bluuebunny/crossref_metadata_2025 huggingface dataset:
Equilibrium and Stability of Large-Amplitude Magnetic Bernstein-Greene-Kruskal Waves
Authors: Berger Richard L. , Davidson Ronald C.
Published: February 2004

The stability of transverse magnetic Bernstein-Greene-Kruskal waves to small-amplitude perturbations is analyzed within the framework of the Vlasov-Maxwell equations. The Vlasov-Maxwell equations are linearized about an equilibrium state which supports (self-consistently) a spatially-periodic finite-amplitude transverse electromagnetic wave. An external magnetic field, B0 = B0êz, is included in the analysis, and spatial variations in equilibrium and perturbed quantities are taken to be in the z direction. A matrix dispersion relation is obtained that relates the (complex) oscillation frequency ω and wavenumber k of the perturbation; stability criteria are obtained for a monochromatic circularly polarized equilibrium wave. As an example, a trapped electron distribution is considered which is isotropic and monoenergetic in the plane perpendicular to the propagation direction of the equilibrium wave, and cold parallel to the propagation direction. The ions are assumed to form a cold neutralizing background. The system is found to be stable to transverse electromagnetic perturbations provided the equilibrium wave amplitude exceeds a certain threshold. The condition for stability is ω¯Be≳γκ where ω¯Be is the magnetic bounce frequency for trapped electrons, and γκ is the linear growth rate in the absence of the equilibrium wave. The results of the stability analysis are consistent with recent computer simulation experiments; for a broad class of transverse electromagnetic instabilities in anisotropic plasmas, these experiments (carried out both for B0=0 and B0≠0) show that the linearly unstable field amplitudes saturate once ω¯Be has increased to a value comparable to γκ.
On Anomalous Resistance due to Cross-Field Electron-Ion Streaming Instabilities
Authors: Forslund D. W. , Morse R. L. , Nielson C. W.
Published: February 2004

There are important features of the nonlinear development of the electron cyclotron drift instability which have not been considered by M. Lampe, W. M. Manheimer, J. B. McBride, and J. H. Orens [Phys. Fluids 15, 2356 (1972)]. In contrast with Lampe et al. it is maintained that in the nonlinear growth phase in a weak magnetic field, many properties of the waves are unlike those of the magnetic field free ion-acoustic instability and that coherent electron trapping explains the dependence of the nonlinear properties on magnetic field strength. On the other hand, it now appears that Lampe et al. agree that this instability leads to a large effective collision frequency associated with sustained electron heating and a high level of turbulence. Details of the areas of agreement and disagreement are given along with a more detailed discussion of the nonlinear electron behavior.
Theory and Simulation of Turbulent Heating by the Modified Two-Stream Instability
Authors: McBride John B. , Ott Edward , Boris Jay P. , Orens Joseph H.
Published: February 2004

Results of an analytical and numerical study of the nonresonant, modified plasma two-stream instability, which is driven by relative streaming of electrons and ions across a magnetic field B0 are presented. The instability has characteristic frequency and growth rate comparable to the lower-hybrid frequency. The linear theory is discussed both in the electrostatic and fully electromagnetic cases, and a detailed numerical study of the dependence of the unstable roots of the dispersion relation for a wide range of plasma parameters is presented. The nonlinear theory includes discussions of (1) quasilinear theory, (2) trapping, which is responsible for nonlinear stabilization, (3) a derivation of a fully nonlinear scaling law which shows how results scale with electron-ion mass ratio, and (4) the effect of cross-field vortex-like motion caused by turbulence induced E × B drifts. One-and two-dimensional computer simulations with dense k-space spectra are presented in support of this theory. The simulations show that the instability can be a very important turbulent heating mechanism that heats the ions (perpendicular to B0) and the electrons (parallel to B0) comparably. The final state has (Ti⊥/mi)1/2 ≈ (Te‖/mi)1/2∼12U, where U is the initial relative drift speed. Applications to experimental situations are discussed.
Spectroscopic Observations of Turbulence in a Fast Theta Pinch
Authors: Davis W. D.
Published: February 2004

The spectrum of fluctuating fields in a collisionless magnetized plasma produced in a high voltage theta pinch is studied using satellite line techniques. Differences in the turbulent spectrum exist depending on whether the initial magnetic field is parallel or antiparallel to the driving magnetic field with the possible identification of electron cyclotron modes in the antiparallel case and electron plasma oscillations in the parallel case. By including quadratic Stark shifts, difficulties in interpretation of an earlier satellite experiment are explained. Predictions of various instability theories are tested experimentally with the aid of additional diagnostic methods.
E
-Layer Compression by a Toroidal Magnetic Field
Authors: Rensink Marvin E.
Published: February 2004

The effect of an adiabatically increasing toroidal magnetic field (Bθ) on the E layer in astron is analyzed. Adiabatic invariants are calculated for particles in combined poloidal and toroidal magnetic fields. The current density increases with Bθ owing to reduction in the minor dimensions of the ring. To obtain significant compression the toroidal field at the ring must be larger than the poloidal guide field. Effects of the self-field of the ring and image currents in nearby conducting walls are included.
Theoretical Aspects of Astron Buildup by Multiple Pulses
Authors: Berk H. L. , Pearlstein L. D.
Published: February 2004

