bluuebunny/crossref_metadata_2025 huggingface dataset:
Neoclassical transport coefficients for tokamaks with bean-shaped flux surfaces
Authors: Chang C. S. , Kaye S. M.
Published: July 2002

Simple analytic representations of the neoclassical transport coefficients for indented flux surfaces are presented. It is shown that a transport coefficient for an indented flux surface can be expressed in terms of a linear combination of the previously known transport coefficients for two nonindented flux surfaces. Numerical calculations based on actual equilibria from the PBX-M tokamak [Phys. Fluids B 2, 1271 (1990)] indicate that, even for modestly indented flux surfaces, the ion neoclassical thermal transport can be over a factor of 2 smaller than in a circular plasma with the same midplane radius or with the equivalent area.
On zero-frequency magnetic fluctuations in plasmas
Authors: Tajima T. , Cable S. , Kulsrud R. M.
Published: July 2002

A plasma sustains fluctuations of electromagnetic fields and particle density even in thermal equilibrium and such fluctuations have a large zero-frequency peak. The level of fluctuations in the plasma for a given wavelength and frequency of electromagnetic fields is calculated through the fluctuation–dissipation theorem. The frequency spectrum shows that the energy contained in this peak is complementary to the energy ‘‘lost’’ by the plasma cutoff effect. The level of the zero (or nearly zero) frequency magnetic fields is computed as 〈B2〉0/8π = (1/2π3)T(ωp/c)3, where T and ωp are the temperature and plasma frequency. The relation between the nonradiative and radiative fluctuations is elucidated. Both a simple collision model and a kinetic theoretic treatment are presented with essentially the same results. The size of the fluctuations is λ ∼ (c/ωp)(η/ω)1/2, where η and ω are the collision frequency and the (nearly zero) frequency of magnetic fields oscillations. Perhaps the most dramatic application of the present theory, however, is to the cosmological plasma of early epoch (say t = 10−2–100 sec after the Big Bang). Implications of these magnetic fields in the early Universe are discussed.
Skin effect and reflectivity in strongly coupled plasmas
Authors: Berkovsky M. A. , Kurilenkov Yu. K. , Milchberg H. M.
Published: July 2002

The skin depth and the Fresnel reflectivity are evaluated in the case of strongly coupled plasmas. Analysis is based on the explicit expression for the dynamic collision frequency. Peculiarities of electromagnetic wave penetration into collision-dominated plasmas and reflectivity in the vicinity of critical density are considered.
Numerical simulations of charge state distribution from a KrF laser-produced plasma
Authors: Tsui Y. Y. , Fedosejevs R. , Offenberger A. A. , Rankin R. , Capjack C. E.
Published: July 2002

A calculation of the charge state distribution of the asymptotic evolution of a plasma produced by an ultraviolet laser has been carried out by coupling the results of a detailed two-dimensional hydrodynamic simulation of the creation and heating of the plasma to a simpler one-dimensional hydrodynamic code. The latter incorporates time-dependent ionization and recombination physics and is used to model the subsequent expansion and cooling of the plasma. The simulation results are compared to experimental charge state distributions obtained by using a single shot electrodynamic charge analyzer. The sensitivity of the results to the rate coefficients used for the recombination calculations was tested and the calculated distributions were found to be most sensitive to the values of the three-body recombination rate and the amount of heat returned to the plasma. Reasonable agreement was found between the measured and calculated charge state distributions.
The fluctuation-induced Hall effect
Authors: Shen W. , Prager S. C.
Published: July 2002

The fluctuation induced Hall term, <J̃×B̃≳, has been measured in the Madison Symmetric Torus (MST) [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)], reversed-field pinch. The term is of interest as a possible source of current self-generation (dynamo). It is found to be non-negligible, but small in that it can account for less than 25% of the dynamo driven current.
Nonlocal electron heat relaxation in a plasma shock at arbitrary ionization number
Authors: Ramírez J. , Sanmartín J. R. , Fernández-Feria R.
Published: July 2002

A recently obtained nonlocal expression for the electron heat flux valid for arbitrary ionization numbers Z is used to study the structure of a plane shock wave in a fully ionized plasma. Nonlocal effects are only important in the foot of the electronic preheating region, where the electron temperature gradient is the steepest. The results are quantified as a function of a characteristic Knudsen number of that region. This work also generalizes to arbitrary values of Z previous results on plasma shock wave structure.
Chaotic behavior of thermal excitations in edge plasmas
Authors: Weiland J. , Mondt J. P.
Published: July 2002

