bluuebunny/crossref_metadata_2025 huggingface dataset:
Perturbation Calculation of Mixed Pair Correlation Functions
Authors: Lowry B. A. , Davis H. T. , Rice S. A.
Published: December 2004

A perturbation calculation of the change in pair correlation function (relative to some reference system) is presented for the case when the intermolecular pair potential is altered (relative to the same reference system). The analysis is developed in detail for the case of a very dilute solution of perturbing molecules in a host dense fluid, but the case of the pure fluid is also examined. Numerical calculations for a variety of inverse power potentials show that when the perturbation potential is much smaller than kT, many body interaction terms are very small and the simplest approximation, g2(R) = g20(R) exp [−βVp(R)] is valid. When Vp ∼ kT, this is no longer true; the many body effects then make an important contribution to the change in g2(R). Explicit formulas are presented for the correction terms to order β2 and general formulas valid for all β are displayed in unexpanded form.
Nonthermal Impurity Radiation from a Spherical Plasma. II.
Authors: Cuperman S. , Engelmann F. , Oxenius J.
Published: December 2004

The steady-state radiation loss of a homogeneous and isothermal spherical plasma due to an optically thick spectral line is calculated under the assumption that all other transitions of the considered atoms remain optically thin. The line profile is approximated by a rectangular profile and by a Doppler profile, respectively. The energy losses found can be described in almost all cases of practical interest by a volume radiation formula and are in general much smaller than the losses corresponding to thermal radiation. In the case of an optically thick plasma emitting radiation far from thermal equilibrium the spectral distribution of the intensity is double humped simulating a self absorption effect of a cold outer layer. The consistency of the assumption of a spatially constant absorption coefficient on which the calculations were based is checked. The Eddington approximation is shown to be in good agreement with the exact solution of the problem. The numerical results are compared with those obtained from algebraic formulae valid in some limiting cases.
One-Dimensional Magnetogasdynamic Flow with Heat Transfer
Authors: Liu Ching Shi , Cambel Ali Bulent
Published: December 2004

The case of one-dimensional magnetogasdynamic flow with heat transfer is analyzed. It is shown that the flow variables can be expressed as functions of the dimensionless K number. The important flow regimes are delineated and it is observed that although the flow is reminiscent of classical flow with heat transfer, there do appear significant differences.
Incompatibility of Beltrami Flow with Viscous Adherence
Authors: Joseph Daniel D.
Published: December 2004

Boundary conditions on the vorticity are deduced to infer conditions under which Beltrami flows of a viscous fluid are possible. The inconsistency of steady and unsteady Beltrami flow with adherence to rigid surfaces is established for a broad class of rigid motions of the bounding surfaces. The implications of isochoric motions are explored, and the possibility of an isochoric Beltrami motion of a Newtonian fluid is eliminated for rigid translatory motions of the boundary surface. The inconsistency of Beltrami flows of any fluid with rotation about an axis of geometric symmetry is also established. It is shown that the adherence condition implies either a vanishing or infinite vorticity at boundary surfaces for certain kinematically possible types of Beltrami motions.
Jet Impingement on a Dust-Covered Surface
Authors: Sibulkin Merwin
Published: December 2004

The effects of a jet exhausting into a vacuum and impinging on a dust covered surface have been studied. The axis of the jet, which issued from a small rocket-type nozzle, was normal to the surface. For thin layers of dust, the erosion caused by the jet resulted in the formation of an annular, dust-free surface. An analytical model is proposed which qualitatively accounts for this annular pattern and its variation with nozzle position. The model is also used to correlate the results of tests made with several types of dust.
Impurity Radiation from Non-Maxwellian Spherical Plasmas
Authors: Cuperman S.
Published: December 2004

The influence of non-Maxwellian free electron energy distributions on the steady state de-excitation radiation of not completely stripped impurity ions persisting in homogeneous spherical plasmas is investigated. A formulation of the source function for arbitrary free electron energy distributions is given. Numerical examples which emphasize the importance of the effect discussed are presented.
Field Correlation Functions in a Plasma
Authors: Oppenheim I. , Van Kampen N. G.
Published: December 2004

The correlation function between the electrostatic field at point a and the electrostatic field at point b in a fully ionized hydrogen plasma is computed. The correlation function is shown to be a long-range function of the distance between points a and b. This result has significance in the treatment of transport properties in a plasma.
Nonsteady Helical Flows of Second-Order Fluids
Authors: Markovitz Hershel , Coleman Bernard D.
Published: December 2004

Some exact solutions of the third-order vector partial differential equation describing nonsteady flows of incompressible second-order fluids are presented. Although periodic simple shearing flow is also discussed, the main emphasis here is on helical flows between moving coaxial cylinders, particularly periodic flows of the Couette and Poiseuille type. The calculations suggest that, for such periodic helical flows, measurements of the radial thrusts on the bounding cylindrical walls supply practicable methods for the determination of normal-stress coefficients.
Small Periodic Disturbances in Polyatomic Gases
Authors: Monchick L.
Published: December 2004

