bluuebunny/crossref_metadata_2025 huggingface dataset:
Doppler Temperatures in the C Stellarator
Authors: Hirschberg Joseph G.
Published: December 2004

A convenient method for the accurate measurement of Doppler temperatures as a function of time has been developed and applied to the C Stellarator. General agreement between Doppler and other temperature measures has been found when the plasma is quiescent. Late in the period of plasma containment however, the ion-Doppler temperatures begin to fall appreciably below the electron temperature. This is shown to be explainable in terms of an influx of cold gas which tends to overcome the heating by the electrons.
Stability of Plane Magnetohydrodynamic Shocks
Authors: Gardner C. S. , Kruskal M. D.
Published: December 2004

The stability of plane magnetohydrodynamic shocks in a perfectly conducting fluid with general equation of state is studied. General (three-dimensional) perturbations are considered. A condition for stability is derived for the special cases of perpendicular and parallel fast shocks. Stability is thereby proved in these cases for a polytropic gas with γ < 3.
Perturbation Method for Waves in a Slowly Varying Plasma
Authors: Baldwin David E.
Published: December 2004

The method of expansion in instantaneous eigenfunctions is used to obtain approximate solutions to the linearized Vlasov equation when the unperturbed function is time-dependent. The method is useful when the time-dependence of the unperturbed function is slow compared with the plasma frequency. The general results are used to obtain the growth of wave energies in the quasilinear limitation of weak two-stream instabilities. Deviations from previous results for this problem are found.
Transfer of Energy in a Quantized Plasma
Authors: Rand S.
Published: December 2004

The exchange of energy between a plasma, and a test particle in a time-independent potential, has been studied. The motion of the test particle and the plasma interactions are treated quantum mechanically. A general formula, obtained for the energy transfer, is applied to the problems of the free particle and to the linear harmonic oscillator in the dipole approximation. Contributions to the energy transfer are separated into parts associated with friction and with thermal agitation or velocity diffusion. The results are compared with the classical limits. For the free particle, the corrections to the classical results are logarithmic, whereas for the harmonic oscillator the corrections are very important, when the oscillator transition energies exceed the random electron energies in the plasma. The frictional contribution to the energy loss by the oscillator is related to the electrical conductivity.
Direct-Interaction Approximation for Shear and Thermally Driven Turbulence
Authors: Kraichnan Robert H.
Published: December 2004

The direct-interaction approximation for turbulence is extended to shear flows and Boussinesq convection contained in regions of arbitrary size and shape. It is pointed out that the approximation provides a consistent generalization of mixing-length concepts which continues to be applicable when the scale of inhomogeneity is comparable to the effective mixing length. The degree of faithfulness to be expected of the approximation is discussed on the basis of inferences from numerical results on isotropic turbulence.
Wiener-Hermite Expansion in Model Turbulence at Large Reynolds Numbers
Authors: Meecham William C. , Siegel Armand
Published: December 2004

A Wiener-Hermite functional expansion is used to treat a random initial value process involving the Burgers model equation. The nonlinear model equation has many of the characteristics of the Navier-Stokes equation. It is found that the functional expansion converges better the larger the separation variable in the correlation function (the nearer to joint normal is the distribution). To the present order, the treatment is similar to a quasinormal assumption. The computations show that the correlation function quickly approaches an equilibrium form for quite different initial values. The power spectrum function approaches an equilibrium form also, where it falls off like the inverse second power of the wavenumber.
Effect of Compressibility on Kelvin-Helmholtz Instability in a Plasma
Authors: Sen Amiya K.
Published: December 2004

The problem of stability of the most general type of Kelvin-Helmholtz discontinuity in a compressible plasma has been formulated. It is found that unlike surface tension, gravity and magnetic field, compressibility can have either stabilizing or destabilizing effect, depending on the stationary state of motion. In general, this may lead to two domains of stability, in contrast to only one that exists in the case of incompressible plasma. Compressibility will have a stabilizing or destabilizing effect, if the streaming speed is sufficiently larger or smaller, respectively, than the magnetoacoustic speed.
Stagnation Point Langmuir Probe in a Shock Tube-Theory and Measurements
Authors: Pollin Irvin
Published: December 2004

Langmuir-type probes consisting of a flat-headed circular cylinder with a collecting electrode at the stagnation point are placed in a shock tube and exposed to supersonic ionized air flow at ion mass fractions less than 10−4 and initial shock tube pressure of 1 cm Hg. Stagnation point measurements of ion current density are obtained using negative electrode potentials. The exact gasdynamic stagnation point boundary layer equations and the one-dimensional Poisson equation are solved for an axially symmetric blunt body and ion mass fractions less than 10−2. Calculations of the ion-electron flow in the stagnation point boundary layer are presented for negative electrode potentials. The measurements and calculations agree within the experimental accuracy and the precision to which the physical constants are known.
Trapping and Loss of Charged Particles in a Perturbed Magnetic Field
Authors: Wingerson R. C. , Dupree T. H. , Rose D. J.
Published: December 2004

