bluuebunny/crossref_metadata_2025 huggingface dataset:
Thermodynamics of Electrically Conducting Fluids
Authors: Chu Boa-Teh
Published: December 2004

By consideration of the equations of motion and the electromagnetic theory of a moving medium, the reversible work done on a fluid, per unit mass, in a small change of state is shown to be −pd(1/ρ) + E · d(D/ρ) + H · d(B/ρ), where p is the pressure due to the joint action of the mechanical and electromagnetic changes; ρ is the density; E and B are, respectively, the electric field strength and magnetic induction; D and H are, respectively, the electric and magnetic excitation. Only the nonrelativistic version of Minkowski's theory has been used in this derivation. This formula provides the basis for a complete study of the thermodynamics of fluid medium under the action of both electromagnetic and mechanical changes.

As an application, basic formulas which may be used to calculate the electrocaloric effect, the magnetocaloric effect, and electro- and magnetostriction effects are deduced. In particular, the additional pressure and pondermotive force due to these effects are obtained in a simple manner which, from the thermodynamic point of view, is better than Kortweg and Helmholtz' derivation given in the classical electromagnetic theory. As a second application, the energy equation of magnetohydromechanics is derived. The derivation is more general than previous derivations in that it does not presuppose the form of the electromagnetic constitutive equations (e.g., D = εE, B = μH) which the medium satisfies.
Model for Vibrational Relaxation of Diatomic Gases behind Shock Waves
Authors: Herman Robert , Rubin Robert J.
Published: December 2004

The problem of the vibrational relaxation of a system of harmonic oscillators is examined for the case in which the oscillators are in contact with a heat bath whose total heat capacity is finite and whose temperature therefore varies during the relaxation process. An analysis is carried out for processes in which the initial distribution of vibrational energy is a Boltzmann distribution. Application is made to the vibrational relaxation of a diatomic gas behind a shock wave.
Theory of Flames Produced by Unimolecular Reactions. I. Accurate Numerical Solutions
Authors: Hirschfelder Joseph O. , McCone Alan
Published: December 2004

The time dependent flame equations are presented in complete generality, including the effects of thermal diffusion, radiation, external forces, and pressure variations. The one-dimensional steady-state laminar flame supported by the unimolecular reaction A → B is studied carefully with special emphasis on the effects of heat transfer to the flame-holder. It is found that in agreement with Spalding's work on a somewhat different model there is a maximum amount of heat transfer which permits a steady state. For heat transfers less than this maximum there are two possible solutions of the flame velocity. The smaller of these flame velocities corresponds to an unstable mode. At exceedingly low pressures the flame velocity becomes comparable to the velocity of sound.
Flow of an Incompressible Fluid in a Hydromagnetic Capacitor
Authors: Chang C. C. , Lundgren T. S.
Published: December 2004

An incompressible electrically conducting fluid is contained in a torus of rectangular cross section. A uniform magnetic field is maintained along the polar axis of the tube. A radial electric field is suddenly applied, causing the fluid to flow through the tube. Over-all properties such as the time required to reach steady state, resistance and capacitance are calculated, and an equivalent electrical circuit is given.
Magnetohydrodynamic Waves in Wave Guides
Authors: Gajewski Ryszard
Published: December 2004

Propagation of magnetohydrodynamic waves is investigated in a fluid bounded by a cylindrical surface of constant, but not necessarily circular, cross section. The fluid is assumed to be nonviscous and perfectly conducting with a constant magnetic field applied parallel to the walls of the cylinder. It is shown that the following types of waves can propagate in such a wave guide: (1) transverse waves propagating without dispersion with the velocity of Alfvén waves; (2) a longitudinal wave, identical with the wave of the principal mode for an acoustic wave guide; (3) waves having both longitudinal and transverse components propagating with a dispersion, their group and phase velocity being close to the respective velocities for an acoustic wave guide; (4) waves having both longitudinal and transverse components propagating with a small dispersion, their group and phase velocity being close to the velocity of Alfvén waves. When the applied frequency is too low, damping of certain modes appears for waves of type (3), only; the cut-off frequencies turn out to be slightly higher than the corresponding cut-off frequencies for an acoustic wave guide.
Dynamic Instability of Accelerated Fluids
Authors: Chang C. T.
Published: December 2004

The asymmetrical growth of an interface separating two fluids of different densities, under the influence of an imposed acceleration (Rayleigh-Taylor instability), is shown to be mainly a nonlinear phenomenon. When the initial disturbance is a simple sinusoidal wave and is started from rest, it is found that the growth of the interface depends explicitly on two dimensionless parameters of the initial disturbance, namely, the dimensionless amplitude (i.e., the amplitude-to-wave-length ratio) and the dimensionless wave number (i.e., the wave number of the initial disturbance to the ``cutoff'' wave number of the medium under the prevailing experimental condition). Results of the analysis show that the asymmetrical development of the interface occurs much earlier for disturbances of larger amplitudes and lower wave numbers than those of smaller amplitudes and higher wave numbers, i.e., those with wave numbers near the ``cutoff.'' Surface tension shows a definite stabilizing effect. Because of the nonlinear effect, for a sinusoidal initial disturbance, a generation of higher harmonics as well as a feed-back to the fundamental is noted. Contrary to the prediction of the linearized theory, the present analysis, based on higher order approximations, reveals an ``over-stable'' phenomenon for disturbances having initial wave numbers beyond the ``cutoff.''
Simple Wave Flow in Ducts
Authors: Gundersen Roy
Published: December 2004

