bluuebunny/crossref_metadata_2025 huggingface dataset:
Shock Structure in a Simple Discrete Velocity Gas
Authors: Broadwell James E.
Published: December 2004

The structure of a shock wave in a simple discrete velocity gas—a gas in which the molecules move with a finite set of velocities—is discussed. The Boltzmann equation becomes, for this gas, a set of coupled differential equations which, in the present example, can be solved exactly. The solution describes an infinite Mach number shock in a gas consisting of hard elastic spheres. Although only six molecular velocities are considered, and the solution is easy to obtain, it compares remarkably well with those of other investigators.
Mechanism of Particle Collision in the One-Dimensional Dynamics of Gas-Particle Mixtures
Authors: Marble Frank E.
Published: December 2004

A theory is developed for the one-dimensional flow of a gas, containing solid particles of two different sizes, in which the effect of particle collisions is accounted for as well as the interaction between the particles and the gas. It is assumed that the particles behave as smooth elastic spheres, that they follow the Stokes drag law and exchange heat with the gas at a Nusselt number of unity. It is shown that there exists a range of parameters which provides that (i) the viscous flow fields about each particle do not interfere during collision, and (ii) the random velocities imparted by one collision are damped before either particle suffers another collision. Using the assumption of small particle slip, the one-dimensional flow problem is solved explicitly up to first order terms in the small slip. It is found, of course, that the tendency of collisions is to cause the two particle-slip speeds to have more nearly the same value than they would in the absence of interparticle collision. It appears that, although the physical assumptions restrict the magnitude of the interparticle forces, the model does provide the proper limit for very strong particle interaction and can conceivably be applied in this range also without gross error.
Coupling of Magnetohydrodynamic to Electromagnetic and Acoustic Waves at a Plasma-Neutral Gas Interface
Authors: Kahalas Sheldon L. , McNeill Dale A.
Published: December 2004

The coupling of magnetohydrodynamic waves to electromagnetic and sound waves at a plane interface between a plasma and a neutral gas is considered for arbitrary direction of the incident wave vector and for the constant external magnetic field lying either in the plane of incidence or perpendicular to it. The relations between the angle of incidence, reflection, and transmission, the ratio of the field amplitude transmitted or reflected to the corresponding amplitude incident, and the energy coupling coefficients are calculated. An incident fast magnetoacoustic mode generates a sound wave with energy coupling coefficient of the order of the ratio of the speed of sound to the Alfvén speed when this ratio is small. An incident slow magnetoacoustic mode generates a sound wave with energy coupling coefficient of the order of unity and an electromagnetic wave with energy coupling coefficient of the order of the ratio of the speed of sound to the speed of light.
Gas Thermal Conductivity Studies at High Temperature. III. Results for SO2
Authors: Baker C. B. , De Haas N.
Published: December 2004

Measurements of the thermal conductivity of SO2 by the line source method over the range 295°–887°K are presented. These measurements are compared with existing experimental data and theoretical results using the modified-Eucken equation. Values of the collision number for rotation relaxation are obtained using the heat conductivity theory of Mason and Monchick for polyatomic gases.
Micro-Instabilities in Magnetically Confined, Inhomogeneous Plasma
Authors: Jukes J. D.
Published: December 2004

Plasma with a density gradient supported in a strong, nearly uniform magnetic field is liable to resistive, gravitationally (g-) driven instability and short-wave drift instability. Waves associated with both propagate almost perpendicular to the field lines. Only a low g, and low density plasma are considered, for which these flutelike perturbations remain quasi-electrostatic, so that dispersion relations are readily found. When the magnetic-field lines are sheared the localized perturbations which arise are treated by a phase-integral approximation and growth rates appear as eigenvalues of certain standard equations. The ions are treated throughout by the Vlasov equation so that fine-scale features such as finite ion Larmor radius ai and Hall current are correctly included. The results for the resistive, gravitational instability are compared with those based on fluid equations and are valid if the perturbation is not localized within ai.
Transport Coefficients Determined Using the Shielded Coulomb Potential
Authors: Liboff Richard L.
Published: December 2004

In the classical Chapman-Enskog theory of a fully ionized gas, the transport coefficients evolve as functionals of certain weighted total scattering cross sections. If a Coulomb potential is assumed between scattering particles, these scattering integrals diverge. A common procedure to circumvent this difficulty is to integrate the Coulomb results up to the Debye cutoff. A more appropriate procedure involves the use of the shielded Coulomb potential, in which case the scattering integrals converge, and there is no need to introduce a cutoff. These integrals are calculated using the shielded Coulomb potential and the resultant transport coefficients are compared with those of the standard ``Coulomb plus Debye cutoff'' calculations. To the ``dominant log term'' the two procedures give identical results. To terms of the next order of accuracy for the viscosity and thermal conductivity the difference between the two formulations is of the order of 0.5%, and for the diffusion and electrical conductivity the difference is of the order of 2%. The major calculation is that of the classical cross section for the screened Coulomb potential.
Ionic Theory of Plasmas and Magnetohydrodynamics
Authors: Green H. S.
Published: December 2004