The time asymptotic response to an incoming current source in the presence of a partially built up E layer in the astron geometry is examined. A one-dimensional Vlasov model which considers only motion in the exial direction (perpendicular to the current direction and tank radius) is studied. It is shown that (1) A back current is induced in the E layer. (2) A new dissipation mechanism (Landau damping) occurs in the E layer as well as in the resistors. (3) The dissipation in the layer causes particle scattering that leads to axial expansion which competes with contraction due to the addition of current. The net effect for a neutralized layer can lead to a saturation in E layer strength, a behavior encountered in numerical experiment. For the unneutralized layer, however, this situation is not nearly as severe and there appears to be a parameter range where stacking should occur.
Magnetic Confinement Configuration for Plasmas Carrying High Currents
Authors: Coppi B. , Dagazian R. , Gajewski R.
Published: February 2004

A magnetic plasma confinement configuration aimed at sustaining high-current densities is proposed. It involves a small triangular and elliptic deformation imposed over a circular cross section of the plasma column by a surrounding conducting shell at close distance. The stability against kink modes is analyzed and shown to be the same as that of an equivalent plasma column with equal area, but circular cross section. An assessment of the over-all stability of this configuration points to a significant improvement, in terms of the Ohmic heating resulting from the induced current, over the known configurations with circular cross section.
Alternating Current Instability Produced by the Two-Stream Instability
Authors: Kainer S. , Dawson J. , Coffey T.
Published: February 2004

Theory and numerical experiments show that large amplitude plasma oscillations are unstable when the mobility of the ions is taken into account. This instability can lead to an anomalously rapid damping of the plasma oscillations. It is expected that large amplitude plasma oscillations produced by the electron two-stream instability would be subject to this instability and the associated damping. Numerical experiments have been performed which indicate that this is so and that there is good correspondence to theory.
Efficient Energy Transfer between Fast and Slow Electron Plasma Oscillations
Authors: Kruer William L.
Published: February 2004

Finite amplitude ion fluctuations are shown to efficiently and rapidly couple energy from very high phase velocity electron plasma oscillations into much slower ones and then into the particles, even when the mode coupling is off-resonant. The magnitude of the ion density fluctuation δn/n0 which gives efficient off-resonant coupling is typically the frequency mismatch between the plasma oscillations normalized to the electron plasma frequency. Such modest level ion fluctuations are often present in plasmas or can be selectively excited. This coupling mechanism is particularly important for allowing energetic beams to rapidly transfer energy to a dense background plasma. A simple calculation shows the principal features of the off-resonant mode coupling. The predictions are then confirmed by computer simulations.
Ion-Probe Current in a Magnetized Plasma
Authors: Sato Masumi
Published: February 2004

Current-voltage characteristics of Langmuir probes in a strong magnetic field are presented. The experiments were performed using argon or helium gases with pressure 0.1-5.6 mTorr and the plasma density ranging from 1011 to 1012 cm−3 for the field 1-5.5 kG. It is found that (1) for electron collection a cylindrical probe behaves like a disk; (2) the ion retardation part becomes unmasked over positive potentials as a result of decreased electron current; (3) the slope of its logarithmic plot gives the ion temperature; and (4) its values (nearly equal to the electron temperatures of 0.3-1.5 eV) derived from the slope seem to be the true temperatures. Errors and limiting conditions for the determination of ion temperatures are discussed.
Anisotropy of the Neutron Fluence from a Plasma Focus
Authors: Lee J. H. , Shomo L. P. , Kim K. H.
Published: February 2004

The fluence of neutrons from a plasma focus was measured by gamma spectrometry of an activated silver target. This method results in a significant increase in accuracy over the beta-counting method. Multiple detectors were used in order to measure the anisotropy of the fluence of neutrons. The fluence was found to be concentrated in a cone with a half-angle of 30 deg about the axis, and to drop off rapidly outside of this cone; the anisotropy was found to depend upon the total yield of neutrons. This dependence was strongest on the axis. Neither the axial concentration of the fluence of neutrons nor its dependence on the total yield of neutrons is explained by any of the currently proposed models. Some other explanations, including the possibility of an axially distributed source, are considered.
Visualization of Boundary Layer Flow Patterns around Proturberances Using an Optical-Surface Indicator Technique
Authors: Sedney Raymond
Published: February 2004

The shadowgraph or schlieren optical system is combined with the oil flow technique to obtain improved visualization of a turbulent boundary layer-shock-protuberance interaction. Simplicity and resolution are the main advantages. Two conjectured flow patterns are presented.
Infrared-Laser Heating of Dense Arc Plasmas
Authors: Jassby D. L.
Published: February 2004

Steady-state dense electric arcs can be heated by the inverse bremsstrahlung process to a temperature of 116 eV with 1 GW 10.6-μ radiation. Rapid thermal conduction limits the maximum temperature.
Improved Korteweg-deVries Equation for Ion-Acoustic Waves
Authors: Tappert Frederick
Published: February 2004