A centered simple wave is generated by the impulsive retraction of a piston. The sound speed perturbation and particle velocity perturbation are determined when the wave passes into a slowly diverging (or converging) section or a section which presents a throat. When the section of varying area terminates in a channel of constant cross section, the result of passage through the transition section of varying area is the superposition of a perturbation which tends to decrease the flow velocity by a term which varies inversely with the time for a point moving with the wave, but increases linearly with the time at a fixed point in the channel, in agreement with results first presented by Chester with the use of a two-dimensional analysis. The flow of an arbitrary simple wave in the section of varying area is solved.
Isotope Separation by a Hot-Wire Thermal Diffusion Column
Authors: Saxena S. C. , Watson W. W.
Published: December 2004

The performance of a hot-wire thermal diffusion column is discussed. The role of spacers used for centering the hot wire has been investigated experimentally for a glass column of 9-mm i.d. cold wall, and hot wall 20-mil tungsten wire; the results suggest that the maximum separation is obtained when the spacers (20-mil nickel wire) are installed every 70 cm along the hot wire. The separation falls when the spacers come either closer together or farther apart. An explanation of this optimum dependence of separation on spacer distance is advanced.
Statistical Study of Accelerating Flames
Authors: Stern R. A. , Laderman A. J. , Oppenheim A. K.
Published: December 2004

Study of velocity fluctuations observed by means of ionization probes during the development of detonation reveals its significance as an indicator of physical characteristics of the flame. The scatter in time of arrival (the reciprocal of the velocity) was found normally distributed at an 85% probability level. The means and standard deviation were determined within 5% and 20%, respectively, at a confidence level of 90%. The intensity of scatter is interpreted consequently as indicative of the combustion front fluctuation that can be considered to delineate the ``effective flame thickness.'' It is found then that, as the flame accelerates, its effective thickness first increases, reaching a maximum in the vicinity of velocity overshoot, and then decreases, attaining finally a minimum, constant value when the steady detonation wave is established. An interesting bimodal distribution of scatter for the 2H2–02 mixture has been observed, indicating a possible existence of two alternative, independent modes for the development of the process.
Boltzmann Equation for an Electron Guide Field Accelerator. I. Quasi-Stationary Solutions for an Electron Beam
Authors: Ehrman Joachim B.
Published: December 2004

A simplified model for dePackh's version of an electron guide field accelerator is set up by substituting for the actual external quadrupole or solenoidal focusing magnetic field an azimuthally symmetric focusing field, and by replacing the actual toroidal geometry by a cylindrical geometry with periodic boundary conditions. The Boltzmann equation for an electron beam in this system is studied, and a set of solutions is obtained which contain just enough parameters to represent the quasi-stationary behavior of the beam realistically. The values of these parameters are related to the initial conditions of the beam by the adiabatic invariance of linear charge density and of the radial and azimuthal action integrals in the absence of collisions and radiation. Thus, the quasi-stationary development of the beam in time is determined without an explicit time dependence in the Boltzmann equation. While the electron energy is being increased by a betatron field, the beam passes from a condition in which its electrons are in almost neutral equilibrium with respect to displacement from the axis (low temperature or `` 32'' regime) to a condition in which each electron is hardly affected by the other electrons (high temperature or betatron or ``½'' regime), as predicted by dePackh. If the beam is initially isothermal, the temperature becomes a monotonic decreasing function of distance from the axis in the course of electron energy increase.
Instability of Contra-Streaming Plasmas
Authors: Kellogg Paul J. , Liemohn Harold
Published: December 2004

The problem of instabilities in colliding ionized hydrogen beams, which has been treated by Kahn and Parker in the special case of zero temperature, is solved for the nonzero temperature case by taking Maxwell distributions for the equilibrium density functions. At sufficiently high temperature it is found that the random thermal motion will prevent growing oscillations. The boundary between the stable and unstable regions is plotted as a function of energy and density parameters. Certain phenomena associated with solar particle streams are discussed in terms of these results.
Asymptotic Value of the Pair Distribution Near a Wall
Authors: Lebowitz Joel L.
Published: December 2004

We calculate the asymptotic value of the pair probability density ρ2(r2, r1) for finding a fluid particle at a point r2 far in the interior of a fluid, when it is known that there is a particle at r1 in contact with the walls (rigid) of the container. This value is different from the well-known expression for the asymptotic value of ρ2(r2, r1) when both r2 and r1 are in the interior of the fluid. Our derivation is based on the virial theorem for total momentum fluctuations in an equilibrium system and makes use of the assumption that there are no long range correlations in a fluid. Application is made of our result to re-derive simply the expression for the second virial coefficient and the exact equation of state of a hard-sphere gas in one dimension. Quantum systems are also treated.
Boundary Layer Over a Flat Plate in Presence of Shear Flow
Authors: Ting Lu
Published: December 2004

