bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Necessity of the Energy Principle of Kruskal and Oberman for Stability
Authors: Kulsrud Russell
Published: December 2004

Kruskal and Oberman have developed an energy principle for stability of hydromagnetic systems in which it is assumed that the particles move adiabatically in the magnetic field. They established the sufficiency of the energy principle but left the necessity an open question. Newcomb has established the necessity of a slightly different principle which takes into account charge neutrality. He shows that the stability equations may be written in a self-adjoint form. A simpler proof is now given which is based on the conservation of energy so that it is not necessary to establish the self-adjointness by an explicit calculation. The proof is the direct analog of that given by Bernstein, Frieman, Kruskal, and Kulsrud on an energy principle for stability from the fluid equations. In both the proof first given by Newcomb, and the present one, the assumption is made that the geometry is not toroidal, but that the particles are trapped in a magnetic field as far as their longitudinal motion is concerned.
Kinetic Equation for a Classical Plasma
Authors: Willis Charles R.
Published: December 2004

The behavior of a fully ionized plasma of nonrelativistic electrons (neutralized by a background of positive charge) which is slightly disturbed from equilibrium is treated by a method that exploits the electron-electron correlations that are present in equilibrium to provide both a short- as well as a long-distance cutoff, and to provide a damping mechanism that dominates the usual Landau damping at small k. To obtain a closed set of equations for the deviations from equilibrium of the one- and two-particle distribution functions a product assumption is made for the deviation from equilibrium of the three-particle distribution function. It is shown that the nonlinear correlations present in the rigorous pair distribution function are sufficient to derive the linearized Fokker-Planck equation. The electron-electron correlations in equilibrium are shown to give rise to a damping of plasma oscillations at long wavelength that dominates the Landau damping which is also present.
Wave Motions of Small Amplitude in a Fully Ionized Plasma under Applied Magnetic Field
Authors: Pai S. I.
Published: December 2004

Wave motions of infinitesimal amplitude in a fully ionized plasma, consisting of singly charged ions and electrons, have been investigated by a two-fluid theory under uniform external magnetic field. The interaction of the basic modes of wave due to external magnetic field has been discussed. If the magnetic field is in the direction of propagation of the waves, two basic transverse waves interact, if the magnetic field is perpendicular to the direction of propagation of waves, two basic longitudinal waves and one basic transverse wave will interact, and if the direction of the magnetic field is at an acute angle with the direction of the propagation, all four basic waves will interact. The dependences of the interacted waves on ion and electron plasma frequencies and ion and electron cyclotron frequencies are analyzed in detail. The effect of finite electrical conductivity on these waves is briefly discussed.
Similarity Solution for a Cylindrical Shock-Magnetic Field Interaction
Authors: Greenspan H. P.
Published: December 2004

A similarity solution is developed describing the propagation of a strong cylindrical shock in an applied azimuthal magnetic field. The stationary gas is nonconductive and the shocked gas is taken to have a finite electrical conductivity. The total axial current is maintained constant by external means. Upon comparison of flows for which the total gas energy is the same, it is found that the interaction reduces the shock velocity by only a few percent although the pressure distributions differ markedly.
Gas Thermal-Conductivity Studies at High Temperature. Line-Source Technique and Results in N2, CO2, and N2-CO2 Mixtures
Authors: Westenberg A. A. , DeHaas N.
Published: December 2004

A new technique for measuring the thermal conductivity of gases over a fairly wide temperature range is described. The method makes use of precise measurements of the thermal-wake widths downstream of a steady line source of heat in a uniform laminar flow of the test gas. The theory and practice of the method are discussed, and it is shown to have advantages over conventional methods in that it is an absolute technique requiring measurement only of distance, gas velocity, and relative temperature differences. The technique has been tested on N2 and CO2 over the range 300–1100°K with results that agree well with previously reported work done by conventional means. Measurements on N2-CO2 mixtures covering the entire composition range and in the same temperature interval are also presented. These are compared with kinetic-theory calculations using the best available input data. The results are then used to predict the thermal conductivity of N2, CO2, and N2-CO2 mixtures up to 2000°K with what is believed to be the most reliability which is presently possible.
Application of a Moment Method to Heat Transfer in Rarefied Gases
Authors: Lavin M. L. , Haviland J. K.
Published: December 2004

A full-range moment method developed by Lees is applied to heat transfer across a large temperature difference in a rarefied gas. Two solutions are obtained: a four-moment result for hardsphere molecules and a six-moment result for Maxwellian molecules. The four-moment solution for hard spheres exhibits the same behavior as Lees' result for Maxwellian molecules. Moreover, the six-moment result differs significantly from the lower-order solution for Maxwellian molecules only in the prediction of a varying pressure.
Nonequilibrium Radiation and the Recombination Rate of Shock-Heated Nitrogen
Authors: Allen R. A. , Keck J. C. , Camm J. C.
Published: December 2004