The Korteweg-deVries equation describing nonlinear ion-acoustic waves in a plasma with finite ion temperature is derived and the temperature dependences of soliton width and speed are obtained.
Intrinsic Bandwidth of Cyclotron Resonance in the Geomagnetic Field
Authors: Schulz Michael
Published: February 2004

Equatorial resonance between electrons and very-low-frequency signals is characterized by an intrinsic bandwidth ∼20 HZ at L=, owing to the inhomogeneity of B. The corresponding interaction time (∼50msec) approximates the length of a Morse dot.
Stochastic Character of Electron Cyclotron Heating in a Nonuniform Magnetic Field
Authors: Kawamura T. , Namba C. , Terashima Y.
Published: February 2004

The rf heating process of electrons in mirrors is thought to be stochastic owing to the nonadiabatic effect before the electron energies reach some critical values. To attain higher energies, other causes of phase radomization should be considered.
Centerline-Bernoulli Equation for Quasisteady Dilute Polymer Flow
Authors: Lumley J. L.
Published: February 2004

The pressure is obtained explicitly in the flow (beginning from uniformity) of a dilute polymer solution on the centerline of an axisymmetric contraction. Use is made of an asymptotic representation (derived elsewhere) for quasisteady behavior of a simple molecular model.
Stability of Parallel Flows of Second-Order Liquids
Authors: Mook Dean T.
Published: February 2004

The Orr-Sommerfeld equation, modified to include viscoelastic terms, is solved using a finite-difference method. Combined Couette-Poiseuille flow and flat-plate boundary-layer flow are considered, and it is shown that, for second-order liquids, the influence of the viscoelasticity is always stabilizing. The present numerical scheme, which is based on central differences, does not involve a filtering or a suppressing process and, consequently, is thought to be an improvement over the previously used methods, all of which are based on forward differences.
Light Scattering by Fluid Mixtures Using Stochastic Equations
Authors: Foch J.
Published: February 2004

Stochastic hydrodynamic equations are used to calculate the spectral composition of light scattered by a binary fluid mixture. The results, two superposed central lines and the Brillouin doublet, are in agreement with the results of Mountain and Deutch. The structure of the central line is examined in detail.
Dynamics of Bilaterally Symmetric Vortex Rings
Authors: Viets Hermann , Sforza Pasquale M.
Published: February 2004

The motion of vortex rings with bilaterally symmetric initial shape is investigated theoretically and experimentally. The induced velocity at each point on the vortex ring is computed from the Biot-Savart law. The induced velocity is related to the motion of the ring according to two different concepts: (1) Hydrodynamic vortex—the ring moves with the same velocity as the local fluid; (2) Rankine vortex—the local relative velocity produces lift and drag forces on the ring which serve to distort the ring. Observable vortex rings are produced by pulsing dyed fluid through a rectangular orifice and by staining the starting vortex behind ring wings of various shapes. Good qualitative agreement between the analyses and experiments is achieved.
Time-Dependent Wiener-Hermite Base for Turbulence
Authors: Clever W. C. , Meecham W. C.
Published: February 2004

A Wiener-Hermite expansion with a time-dependent base for turbulence is tested on Burgers' equation. It is shown that the time-dependent base system improves the rate of series convergence and some useful results can be obtained. The moving-base system, developed by Bodner, allows the equipartition solution to be satisfied exactly with a two-term expansion, and is a modification of Bodner's moving base system for real fluid turbulence.
Propagation of a Rapid Pulse Through a Relaxing Gas
Authors: Parker D. F.
Published: February 2004

The distortion, damping, and dispersion of a large amplitude pressure pulse of arbitrary initial profile, and advancing into a uniform region of relaxing gas in an equilibrium state, is described. Within the pulse an iterative solution based on an asymptotic modulated simple wave procedure is constructed. A relaxation tail is predicted, where a matched small amplitude iterative procedure is developed.
Fluid Motions Induced by an Electric Current Jet
Authors: Sozou C.
Published: February 2004

The flow field induced in an incompressible viscous conducting fluid, occupying the whole space on one side of an infinite plane, by an electric current jet through a circular aperture of the plane, is considered. It is assumed that the velocity field is small and its effect on the electromagnetic field is negligible. It is shown, as in the case of a fluid jet, that the exact solution for the case when the aperture is of infinitesimal dimensions, is the first term of a series expansion of the solution for the case when the aperture has finite dimensions. The first three terms of this series for various values of the parameters occurring in the equations are computed and the solutions are discussed.
Instabilities and Induced Scattering Due to Nonlinear Landau Damping of Longitudinal Plasma Waves in a Magnetic Field
Authors: Porkolab M. , Chang R. P. H.
Published: February 2004