The governing equations of an incompressible boundary layer over a flat plate in the presence of a shear flow with finite vorticity are derived. For large vorticity, a similarity solution is obtained. For moderate vorticity, one of the governing equations is replaced by an approximate one for which similarity solutions exist.
Stability of Inviscid Plane Couette Flow
Authors: Case K. M.
Published: December 2004

The initial-value problem corresponding to a perturbed inviscid plane Couette flow is solved. Difficulties encountered in applying classical hydrodynamic-stability methods are avoided by considering the initial value problem.
Kinetic Equations for Plasma and Radiation
Authors: Simon Albert , Harris E. G.
Published: December 2004

The starting point is the Liouville equation for the density in phase space of a system of charged particles and a denumerably infinite set of field oscillators. By integrating out the coordinates of all but a finite number of particles and oscillators one obtains a chain of equations relating the reduced distribution functions. A complete solution to the chain is obtained by a generalization of the expansion method of Rosenbluth and Rostoker. In lowest order, a coupled set of self-consistent field equations in the one-particle and one-oscillator distributions is obtained. These are partially decoupled to give the usual Vlasov equation and a companion equation for the oscillator distribution. In first order one obtains a similar set of equations for the two-particle and the particle-oscillator correlation functions. An entirely similar pair of equations then relates the first-order distribution functions themselves. It appears that the general solution is obtained by the steady unfolding of higher correlation functions in terms of higher and higher self-consistent field equations. The first-order equations can be regarded as a ``Fokker-Planck'' equation for particles and a ``Fokker-Planck'' equation for radiation.
Electrostatic Instabilities of a Uniform Non-Maxwellian Plasma
Authors: Penrose Oliver
Published: December 2004

A stability criterion is obtained starting from Vlasov's collision-free kinetic equations. Possible instabilities propagating parallel to an arbitrary unit vector e are related to a function F(u)≡Σjωj2∫d3v gj(v) δ(e·v−u), where gi(v) is the normalized unperturbed distribution function, and ωj≡(4πnjej2/mj)12 the plasma frequency, for the jth type of particle. By using a method related to the Nyquist criterion, it is shown that plasma oscillations growing exponentially with time are possible if and only if F(u) has a minimum at a value u = ξ such that ∫−∞∞du(u−ξ)−2[F(u)−F(ξ)]>0. A study of the initial-value problem confirms that the plasma is normally stable if no exponentially growing modes exist; but there is an exceptional class of distribution functions (recognizable by means of an extension of the above criterion) for which linearized stability theory breaks down. The method is applied to several examples, of which the most important is a model of a current-carrying plasma with Maxwell distributions at different temperatures for electrons and ions. The meaning of the mathematical assumptions made is carefully discussed.
Magnetohydrodynamic Wave Propagation in the Ionosphere
Authors: Kahalas Sheldon L.
Published: December 2004

The propagation of magnetohydrodynamic waves in a compressible fluid is discussed with reference to the ionosphere. An investigation of the damping for a gas of finite conductivity shows that different wave modes may be heavily attenuated in certain directions of propagation. Also, the slow wave of the magneto-acoustic mode is shown to exhibit preferentially less damping for propagation along the magnetic field lines. An examination of the Hall and electron pressure terms shows that they may be neglected for low enough wave frequencies. The coupling of electromagnetic to magneto-hydrodynamic waves at a plasma-vacuum boundary is considered. The coupling coefficient is estimated to be one percent.
Radiation by Plasma Oscillations in a Bounded Plasma in a Magnetic Field
Authors: Wyld H. W.
Published: December 2004

The radiation by a thermal distribution of plasma oscillations in a bounded plasma in a magnetic field is calculated in the limit (ωc/ωp)½ « 1, where ωc and ωp are the cyclotron and plasma frequencies. The calculation is performed in two ways leading to the same result: (1) a ``Fresnel formula'' for ratio of the intensity of the electromagnetic wave transmitted through the plasma boundary to the intensity of an incident plasma oscillation is derived; (2) the decaying modes, satisfying a radiation condition at infinity, of a bounded plasma in a magnetic field are found. The results are compared with the synchrotron radiation by a plasma in a magnetic field. It is found that for a thermal distribution of plasma oscillations, the radiation due to plasma oscillations is small compared to the synchrotron radiation.
Cross Stresses in the Laminar Flow of Liquids
Authors: Reiner M.
Published: December 2004