The properties of a nonadiabatic magnetic system for trapping and confining charged particles are derived. The trapping mechanism is a helical perturbation that matches the gyrations of an incoming particle beam. These particles, in resonance with the structure, convert their axial energy into transverse energy even in the absence of a magnetic mirror. By the same scheme, a spiraling beam could be straightened out. The best injection system is a four-conductor set, which is analyzed in detail. Once confined, the particles experience small and almost random nonadiabatic perturbations in their motion; they diffuse in both real and velocity space. A linear operator that governs this diffusion is presented; it is applicable to a uniform magnetic field with small perturbations. The velocity-space diffusion in a magnetic mirror is calculated for a general perturbation and in particular for a helical perturbation. For this last case, the injected particles can be confined for several hundred axial transits. If the charged particles are modified after being initially trapped (e.g., dissociation of molecular ions), the loss in physically realizable systems can be made virtually negligible compared with charge transfer and other conventional losses.
Theoretical Structure of Plasma Equations
Authors: Rosenbluth M. N. , Rostoker N.
Published: December 2004

In high-temperature plasmas, collisions are very infrequent. Thus the charged particles travel on independent orbits determined by the electromagnetic field. At first sight this would seem completely different from a conventional fluid where particles are closely hemmed in by their neighbors. However, there can exist collective modes of motion in which the particles interact with each other by altering the fields.

In this paper a new method is developed for the solution of the linearized transport equation. By facilitating direct use of the properties of particle orbits, a considerable simplification is achieved. In particular, a variational expression is derived for determining stability which is rigorous in the limit of small Larmor radius.
Nonstationary Phase Changes Involving a Condensed Phase and a Saturated Vapor
Authors: Knuth Eldon L.
Published: December 2004

Nonstationary temperature distributions and evaporation (or condensation) rates are calculated for the case in which the condensed phase is initially at uniform temperature, the latent heat is supplied (or absorbed) by the condensed phase, and the vapor is in the saturated state.
On the Partition Function of a One-Dimensional Gas
Authors: Kac Mark
Published: December 2004

A method is presented for calculating the grand-partition function of a one-dimensional gas with the potential V(x) = + ∞ for 0 ≤ x < δ and V(x) = −α e−γx for x ≥ δ.
On the Behavior of Plasma at Ionic Resonance
Authors: Doyle P. H. , Neufeld Jacob
Published: December 2004

An electromagnetic wave having its wave vector parallel to the direction of the steady magnetic field Ĥ is attenuated in plasma very effectively when the frequency ω is equal to the ionic resonance frequency Ωg of the plasma. A small localized periodic disturbance initiated in a plasma in thermodynamic equilibrium at t = − ∞ and having frequency ω = Ωg produces along the direction of the magnetic field a wave motion characterized by a complex wave vector k ∼ (Ω0Ωg/c2u0i) ⅓ (√3 + i) where Ω0 is the Langmuir frequency and u0i is the mean thermal velocity of the ions in the plasma. The attenuation per wavelength at the resonance frequency is substantial since Imk/Rek = 1/√3. However, the attenuation per unit of length is not at maximum at ionic resonance since it increases for increasing frequencies when ω passes through the resonance. This is shown by the fact that for ω = Ωg we have Im(dk/dω) > 0 since at resonance Im(dk/dω) = K1/u0i + (K2/u02ui0) ⅓ where K1 and K2 are appropriate positive constants and u0 is the velocity of the magnetohydrodynamic wave.
Radiation-Induced Cavitation
Authors: Lieberman D.
Published: December 2004

Measurements of the thresholds of radiation-induced acoustic cavitation in pentane and acetone are described. A resonator method was employed. It is concluded that the observed cavitation was nucleated by recoil carbon ions in pentane. The results are compared with calculations based on Seitz's model of the nucleation process. The agreement is within an order of magnitude.
Diagnostic Measurements on a Highly Ionized, Steady-State Plasma
Authors: Gardner Andrew L. , Barr William L. , Kelly Raymond L. , Oleson Norman L.
Published: December 2004

Techniques and results are given for various measurements made on a highly ionized helium plasma in a steady-state plasma system (which employs a longitudinal magnetic field of approximately 1 kilogauss). Neutral-particle pressures ranged from about 3 × 10−4 mm Hg near the source to about 10−5 mm Hg in the downstream region. Spectroscopic measurements showed principal impurities were C, N, and O ions (up to C3+, N4+, and O4+ states). Doppler broadening measurements of He+ λ4686 revealed ion temperatures up to 10 eV. Probe measurements indicated electron temperatures up to 20 eV and maximum ion densities of a little over 1013 cm−3. Microwave transmission measurements (at λ = 4 mm and 8 mm) gave supporting evidence that the electron density exceeds 1013 cm.
Frequency Dependence of Plasma Acceleration by Radio-Frequency Field Gradient
Authors: Swartz G. A. , Reboul T. Todd
Published: December 2004

Plasma acceleration by an rf field gradient has been observed for both 140 and 330 Mc fields. The kinetic-energy gain of the accelerated ions varied inversely with the applied frequency. Comparison with theory indicates that in the interaction region most of the accelerated plasma has a resonant frequency near the applied frequency. The collision frequency which limits the acceleration in the test apparatus is calculated to be 6 Mc.
Flow of a Slightly Conducting Fluid past a Circular Cylinder with Strong, Aligned Magnetic Field
Authors: Tamada Ko
Published: December 2004