The matrix elements for nonlinear wave-particle scattering (nonlinear Landau damping) are obtained in explicit form for electrostatic waves from the Vlasov-Maxwell equations. The waves are allowed to propagate at arbitrary angles to the magnetic field, and no restrictions are imposed upon the Larmor radius or the frequencies. In the case k⊥≫k‖, the symmetry relations for mode-mode coupling are demonstrated by appropriate manipulations of the matrix elements. This allows one to cast the nonlinear Landau damping coefficients in a particularly simple form. The conditions for explosive instabilities are obtained, and a possible stabilization mechanism for these instabilities is pointed out. In the limit of either perpendicular or parallel propagation to the magnetic field, a comparison is made with previous results. The nonlinear stability of two types of velocity anisotropy instabilities are examined. Explosive instabilities are found to exist both for Harris modes and upper hybrid loss-cone modes. In addition, recent experimental results on nonlinear decay (induced scattering) of waves are discussed in the light of the present theory.
Experimental Studies of Nonlinear Landau Damping and Growth of Plasma Waves in a Magnetic Field
Authors: Chang R. P. H. , Porkolab M.
Published: February 2004

The nonlinear Landau damping and growth of longitudinal waves in a magnetic field is studied experimentally. It is observed that a finite-amplitude cyclotron harmonic wave may decay nonresonantly into a similar, small-amplitude wave. This perturbed wave dan be amplified exponentially by increasing the amplitude of the finite-amplitude wave. Similarly, an externally launched small-amplitude test wave, having the same frequency as the perturbed wave, can be amplified at a comparable rate. The spatial growth of the test wave is in agreement with the predictions of a third-order mode-coupling equation. Using a calibrated interferometer system, the nonlinear Landau damping coupling coefficients (matrix elements) are measured quantitatively, and are found to be in good agreement with theory.
Roles of Ion Motion and of Return Currents in Transverse Instability of Colliding Plasmas
Authors: Nebenzahl I.
Published: February 2004

Proper account of the ion dynamics is shown to lead to a significant change in the extent of the unstable range of transverse modes. However, no very high growth rates can be produced by the ions. For relativistic electron beams in a cold plasma, the role of return currents induced in the plasma and of plasma collisions are analyzed. The return currents do not influence the transverse instability except for the extreme relativistic region γnb/np>1 where the plasma electrons “take over” in maintaining the growth rate high. Collisions are unimportant unless their frequency, ν≥ωp2 (plasma) /ωp (beam), where transverse oscillations cease to be electrically neutralized, so that pinching becomes impossible and the growth rate of the instability goes to zero as 1/ν.
Nonlinear Development of Electromagnetic Instabilities in Anisotropic Plasmas
Authors: Davidson Ronald C. , Hammer David A. , Haber Irving , Wagner Carl E.
Published: February 2004

Theory and simulation experiment are presented for a wide variety of transverse electromagnetic instabilities in plasmas with different sources and degrees of anisotropy. In each of the electron bi-Maxwellian, electron-pinch, and ion-pinch experiments, the bulk response of the system during the initial stages of instability is in good agreement with the predictions of quasilinear theory. Furthermore, the two independent energy constants which derive from the fully nonlinear Vlasov-Maxwell equations are found to remain constant to very good accuracy, even when the magnetic field energy reaches a substantial fraction of the total system energy. In each simulation experiment it is found that the magnetic energy saturates once the magnetic bounce frequency has increased to a value comparable to the linear growth rate prior to saturation, i.e., when ω¯B∼γ¯k. It is concluded that amplitude limitation for Weibel instabilities is a result of magnetic trapping for a broad range of system parameters. In many experiments a large remnant anisotropy in kinetic energy persists long after saturation.
Parallel Current and Sheath Effects on Collisional Drift Waves in an Axially Symmetric Device with End Plates
Authors: Tsai Shih-tung , Ellis Richard F. , Perkins Francis W.
Published: February 2004

A theoretical calculation is made of the normal mode structure of collisional drift waves in Q machines, due to the presence of end plates. The two fluid equations for electrons and ions are employed, including the effects of electron temperature perturbations and electron heat flow. Particular emphasis is placed on how a direct electron current along the magnetic field alters this structure. The dispersion relation and the sheath boundary condition resulting from both particle and heat flows are obtained. A slab plasma model is adopted, with a uniform magnetic field perpendicular to both the density gradient and the end plates. The case where the electron flow velocity is comparable to the ion acoustic wave velocity is studied in detail. The dispersion relation indicates that the wave frequency and the temporal growth rate change only very little for devices with end plates. The normal model consists of two oppositely directed traveling drift waves and two small amplitude oppositely directed traveling entropy waves. The drift waves grow spatially in the direction of electron flow and have a small axial phase shift, which varies linearly along the same direction. Good agreement is obtained with recent experimental results.
Computation of E-Layer and Plasma Equilibria in Astron
Authors: Anderson David V. , Killeen John , Rensink Marvin E.
Published: February 2004

The equilibrium magnetic field for astron configurations is computed; a given vacuum magnetic field and the fields due to the E layer and plasma are included, assuming axial symmetry and Bθ≡0. The components Br(r, z) and Bz(r, z) are derived from the stream function ψ(r, z) = rAθ. The E-layer is described by a distribution function that depends on the canonical angular momentum and the energy. Various models of the E layer have been used and are discussed. The function ψ(r, z) satisfies a nonlinear partial differential equation (Ampere's law) that is solved by finite-difference methods, using an iterative procedure. The object is to find equilibrium solutions with a reversed field in the central region that can contain a plasma. Examples of reversed field equilibria corresponding to various E layer distributions are presented. Simple models for the plasma are assumed, and equilibria of the coupled system of E layer plus plasma are computed.
Oscillatory Drag, Lift, and Torque on a Circular Cylinder in a Uniform Flow
Authors: Jordan Stanley K. , Fromm Jacob E.
Published: February 2004

