bluuebunny/crossref_metadata_2025 huggingface dataset:
Dynamical Principle of Stability for Magnetohydrostatic Systems
Authors: Trubnikov B. A.
Published: December 2004

The stability of an arbitrary system is ordinarily determined by means of the variation in its potential energy produced by a displacement of the system from the equilibrium position. In some cases, however, the investigation of stability may be more convenient if it is based on the variation in kinetic energy during a motion of the system past the equilibrium position. In this work it is shown that for magnetohydrodynamic systems such a ``dynamical'' method enables us to very simply obtain a stability criterion equivalent to the well-known energy principle for the stability of such systems. The proposed method also permits derivation of the criterion of Kruskal and Oberman, who investigated the stability of a plasma on the basis of the kinetic equation in the limit as (m/e) → 0. In this connection it turns out to be superfluous to require the various constants of the motion [of the form ∫ dv dV G(L, μ, f)] to be equal to their equilibrium values, as Kruskal and Oberman did.
Simulation of Condensed-Explosive Detonation Phenomena with Gases
Authors: Sommers William P. , Morrison Richard B.
Published: December 2004

The detonation of a condensed explosive within a solid container and the detonation of a gaseous explosive within an inert-gas boundary are found to be hydrodynamically similar situations. Experiments with hydrogen, methane, ethane, and propane-oxygen mixtures confined by air or helium boundaries show that, as with condensed explosives, the properties of the boundary strongly influence the detonation characteristics of the explosive. Schlieren photographs of the interaction process between a gaseous detonation wave and an inert-compressible-gas boundary show that the detonation wave becomes curved, and in some cases is quenched, the quenching process being initiated at the compressible boundary. Either oblique or detached shocks are found to occur in the boundary. These observations parallel those made from experiments in which condensed explosives were confined by solid boundaries. With the use of an idealized-flow model, the acoustic-impedance ratio of the gaseous boundary to the explosive is determined to be the parameter which characterizes the confining ability of the boundary. Application of these results to condensed-explosive detonations provides an understanding of some experimentally observed phenomena
Large-Amplitude Magnetic Compression of a Collision-Free Plasma. II. Development of a Thermalized Plasma
Authors: Auer P. L. , Hurwitz H. , Kilb R. W.
Published: December 2004

Numerical calculations are made of a strong one-dimensional disturbance traveling perpendicular to a magnetic field in a fully ionized and collisionless plasma. When the Alfvén-Mach number Mh is greater than 2, orbit crossings of the ions occur, which rapidly leads to thermalization perpendicular to the magnetic field if the crossings are extensive (Mh > 3). The thermalization approximates the behavior of a classical hydromagnetic shock, with a shock-front thickness roughly equal to the distance the shock front travels in one-half an ion gyration time. This length is somewhat greater than the ion gyration radius. The structure of the front is found to be strongly time dependent, and undergoes large fluctuations in an ion gyration period. It is argued that when the ion-electron mass is large, the magnetic forces tend to suppress electron orbit crossings. This results in relatively cold electrons in the shocked region, with the ions obtaining nearly all of the thermal energy. A relationship between the longitudinal electrostatic potential difference across the shock front and mass flow in the plane of the front is derived on the basis of a simplified model and is found to be in qualitative agreement with the numerical results. The range of applicability of the calculations to real plasmas is discussed.
Instability of Contrastreaming Plasmas with Resonance Distribution Functions
Authors: Ek F. , Kahalas S. L. , Tidman D. A.
Published: December 2004

An analysis is made of the instability of waves in contrastreaming plasmas. The unperturbed distribution function, which occurs in the dispersion relation, is taken to be a ``resonance'' function of the form f0(v) = const (v2 + V2)−3, where V is related to the thermal velocity. This function has the dual advantage of allowing the computation of physical properties such as energy and of yielding a dispersion relation amenable to numerical analysis in important cases. The case of identical contrastreaming plasmas is analyzed in two phases: an electron instability which may arrest the streaming motion and an electron-ion instability involving the static, heated electrons and the ion streams. Critical temperatures for these instabilities are determined and compared with results obtained from Maxwellian distribution functions. Stability criteria for arbitrary temperatures are obtained with the resonance function. Growth rates over the band of allowed wave numbers are given for both phases of instability.
Anomalous Diffusion of a Plasma across a Magnetic Field
Authors: Yoshikawa S. , Rose D. J.
Published: December 2004

The diffusion of a plasma across a magnetic field is considered both theoretically and experimentally. It was found out that the fluctuation of the density can cause an anomalous diffusion that is inversely proportional to the magnetic field B. The mobility of electrons perpendicular to the magnetic field was measured in the experiment; the measurement supports 1/B diffusion. The density fluctuation was also measured. There is good agreement between the observed mobility and the theoretical one derived from the density fluctuation. The potential fluctuation was found to be an increasing function of the external potential and independent of the magnetic field intensity. This fact also indicates that fluctuation or turbulence plays an important role in the anomalous diffusion.
Magnetohydrodynamics at Small Magnetic Reynolds Numbers
Authors: Uberoi Mahinder S.
Published: December 2004

