bluuebunny/crossref_metadata_2025 huggingface dataset:
Width of the Turbulent Trail behind a Hypervelocity Sphere
Authors: Slattery R. E. , Clay W. G.
Published: December 2004

The growth of the gross turbulent trails behind hypervelocity spheres (velocity = 9000 ft/sec) has been measured at 40, 100, and 760 mm Hg of air pressure for about 104 diameters behind the sphere. The pressure range corresponds to a factor of 19 change in Reynolds number. Little difference is noted in the growth as a function of pressure, although the lower pressure trail does tend to grow slightly more slowly than at one atmosphere. The atmospheric trail grows as a ½-power function of length while the lower pressure data follow a ½ power for about the first 50 sphere diameters of trail and a ⅓ power thereafter.
Shock Waves in Radiation-Magneto-Gas Dynamics
Authors: Pai S. I. , Speth A. I.
Published: December 2004

The general Rankine-Hugoniot relations for a normal shock wave in radiation-magneto-gas dynamics are investigated. These relations differ considerably from those without radiation effects, particularly for the case that the gas is initially so hot that the radiation pressure is not negligible. For a given strength of the shock wave, the temperature jump across the shock with radiation effect is much smaller than that without radiation effect. Various limiting cases are discussed. In certain cases, the results may be expressed in terms of an effective ratio of specific heats and an effective gas pressure. A general method of solution by successive approximations is given and some numerical results are obtained.
Electrohydrodynamic and Magnetohydrodynamic Surface Waves and Instabilities
Authors: Melcher James R.
Published: December 2004

Low-frequency dynamics of a plane fluid interface stressed by tangential or perpendicular electric or magnetic fields is studied emphasizing the duality of the magnetic and electric cases. Both configurations are shown to be controlled by an effective Alfvén velocity for the magnetic cases, and by an electrohydrodynamic dual to this velocity for the electric cases. A wavelength and threshold for instability are predicted for a surface stressed by a perpendicular field, and correlated with experimental results. This makes possible a critical experiment to determine the nature of interfacial electrostriction in dielectrics. A dielectric interface stressed by a tangential electric field supports incompressible electrohydrodynamic transverse waves that propagate along the lines of electric field intensity at a velocity strongly influenced by interfacial electrostriction. Experimental results indicate the existence of such waves.
Magnetohydrodynamic Channel Flow under Time-Dependent Pressure Gradient
Authors: Yen J. T. , Chang C. C.
Published: December 2004

Hartmann's work on magnetohydrodynamic channel flow is extended to include the case with a time-dependent pressure gradient. Cases treated are: (a) suddenly applied pressure gradients which are periodic in time, and (b) pressure gradients which, with respect to time, are step and delta functions. The channel walls are assumed to be perfectly conductive. As a limiting case, the solution for hydrodynamic channel flow with a time-dependent pressure gradient is also given. The nature of viscous and magnetic drag on the wall is discussed. By use of the convolution integral and super-position principle, solutions can be obtained for any arbitrary time-dependent pressure gradient. Figures show the physical consequence of the solutions.
Hydromagnetic Stability of Toroidal Equilibria with an Externally Imposed Rotational Transform
Authors: Johnson John L. , Greene John M.
Published: December 2004

An expansion technique is employed to study the stability condition for toroidal hydromagnetic configurations in which the curvature of the system, the rotational transform per unit length, and the pressure which is contained in the system can be treated as small. The most general condition which is necessary for stability with respect to localized perturbations is obtained as a ratio of two infinite determinants.
Viscous Flow through Porous Media
Authors: Prager Stephen
Published: December 2004

The resistance of a porous medium to a fluid streaming through it is estimated by minimizing the rate of energy dissipation for a class of trial stress distributions. Rigorously valid lower bounds on the resistance are obtained in terms of certain two- and three-point averages characterizing the medium. Results are given for flow both with and without slip at the pore walls.
Conductivity of Slightly Ionized Gases
Authors: Taylor Leonard S.
Published: December 2004

A kinetic theory of the conductivity of a slightly ionized gas is developed to distinguish between alternate expressions derived by Desloge et al. from the Boltzmann transport equation. It is determined that the current in a Lorentzian model is obtained by averaging the electron drift velocity over a function resembling the zero field distribution shifted by the drift velocity. The linear term corresponds to one of the proposed expressions. Nonlinear terms may also be obtained. The quadrature current is increased by a factor proportional to the ratio of the average electron kinetic energy in the field to the kinetic energy in the absence of the field when the first nonlinear term is included.
Experiments on Alfvén-Wave Propagation
Authors: Wilcox John M. , DeSilva Alan W. , Cooper William S.
Published: December 2004

