bluuebunny/crossref_metadata_2025 huggingface dataset:
Effect of Magnetic Field and Rotation on Kelvin-Helmholtz Instability
Authors: Alterman Z.
Published: December 2004

The combined effect of a horizontal magnetic field and rotation on Kelvin-Helmholtz instability of a stratified fluid is considered. In two uniform fluids the short-wave perturbations are stabilized by magnetic field and surface tension, while rotation has a second-order effect. In the long-wave range the magnetic field increases the effect of rotational instability. Stability of fluids with exponentially varying density is discussed.
Temperature Dependence of the Thermal Diffusion Factor for Helium, Neon, and Argon
Authors: Saxena S. C. , Kelley J. G. , Watson W. W.
Published: December 2004

The isotopic thermal diffusion factor for He, Ne, and Ar has been measured by an all-glass ``swing separator'' with its lower tube ends at 78° and 195°K, extending the temperature range of earlier data. These new data, along with the older ones, have been interpreted in terms of the L-J (12–6) and modified exp-six potentials. Various equilibrium and nonequilibrium properties are calculated and compared with the experimental data. An equation has been developed which relates the thermal diffusion factor with the absolute values of the viscosity, diffusion coefficient, and their derivatives and is essentially independent of the nature of intermolecular force. The thermal diffusion values are consistent with the available experimental data of viscosity and diffusion, through the use of the proposed relation, but more accurate data on diffusion as a function of temperature are needed for a precise evaluation. Approximate calculations are given to estimate the quantum corrections for He at 78° and 195°K.
Effect of Collisional Energy Loss on Ionization Growth in H2
Authors: Pearlstein L. D. , Stuart G. W.
Published: December 2004

A model is studied for the growth of ionization in H2 gas with a constant electric field. The model includes a feature that stipulates an electron loses a fixed energy per collision with an H2 molecule, independent of the electron energy. Exact solutions are obtained for the time-growing part of the electron distribution function, averaged over velocity orientation, for the case that zero-energy electrons are uniformly supplied through all space at time zero. It is argued that this model provides a reasonable description of physical reality for E/P > ∼200.
Diffusion from a Slightly Ionized Region in a Uniform Flow
Authors: Pipkin A. C.
Published: December 2004

A simplified version is treated of the problem of charge diffusion from the ionized gas behind an infinite plane shock wave in steady motion. The main features of the results are independent of the mechanism of ionization. A charged double layer appears at the upstream edge of the region in which ionization takes place. The electric field between the positive and negative layers is strong enough to prevent any large number of electrons from diffusing far upstream.
Nonlinear Effects in Transport Theory
Authors: McLennan James A.
Published: December 2004

A method for the formal statistical description of transport processes beyond the linear approximation is discussed. External forces which maintain a deviation from equilibrium are introduced into the Liouville equation, and solution of this equation yields an ensemble characteristic of the non-equilibrium state. The transport relations are obtained with the aid of the resulting ensemble. For simplicity, the discussion is restricted to heat flow, but the generalization to the processes of viscosity and diffusion is straightforward.
Damping of Plasma Oscillations in the Linear Theory
Authors: Hayes John N.
Published: December 2004

The problem of stable oscillations of an infinite plasma is re-examined from the standpoint of an integral equation for the electric potential in the plasma. The behavior of a plasma with a Lorentz distribution is solved completely. We show how one may compute, under suitable restriction, the initial velocity distribution when the electric potential has been specified for all time. We then solve for an initial velocity distribution which yields an electric potential which is nonoscillatory in character and damps as a Gaussian distribution in time; the initial velocity distribution is proved to be an entire function in velocity space. Since this result is contrary to that of Landau, we re-examine his method of determining the electric potential.
Stability of Plasmas against Electrostatic Perturbations
Authors: Fowler T. K.
Published: December 2004

With the notation (∂f/∂t) + Vf = 0 for the linearized self-consistent field (Vlasov) equation governing ``collisionless'' plasmas, it it shown that, if only the Coulomb force between particles is taken into account, a sufficient condition for stability of an equilibrium distribution f0(x, v) against small perturbations f is that the linear operator V, a function of f0, be anti-Hermitian in some representation. Using this symmetry requirement, a class of stable functions is found, essentially by inspection, which includes spatially confined distributions which might represent a plasma held together by gravitational forces. Also, some qualitative limits on the nature of unstable perturbations in thermonuclear ``mirror'' machines are determined.
Investigation of Spinning Detonation and Detonation Stability
Authors: Duff Russell E.
Published: December 2004

The stability of a detonation wave and the nature of a spinning detonation have been investigated by observing the patterns inscribed by the wave in soot coatings on films located on the circumference of the detonation tube and on the end plate. The detonation instability reported by others persists to an initial pressure of over 2 atm and to wave velocities at least 75% greater than the equilibrium value. The wave front of a simple spinning detonation contains a complex Mach interaction with wave inclinations as high as 37° to the tube diameter. The acoustic theory of spinning detonation does describe high-order spin if it is assumed that two or more modes of vibration coexist.
Cluster Integral Theory of Distribution Functions of Spatially Nonuniform Systems
Authors: Hanks Russell V.
Published: December 2004

