bluuebunny/crossref_metadata_2025 huggingface dataset:
Slow Flow of a Dissociated Gas about a Catalytic Probe
Authors: Hartunian R. A. , Liu S. W.
Published: December 2004

A solution to the problem of the flow at low Reynolds number of a dissociated gas about a catalytic probe has been obtained using the method of inner and outer expansions. The solution gives the atom concentration distribution about the probe as a function of the Reynolds number based on diffusion and the parameter K = kw′a/D, where kw′ is the effective speed of the surface reaction, D is the diffusion coefficient, and a the radius of the probe. It is shown that, from a measurement of the heat transfer to the probe and an independent measurement of the free stream atom concentration, one can establish the catalytic efficiency of the surface when K « 1 and the diffusion coefficient when K » 1. Conversely, knowing either the diffusion coefficient or the catalytic efficiency, the probe may be used to determine atom concentrations. The results of the theory are used to establish experimental conditions in a glow discharge facility under which the sought data may be obtained. Plots of valid operating regimes of this facility are presented as examples.
Finite-Resistivity Instabilities of a Sheet Pinch
Authors: Furth Harold P. , Killeen John , Rosenbluth Marshall N.
Published: December 2004

The stability of a plane current layer is analyzed in the hydromagnetic approximation, allowing for finite isotropic resistivity. The effect of a small layer curvature is simulated by a gravitational field. In an incompressible fluid, there can be three basic types of ``resistive'' instability: a long-wave ``tearing'' mode, corresponding to breakup of the layer along current-flow lines; a short-wave ``rippling'' mode, due to the flow of current across the resistivity gradients of the layer; and a low-g gravitational interchange mode that grows in spite of finite magnetic shear. The time scale is set by the resistive diffusion time τR and the hydromagnetic transit time τH of the layer. For large S = τR/τH, the growth rate of the ``tearing'' and ``rippling'' modes is of order τR−3/5τH−2/5, and that of the gravitational mode is of order τR−1/3τH−2/3. As S → ∞, the gravitational effect dominates and may be used to stabilize the two nongravitational modes. If the zero-order configuration is in equilibrium, there are no overstable modes in the incompressible case. Allowance for plasma compressibility somewhat modifies the ``rippling'' and gravitational modes, and may permit overstable modes to appear. The existence of overstable modes depends also on increasingly large zero-order resistivity gradients as S → ∞. The three unstable modes merely require increasingly large gradients of the first-order fluid velocity; but even so, the hydromagnetic approximation breaks down as S → ∞. Allowance for isotropic viscosity increases the effective mass density of the fluid, and the growth rates of the ``tearing'' and ``rippling'' modes then scale as τR−2/3τH−1/3. In plasmas, allowance for thermal conductivity suppresses the ``rippling'' mode at moderately high values of S. The ``tearing'' mode can be stabilized by conducting walls. The transition from the low-g ``resistive'' gravitational mode to the familiar high-g infinite conductivity mode is examined. The extension of the stability analysis to cylindrical geometry is discussed. The relevance of the theory to the results of various plasma experiments is pointed out. A nonhydromagnetic treatment will be needed to achieve rigorous correspondence to the experimental conditions.
Comparison between Langmuir Probe and Microwave Electron Density Measurements in an Arc-Heated Low-Density Wind Tunnel
Authors: Talbot L. , Katz J. E. , Brundin C. L.
Published: December 2004

Measurements were made of the electron density in a low-density supersonic argon plasma jet flow by the stagnation point Langmuir probe method and by a microwave interferometric technique. The two methods yielded results in reasonably good agreement. It was also possible to obtain some information on the radial distribution of ionization in the jet from the microwave measurements.
One-Dimensional Phase Transition in the Spherical Model of a Gas
Authors: Gersch H. A.
Published: December 2004

Thermodynamic properties and molecular pair distribution functions are calculated for the one-dimensional spherical model of a gas with an attractive interaction outside of a hard core, in the limit as the range of attractive forces becomes infinite. In this limit, a phase transition appears, and the equation of state consists of analytically different parts. The calculations are made using the canonical ensemble which permits a description of the two-phase region. Properties in this region are found to have a simple description in terms of the coexistence of gas and liquid phases.
Partition Function for a Generalized Tonks' Gas
Authors: Koppel Donald
Published: December 2004

The partition function of a system of N identical rigid rods connected by identical springs is reduced to a onefold integration. This integration is explicitly performed in the limit N → ∞ by the method of steepest descent. The system behaves respectively as a gas and as a solid in two different limiting cases. The calculated isotherms and specific heat show that the transition between these limiting cases is continuous.
Gas Thermal Conductivity Studies at High Temperature. II. Results for O2 and O2-H2O Mixtures
Authors: Westenberg A. A. , De Haas N.
Published: December 2004