Torsional hydromagnetic waves are generated in a cylindrical hydrogen plasma. The device that generates the plasma is described. Spectroscopic observation of Stark-broadened Balmer lines gives the ion density as a function of time and indicates that the plasma is highly ionized. Reflections of the hydromagnetic waves are observed from high- and low-impedance boundaries, and from a plasma-neutral gas interface. The phases of the reflected waves are found to agree with theory. The driving current that generates the waves is analyzed in terms of Newcomb's principal modes. The measured radial distribution of the wave magnetic field is in fair agreement with this analysis, and the observed wave magnetic field amplitude agrees to within 15% with that predicted on the basis of the voltage applied at the driving electrode, decreased by the measured damping factor. Two different types of measurement suggest that the decaying plasma is electrically isolated from the (conducting) walls.
Alfvén Waves in Solid-State Plasmas
Authors: Buchsbaum S. J. , Galt J. K.
Published: December 2004

Alfvén waves can be studied experimentally in certain solid-state plasmas with greater facility than in gaseous plasmas. This results from the fact that in these solid-state plasmas all the charge carriers have masses equal to or less than the free electron mass. Alfvén waves can thus be studied at microwave frequencies. Previously published experimental results on microwave absorption in bismuth are reinterpreted in terms of the properties of Alfvén waves.
Hydromagnetic Equilibria in a Toroid from the Particle Point of View
Authors: Kulsrud Russell M.
Published: December 2004

Hydromagnetic equilibria are considered as being time-independent solutions of the Boltzmann equations and Maxwell's equations. The short-range collisions are neglected and the magnetic field is taken large enough to make the small gyration radius low-frequency expansion of the equations by Chew, Goldberger, and Low (unpublished work) applicable. The equilibria are discussed only to lowest order in this scheme and in geometries topologically equivalent to a torus. In particular, magnetic surfaces are shown to exist. A set of invariants for slow motions of the system are determined. These invariants are used as constraints in a variational principle which states that subject to these constraints an arbitrary configuration makes the energy stationary if, and only if, it is an equilibrium state. The case of equilibria with trapped particles is treated separately. It is proposed that the values of these invariants serve to characterize toroidal hydromagnetic equilibria.
Stationary Nonlinear Plasma Oscillations
Authors: Wilhelmsson Hans
Published: December 2004

The frequency of nonlinear free oscillations is investigated in the following one-dimensional situations: (1) cold plasma including ion motion; (2) plasma with a spread in the velocity distribution; and (3) the two-stream case. In each case a dependence of the frequency on the degree of nonlinearity is obtained.
Expansion and Contraction of Capillary Jets of Newtonian Liquids
Authors: Middleman S. , Gavis J.
Published: December 2004

Laminar jets of Newtonian liquids are found to contract or to expand upon ejection from a capillary nozzle depending upon conditions of ejection and fluid properties. The ratio of final jet diameter to nozzle diameter is a function of Reynolds number Re and a weak function of Weber number. At Re < 16 the jets expand, above 16 they contract. At Re < 6 expansion becomes independent of Re at a diameter ratio of 1.06, if the Weber number dependence is removed. At Re > 150 contraction becomes independent of Reynolds number at a diameter ratio of 0.87. These results are explained by means of the momentum and energy equations for the motion. The terms in the equations leading to expansion are comparable to relaxing normal stress terms. The existence of relaxing normal stresses in Newtonian liquid jets leads to some questions concerning the origin of normal stresses which are thought to be responsible for the more common observation of expansion in viscoelastic liquid jets.
Upstream Diffusion in Hagen-Poiseuille Flow
Authors: Passell T. O. , Perry C. L.
Published: December 2004

A theoretical study is described for steady state diffusion of a contaminant from a large reservoir of static fluid into a cylindrical tube discharging fluid into the reservoir. Contaminant decay is considered. Numerical results are presented for the rate of decrease along the tube of the concentration of contaminant for Reynolds × Schmidt numbers > 10 and either small or zero decay. The method used explicitly exhibits quantities of physical interest including a simple form for the asymptotic solution. These results are of practical use in estimating the contamination in the tube at points that are relatively close to the mouth of the tube. An estimate is made of the distance from the tube mouth at which the asymptotic solution given becomes valid. Used for the prediction of heat flow, the results are valid for Péclet numbers > 10.
Transient Two-Phase Capillary Flow in Porous Media
Authors: Elrick D. E.
Published: December 2004

The dynamics of two-phase capillary displacement in a finite one-dimensional system following a step change in pressure of one phase at one end is considered. Darcy's law and the equation of continuity for each phase together with the capillary pressure-saturation relation are the fundamental equations describing the flow system. The resulting system of differential equations is linearized by assuming a linear relationship between the capillary pressure and the saturation as well as constant conductivity values of both phases (these assumptions are valid for small step changes in pressure). Solutions of the linearized problem are found and presented in some detail. In the limiting case as the conductivity of one phase becomes much greater than the other, the solution reduces to the (known) single-phase solution.
Exact Relativistic Fokker-Planck Coefficients for Plasma and Radiation: III
Authors: Simon Albert
Published: December 2004

Exact relativistic Fokker-Planck coefficients have been derived earlier [A. Simon, Phys. Fluids 4, 586 (1961)] for the case of a plasma composed of electrons and infinite mass ions. These results are now generalized to the case of an arbitrary number of finite-mass ion species.
Radio Emission by Plasma Oscillations in Nonuniform Plasmas
Authors: Tidman D. A. , Weiss George H.
Published: December 2004