The induced magnetic field is neglected owing to the small conductivity of the fluid. The effect of the magnetic field upon the flow is also assumed to be so small that it can be treated as a perturbation. Thus, the first-order correction to the nonmagnetic potential flow is obtained by a simple perturbation technique. The solution indicates existence of a nondiffusive, vortical, velocity deficiency which extends indefinitely downstream of the cylinder. The flow field at great distances is also reconsidered as a problem of singular perturbation.
Hall and Ion-Slip Effects in a Nonuniform Gas
Authors: Rosa R. J.
Published: December 2004

Under conditions that result in strong Hall or ion-slip effects, a uniform and a nonuniform gas can behave much differently as conductors of electricity. An Ohm's law for a nonuniform gas is derived. It is used to study the performance of normal-current and Hall-current magnetohydrodynamic devices and also the possibility for obtaining significant electron heating or ``extrathermal'' ionization.
Particle Behavior in Static, Axially Symmetric, Magnetic Mirror and Cusp Geometries
Authors: Gibson G. , Jordan W. C. , Lauer E. J.
Published: December 2004

A mean containment time τ of many seconds has been observed for a significant fraction of the energetic (≤ 2.2-MeV) positrons emitted from Ne19 isotropically and uniformly in a mirror geometry with mirror ratio R in the range 1.1–3.7. Long-time containment has been observed for particles that escape through a mirror at radial distances for which the particle orbits do not encircle the axis, as well as for those that escape on or near the axis. The dependence of τ on the Z of the scattering gas, the gas pressure, the positron energy, the coil current, and the diameter and separation of the coils has been investigated. Most of the data were obtained with the two mirror coils separated one coil mean diameter. For sufficiently small values of λ (the ratio of the maximum orbit diameter on axis to the coil mean diameter), τ is independent of λ and its dependence upon the above parameters agrees with the predictions of scattering theory. Also, the fraction of particles trapped as a function of the mirror ratio agrees with calculations based on the loss cone concept. These results demonstrate that the particles ``behave adiabatically'' if λ is less than about 1/10. For larger values of λ the observed τ's are shorter. Results obtained with probes are in agreement with the prediction that the intersections of particle drift surfaces with the plane midway between the mirror coils are concentric circles centered on the axis. In the cusped field resulting from opposite currents in two coils separated by one coil mean radius, containment times of several seconds have been observed at radial distances where the field is of sufficient strength that ``adiabatic behavior'' is expected. Near the axis, however, no long-time (> 0.5-sec) containment has been observed.
Hydromagnetic Instability in a Stellarator
Authors: Sinclair Rolf M. , Yoshikawa Shoichi , Harries Wynford L. , Young Kenneth M. , Weimer Katherine E. , Johnson John L.
Published: December 2004

Stability diagrams are calculated for hydromagnetic kink instabilities in a zero-pressure plasma confined in a stellarator geometry with arbitrary mixtures of l = 2 and l = 3 multipolar helical fields and with various radial distributions of the current parallel to the confining magnetic field. The introduction of small pressure gradients increases the size of the unstable regions. Modes with small azimuthal wavenumber grow more rapidly than those with large m. Experimental data, obtained with the model C Stellarator, show that the plasma is macroscopically stable except for certain intervals of rotational transform. These intervals agree qualitatively with those in which the theory predicts the plasma should be unstable against the kink instability.
Radiative Modes of a Magnetoplasma Slab
Authors: Halpern G. , Schmidt G.
Published: December 2004

There exist modes of oscillation of a cold magnetoplasma slab which generate outgoing electromagnetic radiation. The dispersion equation which relates the frequency and wavenumber of these modes is derived. An analysis of this equation is made with emphasis on waves having phase velocity greater than light in vacuum. These waves are found to have complex frequencies due to radiation damping. For long wavelengths the radiation frequencies are near ωp and (ωp2 + ¼ωc2)½ ± ½ωc, where ωp and ωc are the electron plasma and cyclotron frequencies, respectively. Dispersion curves are drawn for arbitrary values of applied magnetic field. The behavior of these curves is discussed in the transition to an unbounded plasma. Temperature, ion dynamics, and collisions are neglected in the analysis.
Electromagnetic Instabilities in the Nonthermal Relativistic Plasma
Authors: Sudan R. N.
Published: December 2004

The results of a previous investigation of growing electromagnetic waves in a gyrotropic electron plasma are now extended to relativistic electron energies. If γ is the ratio of the longitudinal to the transverse electron thermal energy, then a nonrelativistic analysis predicts instabilities for both γ < 1 and γ > 1. However, for γ > 1 the phase velocity of the growing waves exceeds the velocity of light in vacuo and it is inconceivable that there are electrons that interact strongly with such a wave to give a finite growth rate. The relativistic analysis clears up this difficulty by predicting no instability for γ > 1; the error lies in the use of a Galilean rather than the correct Lorentz transformation to go from the wave frame to the frame in which the electrons are at rest. A criterion for the existence of such instabilities is given. The case of a beam of electrons with γ « 1 drifting at a relativistic velocity v0 through a cold isotropic plasma is also analyzed to be unstable. The growth rates, frequencies and wave vectors of the unstable waves are derived.
Schlieren Photography of a Coaxial Accelerator Discharge
Authors: Lovberg R. H.
Published: December 2004

