical results are restricted to first order. Within the first order perturbation, it is shown that the fluid dynamic analysis is uncoupled from the magnetic field, and the shock shape retains its cylindrical or spherical symmetry. Calculations are carried out for a spherical piston, for several values of γ (specific heat ratio), and a∞/v0 where a∞ is the ambient speed of sound and v0 is the uniform piston velocity. The results show that the shock velocity is nearly insensitive to changes in the piston velocity.
Convective Flexure of a Plasma Conductor
Authors: Thiene Paul
Published: December 2004

The basic magneto-fluid-dynamical and electromagnetic equations are applied to study the flexure of an electrically neutral plasma conductor subjected to low Mach number subsonic forced convection. The basic equations, in particular the equation of energy balance, are shown to provide a linear relation between the curvature of the conductor and the mass flux of convection. For a given mass flux the curvature is found to vary inversely with a parameter introduced as the ``flexural rigidity'' of the conductor. The flexural rigidity is proportional to the coefficient which relates to the thermal conduction and the enthalpy flux due to diffusion. The flexural rigidity also increases with radiation losses and is inversely proportional to the specific heat at constant pressure. The theory is compared favorably with the results of an experimental investigation of the deflection of an arc positive column drawn between local, collinear electrodes in argon near atmospheric pressure. The arc current was varied from 2 to 6 A for various incident convection velocities normal to the interelectrode axis up to approximately 200 cm/sec.
Azimuthal Magnetic Field in the Conical Theta Pinch
Authors: Bostick Winston H. , Wells Daniel R.
Published: December 2004

A simple current-sheet model of a hydromagnetic shock is employed in an attempt to explain the origin of the Bθ and vpoloidal observed previously in the hydromagnetic vortex rings produced in the conical θ pinch. Although this simple model has its limitations, it nevertheless shows clearly that the Bθ and the vortex structure are due to Hall currents which are driven by shear in acceleration, and that the existence of any right handedness and left handedness and of the plasma vortex structure itself depends upon the fact that negative electricity (electrons) are light and positive electricity (protons) are heavy. The model also gives a plausible explanation and description of the origin of θ rotation, i.e., vθ in the θ pinch.
Continuum Theory of Spherical Electrostatic Probes
Authors: Su C. H. , Lam S. H.
Published: December 2004

A continuum theory for spherical electrostatic probes in a slightly ionized plasma is developed. The density of the plasma is taken to be sufficiently high such that both ions and electrons suffer numerous collisions with the neutrals before being collected by an absorbing probe. A general discussion of probes at an arbitrary potential is given. It is found that for very negative probe potentials the sheath thickness can be comparable to the probe radius. Two explicit forms of current-voltage characteristics are given; one for very negative probes, the other for probes at nearly plasma potential. Both of these are based on the assumption that the probe radius is large compared with the Debye length. Numerical computation is also given for negative probes of a wider range of probe sizes.
Effect of a Helical Field on the Plasma Behavior in the Model C Stellarator
Authors: Harries Wynford L. , Yoshikawa Shoichi , Sinclair Rolf M.
Published: December 2004

The superposition of an l = 3 helical field on the uniform confining magnetic field of the Model C Stellarator introduces a rotational transform of up to 58° at 5 cm radius. Measurements have been made of the effect on the plasma of superimposing this helical field on the confining field. If the confining field of the stellarator is made ``symmetric'' (if each line of force is closed when no helical field is applied), superimposing the helical field improves plasma equilibrium and increases the plasma temperature and particle confinement time. When the rotational transform from the Ohmic heating current is in the opposite sense to that from the helical winding, such that the net transform near the outer edge of the plasma is zero, a rapid loss of plasma occurs. The effect of a deliberately introduced lack of closure in the vacuum field is minimized by the helical field.
Time Dependence of the Two-Particle Correlation Function in a One-Component Plasma
Authors: Lamb George L.
Published: December 2004