It is shown that cross-elasticity effects exist in a simple homogeneous liquid such as toluene. These effects manifest themselves in cross stresses observed in an instrument consisting of two circular metal plates, one stationary, the other rotating opposite it. The stator can be displaced along the axis of rotation against forces exerted by springs. Stator and rotor are in contact when at rest. When the rotor is brought into rotation, cross stresses in the liquid separate stator from rotor and a bearing effect is produced.
Measurements on the Blast Wave in a Conical Tube
Authors: Filler William S.
Published: December 2004

Spherical high-explosive blast waves were studied under simplified laboratory conditions using a sector shock tube and detonating at its apex a high explosive. In the experiment, a quantity of explosive equivalent in energy to ½ g of TNT was used. Pressure-time histories of the shock waves produced in the cone were obtained with piezoelectric gauges. These waves were shown to possess the typical features of spherically expanding blast waves. The magnitudes of the peak pressures, positive durations, and impulses of the shock waves were found to be characteristic of those produced by spherical charges of about 60 times the weight of explosive actually used. This falls short of the design amplification of the 22-deg cone used by about 40%. However, amplification effects larger by several orders of magnitude appear possible with the use of cones having smaller angles.
Diffusion of Charged Particles across a Magnetic Field Due to Neutral Particles
Authors: Wright James P.
Published: December 2004

A calculation of the diffusion of charged particles across a magnetic field arising from the presence of neutral particles is compared with the diffusion arising from charged particles. The ratio of the flux of charged particles, arising from the presence of neutral particles, and the flux arising from charged particles is found to be of the order 102 to 105. The actual value of the ratio depends on the types of particles, the temperature, the number densities, and the density gradients.
Plasma Viscosity in a Magnetic Field
Authors: Kaufman Allan N.
Published: December 2004

The viscosity of a fully ionized plasma in a magnetic field is analyzed from two points of view: first, from a consideration of particle orbits; and second, from the solution of a simplified Boltzmann equation. These semiquantitative methods are studied in order to clarify the behavior of the viscosity coefficients.
On Certain Properties of Hydromagnetic Shocks
Authors: Ericson W. B. , Bazer J.
Published: December 2004

Proofs of four basic properties of stationary, planar, nonrelativistic hydromagnetic shocks are presented. These properties are: (P1) the specific entropy behind a hydromagnetic shock exceeds that ahead, if and only if, the shock is compressive; (P2) the specific entropy behind a compressive shock varies in the same sense as the mass flux; (P3) in the region behind (compressive) fast shocks, the fast disturbance speed is greater than the normally directed fluid velocity relative to the shock; (P4) in the region behind (compressive) slow shocks, the slow disturbance speed may be less than, equal to, or greater than the normally directed fluid velocity relative to the shock. The equality holds when the specific entropy and the mass flux assume their maximum values.

In these statements the state in front is assumed fixed and attention is focused on the variation of the state behind with an appropriate shock strength parameter. The proof of P1 is designed especially to cover the case of the slow shock where the dependence of the state behind on the ``natural'' shock-strength parameters is nonmonotonic. Our proofs of P3 and P4 require the medium to be a polytropic ideal gas; however, a less stringent assumption suffices for P1 and P2.
On The Particle Size Spectrum of a Condensing Vapor
Authors: Friedlander S. K.
Published: December 2004

The classical theories of condensation and coagulation are considered as limiting cases of a general theory of new phase formation. By making several assumptions concerning the nature of the vapor and of the cooling process, it is shown that the equation of condensation can be written in a simplified dimensionless form. The embryo size spectrum function at the end of the condensation process is a function of a number of dimensionless groups; hence, condensation can be modeled in the sense that particle size can be controlled by varying certain scale factors. An application to condensation by mixing of a hot vapor with cool air is proposed.
On the Structure of Plane Detonation Waves
Authors: Adamson T. C.
Published: December 2004

A steady planar detonation wave, considered to be a shock wave followed by a reaction zone, is studied with both irreversible and reversible first-order reaction kinetics. A perturbation solution with first-order transport effects, valid in the reaction zone for those cases where the ratio of the characteristic collision time to the characteristic chemical time is small compared to one, is presented with sample calculations of temperature and concentration distributions for typical irreversible and reversible reaction cases. Analysis of the solution shows that simple series solutions and hence the given perturbation solutions do not hold near the hot boundary for all possible final Mach numbers. In the irreversible reaction case, the perturbation solution is a valid approximation for final Mach numbers less than (1 − B)½, where B is the ratio of characteristic times, the approximation becoming less accurate as the Mach numbers tend toward this limiting value. In the reversible reaction case, the perturbation solution is a valid approximation for final Mach numbers up to the Chapman-Jouguet value of unity, if the Mach number is based on the equilibrium speed of sound.
Collision Trajectories for Inverse Power Intermolecular Potentials
Authors: Mott-Smith H. M.
Published: December 2004