The electromagnetic radiation emitted when a field of longitudinal plasma oscillations is incident on a localized fluctuation in density in a plasma is calculated. Use is made of the collisionless Boltzmann equation to describe the electron component of the plasma and compare the results with those previously obtained using the moment equations for this problem.
Effects of Ionization and Magnetic Initial Conditions on a Magnetically Compressed Plasma (Scylla)
Authors: Little E. M. , Quinn W. E. , Ribe F. L.
Published: December 2004

The effects of strong preionization and the application of steady bias magnetic fields on the operation of the magnetic compression device Scylla are studied. It is shown that both strong preionization and a bias field B0 antiparallel to the main compression field Bz are necessary to produce neutrons during the first half-cycle of Bz. Other aspects of the plasma activity are also shown to depend strongly upon the sign of B0. Application of bias fields with weak preionization leads to production of hard x rays which occur on the half-cycle of the discharge which precedes that of neutron emission. When hard x rays are produced the plasma is not hydromagnetic. The hard x rays are extinguished when there is strong preionization, leading to a hydromagnetic plasma. In the case of the hydromagnetic plasma it is concluded that antiparallel B0 plays its role early in a given half-cycle and affects the plasma primarily during its preheating, ionization phase, rather than during the adiabatic-compression phase which follows it. An interpretation is given in terms of a plasma sheath which has special properties when it separates magnetic fields of opposite signs.
Influence of Coulomb Interactions on the Cyclotron Radiation of Electrons Moving on a Single Orbit
Authors: Gajewski Ryszard , Hirshfield Jay L.
Published: December 2004

The incoherent cyclotron radiation at the nth harmonic of the cyclotron frequency from N electrons moving on a single orbit is shown to be reduced by at least a factor π2n2N−ρ as a result of the nearest-neighbor Coulomb interactions (ρ ≥ 1), whenever the electron's random thermal energy is less than the Coulomb energy. The conditions under which this theory is valid are compared with those prevailing in the Astron E layer.
Stability of a Plasma Boundary in a Magnetic Field
Authors: Lehnert B.
Published: December 2004

The stability of a plasma confined by a magnetic field has been discussed by Rosenbluth and Longmire in terms of particle orbits and the results applied to a plasma separated from vacuum by a sharp boundary which is rippled by a sinusoidal perturbation. This earlier theory is reconsidered and extended to include the effects of a finite density gradient. Drift motions along the boundary are also discussed for displacements comparable to and exceeding the wavelength of the perturbation. For small wavelengths it is found that the plasma is stable against small flute deformations not only for a magnetic field which is convex towards the plasma but also for a field which is concave towards the plasma, provided that the latter has a sufficiently strong gradient and that the density distribution is not too steep. Even in the unstable case the growth rate is reduced very much compared to the situation studied by Rosenbluth and Longmire. The result provides a possible explanation of the observed stability of the Van Allen radiation belts and in experiments with magnetic mirrors and rotating plasma devices.
Plasma as a Microwave Amplifier
Authors: Rand S.
Published: December 2004

A mechanism is postulated for which a streaming plasma may transmit energy to a traversing radiation field, and thereby enhance the signal. For a laboratory plasma, only resonance frequencies over a narrow band may be amplified by this method. Large amplification over a broad frequency range is postulated for an astronomical gas.
Injection and Trapping of a β = 1 Plasma into a Cusped Magnetic Field
Authors: Hagerman D. C. , Osher J. E.
Published: December 2004

An experiment using a plasma gun as a source to inject a high-velocity jet of plasma into a picket fence magnetic confinement system is described. The results show that a plasma jet having 5 × 1013 deuterons/cm3 and a mean directed kinetic energy of 1 kev/deuteron is able to traverse a 2-kg magnetic barrier displacing the field completely in its path, i.e., traveling as a β = 1 plasma. Some focusing of the plasma jet occurs during the penetration which increases its density. If the plasma is injected into a higher field it mixes with the field and penetrates as a β < 1 plasma. These two phenomena combine so that the idealized sudden stopping of a given beam at a critical magnetic field (Bc2 > 12πρV2) is not observed. For fields <2000 gauss the plasma jet opens the entrance cusp for ≈ 3 μsec; a biconical diamagnetic region with β = 1 builds up within the picket fence volume and then decays with a time constant of 50 μsec. This indicates that some irreversible process does occur, trapping plasma within the magnetic confining field.
Transient Magnetohydrodynamic Duct Flow
Authors: Lundgren T. S. , Atabek B. H. , Chang C. C.
Published: December 2004

Parallel flow of an electrically conducting viscous incompressible fluid in a rectangular duct with transverse magnetic field is considered. The walls of the duct which are parallel and perpendicular to the imposed magnetic field are taken to be nonconducting and perfectly conducting, respectively. Assuming the fluid to be at rest at the initial moment, exact solutions for the velocity and magnetic field components are obtained in the form of convolution integrals taking the longitudinal pressure gradient as an arbitrary given function of time. Later, taking a step function for the pressure gradient, these expressions are integrated. For this case, the effect of the strength of the imposed magnetic field on the development behavior of the flow is studied. It is found that except for very large magnetic fields, the flows are over damped.
Stability of a Current-Carrying Plasma
Authors: Bernstein Ira B. , Kulsrud Russell M.
Published: December 2004

