bluuebunny/crossref_metadata_2025 huggingface dataset:
Thermal and Radiative Properties of Recombining Atomic Nitrogen
Authors: Marshall Thomas , Kawcyn R. A.
Published: December 2004

A series of experiments on phenomena associated with the atomic recombination of nitrogen atoms is briefly discussed. The temperature dependence of the three-body rate coefficient has been found to fit a power law k(T) ∝ T−0.6 over the temperature range of 200°–400°K. The absolute photon production rate accompanying the atomic recombination in the Rayleigh afterglow has been measured and found to be about one photon per 200 recombinations. The experiments rely on an electron spin resonance technique to measure the absolute atomic nitrogen density, and permit a rough determination of the dissociation energy of nitrogen.
Mean-Free-Path Concept in Gas Dynamics
Authors: Muckenfuss Charles
Published: December 2004

The mean free path of a rigid-sphere gas has been calculated from the most general form of the equilibrium distribution function. The mean free path depends on stream speed through the flow Mach number and increases monotonically with Mach number. The temperature dependence of the mean free path defined for realistic intermolecular forces through a transport coefficient is justified in molecular dynamics.
Structure of Weak Shock Wave in a Plasma
Authors: Whang Yun-Chow , Chang Chieh-Chien
Published: December 2004

The structure of a weak shock wave in a fully ionized plasma is studied by using Grad's thirteen-moment approximation to the nonequilibrium distribution functions for both ions and electrons. The flow field in the transition region is described by equations of transfer which are obtained by taking moments of the Boltzmann equation. Under the assumption of no charge separation, the basic equations are reduced to a pair of nonlinear differential equations. Many numerical solutions are obtained. A simple method of estimating the order of magnitude of shock thickness is given. It is established that shock profiles are thicker than those corresponding to the continuum theory, although they are of the same order of magnitude.
Implosive Phase of a Spherical Explosion in Sea Water
Authors: Berger S. A. , Holt M.
Published: December 2004

The calculation of the development of a spherical explosion in sea water, due to the symmetrical detonation of a charge of pentaerythritol tetranitrate, is carried up to the stage when the second blast wave converges as an implosive wave on the center and is reflected. Continuing earlier calculations by the authors, the complete field of disturbance is determined by the Eulerian approach, using the method of characteristics and boundary-fitting techniques, up to the characteristic ray originating from the center at the time of implosion. At this ray the main shock has traveled approximately 7 charge radii from the center. The implosive phase of the second shock motion is a well-known similarity phenomenon, and a variety of methods for treating this are discussed.
Stability of a Plasma Torus against Disturbances not Dependent on the Azimuth
Authors: Lüst R. , Martensen E. , Suydam B. R.
Published: December 2004

Perturbations of a plasma torus which are independent of azimuth are not covered by the general theory. A method for treating these special modes is presented, uniqueness theorems proved, and a rapidly converging numerical scheme for computation is given. It is also shown that these modes have the same behavior in a torus of infinite aspect ratio as do the corresponding ones in a cylinder; therefore the infinitely thin torus is stable against these modes.
Magnetohydrodynamics and Electrohydrodynamics
Authors: Stuetzer Otmar M.
Published: December 2004

A close analogy is found and mathematically investigated between the dynamic behavior of a plasma in a magnetic field and that of a unipolarly charged fluid in an electric field. The general equations and some of their broad consequences are discussed. Unidirectional flow, small disturbances, and stability are compared for the two systems.
Four-Shock Configuration
Authors: Smith Wesley R.
Published: December 2004

The two-dimensional stationary flow configuration of four plane shock waves intersecting at a point has been calculated for a perfect gas of specific-heat ratio γ = 1.4. The configuration represents the mutual reflection of an initial pair of shock waves of arbitrary strengths. The ratio of the stronger initial shock strength to the weaker ranged from 1 to 100 in terms of the pressure ratios across the shock waves, with the strength of the weaker wave ranging from 1.1 to 10. Calculations were made at 10° intervals over the entire range of angles of incidence for which the four-shock configuration was possible. The ordinary weak solution was entirely machine calculated along with its extreme angle. The sonic angles were calculated by graphical interpolation from calculated flow Mach numbers. The sonic and extreme angles were found not to differ by more than 1.1° in the range of shock strengths used. A new family of solutions which exists for unequal shock strengths was discovered graphically by plotting the machine-calculated shock polars.
Turbulent Transport of a Passive Scalar with a Variable Mean Gradient
Authors: O'Brien Edward E.
Published: December 2004

For low-turbulence-level, homogeneous flows with a uniform mean velocity, the formal consequences of passive scalar tagging at a plane normal to the mean flow are developed by employing Corrsin's ``backward Lagrangian diffusion'' concept. The asymptotic behaviors of arbitrary profiles are deduced and a comparison is made with the behavior of a linear profile in an infinite media. The amplitude of turbulent fluctuations is found to be bounded even in the absence of molecular effects if the profile is periodic or is O(1) at infinity.
Magnetic Properties of a Relativistic Electron Gas
Authors: Visvanathan S.
Published: December 2004