The plasma distribution inside a coaxial pulsed accelerator has been examined by use of the schlieren photography technique. The accelerator was filled uniformly with hydrogen at 0.5 mm Hg pressure, and the circuit externally switched. Under these conditions, the current was carried in a roughly paraboloidal shell which was followed by a dense, planar layer of plasma carrying negligible current. Polarity effects were not observed to be strong. The current in the plasma emerging from the muzzle of the acceleration retained its azimuthal symmetry, and was returned to the center electrode by a well-developed pinch on the system axis.
Theories of Fast Luminous Fronts
Authors: Nelson Raymond A.
Published: December 2004

A brief review is made of the theories of fast luminous fronts that are observed to precede shock waves in electromagnetic shock tubes. A theory proposed by Paxton and Fowler is criticized, and it is suggested that an ionization-front theory may provide a better description of such fronts.
Initiation of Detonation by the Interaction of Shocks with Density Discontinuities
Authors: Mader Charles L.
Published: December 2004

The basic processes in the shock initiation of inhomogeneous explosives have been investigated theoretically using the model of a cylinder of nitromethane containing a void or an aluminum pellet. The interaction of a shock with the density discontinuities, the resulting formation of a hot spot, and the buildup to propagating detonation were computed using two-dimensional numerical hydrodynamics of the ``PIC'' type with chemical reaction and accurate equations of state. The hot spots formed at aluminum pellets exhibit failure or propagation of detonation in approximately the same manner as the one-dimensional, hydrodynamic hot spots studied previously. The failure of hot spots formed at voids could be studied only in those cases in which the failure mechanism did not depend on details of the structure of the reaction zone, as this structure could not be reproduced in the calculation.
Finite Gyro-Radius Corrections to the Hydromagnetic Equations for a Vlasov Plasma
Authors: Macmahon Alan
Published: December 2004

Velocity moments of the Vlasov equation are expanded systematically in m/e and equations obtained giving the fluid velocity transverse to B through second order. These equations include all ``finite gyro-radius'' effects. No a priori form is imposed on the velocity distribution. The transverse electric field E⊥ is allowed to be large. For straight field lines the equations for purely transverse motion are closed. For weak instabilities (E⊥ small) closed equations are obtained only for low plasma pressure.
Longitudinal Oscillations in Unbounded One-Dimensional Nonuniform Plasmas
Authors: Harker Kenneth J.
Published: December 2004

A study has been made of the oscillations in a one-dimensional nonuniform plasma by use of the linearized Boltzmann-Vlasov equation. Particular attention has been given to static potential distributions varying as xn. An integral equation has been derived for the radio-frequency electric field. Examination of the kernel of this equation reveals that Landau damping can only occur when there are unperturbed electron orbits whose periods are some odd multiple of the period of the applied field. Since all the unperturbed orbits in the case of parabolic static potential distributions have the same period, it is clear that in general there will be no Landau damping with this configuration. For the case of a parabolic static potential, the resonances of the plasma are obtained by solving numerically for the eigenvalues of the integral equation. For certain frequencies it is also possible to evaluate the kernel of the integral equation in closed form.
Enhanced Bremsstrahlung from Plasmas containing Nonthermal Electrons
Authors: Tidman Derek A. , Dupree Thomas H.
Published: December 2004

The bremsstrahlung emitted from thermal plasmas which coexist with a flux of energetic (suprathermal) electrons is calculated. It is found that under some circumstances the radiation emitted can be greatly increased compared to the emission from a Maxwellian plasma with no energetic particles present. The enhanced emission occurs at the fundamental and second harmonic of the electron plasma frequency.
Heat Transfer from Argon and Xenon to the End Wall of a Shock Tube
Authors: Friedman Harvey S. , Fay James A.
Published: December 2004

Heat transfer from argon and xenon to the end wall of a shock tube has been measured by using a thin-film heat transfer gauge whose temperature rise is monitored by an infrared photocell. Experiments were carried out at initial pressures between 1 and 10 mm Hg in argon and between 0.75 and 2 mm Hg in xenon. For the range of incident shock Mach numbers tested, between 9 and 13 in argon and 13 and 18 in xenon, partial ionization would exist behind the reflected shock wave if thermodynamic equilibrium were achieved. By extrapolation of measured ionization rates for these gases, it was concluded that no ionization occurred behind the reflected shock wave in argon but that equilibrium was achieved in xenon, at least for the period during which the heat transfer was measured. Calculations of the heat transfer, made in accordance with existing theories for the corresponding thermodynamic state of the gas, were found to be in good agreement with the experimental measurements.
Statistical Theory of Nonadiabatic Magnetic Traps
Authors: Robson A. E. , Taylor J. B.
Published: December 2004