Numerical solutions of the equations governing time-dependent, viscous, incompressible fluid flow past a circle are presented for Reynolds numbers 100, 400, and 1000. These solutions show the dramatic rise of the drag coefficient during the development of the Kármán vortex street and reveal the oscillatory character of the drag, lift, and torque that are experienced by the circle. Contour plots of the vorticity and stream function are compared with histories of the pressure distribution, drag, lift, torque, and separation angles. These comparisons show how the pressure distribution, drag, lift, and torque on the circle are intimately and logically related to the well-known flow pattern of the Kármán street. A new method is described for implementing the infinity conditions. The use of this technique makes it possible to observe the motion of the upstream stagnation streamline and relate this effect to the lift on the circle. The fact that the drag is larger for the oscillatory wake than the symmetric wake is interpreted as a tendency toward an equilibrium state of maximum energy dissipation. Comparisons are made with experimental results. These comparisons suggest that the present results are a valid description of flow past a circular cylinder for Reynolds numbers in the range from 40 to 400.
Uniqueness Theorems for the Linearized Boltzmann Equation
Authors: Case K. M.
Published: February 2004

Two theorems are proved about the solutions of the linearized Boltzmann equation with Maxwell boundary conditions. First, it is shown that the solution of the initial value problem is unique. Then, it is shown that the solution of the time-independent boundary-value problem is unique up to an additive constant. It can be made completely unique by adding a simple additional condition. The only essential property used in the proofs are the negative semidefinite character of the collision operator. The mathematics used are just Gauss theorem and Schwarz' inequality.
Thermal Diffusion and Convective Stability
Authors: Schechter R. S. , Prigogine I. , Hamm J. R.
Published: February 2004

The stability of a two-component fluid layer subjected to a temperature gradient has been studied, and the associated thermal diffusion separation has been found to exert a large influence even when the separations are small. The most unexpected and perhaps important result is that an instability has been found which can give rise to convection currents even though the density gradient is not adverse. Thus, a system heated from above can become unstable even when the fluid is less dense at the top of the system provided the more dense substance rises to the upper plate. Many measurements of the Soret coefficient could be subject to this instabilitity.
Stability of Plane Poiseuille Flow with Heat Transfer
Authors: Potter Merle C. , Graber Edwin
Published: February 2004

The influence of heat transfer on the stability of a plane Poiseuille flow in a channel is under investigation. The liquid flow is affected by the heat transfer through the variation in viscosity with temperature. Additional viscosity gradient terms are included in a modified Orr-Sommerfeld equation, and it is the presence of these terms which leads to a prediction of more unstable flows, for without the inclusion of these extra terms, the flow is stabilized. The results show that a temperature difference between the walls is always destabilizing and, in particular, a temperature difference between the walls of 100°F leads to a reduction in the critical Reynolds number from 7800 to 4600.
Ion-Temperature-Sensitive Effect in Transient Langmuir Probe Response
Authors: Sanmartin Juan R.
Published: February 2004

A theory is presented for a method, recently proposed by Hester and Sonin, of determining the ion temperature in a plasma by measuring the transient current to a cylindrical Langmuir probe after applying a potential Vp(−eVp≫κTe) under conditions where collection is collision free and the ratio of probe radius to Debye length is small. The ion component of the current does not approach its final steady-state value monotonically, but exhibits a strong, ion-temperature-dependent overshoot in the first few ion-plasma periods following the biasing of the probe. Analytical formulas are derived for the case of a Maxwellian plasma, and convenient graphical results are presented. The possible masking of the overshoot by a transient displacement current is discussed; it is shown how to avoid such displacement effects. For the overshoot to be sensitive to the ion temperature Ti, the probe must be near plasma (zero) potential before applying Vp(eVp−<0.1κTe, Vp− being that initial potential); this is not a drawback of the method, but, on the contrary, it can be used to accurately determine plasma potential along with Ti.
Charge Separation Effects on the Profile of a Perpendicular Shock Wave
Authors: Hu Pung Nien , Grad Harold
Published: February 2004

The profile of a plasma shock wave propagating perpendicular to a magnetic field is studied using a system of moment equations derived from a pair of Boltzmann equations for electrons and ions. The system, rigorously closed for weak shocks, describes a fully ionized plasma in which a long list of dissipative mechanisms and Hall effects are coupled. The charge separation effect which is automatically excluded by the usual weak shock scaling [P. N. Hu, Phys. Fluids 9, 89 (1966) and H. Grad and P. N. Hu, Phys. Fluids 10, 2596 (1967)] is retained in this description by a special nonuniform scaling of the Debye length relative to the shock strength. The shock profiles are obtained from an equation with two essential parameters (combining five dimensionless parameters which occur in the problem). The magnetic field profiles cover the entire range from collision-dominated monotonic profiles to damped oscillatory profiles and the limiting collisionless case of purely oscillatory and solitary wave profiles. The profiles of the electric field and the charge density can also be oscillatory or monotonic, and, in some parameter ranges, have long downstream tails, extending far beyond where the velocity and the magnetic field are undisturbed.
Steady Axisymmetric Toroidal Equilibrium in Ideal Magnetohydrodynamics
Authors: Asano Naruyoshi , Taniuti Tosiya
Published: February 2004