The theory of the pair distribution function of quantum and classical systems developed by Fujita, Isihara, and Montroll is extended to apply to spatially nonuniform systems. Cluster integral expansions of the singlet and pair distribution functions are developed for both one- and two-component systems, and are used to derive general expressions for these functions of noninteracting Fermi-Dirac and Bose-Einstein gases. The pair distribution function of a low-density, high-temperature plasma in a homogeneous external magnetic field is also considered and it is shown, under certain assumptions, that the Debye screening length is unaffected by the field.
Experiments on Heat Transport by Convection in Presence of a Magnetic Field
Authors: Nakagawa Yoshinari , Goroff Iza R.
Published: December 2004

The effect of an impressed magnetic field on heat transport by convection has been examined with a layer of mercury bounded between two constant temperature surfaces and subject to a uniform vertical magnetic field. Experiments were performed with the strength of magnetic field varying between 1195 and 1820 gauss. In agreement with the theoretical predictions by Nakagawa, the results show that the convective heat transport is characterized by a linear function of the applied temperature difference in the neighborhood of the marginal state of stability, and the coefficient of proportionality, the Nusselt number, depends on the strength of the impressed magnetic field.
Convective Instability Induced by Gravity in a Plasma with a Frozen-In Magnetic Field
Authors: Newcomb William A.
Published: December 2004

The convective instability induced by gravity in a compressible fluid layer is investigated in the special case of a plasma with a frozen-in magnetic field B. The necessary and sufficient condition for stability, which is here derived from the hydromagnetic energy principle, is that the density gradient should exceed a certain critical value that is independent of B. Thus the rigidity given to the plasma by the frozen-in field does not suffice to remove the instability but only to slow it down. The growth rates of the unstable displacements are calculated by means of a normal mode analysis and are shown to be inversely proportional to B when B is sufficiently large.
Superfast Pinch Studies
Authors: Heflinger Lee O. , Leonard Stanley L.
Published: December 2004

An apparatus designed to accelerate protons of a hydrogen plasma to energies of 1 kev or more by means of the radially converging magnetic piston of a longitudinal pinch has been constructed. A capacitor charged to voltages of up to 350 kv is discharged through the plasma, producing currents of up to 75 ka. The ringing frequency is 18 Mc, so that the rate of current rise is about 0.8 × 1013 amp/sec. Radially converging luminous fronts with maximum velocities in excess of 50 cm/μsec are observed and are interpreted as shock waves driven by a magnetic piston. Magnetic probe measurements and measurements of the electric field at the wall of the discharge tube show that much of the magnetic flux introduced during the first half-cycle is trapped in the hot plasma. The effects of varying such parameters as the total current, the initial pressure of gas, the type of gas, and the frequency of the discharge have been investigated. The experimental results are interpreted in terms of the classical Rosenbluth-Garwin theory of the pinch, which seems to correlate well with the observations.
Hugoniot Curve Determined by Shock Wave Detachment from an Infinite Wedge
Authors: Allen William A. , Rogers James W.
Published: December 2004

A method is presented for the determination of the Hugoniot curve of an arbitrary inviscid compressible fluid flowing at supersonic speed past an infinite wedge. A shock wave is attached to the apex of the wedge provided the wedge angle is less than a certain critical value. The shock wave detaches from the wedge if the wedge angle becomes greater than this critical value. If the Hugoniot curve of the fluid is known, the critical wedge angle can be calculated for a given initial fluid flow velocity. The critical angle also can be determined by an experimental method. This paper treats the theoretical problem of utilizing the discrepancy between theoretical predictions and experimental results to obtain an improved Hugoniot curve of the fluid. A perturbation method is applied to the case of solid copper for which both theoretical and experimental information exists. The actual experimental Hugoniot curve for copper does not differ sufficiently from its theoretical value to yield a fair test of the method; therefore, synthetic experimental data are used to solve a typical numerical example. In the example treated, a 10% discrepancy between theory and experiment was reduced to about 1% by one application of perturbation theory.
Viscosity of Dissociated Gases from Shock-Tube Heat-Transfer Measurements
Authors: Hartunian R. A. , Marrone P. V.
Published: December 2004

Measurements of the heat transfer from dissociated oxygen to the sidewall of a shock tube have been made over a wide range of operating conditions using the methods of thin-film thermometry. Numerical solutions of the equilibrium shock-tube wall boundary layer equations for several values of the Lewis number have been obtained. The results show the heat transfer to be very weakly dependent upon the Lewis number. This fact indicates the shock-tube wall boundary layer to be a source for experimental determinations of the viscosity coefficient of dissociated gases. Experimental data obtained in the equilibrium boundary layer regime agree with the theory at the low temperatures, and rise above the theoretical curves at the higher temperatures. This difference between theory and experiment is attributed to the uncertainty in the calculated viscosity coefficient used in the theory. The experiments were then used to determine new values for the viscosity coefficient of high temperature, dissociated oxygen. These values are considerably higher than those predicted theoretically using a Lennard-Jones potential or Sutherland's formula.
Transverse Wave Motion on a Thin Capillary Jet of a Viscoelastic Liquid
Authors: Goren S. L. , Gavis J.
Published: December 2004