Measurements of the thermal conductivity λ of O2 and O2-H2O mixtures by the line source technique over the temperature range 300–1100 °K are presented. In the case of pure O2, excellent agreement of the data with previously reported results obtained elsewhere with an entirely different method establishes the thermal conductivity of this gas rather well. The composition dependence of λ for O2-H2O mixtures at various temperatures is compared with theoretical predictions. The simple application of the Hirschfelder mixture relation, using all experimental input data and ignoring the polarity of H2O, gives excellent agreement with experiment. A rough attempt to include the effect of resonant interchange of rotational energy (recently treated by Mason and Monchick) leads to poorer agreement.
General Fluid-Displacement Equations for Acoustic-Gravity Waves
Authors: Biot M. A.
Published: December 2004

General equations are derived for the dynamics of a fluid under initial stress in an arbitrary potential field and perturbed from equilibrium. The motion is described in terms of the displacements of the fluid particles from their equilibrium position. A class of equations is obtained which is applicable to large displacements. Complete linearization leads to two types of equations. One type called ``un-modified'' corresponds to the viewpoint of the theory of elasticity. The ``modified'' equations representing the other type are expressed in terms of buoyancy forces. The modified equations lead to a conceptually useful analog model for internal gravity waves in a liquid. For a constant gravity field the linear equations are also applicable to large displacements. Classical examples for a constant gravity field are discussed as illustrations.
Joint Instability of Hydromagnetic Fields which are Separately Stable
Authors: Stern Melvin E.
Published: December 2004

It is found that certain parallel magnetic fields can destabilize the plane Couette flow of a perfectly conducting fluid, though this flow is known to be stable when there is no field. The destabilizing role of the rigidity of the field is attributed to its ability to prevent the stretching of curves of constant perturbation vorticity by the shear. Unstable long waves transfer energy to the mean magnetic field from the kinetic field by means of the Reynolds stresses. This suggests the possibility of maintaining an electrical current which is initially introduced between two differentially rotating cylinders.
Kinetic Theory of Moderately Dense Gases: Inverse Power Potentials
Authors: Snider R. F. , McCourt F. R.
Published: December 2004

There are two effects giving rise to density corrections to the dilute gas transport coefficients. These are, (a) the corrections to the binary collisions due to their finite size and time of duration and (b) the triple collision effect. Neglecting the latter, expressions for the transport coefficients are well known and have been evaluated in the case of rigid spheres. These expressions for the transport coefficients are now simplified and evaluated approximately for inverse power potentials. The approximation consists in an expansion in inverse powers of the repulsion exponent a technique which has been shown by Baroody to give good agreement with exact calculations of the Ω integrals.
Shock Tube Investigation of the Breakup of Drops by Air Blasts
Authors: Hanson A. R. , Domich E. G. , Adams H. S.
Published: December 2004

The breakup of drops exposed to blasts of air is studied in a shock tube. Results are obtained for water, methyl alcohol, and three viscous oils. An acoustical drop holder has been developed in which radiation pressure is used to support the drops at rest in the shock tube. Photographs showing new details in the breakup process are presented.
Collective Electron Instability in a Bounded Region
Authors: Rosenbluth M. N. , Pearlstein L. D. , Stuart G. W.
Published: December 2004

The linearized Vlasov equation is employed to investigate the stability of the various equilibrium solutions determined from the following model: an infinite slab of width 2L contains a uniform density N of infinitely massive, singly charged, positive ions. The bounding planes (cathodes) emit fixed Maxwellian electron distributions and absorb all impinging electrons, so that the total number of electrons in the system, and their energy, need not remain constant. This model permits three types of time-independent, equilibrium solutions for the electron distribution. One of these solutions shows a Maxwellian electron velocity distribution everywhere in the slab and is stable. The other two types of solution have regions where the electron velocity distribution is not Maxwellian. These latter solutions are shown to be unstable for a range of system parameters to a longitudinal electron collective mode with a growth rate on the order of ωp≡(4πe2N/m)12.
Plasma Sheath Formation by Radio-Frequency Fields
Authors: Butler H. S. , Kino G. S.
Published: December 2004

It has been observed experimentally that the application of a radio-frequency voltage (10 kc/sec–50 Mc/sec) to any one of several electrode configurations around the outside of a plasma discharge tube results in a constriction of the luminous portion of the plasma away from the inner walls of the glass tube. This investigation has established that the phenomenon is basically a radio-frequency rectification effect, leading to the formation of thick ion sheath. The interaction is described mathematically in terms of a differential equation which has an approximate solution that fits qualitatively all the observed characteristics of the phenomenon. The differential equation, in its most general form, has also been solved numerically and the solution is shown to quantitatively fit our experimental observations for both radio-frequency sine and square wave signals. An application of this phenomenon as a possible external diagnostic probe technique is proposed.
Navier-Stokes Calculations of Argon Shock Wave Structure
Authors: Schwartz L. M. , Hornig D. F.
Published: December 2004