The magnetic properties of a relativistic electron gas have been studied by evaluating the magnetic moment of an assembly of relativistic electrons in a constant magnetic field. The diamagnetic contribution is found to be a third of the spin paramagnetism as in the nonrelativistic case. The results agree with those deduced by Rukhadze and Silin from the perturbation theory in quantum mechanics.
Experimental Two-Beam Excitation of Plasma Oscillations
Authors: Kofoid M. J.
Published: December 2004

Plasma electron oscillations have been excited in experiments in which the essential conditions of the Bohm and Gross two-beam theory were reasonably fulfilled. Standing waves of longitudinal plasma electron oscillations were produced between boundary electrodes by oppositely directed, independent, interpenetrating electron streams of well-defined velocity passing through a plasma of much higher charge density. In agreement with theory, no velocity modulation of the beam electrons prior to their entering the plasma was needed in order to cause the buildup of large-amplitude oscillations. Standing waves were detected when the ratio of the phase velocity to the beam electron velocity had the value of k + ¼ or k + ¾, where k was a small whole number; it was not necessary for the beams to have equal velocities.
Velocity and Temperature Profiles for Laminar Magnetohydrodynamic Flow in the Entrance Region of an Annular Channel
Authors: Shohet J. L.
Published: December 2004

The entry problem for an annular channel configuration which has the Globe profile for its fully developed condition is solved numerically for various values of the pertinent parameters describing the flow. The nonlinearities present in the momentum and energy equations are utilized in the solution of the problem by placing the equations in a finite difference form. For a large accelerating electric field the velocity profile was found to reverse itself in an area near the outer wall of the channel. Velocity, temperature, and pressure curves are presented from the results of computational work.
Nonadiabatic Particle Motion in Axialsymmetric Fields
Authors: Schmidt George
Published: December 2004

The motion of charged particles in electromagnetic fields under extremely nonadiabatic conditions is investigated. This is the case, e.g., if the particle passes through a region of vanishing magnetic field, either in space or in time. In fields of axial symmetry, the constancy of the canonical angular momentum lends the tool for this investigation. Strict laws for flux conservation are derived including rapid changes of fields in space and time. Particle injection into cusped geometries is studied and compared to experimental results. Particle motion under magnetic-field reversal in time is investigated and compared to findings in θ-pinch experiments under field reversal. A simple self-consistent model for such a particle motion is developed leading to the automatic formation of an E layer as a consequence of field reversal.
Asymmetric Inviscid Modes of Instability in Couette Flow
Authors: Bisshopp F. E.
Published: December 2004

An approximate solution of the equation which governs the inviscid modes of instability of steady flow between concentric rotating cylinders is derived. The problem is treated in the narrow-gap approximation, and the solution is applicable over the entire range of opposite rotation rates, but is limited to the treatment of disturbances which are nearly axially symmetric. Numerical results are given for the limiting cases where the ratio of angular velocities of the cylinders approaches zero and minus infinity. It is found that the growth rates of unstable modes which are very nearly symmetric are always less than the growth rate of the corresponding axisymmetric mode.
Local Atom Concentrations in Hypersonic Dissociated Flows at Low Densities
Authors: Hartunian R. A.
Published: December 2004

The theory of a probe to measure local atom concentrations in hypersonic flows of a dissociated gas at low densities is presented. The probe operates on a principle of measuring the differential heat transfer between catalytic and noncatalytic gauges immediately adjacent to one another on the stagnation line of a cylindrical model. The theoretical performance of the probe in the free molecule, the viscous shock layer, and the boundary layer regimes, respectively, is considered. It is shown that the probe cannot be operated successfully in the free molecule regime, except under unusual circumstances. In continuum flow, it is shown that under those conditions necessary for the atoms in the free stream to reach the surface of the probe (chemically frozen shock layer and boundary layer), we are always working in the viscous shock layer regime. Accordingly, it is this flow regime in which the probe measurements can be interpreted readily. The results of detailed calculations which relate to the application of this probe to measure local atom concentrations in nonequilibrium, hypersonic nozzle flows are presented.
Numerical Experiments with a Plasma Model
Authors: Eldridge O. C. , Feix M.
Published: December 2004

The exact motion of a one-dimensional system interacting through the electrostatic field is followed using a fast computer. The properties of the model are discussed and related to the three-dimensional plasma. New results are presented for the drag and diffusion of test particles and the space and time correlations of the charge density. These ``experiments'' agree with the conventional theory. In an appendix is derived the kinetic equation for this model to first order in the small parameter, the reciprocal of the number of particles in the Debye length. To first order a velocity distribution is constant in time.
Model of an Electrical Discharge in a Neutral Gas
Authors: Aamodt Richard E.
Published: December 2004

An equation determining Townsend's first ionization coefficient is derived for a model of a gas consisting of infinitely massive molecules which have total cross sections varying inversely as the electron energy. The equation is solved, and the results plotted as a function of the ratio of the applied electric field strength to the gas pressure when the parameters are chosen characteristic of the hydrogen molecule.
Chemically Frozen Boundary Layer with Surface Reactions behind a Strong Moving Shock
Authors: Chung P. M.
Published: December 2004