The critical current is obtained for the onset of ion wave instability in the experimentally interesting case of a current-carrying plasma with an electron distribution function given by the conductivity theory of Spitzer and Härm. The results are presented in a form suitable for comparison with experiment.
Diffusion in a Slightly Ionized Gas with Application to Effusion from a Shock Tube
Authors: Sturtevant Bradford
Published: December 2004

A sampling technique for measuring the diffusive flux of charged particles from an ionized gas to a cold wall by measuring the effusive electrical current through a small orifice in the wall has been used to study slightly ionized argon behind reflected shock waves. The technique is described and the transient diffusion process upon which it depends is considered in some detail. Computations based on a simple one-dimensional isothermal charge diffusion model illustrate the features and give the result that the effect of the electric body forces is generally greater on the ions and less on the electrons than originally expected. These results are used in an approximation to the nonisothermal problem to give a relation between the measured effusive current and the ion density in the hot gas. Preliminary observations of the dependence of ion density on time and temperature in the initial stages of ionization relaxation are reported. Simple considerations of the chemical kinetics indicate that for the portion of the process observed (degree of ionization about 10−5 times the equilibrium value) the ionization of argon results from a complicated series of consecutive reactions.
Kelvin-Helmholtz Instability in Media of Variable Density
Authors: Alterman Z.
Published: December 2004

The instability of two fluids separated by a horizontal boundary and in relative horizontal motion is investigated in the case of densities varying exponentially with height. There is a striking similarity between the effects of density variation and of rotation on the onset of instability. Conditions for stability are given, and the effect of a superposed magnetic field is discussed.
Ignition Temperature Approximation for Bimolecular Detonations
Authors: Hirschfelder J. O. , Curtiss C. F. , Barnett M. P.
Published: December 2004

The theory of detonations including the effects of transport properties is applied to a detonation supported by the bimolecular reaction 2 A → 2 B. For simplicity, the ignition temperature approximation is used and it is assumed that the Prandtl number is three-fourths and the Lewis number is unity. Very little difference is found between the properties of a bimolecular and a unimolecular detonation. However, because of the unrealistic nature of ignition temperature chemical kinetics, it is not possible to reach any conclusion regarding experimental gaseous detonations.
Droplet Motion in Purified Systems
Authors: Winnikow S. , Chao B. T.
Published: December 2004

Experimental results are presented of the behavior of droplets, falling in water at Reynolds numbers ranging from 138–971. The location of flow separation and the wake configuration were studied with a shadowgraph optical system. The measured drag coefficients were found to be higher than predicted by Chao, who assumed complete internal circulation and negligible flow separation. The agreement was improved when a correction for the pressure drag was introduced. The latter was found to be essentially due to flow separation but not to the pressure differences across the boundary layer as asserted by Moore. In the nonoscillating range the viscous drag remains predominant, and there exists a systematic dependence of the drag coefficient on a property parameter associated with the propensity of the droplet to develop internal circulation. That parameter is also a significant group in correlating droplet deformation in pure systems. The onset of sustained droplet oscillation was observed to coincide with the onset of the periodic shedding of vortices. The transition to oscillation occurs at a critical Weber number of approximately 4, at which point there is a sharp increase of the drag coefficient.
Flow Nonuniformity in Shock Tubes Operating at Maximum Test Times
Authors: Mirels H.
Published: December 2004

Shock tube flow nonuniformity is investigated in the limit where the shock and contact surface have reached their maximum separation. Ideal gases are considered. It is found that all fluid properties increase in value between the shock and contact surface. The nonuniformity is greatest when γ (ratio of specific heats) is large and Ms (shock Mach number) is low. For γ = 53 and Ms ≥ 3, the static temperature, density, and pressure increase by about 8, 12, and 20%, respectively; the stagnation temperature increases by about 35%, and the stagnation pressure, dynamic pressure, and stagnation point heat transfer increase by about a factor of 2. These results apply to turbulent as well as laminar boundary layers. The variation of flow properties with distance behind the shock, as well as particle time of flight, is given for both wholly laminar and wholly turbulent wall boundary layers. These results are particularly important for chemical rate and heat transfer studies.
Stability of Couette Flow of Dilute Polymer Solutions
Authors: Rubin H. , Elata C.
Published: December 2004

The critical Taylor numbers Tc and corresponding nondimensional wavelengths of the vortex cells εc were experimentally determined for various polymer solutions. The measurements show that for the investigated dilute solutions Tc increases with concentration while εc remains constant. These results, together with normal stress differences measured previously in more concentrated solutions of other polymers, are compared with characteristics displayed by several rheological models of viscoelastic fluids. It is shown that, of the models considered here, only Ericksen's anisotropic fluid may be suitable to describe the investigated solutions.
Numerical Study of the Stability Problem for Couette Flow
Authors: Capriz G. , Ghelardoni G. , Lombardi G.
Published: December 2004