The classical Navier-Stokes theory was used to calculate profiles of plane shock waves in argon. The viscosity-temperature relationship employed in the calculation was based on a Lennard-Jones 6–12 intermolecular potential function for which the parameters were derived from experimental viscosity measurements up to 1100°K. With this viscosity function, the maximum-slope shock thicknesses obtained were smaller than previously calculated assuming viscosity proportional to T0.816. Also it was found that the maximum-slope thickness based on the density profile was less than that based on the velocity profile. The density profile thicknesses calculated with the Lennard-Jones viscosity function were the same order of magnitude as, but not in quantitative agreement with experimental density thicknesses obtained with the optical reflectivity technique. It was found that Navier-Stokes profiles become asymmetric as the shock strength is increased. However, the calculated asymmetry would have a negligible effect on thickness measurements by the optical reflectivity method.
Drift Instabilities in Cylindrical Discharges
Authors: Wesson John
Published: December 2004

Fluid equations are used to determine the drift stability of a general shearless cylindrical discharge. Arbitrary ion and electron temperatures are allowed. It is shown that a sufficiently large or small ratio of ion to electron temperature gives stability, and that, provided the azimuthal field is not too small, marginal magnetohydrodynamic stability implies drift stability.
Solitary Waves in Cold Collisionless Plasma
Authors: Kellogg Paul J.
Published: December 2004

The propagation of finite amplitude waves in a magnetized plasma, in which thermal motion and collisions are neglected, is studied for arbitrary direction of propagation. Solutions for oblique propagation are presented, which complement the analytical solutions for propagation perpendicular to the magnetic field obtained by Adlam and Allen and others, and for parallel propagation obtained by Saffman. Oblique propagation is much more complicated than the two limiting cases in that: (1) In a given direction and at a given speed higher than the Alfvén speed there are a large number of different waves and (2) As shown by Saffman there are additional waves whose speed is less than the Alfvén speed. These submagnetic waves are investigated in the limit of infinite mass ratio, and the results compared with computer calculations. The stability of the waves against the two-stream instability is investigated and it is shown that (1) The supermagnetic waves (speed higher than Alfvén speed vA) are destroyed by the two-stream instability unless vA/c is sufficiently large (2) The submagnetic waves are destroyed by the two-stream instability unless the pressure is non-negligible.
Mach Reflection of Detonation Waves in Condensed High Explosives. II
Authors: Dunne Brian
Published: December 2004

Reflection parameters are derived for two colliding plane detonation waves in a condensed high explosive. The pressure and angle of the reflected shock wave are calculated as a function of the detonation-wave angle to the line of collision. The critical angle for the onset of Mach reflection and the pressure in the center of the Mach stem are also determined. Some comparisons are made between the results of this analysis and experiments.
Performance of Coaxial Plasma Gun with Various Propellants
Authors: Michels Charles J. , Ramins Peter
Published: December 2004

An experimental study of a single-shot coaxial plasma gun is described. A parametric survey of the gun over the operating range is given for each of three propellants: argon, nitrogen, and hydrogen. An optimum delay time (with respect to exhaust puff energy) is described for each propellant between gas injection and bank-voltage application. Bank voltage and mass per shot were varied using the optimum delay time. Gun efficiency, system efficiency, and magnetic-front velocity in the gun were determined.
Ferrohydrodynamics
Authors: Neuringer Joseph L. , Rosensweig Ronald E.
Published: December 2004

A phenomenological treatment is given for the fluid dynamics and thermodynamics of strongly polarizable magnetic fluid continua in the presence of nonuniform magnetic fields. Examples of the fluids treated here have only recently been synthesized in the laboratory. It is found that vorticity may be generated by thermomagnetic interaction even in the absence of viscosity and this leads to the development of augmented Bernoulli relationships. An illustration of a free-surface problem of static equilibrium is confirmed by experiment and information is obtained regarding a fluid's magnetic susceptibility. Another illustration elucidates the mechanism of an energy conversion technique. Finally, an analytical solution is found for the problem of source flow with heat addition in order to display the thermomagnetic and magnetomechanical effects attendant to simultaneous heat addition and fluid motion in the presence of a magnetic field.
Solution of the Kinetic Equation for an Unstable Plasma in an Electric Field
Authors: Field Edward C. , Fried Burton D.
Published: December 2004

The response of a homogeneous plasma to the sudden application of a strong, uniform electric field, E0, is studied by solving, self-consistently, the coupled equations for the one- and two-particle distribution functions. The field is assumed to be large compared to that which produces a ``runaway'' current, so that particle-particle collisions have a negligible effect on the current flow, and particle-wave interactions dominate. The principal approximations are the neglect of intrinsic three-particle correlations (i.e., linearization in fluctuations) and the use of an adiabatic ansatz for the time dependence of the fluctuations. For the case of unequal temperatures, Te ≫ Ti, two different methods of solution are employed: a moment approximation, in which the distribution functions are assumed Maxwellian, with mean velocity and width determined self-consistently; and a more exact treatment in which the distribution function for velocities parallel to the applied field is determined by direct numerical solution of the kinetic equation using on-line computational techniques. In both cases, it is found that the unstable ion acoustic waves grow from the thermal fluctuation level to a magnitude sufficient to cause a sharp and sudden decrease in the current. Examination of the kinetic equation shows this drop to be ascribable to the dynamic friction associated with the unstable waves. Although waves propagating parallel to the applied field are most important at early times, those propagating at finite angles soon become dominant; this casts some doubt on one-dimensional approximations to this problem. The limitation of the exponential growth of unstable waves resulting from the non-linear (or quasilinear) effects is clearly evident, notwithstanding the presence of the external driving force, E0.
Steady and Unsteady Motions and Wakes of Freely Falling Disks
Authors: Willmarth William W. , Hawk Norman E. , Harvey Robert L.
Published: December 2004

