bluuebunny/crossref_metadata_2025 huggingface dataset:
High-Frequency Flutelike Instabilities in Multicomponent Plasmas
Authors: Guest G. E. , Farr W. M. , Dory R. A.
Published: February 2004

Plasma in a magnetic field B is subject to unstable electrostatic gyroharmonic waves propagating across B, if the distribution of f0 of particle velocities v⊥(⊥ to B) has a region where ∂f0/∂v⊥ > 0. Stability limits are found for f0 representative of mirror-confined plasmas having a “warm” Maxwellian species, an otherwise identical “hot” species with a region of positive ∂f0/∂v⊥, and a neutralizing background. The waves are stable if the ratio of mean energies of the warm to hot species exceeds 0.1, or if the ratio of densities does not fall in an unstable interval roughly characterized by 0.01 ≲ NW/NH ≲ 1, with more precise criteria given by Eqs. (5) and (6). It is important for fusion experiments that the conditions necessary for stability are less restrictive than the sufficient condition: ∂f0/∂v⊥ < 0 for all the species.
Ion Distribution Functions in Collisionless Surface Ionized Plasmas
Authors: Buzzi J. M. , Doucet H. J. , Gresillon D.
Published: February 2004

For a low-density surface-ionized plasma (e.g., in a Q machine) where Coulomb or binary collisions are negligible, a simple steady-state model of the plasma is obtained through the Vlasov and Poisson equations. Among the main predictions of this model, the electron-rich regime involves a truncated Maxwellian distribution function for the ion velocities parallel to the magnetic field. Experiments have been carried out in a short single ended Q machine for a cesium plasma. Curves of density versus neutral flux are plotted. With the help of a heated probe and an electrostatic analyzer, whose work functions are carefully taken into account, the ion distribution functions are deduced. In our observations they correspond to beams of 1 km/sec to 1.5 km/sec mean velocity and velocity spread which can be characterized by a parallel temperature of 150-300° K. These experiments and the theoretical model are in good agreement.
Circulation-Preserving Flow of an Inviscid Prim Gas
Authors: Passman S. L.
Published: February 2004

It is shown that, in the circulation-preserving flow of an inviscid Prim gas, the entropy depends on the pressure and time only. In the special case where the entropy is steady and there is no heat flux, the pressure is constant along each particle path.
Density Field near a Wedge in Rarefied Flow
Authors: Hickman R. S.
Published: February 2004

The density field near a 10° wedge in a Mach 9.4 rarefied flow of nitrogen and a flow field picture obtained with the electron beam fluorescence technique are presented. The geometrical resolution is less than the hard sphere mean free path.
Propagation of Ion Waves in a Radio Frequency Electric Field
Authors: Takamura S. , Aihara S. , Takayama K.
Published: February 2004

The wavelength of an ion wave decreases in an rf electric field. This phenomenon is explained by the additional pressure which is produced by the spatial modulation of the rf field by the ion wave.
Downstream State of Collisionless Shock Waves
Authors: Goldberg P. , Schindler K.
Published: February 2004

The downstream state of collisionless shock waves may not, in general, be determined independently of the shock structure and of the dissipation mechanism. Several attempts to determine this state are discussed and shown to be either incorrect or unconvincing.
Linear Instability of Asymmetric Flow in Channels
Authors: Fu T. S. , Joseph D. D.
Published: February 2004

A study of the linear stability of asymmetric channel flows is presented. Three one-parameter families of basic velocity which possess, respectively, no, one, and two inflection points are treated. The competing effects of stabilizing asymmetry and destabilizing vorticity distributions are discussed. An inviscid wave speed theorem which extends a result of Stuart to flows with two inflection points is proved.
Eigenvalues for the Blast Wave
Authors: Stewartson K. , Thompson B. W.
Published: February 2004

Asymptotic expansions can be formed for hypersonic flows past blunt bodies using the blast wave as a leading approximation. Theoretical studies of such expansions have revealed that they are not valid on streamlines which pass close to the body at any stage, but become valid in the neighborhood of the shock wave at large distances downstream of the nose. In order to describe the whole flow field at such distances, an expansion appropriate to the neighborhood of the body is necessary, and when a matching is attempted between the two expansions, irreconcilable logarithmic terms arise unless a certain infinite set of integrals related to entropy all vanish. However, if all these integrals vanish, then the outer expansions of the forms so far proposed are quite independent of any conditions occurring in the inner layer near the nose. In a previous paper the authors advanced the alternative hypothesis that there might exist sets of undiscovered eigenfunctions associated with the blast wave expansion through which the initial conditions near the nose could affect the ultimate flow far downstream. For convenience the problem is studied here in its unsteady analog, and it is shown that there exist two infinite sets of eigenvalues, one real, the other complex. The smallest eigenvalues are computed in the limiting cases γ → 1 + 0 and γ → ∞, and also for an ideal monatomic gas with γ = 53
Nonsteady Flows of Fluids with Microstructure
Authors: Kline Kenneth A. , Allen Stuart J.
Published: February 2004

