bluuebunny/crossref_metadata_2025 huggingface dataset:
Simple and Generalized Condensation in Many-Boson Systems
Authors: Girardeau M.
Published: December 2004

The ground state of a system of interacting Bose particles is examined by a pair-correlation variational method based on exact eigenstates of the total particle number, without assuming macroscopic occupation of the single-particle state k = 0 (``simple'' Bose condensation). Known results are recovered in the case of repulsive interactions of weak and intermediate strengths, where the ground state does in fact exhibit simple condensation. But it is shown that in the case of weak attractive interactions the ground state exhibits ``generalized'' condensation, in which a finite fraction of particles have momenta which are macroscopically negligible, but no one single-particle state is macroscopically occupied. A weak-coupling expansion is derived for the ground-state energy in this case, the leading term of which is three times as low as that of the state one would obtain in the case of simple condensation. By the use of a pseudopotential, this result is adapted to the case of a strongly interacting system with a small negative scattering length α and fixed low density ρ, giving E0/n=−(6π ℏ2 ρ | α | /m)[1−(128/45) π−1/2(ρ | α | 3)1/2+…]. The relationships between equilibrium density, ground-state energy, and sound velocity predicted by this expression are in order-of-magnitude agreement with those obtaining for liquid He4.
Instabilities of a Liquid Conductor
Authors: Ingard Uno , Wiley David S.
Published: December 2004

Observations of pinch and spiral instabilities of a liquid conductor falling in an axial magnetic field are reported. Measured rates of change of the stream diameter and the spiral radius are given, and a stream ``bifurcation'' phenomenon that was induced by spiral instability is described.
Plasmoid Dipole Rotation in a Theta Pinch
Authors: Clark G. L. , Wuerker R. F.
Published: December 2004

The behavior of the toroidal plasmoid formed in a theta pinch due to trapping of magnetic field lines has been photographed with an ultra-high-speed image-converter camera. Photographs show the plasma ring rotating about an axis perpendicular to the applied magnetic field. This rotation is seen not only as a possible explanation for the sudden disappearance of the trapped magnetic field, but as a mechanism for accelerating the ions caught in the plasmoid. A preliminary analysis provides an upper bound to the ion energies obtainable through such a mechanism.
Bremsstrahlung from a Plasma
Authors: Chang David B.
Published: December 2004

The effect of correlations on bremsstrahlung from a plasma is studied by using in Kirchhoff's law an absorption coefficient obtained from a Boltzmann-Fokker-Planck equation. A simple derivation of the Fokker-Planck coefficients is given by relating them to familiar dc coefficients. A dispersion formula giving the principal behavior of the absorption coefficient is obtained from a first iterate solution of the Fokker-Planck equation, treating the scattering of electrons by ions as a perturbation. The absorption coefficient reduces to the incoherent radiation result at frequencies much higher than the plasma frequency. At the plasma frequency it is greater than the incoherent absorption coefficient by a factor of O[(nλD3)12], where n is the electron density and λD is the Debye length. The effect of surface reflections on the net emission is discussed.
Diffusion of Electrons in a Scattering Medium
Authors: Blue E. , Ingold J. H. , Ozeroff W. J.
Published: December 2004

The diffusion approximation to the more exact transport theory of charged-particle flow in a scattering gas is described and used to calculate the potential and electron density distributions for a simple case. In this simple case, electrons are emitted from a plane source and flow to a plane collector through the scattering gas under the influence of a density gradient and of electric fields due to a combination of space charged fields and externally applied fields. The resultant current-voltage relationship is complicated; however, a plot of ln J vs ln Va, where J is the electric current density and Va the applied voltage, has a slope which varies from one to two, according to whether the major component of the electric current is the density gradient or the electric field, respectively. These results are compared to those reported earlier in the literature.
Structure of Strong Plasma Shock Waves in a Transverse Magnetic Field
Authors: Comisar G. G.
Published: December 2004

The structure of a plane stationary shock wave in a plasma with a transverse magnetic field is explored by using the restricted variational principle of Rosen to evaluate the adjustable factors of Mott-Smith's bimodal representation for the ion and electron distribution functions. The resulting solutions, in the strong shock limit, indicate that the particle number densities are essentially those of the nonmagnetic case, and that the transverse magnetic field departs considerably from the usual frozen-in field profile, due to local dissipative effects of electrical conductivity.
Propagation of Sound in a Gas of Rigid Spheres
Authors: Pekeris C. L. , Alterman Z. , Finkelstein L. , Frankowski K.
Published: December 2004

The linearized Boltzmann integral equation for the problem of propagation of sound in a rigidsphere gas was solved by first determining the eigenfunctions of the collision operator and then solving the propagation matrix. Determinants up to order n = 105 were solved, and the results are illustrated. With the maximum order 105 of the matrix solved, the values of the propagation parameters obtained show convergence to within 2% for R > 1.8, where R = 2fc/3πf. The theoretical results are in fairly good agreement with Greenspan's measurements of the speed and attenuation of sound in rarefied helium.
Rate of Ionization behind Shock Waves in Air. I. Experimental Results
Authors: Lin Shao-Chi , Neal Richard A. , Fyfe Walter I.
Published: December 2004