If −cr−n is the intermolecular potential for separation r, b the classical collision parameter, μ the reduced mass, g the relative velocity before collision, and χ the angle of deflection of the relative velocity due to collision, it is found that χ=− ∑ t=1∞Γ(12nt+12)Γ(12)t!Γ(12nt−t+1)[2cμg2bn]t,the series converging only for b > b0, where μg2b0n = ½nn/2(n − 2)1−n/2, this being true both for c positive (attractive potentials) and c negative (repulsive potential). This result makes it possible to calculate, by analytic integrations, the contributions to the elementary collision integrals from the range b > b0. It also simplifies greatly the calculation of the collision integrals for both attractive and repulsive inverse power potentials which can be evaluated entirely by analytic means, for n > 2.
Radiation of Hydromagnetic Waves
Authors: Karplus Robert
Published: December 2004

The dyadic Green's function for hydromagnetic waves in a uniform, fully ionized, perfectly conducting, pressureless fluid is obtained. The electromagnetic field consists of two modes, one that propagates isotropically and one that propagates along the field lines. The radiation rate from some simple model current distributions is derived from the Green's functions. If the source contains a current along the constant static field, then the radiation along the field lines through the source is very intense. This last result also holds in the nonuniform static field of an infinitely long straight wire.
Interaction between Cold Plasmas and Guided Electromagnetic Waves
Authors: Buchsbaum S. J. , Mower Lyman , Brown Sanborn C.
Published: December 2004

The microwave cavity method for the measurement of various parameters of a cold plasma in the presence of a static magnetic field is examined. Emphasis is placed on the determination of the limits of validity of the perturbation theory for various mode configurations of a cylindrical cavity coaxial with a plasma column and coaxial with the static magnetic field. The classes of modes examined are those which in the absence of the magnetic field reduce to the TM0m0, TM1mn, TE1mn, and TE0mn modes. For the TM0m0 and TE0mn modes, exact expressions for the cavity frequency shifts are obtained. These expressions are then expanded in appropriate power series to obtain the limits of validity of the perturbation method. For the TE0mn modes the perturbation theory must be modified to account for the polarization of the plasma. In the absence of a magnetic field, the TM1mn as well as the TE1mn modes are degenerate in their resonant frequencies. The presence of a magnetic field removes the degeneracy and causes the resonant frequency to be double-valued. An experimental test of the validity of the perturbation method can be had by comparing the two resonant frequencies. The relation is given between the characteristics of the various modes and the propagation of plane waves in infinite uniform plasmas.
Ionization Growth in a Gas with a Constant Electric Field
Authors: Gerjuoy E. , Stuart G. W.
Published: December 2004

A model for the growth of ionization in a gas with a uniform electric field is studied by Laplace transform techniques. The total electron-molecule cross section is taken inversely proportional to the velocity; the ionization cross section may have arbitrary velocity dependence; all secondary electrons are created with zero energy; all collisions scatter electrons isotropically but produce no energy loss. With this model, in the steady-state spatially dependent case that primary electrons are continuously furnished by a cathode at z = 0, an exact solution is found for Townsend's α and for the asymptotic (valid at large z) electron distribution function integrated over velocity orientation. Similarly, in the spatially homogeneous time-dependent case that primary electrons are furnished at t = 0 by a uniformly distributed source, an exact solution is found for the time rate of ionization growth and for the asymptotic (valid at long times) electron distribution function integrated over velocity orientation. Numerical results, including effective electron temperatures are presented for several assumed ionization cross sections. Because of the neglect of energy loss, applicability of the model is limited to the high E/p (electric field/pressure) range.
Spectroscopic Study of Helium Plasmas Produced by Magnetically Driven Shock Waves
Authors: McLean E. A. , Faneuff C. E. , Kolb A. C. , Griem H. R.
Published: December 2004

Measurements have been made of the temperature, density, and degree of ionization of plasmas produced by Mach 30 magnetically driven shock waves in helium (ambient pressure 1 mm Hg). Simultaneous photoelectric intensity measurements of the absolute spectral intensities of HeI λ3889, HeI λ5876, HeII λ4686, and HeII λ3203 indicate temperatures of 3.7 ev, electron and ion densities ∼1017 cm−3, degree of ionization ∼99.9%, and a density ratio of ∼4 across the shock front. The estimated error is ±2% for the temperature and ±12% for the electron and ion densities. The electron density was derived independently from the width of HeII λ4686 and agreed with the photoelectric density measurement to within the experimental error for the line width, thus providing a proof of the ionization and excitation equilibrium assumption used in analyzing the absolute intensity data. Continuum intensity measurements also provided a check on the consistency of the results. The temperature calculated from the measured shock velocity using the usual Rankine-Hugoniot equations is lower by a factor of about 2, and the density ratio is higher by a factor of about 3. A plausible explanation of this discrepancy is that ultraviolet radiation emitted by the hot plasma in the arc region is absorbed in front of the shock wave.
Electric Field Distribution in a Dense Plasma
Authors: Jackson J. L.
Published: December 2004

A calculation is presented of the probability distribution function of the electric field at the center of an ion or atom in a plasma in the high ion density limit. In this limit, it is possible to take into account rigorously the effect of the Coulomb interactions on the distribution function. The distribution function in the high-density limit is Gaussian. The Coulomb interaction decreases the mean square electric field by the multiplicative factor [1 + κa0 + ⅓(κa0)2]−1, where κ is the reciprocal Debye length and a0 the radius of the ion or atom at whose center the field is evaluated.
Stability of Thin Electron Layers
Authors: Neil V. Kelvin
Published: December 2004