The Chapman-Enskog approximation to the velocity-energy distribution for a polyatomic gas is reinvestigated and found to yield unacceptable results for small amplitude sound waves. The solution to the linearized Boltzmann equation is then expanded in a set of orthogonal polynomials in the dynamic variables for translational and internal degrees of freedom and an iterative method of approximation is set up. This method of attack is a natural continuation of the work of Maxwell, Waldmann, of Ikenberry and Truesdell. Under some conditions the first iteration approaches the second Chapman-Enskog approximation (or Navier-Stokes approximation) as t → ∞. The polynomial expansion was then truncated and the first iteration was used to calculate the heat flux, pressure tensor, and characteristic temperatures for a small amplitude sound wave. The second iteration was also investigated and was found to affect mainly only the heat fluxes. A useful formula is presented for the thermal conductivity of a polyatomic gas with N internal degrees of freedom in the limit of zero frequency.
Long Wavelength Instability in a Reflex Discharge
Authors: Bingham Robert
Published: December 2004

An examination of the stability of the reflex arc discharge against a long wavelength m = 1 instability has been carried out. In performing the calculation, use was made of the experimental plasma density distribution and the plasma potential distribution as computed by Chen for a hot cathode reflex arc in a strong magnetic field. It is found that the discharge is unstable for helical instabilities with wavelength greater than 1200 R cm, where R is the discharge radius. The growth rate increases with increasing wavelength. This result is consistent with that of Simon's analysis of a slab geometry with crossed electric and magnetic fields.
Decay of Isotropic Turbulence in the Direct-Interaction Approximation
Authors: Kraichnan Robert H.
Published: December 2004

The direct-interaction equations for the decay of isotropic turbulence are integrated numerically with initial spectra of several shapes and initial values of Rλ ≲ 40. Results are presented for the evolution of total energy, dissipation, energy transfer, skewness factor, and other integral quantities, together with the associated wavenumber spectra. Similarity and self-preservation features of the evolving spectra are exhibited. The results are compared with grid-turbulence measurements by Stewart and Townsend. Results are also given for the time-correlation of the total velocity at a fixed point in space and for the time-correlation and response functions of individual wavenumber modes.
Experimental and Theoretical Studies of Instabilities in a High-Energy Neutral Injection Mirror Machine
Authors: Kuo L. G. , Murphy E. G. , Petravić M. , Sweetman D. R.
Published: December 2004

Recent observations with the Phoenix high-energy neutral injection experiment are described. At densities where the electron plasma frequency is greater than the ion cyclotron frequency, strong emission at the ion cyclotron frequency and ½ the ion cyclotron frequency is observed. This is interpreted on the basis of the theory of electrostatic instability developed by Harris and others. Experimentally, the instability results in strong scattering of ions out of the transverse direction but so far as can be observed, there is no actual loss of plasma. Above a density of 5 × 108 particles/cm3, accumulation of particles is limited by the development of strong low-frequency (∼100 kc/sec) oscillations which appear to be an m = 1 displacement of ions and electrons rotating at half the ion precession frequency. This mode is approximately independent of density. During periods of strong emission at the ion cyclotron frequency, however, another mode is observed, the frequency of which is approximately proportional to density. These observations suggest an m = 1 precessional drift instability. The existing theories concerning this low-frequency instability are fully discussed. We present a new calculation in which the cylindrical plasma shape and the associated boundary conditions are taken into account. Its predictions are in reasonable agreement with the experiment. The electric field inside the plasma is found to be nonuniform even for the m = 1 mode, so that finite Larmor radius effects are to be expected for this mode, contrary to common belief. The full equation for the electric potential valid for all densities and including the first order finite Larmor radius effect is presented. However, the finite Larmor radius effect is found to be small at densities around 108 particles/cm3, and at magnetic fields above 10 kG.
Diagonalizing Approximation for Inhomogeneous Turbulence
Authors: Kraichnan Robert H.
Published: December 2004

An approximation for shear and Boussinesq turbulence is introduced which can greatly lessen the computational task associated with spatial inhomogeneity. It yields statistical equations for inhomogeneous flow which are of simplicity comparable to the direct-interaction equations for homogeneous flow. The new approximation presupposes a representation of the turbulent fields by expansion in some appropriate set of orthonormal functions which obey the boundary conditions. The covariances which are off-diagonal in the chosen representation, as well as the triple correlations, are approximated in terms of diagonal covariances and diagonal average response functions by a procedure resembling the direct-interaction scheme. The final equations involve only the mean-field amplitudes and the diagonal covariance and response functions. The approximation is illustrated by applying it to infinite-Prandtl-number Boussinesq convection between infinite horizontal planes. The range of applicability and the limitations of the approximation are discussed.
End-Wall Heat-Transfer Effects on the Trajectory of a Reflected Shock Wave
Authors: Sturtevant Bradford , Slachmuylders Erik
Published: December 2004