The electron density profile behind normal shock waves in air at initial pressures 0.02 ≤ p1 ≤ 0.2 mm Hg and in the shock-Mach-number range 14 ≤ Ms ≤ 20 has been measured, using microwave-reflection and magnetic-induction probes in a 24-in.-diameter shock tube. It was found that the electron density generally rises rapidly behind the shock front without much incubation to a transient peak value which is considerably higher (i.e., by a factor of between 2 and 3) than that corresponding to the final equilibrium value. At a fixed shock Mach number, the maximum electron density gradient behind the shock appears to vary with the square of the initial air density, indicating that all the important rate-governing steps are due to binary collisions. Thus, at Ms = 20, the distance behind the shock required to reach 90% of the transient peak electron density was found to be about 10 times the viscosity mean free path of the undisturbed gas ahead of the shock. At Ms = 14, the corresponding distance was found to be approximately 40 times the initial mean free path.
Effect of Charge Exchange on the Critical Current for the Onset of Ion-Wave Instabilities
Authors: Bernstein Ira B. , Kulsrud Russell M.
Published: December 2004

Recent experimental results on the afterglow in the stellarator indicate that upon passage of an electrical current through the plasma rapid diffusion sets in at a certain critical current. This critical current can be computed theoretically and is found to depend in significant fashion on the tail of the ion distribution function. This tail may well be non-Maxwellian due to charge exchange with neutrals. The ion distribution function is computed by solving the Fokker-Planck equation, and it is found that the tail may be suppressed if there are sufficient neutrals present. This distorted distribution is then used to predict a new critical current for ion-wave instabilities. The calculations are presented in a form which admits of easy comparison with experiment.
Current Sheet in a Coaxial Plasma Gun
Authors: Burkhardt L. C. , Lovberg R. H.
Published: December 2004

Magnetic- and electric-probe measurements have been made on the thin current layer which is accelerated in a coaxial (Marshall) plasma gun. It is found that this layer does not act as a ``snowplow,'' but rather has the character of a strong shock wave.
Stability of an Electrically Charged Droplet
Authors: Ailam (Volinez) Gedalia , Gallily Isaiah
Published: December 2004

The stability of an electrically charged droplet with respect to mechanical deformations is studied under the assumptions that the liquid is perfectly conducting, the medium devoid of external fields of force, and the sum of the electrical and mechanical energies in the system conserved. Unlike Rayleigh's case, which dealt with small perturbations of spherical drops, the deformations considered in the present case are allowed to be large in size but confined in shape to ellipsoids of revolution. The energy of the deformed droplet is expressed as a function of a geometrical parameter and the ratio α between the electrical and surface energies of the corresponding spherical shape. Likewise, the dependence of the extremal points on α is investigated. Conforming with Rayleigh, the spherical droplet is shown to be unstable for α > 4 and stable for α < 4. However, for a certain range of α in the latter case, it is found to be only in a metastable state. In addition, both one prolate and one oblate ellipsoid of minimal energy are shown to exist for every α > 4.
High-Temperature Transport Properties of Dissociating Nitrogen and Dissociating Oxygen
Authors: Yun Kwang-Sik , Weissman Stanley , Mason E. A.
Published: December 2004

Transport properties of dissociating nitrogen and dissociating oxygen have been calculated from 1000° to 10 000°K with the assumption of no ionization or electronic excitation, using rigorous kinetic-theory formulas. The transport coefficients at each temperature are tabulated as a function of composition. The transport properties of the mixtures exhibit no special unusual features (unlike hydrogen). Various approximate formulas for the calculation of transport properties of mixtures have been checked against the results of the rigorous calculations, and give agreement to about 5%. A few checks of the calculations against experimental diffusion coefficients, viscosities, and thermal conductivities are possible, and the agreement seems reasonable.
Plasma Confinement by Direct-Current Magnetic Fields Assisted by an Arbitrary External Force
Authors: Dow D. G.
Published: December 2004

The equations for confinement of an isotropic plasma are formulated to include an arbitrary external force, which can be assumed to be provided by radio-frequency fields. A restriction is found which relates the allowable forms of the magnetic field and external force. Two specific results are as follows: (1) A dc magnetic field in the absence of other forces cannot support a pressure gradient transverse to its radius of curvature; (2) If the arbitrary external force is conservative, equilibrium can only be achieved when the external force just compensates the particle drift due to inhomogeneous magnetic fields at those points where the direct current is along the radius of curvature of the magnetic field. Stability problems are not considered although the time dependent equation, from which they may be studied, is presented.
Propagation of Electromagnetic Waves in a Nonuniformly Ionized Medium
Authors: Miller George Frazier
Published: December 2004

This paper is concerned with the theoretical solution of electromagnetic wave propagation through a nonuniform plasma sheath bounded by a plane infinite conductor. The governing differential equation yields a set of pseudo wave functions upon which all subsequent analysis is based. An exact solution is obtained for normal incidence and an excellent approximate solution for oblique incidence in the particular case of an assumed exponentially varying conductivity distribution. The procedures developed are applied to two practical cases, namely a penetration problem and a radiation problem. After establishing the proper orders of magnitude of the involved parameters from practical considerations, appropriate numerical data are obtained.
Classical Scattering by Some Important Repulsive Potentials
Authors: Baroody E. M.
Published: December 2004