The motions and wakes of freely falling disks were studied and it was found that the diverse motions of the disks exhibit a systematic dependence on the Reynolds number Re, and the dimensionless moment of inertia I*. The relation between I* and Re along the boundary separating stable and unstable pitching oscillations of the disk was determined. The Reynolds number for stable motion of a disk with large I* is 100, in agreement with the Reynolds number for stability of the wake of a fixed disk. Slightly unstable disks of large I* were stabilized by reducing the moment of inertia. The highest Reynolds number for stable disk motion was 172. At higher Reynolds numbers the disks exhibited periodic pitching and translational oscillations. The laminar wake behind certain of the oscillating disks consisted of a staggered arrangement of two rows of regularly spaced vortex rings similar to the wake observed behind liquid drops by Margarvey and Bishop. The dependence of the dimensionless frequency of oscillation on I* and Re was determined along the boundary for stable motion and at higher Reynolds numbers when the wake was turbulent. Tumbling motions of the disks were observed when the Reynolds number was large, Re > 2000, and I* was greater than a certain value, I* =̇ 10−2.
Bremsstrahlung Cross Sections in the Neighborhood of the Plasma Frequency
Authors: Oster Ludwig
Published: December 2004

The spontaneous emission probability due to the bremsstrahlung mechanism for photons whose frequencies are not much higher than the plasma frequency is computed on the basis of classical radiation theory. The particle orbits are calculated using for the interaction potential electron-ion a Coulomb form which is cut off at the Debye distance. It is shown that for all practical purposes shielding corrections can be neglected in computing the Fourier components of the acceleration, but must be applied for frequencies in the neighborhood of the plasma frequency, when the spectrum is averaged over collision parameters. If the respective assumptions on the underlying physical conditions are matched, our results are identical with the results derived by Dawson and Oberman, and by Chang on the basis of kinetic theory.
Hot Flow Length and Testing Time in Real Shock Tube Flow
Authors: Brocher E. F.
Published: December 2004

The influence of viscosity on the hot flow length l and the testing time τ in shock tubes is investigated for the laminar and turbulent cases. Considering the case where the influence of viscosity can be treated as a perturbation of the ideal flow, it is shown that Mirels' theory, which takes into account shock-wave attenuation and wave reflections, can easily be used to evaluate l and τ.

The limitations of the present theory are discussed and the results compared with the previous investigations. For the laminar case, the type of solution obtained is similar to that of Roshko. A ``maximum'' hot flow length, whose significance is mathematical rather than physical, because of the breakdown of the perturbation theory, is found. This ``maximum'' length is approximately twice as large as the one Roshko obtains when using his empirical value of √3 for the boundary layer parameter β. For the testing time in the turbulent case, the results differ somewhat from Anderson's.
Nonlinear Wave Motion in a Linear Pinch
Authors: Chu Chong-Wei
Published: December 2004

The motion of a linear pinch due to finite axisymmetric disturbances is studied. The plasma is considered as a single, inviscid, perfectly conducting, compressible fluid, and the usual magneto-hydrodynamic assumptions are made. Theory of characteristics is applied to study simple waves. A compression simple wave is found to steepen with time and is expected to develop into a shock with area change. It is found that the increase of entropy across such a shock is greater than that across an ordinary normal shock with the same pressure ratio. With respect to a single finite axisymmetric concave or convex disturbance with small area gradient in the axial direction, the pinch is stable in the sense that it will nowhere touch the coaxial wall and its physical quantities will remain finite.
Influence of Ion Loss on Diffusion of Cesium Plasma in the Q Machine
Authors: Goeler S. V.
Published: December 2004

It is shown that neutralization of the ions at the hot end plates dominates over the process of volume recombination in the Q machine. A wall recombination coefficient is defined and calculated for comparison with the experimental data. Further, the maximum plasma density that can be obtained with the Q machine is discussed.
Note on the Inversion of the Boltzmann Equation
Authors: Rott Nicholas
Published: December 2004

A short derivation of Wild's inversion of the Boltzmann equation is given. It is shown that if Wild's formula is to be used for an iterative solution, the Bhatnagar-Gross-Krook equation is recovered as the first step in a particular case, in which the ``initial guess' is supported by classical mean-free-path concepts. Use of different initial guesses is considered, particularly those based on the Mott-Smith model. Connections between the iterative method and the classical expansion procedures are indicated.
Flow Around a Spheroid in a Circular Tube
Authors: Smythe W. R.
Published: December 2004