This paper aims at removing certain sources of confusion in plasma theory by deriving a complete set of macroscopic equations based on the ionic theory. Relativistic and quantum effects are usually neglected, and an approximation equivalent to that of the macroscopic theory of irreversible processes is adopted. But there is no other approximation, and in particular multiple interactions are fully accounted for. The theory of the dielectric constant and permeability of plasmas is sketched, and there follows an ionic derivation of the equations of continuity, and of energy and momentum transport, based on an exact separation of the long-range and short-range forces. It is shown how the short-range forces contribute to the pressure, the energy flux, and the flux of entropy. The ionic basis of the theory of irreversible processes is discussed, and its relevance to the generalization of Ohm's law. In an appendix, the formal statistical thermodynamics of plasmas is developed in a way which avoids certain difficulties associated with the long-range interactions.
Multistage Magnetic Compression of Highly Ionized Plasma
Authors: Coensgen F. H. , Cummins W. F. , Sherman A. E.
Published: December 2004

The mean energy of the charged particles of a plasma which is confined in a magnetic field may be increased by increasing the magnitude of the magnetic field in a time which is short with respect to the ion relaxation time (magnetic compression). It is shown that the necessary stored energy can be reduced and the efficiency greatly increased if the magnetic compression is performed in several stages, such that the plasma is compressed and transferred to successively smaller volumes. The predicted transfer behavior has been confirmed by studying the plasma movement in a three-stage system. In the course of the investigation a plasma source has been developed which provides bursts of plasma of 1016 to 1018 ions with an average velocity of the order of 107 cm/sec.
Cyclotron Radiation from Magnetically Confined Plasmas
Authors: Beard David B.
Published: December 2004

The cyclotron emission from a hot, completely ionized, magnetically confined plasma has been estimated by computing the absorption of an incident plane wave. The harmonics of the fundamental cyclotron frequency, which are emitted perpendicular to the magnetic field direction, were summed over and also treated individually. Because of the Doppler effect and the relativistic variation in mass the behavior of the electrons and the electromagnetic properties of the medium are functions of electron velocity.

Assuming a Maxwell-Boltzmann distribution in electron velocity, the polarization of the plasma was computed by integrating over electron velocity. Solution of Maxwell's equations yielded the absorption of an incident wave, and thus, from Kirchhoff's relation, the emission of the plasma was determined. The entire calculation was carried out nonrelativistically to first order in v2/c2, and at temperatures too low for fluctuations to play a dominant role.
Rotational and Vibrational Relaxation in Diatomic Gases
Authors: Parker J. G.
Published: December 2004

Calculations of rotational and vibrational relaxation times for gases composed of homonuclear diatomic molecules have been carried out. The model used for the molecular interaction potential consists of an attractive component, which acts between geometrical centers of the molecules, and a repulsive component which is assumed to originate from two centers of force in each of the molecules. For large intermolecular separations, the attractive forces prevail while at close distances the repulsive forces control. Using this model, the number of collisions to establish rotational equilibrium ZR and also the number for vibraton ZV are calculated. Both ZR and ZV contain some of the same molecular parameters and are therefore dependent on each other. From the analysis it turns out that ZR is a gradually increasing function of increasing temperature and ZV is a rapidly decreasing function of increasing temperature. Comparison with experiment for the gases chlorine, nitrogen, and oxygen indicates that the calculations are for the most part reliable.
Linearized Swirling Wakes
Authors: Steiger Martin H. , Bloom Martin H.
Published: December 2004

Exact similar and nonsimilar solutions for axisymmetric wakes with small swirl in a constant-property medium are derived. Emphasis is placed on the similar solutions, particularly those associated with the swirl. A unique similar solution for the axial velocity is distinguished from a possible infinite set by invoking the auxiliary condition of invariance of the axial momentum defect. Likewise, for the circumferential velocity only one of the large number of possible similar solutions is shown to satisfy the conditions that the circumferential mass flow, momentum flux, and higher moments are bounded.
End Correction for Slow Viscous Flow through Long Tubes
Authors: Weissberg Harold L.
Published: December 2004

A variational method valid for the creeping-flow regime is used to calculate an upper bound for the pressure drop associated with viscous dissipation near the ends of a long round tube. The result states that this pressure drop, which is an additive correction to that given by the Poiseuille formula, is not greater than 1.154 times the pressure drop through a thin orifice. The orifice pressure drop, in terms of the fluid viscosity μ, the volumetric flow rate Q, and the radius a, is found to be 3μQ/a3, in confirmation of a previous calculation of Roscoe by a different method.
Electrohydrodynamic and Magnetohydrodynamic Nonlinear Surface Waves
Authors: Melcher James R.
Published: December 2004