Classical scattering by repulsive potentials of the form V = Br−n exp (−r/a) is analyzed in terms of two energy-dependent parameters, the distance of closest approach in head-on collision c, and a slope parameter γ = −(d ln V/d ln r)r=c. Use of these brings out important relationships among values of cross sections for various potentials which are in the literature and also facilitates the derivation of certain asymptotic analytic relations, the most interesting applying when γ is large, and others when γ is near unity. For large γ, the differential cross section σ(θ) is given by 4σ(θ)/c2 = 1 + Q1/γ + Q2/γ2, where Q1 is a simple function of θ only, while Q2 is a more complicated function which depends also on n/γ. This asymptotic expression for σ(θ) and transport cross sections σl calculated from it are compared with some of the available data. For the exponential potential, the asymptotic analytic behavior of collision integrals I(l, s) for large values of α = ln (B/kT) is determined and compared with numerical results of Monchick. For the exponentially screened Coulomb potential, a simple expression describing the dependence of σ1/πc2 on γ is selected and used in treating the energy loss of a fast heavy atom being stopped by elastic collisions in a gas of light atoms. This discussion makes clearer the basis and scope of the Bohr-Nielsen range-energy equation.
Mechanisms for Vibrational Relaxation at High Temperatures
Authors: Bauer S. H. , Tsang S. C.
Published: December 2004

Attention is called to several mechanisms which effectively couple translational and vibrational motions through the intermediary of chemical reactions. It is proposed that these processes lead to shorter relaxation times than those expected from direct energy exchange via inelastic collisions. Quantitative estimates are made, and relaxation times for these different processes are compared as a function of the reciprocal temperatures. At high temperatures, it is proposed that the transfer of energy from rotations to vibrations at approximately constant total energy can be induced by distant collisions. These serve primarily to balance the change in rotational angular momentum. Such events provide alternate paths for rapid vibrational relaxation, particularly for the upper vibrational levels, and may account for the fact that the observed rates of dissociation are considerably higher than the rates calculated under the assumption that these are limited by vibrational equilibration via inelastic collisions.
Perturbations of Plane Couette Flow in Stratified Fluid and Origin of Cloud Streets
Authors: Kuo H. L.
Published: December 2004

Small perturbations of plane Couette flow in stably and unstably stratified fluid are considered. It is found that the system is more unstable when it is bounded both above and below than when its depth is infinite, but a finite negative Richardson number J is required to maintain the perturbation for both cases. For the former case, this limiting Richardson number is −3k12/4(k12 + k22), while for the latter it is −2k12/(k12 + k12), where k1 and k2 are wavenumbers in the mean flow and the transversal direction. These results show that in an unstably stratified layer of Couette flow, the preferred mode of motion is roll-type convection, with the dimension in the wind direction much larger than in the transversal direction. The amplification factor σ for the perturbations has been determined as a function of the modified Richardson number J̄ = gSzUz−2(1 + k1−2k22), and the dimensionless wavenumber α = h(k12 + k12)1/2. Four different regimes have been found, each corresponding to a different type of perturbation. An application of the theory is made to the formation of longitudinal cloud rolls observed in the earth's atmosphere and in certain laboratory experiments.
Formal and Asymptotic Solutions in Kinetic Theory
Authors: Sirovich Lawrence
Published: December 2004

Formal solutions are found to the linearized Boltzmann equation for the initial-value problem. These are decomposed into an infinity of modes, which are orthogonal under a suitable inner product. All but five of these modes exhibit an exponential time decay. These five remaining modes form a generalization of hydrodynamics. Under two different asymptotic assumptions one finds quantitative solutions. If the characteristic wavelength of the initial disturbance is large compared to the mean free path, the solution appears as an expansion in their ratio. If the elapsed time is large compared to the mean free time, the solution may be represented as an expansion in their ratio. As a specific example of the theory, the fundamental solution of the one-dimensional shear-free initial value problem is computed. This appears as an infinity of diffusing modes, a subclass of which also propagate.
Excitation of Electrostatic Plasma Oscillations near the Ion Cyclotron Frequency
Authors: Motley R. W. , D'Angelo N.
Published: December 2004

Oscillations near the ion cyclotron frequency have been excited in thermal cesium and potassium plasmas by drawing current in a filament along the axis of the plasma column. The oscillations appear to be electrostatic waves propagating radially from the filament. The waves are present if the electron drift velocity exceeds about 10 times the ion thermal velocity, in agreement with the prediction of M. N. Rosenbluth. The measured phase velocity is also in agreement with the phase velocity calculated from the fluid equations.
Nonequilibrium Ionization in a High-Pressure Cesium-Helium Transient Discharge
Authors: BenDaniel D. J. , Bishop C. M.
Published: December 2004