The theory of nonsteady flows of fluids with microstructure is summarized. For parallel flows a decomposition of velocity and microstructure spin fields is given and used to reduce the governing equations to two uncoupled parabolic partial differential equations. These equations are solved for the suddenly accelerated plane wall problem. The effects of fluid microstructure on the velocity field, boundary-layer thickness, and resultant shear stress are examined.
Generalization of Hydrodynamics to Include Single Particle Modes and Fluctuations
Authors: Clarke Bruce L. , Rice Stuart A.
Published: February 2004

Two exact hierarchies of hydrodynamic equations which follow from Newton's equations for systems of identical particles interacting with a spherically symmetric potential are presented. The first hierarchy, essentially given by Born and Green in 1947, is shown to be capable of predicting hydrodynamic fluctuations and therefore has important applications near the critical point. Explicit microscopic forms of the higher level stress tensors and heat fluxes are given. Detailed macroscopic approximations for these quantities are obtained using the isotropic symmetry of the fluid, reduction conditions which relate these quantities to the ordinary stress tensor and heat flux, and the known equilibrium limit of the hierarchy (the Yvon-Born-Green equation). The second hierarchy is a generalization of Born and Green's hierarchy to include time correlations. At equilibrium it yields an equation for the Van Hove correlation function, G(R, t), which contains both single-particle and collective modes and is the analog of the Yvon-Born-Green equation. From it and the self-part of the Van Hove correlation function, Gs(R, t), the distinct part of the Van Hove correlation function, Gd(R, t), may be obtained by numerical integration.
Supersonic Leading Edge Problem according to the Ellipsoidal Model
Authors: Huang A. B. , Hwang P. F.
Published: February 2004

The supersonic leading edge problem is solved by the molecular approach of kinetic theory using the nonlinear Boltzmann equation with the ellipsoidal model as the governing relation and using the discrete ordinate method as a tool. The local molecular distribution functions for the entire flow field have been calculated, and thus the complete flow field including properties on the plate surface has been generated for the case of M∞ = 1.5 and for various plate temperatures. The calculated results offer considerable insight into the behavior of a rarefied gas flow as it traverses the complete spectrum of flow regimes from near free molecular to continuum. Since the present solutions are based on the ellipsoidal model which yields the correct Prandtl number for a monatomic gas (Pr = 23) and is more realistic than the Bhatnagar-Gross-Krook model (Pr = 1), the calculated results can be used for direct comparison with the existing experimental data. Comparisons between these results and those of the BGK model indicate that the ellipsoidal model gives a thicker boundary layer and slightly stronger shock profiles than the BGK model does.
Finite Source-Reynolds-Number Effects on Temperature Freezing in a Spherically Symmetric Expansion
Authors: Chen Tsu-Yee
Published: February 2004

The finite source-Reynolds-number effects in a spherically symmetric expansion of a monatomic gas are analyzed by asymptotic expansions for high terminal Mach number M∞. The problem is formulated for the Maxwell particles and for the Bhatnagar-Gross-Krook model. Contrary to anticipation from earlier studies, closure of the moment system under the hypersonic condition is found to occur only for even-order moments of the kinetic equation, leading to a development in integral powers of 1/M∞2, or 1/Re*4/3. With the help of an equivalence of the 20th-moment approximation, the third-order moment system may, however, be closed. For this system, matching of asymptotic solutions of the transition and the near equilibrium regions determines heat fluxes and explicit corrections for the density, flow speed, and temperatures. Most corrections, including that for the Mach number, appear to be numerically significant; differences between the BGK model and the Maxwellian gas are limited for temperatures, but large for heat fluxes. Aside from the frozen temperature, the heat flux (per solid angle) also freezes out at far downstream.
Effects of Nonelastic Collisions in Partially Ionized Gases II. Numerical Solution and Results
Authors: Shaw J. F. , Mitchner M. , Kruger C. H.
Published: February 2004

A numerical method of obtaining a self-consistent solution of the coupled free electron Boltzmann equation and the rate equations for the populations of the excited levels of a monatomic gas is described, taking into account both nonelastic collisions and radiation losses. An iterative numerical scheme is used to obtain self-consistent electron distribution functions, excited atom level populations, and ionization rates in a monatomic partially ionized gas. A special numerical filtering technique is used to obtain the distribution function. Results for hydrogen plasmas are presented and discussed. It is shown that photon escape and nonelastic collisions cause a depression in the distribution function tail, in the steady-state electron number density, and in the collisional-radiative ionization rate. Large radiation escape factors and low electron number densities lead to large depressions relative to equilibrium values. Results based on the analytical solutions of paper I are compared with the numerical results and found to be in good agreement.
Unsteady Magnetohydrodynamic Flow in a Circular Pipe under a Transverse Magnetic Field
Authors: Gupta S. C. , Singh Bani
Published: February 2004

An exact solution for unsteady magnetohydrodynamic flow in a circular pipe (with a uniform magnetic field parallel to a diameter of the cross section) with insulating walls has been obtained. For comparison, graphs have been plotted for the magnetic field in the magnetohydrodynamic case and for velocity in the hydrodynamic and magnetohydrodynamic cases at different times.
Shock Waves in Self-Similar Hydromagnetic Shear Flow: Analytic Solutions in a Plane Geometry
Authors: Henriksen R. N.
Published: February 2004