The radiation emitted by hot nitrogen behind normal shocks is studied at an equilibrium temperature from 6000° to 6800°K and densities from 0.01 to 0.20 atm. The various radiating bands are identified by spectroscopic and photometric techniques. The radiation is found to consist of bands from the N2+(1−), N2(1+), and N2(2+) systems. The radiative relaxation of the N2(1+) system in the nonequilibrium region is studied at various densities and shock speeds and is used to determine the recombination rate constants, kRN and kRN2 for the reactions N + N + N → N2 + N and N + N + N2 → N2 + N2, respectively. kRN is found to be 1.8 × 10−32 ± 0.6 cm6/sec at 6400°K and kRN2 to be at least 13 times smaller than kRN. Comparison is made between theoretical calculations based on these rates and observations. The integral nonequilibrium radiation and the time of occurrence of peak radiation behind the shock front are also examined.
Measurement of Hall Electromagnetic Force in Air
Authors: Klein Alan F.
Published: December 2004

An experiment is reported in which an induced Hall electromagnetic force in air is measured in a shock tube. Agreement is found with theory for values of the product of the electron cyclotron frequency and the mean collision time for electrons over a gas temperature range of 3000° to 4200°K. The theory is based upon a mean collision time for electrons that is determined solely by electron-neutral particle collisions, and an Ohm's law that is valid for slightly ionized gases. The induced Hall electromagnetic force is theoretically independent of the electron concentration of the shock-heated air. The experiment thus provides a technique for determining the collision time that does not depend upon the establishment of equilibrium. Details of the time profile of the measured emf are explained qualitatively using an equivalent circuit.
Adiabatic Acceleration of Ions by Electrons
Authors: Hendel H. W. , Reboul T. T.
Published: December 2004

The velocities and angular distributions of different plasmas ejected from pulsed low-voltage (37 v) discharges have been measured. Velocities of metal plasmas greater than 106 cm/sec have been observed. Probe measurements of the initial electron temperature (≈25 ev) in the discharge and measurements of the final electron temperature (≈1 ev) in the drifting plasma are taken as evidence for an acceleration of the ions by the space charge set up by the initially more energetic electrons. The angular distribution of the ejected plasma was isotropic and the plasma velocity was inversely proportional to the square root of the ion mass, in agreement with the theoretical explanation.
Convective Plasma Instability
Authors: Kuckes Arthur F.
Published: December 2004

The current convective plasma instability theory of Kadomtsev and Nedospasov has been extended to highly ionized plasma in very strong magnetic fields. The growth of plasma density fluctuations predicted is discussed with regard to the enhanced diffusion observed in stellarator experiments.
Energy Transfer in a Normally Distributed and Isotropic Turbulent Velocity Field in Two Dimensions
Authors: Ogura Yoshimitsu
Published: December 2004

The dynamical equations which describe the behavior of isotropic turbulence in two dimensions are derived on the basis of the hypothesis that fourth-order cumulants of the velocity field are zero. The equations are then integrated numerically as an initial-value problem for an inviscid fluid. The result shows that the calculated rate of energy transfer is greater toward the larger scales than the smaller scales. The most remarkable feature revealed by the computation is that the energy-spectrum function assumes negative values during the course of time for medium-sized eddies. Truncation errors which arise from finite difference approximations in numerical integration are examined. From this result, it is concluded that the hypothesis of zero fourth-order cumulants does not always guarantee positive energy, at least, for a turbulent flow in two dimensions.
Effects of Diffusion on Interface Instability between Gases
Authors: Duff R. E. , Harlow F. H. , Hirt C. W.
Published: December 2004

Experiments are described concerning the interface instability which arises when an argon-bromine mixture falls under gravity into air or into helium. Existing theories which include viscosity effects fail to explain the observed amplitude growth rate, but it is shown that approximate inclusion of diffusion effects allows calculation of all features of early perturbation growth accurately to within experimental error.
Oscillations in a Relativistic Plasma
Authors: Imre K.
Published: December 2004

The linear oscillations in a hot plasma which is representable by the relativistic Vlasov equation with the self-consistent fields are investigated. The generalization of Bernstein's method for the relativistic case is used to obtain the formal solution of the linearized problem. Particular attention is given to the case when the system initially is in the relativistic equilibrium state. The dispersion equation is derived and studied for the case when the propagation is along the direction of the unperturbed magnetic field, considering the spatial dispersions explicitly. The asymptotic expansions are developed corresponding to the dispersion relations of the cases studied. It is found that transverse waves propagating along the unperturbed field are Landau damped if ν2 ≥ 1 − Ω2/ω2, ν and Ω being the index of refraction and the gyrofrequency, respectively. In the absence of the external field the cutoff frequency, which is found to be the same for both longitudinal and the transverse modes, is shown to be a monotonically decreasing function of the temperature.
Motion of Charged Particles in an Inhomogeneous Magnetic Field
Authors: Karlson Erik T.
Published: December 2004