The problem of the ideal fluid flow around a spheroidal obstacle inside a coaxial cylinder is solved by a slight variation of the method described earlier [W. R. Smythe, Phys. Fluids 4, 756, (1961)]. Errors in the terminal digits of Table I of that paper have been corrected and the table extended. The flow is confined to the space between spheroid and cylinder by thin vortex sheets of variable strength on the spheroid and cylinder surfaces. The vector potential of the flow is expressed in terms of the circulation density on the spheroid surfaces of which tables are given for the disk, oblate spheroid with axial ratio 2 to 1, sphere and prolate spheroid with axial ratio 1 to 2 for equatorial radii 0.1, 0.2, … , 0.95 of the cylinder radius. A table shows the increase in flow resistance due to the insertion of the spheroid in terms of the equivalent additional tube length.
Fluid Mechanical Aspects of Antisymmetric Stress
Authors: Condiff Duane W. , Dahler John S.
Published: December 2004

Basic fluid mechanical concepts are reformulated in order to account for some structural aspects of fluid flow. A continuous spin field is assigned to the rotation or spin of molecular subunits. The interaction of internal spin with fluid flow is described by antisymmetric stress while couple stress accounts for viscous transport of internal angular momentum. With constitutive relations appropriate to a linear, isotropic fluid we obtain generalized Navier-Stokes equations for the velocity and spin fields. Physical arguments are advanced in support of several alternative boundary conditions for the spin field. From this mathematical apparatus we obtain formulas that explicitly exhibit the effects of molecular structure upon fluid flow. The interactions of polar fluids with electric fields are described by a body-torque density. The special case of a rapidly rotating electric field is examined in detail and the induction of fluid flow discussed. The effect of a rotating electric field upon an ionic solution is analyzed in terms of microscopically orbiting ions. This model demonstrates how antisymmetric stress and body torque can arise in ``structureless'' fluids.
X-Ray Diffraction in Liquids-Nitrogen, Oxygen, and their Mixtures
Authors: Furumoto Horace W. , Shaw Charles H.
Published: December 2004

The x-ray diffraction patterns of liquid nitrogen and of liquid oxygen were measured at their saturated vapor pressures at 64° and 77°K. Mixtures of the liquids were examined at the saturated vapor pressures at 77°K. The radial distribution functions of the pure liquids were calculated and effects of truncation errors analyzed. No evidence of multi-atomic molecules other than diatomic molecules was found.
Dynamics and Heat Transfer in the von Kármán Wake of a Rectangular Cylinder
Authors: Harlow Francis H. , Fromm Jacob E.
Published: December 2004

A numerical method has been used to solve completely the full equations for the motion of a viscous, heat-conducting, incompressible fluid flowing through a channel past a rectangular cylinder. The dynamics of the unsteady flow were made visible by means of a number of different types of contour plots, and selected ones are presented and discussed to illustrate various newly discovered features of the von Kármán vortex street. In addition, the heat transfer was measured from the heated rear of the cylinder to the colder fluid, with data presented in the form of Nusselt number correlated with Reynolds number. Corrections are derived for blockage, and Prandtl number scaling is discussed.
Small Perturbation Theory for Shock-Tube Attenuation and Nonuniformity
Authors: Mirels H. , Mullen J. F.
Published: December 2004

Closed form expressions are derived, based on the concept of self similarity, for evaluating small perturbations of shock tube flow due to the wall boundary layer. Ideal diaphragm rupture is assumed. Extensive numerical results are obtained for the perturbations induced by the boundary layer in the driven gas, assuming that the boundary layer is wholly laminar or wholly turbulent. The driven gas is taken to be air. Various driver gases are considered. Attenuation results are obtained for shock Mach numbers up to 20. It is shown that the effect of the driver gas boundary layer on perturbations in the driven gas is small for large diaphragm pressure ratios. The results indicate that a shock tube with an efficient driver, e.g., helium, should have less attenuation for a given shock Mach number than would an inefficient driver, e.g., air. The latter result disagrees with existing experimental data. The source of the discrepancy is not known.
On the Confinement of a Plasma by Magnetostatic Fields
Authors: Weibel Erich S.
Published: December 2004

The plasma is treated as an assembly of classical particles having masses m+ and m− and charges ±e. It is shown that if such a plasma is in thermodynamic equilibrium it is unaffected by a magnetostatic field. In particular, it cannot be confined by a magnetostatic field and at the same time be in equilibrium. In absence of collisions there exist stationary solutions for the magnetic field and the particle distribution in phase space such that the gas is confined. The solutions are self-consistent, meaning that the particle motions generate the field, which in turn maintains the particle distribution. However, this distribution may not be Maxwellian. As an example the linear pinch is treated. The fields, the particle number densities, and the current density are calculated for one particular case.
Magnetic Differential Equations
Authors: Newcomb William A.
Published: December 2004

A necessary and sufficient condition is derived for a magnetic differential equation B·▿r = 0 to have a single-valued solution r, where B is the field of a magnetohydrostatic equilibrium state or, more generally, and field with a system of toroidal magnetic surfaces.
Laminar Steady-State Magnetohydrodynamic Flow in an Annular Channel
Authors: Globe Samuel
Published: December 2004