A nonlinear formulation of electrohydrodynamic and magnetohydrodynamic surface interactions is developed which, in the absence of magnetic or electric fields, becomes the classical ``long'' gravity-wave theory. The results are valid for a shallow highly conducting fluid that interacts strongly with a rigid highly conducting plate in such a way as to either conserve an electric potential difference or a magnetic flux. The growth of surface discontinuities from compression and depression waves is discussed, with transition electrohydrodynamic waves originating from timelike data given to illustrate waves that are partly controlled by gravity and partly by the electric field. Waves initiated from spacelike data are also described, and the integral jump conditions derived.
Electromagnetic Radiation from an Electric Dipole in a Cold Anisotropic Plasma
Authors: Kuehl Hans H.
Published: December 2004

The general solution to the problem of monochromatic radiation from an electric dipole in a magnetically biased, cold, tenuous plasma is presented. It is found that, generally, several waves exist in the radiation zone, traveling in different directions with different indices of refraction. For certain ranges of the plasma, gyro, and operating frequencies, the field becomes very large in certain directions compared with that in other directions, producing highly directive radiation characteristics. In general, the expression for the field is quite complicated although several special cases are treated which yield simple solutions. For high operating frequency it is found that the radiation pattern is identical to the isotropic case although a Faraday rotation takes place. Solutions are given for low and very low frequencies which place in evidence the guiding nature of the magnetostatic field. For the case of a large magnetostatic field it is shown that only two waves exist and that the time-average power flow is purely radial.
Synchrotron Radiation Losses from Energetic Plasmas
Authors: Beard David B. , Baker John C.
Published: December 2004

The synchrotron emission from plasma electrons having an isotropic Maxwell-Boltzmann velocity distribution has been numerically computed as a function of electron temperature, radiation frequency, and the angle between the radiation propagation vector and the magnetic field. The total emission at high temperatures from a cylindrical plasma volume was found to be greater than earlier estimates of others valid at lower temperatures due to contributions at frequencies higher than the critical frequency at which the plasma becomes semitransparent. The increase is temperature dependent. For a 10-m-diameter plasma the increase for a typical plasma is 32% at an electron temperature of 20 keV and rises to 140% at 200 keV electron temperature. The effect of reflectors in diminishing the loss of radiated energy is very much reduced at high temperatures. If r is the over-all microwave reflectivity of the material walls surrounding the plasma, the loss is diminished approximately by (1 − r)0.8 for kT = 10 keV, by (1 − r)0.1 for kT = 200 keV.
Investigation of the Shock-Tube Boundary Layer by a Tracer Method
Authors: Chen Che Jen , Emrich Raymond J.
Published: December 2004

A dark-field oscillatory spark microphotography technique has been developed to study with tracers the structure of the gas boundary layer in the shock tube. By using these particles as tracers, velocity profiles of the boundary layer both in laminar and turbulent regions are measured and the velocity fluctuations observed. The time and space resolution of this technique is high. Laminar velocity profiles show a significant deviation from theoretical expectations. The turbulent average velocity profiles have the usual 1/7th power variation with distance from the wall in the top 90% of the layer. The velocity of the flow within a few microns from the wall is sometimes much greater than the value predicted by Mirels assuming zero velocity at the wall. A possibility of slip flow in the shock tube is discussed. This technique allows measurements to be made as close to the wall as the size of the particle's diffraction pattern, which is about 1 μ.
Electron Distribution Function and Electrical Conductivity of a Slightly Ionized Gas
Authors: Sampson Douglas H. , Enoch Jacob
Published: December 2004

An expansion of a formally rigorous integral solution of the Boltzmann equation in powers of the electric field and m/M is used to demonstrate the correct expression for the conductivity of a spatially homogeneous slightly ionized gas. The conditions under which the isotropic part of the electron distribution function reduces to the Margenau distribution are determined. A discussion of the physical reasons for the possibility of negative conductivity is given.
Nonlinear Plasma Absorption of High-Frequency Radiation
Authors: Albini F. , Rand S.
Published: December 2004

The interaction of electromagnetic radiation with a plasma has been studied. The relationship between the field strength and the induced current density becomes nonlinear when the electrons are accelerated to velocities in excess of the phase velocities of longitudinal electron waves in the plasma. The rate of energy absorption from a radiation field by a plasma has been calculated, in the limit of high frequencies, as a function of power input. The results are applicable when the radiation frequency exceeds the electron plasma frequency as well as the electron-ion collision frequency. It is found that the usual linear dependence of energy absorption on power input is directly applicable when all wavelengths of electron plasma waves, emitted by a particle which oscillates in the radiation field, exceed the excursion distance of the particle from its equilibrium position. When this condition is violated, the deviations from the linearized results are logarithmic, as long as the directed velocities attained by electrons in the radiation field are small compared to the thermal electron speed. Finally, when electrons are accelerated to velocities much in excess of thermal speeds, the deviations from the linearized results become very important.
Effect of Close Collisions on the Plasma Spectrum
Authors: Fante R. L.
Published: December 2004