A self-similar form for a one-dimensional magnetogasdynamic shear flow is presented. Discontinuities are found to arise naturally in the course of the self-similar flow and their properties are discussed. It is suggested that the flow adjusts to two-point boundary conditions by a shock transition in cases of practical importance. An analytic solution is given for an initially isothermal medium in the absence of an external force. The solution is valid in different regions of the x-t plane depending on the value of the velocity at x = 0 relative to the Alfvén speed, and on the value of the Alfvén speed relative to the sound speed. It is shown how the solutions may be joined together, either continuously or across shocks, to provide a solution that is valid in the whole x-t plane. The effect of requiring two-point boundary conditions is made explicit in these examples.
Stability of Gas-Liquid System in a Magnetic Field
Authors: Buti B. , Kalra G. L. , Kathuria S. N.
Published: February 2004

The interfacial stability of a compressible gas flowing past an incompressible, viscous liquid layer is investigated in the presence of a uniform magnetic field and uniform rotation transverse to the field, both the field and the rotation being in the plane of the interface. When the magnetic field is along the direction of the streaming of the gas, there exists a critical magnetic field Hc in the subsonic case such that for H > Hc, the system is stable; in the supersonic case, however, Hc does not occur. The rotation in the previous case tends to stabilize the system whereas in the latter case it has a destabilizing effect. If the magnetic field is transverse to the streaming velocity, then for supersonic flows the system is always stable provided gravity is acting from gas toward liquid. For subsonic flows, there appears to be a critical rotation Ωc such that only for Ω > Ωc is the system stable. However Ωc decreases with the magnetic field which once more acts as a stabilizer.
Comparison of Measured and Predicted Conditions behind a Reflected Shock
Authors: Bengtson Roger D. , Miller Myron H. , Koopman David W. , Wilkerson T. D.
Published: February 2004

Measured thermodynamic conditions behind reflected shocks in a gas-driven diaphragm shock tube are compared to Rankine-Hugoniot predictions. Pressures of the shock-heated neon, which contained small concentrations of spectroscopic additives, were measured by quartz transducers. Temperatures (9000-13 000°K) were simultaneously measured spectroscopically by line reversal and absolute emission techniques, while electron densities were measured by the broadening of the Balmer line Hβ. The temperature has been measured to an accuracy of ±1.5%, while electron densities have been determined with an accuracy of ±10%. Pressure measurements attained accuracies of ±5%. The consistency of the data indicates that a homogeneous local thermodynamic equilibrium model is an adequate description of the shock-heated gas. The state measurements, compared with the real gas Rankine-Hugoniot predictions, show significant departures. Predicted temperatures are typically 3% ± 10% higher than those measured. The predicted electron density is as much as ±30% in error, and the predicted pressures are systematically lower than those measured by approximately 7% ± 15%.
Influence of Plasma Frequency on the Light Emitted by an Exploding Ionized Gaseous Filament
Authors: Skowronek M. , Rous J. , Goldstein A. , Cabannes F.
Published: February 2004

A very dense and easily reproducible plasma was generated by the explosion of a thin preionized gaseous column. The optical thickness of the discharge was measured by means of a laser and the absorption coefficient was found to be higher than 18 cm−1. The spectral brightness of the discharge is measured from wavelengths 0.2μ to 4.8μ. The instantaneous spectral distribution shows an abrupt drop in the near infrared at 1μ. This is interpreted as being due to the plasma frequency with a corresponding electron density of (1 ± 0.2) × 1021 cm−3. The complex index and the emissivity of the plasma are calculated and give a spectral repartition in good agreement with the measured one. Between 0.5 μsec and 1 μsec after the breakdown, the discharge column radiates as a blackbody at 44 000°K over a large spectral region. The free-free transitions, mainly in the infrared, can explain the radiation observed. The light is found to originate from a shell 2 × 10−3 cm thick, in agreement with the structure found for such sparks.
Hydrodynamic Behavior of Solid Deuterium under Laser Heating
Authors: Fauquignon C. , Floux F.
Published: February 2004

A theoretical interpretation is suggested in order to explain the inward propagation of luminous fronts when a powerful laser beam is focused on solid deuterium ice. This model is based on the propagation of a shock wave followed by a laser flux driven deflagration. Calculations have been made and compared with experimental results.
Mechanism for the Breakdown of Adiabatic Invariance
Authors: Lichtenberg A. J. , Jaeger F.
Published: February 2004

Computation of particle orbits in systems with more than one degree of freedom shows that adiabatic invariance is destroyed due to a resonance between the oscillation periods associated with two degrees of freedom. These resonances can be predicted qualitatively from first-order perturbation theory, which also indicates that the breakdown is related to the precentage change in the invariant during one period of the motion.
Electromagnetic Backscattering from a Random Plasma Slab
Authors: Hochstim A. R. , Martens C. P.
Published: February 2004

The computer method developed by the authors for calculating the electromagnetic scattering from a random, plane parallel plasma slab is applied to the near-overdense and overdense regimes. The mean reflection coefficient and incoherent reflected power are calculated for an ensemble of random plasma slabs. The results are compared with the analytic solutions using a perturbation expansion of the wave equation to the second order in electric field. Choosing the correlation length of the random amplitudes fluctuation to be equal to that of the random telegraph signal fluctuation results in identical two-point correlation functions for each, but different higher-order correlations. Hence, the computed differences in the scattering calculated for the plasma slabs having the two types of fluctuations are due to the higher-order correlations.
Radio Waves in Turbulent Magnetoplasmas. II
Authors: Taylor Leonard S.
Published: February 2004