The equation for transverse wave propagation on a thin capillary jet of a viscoelastic fluid in which a spatially varying tensile stress is known to exist is developed. A method of solution is developed for the special case of greatest interest, T0/ρ u12 ≪1, where ρ is the fluid density, and u1 and T0 the average ejection velocity and tensile stress at the nozzle. Although this will allow solution for any form of T variation the solutions will not, in general, be obtainable in analytic form but may be obtained by use of an analog computer, for example. A form in which T decays exponentially to a constant value is selected for illustration of an analytic solution, and the features of the resulting wave pattern are discussed.
Classical Cluster Integral Theory of Fluids in External Fields
Authors: Hanks Russell V.
Published: December 2004

Cluster integral expansions of the classical grand ensemble partition function, and singlet and pair distribution functions of fluids in external fields are discussed. Certain topological properties of terms occurring in the pair distribution function are examined and used to derive an exact integral equation for a subset of these terms. Approximations which form the activity-dependent analogs of the ``chain'' and ``series-parallel'' approximations are obtained from this equation and discussed. The thermodynamic properties of a classical single-component electron gas in a homogeneous electric field are also calculated.
Electromagnetic Radiation in an Atmosphere of Arbitrary Electric Conductivity
Authors: Reiche F. , Ludloff H. F.
Published: December 2004

The interaction of electromagnetic waves with an atmosphere of arbitrary electric conductivity σ has been investigated, whereby σ has been varied all the way from 0 to ∞. It is essential that the displacement current be taken into account. The generation of different kinds of hydromagnetic waves has been analyzed, and their phase velocity, polarization, and damping have been derived as functions of two dimensionless parameters. Also, the relations between the amplitudes of the electromagnetic and fluid vibrations have been discussed. In the two limiting cases (σ = 0 and ∞), the general results coincide with the well-known formulas for a perfectly conducting gas and for a dielectric.
Morse Potential Parameters for O–O, N–N, and N–O Interactions
Authors: Konowalow Daniel D. , Hirschfelder Joseph O.
Published: December 2004

Morse potential parameters are determined for the atom-atom interactions corresponding to the following states having potential minima: the X 3Σg−, 1Δg, 1Σg+, 3Δu,  A 3Σu+, 1Σu−, and B 3Σu− states of O–O (or molecular oxygen); the X 1Σg+, A 3Σu+, B 3Πg, a 1Πg, and C 3Πu states of N–N (or molecular nitrogen); and the X 2Π12, X 2Π3/2, B 2Π,C 2Π,D 2Σ+, B′ 2Δ, E 2Σ+, and A 2Σ+ states of N–O (or nitric oxide). For the nitric oxide excited A, D, and E 2Σ+ states, a unique assignment of dissociation products and unique energies of dissociation were obtained by supposing that these three states have the same shape for their potential energy curves. Previously Barrow and Miescher had made this assumption only for the A and D 2Σ+ states and they obtained two possible interpretations. Our analysis suggests the possibility of an unobserved 2Σ+ excited state of NO having a potential minimum 2454 cm−1 above the minimum for the D 2Σ+ state. This new state should dissociate into a ground state nitrogen atom and a (2s) 2(2p) 3(3p) 3P oxygen atom.
Diffusion and Thermal Diffusion in Ne–CO2
Authors: Weissman Stanley , Saxena S. C. , Mason E. A.
Published: December 2004

Values of the thermal diffusion factor αT and the ordinary diffusion coefficient D for Ne–CO2 mixtures have been measured over a temperature range of about −78° to 350°C by using the radioactive tracer C14O2. The thermal diffusion factor exhibits an unusual negative temperature dependence similar to that for Ar–CO2 mixtures. The data for Ne–CO2 are in good agreement with relations between measurable quantities, derived from the Chapman-Enskog theory, which are independent of the choice of force law. The experimental values have been compared with values calculated from the theory using the Lennard-Jones (12–6) potential. The agreement is good for D but very poor for αT. A corresponding states treatment based on the general form of the relations of the Chapman-Enskog theory has been used to correlate the thermal diffusion factor of Ne–CO2 with those of He–CO2 and Ar–CO2 mixtures. Therefore it appears as if the discrepancy between the theoretical values and the observed values is due primarily to the force model.
Mean-Free-Path Definition in the Mott-Smith Shock Wave Solution
Authors: Ziering S. , Ek F.
Published: December 2004

The bimodal analysis of Mott-Smith yields a reciprocal shock thickness, reduced by a mean free path ahead of the shock, that tends to zero for various intermolecular laws of force with increasing shock strength, yet remains finite for rigid-sphere molecules. It is shown that the introduction of a center of shock mean free path, self-consistent within the bimodal solution, results in finite reciprocal thicknesses for such diverse laws of interaction as inverse fifth and rigid-sphere molecules. When reduced by a center of shock mean free path, the reciprocal thickness is not too sensitive to the particular law of molecular interaction.
Theory of Electron Driven Shock Waves
Authors: Fowler R. G. , Fried B. D.
Published: December 2004