In this analysis is derived a formula for the spectral density of radiation scattered by a nonequilibrium plasma which is valid for all wavenumbers. It is found that the spectrum obtained is equal to the spectrum obtained by Rosenbluth and Rostoker plus a correction representing the effects of close collisions. An order of magnitude analysis indicates that, in general, the additional term represents only a higher-order correction to the Rosenbluth-Rostoker spectrum.
Kinetic Theory Approach to Electrostatic Probes
Authors: Wasserstrom Eliahu , Su C. H. , Probstein Ronald F.
Published: December 2004

A spherical electrostatic (Langmuir) probe in a slightly ionized plasma is studied from a kinetic theory point of view. The two-sided distribution function method of Lees, which embodies the Mott-Smith approach, is used. The velocity space is divided into two regions along the straight cone tangent to the spherical probe, and different distribution functions are defined in the two regions. On satisfying the two relevant moments of the distribution function (continuity and number density flux) three simultaneous ordinary nonlinear differential equations, which are appropriate to all values of the Debye length, collision mean free path and probe potential, are obtained for determining the ion and electron number densities, and the potential. These equations reduce to the usual linear flux equations when the mean free path is much shorter than the probe radius and the Debye length. The equations are first linearized and solved for the case of small probe potential. Explicit solutions are given for the current-voltage characteristics and the distributions of the number densities and the potential. The general case of arbitrary probe potential is also studied. Results for the characteristics and for the potential drop in the sheath are presented for some representative cases. Many of the results which are obtained do not appear in the original simplified Langmuir model. The modifications required to take into account the curvilinear orbits of the charged particles are discussed.
New Method for Measuring Liquid Compressibilities
Authors: Schamp Homer W. , Hastings John R. , Weissman Stanley
Published: December 2004

A novel method for measuring the isothermal compressibility of liquids has been devised. This method can be used to obtain compressibilities over a wide range of pressure quite rapidly. The compressibilities of C6H6, CCl4, and CH2Cl2 have been measured from 200 to 900 bars. When the Tait equation is used to extrapolate the present results to lower pressures, the agreement with other works is good.
Dipole Resonances in a Homogeneous Plasma in a Magnetic Field
Authors: Sturrock Peter A.
Published: December 2004

Radar observations recently made from a satellite orbiting above the ionosphere provide evidence for resonances of a plasma in a magnetic field which may be excited and detected by a dipole. The plasma may be said to be resonant, for a particular mode and frequency, if the group velocity is zero. These resonances are studied theoretically on the assumption that the dipole is of infinitesimal extent and that the plasma is excited by a charge or current impulse. The former assumption restricts the validity of the results to the asymptotic response of the plasma. The latter assumption is not a restriction. There are two electromagnetic resonances at the positive-frequency roots of ω2 ± Ωω − π2 = 0, where Ω is the electron gyro-frequency and π the electron plasma frequency, which occur at k = 0. There is also a resonance at ω = Ω, k = ∞, but this cannot be treated by the infinitesimal-dipole approximation and is deferred for separate study. ``Electrostatic'' resonances are treated in the quasi-electrostatic approximation. The resonant frequencies are π, (π2 + Ω2)½, and nΩ, n = 2, 3, …, and k = 0 at resonance. The infinitesimal-dipole model breaks down for the n = 2, 3, 4 cyclotron harmonics, but the infinitesimal line-dipole model and a line-charge model do not. The analysis shows that the oscillations decay asymptotically as an inverse power of time. The analysis also indicates that the response would be significantly stronger than is observed if measurements were made with a stationary dipole, indicating that the observed duration of the resonances is to be ascribed to the finite velocity of the satellite with respect to the exospheric plasma.
Numerical Solutions of the Nonlinear Equations for a Heated Fluid Layer
Authors: Fromm Jacob E.
Published: December 2004

The equations of the Boussinesq approximation to the Navier—Stokes equations are solved numerically for the problem of a fluid layer heated from below. Solutions are obtained throughout the range of Rayleigh numbers from critical to R = 107. Free boundary solutions are compared with analysis, and rigid boundary solutions are compared with experiment. The dimensionless heat transport varies as R⅓ for free boundaries and for rigid boundaries a variation of about R0.296 is observed. Excellent agreement is obtained with both analysis and experiments and by an examination of various modal behaviors a number of the observed properties of the flow can be explained.
Onset of Convection in a Layer of Fluid Cooled from Above
Authors: Foster Theodore D.
Published: December 2004

Experiments were performed in which a layer of water was cooled by evaporation from its top surface. The top surface temperature was measured using an infrared radiometer. The onset of manifest convective behavior was determined by visual observation of the motion of a thin layer of ink at the bottom of the water layer. Within the accuracy of the observations, the experiments show that at large Rayleigh numbers the time needed for the fluid to manifest convective behavior and the horizontal wavenumber of the disturbances amplified most at manifestation of convection are independent of the depth of the fluid layer.
Stability of a Conducting Fluid Flowing Down an Inclined Plane in a Magnetic Field
Authors: Hsieh Din-Yu
Published: December 2004