Previous results for the effective index of refraction of a plasma with stochastic variation of density are extended to long wavelengths. It is found that the Born approximation has a more stringent range limitation than has previously been applied and that the scattering cross section is larger.
Electromagnetic Instability in an Electron Cyclotron Resonance Plasma
Authors: Gitomer S. J. , Shohet J. L.
Published: February 2004

An electron cyclotron resonance plasma was produced in a magnetic mirror field. Measurements of electron density, electron temperature, stored energy density, electron energy distribution, plasma light variations, and particle fluxes were made. An instability characterized by microwave emission below the electron cyclotron frequency, bursts of high-energy x-rays, particle losses along the magnetic axis, and variations in stored energy density was observed. The dispersion relation for transverse electromagnetic waves propagating in a plasma with an anisotropic Maxwellian electron velocity distribution with loss cones was solved numerically using parameters characteristic of this experiment and was found to yield instability frequencies and growth rates which agreed well with those observed.
Role of Landau Damping in Crossed-Field Electron Beams and Inviscid Shear Flow
Authors: Briggs R. J. , Daugherty J. D. , Levy R. H.
Published: February 2004

Under certain circumstances the problem of the stability of low-density crossed-field electron beams is precisely analogous to the problem of the stability of incompressible inviscid shear flows. The electron density, the drift velocity, and the potential correspond to the fluid vorticity, velocity, and the stream function, respectively. Neutrally stable normal modes of oscillation that are found when certain suitable step-function unperturbed electron density (vorticity) profiles are assumed seem to disappear when small gradients are present. In the context of a Laplace transform solution of the initial value problem, the vanishing normal modes can be found by analytic continuation of the solution onto another sheet of the cut complex ω plane. The “recovered” modes are found to be damped by a fluid-wave resonant interaction which closely resembles the Landau damping of plasma oscillations in warm plasmas by particle-wave resonance. An interesting feature of the neutral waves is that they have a negative energy and so are destabilized by the removal of energy from the system (for example, by slightly dissipative walls). The sign and magnitude of the Landau damping term is evaluated for a simple case and compared (for the electronic case) with the growth provoked by slightly lossy walls.
Alfvén Wave Damping from Finite Gyroradius Coupling to the Ion Acoustic Mode
Authors: Stéfant Robert J.
Published: February 2004

The collisionless damping of shear Alfvén waves in the limit of low frequency and small but finite Larmor radius is discussed. Because the averaging of the wave electric field over the Larmor circle (the so-called finite cyclotron radius effect) creates a small difference in the transverse velocities of the ions and electrons, a longitudinal electric field appears in the Alfvén wave which is responsible for the transfer of the wave energy into the thermal motion of the “resonant” particles Vz = ω/kz. Numerical solutions (in the complex ω plane) of the dispersion relation for two wave modes have been obtained: the shear Alfvén mode and the least damped Fried and Gould ion acoustic mode. The normalized damping rate (Im ω)/(Re ω) has been computed for both waves, and it is shown that the damping factor for the Alfvén wave is maximal when the Alfvén velocity is equal to the real part of the phase velocity of the ion acoustic wave. Moreover, there exists a particular direction of propagation with respect to the magnetic field for which both the Alfvén and the least damped ion acoustic waves have the same Landau damping. The damping factor for the ion acoustic wave is a minimum for this particular mode and it is shown that at low values of the electron-to-ion temperature ratio Te/Ti (Te/Ti ≲ 2), the critical drift velocity necessary for instability occurs at a much lower velocity than is usually predicted.
Nonlinear Oscillations in a Collisionless Plasma
Authors: Bailey V. L. , Denavit J.
Published: February 2004

An approximate solution for electron trajectories in a space sinusoidal electric field with a slowly changing amplitude is constructed by varying the modulus of the Jacobi elliptic functions representing electron trajectories in a constant amplitude field. This solution is used, together with energy conservation, to obtain the time behavior of the amplitude of nonlinear longitudinal oscillations in a collisionless plasma. The resulting integrodifferential equation for the amplitude depends on the ratio γ/α0, where γ is the Landau damping constant, and α0 is the initial value of the frequency of oscillations of trapped electrons in the potential trough of the wave. Numerical solutions are carried out for several values of this ratio. For γ/α0 → 0 (constant amplitude limit) O'Neil's results are recovered. For small but finite values of the ratio γ/α0, the present method shows the effect of the energy exchange between resonant electrons and the decaying electric field. The time of regrowth and the corresponding minimum amplitude are evaluated and compared with the results of O'Neil.
Nonlinear Wave Stability with Collisionless Shock Application
Authors: Spero Donald M. , Sen Amiya K.
Published: February 2004