Voltage gradient vs current density measurements of a discharge in helium seeded with cesium are given over the range of current densities of 0.1 to 20 A/cm2, cesium densities of 4.0 × 1013 to 2.8 × 1015/cm3 and at helium densities of 2.5 and 5.0 × 1018/cm3. Readings are taken at a time (50 μsec) sufficiently long to allow electron temperature and ionization to be established but short in comparison with the heating time of the gas. Results compare quite favorably with the theory of nonequilibrium ionization, also discussed. A positive resistance characteristic is observed in most of the regime.
Instability of a Partially Ionized Plasma in Crossed Electric and Magnetic Fields
Authors: Simon Albert
Published: December 2004

A weakly ionized plasma in a uniform magnetic field is considered. Application of a potential across the magnetic field results in a steady current flow, owing to the finite conductivity. It is shown that this steady state is unstable if the plasma density is nonuniform in the direction of the applied electric field and if the applied potential is large enough. It is necessary that the sign of the product of the electric field and the density gradient be positive.
Linearized Three-Component Magnetohydrodynamics
Authors: Liboff Richard L.
Published: December 2004

A linearized three-component magnetohydrodynamic theory is given. The three components are two oppositely charged species and a neutral species. Linearized macroscopic equations are presented which, in the limit of vanishing magnetic field, reduce to fluid-dynamic equations, and in the limit of vanishing neutral component give the Lundquist equations. The coupling of the components is frictional. In addition, the sound speed that enters is a function of the three equilibrium densities. These equations yield a dispersion relation which is tenth order in the wave speed (ω/k). The decay frequencies [i.e., —Im (ω)] of all ten modes are calculated to first-order terms in the friction, and are found to be all isotropic. In addition, all of the modes are stable.
Hydrodynamic Shock Tube
Authors: Glass I. I. , Heuckroth L. E.
Published: December 2004

An explicit solution is given to the one-dimensional hydrodynamic shock tube problem. The dynamic and thermodynamic quantities in the quasisteady states and the properties of the resulting waves are derived from the diaphragm pressure ratio and the initial conditions of the driver gas and the driven liquid. The planar flow results also apply, at the instant of diaphragm rupture, to the equivalent problem in a cylindrical or a spherical geometry, such as an underwater blast for example, and are therefore useful for establishing the initial blast properties. For this reason, some preliminary experimental data on low-energy, spherical underwater explosions are included.
Variational Principles for Acoustic-Gravity Waves
Authors: Biot M. A.
Published: December 2004

Variational principles are developed for the dynamics of a fluid under initial stress in an arbitrary potential field and disturbed from equilibrium. They are formulated in terms of the fluid displacement. Two distinct principles are obtained which are mathematically equivalent but differ fundamentally from the physical viewpoint. The difference results from expressing the potential energy in terms of buoyancy forces or strain energy. A very general stability criterion is obtained. An important new feature is the inclusion of surface integrals in the potential energy. The simplified principle for the case of a liquid is interpreted by means of an analog model. Lagrangian equations and methods of normal coordinates for the evaluation of transient propagation are applicable along with general theorems on the equivalence of group velocity and energy flux. As an illustration the case of a constant gravity field is discussed.
Hamilton's Variational Principle for a Perfectly Conducting Plasma Continuum
Authors: Lundgren T. S.
Published: December 2004

Hamilton's principle with a Lagrangian density consisting of kinetic energy minus the sum of internal and magnetic energy is used to derive the momentum equation and the pressure jump condition for a compressible nondissipative plasma continuum. This is done for a system consisting of fluid, vacuum and prefectly conducting solid parts by varying the fluid particle paths subject to conservation of mass, conservation of entropy and the Gallilean invariant form of Maxwell's equations. This is done also in Eulerian form for a purely fluid system using Lin's additional constraint.
Direct Measurements of Recombination Rates in a Shock Tube
Authors: Jacobs T. A. , Hartunian R. A. , Giedt R. R. , Wilkins R.
Published: December 2004

By an extension of the ideas embodied in the single-pulse shock tube, a technique has been developed which allows the direct measurement of recombination rates of many atomic species at high temperature. In the present technique, the expansion chamber is located a few tube diameters from the shock tube end plate rather than at the high-pressure end as in the conventional single-pulse shock tube. A cylindrical diaphragm, lying flush with the inside diameter of the tube, is used to control the time of initiation of an expansion wave. Experimental observation has shown that the present technique increases the gas expansion rate by an order of magnitude in comparison with the conventional single-pulse shock tube. The one-dimensionality of the flow at the shock tube end wall has also been investigated. The technique developed, in conjunction with the spectroscopic means of observation, was employed to gain preliminary measurements of the recombination rate of atomic chlorine.
Numerical Solution of the Problem of Vortex Street Development
Authors: Fromm Jacob E. , Harlow Francis H.
Published: December 2004