The trajectory of a reflected shock wave has been measured near the end wall where the motion is perturbed by the displacement effect of heat transfer to the wall. In this experiment an x, t diagram of the reflection of an Ms = 4.08 shock wave was constructed by measuring shock arrival times with small probes. The parameter that measures the (negative) displacement thickness of the end-wall thermal layer, a ``Reynolds number'' R based on the shock velocity, the time after reflection, and the thermal diffusivity was varied between 9 and 600. In this range the measured deviation of the shock trajectory from ideal varied from 1½ to 17 shock thicknesses. The shock velocity was determined by differentiating a least-squares fit of the data to a fourth-order polynomial in R−½. In the range of the experiments the shock accelerated from a velocity that was 20% below ideal to one that was within 4% of ideal. Experiment agrees with boundary-layer theory above R = 150 for the shock trajectory and above R = 25 for the shock velocity, and implies that the exponent of the power-law dependence of the thermal conductivity on temperature is 0.81 ± 0.02. The small deviation of the shock velocity from boundary-layer theory predicted for R < 100 by higher-order theory is not observed, though since this theory falls just within the estimated experimental error this result is somewhat qualified. In any case, the unexpected agreement with first-order theory at small R indicates that molecular effects, such as temperature jump, do not play a large role when the shock is more than ten shock thicknesses from the end wall.
Reflection of Strong Blast Waves
Authors: Chang Tien Sun , Laporte Otto
Published: December 2004

The reflection of strong point-source blast waves is studied using the continuum concept of flow of ideal gases. Methods of obtaining the upper and lower bounds as well as a Taylor series expansion of the position of the reflected shock is considered. The procedure of studying the flow variables near the reflected shock is also described.
Microwave Reflection from Shock-Produced Plasmas
Authors: Bethke George W. , Ruess Allen D.
Published: December 2004

Reflection measurements have been made of very low power X-band microwaves, axially incident on shock-produced xenon and krypton plasmas. The electron density profile at the advancing shock front was measured with a special high-resolution transverse 60-kMcps interferometric probe. On comparison with free space exponential plasma-microwave interaction theory, the measured reflection coefficients were always found to be very significantly lower than the theoretical values, the greatest disagreement being at the lowest plasma densities.
Hall Effect and Electron Drift Velocities in the Plasma of the Positive Column
Authors: Anderson John M.
Published: December 2004

The Hall potential has been observed for positive columns established at pressures near 1 Torr in helium, neon, argon, and nitrogen. Simultaneous measurement of the density of electrons in the column by the microwave cavity technique has given an independent determination of the electron drift velocity. The proportionality factor α between the Hall field measured and the product of the drift velocity and applied magnetic field has been determined. The factor α for the case of helium was 0.50 ± 0.07, which is in agreement with theory. For neon, α ≅ 0.60, also in agreement with theory. The column established in argon or nitrogen was generally noisy, but α ≅ 0.5 and showed a tendency to decrease with decreasing gas pressure, also expected from theory. Electron collision frequency for momentum transfer was determined by microwave methods and also from the dc mobility. The agreement was satisfactory.
Tensile Strengths of Liquid Argon, Helium, Nitrogen, and Oxygen
Authors: Beams J. W.
Published: December 2004

The tensile strengths of several liquids at low temperature were measured by a linear deceleration method. The values found were as follows (expressed in atoms): argon −12, nitrogen −10, oxygen −15, and helium −0.16. The values are somewhat lower than those calculated from the theory.
Flow Field of a Flame in a Channel
Authors: Uberoi Mahinder S.
Published: December 2004

A stationary flame is stabilized in a two-dimensional channel in such a way that it closely corresponds to the case of a flame propagating in a channel. The entire flow field of unburned and burned gases is mapped by taking stroboscopic photographs of small particles suspended in the combustible gases. The asymptotic flow field of the burned gases is analyzed in terms of flow conditions at the flame. The possibility of obtaining an analytic flow field on the basis of constant flame speed is examined. It appears that no solution exists unless the channel walls in the region of burned gases are displaced inward. This investigation, together with the previous work on the flow field of a Bunsen flame, leads to some general remarks about the structure and stability of laminar flames. The various predictions are in agreement with experiments. In particular, the convex flames are possible and concave ones impossible within the framework of the theory based on constant flame speed.
Rayleigh's Problem in Magnetohydrodynamics
Authors: Chang C. C. , Yen J. T.
Published: December 2004

Extension of Rayleigh's problem to magnetohydrodynamics is investigated for a perfectly conducting plate with a transversely applied magnetic field. Induced electric and magnetic fields are both included in the analysis. Results obtained show that along the plate an electromagnetic body force will act in the direction of fluid motion. The results are found to be the same whether the applied magnetic field is fixed-in-space or attached to the moving plate. A comparison of these results with those of Rossow (magnetic field fixed with fluid) shows opposite trends in the velocity profile. Such discrepancies are discussed. Rossow's second case (magnetic field fixed with plate) is also discussed.
Stability Considerations on Nonviscous Jets Exhibiting Surface or Body Tension
Authors: Debye Peter , Daen Jerome
Published: December 2004

The question of the range of ejected liquid streams is connected with the relation of the stability of the jet motion to an initial infinitesimal disturbance. This is investigated as a theoretical problem for the planar and cylindrical cases neglecting any fluid viscosity. In addition, the stabilizing influence of either a surface or ``body tension'' is calculated. Comparison of the theory with some published data is found to yield qualitative and semiquantitative agreement. The possibility of applying this theory to the measurement of dynamic surface tensions is suggested.
Measurement of Turbulent Transition, Motion, Statistics, and Gross Radial Growth behind Hypervelocity Objects
Authors: Slattery R. E. , Clay W. G.
Published: December 2004