A stability analysis is made for the laminar flow of a layer of a viscous and electrically conducting fluid down an inclined plane in a transverse magnetic field. It is found that the effect of the magnetic field, revealed through the Hartmann number, is to stabilize the flow. A simpler and physically clearer approximate treatment of the same problem based on the principle of local balance is also given. The results agree quite satisfactorily with the exact analysis.
Study of Detonation in Condensed Explosives by One-Dimensional Channel Flow
Authors: Cowan G. R. , Balchan A. S.
Published: December 2004

The detonation of mixtures of 80/20 ammonium nitrate/trinitrotoluene was studied using pseudo one-dimensional channel flow. A layer of explosive was confined symmetrically by two relatively massive metal plates whose shock velocity was higher than the detonation velocity of any of the explosive mixtures studied, thus producing a close approximation to a steady-state two dimensional detonation. From measurements of the plate velocity the flow could be analyzed as a pseudo one-dimensional channel flow. The quantity (dP/dp)½ was found to have a maximum which served as an approximate experimental measure of the location of the Chapman—Jouguet point. The observed dynamic quantities were in substantial agreement with the Zeldovich—von Neumann—Doering model. Variation of the particle size of the ammonium nitrate produced a complex effect on reaction time, which could be adequately interpreted in terms of the three reaction steps in the detonation. Flash radiography provided a check on the one-dimensionality of the flow and allowed a rough estimate of the density profile behind the front, which was compared with the optical results.
Nonlinear Alfvén Waves in a Vlasov Plasma
Authors: Bell T. F.
Published: December 2004

Stationary solutions to the nonlinear Vlasov—Boltzmann equations are considered which represent one-dimensional electromagnetic waves in a hot magnetoplasma. These solutions appear in arbitrary reference frames as circularly polarized, sinusoidal waves of unlimited amplitude, i.e., as nonlinear Alfvén waves. Solutions are found implicitly by deriving a set of integral dispersion relations which link the wave characteristics with the particle distribution functions. A physical discussion is given of the way in which the Alfvén waves can trap particles, and it is shown that the presence of ``cyclotron-trapped'' particles introduces a boundary condition which no set of isotropic distribution functions can satisfy. An application of these solutions to theories of very low frequency emissions is briefly discussed.
Harmonic Generation in a Plasma due to a Velocity-Dependent Collision Frequency
Authors: Krenz J. H.
Published: December 2004

Harmonic components associated with the plasma electron velocity distribution function often result from a strong radio-frequency field. In this analysis, an expression is obtained for the third harmonic current which is a result of a velocity-dependent collision frequency. By introducing a low-collision frequency approximation and a collision frequency of the form ν = kvμ, the successive integrations necessary to obtain the third harmonic current are readily performed. As a result of this approximation which is valid for typical harmonic generation experiments, the third harmonic current is then shown to depend only upon various moments of the static isotropic part of the electron velocity distribution function. An estimate of this current is obtained by assuming a Maxwellian distribution. It is then shown that for a typical discharge configuration the third harmonic obtained due to this mechanism is small although not negligible compared to that observed experimentally.
Nonlinear Oscillations in a Hot Electron Plasma
Authors: Nayfeh Ali Hasan
Published: December 2004

The derivative-expansion method is applied to the longitudinal nonlinear traveling oscillations in a hot electron plasma. The frequency and wavenumber shifts obtained by using the above method agree with those obtained by using the Krylov-Bogoliubov-Mitropolsky perturbation method.
Classification of Instabilities from their Dispersion Relations
Authors: Sudan R. N.
Published: December 2004

Necessary and sufficient criteria are derived for classifying waves in complex media into evanescent, propagating, and growing waves (or instabilities). An absolute or nonconvective instability is shown to exist only if the complex group velocity dω/dk vanishes at some point in the upper half of the frequency plane. A physical interpretation of this result is given. The analysis is extended to include slowly varying inhomogeneous media.
On the Hydrodynamic Stability of Parallel Dusty Gas Flows
Authors: Liu J. T. C.
Published: December 2004

The physical implications of the stability of parallel flows of a dusty gas are studied. The over-all (gas plus particle) disturbance kinetic energy balance is contributed by dissipation due to the usual gas viscosity and augmented by the work done due to particle-gas interaction and energy conversion from the mean flow to the disturbances by both the gas and particle Reynolds shear stresses.

The viscous sublayer structure, where viscosity is known to be destabilizing, is obtained. The Reynolds shear stresses of both phases are derived from considering the relaxative nature of the disturbance vorticity diffusion process.
Hydromagnetic Eigenmodes in Multipole Fields
Authors: Carovillano R. L. , McClay J. F.
Published: December 2004

A formalism is developed providing an exact analytical procedure for determining linearized hydromagnetic wave phenomena in a perfectly conducting plasma permeated by a static magnetic multipole field. All perturbations are harmonically represented by scalar and vector spherical harmonics. The vector wave equation for the perturbed electric field is then reduced to a set of coupled equations in the radial variable alone. Different harmonic modes are coupled because the vector wave equation is not simply separable in spherical coordinates (or any other known system of coordinates). The physical significance of operative couplings derives from parity and angular momentum conservation requirements. It is shown that the radial equations are generally soluble in principle.
Stability Diagrams for Magnetogasdynamic Channel Flow
Authors: Hains F. D.
Published: December 2004