The linearized equations governing the time dependence of the one-particle distribution function and the two-particle correlation function in a one-component plasma which is slightly removed from thermal equilibrium are investigated in the plasma limit. The integral equation for the two-particle correlation function is solved by the Wiener-Hopf method. It is shown that a self-consistent evolution of the one-particle distribution function and the two-particle correlation function is not prescribed by the theory unless lengths on the order of the distance of closest approach in a two-body encounter are retained. The relation of the analysis to the conjecture by Bogoliubov concerning the time dependence of multiparticle distribution functions is discussed. In particular, it is shown that although modes corresponding to distances larger than the Debye length are very slowly damped they do not make an appreciable contribution to the kinetic equations.
Laminar Steady State Electrohydrodynamic Flow in an Annular Channel
Authors: Shohet J. L.
Published: December 2004

An analytic solution is obtained for the condition of laminar electrohydrodynamic flow in an annular channel. It is assumed the charged dielectric liquid has a constant density and mobility of charge, and the current density is constant across the channel. Velocity profile curves are presented.
Radiation from a Point Source in a Plasma
Authors: Weitzner Harold
Published: December 2004

The fundamental solution for the linearized relativistic Vlasov equation with Maxwell's equations is obtained. The unperturbed state is assumed to be spatially homogeneous and time independent, with no electric or magnetic fields. The unperturbed distribution function depends only on the magnitude of relativistic momentum. An examination of the asymptotic behavior of the electric field for large time permits a general description of the solution. The electric field may be expressed as the sum of transverse and longitudinal parts. The transverse part looks like an ordinary electromagnetic wave extremely close to the light cone, and within the light cone it oscillates rapidly with varying frequency and wave number and a local phase velocity greater than the speed of light. Near the origin of the disturbance there is a transition to an ordinary plasma oscillation. In addition to a weak precursor wave, the longitudinal wave propagates outward with a definite speed and behind its wavefront the electric field oscillates with local phase velocity greater than the speed of light. Another ordinary plasma oscillation is left near the origin of the disturbance. The longitudinal speed of propagation goes to zero in the nonrelativistic case and to the speed of light in the extreme relativistic limit. The transverse and longitudinal fields defined according to the Fourier transform modes are not each zero outside the light cone, but their sum is zero. Thus, no signal travels faster than the speed of light. This peculiarity illustrates some unnatural aspects of the separation of a solution into modes of Fourier components.
Natural Oscillations of a Bounded Plasma
Authors: Yildiz Asim , Silberg Paul A.
Published: December 2004

The general case of a compressible bounded electron plasma is examined. Linearized equations of motion are set up, boundary conditions are established and the possible oscillations that could occur in the spherically bounded plasma examined. Three different modes of oscillations are established; the plasma type of oscillations, the electric type of oscillations, and the magnetic type of oscillations. Dispersion relations for possible modes are obtained.
Asymptotic Solution of the Boltzmann-Krook Equation for the Rayleigh Shear Flow Problem
Authors: Trilling Leon
Published: December 2004

An asymptotic solution of the Boltzmann-Krook equation is constructed for the Rayleigh shear flow problem. The distribution function is expanded in powers of the square root of the inverse Knudsen number assumed small. If it is required to satisfy boundary conditions on the averaged flow parameters, the first term of the expansion yields a term identical with the solution of the Navier-Stokes equation with no-slip condition; subsequent terms yield slip and satisfy a sequence of linear equations whose coefficients are determined by the no-slip Navier-Stokes solution. If the boundary condition is specified on the distribution function, there is in addition a molecular sublayer whose thickness is of the order of the mean free path.
Studies of Plasma Expelled from a Coaxial Plasma Gun
Authors: Lindberg L. , Jacobsen C. T.
Published: December 2004