The problem considered is the steady flow of an electrically conducting, incompressible fluid, in the annular space between two infinitely long circular cylinders, under a radially impressed magnetic field. The general magnetohydrodynamic equations are simplified by the conditions of the problem to three equations in pressure, velocity, and magnetic field. One equation gives the pressure variation in the radial direction; the other two are coupled equations for the velocity and magnetic field, which are functions of the radial variable only and may be solved for in closed form. In the limiting case where the radii of the annulus become infinite, but their difference remains finite, the solution converges on the expression for magnetohydrodynamic flow between infinite planes under a transverse magnetic field.
Theory of Radiation from Luminous Shock Waves in Nitrogen
Authors: Hammerling P. , Teare J. D. , Kivel B.
Published: December 2004

The physical properties behind a normal shock in nitrogen are calculated as a function of time. These include the variation of temperature, composition, ionization, and the intensity of radiation from the N2+ first negative band system. This calculation incorporates a rate equation for the dissociation of nitrogen, the conservation laws, an equation describing vibrational relaxation, and a method of coupling the vibrational relaxation with the dissociation rate. The N2+ radiation is computed assuming excitation of the radiating state by collision with vibrationally excited nitrogen molecules. A particular case is considered for which experimental data are available, and regions sensitive to particular rates are indicated.
Highly Ionized, Steady-State Plasma System
Authors: Hall Laurence S. , Gardner Andrew L.
Published: December 2004

A system is described which produces a steady-state helium plasma with greater than 95% ionization. The primary plasma is generated in a modified Phillips ion gauge discharge and diffuses along a magnetic field (B ∼ 1 kG) through a region in which neutral particles are preferentially removed. In the downstream region a plasma density of ∼2 × 1013 cm−3 and ion temperatures up to 10 eV have been achieved. The present paper describes the over-all physical assembly, the operating characteristics of the system, and the nature of the plasma that is produced. In addition, a discussion of processes believed important in its operation is given.
Plasma Electromagnetic Instabilities
Authors: Sudan R. N.
Published: December 2004

A gyrotropic plasma with T∥/T⊥ ≡ γ < 1, where T⊥ and T∥ are the transverse and longitudinal temperatures, is shown to be unstable to a perturbation in the form of a transverse wave with a wave vector k such that k2 < k02 = {ωc2(1−γ)2 + ωp2(1−γ)/γ}/c2, ωc and ωp are the gyro and plasma frequencies. For T∥ > T⊥ such an instability arises only if ωc2/ωp2 > 1/γ(γ−1) and then only for k2 < k02. However, in the latter case, the phase velocity of the instability exceeds c and the growth rate must be made to vanish because of relativistic considerations. No such instability arises for complete isotropy T⊥ = T∥.
Numerical Model of an Ion-Cyclotron Wave Experiment
Authors: Hamilton Gordon W.
Published: December 2004

A numerical model has been constructed to demonstrate the propagation and absorption of ion-cyclotron waves in a previously reported experiment. Ion-cyclotron waves in a deuterium plasma induced by a radially applied 8.3-Mc/sec electric field propagate in a magnetic-mirror field to a resonance region where the ion-cyclotron frequency approaches the wave frequency. The numerical model considers the wave propagation in the nonuniform divergenceless magnetic field with spatially nonuniform plasma parameters, subject to boundary conditions modeled after the experiment. The model is based on the macroscopic equation of motion, the generalized Ohm's law, the wave equation, an equivalent resistivity representing the effect of ion-cyclotron damping, and damping by collisions between deuterons and other particle species. The equations are solved numerically by a single-line block over-relaxation technique. The numerical results are compared with the experimental wave measurements and also provide information regarding current distributions, wave polarizations, evanescent compressional waves, and reflections from the resonance under certain conditions.
Excitation of Plasma Resonances by a Small Pulsed Dipole
Authors: Deering W. D. , Fejer J. A.
Published: December 2004

The space and time dependence of decaying resonant oscillations excited in a collisionless plasma by an infinitesimally small pulsed dipole is determined in absence and in presence of an external magnetic field. Oscillations near the plasma frequency, the hybrid frequencies, and harmonics of the electron cyclotron frequency are treated.

At a fixed time and at a short distance from the source, the field of the oscillations is nearly uniform. At longer distances the amplitude of the oscillations is proportional to some power of the distance, which in the presence of an external magnetic field is greater than unity and varies for different resonances. The phase of the oscillations also varies with the distance, and this probably explains the complicated interference effects observed with large satellite-borne antennas in the ionosphere. At very long distances the amplitude of the oscillations decreases after reaching a maximum.