By means of a crossed electric field, charged particles can be forced to move from a region where the magnetic field is comparatively weak into a region where the magnetic field is much stronger, which leads to an increase in the density and the temperature of the plasma. However, if the density is not very low, the inertia drift gives rise to space charges, which modify the electric field and thus strongly influence the motion. The motion of the particles is studied in a two-dimensional case with the influence of the space charges taken into account. The results are that the particle trajectories are considerably changed, but the reduction in the drift velocity is of the same order of magnitude as if the space charges are neglected. If the inhomogeneity in the magnetic field is strong enough, a forbidden region will arise. The shape of this region is given and the currents resulting from the particle motion are computed.
Electromagnetic-Wave Propagation in a Plasma with Nonlinear Electrical Conductivity
Authors: Epstein Melvin
Published: December 2004

A small-perturbation analysis has been carried out to determine the effect of a nonlinear electrical conductivity on the propagation of microwaves normally incident on a homogeneous, slightly ionized gas. The reflecting properties of the interface separating the ionized gas from free space have also been determined. The measure of the nonlinearity is given by the quantity γ, which is the ratio of the energy acquired by the free electrons from the field to the kinetic energy of the electrons in the absence of an applied field. The solution was obtained by performing a series expansion of the field strength in powers of γ. Terms up to order γ2 were retained. It was found that the nonlinearity can cause significant increases in both the wave number and the attenuation factor of the transmitted signal. The transmission coefficient associated with the interface may also be significantly reduced. The change in the phase shift across the interface due to the nonlinearity was found to be positive or negative, depending upon whether the signal frequency is greater or less than the plasma frequency, respectively.
Instability in Low-Pressure Plasma Diffusion Experiments
Authors: Guest Gareth , Simon Albert
Published: December 2004

We consider the stability of a weakly ionized, low-density (1010-1012) plasma in a uniform magnetic field. The plasma is in a finite conducting chamber and there is diffusion across the field lines and streaming to the conducting end walls. The stability analysis is similar to that of Kadomtsev and Nedospasov for the positive column. It is found that instability sets in above a critical field or below a critical background pressure. The driving force is the charge separation produced by the unequal streaming of ions and electrons to the end walls. The unstable mode is helical in space and rotates about the axis of symmetry. Expressions are obtained for the critical field value and for the rotational velocity. These compare favorably with the experiments of Neidigh and Weaver and those of Zharinov.
Stability of a Revolving Fluid with Variable Density in the Presence of a Circular Magnetic Field
Authors: Lai Wei
Published: December 2004

The stability of an electrically conductive and incompressible fluid between coaxial rotating cylinders in the presence of a radial density gradient, as well as a circular magnetic field, is studied. The effects of gravity and of the heat generated through viscous and magnetic dissipation is neglected. An eigenvalue problem is formulated for rotationally symmetrical disturbances. Detailed calculations are made for the case of small spacing between the two cylinders. Three dimensionless parameters, each of which contains only one of the three (momentum, thermal, and magnetic) diffusivities, are defined. Parametric equations for surfaces of marginal stability are given, and several planes cutting such surfaces are drawn for the discussions of the roles played by the diffusivities. It is found that both the momentum diffusivity and the magnetic diffusivity are capable of playing the dual role (i.e., the role of stabilization and destabilization simultaneously) in the problem.
Relation between Thermal Conductivity and Viscosity for Some Nonpolar Gases
Authors: O'Neal Cleveland , Brokaw Richard S.
Published: December 2004

The dimensionless ratio f = λM/ηCv relating the thermal conductivity, molecular weight, viscosity, and constant-volume molar heat capacity has been determined experimentally for helium, argon, nitrogen, oxygen, and hydrogen in the range 90°–290°K. The experimental method provides a direct determination of f by measurement of the subsonic temperature recovery factor. For helium, f = 2.503, and for argon, f = 2.506, in complete accord with the rigorous Chapman-Enskog kinetic theory for monatomic gases. Data on nitrogen, oxygen, hydrogen, and also carbon dioxide confirm, at least qualitatively, a recent approximate theory which relates deviations from the modified Eucken approximation to the relaxation times of internal energy states. Collision numbers for rotational relaxation derived from the experimental data are: nitrogen, 6.8; oxygen, 6.0; and carbon dioxide, 2.4. These collision numbers are very nearly independent of temperature. The results confirm the fact that the interchange of translational and rotational energy is unusually difficult for hydrogen.
Electromagnetic Acceleration of a Shock Wave in a Constant-Area Duct
Authors: Morse T. F.
Published: December 2004