A detailed study of the stability of nonlinear waves in a collisionless plasma has been made. In addition to the ordinary two-stream instability, it has been found that another mode, the cross-stream instability, also plays an important role. The heating of electrons by two-stream instabilities can preclude the existence of nonlinear waves. The cross-stream instability is partly hydromagnetic; it may severely affect the ions and can cause macroscopic breakup of the nonlinear wave. For strong magnetic fields and low temperatures, it is found that the cross-stream instability does not destroy sufficiently weak nonlinear waves. The results are used to construct a collisionless shock wave.
Representation of Fields in a Relativistic Plasma by a Surface Integral
Authors: Weston Vaughan H.
Published: February 2004

The collective motion of electrons in a relativistic isotropic plasma which is described by the linearized Maxwell-Boltzmann equations is treated with time harmonic dependence. It is shown that the electric intensity at any point in an enclosed volume, can be determined when the tangential components of the electric and magnetic field are prescribed along with the electronic distribution function, on the surface enclosing the volume.
Collisional Diffusion in an Axisymmetric Torus
Authors: Rutherford P. H.
Published: February 2004

Collisional cross-field diffusion of plasma in a general axisymmetric torus is calculated using the Fokker-Planck collision term, and a variational principle is found for the diffusion coefficient. Anomalously large transport, as found by Galeev and Sagdeev, occurs where the effective collision frequency is of order or less than the “bounce” frequency of trapped particles. Only unlike-particle collisions contribute, and the ion and electron diffusion coefficients are equal and independent of any radial electric field; these conclusions differ somewhat from those of Galeev and Sagdeev.
Collisional Diffusion in Nonaxisymmetric Toroidal Systems
Authors: Frieman E. A.
Published: February 2004

Collisional cross field diffusion in nonaxisymmetric toruses with high shear has been found, but a region of minimum diffusion is shown to exist which might provide an attractive operating regime for future reactor considerations. The properties of this regime have been calculated and are discussed.
Toroidal Hydromagnetic Equilibrium Solutions with Spherical Boundaries
Authors: Morikawa G. K. , Rebhan E.
Published: February 2004

A family of toroidal hydromagnetic equilibrium solutions with spherical boundaries surrounded by a vacuum field is found. Physically relevant singular solutions are included. All solutions are exact with a smooth pressure profile which goes to zero at the plasma-vacuum interface.
Evolution and Stabilization of Flutes in a Magnetic Mirror
Authors: Colchin R. J. , Dunlap J. L. , Postma H.
Published: February 2004

This paper deals with flutes as observed in a hot-ion, low-β plasma. This plasma was established in an adiabatic, simple mirror trap by Lorentz or gas-collisional ionization of an energetic H0 beam. The studies emphasize: (1) the detailed evolution of the flute mode and comparisons with linear theory and (2) the stabilizing effects of increased electrical connection of the plasma to conducting end walls (line tying). The evolution is traced as a function of density from a stable drift wave at low density to threshold for a growing, unstable wave which quickly exhibited nonlinear frequency behavior. Evolution of the stable drift wave is much as predicted by the linear theories. Instability threshold seems to occur at a somewhat higher density than that calculated even from theories treating bounded plasmas. The line-tying experiments used movable end walls as a control on the electrical connection. Threshold was raised with end walls close to the hot plasma, in a fashion that is in qualitative agreement with a recent calculation. Two possible explanations of the nonlinear frequency behavior of the unstable wave are proposed.
Direct Measurement of Drift Wave Growth Rates
Authors: Rogers Kenneth C. , Chen Francis F.
Published: February 2004

Resistive drift waves in a Q machine can be switched on and off by applying a potential to the aperture limiter. The exponential growth of the waves can be directly observed. The measured growth rates are slower than are predicted by the usual theories of collisional drift waves.
Effects of Plasma Flow on Electrostatic Disturbances in a Q Machine
Authors: Korn P. , Marshall T. C. , Schlesinger S. P.
Published: February 2004

The evolution of a large discontinuity in density in a single-ended Q machine has been found to be adequately described by a free-streaming model of the ions modified by a density gradient electric field due to a finite electron temperature. As the electron temperature is increased through microwave heating at cyclotron resonance, the profile of the discontinuity is found to broaden spatially as predicted by the theoretical model. The plasma ion drift velocity along the magnetic field can be measured from the motion of the discontinuity and is found to be in close agreement with the drift velocity measured from the propagation of small-amplitude ion-acoustic waves. An estimate of the ion thermal velocity parallel to the magnetic field can also be obtained from the broadening of th discontinuity profile. The ion drift velocity exhibits systematic variation with changes in oven and ionizer temperatures which is attributable to the electron-ion balance in the region surrounding the hot ionizer.
Rigid Drift Model of High-Temperature Plasma Containment
Authors: Morse R. L. , Freidberg J. P.
Published: February 2004

A model is proposed which appears to be consistent with certain recent high-temperature plasma heating and confinement experiments, whose behavior is not adequately described by magnetohydrodynamics.
Triple- and Quintuple-Dimpled Wave Profiles in Deep Water
Authors: Nayfeh Ali Hasan
Published: February 2004