At the point of excitation the amplitude decreases as some inverse power of the time; at other fixed positions the amplitude at first grows then decreases as a higher inverse power of the time, and eventually the region of uniform decaying field near the point of excitation expands to include the position considered.
Role of the Interface in the Stability of Stratified Flow down an Inclined Plane
Authors: Kao Timothy W.
Published: December 2004

For the case in which the density of the upper layer is somewhat less than that of the lower layer, a second mode essentially associated with the interface is found to govern the stability of the flow. However, when the upper density becomes much smaller, the free surface mode and the second mode compete for governing the stability. A clarification of the mechanism involved is given. The Reynolds stress transfer of energy at the interface is estimated and is found to be insignificant for long waves.
Lagrangian-History Closure Approximation for Turbulence
Authors: Kraichnan Robert H.
Published: December 2004

The direct-interaction approximation for turbulence is extended to predict the covariance and average Green's function of a generalized velocity u(x, t|r), defined as the velocity measured at time r in the fluid element which passes through the point x at time t. The resulting formulas for triple moments involve integrals over the Eulerian time-history of the fluid. The approximation is then altered so that the integrals are instead over Lagrangian histories, measured along the particle paths. The alteration is determined by requiring simultaneously that energy be conserved; that there exist formal inviscid equipartition solutions; and that the Lagrangian dynamics of homogeneous flows exhibit invariance under random Galilean transformations. In the altered equations, the relaxation times associated with energy transfer are Lagrangian memory times determined by the viscous and pressure forces. As a result, the approximation implies the Kolmogorov inertial- and dissipation-range laws. The corresponding approximation for convection of a passive scalar field yields some exact results of Taylor and implies Richardson's law for the relative diffusion of two particles.
Shock Structure in a Radiating, Heat Conducting, and Viscous Gas
Authors: Traugott S. C.
Published: December 2004

A differential, one-dimensional model for radiative transfer with any opacity has been applied to a radiating shock in an infinite diffusive gas. The case of partly or fully dispersed, radiation resisted shocks is included. The parameters through which collision effects enter have been obtained over a wide range of conditions to show when collisions may be expected to matter, both for a perfect gas and for real air. Solutions are given which illustrate the modification of the dispersed shock profiles by viscosity. It is found, primarily because of the way in which the grey absorption coefficient varies with temperature, that the effect of viscosity on an isolated traveling shock in real air will be very small. For a reflected shock, viscosity can be important enough to modify the dispersed solutions, the modification occurs for the rear tail and reduces the temperature overshoot there.
Equation of Motion of a Dielectric Medium
Authors: Kaufman Allan N.
Published: December 2004

Expressions for the macroscopic force density and stress tensor are derived for a noncrystalline dielectric medium in a nonequilibrium state. The calculation utilizes the exact Coulomb interaction between molecules with internal structure.
Kinetic Theory of Sound Propagation in Rarefied Gases
Authors: Kahn David , Mintzer David
Published: December 2004

The problem of sound propagation in highly rarefied monatomic gases is investigated from the point of view of general orthogonal polynomial solutions (in velocity space) of the Boltzmann equation. It is shown that the usual expansion solutions of the Boltzmann equation (Chapman-Enskog-Burnett, and Grad) are not valid for this problem. Solutions, instead, are obtained by means of an expansion of the distribution function in a set of velocity polynomials which have been orthogonalized with respect to a zero-order distribution function characteristic of a collisionless gas, rather than a Maxwell distribution function as is usually done. These solutions are used to derive absorption and dispersion functions characterizing the sound propagation. These are shown to be in agreement with experimental data for the problem.
Ideal Flow Along a Row of Spheres
Authors: Michael Paul
Published: December 2004

The solution for the flow of an ideal fluid parallel to the axis of an infinite row of spheres has been obtained by an extension of the method of Smythe [Phys. Fluids 4, 756 (1961)]. Considered are spheres whose separation of centers varies from one diameter to infinite, the latter, of course, being the well-known case of an isolated sphere. The induced mass per sphere has been found as a function of separation; for touching spheres the ratio of induced mass to the mass of fluid displaced is 0.173, this ratio increases with increasing separation reaching 90% of the isolated sphere value of 0.5 when the sphere centers are a little over two diameters apart.
Equilibrium of a Toroidal Plasma with Finite Resistivity and Inertia
Authors: Knorr Georg
Published: December 2004

A theoretical study of the equilibrium of a dilute plasma in toroidal geometry with rotational transform has been carried out, taking into account finite resistivity and finite inertia. If an additional nonvanishing density gradient drift of the plasma perpendicular to the magnetic field is assumed, the plasma drifts out of the toroid. The characteristic time of this process is found to be a factor of 2 r/R (where R and r are the major and minor radii of the toroid, respectively) smaller than the time which is associated with the mere diffusion from a toroid.
Influence of Small Transverse Fields and Impurities on θ-Pinch Stability and Confinement
Authors: Hintz Eduard , Kolb Alan C.
Published: December 2004