When a rapid current discharge occurs in a gas between two electrodes, a current sheet forms which accelerates into the gas and produces a shock wave, much as a piston in conventional gas dynamics. Due to the high velocities which it reaches, the shock wave ionizes the gas, and a plasma is formed in the region between the current carrying contact front and the shock wave. Nonsteady electromagnetic acceleration of a one-dimensional shock wave has been studied for the case of an arbitrary but constant specific-heat ratio of the plasma. Approximate closed-form solutions for the velocity of the contact surface and shock wave have been obtained, illustrating both the weak dependence of the contact front velocity on γ, and the relation between the fluid mechanical and ``snowplow'' models of the shock acceleration. It has also been shown, for the case under consideration, that the contact surface and shock positions are initially parabolic, and finally hyperbolic functions of time, and that the pressure may be approximated by a linear function of the Lagrangian variable.
Nonequilibrium Expansions of Air with Coupled Chemical Reactions
Authors: Eschenroeder Alan Q. , Boyer Donald W. , Hall J. Gordon
Published: December 2004

Analysis and solutions of the streamtube gas dynamics involving coupled chemical rate equations are carried out. Results are presented for airflows along the surface of blunt bodies and through hypersonic nozzles. Speeds and altitudes corresponding to re-entry were selected to obtain initial conditions for the external flow calculations. Conditions appropriate to hypersonic tunnel testing were chosen for the nozzle flow calculations. Composition histories are shown for a kinetic mechanism including 6 species and 14 reactions. Gas-dynamic effects of nonequilibrium processes qualitatively resemble those reported earlier. However, the freezing process is complicated by the coupling of the nitric oxide shuffle reactions with the dissociation-recombination reactions. In many cases of hypersonic nozzle flows where the energy in nitrogen dissociation is significant, the fast shuffle reactions prevent nitrogen-atom freezing which would otherwise occur if three-body recombination were the only process operating. Nitric oxide concentrations undershoot the equilibrium values if the ratio of nitric oxide to oxygen molecule concentrations exceeds unity in the freezing region. This depletion of nitric oxide leads to nitrogen-atom freezing.
Nonlinear Oscillations of a Particle in a Long Wave in a Rotating, Viscous Fluid
Authors: Kao S.-K.
Published: December 2004

Analysis is made of the effects of a long wave of finite amplitude on the oscillation of a particle in a rotating, viscous fluid. It is shown that the zeroth-order solution of the Lagrangian equations of motion consists of the pressure wave and inertial frequencies, whereas the first-order solution gives three frequencies, namely the sum and difference of the pressure-wave and inertial frequencies, and a frequency of twice the pressure-wave frequency. The effects of the frictional force are to damp out the inertial oscillation but leave the other physically significant oscillations intact. Furthermore, it eliminates the solution which contributes to the amplification of the amplitude of particle trajectories in an inviscid fluid. A comparison of the frequencies predicted by the theory with those obtained from the flights of constant-pressure balloons is made.
Microwave Probing of Ionized-Gas Flows
Authors: Jahn Robert G.
Published: December 2004

The measurement of free-electron densities and collision frequencies in ionized-gas flows by a probing transverse microwave beam is described. Interpretation of the observed reflection and transmission coefficients and their phases is developed on the basis of an idealized plane wave-plane slab model, for which typical results are displayed. Application of the device and technique to a specific experiment—the buildup of ionization behind a strong shock in argon—is outlined. Effects of various departures of the microwave radiation patterns and flow configurations from the slab assumptions are discussed and examples evaluated.
Confinement of a Partially Ionized Gas by a Periodic Magnetic Field
Authors: Zauderer Bert
Published: December 2004

Two sets of experiments were performed to test the confinement of a partially ionized argon plasma cylinder by a coaxial 67-kc magnetic field. The 10 000°K argon plasmas were produced by a chemically driven shock tube and by an electrodeless ring discharge. Smear photographs showed that in both experiments the plasma was periodically compressed by the field at a rate equal to twice the field frequency. Magnetic probes showed that the plasma diameter was on the average 80% of the shock tube i.d. and that the skin depth of the field was equal to one-third the plasma radius. A similar ring-discharge experiment in hydrogen led to the conclusion that the speed of sound divided by the tube diameter must be very small compared to the angular field frequency to obtain a steady continuous confinement of the plasma by the field.
Theory of High-Impedance Radio-Frequency-Force Plasma Devices
Authors: Lorber H. W.
Published: December 2004

It is shown that in the absence of a magneto-static field, in the case of high frequency and high impedance, the steady force exerted by an rf field on a plasma is essentially proportional to the energy density gradient of the rf electric field. As an example, a simple rf plasma propulsion problem is solved, involving a plasma and an electrode structure, both of finite extent. The solution is consistent with experimental results which show that a finite body of plasma whose density is greater than critical is pulled in the direction of increasing electric field whereas a plasma whose density is less than critical is pushed in the direction of decreasing electric field.
Theory of an Electrostatic Probe in a Strong Magnetic Field. II
Authors: Bertotti Bruno
Published: December 2004