Previous calculations of the time required for ion heating in the discharge or driver section of an electrical shock tube yielded values much greater than that in which formation and acceleration of the first luminous front is observed to occur. The model of an electron driven shock presented here shows that the relation between shock velocity V and electron temperature Te, which has been established experimentally over a wide range of parameters, remains valid even though the conventional picture of a shock driven by hot ions must be abandoned. Thermal expansion of the hot electron gas accelerates the cold ions, resulting in a shock front or moving electrostatic double layer. Assuming conditions behind the shock to be coupled to those in the discharge region through a simple rarefaction wave, it is found that MV2/kTe is a universal function of W/MV2, where W is the effective ionization potential. This is shown to be in excellent agreement with a wide variety of experimental data.
Internal Waves in the Ocean
Authors: Eckart Carl
Published: December 2004

Salinity, temperature, and pressure gradients all cause the density of sea water to vary with depth in the ocean, and the density gradient affects the motion of the waters. A quantity N, having the units radians per second, can be defined using the density gradient, the velocity of sound, and the acceleration of gravity.

The simplest motions have the form of horizontally progressive waves of frequency ω, wave number κ, and velocity V. If h is the amplitude of the vertical displacement of the water and z the vertical coordinate, then V2(d2h/dz2) + [N2(z) − ω2]h = 0; this equation is formally identical with Schrödinger's wave equation. The stream function of these waves is φ = Vh(z) sin (κx − ωt), and the variable part of the pressure is − ρ dφ/dz, while the vorticity is R = −N2φ/V2. The wave may be described as a lattice of vortices moving with velocity V. In the ocean N(z) ordinarily has one or two maxima called thermoclines. The analogy with the quantum-mechanical problems of one and two potential minima is exploited to obtain semiquantitative solutions for the internal waves associated to thermoclines.
Dual Role of Viscosity in the Instability of Revolving Fluids of Variable Density
Authors: Yih Chia-Shun
Published: December 2004

The stability of a viscous fluid between rotating cylinders and with a radial temperature gradient against the formation of axisymmetric disturbances (Taylor vortices) is considered, and it has been found that viscosity has a dual role. If the circulation increases radially outward (so that the flow would be stable in the absence of density variation) but the density decreases with the radial distance, the situation can arise that viscosity actually has a destabilizing effect. In the opposite circumstance, thermal diffusivity is always destabilizing. Detailed results for small spacing of the cylinders and sufficient conditions for stability of a revolving fluid of variable density or entropy also are given.
Hydromagnetic Stability of a Toroidal Gas Discharge
Authors: Lüst R. , Suydam B. R. , Richtmyer R. D. , Rotenberg A. , Levy D.
Published: December 2004

The stability of a toroidal gas discharge is examined by using an energy principle. In the equilibrium configuration the plasma is assumed to have constant pressure and density. It is shown that the toroidal pinch can be stabilized under conditions which in most cases can be inferred, at least approximately, from knowledge of stability conditions for a cylindrical pinch.
End-Losses from Mirror Machines
Authors: Bing George F. , Roberts John E.
Published: December 2004

Theoretical calculations are described, based on the Fokker-Planck equation, of the loss of plasmas from the ends of simple magnetic mirror machines. The plasma losses are described in terms of the evolution in time of distribution functions. The effects on the loss rate that arise from varying the mirror ratio of the machines and from varying the shape of the initial distribution function of the plasma are discussed.
Statistical Theory of the Dielectric Constant of an Imperfect Gas
Authors: Kaufman Allan N. , Watson Kenneth M.
Published: December 2004

By means of the linked-diagram expansion of the grand partition function of a molecular gas in an electrostatic field, an expression for the polarization P(R) of the gas is obtained. Spatial variation of the external electric field E0(R) requires an explicit treatment of long-range cooperative interactions between ``clusters'' of molecules. For fields that vary appreciably over microscopic dimensions, an integral relation is found relating the polarization P(R) to the electric field E(R). For fields varying negligibly over microscopic regions, an expression for the dielectric constant K of the gas is obtained: (K − 1)/(K + 2) = (4/3) π Σ∞m=1 nmαm(θ). This generalization of the Clausius-Mossotti formula involves the density n and the temperature-dependent polarizabilities of m-molecule linked clusters: α1(θ) is the effective polarizability of a single (possibly polar) molecule; α2(θ) is the diagonal element of the scalar tensor α2(θ) = ∫ d3R exp [−βφ(θ, R)][½α2(θ, R) − α1(θ)]. In this expression α2(θ, R) is the effective polarizability tensor of two molecules with fixed positions of their centers of mass; φ is the free energy of the two-molecule system, relative to infinite separation.
Estimated Collision Integrals for the Exponential Attractive Potential
Authors: Brokaw Richard S.
Published: December 2004

Collision integrals for the exponential attractive potential φ(r) = −A exp(−r/ρ) have been estimated from the known integrals for the inverse power attractive potentials φ(r) = −ar−n. The exponential attractive potential should be suitable for interactions between atoms or free radicals corresponding to bound molecular states, provided the temperature is not too high. Integrals for calculating the first Chapman-Enskog approximation to the coefficients of viscosity, thermal conductivity, and diffusion have been estimated. The auxiliary functions A*, B*, and C*, which are required to calculate the coefficients of viscosity, thermal conductivity, and thermal diffusion in gas mixtures, are also tabulated. There is no simple way of assessing the accuracy of these estimates; however, when the same method is applied to the exponential repulsive potential, the estimated integrals agree with rigorously computed values to within 5% or better.
Shock Wave Phenomena in Coaxial Plasma Guns
Authors: Chang C. T.
Published: December 2004