Two problems are considered, each of which represents a class of flows. In the first problem the motion is induced by passage of electric current through an incompressible viscous electrically conducting fluid contained in an insulated axisymmetric tube. The solution is obtained in closed form by assuming small Reynolds numbers such that the electromagnetic forces are balanced by viscous forces. In the second problem incompressible inviscid electrically conducting fluid flows through an axisymmetric tube and the flow is modified due to passage of electric current. The complete solution of the resultant rotational flow is obtained in closed form for small changes in tube diameter. At appreciable rates of current flow the fluid in the central part of a contracting tube behaves as if the tube were expanding; the opposite is true for an expanding tube. This is shown to be the case quite generally even when the assumption of small magnetic Reynolds number is dropped. Further, at large rates of current flow there may develop a secondary flow.
Stability Criterion for Arbitrary Hydromagnetic Equilibria
Authors: Greene John M. , Johnson John L.
Published: December 2004

A necessary and sufficient condition for the stability with respect to localized displacements is obtained for arbitrary bounded hydromagnetic equilibria. The use of a natural coordinate system which contains the important properties of the equilibrium configuration facilitates the understanding of the instability.
Kinetic Equations for a Plasma
Authors: Varma Ram K.
Published: December 2004

Starting with Liouville's equation, a set of equations is derived in the random-phase approximation for the evolution of the spatial Fourier components of the complete distribution function of a particle in a plasma. A procedure is used which takes account of all the contributions coming from many-body interactions in the random-phase approximation. The equations thus describe the collective part of the response of plasma to the particle. The equations which have the structure of the Fokker-Planck equation describe collisions of electrons carrying an envelope of plasma waves emitted by them. It is shown that in the Markoff approximation this envelope degenerates into a Debye shielding cloud, so that in this approximation the equations describe the collisions of electrons clothed in Debye shielding clouds.
Velocity and Temperature Profiles for Laminar Magnetohydrodynamic Flow in the Entrance Region of a Plane Channel
Authors: Shohet J. L. , Osterle J. F. , Young F. J.
Published: December 2004

The entry problem in plane laminar magnetohydrodynamic flow is solved numerically for various values of the pertinent parameters describing the flow. The channel configuration is a parallel-plate channel which has the Hartmann profile for its fully developed velocity flow. The equations are placed in a finite difference form to enable the essential nonlinearities of the principal equations to be used in the solution of the problem. Velocity, temperature, and pressure curves are presented from the results of computational work.
Interaction of Shock or Rarefaction with a Bubble
Authors: Evans Martha W. , Harlow Francis H. , Meixner Billy D.
Published: December 2004

Interactions of a shock or rarefaction wave with a bubble have been studied theoretically, using a numerical method for solving the equations of compressible flow. Detailed configurations and isotherms are presented for times up to late stages of the interactions, and the results are compared with experiments.
Asymptotic Solutions for Sink Flow in a Strong Magnetic Field
Authors: Kovasznay L. S. G. , Fung F. C. W.
Published: December 2004

For fluid with finite electric conductivity placed in a magnetic field the dissipative term of magnetic origin causes the governing equation to be nonsymmetric with respect to source and sink. Sink flow of an incompressible, nonconductive, perfect fluid is spherically symmetric with the velocity falling off according to an inverse square law. If the fluid is endowed with finite electrical conductivity and a strong parallel uniform magnetic field is imposed, the magnetic lines will channel the flow along the preferred direction. Far away from the sink a similarity solution exists. Both the velocity field and the magnetic perturbation field have been computed and they represent an axisymmetrical wake-type configuration. It was found that the velocity on the axis falls off as z−½ and the width of the wake increases as z¼. The axial disturbance of the magnetic field is maximum on the z axis and drops off as z−1. The radial component vanishes on the axis and for a given relative position falls off asz−7/4.
Equilibrium Properties of Hydrogen Gas from 5000° to 20 000°K
Authors: Sinanoğlu O. , Vardya M. S. , Mortensen E. M. , Johnson W. C.
Published: December 2004

Equilibrium properties of hydrogen gas are calculated from 5000° to 20 000°K by considering it as a monatomic gas with imperfections. The usual ``H2 and H equilibrium'' method is not suitable at high temperatures even with anharmonicity corrections. Properties are obtained from the second virial coefficient B(T) of the monatomic gas and its derivatives. For the 1Σ state the Rydberg potential and for the 3Σ the best numerical potential is used. Ionization, higher excited states, and quantum effects are examined. The third virial coefficient for H3 is estimated and it is shown that properties from B(T) part alone are sufficient up to pressures of 1000 atm at 10 000°K and 13 000 atm at 20 000°K. Results are compared with those of the ``equilibrium constant'' approach.
Kinetic Modeling of Gas Mixtures
Authors: Sirovich Lawrence
Published: December 2004