A probe is considered in a magnetic field so strong as to impair collective transverse drifts. Then the charges supplied to the probe come mainly from a long tube of force, whose radius is about one Larmor radius larger than the probe. Assume that there is acting a diffusion process, more efficient than ordinary drifts, which continuously exchanges particles between the inside of the tube of force and the rest of the plasma. In a previous paper we have proposed a one-dimensional model of this process, leading to an integro-differential Poisson's equation, which has now been fully investigated in the case of slow diffusion. The solution consists of a chargeless, slowly decaying potential which describes the geometrical screening effect of the probe; while in the sheath an approximate boundary-layer solution matches with the probe's potential VP. The asymptotic relation between the current collected and VP is computed. This model may be suited to the case of diffusion due to random wave fields.
Long-Wavelength Phenomena in a Plasma
Authors: Liboff Richard L.
Published: December 2004

The long-wavelength modes of excitation of a two-component plasma in a steady magnetic field are examined. Two linearized Boltzmann equations are given with collision terms which are coupled through the difference in temperatures and difference in velocities of the two gases. A formal means of classification of phenomena is described in terms of the nature of the roots about k = 0. Two types of behavior are uncovered: magnetohydrodynamics, which includes finite phase-speed phenomena near k = 0; and plasma electromagnetics, which includes infinite-phase-speed phenomena near k = 0. The dissipative effects of collisions are included. In the limit of vanishing collision frequency, roots previously obtained are recaptured. The relevance of the pertinent domains are discussed and the complex interplay between the ``fast'' and ``Alfvén'' modes of magnetohydrodynamics and the plasma-magnetic modes of the plasma electromagnetic domain is demonstrated. Equations macroscopic in appearance are derived which include the effects of the initial configuration. In the limit of large collision frequency these equations reduce to standard forms. The dispersion of the Nth-order Larmor resonance is given which includes the effect of the mass ratio.
Instability of a Plasma Column in a Longitudinal Magnetic Field
Authors: Johnson Roy R. , Jerde David A.
Published: December 2004

The stability of a positive column in a longitudinal magnetic field is investigated by linearization of the macroscopic equations of motion and continuity for ions and electrons. The treatment is more general than similar calculations by Kadomtsev and Nedospasov and Hoh, in that diffusion and magnetic field interaction terms are included in the ion equation of motion, and also in that the equations are solved in a rigorous manner without any a priori assumptions regarding the form of the radial dependence of the perturbations of density and potential.

In the one example calculated, for the helical instability, an important result is the existence of a finite perturbed potential at the wall radius. The boundary between stability and instability as a function of longitudinal electric and magnetic fields is shown graphically, along with the wavelength and frequency of the helical mode at the critical value of the magnetic field.
Low-Frequency Stability of Nonuniform Plasmas
Authors: Krall Nicholas A. , Rosenbluth Marshall N.
Published: December 2004

A collisionless plasma in equilibrium with a slightly nonuniform magnetic field is studied to determine its stability against growing low-frequency oscillations whose propagation vector is perpendicular to the magnetic field. The method employs the collisionless Boltzmann equation and Maxwell's equations to obtain the eigenfrequencies of the oscillations. Previous work on this problem was based on a longitudinal approximation, i.e., the oscillation was assumed to have electric vector parallel to its direction of propagation. The present work does not make this approximation and finds: (i) a mode which corresponds to the mode found in longitudinal approximation, with the same eigenvalue as given by that approximation; (ii) modes with polarization similar to the ``longitudinal'' mode which are purely oscillatory; (iii) a purely transverse mode which is unstable. These results are compared with magnetohydrodynamic and other approximations.
Theory of the Fully Ionized Plasma Column with External Particle Production
Authors: Ecker Günter
Published: December 2004

The density and temperature distribution in a fully ionized cylindrical plasma with external particle production and without volume recombination are derived from the transport equations for the conservation of mass, momentum, and energy. It is found that the Schottky approach using a constant temperature and a simplified boundary condition is not applicable to this problem. The general calculation, which includes temperature variation and utilizes a more general boundary condition, produces results which cannot be represented in an analytical form but are determined by machine solutions. The results show density and temperature distributions which vary strongly with the discharge parameters. The general features of these distribution functions are discussed and interpreted in physical terms. The calculations also produce the maximum density n0 at the edge of the core as the eigenvalue of the problem. The dependence of n0 on the experimental parameters can be reasonably approximated by a simple analytical relation. A general similarity law relating the discharge parameters is given.
Shock and Hot Spot Initiation of Homogeneous Explosives
Authors: Mader Charles L.
Published: December 2004

The shock initiation of detonation in nitromethane, liquid TNT, and single-crystal PETN has been studied using a numerical method for solving the reactive fluid-dynamic equations. Agreement was obtained with previously reported experimental results.