An instability that consists of a bunching transverse to the directed motion of an infinitely thin layer of electrons is investigated theoretically. The initial model is a plane sheet, infinite in extent, and neutralized by positive ions. This configuration is found to be unstable if all electrons travel with the same relativistic velocity. If the electrons are monoenergetic, but have a small angular spread in velocities, a criterion for stability is obtained that places a lower limit on the spread. This limit is directly proportional to the wavelength of the perturbation. The theory is also applied to a thin cylindrical sheet inside a perfectly conducting cylinder. The system is infinite in the axial direction, and the electrons move in the azimuthal direction. In the absence of axial velocity, the instability is present as in the plane sheet. Considering a spread in axial velocity leads to a stability criterion independent of perturbation wavelength. A numerical example, employing the proposed parameters of the Astron device, indicates that an angular spread of about 60° is necessary for stability.
Plasma Oscillations and Landau Damping in a Relativistic Gas
Authors: Buti B.
Published: December 2004

The problem of Landau damping in plasma oscillations is studied in a relativistic gas and the asymptotic forms of the dispersion relation and the damping coefficient are obtained in the non-relativistic as well as in the relativistic limits. In the relativistic limit it is found that while the damping is very strong in the case where the phase velocity is small compared to the velocity of light, it is absent when the phase velocity exceeds the velocity of light. Moreover, in the former case, in the extreme relativistic limit the damping becomes independent of the plasma temperature.
Dispersion of Ion Cyclotron Waves in Magnetoplasmas
Authors: Engelhardt A. G. , Dougal A. A.
Published: December 2004

Dispersion of waves propagated at frequencies near the ion cyclotron frequency in collision-dominated plasmas subjected to axial magnetic fields is investigated. Radial and axial propagation constants, satisfying Maxwell's equations, and including the contributions of binary elastic ion-ion and ion-electron interparticle forces to an ion conductivity tensor, are calculated. Elements of the ion conductivity tensor are found analytically by expressing the ion distribution function in the Boltzmann equation as a series of orthogonal Laguerre polynomials in velocity space with time-dependent expansion coefficients. Right-handed and left-handed elliptically polarized waves are found from a numerical solution for a range of values of the ion cyclotron frequency about the fixed wave frequency of 7.62 Mc. The axial wavelengths λzL, λzR, and damping lengths λDL, λDR are calculated as functions of the magnetic field for a plasma density of 1021 m−3, and temperature of 104, 105 and 106 °K. Enhanced dispersion occurs with increasing temperature. Stronger dispersion is associated with the left-handed elliptically polarized wave; for 105 ° and 106 °K, above resonance λDL ≫ λzL, whereas below λDL ≈ λzL. Ion-ion collisions broaden the resonance width and decrease absorption at resonance.
Plasma Acceleration with Coaxial Electrodes
Authors: Hart Philip J.
Published: December 2004

The acceleration of a plasma by a capacitor discharge between coaxial electrodes is studied for (1) a shock tube having an initially uniform gas distribution and for (2) a plasma gun which accelerates a constant mass into a vacuum. Differential equations written for the first case for a simple snowplow model and solved by analog computer, are found to closely predict peak plasma velocities for a certain range of pressures. However, experimental study by means of a ``difference'' magnetic probe shows that the actual current distribution in the space between the electrodes is rather complex. Near the time when peak plasma velocity is reached, the first pulse splits into two pulses and persisting loop currents form in the plasma. An efficient mode of plasma acceleration which produces faster and more sharply defined shock waves is observed at low pressures when the center electrode is initially positive. Computer solutions are also obtained for the plasma gun, which seems to be intrinsically capable of greater efficiency than the shock tube.
Differential Rotation in Slowly Dissipating Systems
Authors: Balazs Nandor L.
Published: December 2004

If a body does not rotate uniformly it suffers differential rotation. Under certain conditions the existence of differential rotation of a body is a consequence of quite general properties of dissipative processes. Let E be the kinetic energy of rotation, A and I the angular momentum and the moment of inertia along the axis of rotation; then the body cannot rotate rigidly unless the positive semidefinite form K = E - A2/2I vanishes. If this condition is not satisfied, the motion of the system can still be specified provided the relaxation time for establishing a steady state corresponding to a given value of the energy and angular momentum is much less than the relaxation times of the energy and angular momentum. If this be the case, the steady state of the system can be approximated with a state in which the dissipation is a minimum subject to the constraints that E and A have fixed values. This leads to the investigation of states of least dissipation subject to auxiliary conditions. The resulting eigenvalue problem is solved for several simple models in which the dissipation is due solely to viscous friction. If the values of E and A specified through the auxiliary conditions do not make K vanish, the models exhibit differential rotation.
Static Temperature Measurements in a Flowing Gas
Authors: Muntz E. P.
Published: December 2004