A numerical method was used to solve the equations for the viscous flow of a liquid between concentric rotating cylinders at Taylor numbers above the critical value. Thus, the intensity of Taylor vortices and the value of the viscous losses could be determined; the results are expressed in a number of graphs.
Continuum Feedback Control of Instabilities on an Infinite Fluid Interface
Authors: Melcher James R.
Published: December 2004

Field-coupled Rayleigh-Taylor instabilities on a fluid interface can be suppressed by means of feedback. Deflections of the interface are detected to provide a signal which is amplified and fed back to a structure coupled to the interface through the fields. A theoretical study is given of the conditions for stability of an infinite interface coupled to an active structure through a perpendicular electric field and a tangential magnetic field. In both cases the interface is assumed to be perfectly conducting. A traveling wavetrain analysis is used to show the regimes of stability as they depend on the Taylor wavelength, electric or magnetic pressure, feedback gain, and technique of sampling interface deflections. Emphasis is given to the effect of feedback derived from detecting surface deflections averaged over a sampling area and feeding back to that same area.
Kinetic Model for Three-Component Plasmas with Ionization
Authors: Hu Pung Nien , Ziering Sigi
Published: December 2004

Ionization processes are usually introduced into the equations of magnetohydrodynamics as gross parameters to be determined by experiment. The mathematical accessibility of model kinetic equations in neutral and ionized gases motivates the formulation of kinetic equations for a three-component plasma which incorporate the ionization process in this study. As a first attempt, only the ionization processes resulting from electron-neutral collisions are considered. The resulting mathematical formalism yields a set of model equations which are mathematically not more complicated than those for plasmas without consideration of ionization. The possible application of the present model equations to various problems is discussed, such as the ionization growth in a gas, the cathode sheath, and the structure of an ionizing shock wave.
Plasma Thermal Conductivity with Collective Effects
Authors: Rand S. , Levinsky E. S.
Published: December 2004

The electron thermal conductivity of a fully ionized Lorentz gas has been studied. The energy transfer among regions of the gas at different local temperatures has been determined by considering the emission and absorption of longitudinal plasma waves. These waves are both collision and Landau damped; the latter type of damping effects the energy transfer only secondarily, since the resulting energy does not go directly into the heating of the gas. The results obtained by assuming infinite Landau damping are expected to agree with typical two-body collision treatments. However a non-vanishing plasma parameter, which results in finite Landau damping, facilitates the introduction of a variety of collective effects. Thus, it is found that, beyond the dependences obtained in conventional two-body collision studies, the thermal conductivity exhibits an additional weak dependence on the plasma parameter.
Pair Production of Plasma Vortices
Authors: Bostick W. H. , Prior W. , Grunberger L. , Emmert G.
Published: December 2004

Image converter photographs of various interfaces between a magnetic field and an accelerated plasma show clearly the production of plasma vortex filaments in pairs. These vortex filaments fall into two classes: those parallel to B0 (the background magnetic field) and those perpendicular to B0.
Continuum Feedback Control of a Rayleigh-Taylor Type Instability
Authors: Melcher James R. , Warren E. Paul
Published: December 2004

The electrohydrodynamics of a highly conducting interface stressed by a perpendicular electric field and attached (by surface tension) to a rigid circular wall are described in terms of a set of normal modes which satisfy four boundary conditions. The interface can be unstable either because of gravity (a heavy fluid on top of a light fluid) or because of the electric field. The experimental eigenfrequencies, eigenfunctions, and conditions for instability are compared to the theory. These modes are then used to describe the dynamics when the interface displacement is detected and a proportionate potential is fed back to the segmented electrode which imposed the quiescent electric field. Electronic means for detecting interface disturbances are described, together with the relationship between the sampling scheme and possible overstability. A comparison of theory and experiment is made for the eigenfrequencies with feedback, and conditions for significant improvement in stability are given.
Heat Transfer from a Flat Plate in Magnetohydrodynamics
Authors: Fillo John A.
Published: December 2004

Subject to large magnetic Reynolds numbers, the heat transfer in a laminar boundary layer for flow of a viscous, electrically conducting, incompressible fluid past a semi-infinite flat plate is investigated. Attention is focused on the ``cooling'' problem; i.e., heat transfer in the boundary layer with a prescribed temperature difference between the plate surface and external stream. Viscous and Joule heating are neglected. The applied, free-stream magnetic field is coincident with the free-stream velocity field. Prandtl numbers of order one (slightly ionized gases) and of order 10−2−10−3 (highly ionized gases) as well as both large and small magnetic Prandtl numbers are included in the analysis.
Low-Frequency Whistler Mode
Authors: Kennel C.
Published: December 2004