Surface recombination of dissociated atoms is studied behind a strong shock moving into a stationary diatomic gas. The chemically frozen laminar boundary layer is analyzed behind the moving shock. A solution is obtained for surface distribution of atoms and heat transfer when the atom concentration varies arbitrarily in the inviscid dissociating gas stream and, at the same time, the surface has an arbitrary but uniform catalycity. The applicability of the theory to the chemical diagnostics of shock tubes is studied.
Thermal Ionization in a System with a Distribution of Ionization Potentials
Authors: Maitland A. , Dunn M. H.
Published: December 2004

In a hydrogen plasma, the microfields act upon the neutral atoms and cause Stark effects which result in a distribution of ionization potentials. The distribution function is derived and used with the Saha equation to calculate the electron densities which are then compared with those calculated from a single ionization potential derived from an average microfield given by Cene⅔ where C = 4.2, 3.7, and 2.6, respectively, depending on the method of averaging. The temperature range considered is 5 750°K to 10 700°K in which the electron densities are between 1014 and 1017cm−3 when the neutral particle densities are 1017 – 1019cm−3. Within these ranges, whereas the electron density calculated from a single ionization potential based on an average field is up to about 1% greater than that given by the Saha equation using the ionization potential of an isolated atom, calculation using the distribution equation gives values up to about 2% greater.
Hydromagnetic Free Jet
Authors: Peskin Richard L.
Published: December 2004

Laminar and turbulent two-dimensional incompressible viscous free jet flow is studied for a conducting fluid. A constant magnetic field transverse to the axis of the jet is considered and the stream functions are expanded about the nonmagnetic jet solutions. The parameter of expansion is the square of the Hartmann number divided by the Reynolds number and results are computed to the first order in the expansion parameter. The results indicate a qualitative similarity for both the laminar and turbulent cases. The magnetic field depresses the axial velocity of the jet near the center of the jet but increases the axial velocity in the outer regions of the jet. The transverse velocity at the jet boundary is reduced in the presence of the magnetic field. The discharge rate of the jet is also reduced in the presence of magnetic field.
Shock Interaction with an Electromagnetic Field
Authors: Rosciszewski J. , Oppenheim A. K.
Published: December 2004

The interaction between a traveling shock wave and a stationary magnetic field is analyzed for the simplest case of one-dimensional flow across a rectangular system of a magnetic and an electric field, while the flowing substance is a plasma of finite conductivity but associated with a sufficiently small magnetic Reynolds number to render the induced magnetic effects negligible. The acceleration of the shock wave produced by a constant electric field applied across the duct walls in the presence of a perpendicular magnetic field, as well as its attenuation due to a distributed system of outside resistances connecting a series of electrodes on the sidewalls of the duct, have been calculated by quadratures. The flow field behind the wave has been determined by means of a perturbation technique whose validity is restricted to cases of small Lorentz forces and moderate Joule heating effects. To gain more familiarity with the interaction process a hydraulic analog is proposed, based on the use of a piston driven, free surface, mercury channel. In this connection, a general solution is consequently obtained for the interaction of a hydraulic jump traveling in a conducting liquid with a vertical magnetic field in the presence of a horizontal electric field.
Magneto-Acoustic Oscillations in a Cylindrical Plasma Column
Authors: Lindberg L. , Danielsson L.
Published: December 2004

A radial low frequency oscillation in a cylindrical plasma column located in a homogeneous axial magnetic field has been observed. A theory for radial magneto-acoustic waves in a plasma of finite conductivity is developed and applied to the experiment. The temperature and conductivity of the plasma can be determined from the frequency and damping of the waves.
Acoustic-Gravity Waves as a Particular Case of the Theory of Elasticity under Initial Stress
Authors: Biot M. A.
Published: December 2004

General equations for acoustic-gravity waves in a fluid are derived as a particular case of the theory of elasticity of initially stressed continua. The differential equations for the fluid dynamics and the corresponding variational principles are obtained from the more general results for the elastic solid established earlier by the writer. The transition from solid to fluid is illustrated for the special case of a constant gravity field. The dynamics of a fluid under initial stress is thus brought within the scope of the theory of elasticity providing a unified treatment of wave propagation in composite fluid-solid systems.
Experimental Trajectory Analysis of Charged Particles in a Cusped Geometry
Authors: Sinnis James , Schmidt George
Published: December 2004

Electrons are injected axially from an external source into a cusp field. For the particles to be transmitted through the cusp they must be injected inside a ``loss disk'' of radius ρcritical = (mv)/(qB0). At larger values of injection radius the depth of penetration beyond the median plane is measured and is in agreement with the maximum penetration depth predicted by the theory. The question of trapping is investigated and no long time confinement is obtained. The maximum number of reflections observed inside the cusp region is five.
Initial Spectral Behavior of a Scalar Field Transported by Turbulence
Authors: O'Brien Edward E.
Published: December 2004