The trapping and containment of particles injected into a nonadiabatic magnetic mirror trap are considered. The results of numerical orbit calculations are compared with a statistical theory which is shown to give essentially identical results. This statistical theory leads to simple expressions for the mean containment time and the mean density of trapped particles. These results indicate that the most significant factors in the nonadiabatic trapping process are the width of the acceptance cone (i.e., the solid angle in velocity within which the injected particles have a finite chance of capture) and the angular spread of the input beam. Optimum trapping requires that these two quantities be appropriately matched. When this is done the density approaches a limiting value (which is generally below the usually quoted ``Liouville limit'') and the buildup time is a minimum. Provided this matching can be achieved, there appears to be no special merit in using resonant nonadiabatic traps over any other form.
Radiative Shock Structure
Authors: Koch Paul A.
Published: December 2004

A study is made of plane gas dynamic and transverse magnetogasdynamic shock waves in fully ionized hydrogen at conditions such that radiative processes are significant. The length scale required for a radiative shock wave to be steady is large, and the establishment of a truly steady-state flow is found only for dimensions relevant to astrophysical cases. In the case of such an established flow the Rankine-Hugoniot jump equation (i.e., the relationship between the flow variables in the initial and final states) is analyzed. It is shown that of the twelve roots of this equation only two are physical, corresponding to the super-signal initial and sub-signal final states. The differential equations which describe the above shock waves are analyzed for cases where the shock is optically thick, i.e., the mean free path for absorption of radiation is much smaller than the characteristic lengths for change of the flow variables. A new criterion is given for the validity of this approximation.
Two-Fluid Model for Shock Wave Structure
Authors: Toba K. , Melnick J. D.
Published: December 2004

A critical study is made of the two-fluid model of a shock wave which was first introduced by Glansdorff and, also, independently by Rott and Whittenbury, and which has recently been modified by Ziering, Ek, and Koch. It is proposed that a cutoff relative velocity be introduced in the inelastic collision operator which yields various collision frequencies for the transferred quantities. This cutoff velocity is not known initially but is determined by the analysis. Numerical results are given for molecules of rigid sphere, point centers of repulsion, and the Sutherland model. Comparisons with other solutions and experimental data are made.
Failure of the Chapman-Jouguet Theory for Liquid and Solid Explosives
Authors: Davis W. C. , Craig B. G. , Ramsay J. B.
Published: December 2004

The usual treatment of unsupported detonation, often called the Chapman-Jouguet theory, is based on four assumptions: (1) the detonation approaches a steady state, (2) the flow is laminar and one-dimensional, (3) the detonation products approach a state of chemical equilibrium some distance behind the detonation front, and (4) the detonation velocity is the minimum permitted by the conservation conditions. Wood and Fickett proposed experiments to test the validity of the Chapman-Jouguet ``theory,'' not requiring knowledge or assumptions about the nature of the equation of state of the detonation products, by making variations of the initial state of the explosive. The results of experiments are reported in which the initial state was varied (1) by using mixtures of nitromethane and another liquid which has the same atomic composition as nitromethane, and (2) by using TNT as liquid and as solid. These results show that the Chapman-Jouguet theory is violated. The calculated pressures are 15 to 20% below the measured pressures. Results of measurements using other explosives are also presented to support the conclusion that the theory fails. No explanation or alternative theory is offered.
Landau Solution of the Plasma Oscillation Problem
Authors: Taylor E. C.
Published: December 2004

The controversial aspects of Landau's treatment of the initial value problem are discussed. It is demonstrated that any kind of decaying solution other than that of Landau can be obtained for some initial velocity distribution function. Nevertheless, it is shown that several phenomenologically motivated distributions—Maxwellian functions, Lorentzian functions, and smoothly cutoff functions—yield solutions which are dominated by the plasma wave for long periods of time, although the plasma wave may not be present in the asymptotic limit. The distribution functions that are chosen lead to specific examples of each conceivable type of singularity structure for the integrand in the representation of the solution. It is suggested, therefore, that Landau's conclusion that all long-wavelength disturbances in a plasma produce a damped plasma wave which dominates the ensuing behavior is physically correct.
Computer Experiments on the Randomization of Electrons in a Collisionless Plasma
Authors: Burger P. , Dunn D. A. , Halsted A. S.
Published: December 2004

The large-signal, time-dependent behavior of a one-dimensional, collisionless plasma is simulated on a computer by calculating the trajectories of a large number of charge sheets in a one-dimensional space. The equations of motion of the charge sheets are calculated self-consistently with the electric fields that the charges themselves set up in the diode. A plasma is formed in the diode by the generation of electron and ion sheets at a constant rate in time and space. The velocity distribution, charge distribution, and potential distribution of the simulated plasma are investigated. Electrons and ions are generated with prescribed initial velocities. Because of the heavy mass of the ions, the potential in the middle of the diode becomes positive with respect to the wall. The potential does not settle down to a dc state, however, but exhibits fluctuations at the electron plasma frequency. It is shown that these rf fluctuations randomize the velocities of the electrons. A clear similarity is shown between the effects of these rf fluctuations and elastic collisions.
Excitation of Hydromagnetic Waves by a Gyrating Proton Stream
Authors: Neufeld Jacob , Wright Harvel
Published: December 2004