A method has been developed to measure vibrational and rotational static temperatures at any point in nonradiating low-density flows of nitrogen. An electron beam is used to excite emission in the first negative system of nitrogen. The relative intensities in the rotational and vibrational structure of the emission spectra are predicted theoretically. The theoretical predictions are used to obtain rotational and vibrational temperatures of the nitrogen through which the beam passes.
Deviation of Magnetic Annular Shock-Tube Operation from One-Dimensional Model
Authors: Fishman F. J. , Petschek H. E.
Published: December 2004

In a magnetic annular shock tube the gas is pushed axially by an azimuthal magnetic field. Since this field varies inversely as the radius, there are radial nonuniformities in the resulting flow which are analyzed for small values of the ratio ε of annulus spacing to radius. The pressure variation across the annulus at the interface between plasma and driving field results in a tilting of the interface. This flow is analogous to the flow resulting from a dam break in shallow-water theory; it is characterized by a wave of speed (εp/ρ)½. The maximum value of ε for which the interface and shock wave remain separated is calculated. Nonuniformities are also produced at the shock front when an azimuthal magnetic field is present ahead of the shock; the shock becomes nonplanar and radial variations in the flow persist far behind the shock. For some cases these nonuniformities are appreciable even for values of ε so small that the interface and shock wave remain separated.
Exchange of Energy between Gases at Different Temperatures
Authors: Desloge Edward A.
Published: December 2004

An expression for the energy exchange between two Maxwellian gases at different temperatures is derived. The resultant formula contains an integral in which the scattering cross section for momentum transfer appears. If the cross section for hard-sphere collisions is used, the expression reduces to an expression obtained by Cravath for this case. If the cross section for screened Coulomb interactions is used, the results agree with results for the same case obtained by Spitzer and others.
Conductivity Tensor and Dispersion Equation for a Plasma
Authors: Lewis Robert M. , Keller Joseph B.
Published: December 2004

Periodic plane waves are considered in a plasma pervaded by a uniform magnetic field. The appropriate linearized Boltzmann equations for the distribution functions of the electrons and of each type of ion are solved exactly. Collisions are taken into account by the inclusion of a simplified collision term. The solutions are used to compute the electric current, from which the conductivity tensor of each ionic species is found. The total conductivity is then used in Maxwell's equations to determine the electromagnetic field, and this leads to the dispersion equation for plane waves. This equation is solved in various parameter ranges for the case of longitudinal waves when the conductivity of only one species is taken into account. The solutions of Landau, Gordeyev, Gross, Bernstein, and others are recovered when the collision frequency vanishes. In addition, various power series and asymptotic expansions for the conductivity tensor are given, and it is shown to reduce to that of the magneto-ionic theory under suitable conditions. The Appendix contains a systematic study of a function which plays a central role in the theory.
Experiment on the Spatial Confinement of Plasma in the Heliotron B Magnetic Field
Authors: Uo Kōji , Mōri Akihiro , Oshiyama Hiroshi , Katō Risō , Ishii Keishi
Published: December 2004

A magnetic field is produced by an electric current in a series of pair coils wound around the discharge tube at regular intervals. The electric current in each coil of the pair differs both in intensity and direction. The lines of force near the tube axis undulate without crossing the wall, while those near the tube wall cross the wall. Thus the high-temperature plasma can be produced by Ohmic heating in the central region of the field. Experiments were carried out in order to verify the spatial confinement of the plasma in this field. The plasma current flows only within the central region whose mean-cross-section diameter is about 3 cm, and the plasma has a sharp boundary. Outside the region there is no current. The spectra from the hydrogen discharge are mainly composed of the pure Balmer series, and the impurity spectral lines are very weak or hardly perceptible. From these experimental results, it can be concluded that the hot plasma is almost perfectly isolated from the stainless-steel-tube wall by the Heliotron magnetic field and has very low impurity level.
Shock-Tube Investigation of the Ionization of Cesium Vapor
Authors: Haught Alan F.
Published: December 2004

A conventional pressure-driven shock tube was used to produce ionizing shocks in a uniformly heated test section containing argon and vaporized cesium. The radiation from the shock-heated cesium vapor was used to measure the thermal ionization rate of the cesium vapor as a function of temperature and density. A number of significant differences are noted between the results obtained here and those obtained in similar experiments with inert gases. In particular, unlike the inert gases, the luminosity profile of the ionizing cesium shows a delayed radiation overshoot. The overshoot apparently arises from the two-stage nature of the ionization process, and on the basis of a qualitative model for the ionization, permits an experimental evaluation of the temperature and density dependence of both the first-stage atom-atom process and the second-stage electron-atom reaction. The results are discussed in terms of the present theories of the ionization kinetics.
Instability of a Vortex Sheet in Nonequilibrium Flows
Authors: Wang Kuo Chang
Published: December 2004