A method is described for the solution of time-dependent problems concerning the flow of viscous incompressible fluids in several space dimensions. The method is numerical, using a high-speed computer for the solution of a finite-difference approximation to the partial differential equations of motion. The application described here is to a study of the development of a vortex street behind a plate which has impulsively accelerated to constant speed in a channel of finite width; the Reynolds-number range investigated was 15 ≤ R ≤ 6000. Particular attention was given to those features for which comparison could be made with experiments, namely, critical Reynolds number for vortex shedding, drag coefficient, Strouhal number, vortex configuration, and channel-wall effects. The nature of the early stages of flow-pattern development was also investigated.
Extension of Howard's Circle Theorem to Adiabatic Jets
Authors: Eckart Carl
Published: December 2004

L. N. Howard proved an inequality concerning the complex velocity of the propagation of waves disturbing the laminar, unidirectional flow of an incompressible stratified fluid. It is shown that this theorem is closely related to the virial theorem of hydrodynamics. It can be generalized for the steady motion of a compressible fluid, provided the streamlines are either parallel straight lines or coaxial circles. The connection of the circle and virial theorems provides an interpretation of the former in terms of the energy of the perturbation. A positive potential energy always exerts a stabilizing influence, as does the angular velocity in the case of circular streamlines. This latter is diminished for short waves; it is also complicated by the fact that radial variations of the angular velocity may contribute negative terms to the potential energy. Zonal flow, such as the jet stream of the Earth's atmosphere, is generally baroclinic. In the barotropic case, the potential energy of the perturbation is simply proportional to the Väisälä-Brunt frequency. In the baroclinic case, this frequency cannot be usefully defined, and the more elaborate formulae are derived.
Relaxation Phenomena in Plasmas
Authors: Liboff Richard L.
Published: December 2004

The influence of four basic relaxation mechanisms on two-component plasma waves is examined. The analysis stems from a set of generalized macroscopic equations that include two self-relaxation mechanisms in addition to terms which dampen difference in temperatures and difference in flows between the gases. The emergent dispersion relation is diagonal with respect to longitudinal and transverse components of the state vector. The longitudinal relation is linear in the temperature coupling parameter while the transverse relation is independent of the self-relaxation rates and the difference in velocity relaxation rates. The longitudinal determinant yields well-known roots in the limit of long temperature relaxation times, while in the opposite limit new relations are obtained.
Test Time in Low-Pressure Shock Tubes
Authors: Mirels Harold
Published: December 2004

The reduction of test time in low pressure shock tubes, due to a laminar wall boundary layer, has been analytically investigated. In previous studies by Roshko and Hooker the flow was considered in a contact surface fixed coordinate system. In the present study it was assumed that the shock moves with uniform velocity, and the flow was investigated in a shock fixed coordinate system. Unlike the previous studies, the variation of free stream conditions between the shock and contact surface was taken into account. It was found that β, a parameter defined by Roshko, is considerably larger than the estimates made by Roshko and Hooker except for very strong shocks. Since test time is proportional to β−2, previous estimates of test time are too large, particularly for weak shocks. The present estimates for β appear to agree with existing experimental data to within about 10 percent for shock Mach numbers greater than 5. In other respects, the basic theory is in general agreement with the previous results of Roshko.
Chemical Relaxation with Preferential Dissociation from Excited Vibrational Levels
Authors: Marrone Paul V. , Treanor Charles E.
Published: December 2004

The rate of molecular dissociation behind strong shock waves is calculated with the assumption that dissociation can occur preferentially from the higher vibrational levels. An exponential probability of dissociation from the various vibrational levels is employed using an anharmonic oscillator model. Results for the dissociation of oxygen in an argon diluent are presented. Vibrational non-equilibrium introduces a T−3 temperature dependence into the oxygen dissociation rate constant in the range 4000°–8000°K. A dissociation lag-time of the order of the extrapolated vibrational relax ation time is predicted immediately behind the shock front. The computed results are shown to be in agreement with available experimental results.
Microwave Studies of Electrically Driven Shock Waves
Authors: Gerardo J. B. , Hendricks C. D. , Goldstein L.
Published: December 2004

The application of microwave interaction with gaseous plasmas to the study of electrically driven shock waves in nonionized gases and gaseous plasmas is discussed. The microwave measurements are supplemented by observation of the visible light emitted from the shocked gas and by voltage induced signals on small metallic probes placed in the path of the propagating shock waves. The investigated shock waves were in the Mach 4 to Mach 14 velocity range in neon and argon gases at pressures from 0.1 to 5 mm Hg. It is demonstrated, in agreement with other workers, that the background gas through which the shock waves subsequently passes is ionized to a nonnegligible degree at the instant of the electric discharge by photons of adequate energy from the discharge chamber. It is also shown that at least in the particular shock tube used in this investigation, this preionization is consistent with ionization by soft x rays from the electron bombarded anode in the discharge chamber. The effect of the free electron constituent of the ionized background gas on the properties of the shock wave as well as its direct effect on some commonly used shock wave investigation techniques is discussed.
Initial Response of the Spectrum of Isotropic Turbulence to the Sudden Application of a Strong Magnetic Field
Authors: Nestlerode James A. , Lumley John L.
Published: December 2004