Under the assumption that the scalar field and the velocity field which transports it are both isotropic and Gaussian the small-time behavior of the scalar transfer function can be obtained for any initial spectral distribution of turbulent energy and scalar ``energy.'' Specific spectra are calculated in detail and comparisons are made with work on the dynamics of isotropic turbulent fields. The effect of the relative scale of the energy containing regions of the velocity and scalar spectra is clarified. In particular wrinkling of a large scale scalar ``blob'' in a small scale turbulence field and the reverse phenomenon of stretching of a typical scalar ``blob'' when the scalar field has a characteristic size somewhat smaller than that of the velocity field are made evident.
Equilibrium of a Current-Carrying Toroidal Plasma
Authors: Yoshikawa Shoichi , Sinclair Rolf M. , Kessler John O. , Harries Wynford L.
Published: December 2004

A current-carrying plasma confined in a smooth toroidal magnetic field tends to expand due to the nonuniformity of the field and the self-interaction of the current. This expansion can be nullified, in the absence of externally imposed rotational transform, by means of a vertical magnetic field (perpendicular to the plane of the toroid). Macroscopically considered, such a vertical magnetic field interacts with the Ohmic heating current to supply an inward ponderomotive force. This paper derives the magnitude of the plasma expansion tendency and of the vertical field required to achieve steady state conditions. It is also demonstrated that if the plasma configuration is determined by an aperture limiter, helical fields are equivalent to an applied vertical field, insofar as the plasma equilibrium is concerned.
Two-Particle Correlation Function for an Unstable Plasma
Authors: Rutherford P. H. , Frieman E. A.
Published: December 2004

The usual kinetic equation derived from the B-B-G-K-Y hierarchy for a plasma with Coulomb interparticle forces breaks down for plasmas with distribution functions which the linearized Vlasov equation would predict to be unstable. As the first step towards deriving a kinetic equation for an unstable plasma in this paper the equation for the two-particle correlation function is solved for times for which the distribution function may be regarded as time independent. Part of the correlation function is shown to grow exponentially in time; thus the Bogoliubov adiabatic hypothesis breaks down. Taking only the fastest growing part of the correlation function, a velocity space diffusion equation is obtained for the distribution function with a time-dependent diffusion coefficient.
Stability of Hydromagnetic Kelvin-Helmholtz Discontinuity
Authors: Sen Amiya K.
Published: December 2004

The most general form of hydromagnetic Kelvin-Helmholtz discontinuity in ideal incompressible fluids has been considered. The presence of surface tension on the surface of discontinuity and gravity is also assumed. The stability of the hydromagnetic flow of two uniform infinite streams with planar interface exhibiting this type of discontinuity, has been analyzed in detail. Two necessary and sufficient criteria for its stability have been obtained, in contrast to only one that is usually given. The stabilizing effect of magnetic field is strongly dependent on its discontinuity at the interface and its orientation relative to that of streaming. The consideration of the stability to a single mode of perturbation leads to the conclusion that this is dependent on the above mentioned factors, as well as the following ones. The effect of surface tension and gravity is dependent on the wavelength, while that of the magnetic field is dependent on the direction of propagation of perturbation.
Instability of Penning-Type Discharges
Authors: Hoh F. C.
Published: December 2004

It is shown that a weakly ionized plasma column in an axial magnetic field and an inward-directed radial electric field—a Penning discharge at higher pressures—is unstable against a macroscopic m = 1 perturbation. The instability is analyzed by dimensional analysis. The applicability of this method is discussed. A steady-state model of some experimental Penning discharges is developed. On the basis of this model, the critical magnetic field for the onset of instability as predicted by the theory agrees well with the values observed. The instability discussed here is caused by the presence of a third fluid, the neutrals, in an electron-ion plasma. The same mechanism is also applicable to the initial phase of some rotating plasmas of the homopolar type.
Magneto-Fluid Dynamic Turbulence with a Uniform Imposed Magnetic Field
Authors: Deissler Robert G.
Published: December 2004

Two point correlation and spectral equations for this case are derived from the equations of fluid and electrodynamics. Solutions are obtained by assuming that the turbulent field is homogeneous and weak enough for triple correlations to be negligible. For initial conditions, it is postulated that the turbulence is initially isotropic, and that the turbulent magnetic field fluctuations are initially zero. The interaction of the mean magnetic field with the turbulent velocity field then causes magnetic field fluctuations to arise at later times. In general, the turbulent energy in the mechanical and magnetic modes tends toward equipartition for large values of time or of mean magnetic field. However, when the kinematic viscosity is much less than the electrical resistivity (or magnetic diffusivity), as for liquid metals, equipartition is not approached before the turbulence is damped out by the mean magnetic field.
Velocity of a Fluid Mass Imbedded in Another Fluid Flowing in a Porous Medium
Authors: Yih Chia-Shun
Published: December 2004