A self-consistent theory of steady axisymmetric toroidal equilibrium in ideal magnetohydrodynamics with poloidal rotation about the magnetic axis and toroidal flow around the torus is described. An application of the characteristic theory of hyperbolic partial differential equations to the steady hydromagnetic equations yields critical rotational velocities (poloidal) for the formation of standing hydromagnetic waves, which depend on the direction of the wave normal. For low β and large aspect ratio, the critical velocities for the slow (magnetosonic) mode are, for any direction, nearly equal to a velocity found by Stringer for the onset of anomalous diffusion. Flows with poloidal motion about the critical slow velocities are investigated by analogy with nozzle flow in conventional gasdynamics, the distance along the axis of nozzle corresponding to the poloidal angle. The periodicity of entropy with respect to the poloidal angle excludes shock transitions and, as a result, trans-slow-magnetosonic flows. A class of continuous, self-consistent solutions in the standard tokamak ordering is obtained in terms of the expansion of the square root of the inverse aspect ratio, in which the poloidal flow approaches, at a point corresponding to the throat of nozzle, the critical slow velocity in the poloidal direction; the solutions are found to be approximated by continuous solutions in the usual low-β approximation which does not make use of Ampere's law.
Rotation during the Implosion of a Theta Pinch
Authors: Benford James
Published: February 2004

Measurements of fields and pressure gradients during the collapse of a theta pinch allow determination of the ion azimuthal velocity from the radial component of Ohm's law. In hydrogen and nitrogen discharges Vθ was found to change sign across the current sheet. Ions rotated so as to carry an appreciable fraction of the current in the front of the sheet and moved so as to oppose current flow in the rear. The total angular momentum was approximately zero. These results agree well with the Düchs calculations of the influence of small transverse fields. Measurements of small transverse fields in the current sheet are presented.
Anomalous High-Frequency Resistivity of a Plasma
Authors: Kruer W. L. , Dawson J. M.
Published: February 2004

In one- and two-dimensional computer simulations an anomalous high-frequency resistivity in a plasma driven by a large electric field oscillating near the electron plasma frequency is investigated. The large field excites the oscillating two-stream and the ion-acoustic decay instabilities in agreement with the linear theory. When the ion and electron fluctuations saturate, a strong anomalous heating of the plasma sets in. This strong heating is due to an efficient coupling of the externally imposed large electric field to the plasma by ion fluctuations. The anomalous collision frequency and the saturation fluctuation amplitudes are determined as a function of the external field amplitude and frequency, and the electron-ion mass ratio. A simple nonlinear theory gives results in reasonable agreement with simulations.
Nonlinear Theory of Frequency Shifts and Broadening of Plasma Waves
Authors: Weinstock Jerome
Published: February 2004

It is shown that the linear dispersion relation for plasma waves is converted into a nonlinear one by making the replacement ω→ω+δω+idw. Here, ω is the wave frequency, and δω and dw are real nonlinear wave quantities that are explicitly calculated. The wave damping decrement dw has been determined in previous investigations, and shown to increase wave damping. Here, the nonlinear frequency shift δω is determined for a wide class of conditions. It is shown to have a direct and calculable influence on the frequencies of general electrostatic waves in magnetoplasmas. It is further shown that δω implies a splitting and broadening of frequency spectra of low-frequency waves. The calculated value of such broadening is in good agreement with observations by Sheffield, and Halseth and Pyle. The present method is based on the use of an averaging operator to express the nonlinear dispersion relation in terms of perturbed orbit function. Cumulant expansions are then used to express the orbit function in terms of δω, and to evaluate δω in terms of the plasma parameters in the same fashion as has been done for dw.
Fluctuation Spectrum of Plasma with Few Electrons in Debye Volume Observed by Collective Light Scattering
Authors: Kato M.
Published: February 2004

The validity of the usual light-scattering theory (i.e., Λ≫1 has been verified for Λ = 2, where Λ = NλD3 is the number of electrons in the Debye volume, N is the electron density, and λD is the Debye radius. Spectra of the light scattered from plasmas with Λ = 2 and Λ = 12 were measured and compared with the spectra predicted by Λ≫1 theory, with plasma parameters being independently obtained by the technique of plasma spectroscopy. Comparison between the plasma parameters (n = 2−3×1017 cm−3, T = 2−6 eV) determined from scattered light and those deduced from spectroscopic measurement was also made. It was found that they agreed within the experimental errors.
Some Experimental Results on Acoustic Wave Propagation in a Plasma
Authors: Fitaire M. , Mantei T. D.
Published: February 2004