The method of multiple scales is used to obtain a third-order expansion for the interaction of gravity and capillary waves. The expansion is found to break down for wavelengths of 2.44 and 2.99 cm in deep water, in agreement with Wilton. A second expansion valid for wavelengths near the latter critical wavelength is obtained. The latter expansion shows that three different wave profiles could exist at wavelengths near 2.99 cm. One is a gravity-like profile (wave velocity increases with increasing amplitude) having triple dimples. The other two are capillary-like profiles (wave velocity decreases with increasing amplitude) having quintuple dimples.
Free-Streamline Theory for Inviscid Stratified Flow into a Line Sink
Authors: Kao Timothy W.
Published: February 2004

A free-streamline theory is given for the steady flow of an inviscid, stratified fluid into a line sink, with the fluid stagnant above the dividing streamline. It is shown that an infinite number of such solutions exist for 0.33 ≤ F1 ≤ ∞. A constructive procedure is used to obtain the solutions. Error estimates are given through suitable perturbation schemes. An answer to the question of uniqueness is presented with F1 = 0.33 given as the unique Froude number for all separated flows.
Stability of a Relaxation-Type Viscoelastic Fluid with Slight Elasticity
Authors: Tlapa G. , Bernstein B.
Published: February 2004

A viscoelastic fluid of a relaxation type having a single relaxation time is studied. The effect of slight elasticity on the hydrodynamic stability of a plane Poiseuille flow is investigated by the linearized method of small two-dimensional disturbances since it is shown that Squires' theorem is valid for the fluid chosen. The resulting equation is a modified Orr-Sommerfeld equation. The equations are solved numerically, and it is shown that the critical Reynolds number is lowered as the magnitude of the relaxation number is increased.
Instability in Fully Developed Turbulence
Authors: Kraichnan Robert H.
Published: February 2004

The direct-interaction approximation is used to examine the growth and propagation of the energy spectrum of the point-to-point velocity difference between two isotropic turbulent flows which are statistically identical. If the two systems are driven by identical stirring forces, the question of whether an initial velocity-difference spectrum grows or decays is found to be similar to that of growth or decay of magnetic seed fields in a turbulent fluid. Numerical calculations appear to be necessary to decide whether deviations between the two systems at high wavenumbers are swept out, to be destroyed by viscosity, or propagate down to make the velocity field in the energy-containing range unpredictable in detail. The analysis is principally for three-dimensional turbulence, but the direct-interaction equations for the two-dimensional case are stated also.
Multi-Point, Multi-Time Velocity Correlations and Decay of Homogeneous Turbulence
Authors: Kumar Prem , Dash R.
Published: February 2004

Following Deissler's approach, the multi-point, multi-time correlations for the fluctuating velocity in homogeneous turbulence have been studied. To make the set of equations determinate, the terms containing quintuple correlations are neglected in comparison with those containing quadruple correlations. The solution so obtained gives the state of homogeneous turbulence between its initial and final periods. In the limiting case when Δt = Δt′ = Δt” = 0, the results of the present paper agree with those of Deissler for the correlations considered at four points and one time.
Constitutive Relations for Stress and Heat Flux in a Shock Wave
Authors: Baganoff D. , Nathenson M.
Published: February 2004

A form of Maxwell's moment method is used to obtain constitutive relations for stress and heat flux for a gas passing through a shock wave. The cx2 moment of the Boltzmann equation together with several physical approximations are used to obtain a nonlinear expression relating stress and deformation rate, with Mach number as a parameter. It is shown that the constitutive relations for both stress and heat flux reduce to the Navier-Stokes relations for the case M = 1 and |τ/p| ≪ 1, and differ from these relations by almost a factor of 2 for M = 1 and |τ/p| = 1. Theoretical density profiles for shock-wave Mach numbers between 2.8 and 8 are compared with experimental data for shock waves in argon, and the agreement is shown to be excellent, thus supporting the use of the proposed constitutive relations. The physical significance of the approximations used and areas for further improvement in the theory are discussed.
Measurements of Electrical and Thermal Conductivity of Hydrogen, Nitrogen, and Argon at High Temperatures
Authors: Morris J. C. , Rudis R. P. , Yos J. M.
Published: February 2004

The electrical and thermal conductivities of hydrogen, nitrogen, and argon have been measured up to 14 000°K for pressures between 0.5 and 2.0 atm using a wall-stabilized electric arc as a plasma source. Generally satisfactory agreement is noted between theory and experiment for the electrical conductivity. Equally good agreement is found for the thermal conductivity for nitrogen and argon when the energy transfer by vacuum ultraviolet radiation is included in the energy transport calculations. For hydrogen a difference between theory and experiment of as much as a factor of 2 is observed at the lower temperatures; this difference is dependent on arc current and may be the result of nonequilibrium effects.
Stabilization of the Rayleigh-Taylor Instability with Magnetic Feedback
Authors: Zrnić Dušan S. , Hendricks Charles D.
Published: February 2004