Studies were made which explain in detail the mechanism of initiation of detonation at hot spots created by the interaction of a shock with an inhomogeneity. Energy transfer is accomplished by shocks and rarefactions. It is shown how experimentally observed criticality in bubble size can be related to the divergence rate of the shock, and to other features of the fluid flow. The relation of these results to initiation of detonation in inhomogeneous explosives is discussed.
Effect of Ion Correlations on High-Frequency Plasma Conductivity
Authors: Dawson John , Oberman Carl
Published: December 2004

In an earlier work the ac conductivity of a plasma was investigated by means of an elementary model. The validity of this model has been borne out by a rigorous treatment of plasma at thermal equilibrium. The elementary model is now extended to include the effects of ion correlations for arbitrary fixed ion distributions. For thermal equilibrium correlations it is found that the ion shielding reduces the maximum effective impact parameter by the factor (1 + Z)½ (i.e., both ions and electrons contribute to the shielding) for frequencies low compared to the plasma frequency ωp. For frequencies high compared to ωp, the previous results obtain. The resistance due to the excitation of longitudinal waves at frequencies just in excess of ωp is reduced by the factor (1 + Z)−1. However, if large-amplitude (nonthermal) ion fluctuations are present, the longitudinal wave contribution to the resistance may be greatly enhanced.
Low-Frequency Oscillations in a Potassium Plasma
Authors: D'Angelo N. , Motley R. W.
Published: December 2004

Low-frequency oscillations (10–30 kc/sec) have been observed in thermal potassium plasmas, produced by surface ionization of potassium atoms on a hot tungsten plate. The oscillations are associated with the presence of an ion sheath near the tungsten plate and seem to be reasonably well described on the basis of a simple picture of ion waves propagating across the magnetic lines of force, in the presence of a density gradient.
Pitch Angle Diffusion in a Magnetic Mirror Geometry
Authors: Wentworth R. C.
Published: December 2004

The diffusion in pitch angle produced by Coulomb scattering of charged particles in a magnetic mirror is derived by geometrical arguments neglecting energy loss. The resultant diffusion equation in particle pitch angle and time agrees with the more fundamental Fokker-Planck equation when energy loss is neglected.

The diffusion coefficient may be defined as the inverse of a ``lifetime'' and for particles in the Van Allen radiation belt it is compared to the energy loss time neglecting pitch angle diffusion. It is shown that both energy loss and pitch angle diffusion must, in general, be considered simultaneously. However, the special problem of the early diffusion of mirror points of a monoenergetic group of electrons injected at very low pitch angle is discussed, and it is shown that significant changes in mirror altitude take place before energy loss is appreciable. Thus the present analysis has a limited but potentially important application to such problems of low injection as the Argus experiment.
Gaseous Self-Diffusion in a Temperature Gradient
Authors: Wendt R. P. , Mundy J. N. , Weissman Stanley , Mason E. A.
Published: December 2004

Deviations from the quasistationary state in diffusion have been studied experimentally by measuring self-diffusion of gases, both isothermally and in a temperature gradient. Thermal diffusion is negligible in the cases considered. The nonisothermal measurements also serve as a check on the fundamental diffusion equation, which has not previously been tested except under isothermal conditions. The technique is convenient for obtaining diffusion coefficients over wide temperature ranges without the necessity of having all parts of the apparatus at an extreme temperature. Self-diffusion coefficients for CO2 and Kr have been obtained over the range of about 230° to 470°K by this method. Although the corrections for nonattainment of the quasistationary state are not small in the apparatuses used, the values for CO2 are in good agreement with those from other sources and the values for Kr are in fair agreement with others, provided the temperature gradients were not too large.
Investigation of the Chapman-Jouguet Hypothesis by the ``Inverse Method''
Authors: Wood W. W. , Fickett Wildon
Published: December 2004

Generalizing a particular case studied by Jones, Stanyukovich, and Manson have given general equations connecting (1) the Chapman-Jouguet detonation pressure; (2) the derivative α = p(∂v/∂E)p of the equation of state E(p, v) of the product gases; (3) the derivatives of the detonation velocity D with respect to the thermodynamic variables defining the initial state of the explosive, such as the initial density ρ0; (4) the variables D and ρ0 themselves.

After presenting a careful derivation of this result, it is pointed out that in conjunction with experimental observations of (a) the unsupported detonation-wave pressure p and velocity D and (b) the derivatives of D with respect to two independent initial variables (e.g., ρ0 and E0), it permits an experimental test of the basic assumptions of detonation theory, namely the assumption of laminar flow and the Chapman-Jouguet hypothesis. Several experimental possibilities are suggested for condensed explosives, where direct experimental observations (such as White's interferometric detection of apparent turbulent flow in gaseous detonations) are difficult. An erroneous criticism, by Pujol and Manson, of Jones' relation as applied to the density dependence of the detonation velocity in low-density solid explosives is also corrected.
Streaming of a Plasma through a Magnetic Dipole Field
Authors: Karlson Erik T.
Published: December 2004