The velocity of a fluid mass imbedded in another fluid, which is of a different viscosity and a different specific weight and flowing in a porous medium under a prevailing uniform pressure gradient, is investigated. The fluid mass may take the form of a circular or elliptic cylinder, a sphere, or an ellipsoid, and the orientation of the fluid mass, if not spherical, is completely arbitrary with respect to both the direction of the pressure gradient and that of gravity. Exact closed solutions are obtained. The results for two-dimensional flows are applicable to Hele-Shaw cells.
Energy and Momentum Exchange between Nonequipartition Gases
Authors: Morse T. F.
Published: December 2004

The energy and momentum relaxation of a nonequipartition gas mixture is considered. It is assumed that each component of the mixture has a Maxwellian distribution at a temperature Ti, with the peculiar velocity of the Maxwellian measured relative to the mean velocity of the ith species. For the case in which a ``diffusion'' Mach number is not too large, the results have a particularly simple form. The calculations were carried out for the hard sphere, Coulomb, and Maxwell force laws of interaction. It is also noted how these results may be used to construct kinetic model equations for the case of hard sphere and Coulomb interaction, in a manner similar to that proposed by Sirovich.
Nonlinear Transverse Waves in Plasmas
Authors: Wang H. S. C. , Lojko M. S.
Published: December 2004

The propagation of nonlinear stationary transverse waves in plasmas is investigated by first solving a relativistic Vlasov equation for the electrons under the influence of a Lorentz force, due to a propagating 4-potential, rigorously and without linearization. The solution, which reduces to a given equilibrium electron velocity distribution function, is then substituted into the Maxwell equations, and a set of wave equations is obtained. While nonlinearity couples the transverse and longitudinal modes except for one special case, propagation of plane-polarized transverse waves in both cold and hot (Maxwellian) plasmas is studied in the quasineutrality approximation. The conditions for the existence of periodic solutions for the nonlinear transverse wave equations indicate that propagation is possible only when the wave velocity exceeds the velocity of light (for plasmas free from external magnetic field). Expressions for waveform and frequency in terms of elliptical integrals are derived. Unlike the case of longitudinal waves, the nonlinear effect on transverse waves is manifested primarily in the reduction of frequency rather than distortion in waveform. Several typical examples of waveform and dispersion characteristics (frequency vs phase velocity) are computed and plotted, ranging from cold to ultrarelativistically hot plasmas. The nonlinear effect is more pronounced at lower electron temperatures.
Observation of Plasma Instability with Rotational Effects in a Mirror Machine
Authors: Perkins W. A. , Post R. F.
Published: December 2004

Two types of hot plasmas were produced and confined between magnetic mirrors by plasma injection followed by slow magnetic compression in the Table Top III device: (1) a ``hot-electron plasma,'' in which the plasma was highly compressed and the electron temperature was 10 to 25 keV, and (2) a ``hot-ion plasma'' in which the compression was less but the ions were hotter than the electrons. In both cases, regimes could be found in which gross instability occurred. The plasma column was observed to leave the axis and spiral, as a whole, outward to the chamber walls with a radial velocity of about 5 × 105 cm/sec. On the basis of the observations and a comparison with theory this behavior is interpreted as a simple azimuthal mode number M = 1 interchange instability accompanied by a rotation arising from the fact that the plasma has a net charge. No multiple flutes (M > 1) have been observed during this motion, although occasionally simultaneous existence of two plasma columns has been detected. The lower critical density for the onset of the instability was approximately that density for which the Debye distance was equal to the plasma diameter. Stabilized regimes were also obtained by operation with high injected densities or at higher base pressures and the plasma remained confined for many milliseconds. There was also an intermediate regime in which instability could be deliberately ``triggered'' by a finite electrostatic perturbation in a plasma that had been quiescent for milliseconds. Some aspects of the observed stabilization, particularly the nonobservance of multiple flutes, occurring under conditions in which simple hydromagnetic theory predicts instability for all values of M > 0, seem to be explainable in terms of a ``finite-orbit'' theory, although other effects seem also to be present.
Hall Currents and Vortices in the Coaxial Plasma Accelerator
Authors: Bostick W. H.
Published: December 2004

The fact that the current sheet in a coaxial plasma accelerator is planar with the center conductor negative, and bullet-shaped when the center conductor is positive can be at least partially explained by a combination of Hall currents and plasma vortices, both of which should be expected to occur in such an accelerator. This explanation asserts that the peculiar asymmetrical behavior of this accelerator is a consequence of the fundamental property of ordinary-matter plasma: that electrons are light and positive ions are heavy. The sign of the asymmetry would be changed if antimatter plasma were employed. It is doubtful whether a planar current sheet could be achieved with a positronium plasma.
Final Stage Decay of Grid-Produced Turbulence
Authors: Tan H. S. , Ling S. C.
Published: December 2004

A kinetic model of the final-stage decay of grid-produced turbulence is presented. Theoretical analysis leads to an inverse-square energy decay law. The prediction has been confirmed by measurements in a low-speed water channel. A replot of the Dryden-Schubauer and Batchelor-Townsend wind-tunnel data also indicates better agreement with the present inverse-square, rather than the52-power decay law proposed by earlier investigators.
Kinetic Theory of Plasma and the Electromagnetic Field
Authors: Dupree Thomas H.
Published: December 2004