Resonant growth (or damping) of electromagnetic waves propagating at an angle to the magnetic field in a model plasma is assumed to arise from a two component velocity distribution consisting of a dense, cold background plasma propagation medium, and a diffuse energetic nonthermal ``tail,'' responsible for resonant particle effects. The low-frequency whistler mode, cB/M+c « ω « eB/M−c, is treated in detail. When the energetic resonant electrons have a sufficiently hard-energy spectrum, and a pitch angle anisotropy corresponding to more electron energy perpendicular than parallel to the magnetic field, the whistler can be unstable over a significant cone of wave propagation angles to the magnetic field. Detailed computations of this growth rate for various energy and pitch angle distributions are presented as a function of wave normal angle to the field. The unstable cone is small when the high-energy tail is not well populated. For this reason, whistlers are usually thought to be heavily damped in low β (= 8πp/B2) plasmas. Whistler instability may limit the intensity of trapped high-energy electrons in the earth's Van Allen belts.
Moving Striations in the Argon Positive Column. I. Theory
Authors: Gentle Kenneth W.
Published: December 2004

The equations governing the plasma in the positive column of a dc discharge are analyzed for wavelike perturbations about equilibrium. Conservation-of-number equations are used for ions and metastables; the Boltzmann equation is used for electrons. The tail of the distribution determines the important source terms in the number equations. The equations are solved numerically for several cases in argon to determine the properties of the waves. Growing waves that propagate from anode to cathode are found for densities below a critical value, corresponding to the Pupp limit. The group velocity is in the opposite direction.
Transverse Wave Instabilities in Anisotropic Hydrogen Plasmas
Authors: Noerdlinger Peter D.
Published: December 2004

In the presence of a uniform magnetic field B0, an extensive family of uniform, collisionless hydrogen plasmas is examined for instability with respect to transverse waves. Only waves propagating along B0 are considered. The initial pressure along B0 is p∥ and that perperdicular to B0 is p⊥, with p⊥ ≠ p∥. For p1 > p∥, the unstable electron waves are almost identical to those in a plasma with immobile ions, and there is an unstable family of ion waves similar to those that would be found if the electrons were taken to be an immobile background. The ion waves are confined to a small band of wave numbers as B0 is made small, however, and they disappear when B0 = 0. For p∥ > p⊥, the plasma is found to be unstable if p∥ − p⊥ > B02/2π. When this criterion is satisfied, growing waves exist with growth rates generally of the order of a few tenths of the ion gyrofrequency. The classical firehose instability criterion is p∥ − p⊥ > B02/4π, which represents a domain of instability twice as large as that found here. The classical result was obtained in the extreme low-frequency long-wavelength limit, where the present treatment runs into difficulty from relativistic effects. Hence it is expected that for plasmas satisfying the old instability criterion but not the one found here, there exist unstable waves with growth rate very much less than the ion gyrofrequency. The growth rates and other properties of the fastest growing of these waves could only be found in a relativistic treatment.
Finite β Effects in a Weakly Unstable Plasma
Authors: Pearlstein L. D. , Krall Nicholas A.
Published: December 2004

The effect of finite plasma pressure (β) on the interchange mode is calculated in the finite Larmor radius limit. The method follows earlier zero β calculations of Rosenbluth and Simon, expanding the Vlasov equation with the ion Larmor radius ai considered small compared with the plasma radius L. The plasma pressure is taken to be zero order in ai/L. A differential equation is obtained for the stability properties of systems with arbitrary radial dependence of density, electric field, magnetic field, and β. Several simple examples show that increasing β moves marginally flute unstable systems to stability, if the change in β does not include violent changes in the density and field profiles.
Interchange Instability in a Hot-Electron Plasma
Authors: Kuckes A. F.
Published: December 2004

A recent experiment by Ferrari and Kuckes on the containment of a three-component plasma consisting of hot electrons, cold electrons, and cold ions in a simple magnetic mirror device is considered. The conditions for ``gravity-driven'' instability in such a plasma are derived and found to quantitatively coincide with the experiment. The lack of stabilization by a conducting end plate observed is found to be in accord with the theory. The total ejection of plasma across the magnetic field lines observed can be understood by considering the generation of ambipolar potentials and currents.
Linearization of the Oscillations in a Plasma Slab
Authors: Schneider H. M.
Published: December 2004

A discrete model has been used to study oscillations in a finite plasma with two types of boundaries. The numerical results which are presented show that the coherent motion is gradually destroyed by a ``scrambling'' which initially occurs near the surface.
Rarefied Gas Channel Flows for Three Molecular Models
Authors: Huang A. B. , Stoy R. L.
Published: December 2004

An analytic solution of the Boltzmann equation for the problem of a rarefied gas flowing between two parallel, infinite plates is developed for three different molecular models. They are the (1) Bhatnagar-Gross-Krook model, (2) hard-sphere model, and (3) Maxwellian model. The half-range moment method, which is used in the analysis for the three models, yields satisfactory results (with the expected minimum in the volume flow rate) for the transition, slip, and continuum regions. For the Bhatnagar-Gross-Krook model, the Willis iteration method provides good results for the near-free-molecular region even when, as a first guess, the first approximation by the half-range moment method is used. The comparisons between the analytic results and the experimental data indicate that the Bhatnagar-Gross-Krook model is a satisfactory approximation to the collision integral for the purpose of this study, and that the Maxwellian model provides an upper limit for the volume flow rate, and the hard-sphere model, a lower limit.
Streaming Instabilities in Plasmas with Zero-Order Density Gradients
Authors: Lee Kai Fong
Published: December 2004