Three aspects of the theory of propagation of sound in a plasma are experimentally confirmed. It is shown: (1) That the source term for the generation of sound in the neutral gas is proportional to the time derivative of the power input to the electrons from an externally applied electric field, (2) that at low frequencies the electronic and neutral fluid components move together approximately in phase when an acoustic wave propagates through the plasma, and (3) that the resonance curve of an acoustic cavity is sharpened by the presence of plasma; the latter effect is attributed to the collisional transfer of energy from the electrons to the neutrals.
Coupled-Mode Propagation in an Inhomogeneous Plasma in the Presence of Shear
Authors: Cano R. , Schwartz M. J. , Zanfagna B.
Published: February 2004

An experiment is discussed in which an electromagnetic wave polarized in the extraordinary mode is propagated through a plasma confined by a magnetic field having a weak shear, which results in creation of an ordinary wave component. Resonant and nonresonant conditions of propagation are explored for the incident extraordinary wave. The transmitted power in the extraordinary and ordinary modes is measured as a function of magnetic field for constant plasma density. Theoretical results obtained numerically from the coupled second-order equations describing propagation in a weakly inhomogeneous plasma with shear are found to be in substantial agreement with the experimental results. Relevance of this work to the spatial determination of the poloidal magnetic field in tokamaks is suggested.
Interaction of a Highly Energetic Electron Beam with a Dense Plasma
Authors: Kainer Selig , Dawson John , Shanny Ramy , Coffey Timothy
Published: February 2004

The interaction of an electron beam with a relatively dense background plasma was examined through numerical experiments, where the beam velocity is much greater than the thermal velocities. It is shown that the initial growth of the unstable waves is described by the two-stream instability and that the phenomena can be separated into two regions, (high and low density) depending on whether or not merging of space-averaged velocity distributions occurs during the growth of the initially most unstable wave. The occurrence of these regions is shown to follow from energy and momentum considerations. The long-time behavior of the low-density regime, where the merging does not take place during the initial growth of the instability is shown to be described quite well by quasilinear theory.
Curved Characteristics Behind Blast Waves
Authors: Laporte O. , Chang T. S.
Published: February 2004

Exact solutions, expressed in closed form in terms of elementary functions, are presented for the three sets of curved characteristics behind a self-similar, strong blast wave.
Solution of Forced Burgers Equation
Authors: Jeng D. T. , Meecham W. C.
Published: February 2004

Burgers' model equation of turbulence is studied for the case when the driving force is periodic. Analytical solution is obtained for the inviscid flow and numerical integration is performed for the viscous flow.
Numerical Analysis of a Gasdynamic Laser Mixture
Authors: Munjee S. A.
Published: February 2004

A system of nonlinear vibrational relaxation equations for a CO2-He-N2 gas mixture is presented. Sample numerical results of mode temperatures and gain coefficient have been obtained for nozzle flows with a stagnation pressure of 20 atm.
Spatial Evolution of Low-Frequency Perturbations Produced by a Grid in a Plasma
Authors: Sato N. , Sasaki A.
Published: February 2004

The phase velocity and damping factor of grid-excited perturbations are observed to depend on the position over about half a wavelength from an exciting source. Beyond there, Landau-damped ion acoustic waves propagate, as predicted theoretically.
Mirror Containment with Low-Frequency Short-Wavelength Fluctuations
Authors: Aamodt R. E.
Published: February 2004

Low-frequency fluctuations with short wavelengths perpendicular to the magnetic mirror field are shown to only weakly affect particle containment. A critical fluctuation level is determined, below which no losses occur, and above which nonexpandable, nonlinear phase space transitions induce small losses.
Viscous Stability Theory for Thermally Stratified Flow: Discontinuous Jets and Shear Layers
Authors: Gage K. S.
Published: February 2004

The method used by Drazin to investigate the stability of unbounded, viscous, homogeneous, parallel shear flow to small wavenumber disturbances is extended to study the effect of thermal stratification on the stability of unbounded jets and shear layers. By this method the stability characteristics of continuous profiles are inferred from the stability characteristics of discontinuous profiles. The characteristic value problem for discontinuous jet and shear layers is posed by the requirement that the solutions of the governing differential equation satisfy the matching conditions and boundedness conditions for layers that extend to infinity. The analysis leads to a characteristic determinant which is required to vanish for the characteristic values of the parameters: the Reynolds number, the wavenumber, and the wave speed. The stabilizing effect of the thermal stratification as parameterized by the Richardson number was found to be most stabilizing for small wavenumber (large-scale) disturbances.
Laser Anemometer Measurements of Turbulence in Non-Newtonian Pipe Flows
Authors: Chung J. S. , Graebel W. P.
Published: February 2004

The structure of turbulence for pipe flows of dilute polyethylene oxide and polyacrylamide solutions is investigated using a laser anemometer technique. The instrumentation of the optical system and signal processing needed to satisfy the optical requirements and the signal-to-noise ratio are presented. The spatial requirement of the beam signal is described with regard to the lens, aperture, wavelength, and the angular alignment of the scattered and reference beams. A gravity-flow system is used to minimize the degradation of polymer solutions. The measurements of wall pressure drops indicate that the polymer additives used give a consistent delay of transition from laminar flow to turbulence, as compared with Newtonian fluids. The axial turbulence intensities for polymer solutions are found to be substantially reduced, compared with results obtained for water.
Spin Down of Radiation-Penetrated, Opaque, Compressible Fluid in a Circular Cylinder
Authors: Sakurai Takeo
Published: February 2004