Stabilization of the Rayleigh-Taylor instability with magnetic feedback was studied. A thin rectangular container was developed in which only a one-dimensional instability occurred while the effects of weight were eliminated. Using long wave approximations, solutions for natural modes, with the free surface stuck at the lateral edges, were obtained. A two-station ac magnetic feedback system was built and successfully applied to stabilize the instability. The change in intensity of tangential magnetic fields controlled by the displacement of the fluid was used to exert pressure on the conducting liquid. A Ga-In alloy was used as the heavier fluid in contact with a dilute solution of HCl. The disturbances which influenced the intensity of the fields were optically detected by means of solar cells placed at the expected maxima. A modal analysis showed that feedback shifts the resonant frequencies to higher values and thus precludes the impending instability. Stabilization of the longest wavelength disturbance was successful while higher wavelengths for larger containers were not affected by two-station feedback. Theoretical investigation of the overstability showed that overstability would occur if the intervals over which the disturbance is integrated were smaller than half the width of the container.
Interaction of Hydromagnetic Waves with Hydromagnetic Shocks
Authors: McKenzie James F. , Westphal Karl O.
Published: February 2004

The problem of the interaction of small-amplitude plane hydromagnetic waves with plane, oblique hydromagnetic shocks is treated. When the perturbations of the flow field on either side of the shock are expanded in terms of incident and diverging eigenwaves, the linearized de Hoffmann-Teller relations across the shock yield a system of equations for the amplitudes of the diverging waves and the motion of the perturbed shock. The shock motion and the amplitudes of the diverging waves as a function of the amplitude and direction of any given incident wave are found using this system of seven linear, inhomogeneous equations, along with Snell's laws. Snell's laws are interpreted graphically by making use of the geometry of the hydromagnetic wave normal surfaces in a moving medium. By considering some special cases it is shown that hydromagnetic waves are amplified on passage through a fast shock. The turbulent character of the region between the bow shock of the earth and the magnetopause may be due in part to the amplification of turbulent waves in the solar wind on passing through the bow shock.
Laboratory Study of the Wakes of Small Cylinders under Ionospheric Satellite Conditions
Authors: Hester S. D. , Sonin Ain A.
Published: February 2004

The wakes of cylinders small compared with the Debye length have been studied in a collision-free plasma wind tunnel where the flow around ionospheric satellites can be simulated. No magnetic field was applied in these experiments. A small cylinder was found to excite in its path a disturbance consisting of a decaying oscillation on the centerline at the ion plasma frequency and a series of “waves” which originate at the centerline oscillation. The wake angle was dependent on the body potential and on the ratio of body radius to Debye length, and took on values well above and well below the Mach angle based on the ion wave speed. At large negative body potentials, the first “wave” emanating from the body was identified as a group of ions which had been deflected by the electric field of the cylinder.
Theory of the Plane Plasma Resonance Probe
Authors: Li Nelson C. , Gustafson W. A.
Published: February 2004

The response of a semi-infinite plasma adjacent to an infinite plane probe is established theoretically when a small-amplitude alternating potential is superposed on a dc potential. The dc potential distribution in the sheath is found by solving Poisson's equation making use of Bohm's sheath criterion. The linearized Boltzmann-Vlasov equation for electrons along with the appropriate Maxwell equations are used to formulate a linear integral equation for the perturbed electric field. The average dc electron current is computed which indicates a maximum value (resonance) that depends on the probe potential for frequencies less than the plasma frequency.
Measuring Method for Collision Frequency by a Radio-Frequency Probe
Authors: Uramoto Johshin
Published: February 2004

A method of determining the electron-neutral collision frequency in a low-density plasma is described. A radio-frequency signal of constant frequency and voltage is applied between plane probes while the plasma density is varied to determine an antiresonance point, i.e., a current minimum. Compared with the ordinary resonance probe method using the resonance peak half-width, the new method is insensitive to external circuit impedance and avoids the perturbing effect of the strong rf fields at resonance.
Collisional Drift Waves in the Linear Regime
Authors: Rowberg Richard E. , Wong Alfred Y.
Published: February 2004

A method of external excitation of density gradient drift waves in a stable, collision-dominated plasma is presented whereby the linear theory of drift waves is verified. The procedure permits limitation of the perturbation amplitude such that e∅1/kT < 0.1. This represents a new approach in the study of drift waves since nonlinear saturation effects present in all previous experiments on these waves are avoided. The driven oscillations are coherent, nearly sinusoidal modes on which measurements of ω and k as a function of the plasma parameters are made. In this manner the linear dispersion relation derived from the fluid equations is verified demonstrating the strong stabilizing effect of transverse diffusion resulting from ion viscosity. In connection with this an additional damping process resulting from ion loss at the cathodes is introduced whereby complete stabilization of the plasma to drift waves is possible. Next, the functional dependence of the phase angle between the density and potential perturbation is shown and correlation between the phase angle and the growth rate is discussed. Finally, verification of the dependence of the axial wavelength on the sheath conditions at the plasma cathode boundary and on the length of the plasma column is demonstrated.
Parametric Mode-Mode Coupling between Drift Waves in Plasmas
Authors: Hai Francis , Wong Alfred Y.
Published: February 2004