In a plasma gun (or a magnetically driven shock tube) shocks are usually obscured by a luminous front. Using a reflection technique and a pressure probe, the existence of a shock wave is confirmed experimentally. For weak shocks the luminous front lags definitely behind the shock front. For strong shocks there is an indication that the two fronts might coincide. The reflection technique also indicates the presence of a possible relaxation process. Since the amount of energy loss to the wall is not certain at present, no attempt is made to inquire further in the detail of the process. A simple analytical model is formulated, from which the shock speed is related to the discharge conditions. Some of the analytical results are compared with those obtained experimentally.
Diffusion of Plasma Ions across a Magnetic Field
Authors: Taylor J. B.
Published: December 2004

Earlier work on the application of the correlation function of the electric field in a plasma is extended to the problem of diffusion of ions across a magnetic field. It is shown that the flux can be considered in three parts; one depends on the electric field correlation function and the others on the dynamic friction, which is related to the correlation function by Nyquist's theorem. When the ion and electron temperatures are unequal the present result differs from that obtained by a Chapman-Enskog type analysis of the transport equation and the interpretation of this difference is discussed. Some consequences of the diffusion formula, as it concerns impurities, are noted.
Kirchhoff's Radiation Law for Plasmas with Non-Maxwellian Distributions
Authors: Bekefi G. , Hirshfield Jay L. , Brown Sanborn C.
Published: December 2004

Calculations are given for the radiation temperature in terms of the average electron energy, to be used for interpreting microwave radiation measurements from plasmas with non-Maxwellian distributions of electron velocities.
Cyclotron Radiation from a Hot Plasma
Authors: Hirshfield Jay L. , Baldwin D. E. , Brown Sanborn C.
Published: December 2004

Calculations of the incoherent cyclotron radiation from a hot plasma, based upon the single-particle model of Trubnikov and Bazhanova are presented. It is shown that the emission at frequencies higher than the blackbody cutoff frequency is not negligible under certain conditions, especially since it is relatively unaffected by proposed reflectors. An approximate absorption coefficient, which is inferred from the calculations, is used to obtain the real part of the refractive index from the Kramers-Kronig transform for comparison with the results of Drummond and Rosenbluth.
Critical Length Determination for Convective Instabilities in Weakly Inhomogeneous Plasmas
Authors: Aamodt R. E. , Book D. L.
Published: December 2004

A convergent perturbation expansion procedure for determining the reflection coefficient for unstable convective modes in a plasma with small changes in the density is derived. If the total variation of the local wave vector is small, the lowest-order reflection coefficient can be used to determine the critical length of the system. The technique is used to determine the critical length of mirror machines which are subject to the convective loss-cone instability. Even for small rapid or large gentle changes in the local wave vector, critical lengths less than ten e-folding distances can be realized.
Plasma Column End Effects
Authors: Rynn N.
Published: December 2004

The end effects, or sheaths, of the plasma column of the Q-1 device are analyzed. The analysis utilizes an adaptation of the methods that have been used by Auer and McIntyre to predict the potential distributions in thermionic converters. Poisson's equation is solved under the assumptions of no collisions, no trapping, and a Maxwellian distribution of particles at the emitting boundaries and in the plasma. The model used requires the presence of a potential well in front of each plate. Although simpler than the actual situation with collisions and trapping, the model nevertheless seems to predict, qualitatively, the observed asymmetries in the volt-ampere characteristics, the observed density variations with current flow, and other observed variations with operating conditions. The analysis also indicates a possible explanation for certain of the observed instabilities.
Direct Initiation of Cylindrical Gaseous Detonations
Authors: Lee John H. , Lee Benedict H. K. , Knystautas Romas
Published: December 2004

Experimental results on the variation of the critical energy for direct initiation of cylindrical detonation waves with mixture composition and initial pressure are reported for acetylene-oxygen mixtures.
Ion Acoustic Waves in Mercury-Vapor Discharges
Authors: Tanaca Hiroshi , Hagi Mikiko
Published: December 2004

The external excitation of the ion acoustic waves is examined. The propagation and reflection of the waves and the standing waves between the probe and anode are observed.
Tracer Study of Pipe Flow Behavior to within Two Microns of the Wall
Authors: Elrick Richard M. , Emrich Raymond J.
Published: December 2004

A high precision, high spatial resolution tracer technique was used to study low noise, steady air flow in a 1½ by ½ in. rectangular pipe with particular attention to the flow several microns from the pipe floor. The flows investigated had velocities which correspond to pipe Reynolds numbers of 16–4300. Experimental velocity profiles for the flows extrapolate to the no-slip condition at the floor. However, close attention to the measurements of the flow 2–10μ from the floor reveals a preponderance of data points lying on the high velocity side of the profile. The data are believed to mirror a real deviation of the flow velocity from the theoretical profile in the region of the floor and greater than 2 μ from it. The cigarette smoke tracers could be located within a micron from the floor, and the measuring error in determining the velocity varied from 0.02 mm/sec in flow of 5 mm/sec and less, to 0.15 mm/sec in a flow of 50 mm/sec.
Vlasov Equation Study of Plasma Motion across Magnetic Fields
Authors: Sestero A.
Published: December 2004