The linear impulsive spin down from a rotational equilibrium of rigid body rotation of an opaque, compressible fluid in a circular cylinder under the effect of radiation is investigated. The opacity of the fluid is assumed to result from the electron scattering, and the radiative Prandtl number PR is assumed to be proportional to the square root of the Ekman number E where P = ν/κR, E = ν/R02Ω, and ν is the kinematic viscosity, κR is the radiative thermal diffusivity, R0 is the radius of the cylinder, and Ω is the unperturbed angular velocity, respectively. The treatment is also restricted to the case for which the ratio of the thermal energy to the rotational kinetic energy (H1 = RT0/Ro2Ω2, where T0 and R are the temperature and the universal gas constant, respectively) is very large corresponding to typical conditions in stellar spin down. As a new aspect of the linear spin down of the non-Boussinesq compressible fluid, the quasisteady asymptotic state is shown to be rotating nonuniformly despite the fact that such an asymptotic state in Boussinesq fluid is characterized by rigid body rotation. This nonuniform asymptotic state is one in which each horizontal fluid layer rotates like a rigid body with a perturbation angular velocity proportional to the unperturbed temperature. It is also shown that the spin-down time is of the order of H1τc, where τc is the thermal diffusion time. Because H1 can be rephrased to be equal to the square ratio of the Brunt-Väisälä frequency to Ω, we may say that our spin-down process is similar to that of the Boussinesq fluid case except for the above quasistatic asymptotic state.
Experimental Investigation of Normal Shock Wave Velocity Distribution Functions in Mixtures of Argon and Helium
Authors: Harnett L. N. , Muntz E. P.
Published: February 2004

The electron beam fluorescence technique for measuring simple one-dimensional moments of helium velocity distribution functions has been extended for use with argon. Measurements made in argon-helium gas mixture shock waves at low Mach numbers are presented. Parallel and perpendicular temperature profiles are shown for each gas. Macroscopic velocities for each gas were measured by determining the blue shifts in the line profiles when the line of sight was directly upstream. The results are compared with existing theories and other experimental results.
Development of the Distribution Function on the Centerline of a Free Jet Expansion
Authors: Willis D. Roger , Hamel B. B. , Lin J. T.
Published: February 2004

Spherical source flow which closely approximates the flow on the centerline of an axisymmetric free jet expansion, is used as a theoretical model. The ellipsoidal statistical model is used to describe the intermolecular collisions. Three partial moments of the distribution function, and the value of the distribution function for a zero perpendicular component of molecular velocity, are calculated as functions of distance and molecular velocity for two values of the Prandtl number (23 and 1), and for two gross collision rates such that the viscosity would be proportional to T1/2 and T, where T is the temperature. The quantities calculated correspond to idealized experimental measurements. It is found that the distribution function is, to a good approximation, ellipsoidal in velocity space for (Tr − Tp)/T≲1, where Tr and Tp are the parallel and perpendicular temperatures, respectively. It is also found that the deduction of Tp and Tr from the experimental quantities by fitting with an assumed Gaussian velocity dependence can lead to serious errors as the flow becomes frozen. There is a significant effect of the Prandtl number upon some of the results.
Prediction of Molecular Scattering in Free-Jet Expansions
Authors: Benek J. A.
Published: February 2004

A theoretical model of the background interaction with a free-jet expansion is developed. The background is shown to be separable into two components: one originating from jet particles reflected from the chamber walls and the other from residual particles unremoved by the pumping system. Comparisons of the data of several investigators are made with theoretically predicted values of intensity as a function of either separation distance or source pressure.
Kinetic Theory of Parallel Plate Heat Transfer in a Polyatomic Gas
Authors: Hsu S. K. , Morse T. F.
Published: February 2004

A kinetic model equation for a polyatomic gas is used to investigate heat transfer between two parallel plates. In particular, a general kinetic boundary-value problem is studied for the case of arbitrary accommodation coefficients on the plates. This problem is solved for all ranges of Knudsen number using a variational principle with a simple trial function. The dependence of heat transfer on Knudsen number, the internal energy, the Eucken factor and the ratio of translational collision time to internal collision time for a polyatomic gas has been obtained. Moreover, density and temperature profiles have been calculated. Comparison is made with measurements on nitrogen, and it is found that the solution is in very good agreement with experiment for heat transfer, and in qualitative agreement with experimental density profiles.
Nonequilibrium Viscous Shock Layer in a Partially Ionized Gas
Authors: Nishida M.
Published: February 2004

The structure of a nonequilibrium, partially ionized viscous shock layer of a blunt body which is at floating potential is described. Electron temperature and electron-ion density profiles across the shock layer have been theoretically investigated for the case where electrons are in thermal nonequilibrium with heavy particles in a free stream. Immediately behind the shock, the electron temperature profile across the shock layer has been matched with that in a free stream, using the relation for the jump of the electron temperature gradient across the shock. The method of matching is described. Dependence of the electron temperature profile across the shock layer upon the degree of thermal nonequilibrium in the free stream has been investigated.