The laminar-turbulent transition behind 0.500-in.-diameter spheres at 8500 ft/sec and behind 12.5° half-angle cones at 5500 ft/sec in air have been measured as a function of pressure. Schlieren motion-picture techniques were used to analyze the turbulent motion and the results are described. Autocorrelation functions of the density fluctuations of the turbulence have been measured. From these values Δρ/ρ has been calculated and the results are given for several positions in the turbulent trail at 30 mm Hg downstream air pressure. In addition the authors' previous measurements of the gross radial growth of the turbulent wake have been extended to pressures of 10 mm Hg for the case of 0.500-in.-diameter spheres and to the trail behind 12.5° half-angle cones for two pressures.
Density in a Simple Model of the Exosphere
Authors: Aamodt R. E. , Case K. M.
Published: December 2004

The particle density of a simple model of the exosphere is obtained by solving exactly the collisionless Boltzmann equation. The main point of the solution is that it is a discontinuous, multivalued function of the constants of motion. Results, of course, agree with those of other methods based on Newtonian mechanics.
Plasma Behavior in a Cusp-Mirror Magnetic Field
Authors: Combes L. S. , Gallagher C. C. , Levine M. A.
Published: December 2004

A plasma containment device has been constructed in which an attempt has been made to combine the basic stability advantages of a four-pole line cusp with the low loss rate of a mirror field. The magnetic field was produced by the addition of the mirror field orthogonally to the cusp field. Using pulse techniques an ionized gas was created within a biconical chamber and a magnetic field produced transiently with the mirror field along the axis of the chamber (Z axis) and the cusp field in the X-Y plane. Measurements with magnetic probes and light pipes show that a disturbance in the magnetic field accompanied by an increase in light intensity started at the periphery of the plasma chamber and was propagated inward at two velocities to the central axis. Detailed measurements made on the magnetic-field configuration indicate that, at the time of arrival of the second wave at the axis, the mirror field had been to a large extent separated from the cusp field so that mostly mirror field existed throughout the central region, while mostly cusp field existed in the outer region. The intensity of the field at this time in the central region indicates that the cusp field was compressing the plasma and mirror field so that the intensities of the mirror field in this region were even larger than the maximum intensity of the applied mirror field.
Ambipolar Diffusion of a Plasma in a Weak Magnetic Field
Authors: Fredricks R. W. , Mastrup F.
Published: December 2004

A generalization of the phenomenological description of ambipolar diffusion of a plasma is made to include the effects of a weak impressed magnetic field. The assumptions of congruence of the flow vectors (div Γ+ = div Γ−) for ions and electrons and of proportionality [n−grad (n+) = n+ grad (n−)] on the signed charge densities are utilized as in the existing theory of ambipolar diffusion; however, because of the rotational effects of the magnetic field, and additional assumption is made on the curls of Γ±. This assumption is curl Γ+ = curl Γ−. The resulting diffusion is found to be a combination of electronic and ionic diffusion, and the components of the ambipolar diffusion tensor are calculated for a unidirectional magnetic field.
Collisional Damping of Plasma Oscillations
Authors: Comisar G. G.
Published: December 2004

The attenuation of electron oscillations in a fully ionized plasma with a small amount of Coulomb scattering is investigated by means of the Fokker-Planck equation. In the present treatment, dynamical coefficients with the proper velocity dependence are utilized in contrast to previous work based upon simplified collisional models. The use of transform methods leads to a modified Landau dispersion integral from which follow the temporal damping decrement for ion-electron collisions: γi = [νcoll/3(2π)½] [1 + 4 (k rD)2]; and the corresponding electron-electron decrement: γe = [νcoll/3(π½)] [1 + 3.85 (k rD)2], where νcoll is the electron collision frequency, k is the oscillation wavenumber, and rD is the Debye correlation length.
Kinetic-Theoretic Description of the Formation of a Shock Wave
Authors: Chu C. K.
Published: December 2004

The flow of a gas in a shock tube is treated in the context of kinetic theory as an initial value problem for the one-dimensional Krook equation. The only simplifying assumption made is that the gas is one-dimensional. This corresponds to a gas with an adiabatic constant γ = 3. A finite difference method is proposed, utilizing the fact that, for sufficiently small time intervals, the gas experiences essentially free molecular flow, so that the collision effects can be treated as a first-order correction. The conservation laws are not used. The computed solution agrees excellently with the classical solution, but in addition, has shock structure, diffusion of the contact discontinuity, and dispersion of the expansion wave, all incorporated. The same procedure is used to calculate steady-state shock structure, to which the shock developed in the shock tube is compared. It is seen that for the strength of the shock calculated (Pressure ratio of tube 10:1, shock Mach number 1.43, γ = 3), the shock is essentially ``fully developed'' after about 20 mean collision times of the low-pressure gas. In conclusion, an exact reduction procedure is given by which problems for a monatomic three-dimensional gas (γ=53) are reduced to the solution of two simultaneous Krook equations, manageable by the present procedure without vastly increasing the need for computing capacity.
Spectral Line Emission from a Transient Nonuniform Plasma
Authors: Oertel G. K. , Griem H. R.
Published: December 2004