An experimental study of the plasma leaving a coaxial gun is described. The plasma shows a conical shape with a central axial pinch. When a radial magnetic field is applied at the muzzle of the gun, magnetized plasma rings are formed. Under certain conditions the central pinch shows a helical instability, resulting in a considerable increase of the poloidal magnetic flux in the plasma rings. Different types of discharges are described, associated with the occurrence of a ``short-circuit'' in the gun. During the decay of the plasma, magnetoacoustic oscillations are observed.
Inference of Plasma Parameters from Measurement of E and B Fields in a Coaxial Accelerator
Authors: Lovberg R.
Published: December 2004

The current layer formed in a coaxial pulsed plasma accelerator has been examined with magnetic and electric field probes. The mappings of E and B indicate that if electrons are assumed to carry the plasma conduction current, the advancing current sheet cannot act as an impermeable piston; rather, it has the character of a strong ionizing shock which imparts some forward momentum to the gas, but does not bring plasma up to its own speed.
Landau Damping and Related Phenomena
Authors: Chang David B.
Published: December 2004

The physical interpretation of the Vlasov equation singularity-related phenomena, i.e., Landau damping, quasi-linear phase-space diffusion, and wave-wave scattering is sought by deriving these phenomena avoiding singularities. The net impulse experienced by a particle in the presence of a damped wave is calculated; and a Fokker-Planck-like equation is constructed to describe the evolution of an ensemble of particles interacting with such waves. The three phenomena are seen to arise directly from the fact that a particle experiences a net impulse in the presence of waves which are growing or damping.
Boltzmann Equation for Hard Spheres in Differential Form
Authors: Wachman Murray
Published: December 2004

It is shown that it is possible to recast the Boltzmann integro-differential equation for hard spheres into a pair of linear partial differential equations of first and eighth orders respectively. The eighth order equation is shown to be the nine-dimensional Laplacian four times repeated. The first order equation is the familiar df/dt with a different forcing function on the right hand side.
Extension of the Mott-Smith Method for a One-Dimensional Shock Wave
Authors: Salwen Harold , Grosch Chester E. , Ziering Sigi
Published: December 2004

A method has been developed for adding an arbitrary number of additional terms to the two-term Mott-Smith distribution function for a one-dimensional shock wave and a calculation has been carried out, for a monatomic gas of Maxwellian molecules, with a three term distribution function. For weak shocks, the calculated reciprocal shock thicknesses are within 2% of the Navier-Stokes results. This is a substantial improvement over the Mott-Smith results which, for the same force law, are 15 to 30% too low. For strong shocks, our reciprocal shock thicknesses are below the Mott-Smith results for vx2 and for vx3 moments.
Continuum Theory of a Plasma
Authors: Jackson J. L. , Klein L. S.
Published: December 2004

A continuum description of a classical plasma in equilibrium is presented. Thermodynamic properties and equilibrium fluctuations are discussed in terms of the fluctuations of the net charge density function n(r). The probability distribution function of the potential at a typical point, and the joint distribution of the potential at two points are calculated. As was noted in the preceding paper, these results lead to the chemical potential and two-particle distribution function of classical Debye-Hückel theory. A first order correction to the potential distribution of the continuum theory is obtained by treating the nearest neighbor charge as a discrete charge and the remainder of the plasma as a continuum. The corresponding correction to the free energy is obtained and compared with the results of diagrammatic calculations, to which the present results are similar.
Frequency- and Wavelength-Dependent Electrical Transport Equation for a Plasma Model
Authors: Berk Herbert L.
Published: December 2004

The plasma model used by Dawson and Oberman is extended to frequencies embracing the collision frequency and to finite wavelengths. To the so-called dominant order, the collisional term is a Fokker-Planck equation which is frequency dependent. At low frequencies, the electrical conductivity is found to agree with conventional Lorentz-gas theories, while at high frequencies, the electrical conductivity is that predicted by Oberman and Dawson. The finite wavelength corrections to the electrical conductivity are obtained.