The two-dimensional motion of a plasma in an inhomogeneous magnetic field with circular symmetry and a homogeneous external field under the influence of an electric field was studied previously [E. T. Karlson, Phys. Fluids 5, 476 (1962)]. The influence of space charges was taken into account. However, the treatment was generally valid only when no forbidden regions for the particles exist. When the inhomogeneity is strong enough, such forbidden regions will arise. The treatment is now generalized, so that it is valid for this case also. A discussion is given of the possibility to explain geomagnetic storms and auroral phenomena within the framework of the present theory.
Bound on the Energy Available from a Plasma
Authors: Gardner Clifford S.
Published: December 2004

The motion of an ideal collisionless plasma subject to periodic boundary conditions, with velocity distribution given initially, is studied. The minimum value which the kinetic energy can subsequently attain is determined, on the assumption that the system is subject only to the constraint that phase-space volume is conserved.
Toroidal Discharge Experiments with Rapid Programming
Authors: Ohkawa T. , Forsen H. K. , Schupp A. A. , Kerst D. W.
Published: December 2004

Five plasma configurations were studied in a fast-programmed toroidal discharge device where magnetic field errors were minimized. The effects of the programming on the plasma were examined with magnetic probes. a Kerr cell camera, and a monochromator. Without programming, the plasma developed a well-defined kink which corresponded to the worst mode of the instability predicted by hydromagnetic theory. By programming, the plasma lasted for 10 to 15 μsec at ion temperatures up to 130 eV and with densities up to 3 × 1016 cm−3.
Wave Propagation in a Tubular Plasma
Authors: Napoli L. S. , Swartz G. A.
Published: December 2004

The configuration consisting of a dielectric rod, surrounded by a plasma shell and a concentric outer conducting cylinder, is investigated theoretically and experimentally for its propagation characteristics. It is predicted from the theory that such a configuration will support propagation in a backward wave mode (oppositely directed phase and group velocities). These backward waves were observed in experiments using a configuration essentially identical to the above (the dielectric rod had an air space down the center used to insert a probing antenna), with the plasma provided by a cesium discharge. Agreement between these observations and calculations is excellent. A forward wave was also observed at low frequencies, and is attributed to the influence of the sheath at the plasma-conductor interface. The observed dispersion curve for this forward wave is also in good agreement with that calculated using the expected sheath size of the cesium plasma-metal interface.
Effects of Ionization on Stagnation-Point Heat Transfer in Air and in Nitrogen
Authors: Pallone Adrian , Van Tassell William
Published: December 2004

A study of the effect of ionization on the stagnation-point heat transfer to a noncatalytic wall is reported. The role of transport properties in heat-transfer calculations and a comparison of currently available results are made. The applicability of using a nitrogen model for heat transfer in the ionization regime is discussed and comparisons with available air results are made. Correlation formulas for heat transfer in air and in nitrogen are presented
Heat Transfer from Single Spheres in a Low Reynolds Number Slip Flow
Authors: Taylor Thomas D.
Published: December 2004

The effect of velocity slip and temperature jump on the heat transfer from a sphere in a low Reynolds number flow is investigated theoretically for large and small values of the Péclet number. A singular perturbation technique is used to obtain the small Péclet number solution while a boundary layer analysis is used to obtain the large Péclet number results. Expressions are derived for the average Nusselt number in each case. It is shown that for small Péclet numbers velocity slip can be neglected in the first approximation however this is not found to be the case for large Péclet numbers.
Some Transformations of the Hydrodynamic Equations
Authors: Eckart Carl
Published: December 2004

The Lagrangian equations of hydrodynamics are transformed to general coordinates. Since they involve two sets of variables (dependent and independent) two transformations are involved. The independent coordinates are usually taken to be the time and the initial positions of the particles of the fluid. Other kinds of independent variables are often useful. If they are chosen so that they describe the motion of a second fluid, the Lagrangian equations become a tool for comparing the motion of the two fluids. If the second fluid obeys the same laws as the first, the comparison is between two modes of motion of the same fluid. The study of this problem leads to a new derivation of the Eulerian equations from the Lagrangian. If the two modes of motion differ only slightly, the perturbation equations are obtained in generalized coordinates. They satisfy a variation principle. This can be transformed so as to exhibit the general form of a pseudo potential energy function that is useful in the study of stability problems.
Nonequilibrium Flow over a Reactive Surface
Authors: Kulgein Norman G.
Published: December 2004

A reacting flow situation is considered wherein a gas mixture initially in a state of chemical equilibrium flows over a surface having a chemical affinity for one of the components in the flowing gas. A gas-solid reaction results which, in turn, upsets the gas phase equilibrium so that a reaction starts there also. Evolution of gaseous products of the wall reaction serves to lower skin friction and to further complicate the situation. The flow is taken to be over a flat plate, and the simplest forms for the two reactions are used. The interactions among the processes are viewed in terms of an interaction parameter G, which is the ratio of the square of the characteristic time for wall reaction processes to the product of characteristic times for the gas phase and diffusion processes, and a stoichiometric factor K̄. The latter represents the mass of wall material that can react with unit mass of the free-stream gases. Typical results for drag show that when G = 1 and K̄ = 5, a 45% reduction occurs; when G = 5 and K̄ = 5, a 55% reduction is obtained. Even greater differences are found between values of skin friction when K̄ varies at constant G.
Heat Conductivities of Polyatomic Gases and Their Binary Mixtures
Authors: Pereira A. N. G. , Raw C. J. G.
Published: December 2004