Some effects of spatial gradients and transient behavior on spectral line radiation from impurities in a low-energy θ-pinch plasma are discussed for a case where local thermodynamic equilibrium could not be assumed. The plasma was produced and preheated by a fast capacitor bank discharge, a controlled trapped magnetic field was generated by a slower discharge through the same coil, and magnetic compression was achieved by a fast rising reverse magnetic field. Measured carbon impurity line intensities were compared to predictions on the basis of magnetohydrodynamic calculations coupled with spectroscopic theory. Large errors are incurred in electron temperatures from relative intensities of lines from successive stages of ionization if the radial variation of ionization and excitation is ignored.
Unified Theory for the Langmuir Probe in a Collisionless Plasma
Authors: Lam S. H.
Published: December 2004

An asymptotic analysis is presented of the Langmuir-probe problem in a quiescent, collisionless plasma in the limit of large body dimension to Debye length ratio. The structures of the electric potential distribution about spheres and cylinders are analyzed and discussed in detail. It is shown that when the probe potential is smaller than a certain well defined value, there exists no sheath adjacent to the solid surface. At large body potentials, for which a sheath is present, the electric potential distribution is given in terms of several universal functions. Master current-voltage characteristic diagrams are given which exhibit clearly the effects of all the pertinent parameters in the problem. An explicit trapped-ion criterion is presented. The general problem with an arbitrary body dimension to Debye length ratio is qualitatively discussed.
Thermal Choking and Condensation in Nozzles
Authors: Pouring Andrew A.
Published: December 2004

An experimental and analytic analysis of water-vapor condensation zones in moist-air expansions is considered where the heat addition of condensation exceeds that for thermal choking. The transition from an unchoked to a choked flow is shown experimentally and described from the viewpoint of an analogous isentropic nozzle. Solution of the one-dimensional equations of motion for a fully choked nozzle flow involving shock waves is given, and sonic point locations are verified experimentally. Special emphasis is given to the effect of heat addition and area variation on flow behavior in the region of sonic points. It is concluded that the onset of condensation in experiments involving shock waves can be used in testing theories of homogeneous nucleation.
Microinstability of a Mirror-Confined Plasma
Authors: Guest G. E. , Dory R. A.
Published: December 2004

Infinite uniform magnetized plasmas with non-Maxwellian particle distributions are subject to electrostatic longitudinal instabilities of the type discussed by Harris. Mirror confinement leads to depletion of low energy ion populations and thus to the Rosenbluth-Post ``maser'' instability at frequencies ω » ωci, the ion gyrofrequency, and to the flute-like instability of Dory, Guest, and Harris with ω ≃ ωci and wave vector normal to the external magnetic field. This study is concerned with unstable waves which propagate obliquely with ω ≃ ωci and wavelength ≲ ρg, ion gyroradius. For their appearance it is necessary that ωpe/ωci exceed a threshold value of order n(1 + 8a2v2∥e / v2⊥i)½, where n is the harmonic number of the unstable wave, and v∥e and v⊥i are the components of electron and ion thermal velocity, parallel and perpendicular to the external magnetic field. Over a wide range of interesting conditions, the parameter a lies between 2 and 3. Furthermore, the plasma is stable if nωci ≲ ak∥v∥e or if ωpe ≲ ak∥v∥e, where k∥ is the parallel component of the wave propagation vector and ωpe is the electron plasma frequency. These waves are not fully stabilized by increasing ion temperature parallel to the field as are the anisotropy modes in a two-temperature Maxwellian plasma.
Slow Viscous Shear Flow past a Plate in a Channel
Authors: Graebel W. P.
Published: December 2004

Flow past a plate midway between two walls is studied analytically using the Stokes approximation. An exact solution is found for the semi-infinite plate using the Wiener-Hopf technique. For the finite plate an approximate technique related to variational principles is discussed which provides both upper and lower bounds on the drag.
Fluids of the Second Grade Regarded as Fluids of Convected Elasticity
Authors: Truesdell C.
Published: December 2004

A fluid of the second grade is shown to be indistinguishable by viscometric experiments from a fluid with convected elasticity. The sign of one coefficient in the constitutive equation of a fluid of second grade is that of the response time. The requirement that the fluid remember past, not future, is thus proved to be equivalent to an inequality derived from other grounds by Coleman and Markovitz.
Cusp Compression Experiments
Authors: Allen T. K. , Spalding I. J.
Published: December 2004

A shock-heated plasma of density 3.5 × 1015 cm−3 and temperature 4 × 104 °K is compressed by a rising cusp field which reaches 34 kG between the coils in 15 μsec. Time resolved measurements of electron density and temperature, plasma radius and hole size (at the ring cusp) are described and compared with the predictions of a simple hydrodynamic model in which the primary loss is by classical diffusion across field lines. The agreement between theory and experiment is within a factor of two and strengthens evidence provided by framing pictures that the plasma is stably confined for times of the order 10 μsec, with peak densities and temperatures of 2 × 1016 cm−3 and 16 ×6 104 °K, respectively.
Measurements on the Development of Thermal Turbulence in Air between Horizontal Plates
Authors: Willis G. E. , Deardorff J. W.
Published: December 2004