An exact kinetic equation for plasma and the electromagnetic field is derived. This equation describes the fluctuations of the fields and particle distributions. The solution is obtained by expanding in a parameter which characterizes the amplitude of these fluctuations. A systematic procedure is given for generating the solution to arbitrary order in the expansion. Some typical applications of the theory are presented. These include calculations of a collision integral, incoherent scattering, and bremsstrahlung emission and absorption.
Kinetic Treatment of the Stability of a Relativistic Particle Beam Passing through a Plasma
Authors: Mjolsness R. C.
Published: December 2004

The equilibrium configuration consists of a uniform particle beam of circular cross section and infinite extent streaming at highly relativistic velocity through a uniform, dense background plasma. The plasma is characterized by a scalar conductivity, and the beam is described by a collisionless Boltzmann equation in which a two mass approximation to the relativistic dynamics has been made. The stability problem for this configuration is formulated as a set of three linear, coupled integral equations for three field variables (certain Hankel transforms of the perturbed electric field), and a formal solution of the equations is obtained by iteration. The dispersion relation appears as a solvability condition. The treatment gives a full account of the betatron orbits of the beam particles. Asymptotic results are obtained for low-frequency, long-wavelength disturbances and for high-frequency, highly localized disturbances.
Propagation of Longitudinal Waves in a Weakly Ionized Gas
Authors: Sessler G. M.
Published: December 2004

The propagation of longitudinal waves in a weakly ionized gas consisting of three species of particles (neutrals, ions, and electrons) is analyzed giving full consideration to the influence of collisions between all three kinds of particles. The calculations are based on Euler's and Poisson's equations. Damping and phase constants for the neutral-particle wave, the ion wave, and the electron wave are presented for different values of particle densities and for frequencies lower than, or comparable to the plasma frequency of the ions. The main result of the calculations is that in a certain frequency range the damping of the ion wave can be smaller than the damping of the neutral-particle (sound) wave. This suggests the stimulation of ion waves by means of acoustic transmitters. Such an ion wave would be free of the potentially disturbing neutral-particle wave at some distance from the source. This method would make it possible to stimulate a purely longitudinal plane wave.
Recombination Coefficient of Electrons with NO+ Ions in Shock-Heated Air
Authors: Stein R. P. , Scheibe M. , Syverson M. W. , Shaw T. M. , Gunton R. C.
Published: December 2004

A measurement of the electron-positive-ion recombination coefficient has been made in air of density near 0.1 atm. and of temperature about 2900°K, yielding the value, α = (4 ± 2) × 10−8 cm3 sec−1. The results indicate that dissociative recombination, NO+ + e− → N + O, is the dominant electron depletion process. Air behind a reflected shock wave at a temperature of 3600°K is expanded rapidly into a thin-wall quartz tube. The tube serves as a post in three X-band waveguides. Electron densities are computed from the measured phase shifts of transmitted microwave signals. The relation between electron density and phase shift is determined with discharge plasmas of known electron densities. The recombination coefficient is computed from the measured electron depletion rate and the time variation of the temperature and velocity of the gas in its unsteady expansion down the quartz tube. The effects of diffusion, attachment, and impurities are also investigated. The measured value of α is in reasonable agreement with that of Lin et al., at 5000°K when a T−3/2 temperature dependence is assumed. This result is also compared with other laboratory measurements near 300°K.
Models of Collisionless Shock Fronts
Authors: Buneman O.
Published: December 2004

In the absence of collisions one must attribute the interaction between plasmas of different speeds in a shock front to collective mechanisms of energy and momentum transfer, such as growing plasma oscillations, ion waves, hydromagnetic waves, etc. Numerical one-dimensional plasma models have produced evidence that nonlinear wave interaction provides an efficient alternative to collisions for creating shock fronts between two interpenetrating streams of noncolliding particles and, specifically, that the conservation of entropy normally associated with collision-free conditions will, in a practical sense, be violated.
Boltzmann Equation Applied to a Problem of Two-Phase Flow
Authors: Culick F. E. C.
Published: December 2004

A limiting case of the interaction between particles in a viscous fluid is described by a linear form of Boltzmann's equation. The distribution function, f(v), is found for small particles falling under the action of gravity and viscous drag, and colliding with large particles. Several approximate procedures for computing f(v) and the connection with flows of gases containing solid particles are examined.
Stagnation-Point Heating in Ionized Monatomic Gases
Authors: Reilly James P.
Published: December 2004