A strong uniform magnetic field is suddenly imposed on a mass of conducting incompressible fluid initially in isotropic turbulent motion. Initial time derivatives of the spectrum are calculated through third order. After identification of terms, the simplifying assumptions of large mechanical and small magnetic Reynolds numbers are made, and the initial three-dimensional spectrum assumed to be a Dirac shell; these permit the calculation and plotting of the one-dimensional spectra. Interpretation of these spectra leads to the conclusion that the immediate effect of the field is to attenuate modes having cross-field velocities and those having cross-field node lines.
Bimodal Distributions and Plasma Shock Wave Structure
Authors: Comisar G. G.
Published: December 2004

The distribution of molecular velocities in a strong shock wave is usually assumed to be bimodal, on the basis of mean free path arguments. Indeed, this assumption has been confirmed by Sakurai for the case of rigid sphere molecules. It turns out that such a confirmation is no longer possible when the intermolecular forces have sufficiently long ranges; in particular, it is shown that, for the case of a fully ionized gas, the Boltzmann equation is not satisfied by a bimodal distribution, regardless of the choice for the shock thickness parameter and Mach number. This breakdown of the bimodal solutions is ascribed to an inadequacy in the usual mean free path concept for a plasma, due to the dominance of weak collisions at high temperatures.
Excitation of Longitudinal Waves in a Bounded Collisionless Plasma
Authors: Taylor Edward C.
Published: December 2004

The relativistic form of the Vlasov equation is used to derive an integral equation for an externally produced electric field oscillating with frequency ω in a plasma bounded by two specularly reflecting walls. A tentative solution is constructed from exact solutions of the half-space problem. It is shown that the exact equation is satisfied by the tentative solution up to terms which are exponentially small in the number of Debye lengths across the plasma. It happens that the bounded plasma acts like a medium with a dielectric constant κ=[1−ωp2/ω2(1−5KT/2mc2)], unless the driving frequency lies in the small band ωp2(1−5KT/2mc2)<ω2<ωp2(1+KT/2mc2). When the driving frequency satisfies the inequality, then the plasma also supports standing waves which satisfy the relativistic dispersion relation for longitudinal waves.
Wall Stabilization Effects in Theta-Pinch Configurations
Authors: Kilb R. W. , Hurwitz H. , Westendorp W. F.
Published: December 2004

If flux lines cannot penetrate into the conducting walls of a theta-pinch coil, then a repulsion force arises as a diamagnetic plasma approaches the coil wall. This results from the three-dimensional curvature of the flux lines when the plasma is near the wall. Neglecting changes in plasma shape, the stabilization energy is obtained by computing the energy needed to ``turn on'' the plasma surface currents in the presence of the coil wall. This is done accurately for spherical plasma shapes in cylindrical coils, and approximately for ellipsoidal shapes. The stabilization energy of spheres is proportional to the square of their volume, and becomes effective within a sphere diameter from the wall. It is approximately 10% of the energy needed to introduce the sphere into the coil center. Ellipsoids show roughly the same stabilization as spheres, but the force comes into play farther from the wall. By replacing the plasma with a conducting object of the same shape, an analog experiment is performed to determine the change in inductance as the object is moved about in the coil. For spheres and ellipsoids, agreement is found between the calculations and experiment. The experiment may be used to find the stabilization for complex shapes.
Note on the Weak Interaction Region in a Hypersonic Flow
Authors: Riley N.
Published: December 2004

The boundary layer in the weak pressure interaction region of a plane hypersonic flow over a thermally insulated surface is discussed.
Stability of a Shear Layer between Parallel Streams
Authors: Betchov Robert , Szewczyk Albin
Published: December 2004

The stability of a free laminar layer between parallel streams is examined. The neutral curve and the curves of constant amplification are obtained by a numerical method for Reynolds numbers ranging from 0 to 40 as well as for the inviscid case. No minimum Reynolds number is found. The eigenfunctions are discussed. The case of a layer of increasing thickness is considered, and it is concluded that turbulent transition will occur when the Reynolds number reaches 150.
Experimental Determination of Desorption Rates and of Heats of Desorption
Authors: Porter J. W. , Penner S. S.
Published: December 2004

Gas discharge rates through a de Laval nozzle from a closed chamber have been measured for Ar, He, and CO2. The effective desorption rates from vessels containing sand and silica gel have also been determined at various temperatures by measuring the time rate of pressure decay in the chamber. The experimental data have been used, in conjunction with a theoretical expression for diffusion-controlled desorption rates, to estimate heats of desorption from silica gel. Results have been obtained that are in approximate agreement with estimates made by other investigators using more conventional procedures.
Hose Instability for Relativistic Particle Beams in a Plasma Background
Authors: Mjolsness R. C. , Enoch J. , Longmire C. L.
Published: December 2004

A macroscopic analysis is given of the low-frequency, long-wavelength instabilities of the relativistic beam-plasma configuration. A two mass approximation is used for the particle dynamics. Plasma effects are accounted for by means of a tensor conductivity whose nondiagonal elements are due to the self-magnetic field of the beam. The analysis is directed toward establishing the effect of the nondiagonal terms on growth rates. Three approximate methods of analysis are discussed. The conclusion is that the nondiagonal terms, even when large, contribute minor modifications to the dispersion law.
Plasma-Beam Instability in the Hartree-Appleton Approximation
Authors: Neufeld Jacob
Published: December 2004