Kinetic models for multicomponent gases are given. It is shown that some of the most important features of the Boltzmann equation are retained in spite of the simplicity of the model equations. An iteration procedure on the model equation is carried out and is identified with the Chapman-Enskog procedure. Linear and nonlinear formal procedures for developing the models and their extensions are also given.
Kinetic Model for High Velocity Ratio near Free Molecular Flow
Authors: Enoch Jacob
Published: December 2004

A kinetic model, which is based on an approximation to the complete Boltzmann equation, is developed for the purpose of solving flow problems in the high velocity ratio, large Knudsen number regime. The approximation consists of substituting appropriate δ functions for certain portions of the distribution function wherever they appear in a collision integral. The Boltzmann equation reduces to a first-order linear inhomogeneous partial differential equation in this approximation, and the detailed intermolecular differential scattering cross section appears explicitly in the inhomogeneous term. The model is applied to the solution of the hypersonic Couette flow of a rarefied hard-sphere gas.
Boltzmann-Vlasov Equation in a Bounded Region
Authors: Montgomery David , Gorman David
Published: December 2004

The problem of the oscillations of a ``collisionless'' electron plasma confined by specularly reflecting walls is solved. The device is to replace the boundary conditions by an equivalent, infinite, spatially periodic plasma which has a certain symmetry in velocity space. The spectrum of eigenfrequencies can be determined from a consideration of the equivalent unbounded situation.
Wave Motion in a Plasma with Anisotropic Pressure
Authors: Jaggi R. K.
Published: December 2004

The moment equations, neglecting the heat-flow tensor, have been used to study the wave propagation in a plasma consisting of electrons and singly charged ions, in a magnetic field, with anisotropic pressure tensors for both components. Two cases of wave propagation along the magnetic field and perpendicular to it have been worked out separately. In the first case of propagation along the magnetic field, the waves separate into a pure longitudinal and a pure transverse wave, the second of these only being affected by the anisotropy of the pressure tensor. Conditions are deduced under which the anisotropy of the pressure tensor can alter the propagation conditions of the waves. Attention is also given to the possibility that it can give rise to an instability. One important result which follows for magnetohydrodynamic waves is that an anisotropy in the electron pressure can give rise to an instability of the Alfvén waves. In the other case of the propagation across the field, the waves separate into a pure transverse wave and a wave which represents a combined longitudinal and transverse wave. The second of these is unaffected by the anisotropy of the pressure tensor. For the pure transverse wave, conditions are obtained under which instability can arise.
Coupling of Magnetohydrodynamic to Electromagnetic Waves at a Plasma Discontinuity. I. Radiation Field
Authors: Ullah Nazakat , Kahalas Sheldon L.
Published: December 2004

The coupling of magnetohydrodynamic waves to electromagnetic waves at a plasma-vacuum interface is studied for a general orientation of the external, constant magnetic field and of the direction of the incident wave propagation vector with respect to the normal to the boundary. It is found that there is a cone with its axis along the normal to the boundary within which the incident magnetohydrodynamic wave vector must fall in order that the transmitted electromagnetic wave be radiated, i.e., in order that the Poynting vector be real. The cone has a half-angle of the order of the ratio of the Alfvén velocity to the light velocity, which is very small in most cases. The ratio of the transmitted to the incident Poynting vectors is usually of the order of the ratio: Alfvén velocity/light velocity, but exhibits an anomaly for the extraordinary magnetohydrodynamic wave propagating in a constant magnetic field inclined to the interface. The variation of the individual electric and magnetic fields across the interface is discussed. In some cases, the fields in the vacuum are greatly increased over their values in the plasma.
Dispersion Function for a Plasma with a Cauchy Equilibrium Distribution
Authors: Liemohn H. B. , Scarf F. L.
Published: December 2004

The dispersive properties of a plasma with a generalized Cauchy equilibrium velocity distribution of the form (v2 + a2)−3 are derived for certain modes of propagation. The plasma dispersion function is found in a simple algebraic form which makes the solution of the dispersion equations readily accessible. A quartic dispersion relation which is obtained for right-hand circularly polarized electromagnetic waves propagating along a uniform static magnetic field is solved for all frequencies including cyclotron resonance. The complex index of refraction for this mode is plotted for several values of the temperature and the plasma-cyclotron frequency ratio. In general, thermal effects reduce the infinite discontinuity in phase at the cyclotron resonance to a finite value and cause thermal damping of the propagating wave below resonance. The results are compared with previous numerical analyses using the Maxwell distribution.
Coupling of Magnetohydrodynamic to Electromagnetic Waves at a Plasma Discontinuity. II. The Nonpropagating Field
Authors: Kahalas Sheldon L.
Published: December 2004