The transition from steady to turbulent thermal convection in air between horizontal plates is inferred from temperature measurements. Spatial and temporal records of air temperature for Rayleigh numbers ranging from 5000 to 1.5 × 106 are presented along with spatial temperature spectra. A region of transition from nearly steady organized convection to irregular turbulent convection was found to exist between Rayleigh numbers of about 6300 and 10 000, although a dominant wavelength continues to exist at much larger Rayleigh numbers. Spatial scales of temperature are noted to extend to both larger and smaller wavelengths with increase in Rayleigh number.
Transition of Hypersonic Boundary Layer
Authors: Nagamatsu H. T. , Graber B. C. , Sheer R. E.
Published: December 2004

An investigation was conducted in a hypersonic shock tunnel to study the boundary layer on a 10° cone of 4 ft length having a wall to stagnation temperature ratio of 0.214. An impact pressure survey of the various types of boundary layer flows was made at 34.5 in. from the cone tip. The free-stream conditions at this location for Mach number and stagnation temperature were approximately 10° and 1400°K. The tunnel operating conditions and cone tip configurations were combined such that laminar, transition, and turbulent flows were obtained at this location. The impact pressure data was reduced to velocity, temperature, and density profiles for comparison. Surface heat transfer results were also obtained at this location along with schlieren photographs of the boundary layers. All three types of information showed that the various boundary layer flows actually existed. The heat gauge showed the passage of turbulent bursts in the transition flow, as observed on a flat plate at subsonic velocities. From the velocity profiles, the local skin friction coefficient was determined for the laminar and turbulent flows, and it agreed reasonably well with the corresponding theories. For the smooth cone, it was not possible to develop fully turbulent flow at the 34.5-in. location for any of the present stagnation conditions but with tip roughness, the transition Reynolds number was sufficiently reduced to force this location into completely turbulent flow.
Hydrodynamic Stability of a Tangential Flow Between Cylinders Induced by Rotation and External Pumping
Authors: Sparrow E. M. , Lin S. H.
Published: December 2004

Consideration is given to the conditions marking the onset of instability for flow that is induced between concentric cylinders by simultaneous rotation of the cylinders and an imposed tangential pressure gradient. Critical Taylor numbers and corresponding disturbance wavenumbers have been determined by an analytical method that is applicable for arbitrary spacing between the cylinders. Numerical results are presented for a wide range of rotation and pumping conditions for cylinder radius ratios ranging from 0.95 to 0.35. The critical Taylor numbers are found to exceed those predicted on the basis of the narrow-spacing hypothesis.
Hydromagnetic Stability of Dissipative Vortex Flow
Authors: Chang Tien Sun , Sartory Walter K.
Published: December 2004

An analysis which considers the stability of dissipative, conducting, incompressible, pure vortex flow (vortex flow with 1/r-transverse velocity profile) in an axially applied magnetic field is presented. The vortex is assumed to be confined within two nonpermeable, rotating, perfectly conducting, cylindrical walls. The results of the analysis confirm the exact criteria reported previously for the limiting cases of inviscid flow with finite or infinite electrical conductivity. The paradox between the inviscid hydromagnetic results and Rayleigh's criterion for inviscid, incompressible, pure vortex flow without magnetic interaction is resolved. The analysis presented in this paper is quite general and does not require the usual assumptions pertaining to the magnitudes of the electrical conductivity and viscosity, or the gap-width between the cylindrical walls.
Propagation and Reflection of Sound in Rarefied Gases. II. Experimental
Authors: Maidanik Gideon , Heckl Manfred
Published: December 2004

Experiments were conducted to investigate the propagation and reflection of sound in air at low pressures (down to 5 × 10−5 mm Hg). The range of pressures of particular interest are those where the mean free path of intermolecular collisions is longer than the separation between the transmitter and receiver. The frequency range extends from 2 kcps to 12 kcps. Evidence of considerable multiple reflection is found when the separation is small. At larger separation the experimental results are in good agreement with theoretical predictions. The reflection of ``sound'' (i.e., a coherent component of alternating momentum which is partly preserved during molecular encounters with a solid surface) was also verified by using standing wave technique.
Bounds on Plasma Fluctuations and Anomalous Diffusion
Authors: Fowler T. K.
Published: December 2004