The interaction of a beam of protons of small intensity moving with velocity cβ (where c is the velocity of light) through a stationary plasma is investigated under the assumption that the beam is aligned along the direction of an impressed static magnetic field. Expressions are derived for frequencies and rates of growth characterizing the transverse waves excited by the beam and aligned along the direction parallel to that of the impressed field. It is assumed that the frequencies of the excited waves are large when compared to the proton gyrofrequency and are sufficiently high so that the motion of the plasma ions perturbed by these waves are neglected. It is shown that two waves are simultaneously excited by a beam having velocity cβ < cβmax and a relationship is obtained between βmax and the parameters charaterizing the stationary plasma.
Electrical Characteristics of Couette and Stagnation Boundary-Layer Flows of Weakly Ionized Gases
Authors: Chung Paul M.
Published: December 2004

The electrical behavior of weakly ionized, compressible gases flowing along a solid boundary is studied. Analysis is made for flows wherein the range of electrical effects, such as the sheath thickness, is much greater than the mean free path between the charged and the neutral-gas particles. The relationships between the surface potential, currents, and the boundary-layer flow parameters are analyzed.
Unsteady Linearized Relaxing Flow Past Slender Bodies
Authors: Wang K. C.
Published: December 2004

A linearized, unsteady, inviscid, compressible, relaxing gas flow over slender bodies of general cross sections is considered. Its difference from the classical nonrelaxing case is found to occur entirely because the propagation of one-dimensional impulsive disturbances differs in the two cases. The lateral forces and moments, to the linearized approximation, are shown not to be affected by nonequilibrium relaxation, but the drag expression contains nonequilibrium terms. Thus, only the decelerated (or accelerated) motion in the direction of flight had to be investigated. General solution is obtained analytically by transform method for arbitrary speeds (subsonic, transonic, or supersonic) and accelerations (or decelerations). A special example is calculated to illustrate the relative magnitude of relaxing drags.
Kinetic Theory of the Electron Gas in a Positive Background. II. Nonequilibrium Theory
Authors: Guernsey Ralph L.
Published: December 2004

A kinetic equation for the electron gas which is not subject to the usual short-range divergence is derived. The method used is the division of the Coulomb potential into a weak part and a short-range part. The result is expressed as the sum of a Boltzmann integral for the short range potential and a Balescu integral for the ``weak'' part, both of which are convergent. The ``dominant'' terms are identical with those obtained from the usual (divergent) Balescu equation with a cutoff in the k integration. An expression is obtained for the nondominant (i.e., nonlogarithmic) correction.
Scattering of Electrons and Ions by Dust Particles in a Gas
Authors: Dimick R. C. , Soo S. L.
Published: December 2004

Interaction of a partially ionized gas with dust particles was studied. Results generalize the earlier approximation by Rosen.
Current Speed in a Magnetic Annular Shock Tube
Authors: Keck James
Published: December 2004

A parametric study of the speeds of the current sheet and center-of-gravity of current in a magnetic annular shock tube has been carried out. The parameters varied include: (1) the drive current, (2) the polarity of the inner electrode, (3) the gas pressure, (4) the nature of the gas, (5) the radius of the inner electrode and (6) the material of the inner electrode. The most interesting result of the investigation was the observation of limiting speeds for the current sheet and center-of-gravity of current of approximately 8 cm/μsec and 3 cm/μsec, respectively. These speeds were not exceeded even under conditions where the magnetic pressure exceeded the dynamic pressure by a factor of 10. The most probable explanation of the limiting speed is that it is due to the inertial drag of material ablated from the insulator at the driver end of the shock tube.
Experimental Study of the Propagation of an Ionizing Wave in a Coaxial Plasma Gun
Authors: Wilcox John M. , Pugh Evan , Dattner Adam , Eninger Jan
Published: December 2004

A coaxial plasma gun experiment is described. The gun has an azimuthal bias magnetic field, which is strong compared to the field from the discharge current. The discharge voltage is shown to depend linearly on the bias field, thus defining a velocity that is found to be almost independent of the pressure and the discharge current. This velocity is close to the ``critical velocity'' which has been found in rotating-plasma experiments. The velocity of the current layer is also measured; it is always smaller than or equal to the critical velocity and it decreases with increasing pressure and decreasing magnetic field.
Plasma Gun Aspects of an E × B System
Authors: Halbach Klaus , Baker William R.
Published: December 2004

Experiments performed with the Homopolar V, an apparatus consisting of a coaxial electrode system immersed in a longitudinal field and with neutral gas injection in the middle plane are analyzed from the point of view of converting this device into a plasma gun. The discussion of these experiments leads to the conclusion that Homopolar V produces a deuterium plasma with a kinetic temperature in the keV range at a density of the order of 1014 ions/cm3. Since such a plasma is very desirable for injection purposes a modified homopolar device, the Homopolar Gun I is proposed. The basic considerations of the design and expected operation of this gun are discussed.
Energetic Electrons from a Beam-Plasma Overstability
Authors: Stix Thomas H.
Published: December 2004