A study is made of the influence of a coplanar magnetic field on the stability of a conducting fluid flowing between parallel planes. After derivation of the general stability equations for small magnetic Reynolds number, numerical results are obtained for the case where initial perturbations of the magnetic field vanish. This must occur if the channel walls have zero or infinite conductivity. Four sets of stability diagrams are presented so that each stability curve will represent the effect of a given applied magnetic field as only one of the four quantities in the Reynolds number is changed. The flow is always stable for initial disturbances of the field produced by passage of a pulsating current through walls of finite conductivity.
Insulator Ablation in Magnetic Piston Shock Tubes
Authors: Workman J. B.
Published: December 2004

The effect of end wall insulator ablation on the performance of magnetic piston shock tubes has been investigated theoretically. From the analysis of a steady flow model, a simple correlation parameter has been derived that permits a quick determination of the loss in a given experiment. The parameter is a function only of the magnetic drive field, initial test gas density, and the ionization energy of the insulator vapor. The transient heating of the insulator that initiates the vaporization is discussed as is the effect of degassing adsorbed material at the wall surface.
Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface
Authors: Harlow Francis H. , Welch J. Eddie
Published: December 2004

A new technique is described for the numerical investigation of the time-dependent flow of an incompressible fluid, the boundary of which is partially confined and partially free. The full Navier-Stokes equations are written in finite-difference form, and the solution is accomplished by finite-time-step advancement. The primary dependent variables are the pressure and the velocity components. Also used is a set of marker particles which move with the fluid. The technique is called the marker and cell method. Some examples of the application of this method are presented. All non-linear effects are completely included, and the transient aspects can be computed for as much elapsed time as desired.
Eddy Formation in an Eccentric Annular Domain
Authors: Bentwich M. , Elata C.
Published: December 2004

The slow motion of a viscous incompressible fluid in the space bounded by two long parallel non-concentric circular cylindrical solid surfaces is studied. The outer one is stationary while the inner one rotates steadily. Both analysis and experiment show that when the ratio of eccentricity to average gap width is sufficiently large an eddy is formed. In such case part of the fluid rotates around the inner surface. The rest rotates in the opposite direction around a line parallel to the axes. This phenomenon has an interesting analogy in the theory of plates' deflection.
Laminar Boundary Layer on a Cone with Uniform Injection
Authors: Libby Paul A.
Published: December 2004

A solution for the laminar boundary layer on a cone with uniform mass transfer is obtained. The velocity field is found for either suction or injection, but the related solution for the energy field is subject to an energy balance at the exposed surface and is therefore valid only for injection. This latter solution is equally applicable to certain species fields as well. The present results along with those presented previously for the two-dimensional case permit a comparison of the effect of injection on boundary layers over two-dimensional and conical surfaces.
Collisionless Damping of Nonlinear Plasma Oscillations
Authors: O'Neil Thomas
Published: December 2004

It is well known that the linear theory of collisionless damping breaks down after a time τ ≡ (m/eεκ)½, where κ is the wavenumber and ε is the amplitude of the electric field. Jacobi elliptic functions are now used to provide an exact solution of the Vlasov equation for the resonant electrons, and the damping coefficient is generalized to be valid for times greater than t = τ. This generalized damping coefficient reduces to Landau's result when t/τ ≪ 1; it has an oscillatory behavior when t/τ is of order unity, and it phase mixes to zero as t/τ approaches infinity. The above results are all shown to have simple physical interpretations.
Heat Transport Between Parallel Plates in a Rarefied Gas of Rigid Sphere Molecules
Authors: Frankowski K. , Alterman Z. , Pekeris C. L.
Published: December 2004

The linearized Boltzmann integral equation is solved for the problem of conduction of heat between parallel plates in a rarefied gas of rigid sphere molecules. The solution is obtained as an expansion in terms of the eigenfunctions of the Boltzmann collision operator for a Maxwell gas. The temperature distribution between the plates has been determined for Knudsen numbers X0 = d/2l ranging from 0.01 to 500, d denoting the distance between the plates and l the mean free path. The temperature varies linearly through most of the region, except for a ``Knudsen layer,'' of a thickness of a few mean free paths, near the wall, where the temperature rises above the straight line. Near the wall there is also a temperature jump ΔTw whose magnitude becomes negligibly small as the distance between the plates exceeds a few mean free paths. In the linear region, the gradient of the temperature can be determined by assuming a virtual extension of the spacing between the plates by a distance Δ which is equal to 2l in the Knudsen limit, and reaches an asymptotic value of around 7l in the Clausius limit of a dense gas. In the Knudsen limit of extreme rarefaction, when the spacing between the plates is only a small fraction of l, the temperature in the gas is nearly constant, and the deviation from the average temperature of the plates takes place entirely as a temperature jump ΔTw at each wall.
Scattering of Electrostatic Waves by Inhomogeneities in a Plasma
Authors: Sturrock P. A.
Published: December 2004