Measurements were made of the heat transfer to the stagnation point of a cylinder in partially ionized monatomic gases, and the effect of free electrons on the total gas thermal conductivity was assessed. Shock-heated argon and xenon were used as the test media, thus bypassing the dissociation phase present in diatomic gas heat transfer, and passing directly from the ideal gas to the ionized gas. Comparison of the experimental data is made with two real-gas estimates, the first including the effects of ionization only on the thermodynamic properties involved, and a second including the effects of ionization on both the thermodynamic and transport properties. The experimental results are in substantial agreement with the latter prediction where equilibrium is attained, and confirm the prediction of an increased gas thermal conductivity due to the presence of free electrons. An estimate of the contribution of radiative heating is made both numerically and experimentally, and found to be less than 10% of the aerodynamic heating for the test conditions. The test gas is shown to be in thermochemical equilibrium under those conditions where ionization is significant.
Finite Amplitude Effects on Hydromagnetic Waves
Authors: Woods L. C.
Published: December 2004

Hydromagnetic waves traveling along an axial magnetic field in a cylindrical plasma bounded by a conductor have a frequency ω determined by the exciter. The nonlinear terms appearing in the equation of motion and in Ohm's law, usually neglected in wave theory, will induce a small amplitude wave of frequency 2ω accompanying the basic wave. In addition, the boundary conditions at the exciter will produce further double-frequency waves, but moving at speeds different from the basic wave. In this paper the amplitudes of these double-frequency waves are calculated for all the components of the magnetic field and for the plasma density. The existence of certain critical frequencies, at which resonance between the basic and double frequency waves occurs, is established. In the limit as Ω ≡ ω/ωci tends to zero, the amplitudes of the magnetic double-frequency waves are shown to depend on Ω/ε, where ε−1 is the damping length of the wave, whereas the corresponding density wave amplitude is found to be independent of both ε and Ω.
Thermal Instability of the Plasma Column
Authors: Ecker G. , Kröll W. , Zöller O.
Published: December 2004

So far the stability of a cylindrical collision dominated plasma column has been studied under the assumption of constant temperatures. Temperature inhomogeneities are now taken into account to calculate the thermal instability of the plasma column. The external influence is due to an Ohmic resistance. Normal mode analysis and trial functions methods are applied to derive a criterion for the instability onset, caused by the local coupling between temperature and charged particle density. For given discharge parameters instability occurs beyond a critical current depending on the outer resistance.
Magnetohydrodynamic Stability of Toroidal Plasmas
Authors: Ware A. A.
Published: December 2004

The sufficient stability condition which follows directly from the energy principle is divided into the parts which depend, respectively, on j∥ and j⊥, which are the components of the equilibrium current parallel to, and perpendicular to, the magnetic field. The sufficient condition for j⊥ not to cause instability is found to depend on the average normal curvature of the magnetic surfaces in the direction of B. The corresponding condition for j∥ depends on the average geodesic torsion of the magnetic surfaces in the direction of B. For currents below approximately the Kruskal limit in a circular torus, the average normal curvature becomes negative and the j⊥-modes are stable for negative pressure gradients. This confirms Mercier's earlier results for localized perturbations. On the other hand, to zero and first order in the aspect ratio of the torus (r/R0) the average geodesic torsion is the same as for a straight cylinder so that there is no toroidal stabilizing effect for j∥-driven modes. Completely stable toroidal equilibria are possible which do not rely on magnetic shear. The relationship of these stability conditions with the ∫ (dl/B) criterion is discussed.
Interaction of a Stationary Plasma with an Electron Beam
Authors: Neufeld Jacob
Published: December 2004

This investigation deals with a plasma-beam system in which an electron beam of small intensity interacts with a stationary plasma immersed in a magnetic field. Expressions are derived for frequencies and rates of growth of the transverse waves excited by the beam. It is shown that the rate of growth attains a maximum value for a beam velocity β = βm, and a relationship is formulated between the quantity βm and appropriate parameters characterizing the stationary plasma. An analysis is given of the behavior of the plasma-beam system in the neighborhood of ion gyroresonance. This investigation applies to all velocities of the electron beam except those in a highly relativistic range.
Experiments on Condensation of Water Vapor by Homogeneous Nucleation in Nozzles
Authors: Wegener Peter P. , Pouring Andrew A.
Published: December 2004

Condensation of water vapor in a highly supersaturated state was studied with steady flow of moist air in supersonic nozzles of different temperature gradients. With measured centerline static pressures, known initial conditions, and known nozzle geometry, the equations of motion could be solved. From these results heat addition to the flow owing to condensation could be determined. By estimating latent heats, condensate mass fractions and condensation rates have been found. It was inferred that at temperatures from 200 to 220°K the condensate was ice. Classical steady-state nucleation theories in conjunction with a droplet growth law were applied to solutions of the condensation integral equation. It was found that on this basis the onset of measurable condensation cannot be predicted from first principles. In a qualitative manner, however, the observations could be correlated with the theory. A contributing factor to the failure of nucleation theory is the lack of knowledge of material properties at the low temperatures in question. In conclusion, new work based on the findings of the conditions at the onset of condensation is suggested.
Contribution to the Nonlinear Stability Theory of Inviscid Shear Layers
Authors: Schade H.
Published: December 2004

Stuart's nonlinear stability theory is applied to two-dimensional neutral disturbances of the basic velocity profile u0 = tanh y at infinite Reynolds number in order to calculate the equilibrium amplitude of this disturbance.
Interaction of a Streaming Plasma with the Magnetic Field of a Two-Dimensional Dipole
Authors: Levy R. H.
Published: December 2004