A detailed examination is made of a large-amplitude beam-excited electron plasma wave, and of the acceleration to high energies of favored electrons by the electric field of this wave. In laboratory experiments x rays with energies greater than 100 keV have been observed coming from a plasma in a magnetic field, typically 2000 G, penetrated by an electron beam, typically one ampere at 10 keV. To account for the impressive energies reached by the electrons producing these x rays, an acceleration process is invoked in which individual steps of coherent cyclotron acceleration are summed stochastically. The increase in the perpendicular energy of the favored electrons enhances their magnetic mirror confinement and enables the acceleration process to occur within a small volume of plasma. The overstable mode under consideration is the double-hump-excited electrostatic wave in a magnetic field, with k and E not quite parallel to B0. The wave frequency is close to the electron plasma frequency, the phase velocity is close to the beam velocity. It is electrons, often with low parallel energy, which feel the wave at their own cyclotron frequency (or a harmonic thereof) which are favored in the acceleration process. The rapid growth of the electric fields to the large amplitudes requisite for the acceleration mechanism is difficult to account for, however, since electron trapping would be expected to occur and the linearized Vlasov-equation theory loses validity. An efficient untrapping process is therefore invoked: The plasma is thought of as a conglomerate of wave regions which are individually coherent but mutually incoherent. As an electron passes from one coherent region to another it is subjected to a new electric field randomly phased with respect to the first. A short correlation length improves the ability to account for overstability growth to large amplitude, but lengthens somewhat the calculated time for electron acceleration. Computations show efficient acceleration when the electron plasma frequency is of the same order or larger than the electron cyclotron frequency.
Experimental Study of Compressional Hydromagnetic Waves
Authors: Swanson D. G. , Gould R. W. , Hertel R. H.
Published: December 2004

An experiment is described in which a compressional hydromagnetic wave is observed in a hydrogen plasma-filled waveguide. The theory of a cool, partially ionized, resistive plasma in a magnetic field is described briefly and expressions are derived for the dispersion relation and transfer function which include both the propagation and attenuation constants as a function of frequency. Measurements of the cutoff frequency are presented, which verify its linear dependence on the magnetic field, and they show good agreement with theory on the variation with the ion mass density. The impulse response of the plasma is studied, transformed into the frequency domain, and quantitative comparisons are made with the theoretical transfer function to determine the degree of ionization, the resistivity, and the ion-neutral collision frequency.

Results indicate that the degree of ionization varies over a range from 75% to 45% when the initial density varies from 1.3 × 1021 to 1.4 × 1022 atoms/m3. The measured resistivity appears to increase with the magnetic field, with the mean value corresponding to a temperature of the order of 5 × 103 °K. The average value of the product of the charge exchange cross section and the neutral thermal speed is found to be approximately (5.5 ± 1.3) × 10−15 m3/sec.
Application of the Virial Theorem to Equilibria of Toroidal Plasmas
Authors: Yoshikawa Shoichi
Published: December 2004

Necessary conditions for equilibrium of a current-carrying toroidal plasma are derived under the assumption of azimuthal symmetry. It is demonstrated that an azimuthally symmetric toroidal plasma can be in equilibrium only if an additional transverse magnetic field is present, which absorbs the expanding force of the plasma. An expression of parabolic pressure distribution is obtained, when the plasma minor radius is much smaller than the major radius. Stability criterion of the plasma ring against displacement is discussed. The weak focusing can be employed to stabilize the plasma ring.
Macroscopic Transport Properties of a Fully Ionized Alkali-Metal Plasma
Authors: Rynn N.
Published: December 2004

The one dimensional, macroscopic transport equations are solved for the special case of a fully ionized potassium plasma generated in the Q-device, and the solution is used to predict the volt-ampere characteristic. Agreement between predicted and measured volt-ampere characteristics is very good at low currents but not as good at high currents. The disparity is believed to be due to the presence of large potential and thermal gradients in front of the hot plates at high currents, which are predicted by the theory when the thermoelectric coefficients are taken into account. The average experimentally determined electrical conductivity is 1.2 times the Spitzer-Härm value with an rms error of about 10%. The average experimentally determined thermal conductivity is 0.98 times their value with an rms error of about 10%. A criterion is established for determining when the sheaths in front of the plates do not affect the volt-ampere characteristic, and for determining when the plasma is truly collision-dominated. The axial variations of temperature and potential are also determined. A sudden change in the volt-ampere characteristic that coincides with the onset of instabilities in the plasma is not explained by the theory or by a simple interpretation of the sheath properties. The value of lnΛ was assumed to have a constant value of 7.
Measurement of Magnetically Induced Sound Absorption in Liquid Sodium and Potassium
Authors: Letcher S. V. , Beyer R. T.
Published: December 2004

The attenuation of ultrasonic waves in liquid sodium and potassium due to an external, de magnetic field has been measured between 2.25 and 40 MHz. The experimental results have agreed with the theoretical expression within experimental error, indicating a coupling of acoustic and hydromagnetic modes at low frequencies.