The stability of a plane vortex sheet between two uniform streams is examined with respect to small disturbances when the two media are relaxing diatomic gases (such as oxygen or nitrogen). For the equilibrium and frozen cases, the eigenvalue equation is identical in form with that of the conventional case, and the stability is decreased due to the relaxation. For the nonequilibrium case, the eigenvalue equation is complex and depends on the wavenumber of the disturbances; the vortex sheet is shown to be always unstable.
Equivalence of the Chapman-Enskog and the Mean-Free-Path Theory of Gases
Authors: Monchick L.
Published: December 2004

The model considered is restricted to monatomic particles interacting with a finite-range central field force. The integral equation for the second Chapman-Enskog approximation to the velocity distribution function is solved by a Liouville-Neumann iteration scheme. It is then shown that the Nth iteration corresponds to a mean-free-path theory where the trajectory of a particle has been followed through N + 1 collisions. The zeroth-order approximation is then compared with the elementary mean-free-path theory to show their equivalence.
Measurement of the Properties of Plasma Eddies Produced by Shear in Velocity in a Magnetic Field
Authors: Bostick Winston H.
Published: December 2004

Velocity shear is deliberately introduced by firing two plasma guns, laterally displaced, at one another across a magnetic field. Double-probe measurements of electric fields (and hence velocity) in the plasma clearly show the existence of traveling vortices or eddies which contain most of the plasma. Simultaneous velocity and density profiles of eddies have been obtained and examples are shown.
Some General Characteristics of Two-Dimensional Incompressible Magnetohydrodynamic Flows
Authors: Pan C. H. T.
Published: December 2004

The velocity field of a liquid conductor will be planar, with all field quantities being invariant in the normal (z) direction, for two different categories of conditions. (1) Planar components of B and J are parallel. This poses a strong restriction on the electrical and magnetic boundary conditions. The magnetic field has a nontrivial influence on the flow field only when Jz is nonuniform. Bz has a precise analog in the laminar heat convection in a liquid with negligible viscous dissipation. (2) The total current field is normal to the planar velocity field. Consequently, Bz must be uniform. There is a space-charge density proportional to the product of Bz and vorticity. If the B field is both static and coplanar with the velocity field, then the electric field must be uniform parallel to the normal direction, and has only a higher-order influence on the velocity field, if the magnetic Reynolds number is small.
Close Collisions in a Plasma
Authors: Baldwin David E.
Published: December 2004

A two-body distribution function in a plasma is developed for use in a kinetic equation for the one-body distribution function. The kinetic equation is obtained for a uniform plasma for circumstances in which the time dependence of higher-order distribution functions can be assumed to occur within a functional dependence on the one-particle distribution function. The resulting interaction term is new, in the sense that it contains no divergent integrals, and is considered accurate to first order in (e2/KTλD). The interaction term is composed of two parts. The first is a Boltzmann collision integral with a Debye-shielded interaction. The second term is due to the deviation of the shielding cloud from a Debye shield and is of the Fokker-Planck form, the coefficients of which are finite and well behaved. Because of its form, with a convergent collision integral and convergent Fokker-Planck coefficients, the solution may be considered a joining of the previous solutions to the problem.
Moment Equations and Boundary Conditions for Magneto-Gas Dynamics
Authors: Yang H. T.
Published: December 2004

Based on the work of Burgers and particularly of Kolodner, moment equations are obtained from the Boltzmann equation for a conducting gas in electric and magnetic fields. Relatively simple stress and heat-flux equations yielding one-fluid description of a slightly ionized gas mixture have been obtained. The associated boundary conditions are obtained by applying conservation laws near the wall. These moment equations and boundary conditions together with Maxwell's electromagnetic equations and their boundary conditions form a determinate system to describe the dynamics of a rarefied conducting gas in electric and magnetic fields. This system includes, as limiting cases, both the Grad thirteen-moment equations for rarefied gases and the usual continuum magneto-gas-dynamic equations.
On Thin-Film Heat-Transfer Measurements in Shock Tubes and Shock Tunnels
Authors: Hartunian R. A. , Varwig R. L.
Published: December 2004

In the measurement of aerodynamic heat transfer in shock tubes and tunnels utilizing thin-film resistance thermometers, it is assumed that the thermal properties of the gauge (film and substrate) are constant. Since surface temperatures of bodies in hypersonic flow often reach temperatures of several hundred degrees, the validity of this assumption should be tested. A technique is described for measuring the temperature dependence of the product of the density, thermal conductivity, and heat capacity of various substrates for thin-film resistance thermometers. The results for Pyrex, quartz, and plate glass, which have been used as backing materials for thin-film resistance thermometers, indicate that sizable errors may be encountered in inferring heat-transfer rates from measured surface-temperature histories if the thermal properties are assumed constant. The corrections which must be applied to account for the temperature dependence of the thermal conductivity and the specific heat have been established through an approximate theoretical solution of the nonlinear one-dimensional heat-conduction equation. The magnitude of the correction depends on the material of the substrate and the surface temperature. For Pyrex at 150°C it is about 45% and for fused quartz and glass about 15%.