The flow of an infinitely conducting plasma past a two-dimensional magnetic dipole oriented parallel to the flow has been considered by Hurley, among others. The problem consists of finding a vacuum magnetic field such that along a bounding field line whose location is to be found, the magnetic pressure balances the Newtonian dynamic pressure appropriate to the local slope of the boundary. A related problem has been solved by Cole and Huth; in their case there is no flow, but an isotropic static plasma surrounding the magnetic field region which exerts a constant pressure on the boundary. In the actual flow problem we would expect there to be a stagnant (trapped) region near the front. The stagnant flow would be at nearly constant pressure. Away from this region the Newtonian pressure would again be applicable. This problem, which is a mixture of those cited above, has been solved by an approximate technique due to Cockcroft. The solution is shown to have features of both the cited problems, as appropriate.
Microwave Propagation in an Overdense Bounded Magnetoplasma
Authors: Wieder Bernard
Published: December 2004

In the last few years experiments were reported which demonstrated propagation of electromagnetic waves through an overdense magnetoplasma, i.e., a plasma whose plasma frequency is greater than the frequency of the probing wave. The interpretation of the experimental results was based on the ``whistler mode.'' The ``whistler mode'' appears in the infinite plane wave solutions of Maxwell's equations for an infinite homogeneous magnetoplasma. In a laboratory plasma, the effects of the boundaries of the plasma may play an important role in determining the propagation properties of the waves. These effects are examined and the analysis shows that the waves may, under certain circumstances, exhibit sufficiently different qualitative and quantitative characteristics to seriously limit the applicability of the infinite medium theory to bounded plasmas. To illustrate this point, the properties of waves propagating in a dense, homogeneous, cylindrical plasma bounded by a conducting wall are examined and compared with the properties of the wave predicted from infinite plane wave theory.
Electron-Ion Relaxation Times
Authors: Rand S. , Albini F.
Published: December 2004

The approach to equilibrium of the electron and ion components of a plasma has been studied. The interactions between particle pairs are determined in a polarizable plasma, so that collective effects are included at the outset. The pairwise interactions are treated quantum mechanically, in the Born approximation, whereas the collective effects are, in a consistent manner, treated classically. Corrections to previously quoted results, due to the proper inclusion of shielding, as well as quantum effects, are logarithmic.
On the Production of Plasma by Giant Pulse Lasers
Authors: Dawson John M.
Published: December 2004

Calculations are presented which show that a laser pulse delivering powers of the order of 1010 W to a liquid or solid particle with dimensions of the order of 10−2 cm will produce a hot plasma with temperatures in the range of several hundred eV. To a large extent the plasma temperature is held down by its rapid expansion and cooling. This converts much of the energy supplied into ordered energy of expansion. This ordered expansion energy can amount to several keV per ion. If the expanding plasma can be caught in a magnetic field and its ordered motion converted to random motion this might be utilized as a means for filling controlled thermonuclear fusion devices with hot plasma. Further, it should also be possible to do many interesting plasma experiments on such plasmas.
Variational Principle for Rayleigh-Taylor Instability
Authors: Selig F.
Published: December 2004

The variational principle which describes the stability problem of superposed fluids can be written in a form which is free of any ambiguities and allows a very simple physical interpretation.
Kinetic Equation of Classical Boltzmann Gases
Authors: Su C. H.
Published: December 2004

By use of the multiple-time-scale method, the low density expansion is carried to the order of the triple collision integral. The validity of Bogoliubov's assumption that the multiple distribution depends functionally on a single particle distribution is carefully examined. It is found that such an assumption is valid except locally for those particles which have a large separation at a time t and which have their relative velocity so oriented that they were in collision at t = 0. Since this local breakdown is very selective, the triple collision integral which is found in the literature is still correct. As a by-product of the multiple-time-scale method, the rate at which a system approaches the kinetic state is obtained; it is also found that up to the order considered the Maxwellian distribution is the only solution at thermal equilibrium.
Drag on an Object in Nearly-Free Molecular Flow
Authors: Rose Marian H.
Published: December 2004

In the nearly-free molecular flight of a body through a neutral gas the departure from free-flow conditions becomes marked within roughly the distance of a mean free path from the body. This is the region to be studied here. In order to do this as simply as possible, the distribution function for the gas is assumed to be governed by the Krook equation with the addition of a point source term; this term is identified with the radial flow issuing from the object and is easily related to its shape and to the boundary condition both at its surface and at infinity. The Krook equation may be linearized about the distribution function at infinity and then solved using Fourier transform techniques. The knowledge thus obtained of the distribution function near the body leads to the expression for the first order perturbation of the drag over its free-molecular value. This is the exact first-order solution in the sense that all collisions between particles are taken into account and not merely ``first collisions.'' The case of a sphere undergoing diffuse reflection at high Mach number is worked out in detail and an explicit expression for the drag is derived.