The coupling of magnetohydrodynamic to electromagnetic waves at a plasma-vacuum boundary is considered for the case in which the angle of incidence of the magnetohydrodynamic wave falls outside the cone for radiation. When this occurs, the electric and magnetic fields transmitted into the vacuum region decay exponentially in space in the direction of the normal to the boundary. The phase velocity in a direction parallel to the plane boundary has a value between the Alfvén velocity and the velocity of light, depending upon the angle of incidence of the magnetohydrodynamic wave. The magnitude, frequency, and angular dependence of the transmitted electric and magnetic fields are explored. In one situation a phenomenon called a transmission resonance is found to occur; i.e., the ratio of the transmitted to the incidence electric field becomes very large over a restricted range of angles of incidence.
First- and Second-Order Perturbations of Plasmas with Cauchy Equilibrium Distributions
Authors: Liemohn H. B. , Scarf F. L.
Published: December 2004

The space—time behavior of initial density perturbations (acoustic mode) in hot plasmas is analyzed, including second-order effects, using a one-dimensional Cauchy velocity distribution of the form (v2 + a2)−2 for the equilibrium distribution. The initial density perturbation is assumed to be sinusoidal in space and to have the same Cauchy velocity distribution. The first-order solution has an exact analytic form which gives damped oscillations at a thermally shifted plasma frequency. The nonlinear interference between the density wave and its electric field produces second harmonics in both space and time which appear in the analytic second-order solution. The harmonic structure suggests a ``spectral decay'' of the initial perturbation energy. In general, the oscillation frequency and damping decrement increase with temperature so that at sufficiently high temperatures, all forms of ordered motion are destroyed by the random thermal motion.
Hydromagnetic Reflection and Refraction at a Fluid Velocity Discontinuity
Authors: Fejer J. A.
Published: December 2004

The problem of hydromagnetic reflection and refraction at a fluid velocity discontinuity is solved. Expressions for the propagation vector of the refracted wave and for the reflection coefficient are derived. It is found that the reflected and refracted waves are pure characteristic waves if the incident wave is a pure characteristic wave.
Energy Transfer in Rotating Fluids by Reflection of Inertial Waves
Authors: Phillips O. M.
Published: December 2004

If inertial waves in a uniformly rotating fluid reflect from a rigid plane surface, it is shown that the magnitudes of the incident and reflected wavenumbers are generally unequal. The reflection process thus provides an interchange of energy among different scalar wavenumbers k. In an inviscid fluid, the ratio α(k)/k is conserved on reflection, where α is the particle orbit speed associated with the wavenumber k. In a viscous fluid the reflection coefficient is generally 1 - O(R1/2), where R is the wave Reynolds number 2Ω/νk2, though there is an exceptional case in which the incident energy flux is totally absorbed. When the fluid is contained in a large rotating box of general shape, the energy interchanges from repeated reflections can result in a statistical radiative equilibrium over the high wavenumbers. A dynamical equation is derived that specifies Eϑ(k), the energy distribution among wavenumbers inclined at an angle ϑ to the rotation vector. An approximate solution shows that Eϑ(k) is constant when k « kν = (Ω/νL)1/3, where L is the size of the domain. When k » kν, the spectrum decreases exponentially.
Progressive Deformation of a Perturbed Line Vortex Filament
Authors: Hama Francis R.
Published: December 2004

When a straight two-dimensional vortex filament, which is laid on the x axis, is perturbed by a three-dimensional distortion, it deforms progressively by its own induction. The progressive deformation is numerically obtained in this paper for a localized distortion y = a exp(−x2) and for a periodic distortion y = 2a cos[¼(πx)], a being the amplitude relative to the lateral extent of the distortion. When a is small, the Gaussian distortion causes a helical deformation which first moves in and then moves away toward far ends along the vortex filament, whereas the central portion where the disturbance was originally located, subsides and straightens. The plane of the sinusoidal distortion simply rotates in the direction opposite to that of the translation of fluid in the undisturbed vortex. The retrograde rotation is the same as that formulated by Kelvin. For these cases of small amplitude, a linearlized theory is also put forward. When a2 is large compared with unity, on the contrary, a nonlinear effect comes in, causing higher-order deformations to take place in both cases near the tip of the distorted pattern. This substantiates in part the author's experimental observation of the progressive deformation of a vortex loop in the final stage of boundary-layer transition. A possible mechanism of three-dimensional amplification of initially small perturbation in a shear flow is also discussed.
Effect of Diffusion on Interfacial Taylor Instability
Authors: Aranow R. H. , Witten L.
Published: December 2004

A theory is developed concerning the onset of interfacial instabilities at the liquid—liquid interface between two solvents when they are mutually immiscible and when a third species, the solute, is diffusing across the interface. The analysis made involves solving the linearized hydrodynamic equations of motion for an idealized model with appropriate boundary conditions at the interface. The interface becomes unstable and turbulence at the interface develops under certain conditions which depend upon the densities of the solutions, the strength of the frictional forces between solute and solvents, concentration gradients, and the direction and rate of diffusion of the solute. The effects of surface tension and viscosity are considered. Some experimental results pertaining to the instability are cited.
Electrical Conductivities of Lithium and Helium Gases
Authors: Ree Francis H.
Published: December 2004