A description is given, in terms of distribution functions, of the phenomenon of a plasma crossing magnetic field lines by virtue of beam polarization. The task requires solving two steady-state, nonlinear Vlasov equations for ions and electrons, coupled with Maxwell's equations. Studying the plasma in a neighborhood of the moving beam surface, a distinction is made between two asymptotic regions of plasma in equilibrium, and an intermediate, transition region. In the so-called charge-neutral approximation, actual transition profiles are computed in closed form, in terms of quadratures. Some general conclusions are drawn concerning the minimum width of the transition region and the maximum change in the macroscopic velocity that the plasma can support over such minimum distance.
High-Temperature Plasmas Produced by Laser Beam Irradiation of Single Solid Particles
Authors: Haught Alan F. , Polk Donald H.
Published: December 2004

The focused 20-MW giant pulse beam of a Q-spoiled ruby laser has been used to form a high-temperature, high-density plasma from a single 10- to 20-μ-diam solid particle of lithium hydride suspended by a set of ac electric fields in a vacuum environment. Charge collection measurements show that total ionization of the 1015 atoms in the lithium hydride particle is achieved in the plasma produced. Time-of-flight studies of the expanding plasma yield plasma energies of more than 100 eV. Measurements have been carried out which show that the mass and energy density of the expanding plasma are isotropically distributed in space. The results obtained are in good agreement with a simple model of the plasma formation and expansion. Further studies of these laser-irradiated, single particle plasmas are in progress and include measurements of the lifetime of the plasma in magnetic confinement fields.
Kinetic Theory of a Spherical Electrostatic Probe in a Stationary Plasma
Authors: Chou Y. S. , Talbot L. , Willis D. R.
Published: December 2004

The spherical electrostatic probe in a weakly-ionized gas is analyzed on the basis of kinetic theory using a Krook-type model for the collision integral. The charged particle motions are analyzed in energy-angular momentum phase space, and formal integral solutions for the distribution functions are obtained. Moment equations based on the Less method are derived, taking into account curvature of the particle paths, and sample solutions of these equations are presented. The results obtained agree well with the numerical analysis of Laframboise, in the collisionless limit. It is found that the effect of charged-neutral particle collisions is to extend the probe sheath farther into the plasma and reduce the electron and ion currents, as well as the departures from neutrality within the sheath. Fair agreement is obtained with a moment method based on straight-line trajectories for the charged particles. The continuum limit is not included in the computations.
Collisionless Theory of a Plasma Sheath near an Electrode
Authors: Hu Pung Nien , Ziering Sigi
Published: December 2004

The existing collisionless theory of a plasma sheath near an infinite planar electrode is examined in detail. Ranges of validity as well as difficulties with the existing sheath models are investigated. The assumption of monoenergetic particle distributions, as used for instance in ``Bohm's sheath criterion,'' restricts the usual analysis. To remove this difficulty Maxwellian particle distribution functions are assumed. In addition, microscopic boundary conditions are assumed to incorporate the respective electrode and plasma parameters. A new sheath model is then developed without imposing the usual sheath criterion for the conditions specified at the sheath edge. Explicit results for the current-voltage relation and for the sheath thickness are obtained for the improved sheath model proposed in this study. Other important physical quantities are expressed in terms of the electrostatic potential, which can be calculated by a quadrature subject to the physical parameters to be specified. The general solution reduces to a simple analytic form for the special case where the temperature of the electrons, ions, and the electrode are identical.
Test Time and Particle Paths in Low-Pressure Shock Tubes
Authors: Fox J. N. , McLaren T. I. , Hobson R. M.
Published: December 2004

Measurements are reported on shocked-gas-flow duration in small-diameter shock tubes at low initial pressures. They are correlated with expressions derived from Mirels' theory for such flows, and substantial agreement is obtained, with closer correlation in the smaller-diameter shock tube. An expression is developed from Mirels' theory to relate particle and laboratory time coordinates, and a direct experimental measurement of particle paths in the flow is described. The time transformation introduces a significant correction to the ρ2/ρ1 linear transformation more generally used, and this is seen to be important in investigations of relaxation processes and rate kinetic measurements carried out in shock tubes. Some of the values of rate coefficients previously reported in the literature may well require revision in the light of this correction.
Wave Propagation near Electron Cyclotron Harmonics in Nonuniform Plasmas
Authors: Pearson Gary A.
Published: December 2004

Equations are derived that describe the excitation and propagation of longitudinal waves (Bernstein modes) in nonuniform plasmas with a uniform applied magnetic field perpendicular to the direction of wave propagation and to the gradients of the unperturbed plasma. Certain features of the microwave absorption by plasma columns have recently been explained on the basis of such modes. Comparison shows that the equations derived by most other authors are correct only when the scale of the plasma inhomogeniety is long compared to the wavelength considered; this is primarily because they ignore the ambipolar electric field and the anisotropy of the unperturbed electron velocity distribution. The inclusion of these effects does not complicate the equations.
Effect of Temperature Gradients in Thermionic Plasmas
Authors: Chen F. F.
Published: December 2004