It is shown that hydromagnetic waves excited by a stream of protons gyrating around the lines of a static magnetic field (helical proton beam) result from superluminous and counterstreaming instabilities. Physical conditions under which hydromagnetic P and B instabilities can occur are investigated with particular reference to the intensities of the helical proton beam and the rate of growth of the excited waves. It is found that in some instances the qualitative behavior of instabilities is different for different beam intensities. When the beam is very tenuous, the hydromagnetic B instability has a lower rate of growth than the P instability. However, for larger beam intensities the B instability has the larger rate of growth. Therefore it represents the dominant instability. The applicability of the results of the investigation to the analysis of low frequency pulsations of the terrestrial magnetic field is discussed.
Gravitational Resistive Instability of an Incompressible Plasma in a Sheared Magnetic Field
Authors: Roberts K. V. , Taylor J. B.
Published: December 2004

The gravitational resistive instability analysed by Furth, Killeen, and Rosenbluth and subsequent authors is examined from a new point of view, which brings out the connection with ordinary Rayleigh-Taylor instability and thermal convection. In contrast to the modes found by earlier authors, which are either sharply localized in the vertical direction or require a boundary layer, it is shown that coherent motions of arbitrary vertical extent can occur. These alternative modes are derived by first considering a simpler but related model in which resistivity is concentrated at the ends of a system of finite length. This analysis shows that such systems may be unstable even if they satisfy the Newcomb criterion. The new resistive modes do not have the usual periodic dependence along the horizontal direction of the main field, but have finite length and represent convective rolls which are twisted to conform to the field lines. The relation of these new modes to the original periodic localized modes is examined.
Finite Amplitude Instability of a Plasma Column
Authors: Holter O/ivin , Johnson Roy R.
Published: December 2004

A weakly ionized cylindrical plasma column is investigated in a longitudinal magnetic field larger than the critical field which makes the column unstable to small perturbations. The restriction of small perturbations is removed by superimposing a finite amplitude helix upon the steady state density and potential. The stability of this system is investigated and conditions for marginal stability are found as a function of the amplitudes of the superimposed helix. Results of numerical calculations of electric field, wavelength, and frequency as functions of the magnetic field are given for the helical (m = 1) mode for different values of the amplitude parameter. Two sets of solutions are found. One set is singled out and combined with the energy balance theory of the positive column. The results given in plots are compared with experimental data and found to be in qualitative agreement with measurements of electric field, wavelength, and frequency. A hysteresis effect is predicted, and the paramagnetism of the positive column above a certain gas pressure is verified.
Frequency and Wavenumber Shifts for Nonlinear Waves in a ``Hot'' Plasma
Authors: Tidman D. A. , Stainer H. M.
Published: December 2004

The perturbation methods of Krylov, Bogoliubov, and Mitropolsky are applied in a generalized form to some cases of wave propagation in a ``hot'' electron plasma. Amplitude-dependent frequency and wavenumber shifts are derived from the condition that the perturbation expansions be free of secular terms.
Lowering of the Ionization Energy in a Plasma with Different Temperatures
Authors: Ecker G. , Kröll W.
Published: December 2004

The lowering of the ionization energy in a plasma is due to the interaction of all particle components. The magnitude of this effect in the Saha equation of a plasma in thermodynamic equilibrium has been treated in a number of investigations. Here we study the same problem for a plasma with different temperatures of the particle components. Each component is uniformly distributed in the configuration space and quasi-Maxwellian in the velocity space. A generalized Saha equation is derived using the methods of irreversible thermodynamics. The lowering of the ionization energy can be calculated with the help of the correlation functions. It is given in terms of particle number density and temperatures.
Kinetic Model for Binary Gas Mixtures
Authors: Hamel Bernard B.
Published: December 2004

A method has been developed for treating the Boltzmann equation for a binary gas mixture with inverse fifth power molecular interaction. This method involves replacing the complete collision integral in the Boltzmann equation with a kinetic model. This kinetic model reproduces the collisional transfer of momentum and energy for Maxwell molecules, as well as conserving mass, momentum and energy. Several interesting linearizations of the model equations are presented, among which is a simplified form particularly well suited to the case of disparate masses.
Sphere Drag in Flows of Almost-Free Molecules
Authors: Liu Vi-Cheng , Pang Sing-Chin , Jew Howard
Published: December 2004

A kinetic theory of sphere drag in the transition flows, based on the Boltzmann equation for the Maxwellian molecules, is presented. The exact binary collision integral, in the first order Knudsen iteration, is expanded as a function of Hermite polynomials in molecular velocity. The drag of a sphere at free stream temperature with molecular diffuse reflection is calculated. The results agree well with Millikan's measured values over a wide range of Knudsen number (0.5 < λ/d < 10). It is found that the sphere drag of the almost-free molecular flows normalized by the corresponding collisionless drag is essentially independent of the speed ratio for the present range of calculations.
Reaction Dwell Time and Cooling Rate in a Single-Pulse Shock Tube
Authors: Tschuikow-Roux E.
Published: December 2004