Electrical conductivities of a multicomponent system in a uniform temperature, density, pressure, and magnetic field are obtained by using the transfer equations obtained by Burgers. The resulting formulas give the zero-order contribution to electrical conductivities by elastic scattering of colliding particles as a function of temperature and density. These formulas are applied to lithium and helium gases. The screened Coulomb cross sections and geometrical cross sections are used, respectively, for collisions involving charged particles and for collisions involving a charged particle and a neutral atom. The relative abundances of various species are obtained by using the Saha formulas. The limitations associated with the uses of the electrical conductivities are discussed.
Flow of a Non-Newtonian Fluid between Rotating Cylinders with Suction and Injection
Authors: Kapur J. N. , Goel Shashi
Published: December 2004

The steady flow of a certain non-Newtonian fluid in an annulus between two coaxial cylinders rotating with uniform angular velocities about the common axis is studied when there is suction at one wall and injection at the other. The stress matrix T for the non-Newtonian fluid is given by T = -pI + α1A1 + α2A2, where p is the pressure, I is the unit matrix, α1, α2 are constants and A1, A2 are kinematic matrices. It is found that in the case of no suction and injection, the velocity field is not affected by the presence of the non-Newtonian term α2A2, though the pressure field is affected. On the other hand, if there is suction and injection, however small, the non-Newtonian term affects the velocity field and the nature of this effects is investigated for sufficiently small suction and injection velocities.
Growth of a Weak Magnetic Field in a Turbulent Conducting Fluid with Large Magnetic Prandtl Number
Authors: Pao Yih-Ho
Published: December 2004

The behavior of a weak fluctuating magnetic field in a turbulent electrically conducting fluid with large magnetic Prandtl number is re-examined, without using vorticity analogy. For large magnetic Prandtl number, the characteristic length of the small eddies of turbulence is much larger than that of the small loops of the magnetic field. By inferring that the small eddies of turbulence are mainly responsible for the change of the fluctuation intensity of the magnetic field and by utilizing Batchelor's mixing approach, visualizing the turbulent velocity field as effectively a rather persistent uniform straining motion for the small-scale variation of magnetic field, it was found that the fluctuation intensity of the magnetic field grows due to turbulent motion for very large magnetic Prandtl number [(ν/λ) > 100, say] and approaches a constant value asymptotically. The rate of growth is found to be a function of ν/λ and τ (the product of time and the turbulent straining rate).
Structure of Weak Non-Hugoniot Shocks
Authors: Sichel Martin
Published: December 2004

As the curvature of shock waves increases, the shock structure becomes two dimensional, and the usual Hugoniot jump conditions no longer hold. An equation has been derived for the structure of such a two-dimensional non-Hugoniot shock in the case of weak shocks with Mach numbers close to one. The development of this equation from the Navier-Stokes equations is based on the assumptions that the vertical velocity is of order (M1* − 1)3/2 and that the flow within the shock is irrotational. From the derivation it appears that the non-Hugoniot region behaves as an acoustic wave driven by higher-order viscous effects. The properties of the above equation, which has been called the viscous-transonic or V-T equation have been investigated. The V-T equation appears to be a combination of Burgers' equation for weak normal shock structure and the transonic equation. It is shown that the structure of oblique shocks is a similarity solution of the V-T equation. Proper formulation of boundary conditions is considered and a uniqueness proof is given for a particular restricted boundary value problem.
Interpretation of Luminous Phenomena Observed in Electromagnetic Shock Tubes
Authors: Cloupeau M.
Published: December 2004

A series of experiments with electromagnetically driven shock waves in various gases have shown that the luminous emission observed along the tube should often be interpreted as being due to direct ionization produced by the driver discharge and not to thermal ionization produced by the shock wave. The experiments also show that for high Mach numbers obtained at low initial pressures (of the order of 1 mm Hg), the shock front and the front of the discharge plasma jet (contact front) practically coincide. Thus, in contradiction with the conclusions reached by Kolb, Griem, and others, the state of the luminous gas following ths shock front cannot be calculated by the Rankine-Hugoniot equations from the velocity of the front.

The results presented have been obtained by spectrographic investigation of the light emitted along a special H-shaped glass tube in which the gas between one of the electrode pairs is initially different from that filling the rest of the tube.
Equation of State of Gaseous Metallic Plasmas
Authors: Villars D. S.
Published: December 2004

This work implements a theory of H. S. Green who formulates contributions to pressure from interactions between different types of charged particles in an ionized system in terms of correlation functions gij(r). These functions can be estimated by successive iteration of an exponential involving the product of the pair of charges and a double integral using an IBM 709/7090 computer. Mathematical studies have elicted two principal sources of divergence of the numerical procedure. In the first place it is essential that a correction be made for neglect of tails of the g curves beyond the region of numerical integration. In the second place a method of renormalizing the g probabilities is developed which involves distinguishing between time averages of products of instantaneous probabilities. Computations converge rapidly for temperatures of 107 and 106 °K, begin to entail an expensive amount of machine time for 105 °K and blow up for 104 °K. It is believed that they may be reliable for charge densities of order 10−6 (in atomic units) and temperatures equal to or greater than 105 °K but for these conditions the interaction correction to the ideal gas pressure turns out to be unimportant. For lower temperatures or higher densities it is indicated that a functional relationship to correctly express dependence of g on small distances r is highly essential.
Thermodynamics of He3 and He4 Solutions above the λ Temperature of Pure He4
Authors: Chandra R. , Nanda V. S.
Published: December 2004