Treatments of drift wave velocities in Cs and K plasmas up to now have neglected the radial electric field in the plasma. It is shown that this field greatly affects such measurements, but can be made negligible by reducing the cathode temperature gradient.
Kinetic Structure of a Plasma
Authors: Dawson John M. , Nakayama Toshio
Published: December 2004

The kinetics of a plasma is investigated by expanding the motion in terms of the deflection of the particles from their noninteracting orbits. It is shown that this procedure leads to the following results. At the first stage, the dressed-particle picture of Thompson and Hubbard, and of Rostoker for obtaining fluctuations in a plasma is obtained. Rostoker's principle for obtaining two-particle correlations in terms of test particle results is also obtained at this stage. At the second stage, encounters between shielded particles appear and the picture of Birmingham, Dawson, and Oberman for computing bremsstrahlung emerges. The usual Fokker-Planck equation may also be obtained at this stage. The treatment applies to the full electromagnetic field.
Stability of Sheet Pinch
Authors: Hoh F. C.
Published: December 2004

The growth rate of the sheet pinch instability is calculated in the small Larmor radius limit using the method of integration along unperturbed orbits. It is found that the instability is driven by a small group of ``resonant'' electrons which cross and drift about the neutral plane having zero velocity along the field lines. The microinstability is absolute and develops fastest for a critical perturbation wavelength, of the order of several times the thickness of the plasma sheet.
Equation of State and Derived Shock Initiation Criticality Conditions for Liquid Explosives
Authors: Enig Julius W. , Petrone Francis J.
Published: December 2004

An E,P,V equation of state based on an assumption of Walsh and Christian and experimental shock data has been derived for nitromethane and liquid TNT. From experimental temperature data along the 1 bar isobar, the temperatures, specific heats at constant volume, and ``internal pressures'' are calculated. Application of this equation of state and simple adiabatic explosion theory leads (i) to accurate predictions of the experimental explosion times for shocked homogeneous nitromethane and liquid TNT at 86 and 125 kbar, respectively, and (ii) to a predicted steady-state reaction zone width of 0.0011 cm for detonation in nitromethane that is in satisfactory agreement with the widths deduced from detonation failure and electrical conductivity experiments. In addition, the problem of the initiation of explosives by the formation of hot spots by shocks is considered. A critical hot spot size is obtained that is in satisfactory agreement with the experimental critical bubble size for propagation of detonation in nitromethane.
Transition and Turbulence in Hypersonic Wakes
Authors: Birkhoff G. , Eckerman J. , McKay W.
Published: December 2004

Schlieren photographs are shown of hypersonic wakes behind cones and smooth spheres with diameters d between ⅛ in. and ½ in. for free-stream Mach numbers M = M∞ in the range 5 < M < 20 and at pressures from 0.05 atm to atmospheric. An analysis is made of the laminar wake core, of the distance xtr to transition, and of the wake diameter dw as a function of the distance x behind the missile. For slender cones, the formula ξtr = xtr/d = K(α)M1.3(Re × 10−4)−0.5 fits the data well over the range specified, 2α being the cone vertex angle. Correlations with local Mach and Reynolds numbers are also given. For all shapes, rw = Ax1/3 approximately for x > 50d. The effective ``turbulence Reynolds number,'' defined as Ret = Δ(δw3)/CDΔξ, where δw = dw/d and ξ = x/d, is found to be about unity for all turbulent hypersonic wakes observed. However, the photographic evidence does not support the hypothesis of universal similarity in turbulent hypersonic wakes. Qualitative discussions are given of observed bifilar and ablation wakes.
Electrostatic Damping on the Motion of a Charged Particle in a Plasma
Authors: Tam Christopher K. W.
Published: December 2004

The electrohydrodynamic phenomena associated with the motion of a charged particle in a plasma are investigated. It is shown that the type of disturbance produced in the plasma depends significantly on the speed of the particle, i.e., whether it is subsonic, transonic, or supersonic. In the subsonic case, the electrohydrodynamic drag experienced by the particle is caused by an unsymmetric wake formed by the screening electrons. In the supersonic case, electron screening is confined to the Mach cone. Ahead of the Mach cone, the plasma behaves as if it were an incompressible fluid. The electrohydrodynamic drag in this case has a logarithmic nature.
Propagation in Plasmas along the Magnetic Field I. Circular Polarization
Authors: Bachynski M. P. , Gibbs B. W.
Published: December 2004

A carefully designed experiment has been conducted in which the propagation of circularly polarized plane waves through a helium plasma along the direction of a static magnetic field has been quantitatively investigated. Determination of electron densities from independent measurements using the left-hand and right-hand circularly polarized wave modes show excellent agreement with each other and with theory over all ranges of magnetic fields. Attenuation measurements also agree well with theory, except when the cyclotron frequency exceeds the radio frequency for the right-hand mode, the dependence of the collisional effects on electron velocity should be included in the analysis. The regions of the parameters where boundary effects are important can also be ascertained from the measurements.
Bounds on Fluctuations in a Homogeneous Plasma
Authors: Chen Robert L. W.
Published: December 2004