A plane wave excited in an infinite uniform plasma preserves its identity but a similar wave set up in an inhomogeneous plasma will change in the course of time. If the inhomogeneities are weak, one may analyze the excitation at any instant into plane waves, the normal modes of the homogenized plasma. The effect of inhomogeneities is to distribute the energy of a single initial plane wave among a spectrum of waves. By studying the time-development of this process, one can assign an equivalent damping coefficient. There is discussion of the possibility that inhomogeneities may, in this way, suppress an instability, such as two-stream instability.
Radiation Processes in Plasmas
Authors: Birmingham T. , Dawson J. , Oberman C.
Published: December 2004

The problem of arbitrary test current sources embedded in an infinite spatially homogeneous Vlasov plasma is considered. By computing the rate at which the test sources do work on the plasma, the energy emission into transverse and longitudinal waves is obtained. A variety of radiation problems can be handled by appropriate choice of the current sources. Use of the time varying dipole moment due to encounters between shielded electrons and ions leads to expressions for the bremsstrahlung spectra. If the currents are produced by the interaction of waves with density fluctuations, the scattering and coupling of waves is obtained. By equating the rate of emission of longitudinal or transverse waves to their rate of absorption, expressions for the steady-state energy densities of such waves are obtained.
Magnetic Compression of Collision-Free Plasmas with Charge Separation
Authors: Rossow Vernon J.
Published: December 2004

An analysis made previously by Auer, Hurwitz, and Kilb on one-dimensional unsteady magnetic compression waves passing through a cold, collisionless, fully ionized plasma in a direction perpendicular to the ambient magnetic field is extended here to include charge separation. Introduction of a charge attachment parameter, Rf = (ωpi/ωci)2, makes it possible to treat the ions and electrons as two separate fluids that are coupled through electric and magnetic fields in the plasma. Changes in the structure of the compressed layer with the charge attachment parameter from the loosely coupled situation, Rf = 1, to the one where rigid fastening is assumed, Rf = ∞, are illustrated for both a weak and a strong compression wave. A fine structure attributable to electron oscillations in the flow field is found when the two species are loosely coupled. The wavelength of both the small and large oscillations are associated with the upper and lower hybrid frequencies, respectively. It is also found that ion sheets interchange positions or mix on a large scale but the electrons do not for moderately strong compression waves. However, both ions and electrons are found to mix if the compression wave is very intense. An approximate rule is presented for the lower limit of the Alfvén Mach number of the wave front at which electron mixing on a large scale is induced.
Structure of the Boltzmann Collision Operator
Authors: Finkelstein Leib
Published: December 2004

The full Boltzmann collision operator with an infinite collision cross section is investigated. It is shown that in the general case the operator is bilinear in F and ∂F/∂ξ and three different representations of it are given. The linearized collision operator is further explored and a new expression for the kernel in the form of a divergence is obtained. An approximation to the linearized operator is indicated, which may prove of value in numerical calculations.
Experimental Study of the Collimation Problem in a High-Intensity Molecular Beam
Authors: Skinner G. T. , Moyzis J.
Published: December 2004

The discrepancy between the experimentally observed beam intensities obtained with nozzle sources, and the intensities predicted by the inviscid theory is generally attributed to viscous effects upstream of the ``skimmer.'' Experiments are described which show the scattering of a 1.2-eV nitrogen beam downstream of a ``skimmer'' or collimator. Such scattering can only result from collisions with slow molecules, traveling with the beam, coming from the viscous region upstream. Elimination of this scattering was accomplished by limiting the radial extent of the flow field approaching the ``skimmer,'' and beams were obtained having the theoretically available intensity.
Spectroscopic Study of a Highly Ionized Hydrogen Plasma
Authors: Cooper William S. , Kunkel Wulf B.
Published: December 2004

Experimental details are given for time- and space-resolved determinations of electron temperature and density in a highly ionized, decaying-hydrogen plasma. The technique used involves absolute intensity measurements of the Hβ line and of two widely separated portions of the continuum. A carbon arc is used as a radiation standard. The inferred ion density agrees satisfactorily with that deduced from Stark broadening of the Hβ line. Internal consistency among various methods of inferring a temperature indicates when and where the technique yields reliable results. It is shown that the plasma (Ne ≈ 4 × 1015 cm−3, Te ≈ 1 to 2 × 104 °K), which is produced in a long cylinder in a strong axial magnetic field, decays by volume recombination. Diffusion losses appear to be negligible.
Hydromagnetic Waves in a Nonuniform Current Carrying Plasma Column
Authors: Pneuman G. W.
Published: December 2004