The nonlinear phenomenon of parametric excitation of stable resonant drift modes through mode-mode coupling is examined in the potassium plasma of a Q device. The scheme, which was extensively investigated, is the degenerate case of three-mode parametric coupling in which the stable resonant mode (m = 1) at ω1 is excited by the externally driven pump mode (m = 2) at ω0 = 2ω1. The usual frequency and wavenumber matching conditions are satisfied. The additional new aspects examined are the enhancement of thermal fluctuations, the threshold for excitation, and the power balance between the coupled modes and the external source. The main results obtained are the measurement of the coupling coefficient and the determination of the functional behavior of the modes. General agreement between the experimental results and theory derived from the expansion of the governing fluid equations to second order is attained. To describe the steady-state amplitudes observed experimentally, nonlinear saturation phenomena are included. Nondegenerate and higher-order coupling schemes are briefly considered. Parametric coupling as a mechanism limiting the amplitude of an unstable mode and leading to a turbulent plasma is presented and discussed. The modification of the linear stability of a lower mode due to mode coupling from a higher mode is illustrated.
Convection Arising from Large-Amplitude Plasma Waves
Authors: Chen Francis F. , Etievant C.
Published: February 2004

It is found that large-amplitude plasma waves can cause dc particle drifts which can have a deleterious effect on plasma confinement during rf heating. A standing wave in an inhomogeneous plasma is likely to cause convective cells with a periodicity equal to half the wavelength of the wave. As examples, ordinary and extraordinary electromagnetic waves and ion cyclotron waves are chosen for detailed treatment.
Ion Cyclotron Wave Generation in the Model C Stellarator
Authors: Hosea J. C. , Sinclair R. M.
Published: February 2004

To permit quantitative comparisons between experiment and theory, ion cyclotron wave generation by the Stix coil system of the Model C stellarator is analyzed using a coil-plasma model which closely approximates the physical system: filamentary currents at the coil loop positions induce plasma waves which propagate along the “cold” plasma column which is coaxial with a cylindrical waveguide. Most important in the analysis is the inclusion of finite electron inertia effects which cause the natural modes of the system to be characterized by two radial wavenumbers in place of one and which can seriously modify the properties of the ion cyclotron waves. Coil loading predictions are in good absolute agreement with experimental observations for wide ranges of plasma density and magnetic field, thus demonstrating the relevance of the cold theory to the laboratory plasma. However, magnetic field predictions are larger than the fields measured far from the Stix coil, suggesting wave attenuation by processes not contained in the theory.
Shear Stabilization of Drift Cyclotron Instabilities in Plasma
Authors: Davidson James N. , Kammash Terry
Published: February 2004

Shear stabilization of low-frequency drift modes in plasma has been studied intensively in recent years, but little if any work has been done regarding the effect of shear on the drift cyclotron instabilities. The linearized Vlasov equations are used to examine the stability of electrostatic oscillations with frequency near integral multiples of the ion cyclotron frequency, propagating in an infinite inhomogeneous collisionless plasma situated in a sheared magnetic field. A normal mode analysis is employed to investigate the stability of waves propagating nearly normal to the magnetic field, and it is found that shear has a destabilizing effect although it does not alter the over-all condition for marginal stability obtained in the uniform field case. A wave packet approach is then utilized to investigate the stability of these high-frequency oscillations when they propagate at an arbitrary angle to the field lines. For low-density plasma, it is shown that the drift cyclotron modes are stabilized by approximately the same shear required to stabilize the low-frequency modes, while at high densities, a more stringent but physically realizable shear is required for stabilization.
Stability of an Inhomogeneous Beam-Plasma System
Authors: Leavens William M. , Love C. H.
Published: February 2004

The stability of realistic, inhomogeneous, plasmas with sheaths is studied by examining the interaction between an electron beam and the discrete, longitudinal, normal modes of a stable, Maxwellian plasma. A weak beam just displaces the discrete plasma eigenfrequencies in a way depending on beam current and energy. For first four eigenfrequencies we calculate ω-plane maps. Instability is confined to a few intermediate modes, and growth rates are not large.
Nonlinear Landau Damping—The Spectrum
Authors: Eldridge Owen
Published: February 2004

The spatial damping of large-amplitude electrostatic waves in a collisionless plasma is derived. The theory leads to differential equations which describe the nonlinear oscillation of the electric field amplitude, the broadening of the frequency spectrum, and the growth of sidebands. When driven at a single frequency the sidebands are displaced by a frequency ±0.8Ω = ±0.8(eκE0/m)1/2, where e and m are the electron charge and mass, κ is the wavenumber, and E0 is the amplitude of the electric field. The sidebands oscillate in space with a periodicity L = (2π/0.8Ω)(dω/dκ). The upper sideband is suppressed by linear Landau damping for large amplitudes.
Electromagnetic Electron-Ion Streaming Instability
Authors: Ross David W.
Published: February 2004

Instabilities produced by a current across a magnetic field and propagating obliquely to the field are studied in connection with the description of hydromagnetic shock waves. It is shown that there exist unstable waves of mixed polarization which can be described as coupled ion beam and whistler modes with frequencies given by ω≈k·u where u is the streaming velocity of the ions relative to the electrons. These waves are investigated in the small electron Larmor radius approximation and in the frequency range Ωi ≪ ω ≪ Ωe where Ωi and Ωe are the cyclotron frequencies of the ions and electrons, respectively. The maximum growth rate is limited by γ < 123 (meu/2miυ¯e)1/3Ωe where υ¯e is the electron thermal velocity. The effect of collisions is considered, and the possibility of observing the instability in oblique shock wave experiments is discussed.