A homogeneous collisionless plasma is considered whose velocity distribution is initially unstable. Making use of the constraints inherent in the Maxwell-Vlasov equations—along the lines of C. S. Gardner and of T. K. Fowler—it is shown that the nonlinear fluctuations grown out of the instability are subject to the following bounds: (Δρ)2¯(ρ̄)2⪅0.4εGεtotal−εG,     ∑ k≥k0E2(k)8π⪅εG1+1.2(hk0)2,where ρ and Δρ are density and its fluctuation, εG the available energy in the plasma in the sense of Gardner's, E(k) the Fourier component of the electrostatic oscillations, and h the Debye length. The variation of the density function f(r, v) is considered from an originally homogeneous and Maxwellian density fo(v) under the constraint of Liouville invariance. The total kinetic energy is then minimized under the further constraint that a given level of density perturbation Δρ is maintained. Solutions to this variational problem yield minimum energies associated with density fluctuations and lead to results which, in their approximate forms, are given in the above inequalities.
Electron Probe Current in a Magnetized Plasma
Authors: Sugawara Minoru
Published: December 2004

An experimental study is presented of the electron saturation current arriving at a plane probe situated in a magnetized plasma. Using a simplified Bohm's model, the equations of electron probe current in a magnetized plasma are derived and compared with the experimental results. The equations show that the electron temperature is determined for a sufficiently large range of negative probe potentials and an apparent space potential is lowered by the presence of the magnetic field.
Confined and Nonconfirmed Interchange Instabilities Obtained from Nonlinear Computer Models
Authors: Byers J. A.
Published: December 2004

Initial results are presented for a nonlinear computer model capable of following the nonlinear motion of low beta interchange modes. Details of the motion are shown for two widely different interchange modes.
Plasma Heating in Stochastic Electric Fields
Authors: Puri S.
Published: December 2004

Using a ``test particle'' approach, it is found that an electron plasma situated in a random electric field extracts energy from the field. An initially Maxwellian distribution stays Maxwellian, and the heating rate has been computed as a function of the electric field.
Wall Region in Turbulent Shear Flow of Non-Newtonian Fluids
Authors: Tennekes H.
Published: December 2004

A revision of mixing-length theory for wall-bounded turbulent shear flows is proposed. An analysis of the energy balance of medium-sized eddies (those that scale with the distance from the wall) suggests that the slope of the logarithmic velocity profile should be proportional to the square root of the Reynolds stress at the location where most of the turbulent energy is produced. Application of this prediction to turbulent flow of power-law fluids indicates that the slope of the velocity profile decreases with decreasing flow-behavior index, in excellent agreement with experimental data. Visco-elasticity may change the thickness of the viscous sublayer, but not the slope of the velocity profile.
Quasi-Linear Theory of Plasma Waves
Authors: Bernstein Ira B. , Engelmann Folker
Published: December 2004

The quasi-linear theory of plasma waves in a collision-free plasma is formulated in such a way that corrections to the adiabatic assumption and those due to nonlinear effects can be readily estimated in terms of the properties of the initial spatially homogeneous part of the distribution function. Decaying Fourier components of the electric field are treated in a uniform way with unstable Fourier components. It is shown that the case of a three-dimensional plasma is qualitatively different from a one-dimensional plasma, the former leading to a decay to zero of the fluctuating electric field.
Stability of a Circular Toroidal Plasma under Average Magnetic Well Conditions
Authors: Ware A. A. , Haas F. A.
Published: December 2004

The simplest closed-line-of-force plasma containment system whose average magnetic curvature is stabilizing against pressure-driven instabilities for zero β is the circular torus with small rotational transform. The energy principle is applied to the simplest case, where the rotational transform is produced by a plasma current and where r/R, Bθ/B, and (β)1/2 are taken as small quantities of the same order so that an expansion procedure can be adopted. Final minimization of the energy integral leads to three simultaneous second-order differential equations, which are the toroidal equivalent of the well-known Euler equation for the linear pinch discharge. In addition to the necessary stability criterion which follows from these Euler equations, a sufficient condition shows that a β at least as high as r2/4R02 will be stable against both pressure-driven and j∥-driven instabilities.
Microinstability and Shear Stabilization of a Low-β, Rotating, Resistive Plasma
Authors: Chen Francis F.
Published: December 2004

A magnetoplasma in a radial electric field Er suffers from a gravitational instability driven by the centrifugal force. By using only fluid equations, the theory of Rosenbluth, Krall, and Rostoker was extended to finite k∥ and finite resistivity. The theory of resistive drift modes in cylindrical geometry is included as the limit Er → 0. The shear stabilization was computed, and it was found that the drift modes are not localized by shear unless ion Landau damping is taken into account. A stabilization criterion was obtained which is much more severe than those found previously and which is almost impossible to fulfill experimentally. However, it is the modes with short radial wavelength which are most difficult to stabilize, and these may not be harmful to plasma confinement. The role of the Coriolis force and the importance of these instabilities to experiments in cesium plasmas, stellarators, rotating plasmas, and beam-plasma discharges are also pointed out. This theory is particularly germane to cesium plasmas, in which it is shown that Er cannot be ignored.