Current-carrying plasmas with zero-order density gradients are analyzed for instability using the Vlasov and Maxwell's equations. The plasmas are confined by a strong axial magnetic field, and the densities are nonuniform in the transverse directions. By means of a variational method, it has been found that the density inhomogeneity (1) decreases the real frequency of oscillation, (2) reduces the maximum unstable wave number, and (3) increases the minimum current required for instability and imposes an upper limit on the streaming velocity beyond which the plasma is stable against perturbations of all wavelengths. Explicit results are given for Gaussian and exponential density profiles with resonant, Maxwellian, and delta function velocity distributions. The physical mechanisms that are responsible for these changes are discussed.
Longitudinal Modes in Magnetized Nonuniform Plasma Columns
Authors: Frisch H. L. , Pearson Gary A.
Published: December 2004

Certain resonant frequencies of magnetized cylindrical plasma columns were calculated using the theory of Buchsbaum and Hasegawa as well as an improved theory that takes into account the ambipolar electric field and the anisotropy of the electron velocity distribution. Attention is restricted to longitudinal modes with no propagation along the column axis and with frequencies near the second harmonic of the electron cyclotron frequency. For azimuthally symmetric modes (and for analogous planar models), the resonant frequencies calculated numerically using these two theories differ little; both theories agree with experiment to within the experimental uncertainties. Modes that are not azimuthally symmetric are described by a fourth-order differential equation that has not been solved exactly. An approximate perturbation theory treatment we have carried out suggests that the true eigenfrequencies are close to those obtained from a much simpler second-order equation.
Stability of the Theta-Pinch
Authors: Haas F. A. , Wesson J. A.
Published: December 2004

A model of a β = 1 axisymmetric plasma in which the equilibrium quantities are assumed to vary slowly in the axial direction is set up. The energy principle is used to investigate stability, and it is shown that the theta-pinch configuration is stable to the m = 1 mode.
Laser Interferometry as a Measure of Turbulent Fluctuations
Authors: Guthart H. , Scharfman W. E.
Published: December 2004

The power spectral density of the integrated neutral particle density fluctuations in the turbulent exhaust of a sonic jet has been measured using a laser interferometer. The measurements are compared with calculations of the power spectral density function.
Helical Instability in a Penning Discharge
Authors: Kerr Donald M.
Published: December 2004

Rotating helical perturbations in a Penning discharge were found to accompany low-frequency oscillations and enhanced particle transport across the magnetic field for a wide range of discharge parameters.
Ion Waves on Bounded Plasmas
Authors: Andersson Bengt , Weissglas Peter
Published: December 2004

Ion acoustic waves propagating along a cylindrical plasma column are studied theoretically. By neglecting the ion temperature, it has turned out possible to derive a simple boundary condition at the plasma surface. In addition to the infinite number of ion wave modes which degenerate into purely longitudinal waves in an infinite plasma, it is found that there exists a surface mode which is the ion equivalent of the electron surface mode of Gould and Trivelpiece. It is also shown that due to interaction between the ion modes and the Gould and Trivelpiece mode the dispersion curves of the ion waves are strongly modified.
Low-Frequency Spatial Response of a Collisional Electron Plasma
Authors: Fried Burton D. , Kaufman Allan N. , Sachs David L.
Published: December 2004

A study is made of the linear spatial response of an electron plasma to a localized one-dimensional electric field, whose frequency ω is low compared with the electron-collision frequency ν. For a fully ionized plasma, both electron-electron and electron-ion collisions are included in the calculations, the ions being treated as fixed scatterers. It is shown that the neglect of ion dynamics is justified for a suitable choice of parameters. In the hydrodynamic regime, the response function decays exponentially, with decay length equal to a diffusion length a(ων)−½, where a is electron thermal speed, and its amplitude is proportional to ω3/2. In the kinetic regime, the amplitude is proportional to ω, and the decay is not exponential, with characteristic distance being the mean free path a/ν. For a weakly ionized gas, only electron-neutral collisions are included; in the hydrodynamic region, the dependence of amplitude and decay length on ω is the same as for the fully ionized gas, but the decay is no longer exponential.
Convective Stability in a Plasma with Horizontal Magnetic Fields
Authors: Yu C. P.
Published: December 2004

Convective instability induced by gravity in a perfectly conducting, inviscid, and compressible plasma permeated by a general horizontal magnetic field is considered. Stability conditions obtained by Tserkovnikov and Newcomb are interpreted following the reasoning of Schwarzschild.
Nonlinear Equations for Circuits containing Exploding Wires
Authors: Bennett F. D.
Published: December 2004

A set of nonlinear, ordinary differential equations applicable to damped oscillatory circuits with exploding wires is developed. From these an exact first integral, or conservation law, is obtained and approximate solutions of the set are found by the Picard method. The ranges of validity of these approximate solutions are examined and criteria developed for scaling exploding wire experiments so that the theoretical expressions will be applicable. Calculations of time-to-melt are made and compared with experimental values. Agreement is good enough to justify confidence in the approximations used. The major regimes of circuit behavior are delineated and discussed.
Diffusion Measurements in a Fully Ionized Cesium Plasma
Authors: Eastlund Bernard J.
Published: December 2004