The thermodynamic properties of He3 and He4 solutions in the temperature range 2.2 °K to 2.6 °K have been investigated on the basis of some of the classical theories of nonideal solutions. Calculations have also been made of the excess chemical potentials from the vapor pressure data using some general thermodynamical considerations. These results are then compared with those obtained from the theories considered.
Variational Technique for Determining Dispersion Relations in Plasma Systems
Authors: Barston E. M.
Published: December 2004

Sturrock's variational principle seems particularly well suited to the study of small-amplitude disturbances of plasma systems and is formulated in a sufficiently general manner so as to be applicable to relativistic as well as nonrelativistic multistream problems. The use of this variational principle is shown to be effective (in conjunction with the trial-function method) in approximating dispersion relations. To this end the variational procedure is applied to two simple plasma problems which admit of exact solution. It is found that a first-order error in the trial functions leads to only a second-order error in the dispersion relation—a behavior typical of variational procedures and which renders them so useful.
Plasma Containment in the Theta Pinch
Authors: Green T. S.
Published: December 2004

An experimental investigation of the containment time of plasma in a theta pinch is described. Observations of changes in the plasma diamagnetism have been made, analysis of which leads to a determination of the field trapping conditions in the plasma and of the variations in line density of the plasma which take place during a discharge. The results show that in parallel field discharges the containment time of the plasma depends on the flux trapped within the plasma, in agreement with theoretical predictions. In particular, the containment time increases as the flux approaches zero. In reversed field discharges the plasma containment is limited by an axial contraction instability, which is slower the lower the amount of reversed trapped flux. At very low values of this flux, the plasma appears to stay contained and stable in a closed reversed field configuration for the period of observation (6 μsec).
Structure of Gaseous Detonation. III. Density in the Induction Zone of Hydrogen Detonation
Authors: White Donald R.
Published: December 2004

Interferometric studies of low pressure laminar detonations have shown the existence of an induction zone with a maximum density in accord with that calculated for the shocked and vibrationally relaxed but unreacted initial mixture. In 2H2 + O2 + 2CO and 7H2 + O2 the vibrational relaxation time is short compared to the induction time, and the latter time is in approximate agreement with the data of Schott and Kinsey. In H2 + 3O2 the observations suggest that the vibrational relaxation time is comparable to, and may in fact determine, the induction time.
Further Studies of Plasma Motion in a Curved Magnetic Field
Authors: Eubank H. P. , Wilkerson T. D.
Published: December 2004

Additional measurements of the transmission of a burst of plasma through a 90° bend in magnetic field include a mass and energy analysis of the incident and transmitted plasma. Under certain conditions of input density and bend magnetic field, tenfold reductions in plasma contaminants (atomic mass > 3) may be realized. Some further results on the source of neutralization of the polarization field are presented and discussed.
Structure of a Prandtl-Meyer Expansion in an Ideal Dissociating Gas
Authors: Appleton J. P.
Published: December 2004

The effect of a finite rate of chemical recombination on the structure of a Prandtl-Meyer expansion is studied theoretically. A numerical technique, based on the method of characteristics, is used to obtain an exact solution for a representative set of initial conditions. Wall expansion angles up to and including 30° are considered. From the results it is concluded that the flow departs from that appropriate to constant composition at the corner and approaches the infinite rate equilibrium solution at very large radial distances. Subsidiary wave reflections between vortex layers (due to the thermodynamically irreversible chemical reaction) and the wall can cause pressure fluctuations in the region following the primary expansion. Finally, the flow in the vicinity of the wall is bounded by a constant pressure region at a very large distance downstream.
Instability of a Current-Carrying Fluid Jet Issuing from a Nozzle
Authors: Uberoi Mahinder S. , Chow Chuen-Yen
Published: December 2004

The velocity across a jet becomes nonuniform due to contraction or expansion of fluid in the presence of electric current within the nozzle from which it issues. The results obtained elsewhere on the instability of a jet of uniform velocity due to electric current and surface tension are corrected. It is further shown that velocity nonuniformity reduces this instability. The available data on the instability of a mercury jet issuing from a contraction are for small current density and, hence, low velocity nonuniformity. However, for reasons yet unknown, the data do not agree with the (corrected) theory for the case of uniform velocity.
Dynamic Friction and Ion Wave Radiation Reaction in a Plasma
Authors: Rand S.
Published: December 2004