The stability and confinement of θ-pinch plasmas in the relatively slow Pharos discharge, where the duration of the current pulse is ∼20–30 μsec, was investigated. The heating rates (∼100 eV/μsec early in the discharge) are modest because of the relatively low voltage on the coil (∼15 kV). Care was taken to reduce field nonuniformities in the coil-collector assembly so that the compressed plasma would not drift toward the wall. It is shown that small transverse fields (<1% of the maximum Bz) cause rotational instability: in particular, a pulsed Ioffe-hexapole field induces rotational instability if the field is present in the plasma before the start of the main compression. The time constant for the growth of the instability depends on the electron temperature and can be altered with 0.1% added impurity. The plasma is lost out the ends in 10–15 μsec without an initial bias field. The confinement time can be extended to ∼30 μsec with a reverse bias field. In the latter case the plasma contracts axially to a length of 60–80 cm with a 1.8-m coil; this central plasma column is connected to the ends by a narrow thread of plasma with a radius of a few millimeters. Axial studies show that instabilities, when they occur, grow faster at points away from the midplane. The origin of the rotation is discussed in terms of a model in which axial Hall currents, due to transverse fields, lead to a torque.
Radial Distribution Functions in a Two-Component Plasma
Authors: Schram P. P. J. M. , Kegel W. H.
Published: December 2004

General expressions for the radial distribution functions in an electron-ion-plasma outside thermal equilibrium are obtained from the hierarchy equations in first order of the plasma parameter. It is shown that these expressions can also be derived in the framework of the test-particle problem. In the special case of Maxwellian distributions with different temperatures for electrons and ions, and under the mild restriction that the thermal velocity of the ions is much smaller than that of the electrons, the results reduce to expressions first given by Salpeter. The results of Kadomtsev and Renau for the electron-electron radial distribution function Wee(r) disagree with ours and those of Salpeter. The reason for this is discussed. A curious ``anti-shielding'' phenomenon is shown to follow from Wee in the case where the electron temperature is smaller than the ion temperature. It is studied in some detail. Finally, the influence of a magnetic field is shown to vanish in the special case of two Maxwellians.
Almost Longitudinal Instabilities in a Plasma-Beam System
Authors: Wright Harvel , Wiginton C. L. , Neufeld Jacob
Published: December 2004

A plasma-beam system immersed in a magnetic field B0 is investigated under the assumption that the plasma is stationary, cold, uniform, and extended and that the beam of charged particles is uniform in density and moving in a direction parallel to that of B0. Instabilities which are almost longitudinal are investigated with respect to conditions of occurrence, strength and type of instabilities, and dependence on the angle between the direction of B0 and the direction of the excited waves. Two logically distinct types of waves which occur are defined and investigated. An almost longitudinal Čerenkov wave has a phase velocity equal to the projection of the beam velocity in the direction of the wave. An almost longitudinal cyclotron wave has a frequency equal to the Doppler-shifted gyrofrequency of the particles in the beam. Typical examples are analyzed numerically and presented graphically. Certain simple analytical expressions which apply to the significant regions of instability are derived and tabulated.
Partition Functions and Thermodynamic Properties of Nitrogen and Oxygen Plasmas
Authors: Drellishak K. S. , Aeschliman D. P. , Cambel Ali Bulent
Published: December 2004

The equilibrium chemical composition and thermodynamic properties of nitrogen and oxygen plasmas have been calculated for six pressures (0.01, 0.1, 0.5, 1.0, 2.0, and 5.0 atm) at 100° K increments for the temperature range 2000–35 000° K. The plasma is assumed to be a perfect gas complex consisting of seven components for nitrogen (i.e., molecules, singly ionized molecules, atoms, electrons, and the first three atomic ions) and eight components for oxygen (same as for nitrogen plus the first negative atomic ion). The internal partition functions for nitrogen molecular species were calculated by an approximate technique proposed by Mayer and Mayer using the most recent spectroscopic data available. For oxygen molecular species, the method of Stupochenko et al. was employed to determine the intermolecular potential curves, and the internal partition function was computed by direct summation over the energy states so determined. The electronic partition functions for atoms and atomic ions were computed using published data for observed electronic energy levels plus estimated energies for electronic states which are predicted but not spectroscopically observed. These electronic partition function series were terminated by application of the Debye cutoff criterion, and a corresponding lowering of the ionization potential was included. The two methods of computing the molecular internal partition function are compared and evaluated. Typical calculated data are presented in graphical and tabular form.
Normal Ionizing Shock Waves
Authors: Taussig Robert T.
Published: December 2004

Solutions to the steady-state jump equations are obtained for a normal ionizing shock wave propagating into a nonconducting, quiescent gas in an electromagnetic field. Comparison of these solutions to pure magnetohydrodynamic shocks and ordinary gas shocks indicates that ionizing shocks are hybrids having some properties common to both magnetohydrodynamic and gas shocks. Some completely novel effects are produced by the upstream electromagnetic field. The shock velocities are bounded for a given upstream electric field strength where the electric field is assumed parallel to the shock plane. For electric fields larger than a critical value, Ec, no steady compressive shocks exist, and for nonzero electric fields ``switch-on'' behavior is extended to slow shocks. Solutions analogous to detonation-deflagration waves have been found, and the Chapman-Jouguet condition is applied to them. The complete boundary value problem is solved in the context of an electromagnetic annular shock tube to place the analytic results in the framework of experimentally observable phenomena.