The axially symmetric modes of propagation of hydromagnetic disturbances in a current-carrying plasma column with a nonuniform mass-density distribution are investigated. The current density is assumed to be uniform. The column is surrounded by a vacuum and immersed in a uniform axial magnetic field. In the limit of small discharge current, two uncoupled modes of oscillation can take place. One involves a radial pulsation of the column with associated pressure, density, and temperature fluctuations, while the other is a torsional motion. The torsional mode is not accompanied by fluctuations in the thermodynamic properties. The properties of both the radial and torsional mode such as phase velocity, group velocity, cutoff frequency (radial mode only) and attenuation are discussed in detail. The density gradient in the plasma is found to appreciably alter the torsional mode producing distortions in the wave fronts and significantly increasing the attenuation.
Control of Plasma Drift in the Thetatron
Authors: Reynolds J. A. , Aldridge E. E. , Keilhacker M. , Niblett G. B. F.
Published: December 2004

The linear theta pinch drifts laterally with an acceleration directly proportional to the magnetic field gradient and temperature; for example, a magnetic field gradient of only 1 G in 100 kG causes a 1-keV plasma to drift to the wall of a 10-cm-diam tube in 100 μsecs. Four main sources of magnetic field gradient are proposed and examined experimentally; the coil end, the collector shape, the collector-coil discontinuity and the plasma influence. The magnetic field gradient may be controlled by sectionalizing the coil at regular intervals, or by a tab between the coil and collector or, more conveniently, by the use of an ``inductive lens.''
Laminar Boundary Layer with Uniform Injection
Authors: Libby Paul A. , Chen Karl
Published: December 2004

The nonsimilar velocity distribution in a two-dimensional laminar boundary layer with uniform external stream and with either uniform suction or injection is obtained by a series expansion in terms of a mass transfer parameter. The results are compared with more accurate analysis and shown to be in good agreement for a range of values of this parameter. The solution for the velocity distribution is then employed for the calculation of the distributions of energy and element mass fraction when there are imposed requirements for energy and mass balance at the exposed surface of a porous plate with uniform injection. As one example of several possible applications of these solutions, there is computed the flow associated with the injection of hydrogen into an air stream according to the flame sheet model.
Shock Structure in a Partially Ionized Gas
Authors: Jaffrin Michel Y.
Published: December 2004

The structure of a steady plane shock in a partially ionized gas is investigated using the Navier-Stokes equations for the atom, electron, and ion fluids. Across the shock, quasi-neutrality and frozen ionization is assumed. For all degrees of ionization there is shown to be a broad thermal layer of elevated electron temperature ahead of the shock front and a precursor and imbedded axial electric field induced by the charge separation. Because of the large atom-ion charge exchange cross section, ion slip is small for less than 30% ionization. In a weakly ionized plasma, the atom flow is unaffected by the ionized particles and the structure consists of an ordinary atom shock imbedded in the thermal layer. For substantial ionization, the heavy particles are compressed and heated in the thermal layer and in the shock the ion and atom temperatures overshoot their downstream values. The induced electric fields increase with degree of ionization and free stream Mach number while the shock thickness decreases. A measurement in partially ionized hydrogen of potential variation in a strong shock gives a potential rise across the imbedded shock and thickness in good agreement with the calculated values.
One-Dimensional Gases with Hard-Core Repulsion
Authors: Baxter R. J.
Published: December 2004

An elementary mathematical device previously employed to derive the statistical mechanical properties of a classical one-dimensional gas with interaction potential that satisfies a linear differential equation with constant coefficients over the domain (0, ∞) is shown to be also applicable when the potential contains a repulsive hard core. In particular, the thermodynamic properties of a one-dimensional plasma of hard rods and of the gas model of Kac are derived. The infinite-range phase transition obtained in the latter case by Kac, Uhlenbeck, and Hemmer is found to be amenable to investigation by the methods used.
Equilibrium Distribution Functions for a Classical Electron Gas
Authors: Hirt C. W.
Published: December 2004

The cluster expansion techniques of Mayer and Abe are applied to a calculation of the exact equilibrium s-particle distribution function for a classical electron gas in a positive background. The radial distribution function is found to be well approximated by the Boltzmann factor for a Debye—Hückel potential. Corrections to the Debye—Hückel expression are discussed. A simple approximation for the s-particle correlation function is given in terms of a three-fold integral.
Experimental Studies of the Penetration of a Plasma Stream into a Transverse Magnetic Field
Authors: Baker D. A. , Hammel J. E.
Published: December 2004

The interaction of a dense (n ≃ 3 × 1013 cm−3), fast (v ≃ 4 × 107 cm/sec) plasma stream with a transverse magnetic field is studied experimentally by injecting a plasma from a coaxial gun perpendicular to the magnetic field of a pair of mirror coils. The experiments show that the stream from such a gun can penetrate magnetic fields up to ∼9 kG. A rapid field-plasma intermixing takes place and the injected stream crosses the magnetic field by electrically polarizing and producing an E × B drift. It was found that the forward motion of the stream can be stopped by draining the polarization charge by current flow along field lines to a shorting conductor located outside a magnetic mirror. Measurements of stream thickness normal to the magnetic field and the effectiveness of the depolarizing conductors have been made as a function of the strength of the transverse field. The exclusion of the plasma from high magnetic fields, and the variation of stream width with magnetic field intensity are due to plasma polarization effects rather than plasma diamagnetism. Observations on high energy electrons > 200 keV which are produced during the experiment are discussed.