A hot-wire apparatus of the ``potential leads'' type has been used to determine the thermal conductivities of nitrogen, oxygen, nitric oxide and nitrous oxide, and the binary mixtures: N2O–N2, N2O–O2, N2O–NO and NO–N2, over the temperature range 30° to 200°C. Corrections were made for the various possible sources of error, and the final results are accurate to within 2%. The results for single gases are discussed in terms of the original Eucken formula, the diffusion-mechanism theory and the Mason-Monchick theory. The mixtures are treated in terms of the general Hirschfelder equation, and also by use of the Wassiljewa-type relation. In the latter case, the experimental Wassiljewa coefficients are compared with those calculated by the Mason-Saxena and Lindsay-Bromley approximate relations.
Quantum Corrections to the Second Virial Coefficient for Helium at High Temperatures
Authors: Mohling Franz
Published: December 2004

The high temperature quantum corrections to the second virial coefficient are calculated for a square-well repulsive core model. It is shown that the hard core correction is large for He4 at all temperatures for which present measurements exist. The correction can be verified experimentally, because it leads to a 5% difference between He4 and He3 values at high temperatures.
Plasma Oscillations in an External Electric Field
Authors: Fried Burton D. , Culler Glen J.
Published: December 2004

The fluctuation longitudinal electric field, Ek, is studied for a two component plasma immersed in a uniform, external electric field E0. Since the time dependence of the space-averaged part of the distribution functions precludes the usual Laplace transform approach, computational techniques are developed to solve the integral equation for Ek directly in the time domain. Solutions are given for the case where E0 is large compared to the critical field for runaway and compared with the familiar constant-drift solutions. Growth in the vicinity of resonance (vdrift ≈ ωp/k) is observed, followed by Landau damping at longer times.
Skin Effect in Magneto-Fluid Dynamic Traveling Wave Devices
Authors: Neuringer Joseph L. , Migotsky Eugene
Published: December 2004

Electromagnetic propagation through an infinite circular cylindrical traveling wave tube in which a conducting fluid of constant conductivity is moving axially with uniform speed is studied. Asymptotic solutions valid for |αR0|«1 and |αR0»1, where α is the complex separation constant and R0 the tube radius, are obtained and analyzed. Concentrating specifically on the axial body force per unit tube length induced in the fluid, the |αR0|»1 solution indicates, fixing the current sheet input and geometry, that the magnitude of the induced axial force is a marked function of the dimensionless parameter β, equal to the magnetic Reynolds number based on wavespeed and wavelength multiplied by the slip. The body force rises linearly with β for small β, reaches a peak and then, because of the inability of the electromagnetic field to penetrate into the conductor with increasing β (skin effect), falls like β−1/2 for large β. From the practical viewpoint, the results suggest the adjustment of the electrical and fluid mechanical parameters so that operation occurs at that value of β which optimizes the force. It is further indicated, especially for moderate to high β operation, that for efficient utilization and conservation of working fluid mass and electrical energy, injection and acceleration take place in an annulus close to the coils rather than throughout the entire cross section.
Effect of Resistivity on Hydromagnetic Instabilities in Multipolar Systems
Authors: Johnson John L. , Greene John M. , Coppi Bruno
Published: December 2004

The effect of electrical resistivity on hydromagnetic instabilities is studied with special emphasis on interchange instabilities. A ``stellarator'' expansion is utilized to reduce the stability problem to one of solving two coupled second-order ordinary differential equations. This expansion enables one to treat a general geometry in a simple manner. A low-pressure strongly stabilized pinch is one special case. Further expansions are made in which perturbations vary rapidly in a thin layer the width of which is related to the resistivity. Highly localized interchange instabilities are found with growth rates which are independent of the resistivity in the limit as it goes to zero. These exist whenever the pressure decreases outwards. Interchanges with eddies of finite length grow more slowly, as the cube root of the resistivity. A stability criterion for king modes, which are characterized by vanishing pressure gradients in the resistive layer, is obtained. It depends on the entire plasma configuration and is identical to the one that would be obtained from the energy principle if the resistive layer were replaced with a vacuum. Gyration radius effects which are not included may significantly affect these resistive instabilities because they have slow growth rates and vary rapidly in a localized region.
Equations of Motion of a Current-Carrying Plasma Filament
Authors: Lundgren T. S.
Published: December 2004

The equations of motion of a perfectly conducting, current-carrying, plasma filament are derived from Hamilton's principle. The result is a nonlinear second order vector partial differential-integral equation, the solution of which gives the equation of the centerline of the filament. This is extended to the dissipative case for an incompressible fluid. A stability example is worked out.