Upper limits on the intensity and growth rate of plasma fluctuations are calculated from purely thermodynamic considerations. From these limits, an upper bound on diffusion across a magnetic field by microinstabilities is estimated. Experimental results do not violate the bound. At low β, the dominant contribution to the bound is thermal energy which feeds fluctuations through a mechanism akin to expansion cooling of a gas, possible only in finite plasmas. A rapid decrease in anomalous diffusion in discharge afterglows when the radius R exceeds a critical value R0 ∼ 10–20 ion gyroradii can be explained if the instability radial wavelength, a parameter in the theory, is restricted to ≲R0. Then the bound on the stochastic diffusion coefficient decreases like R−3 if R > R0. With this restriction on wavelength, the bound used as a scaling law predicts adequately long thermonuclear confinement (≳0.1 sec) in a torus of 100 cm minor radius if the torus is stabilized against frequencies below the ion cyclotron frequency, now perhaps feasible. Otherwise, low-frequency resonant diffusion may limit containment. This result holds at least up to β of a few percent. Bounds on velocity diffusion are obtained, also. Both spatial and velocity diffusion are slow if electrons are cold compared to ions, which may account for observations in plasmas created by energetic ion injection.
Radio Waves in Turbulent Magnetoplasmas
Authors: Taylor Leonard S.
Published: December 2004

The Ewald-Oseen extinction theorem is generalized to account for electromagnetic propagation in a turbulent magneto-ionic medium. Using the Born (single-scatter) approximation, the effective dielectric constant for the medium is determined. The scattered field is derived and a general expression for the second-order term in the Born series for the mean-square amplitude of the scattered field is obtained.
Localized-Induction Concept on a Curved Vortex and Motion of an Elliptic Vortex Ring
Authors: Arms R. J. , Hama Francis R.
Published: December 2004

The localized-induction concept for the induction effect of a smooth curved vortex on itself is derived. This is an approximation applicable to the limiting case of a vortex filament of infinitesimal core size and of negligible long-distance effect, and was already successfully utilized in the investigations of the motion and deformation of a curved vortex filament given various initial configurations. Two theorems obtained under this concept are that the arc length of a vortex filament and the projected area of a closed vortex filament are both invariant with respect to time. These theoretical predictions are examined by a numerical analysis of the motion of an initially plane elliptic vortex ring of various eccentricities.
Experimental and Theoretical Study of Magnetohydrodynamic Ionizing Fronts
Authors: Patrick Richard M. , Pugh Evan R.
Published: December 2004

An experimental and theoretical description of ionization fronts propagating into hydrogen with a bias magnetic field in the plane of the front is presented. The experimental evidence showed that the absolute light intensity behind the front corresponds to a fully ionized plasma. The density ratio was obtained by measuring the magnitude of the current in the front, the front speed, and using the equation of mass and momentum. The front speeds are small compared to the Alfvén velocity and are characterized by a critical velocity Uc, where Uc is the velocity a molecule must have so the kinetic energy equals the energy necessary to ionize it. A theory for the ionization front was developed which neglects the plasma pressure and abandons the condition E = V × B both ahead and behind the front. The theory predicts the front velocity and the rather unusual variation of the density ratio across the fronts with the front speed.
Kinetic Theory of Dense Gases. IV. Transport Virial Coefficients
Authors: Hoffman David K. , Curtiss C. F.
Published: December 2004

The generalized Enskog equation, introduced by the authors in a previous paper, is solved and expressions for the transport coefficients are obtained. The method of solution is similar to the Chap-man-Enskog technique. First density corrections are obtained for the coefficients of shear viscosity, and thermal conductivity; and the first term in the density expansion of the bulk viscosity is also obtained. These density effects differ from those previously given by Snider and Curtiss in the inclusion of three-body collision effects. The coefficients are calculated explicitly for a gas of rigid spheres, and are shown to be identical with the Enskog results.
Transport Equations for a Gas Mixture
Authors: Tanenbaum B. Samuel
Published: December 2004

The Boltzmann equation is applied to a gas mixture in which each constituent is separately in equilibrium without necessarily being close to equilibrium with the rest of the gas. Exact conservation equations for the number density, momentum, and energy of each constituent in the mixture are derived for inverse power interparticle force laws. In the limit when the differences among the individual flow velocities, us — ut, are all small compared to a ``sound speed'' a0 = (2k)½[(Ts/ms) + (Tt/mt)]½, it is found that the conservation equations reduce, for all force laws, to a form similar (but not identical) to the continuum equations commonly used in plasma physics. For larger relative flow velocities, the equations retain this simple form only for Maxwell molecules. For other inverse power laws all the collisional transfer terms increase relative to the Maxwell molecule results with increasing a0 or |ut — us| for shorter-range forces (hard spheres, for example) and decrease with increasing a0 or |ut — us| for longer-range forces (Coulomb, for example). Finally, in the limit when a0 is small compared to |ut — us| it is shown that, with one exception, all collisional transfer terms become temperature independent.
Resistive Overstabilities and Anomalous ``Diffusion''
Authors: Chen Francis F.
Published: December 2004

A physical picture is given of microinstabilities which can occur in plasmas of finite resistivity with or without an effective gravitational field, and of finite Larmor radius stabilization. The drift waves become overstable because of a phase shift between the density and potential fluctuations. Transport of plasma across a magnetic field also arises from this phase shift; this transport does not necessarily resemble a diffusion process. This mechanism may account for the ``anomalous diffusion'' commonly observed in fully ionized plasmas. Particular attention is paid to the real part of the frequency and to the phase correlations, which can easily be measured to test this hypothesis. In regard to stellarator ``pumpout'', it is found that increasing the conductivity will not reduce the part of the loss rate which is due to the ``universal'' resistive overstability.
Nonlinear Effects in the Two-Stream Instability
Authors: Freidberg J. P.
Published: December 2004