Diffusion coefficients both parallel (D∥) and perpendicular (D⊥) to a magnetic field have been measured in a fully ionized plasma. Pulses of potassium plasma were launched at one end of a steady state, fully ionized cesium plasma column, and D∥ and D⊥, along with the macroscopic drift velocity of the column, were found from the change of pulse shape. Experimental values for D∥ agree very well with theory. However, values for D⊥ do not agree with present theoretical predictions. It is observed that D⊥ is inversely proportional to the number density, while theory predicts direct proportionality.
On the Equivalence of Vortices and Current Filaments
Authors: Fetter A. L. , Donnelly R. J.
Published: December 2004

The analogy between vortices and current filaments is discussed for the case of vortices in a rotating container. It is shown that care must be taken to avoid errors in applying the analogy in certain situations.
Measurement of an Anomalous Diffusion Coefficient
Authors: Thomassen K. I.
Published: December 2004

A diffusion coefficient is calculated for the fluctuations due to a flute instability in a low pressure Penning discharge using the measured correlation times and flute amplitudes, eliminating the very difficult task of having to calculate the spectra due to the instability.
Compressible Low Reynolds Number Flow around a Sphere
Authors: Kassoy D. R. , Adamson T. C. , Messiter A. F.
Published: December 2004

The low Reynolds number flow past a sphere is studied for cases involving significant variation in density and temperature. An order of magnitude analysis of the governing equations for a continuum flow indicates the relative importance of compressibility, variable transport properties, and viscous dissipation. The order of magnitude of the nondimensional impressed temperature difference τ is shown to be useful as a guide for distinguishing problems with different governing physical characteristics. The cases τ = O(1) and τ = O(Re), where Re is the Reynolds number, are analyzed in detail. Inner and outer asymptotic expansions are derived for each of the flow variables in terms of the parameters Re τ and Mach number M∝. For τ = O(Re) the solutions are developed up to and including the first effect of nonzero M∞. For τ = O(1) the velocity expansions are calculated to zeroth order and the temperature expansions to order Re. Drag and heat transfer coefficients are calculated for each case.
Electrostatic Instabilities in Finite Mirror-Confined Plasmas
Authors: Post R. F. , Rosenbluth M. N.
Published: December 2004

Three classes of electrostatic instabilities deemed likely to be encountered in magnetic mirror-confined plasmas are examined theoretically: (A) a convective type, maser-like in nature, with waves propagating essentially parallel to the field lines; (B) a nonconvective (absolute) instability, arising in the presence of radial density gradients; and (C) a limiting case of (B), not requiring radial density gradients for its stimulation. All three instabilities, which owe their origin to the loss-cone nature of the particle distributions, exhibit critical conditions for onset or growth that are sensitively dependent on the shape of the distribution functions. These conditions are least restrictive for plasmas that have reached a state of collisional equilibrium in confining fields of high mirror ratio. In this limit (C) disappears and the critical conditions imposed by (A) and (B) are not unduly restrictive. In particular, at high plasma densities it is required: (1) for adequate stability against (A), the length of the plasma between the mirrors must not be greater than about 300 to 500 ion-orbit radii, and (2) to satisfy conditions (on the radial density gradient) imposed by (B), the plasma dimensions transverse to the field must also be of the same order; i.e., the plasma must be roughly spherical. Examples are also given which show that the confinement of highly peaked distributions leads to required conditions of orders of magnitude more restrictive than those found for well-randomized distributions.
Ionization Process of a Plasma
Authors: Lehnert B.
Published: December 2004

The ionization due to thermal electrons is discussed. Earlier theories on the voltage characteristics of a partially ionized homopolar cell are reconsidered. It is found that the results obtained from the theory on thermal ionization do not agree with experiments within the range of neutral gas densities studied so far, but a better agreement is expected at higher densities. In several cases the ionization rates estimated from experiments suggest that there exists a more powerful ionization mechanism than that provided by thermal electrons. Such a mechanism is probably associated with a highly nonthermal distribution of electron velocities within considerable parts of the plasma volume.
Equivalence of Electron and Excitation Temperatures in an Argon Plasma
Authors: McGregor W. K. , Brewer L. E.
Published: December 2004

The excitation temperature, measured spectroscopically in a low density, flowing, argon plasma using relative line intensities, was found to agree very well with the electron temperature, measured using a conventional Langmuir probe, across a diameter of the plasma stream.
Rotating Plasma as a Source for Injection into a Magnetic Mirror
Authors: Forsen H. K. , Trivelpiece A. W.
Published: December 2004

A two-stage, magnetic-mirror, compression experiment was constructed to investigate a rotating plasma as a clean, high-temperature, plasma source. Kilovolt deuterons are created in the static, crossed electric, and magnetic fields of the first stage for transfer or injection into the second stage. It was found that the purity of the plasma is limited by electrode effects and that anomalous plasma loss occurs along the flux lines through the mirrors. These electrode effects are described and explained. The plasma loss is related to an instability associated with the anisotropic velocity distribution.