A method for the production of a constant, well-defined reaction dwell time in a single-pulse shock tube is discussed and an expression is derived giving the dwell time in terms of geometric and flow parameters. The effect of finite cooling rate on the reaction rate is considered and a correction factor to the observed rate constant is given. This cooling correction is shown to be directly proportional to T2, inversely proportional to the cooling rate dT/dt, and the reaction dwell time t1, and, to a first approximation, independent of the heat-capacity ratio, γ = Cp/Cv.
Current Sheet Tilt in a Radial Magnetic Shock Tube
Authors: Johansson Rolf B.
Published: December 2004

An experiment is carried out in a radial (inverse pinch) shock tube with argon of 50–400μ pressure and hydrogen of 100μ pressure. The current sheet was found to be tilted so that the cathode side lagged the anode side. At the anode the shock has a tilt in the same direction as the current sheet. At the cathode the shock is normal. These phenomena can be correlated by physical models which assume that the current is predominantly carried by the ions.
Evaluation of Parasitic Remixing in Thermal Diffusion Columns
Authors: Raman S. , Dave S. M. , Narayanan T. K. S.
Published: December 2004

A quasi-theoretical method to evaluate the parasitic remixing constant in a thermal diffusion column is given. The method is applied to the Saxena and Watson column measurements on neon. It is shown that calculated values of separation agree well with experimental values when parasitic remix ing constant, thus evaluated, are included in the expression for separation. The agreement is better for the more realistic Lennard-Jones (12–6) potential than the inverse power potential. It is found that parasitic remixing increases with pressure, though no simple power relation exists.
Asymptotic Theory of the Positive Column of a Gas Discharge
Authors: Cohen Ira M. , Kruskal Martin D.
Published: December 2004

Within the positive column of a glow discharge a balance is struck between production of charged particles by ionizing collisions of electrons with neutrals and loss of charged particles by diffusion to the walls where they recombine. Since the column is assumed to be longitudinally uniform, it is the cross-sectional distribution of electric field and ion and electron densities that are found from a solution of the flux equations and Poisson's equation. In the limit D+/D− → 0 (D+,− are diffusion coefficients), the relation between ionizing collision frequency and density of electrons at the center of the discharge, splits into two distinct regions. Within each of these regions the governing system of equations is reduced to a single second-order differential equation which is solved numerically, together with the associated boundary layers which are solved explicitly. Further, the large charged particle density (or small Debye length) limit is taken. The solution splits into a quasi-neutral main region and a space charge sheath boundary layer. The quasi-neutral solution is given to second order in the expansion. It is noted that the space charge sheath equations are equivalent to those solved in an earlier paper by the first author. The matching between the quasi-neutral and space charge regions is carried out to a high order in the expansions. A new and unexpected result is found—the ionization frequency tends to its limiting value for large charged particle densities from below—implying a minimum in the characteristic curve.
Stability of a Liquid Layer Adjacent to a High-Speed Gas Stream
Authors: Chang I-Dee , Russell Paul E.
Published: December 2004

The interfacial stability of a liquid layer with a compressible gas flowing over it is investigated. The liquid is assumed to be incompressible and viscid; the gas to be inviscid and to obey the equations of linearized compressible flow theory. The effects of surface tension at the gas-liquid interface and a gravitational body force are included. The criteria for the stability of a chosen equilibrium configuration of the system are determined by solving the linearized equations of motion for small perturbations about the equilibrium configuration. The configuration is considered to be stable if the perturbations decrease with time and unstable if they increase. Marginal stability is defined as the periodic, oscillatory motion of the perturbations. First, the interfacial stability is analyzed by means of a steady-gas-motion approximation. The effects of viscosity are neglected. Then the analysis is extended to include viscosity and the effect of the finite depth of the layer.
Gravitational Instability between Horizontal Plates with Shear
Authors: Deardorff J. W.
Published: December 2004

The problem of stability of infinitesimal disturbances within a Boussinesq fluid confined between horizontal plates, the lower of which is maintained warmer than the upper, is examined for the case of small, constant shear and for several different Prandtl numbers. The results indicate the stabilizing effect of increasing Reynolds and Prandtl numbers for disturbances in a vertical plane aligned in the direction of mean flow. For disturbances in a vertical plane transverse to the mean flow, the stability criterion with shear remains the same as that for pure convection.
Structure of Turbulent Velocity and Scalar Fields at Large Wavenumbers
Authors: Pao Yih-Ho
Published: December 2004

For incompressible turbulent flow with large Reynolds and Péclet numbers, mechanisms for the spectral transfer of kinetic energy, heat, and mass at large wavenumbers are proposed. Based on these mechanisms, turbulent energy, temperature, and the concentration spectrum functions are deduced for the entire universal equilibrium range of wavenumbers. The resulting one-dimensional energy, temperature, and concentration spectra are compared with measurements.
High-Temperature Cores in Exploding Wires
Authors: Bennett F. D.
Published: December 2004