The reaction forces on a small charged body which traverses a low density plasma have been studied. The contributions to these forces are discussed with respect to individual particle and collective plasma action, with the relationships between these two contributions demonstrated. The reaction forces are obtained for a subsonic accelerating body, and, in various limiting cases, for a supersonic body undergoing a small degree of acceleration.
Precursor Waves in Shock Tubes
Authors: Pipkin A. C.
Published: December 2004

Weymann's observation of a wave of electrons propagating from a strong shock into the region ahead of it is considered. By taking into account the mutual electrostatic repulsion of the electrons through a simple approximation, the main features of the precursor wave motion can be explained. In particular, the theory predicts the relatively gradual decrease in electron density from the shock to the electrostatic front, followed by exponential decay upstream from the electrostatic front.
Generalized Normal Solutions of the Boltzmann Equation
Authors: Sirovich Lawrence
Published: December 2004

Solutions of the linearized Boltzmann equation which may be found from finite moment equations are studied. A general solution to this problem is found and its properties discussed. A more restrictive class of such solutions, called generalized normal solutions, are then uncovered. These constitute a wide class of solutions in any desired number of moments. The governing equations are rendered determinate by exact expressions relating higher moments to the distinguished moments. In certain circumstances the initial data must be altered, and the resulting ``ersatz'' initial data used in connection with the equations. A case in point is the usual normal solution of the Hilbert-Chapman-Enskog theory. The ``ersatz'' initial data then renders the latter into an exact asymptotic theory. In addition higher moment systems are discussed in detail. It is shown that the generalized normal solutions are by no means a comprehensive class. Exact solutions of the Boltzmann equation which are also exact solutions of the Euler equations, the Navier-Stokes equations, the Burnett equations, the Thirteen moments equations (among others) are exhibited. Furthermore, these can satisfy the Boltzmann equation in an infinite variety of ways.
Incoherent Scatter from a Hot Plasma
Authors: Pappert Richard A.
Published: December 2004

Within the limits of the first Born approximation, the incoherent scatter from a hot plasma is determined in terms of the spectral density of the induced current fluctuations. A significant parameter βe for assessing the importance of relativistic effects is the square root of the ratio of the electron temperature to the rest mass energy of the electron. First-order corrections in this parameter to the incoherent spectrum are calculated for a plasma in the absence of an external magnetic field. To first order in βe the total cross section remains unaltered. However, an asymmetry in the cross section per unit frequency about the incident frequency, Ω0, does occur. The magnitude and shape of this correction are determined.
Plasma Diffusion in a Magnetic Field
Authors: Whitehouse D. R. , Wollman H. B.
Published: December 2004

The two-dimensional diffusion of a partially ionized plasma in a magnetic field is studied using the macroscopic plasma equations. For a stable steady-state plasma with uniform electron temperature and ionization frequency, it is shown that the density distribution can exist only in the lowest mode by virtue of the internal constraint that the space charge potential is conservative. While the electron and ion diffusion currents in an insulating cavity are everywhere equal, similar to Schottky's ambipolar diffusion theory for one dimension, the plasma in a conducting cavity exhibits an increase in the net particle current to the walls and an unbalance of ion and electron currents in the plasma. Thus an amperian current flows through the plasma and returns through the walls. With adjustable dc potentials applied to the walls of a split cavity, these currents may be continuously varied and even decreased below those given by the ambipolar condition. An experiment with a microwave cavity discharge demonstrates the existence of these unbalanced currents.
Particle Trajectories in a Static Mirror Field
Authors: Lafferty D. L. , Lamborn B. N. A.
Published: December 2004

The properties of median-plane trajectories of a charged particle injected tangentially into a magnetic mirror field are studied. An effective radial potential is used, and the possible motions of the particle are determined from the corresponding radial phase-plane trajectories. It is shown that fields with a variable radial gradient can have phase plots containing saddle-point singularities. The particle trajectories near these singularities are characterized by long radial periods and, consequently, long path lengths. The critical trajectory passing through a saddle point has an infinite radial period; a particle injected along such a trajectory would then spiral inward toward the saddle-point and never return to the injection radius.
Nonadiabatic Injection into a Static Mirror Field
Authors: Lafferty D. L. , Lamborn B. N. A.
Published: December 2004

An analysis is made of a conservative trapping mechanism in a static mirror field. The discussion is specialized to the tangential injection of particles in the midplane. The analysis is based on single-particle dynamics in a conservative system. The adiabatic conditions are violated in two distinct ways: A random exchange of energy between transverse and longitudinal motion can occur due to fast characteristic loops in the particle trajectory; a second-harmonic angular perturbation in the midplane field produces parametric resonance in the longitudinal degree of freedom and results in energy transfer from transverse to longitudinal motion. Energy tends to be absorbed in the longitudinal degree of freedom until the resonance conditions are no longer satisfied. This tendency toward the accumulation of energy in longitudinal motion arises from the asymmetry of the equations of motion; energy is transferred to longitudinal motion by virtue of an unstable solution of the Mathieu equation and in the opposite direction by ordinary resonance. Computer studies of the coupled nonlinear equations of motion of a single particle verify the analytic prediction of rapid growth of the longitudinal oscillation.
Single-Particle Cyclotron Radiation near Walls and Sheaths
Authors: Simon Albert , Rosenbluth Marshall N.
Published: December 2004