The problem of the nonlinear interaction of two cold interpenetrating electron and ion streams is treated. By seeking traveling-wave-type solutions to the nonlinear two-fluid system of equations, an amplitude dependent dispersion relation is obtained. An examination of the solutions and the dispersion relation indicates that there is a range of values for k, where the two-stream stability levels off before the onset of overtaking.
Deviations from Ionization Equilibrium in Plasmas Generated by Electric Shock Tubes
Authors: Isler Ralph C. , Kerr Donald E.
Published: December 2004

Temperatures and particle concentrations of helium plasmas generated in a linear electric shock tube of 15-mm diam. have been measured by spectroscopic techniques for initial pressures less than 1.0 Torr. The ratio of doubly-charged to singly-charged ions is always found to be greater than the value expected in ionization equilibrium, implying that the measured luminosity arises from a decaying plasma that has been heated by the discharge rather than gas excited by a shock wave. Although measured plasma parameters at luminosity fronts are close to values calculated from the Rankine—Hugoniot equations in some experiments, the use of shock theory to calculate the state of the plasma does not seem justifiable.
Diocotron Instability in a Cylindrical Geometry
Authors: Levy R. H.
Published: December 2004

The diocotron (or slipping stream) instability of low density (ωp « ωc) electron beams in crossed fields is considered for a cylindrical geometry. For a simple density distribution, the normal modes of the electron beam correspond to a continuum of eigenvalues, plus two discrete eigenvalues. Work due to Case and Dikii appears to show that the continuous spectrum is not important in stability studies of this type. The condition for stability considering the discrete modes only is derived; under suitable geometrical and electrical conditions, it is shown that these modes can be stable. The analogy between the electromagnetic problem considered here and the problem of the stability of an ideal rotating fluid is discussed. It is shown that stability conditions derived for the latter problem depend on the possibility of axial perturbations; what this implies for the electron beam problem is briefly discussed.
Dynamics of Vapor Bubbles in General Temperature Fields
Authors: Skinner L. A. , Bankoff S. G.
Published: December 2004

Earlier work [L. A. Skinner and S. G. Bankoff, Phys. Fluids 7, 1 (1964)], limited to spherically symmetric temperature distributions, is extended to an analysis of vapor bubble dynamics in general fields. Particular attention is given to nucleate boiling situations.
Highly Ionized Dense Plasma in a Cesium Penning Arc
Authors: Swartz G. A. , Napoli L. S.
Published: December 2004

A stable cesium plasma with a density of 1015 ions/cm3 and 50% ionization was produced by a Penning arc. A hot, high work function, anode is shown to be a significant factor in the achievement of this very dense highly ionized plasma. Plasma instabilities, which are normally present in the Penning arc, were found to be rotating in the j × B direction. These instabilities are damped when the arc pressure is 0.5 torr and the arc boundary is irregular. Radial and axial plasma density variations were measured. The radial density gradient decreased when the plasma became stable. The axial plasma density variation indicates that the prime source of plasma electrons is the hot cathode.
Virial Coefficients for the Exponential Repulsive Potential
Authors: Sherwood A. E. , Mason E. A.
Published: December 2004

Second and third virial coefficients for the exponential repulsive potential are calculated by accurate numerical integration and by asymptotic formulas. These results are useful for the calculation of the equation of state of gases, especially at high temperatures.
Electronic Population Inversions by Fluid-Mechanical Techniques
Authors: Hurle I. R. , Hertzberg A.
Published: December 2004

The promotion of population inversions between electronic excited states by fluid-mechanical techniques is suggested. Three methods are proposed as illustrations, and the possible degree of inversion in each is estimated. The first makes use in part of the known inversion obtained in excited Ne levels by energy transfer from He metastables. A flow system separates the region of excitation of the He from the region of the resonant excitation of the Ne by the He metastable, and the undesirable electron excitation of the lower Ne state is avoided. The second proposal involves the supersonic expansion of a dissociated mixture of O and H atoms obtained by combustion. An inversion is anticipated between the v′ = 2 and v′ = 1 vibrational levels of the OH(2Σ+) state through the process of inverse predissociation occurring during the expansion. The third illustration involves the rapid expansion of a highly excited gas where radiative depopulation of the lower state promotes an inversion. Results of exploratory experiments involving this particular scheme are discussed. However, it was not possible to observe a population inversion within the noise level of the experiment which involved the sudden expansion of Xe heated by a shock tube.
Flow in a Cavity at Low Reynolds Number
Authors: Weiss Robert F. , Florsheim Bruce H.
Published: December 2004

Approximate solutions are obtained for the flow fields in rectangular cavities by neglecting the convection of vorticity. These solutions yield multi-cell recirculation regions for high aspect ratio cavities. Water tank experiments at a Reynolds number of 150 confirm the prediction of double-celled cavity flow and show good agreement with the theoretical cell dimensions. It is inferred that zero Reynolds number solutions have an extensive range of validity in flows with closed streamlines.