Our recent studies show that the precipitous rise in resistance during the initial expansion of the wire occurs because of a radially symmetrical, inward travelling, vaporization wave which transforms the wire to a nonconducting gas. Presence of the inward travelling vaporization wave implies longer heating of the wire interior and a temperature rise with decreasing radius. An approximate theory of the expansion is given which allows estimates to be made of the core temperatures achievable by varying the wire and circuit parameters. The experimental production of high-temperature cores is limited at present by the occurrence of voltage breakdown at the interface between wire and ambient atmosphere.
Triplet Correlation for a Plasma
Authors: O'Neil Thomas , Rostoker Norman
Published: December 2004

The three-body and two-body electron-correlation functions are calculated for a plasma in thermal equilibrium. The method involves convergent kinetic equations developed from the hierarchy by an expansion in ε = 1/4πnLD3 which is carried to second order. The free energy determined by this method agrees with the previous result of Abé.
Steady-State Plasma in a Plane
Authors: Hurley James P.
Published: December 2004

A self-consistent solution of the steady-state magnetohydrodynamic equations for a charge neutral plasma in a plane is determined. In the absence of any external magnetic field a general solution for the magnetic field generated by the plasma is determined in terms of any prescribed pressure distribution. A solution is also obtained for certain singular external fields.
Superfluid Flow in a Venturi Tube
Authors: Meservey R.
Published: December 2004

It is shown from Bernouilli's equation that a Venturi tube or Pitot tube as ordinarily used will have practically no level difference with irrotational fluids. A quantitative solution is given in the case of a Venturi tube of various dimensions. The observed level difference with water follows simply from the rotational acceleration term of the Navier-Stokes equation. This result for irrotational fluids is discussed with respect to experiments using liquid helium and superconductors.
Antinormalization Properties of the Correlation Functions
Authors: Liboff Richard L.
Published: December 2004

An antinormalization condition is derived for the s-particle correlation function 𝒞s, according to which ∫ 𝒞s dk = 0, 1 ≤ k ≤ s ≤ N. The differential of phase for the kth particle is written dk. There are N particles in the whole system. When added to two previously known asymptotic conditions on the s-particle distribution about vanishing and infinite interparticle distance, respectively, this constraint forms three independent properties of the s-particle correlation. For the special case of the two-body (equilibrium) correlation 𝒞2(r), it is proved that a sufficient condition in order that 𝒞2 have two zeros on the open r axis (0 < r < ∞) is that 𝒞2 be negative in an interval about the point at infinity. Application to the Debye correlation is discussed, and it is concluded that this function has at least two zeros in the nonlinear domain about the origin.
Role of Diluent Gases in Oxygen Sensing by Magnetic-Field Induced Viscosity Changes
Authors: Hoeksema H. M.
Published: December 2004

The viscosity of oxygen is reduced in the presence of a magnetic field. This is generally assumed to be due to a change in the collision probability of the paramagnetic oxygen molecules. With the aid of formulas derived by Chapman and Enskog, the viscosity change in a mixture of gases is calculated and compared with the change for 100% oxygen. The calculations predict that the magnitude of the change is not necessarily proportional to the mole fraction of oxygen. For a mixture of 50% oxygen and 50% helium the relative viscosity change is not 50% of the change obtained with 100% oxygen but larger, namely 71.5%. Conversely, when diluted with the heavier gas, carbon dioxide, it is smaller, namely 42.5%. An instrument using the viscosity change to measure the amount of oxygen in space vehicles is described. Measurements of different gas mixtures are made with this instrument. Contrary to earlier measurements by Senftleben of the change of heat conductivity of gas mixtures in a magnetic field, the measurements of a viscosity change reported herein agree satisfactorily with theory.
Stability of a Non-Newtonian Liquid Film Flowing Down an Inclined Plane
Authors: Yih Chia-Shun
Published: December 2004

A layer of a non-Newtonian liquid, of which the constitutive equation is triply nonlinear, flows down an inclined plane under the action of gravity. The stability of the flow against wave formation is investigated. With M denoting a parameter involving the first and the second viscosities, the critical Reynolds number is given as a function of M and the slope of the plane, for small values of M. The theory presented here shows how free-surface instability of non-Newtonian fluids can be attacked, and provides a basis for stability experiments with non-Newtonian fluids.
Self-Similar Motions for Compressible Media
Authors: Lee T. S.
Published: December 2004

A new self-similar plane flow model is discovered through an unsteady flow theory previously developed. The physical situation considered concerns the possible generation of a shock-led recompression layer in front of an interface when the latter is moving against a fully-developed centered rarefaction wave in such a way that its distance from a certain virtual vacuum boundary has some w power-law dependence on time after initiation. The present study treats the detailed character of this recompression and shows conclusively that similarity solutions exist for any constant-γ medium driven by a constant-w (>1) interface motion. Their main features are (1) that flow similarity is exact only when viewed from the virtual vacuum boundary, (2) that entropy distribution is uniform, and (3) that any family of flows sharing common w and γ lead to identical flow profiles and shock strength with the latter explicitly given by a Mach number M = (γ + 1) (γ − 1)−1 w − 2(γ − 1)−1. Test calculations for a w = γ = 2 special case have been included as a demonstration. The analogy in the two-dimensional steady hypersonic flow is noted.