A particle which moves perpendicular to a magnetic field while undergoing periodic elastic collisions with a rigid wall emits radiation which is rich in higher harmonics. Collisions with a sheath, instead of a wall, also produces radiation of this sort. The resulting radiation is calculated utilizing a simplified model of a sheath and also assuming an exponential plasma density distribution, and is then compared with experiment. One can fit either the observed spectral shape or the observed intensity, separately, but a simultaneous fit is rather difficult. The best results are obtained for a sheath thickness of the order of a Debye length.
Statistical Derivation of Hydrodynamics for a Coulomb System
Authors: Kaufman Allan N.
Published: December 2004

The equations of hydrodynamics, derived by Irving and Kirkwood for short-range interactions, are here derived for a classical system with Coulomb interactions. The stress tensor, energy density, and energy flux density each consist of a kinetic term, a self-consistent field term, and a correlation term. The correlation terms are meaningful for systems whose correlation length is small compared to the macroscopic scale of length. No restriction is placed upon the density of the system, nor upon the time scale.
Onsager Phenomenological Coefficients for a Weakly Ionized Cesium Plasma
Authors: Robinson Lawrence Baylor , Beaty Robert Carroll
Published: December 2004

The Onsager phenomenological coefficients are calculated for coupled electrical and thermal fluxes in a ``weakly ionized'' cesium plasma, when the only collisions of importance are those between electrons and neutral atoms. The phenomenological coefficients are converted into (a) isothermal electrical conductivity, (b) thermal conductivity in the absence of an external electric field, and (c) thermal conductivity in the presence of an external electric field. Numerical values of the ratio of the thermal conductivity to the product of temperature and electrical conductivity compare closely with the theoretical Wiedemann-Franz ratio. The ratio as calculated is temperature dependent, however.
Oscillations of a Capillary Jet of Finite Electrical Conductivity in the Presence of a Uniform Axial Magnetic Field
Authors: Nayyar N. K. , Trehan S. K.
Published: December 2004

The oscillations of a capillary jet of finite electrical conductivity in the presence of a uniform axial magnetic field are investigated for general perturbations. The dispersion relation is obtained and examined under various limiting cases of electrical conductivity; in particular, for the case of high resistivity an approximate formula for the frequency of oscillations of the jet is obtained. It is found that for nonaxisymmetric perturbations, the modes of oscillation of the jet are always stable and damped. The damping constant of the oscillations for different values of the wavenumber are tabulated for the case m = 1.
Direct-Interaction Approximation for a System of Several Interacting Simple Shear Waves
Authors: Kraichnan Robert H.
Published: December 2004

The direct-interaction approximation is applied to the evolution in time of systems of several interacting, inviscid, simple, shear waves whose initial amplitudes have a Gaussian statistical distribution. The results are compared numerically with exact statistical solutions obtained by numerical integration of the equations of motion of the wave amplitudes for a large Gaussian sample of initial conditions. It is found that the direct-interaction results can provide an adequate approximation in cases where both perturbation theory and the quasinormality approximation give physically unacceptable results.
Thermally Driven Nonlinear Oscillations in a Pipe with Traveling Shock Waves
Authors: Chu Boa-Teh , Ying S. J.
Published: December 2004

Nonlinear vibrations in a pipe closed at both ends with a plane heater in its midsection and containing a perfect gas are studied. When the frequency of a sinusoidal heat release is equal to twice the fundamental resonance frequency of the pipe, the level of fluctuation increases with time; shock waves are formed and ultimately the fluctuation attains a limiting value. It is shown that if the rate of heat release is small compared to the total enthalpy in the volume traversed by an acoustic front in a unit time, the fluctuation in the pipe, after many oscillations, builds up to (σ0/p0a0)½, where σ0 is the amplitude of the rate of heat release per unit area of the heater, and p0, a0 are respectively the initial pressure and sound speed. The nature of vibration in the pipe is found to be similar to that excited in a cylinder by a piston driven sinusoidally near a resonance frequency. The pressure and velocity at a fixed point in the pipe are shown to vary sinusoidally with time between the successive arrivals of the shock waves; the state of flow, of course, exhibits a discontinuous change whenever a shock wave traverses the point.
Radiation Smoothing of Shocks with and without a Magnetic Field
Authors: Mitchner M. , Vinokur M.
Published: December 2004

A transverse magnetic field imposed on a radiating shock wave is shown to inhibit the smoothing tendency of radiation energy transfer, and to alter the conditions for the occurrence of a temperature overshoot. Necessary and sufficient conditions for the smoothing of shocks by the mechanism of radiation energy transfer acting alone are discussed and numerical results are derived for the case of no magnetic field. A possible experimental test is proposed.