It is found that an electromagnetic analog of the current convective instability in the nonlinear regime may develop into a chaotic system. Comparison is made with the corresponding electrostatic strongly nonlinear case which may show chaotic behavior of the Lorenz type, and the nonlinear cascade properties are discussed.
Joint statistics between temperature and its dissipation in a turbulent jet
Authors: Anselmet F. , Antonia R. A.
Published: July 2002

The joint probability density function of the temperature θ and its instantaneous dissipation χ is important for the development of turbulent reacting flow models. Measurements are presented, in the nearly self-preserving region of a turbulent plane jet, of the joint statistics of θ and an approximation χ1 to χ. Properties of the three, separately obtained, dissipation components are first compared to justify the choice of χ1. The quantity chosen is an appropriately weighted linear combination of the squared values of the temporal derivative, shown to be an adequate substitution for the derivative in the streamwise direction, and the derivative, in either the lateral or spanwise directions, of temperature. The correlation between θ and χ1 is weak, receiving contributions primarily at small frequencies. The assumption of independence between θ and χ1, allowing the joint probability density function of these two quantities to be written as a product of the individual probability density functions, improves with distance from the jet centerline.
Quasilinear stabilization of the free electron laser instability for a relativistic electron beam propagating through a transverse helical wiggler magnetic field
Authors: Dimos Anna M. , Davidson Ronald C.
Published: July 2002

A quasilinear model is developed that describes the nonlinear evolution and stabilization of the free electron laser instability in circumstances where a broad spectrum of waves is excited. The relativistic electron beam propagates perpendicular to a helical wiggler magnetic field B0=−B̂ cos k0 z êx−B̂ sin k0 z êy, and the analysis is based on the Vlasov–Maxwell equations assuming ∂/∂x=0=∂/∂ y and a sufficiently tenuous beam that the Compton-regime approximation is valid (δφ≂0). Coupled kinetic equations are derived that describe the evolution of the average distribution function G0( pz,t) and spectral energy density ℰk(t) in the amplifying electromagnetic field perturbations. A thorough exposition of the theoretical model and general quasilinear formalism is presented, and the stabilization process is examined in detail for weak resonant instability with small temporal growth rate γk satisfying ‖γk/ωk‖≪1 and ‖γk/k Δvz‖≪1. Assuming that the beam electrons have small fractional momentum spread (Δ pz/p0≪1), the process of quasilinear stabilization by plateau formation in the resonant region of velocity space (ωk−kvz=0) is investigated, including estimates of the saturated field energy, efficiency of radiation generation, etc.
Geometric interpretation of the possible velocity vectors obtained with multiple-sensor probes
Authors: Willmarth William W.
Published: July 2002

A geometric interpretation for the operation of probes that use multiple sensors is presented. This interpretation provides a method for visualizing how the individual sensor reponse and the geometrical arrangement of the sensors are related to the measurements made with a given probe. The interpretation also provides a simple explanation for the occurrence of multiple solutions of the nonlinear equations for a probe. It is shown that a measured set of three cooling velocities, using a three-sensor hot-wire probe, can be produced by as many as eight different velocity vectors, only one of which is the correct velocity vector.
An analytical study of the Kelvin–Helmholtz instabilities of compressible, magnetized, anisotropic, and isotropic tangential velocity discontinuities
Authors: Roy Choudhury S.
Published: July 2002

An analytical study is made of the linear stability of tangential velocity discontinuities in anisotropic and isotropic compressible, magnetized plasmas. A new analytical technique leads to entirely new results for both cases, and recovers previously obtained numerical results for the isotropic case. For both the anisotropic and isotropic vortex sheets, the structure of unstable, standing wave modes is mapped out in the (inverse plasma beta, Mach number) plane for modes at arbitrary angles to the flow and the magnetic field. Solutions are obtained for unstable standing and traveling modes of the anisotropic vortex sheet propagating parallel or antiparallel to the magnetic field, and at small angles to these directions. Numerically computed unstable standing modes obtained previously for the isotropic case are recovered analytically and extended to more general configurations. Also, it is shown that modes propagating along or opposite to the magnetic field direction, and at a general angle to the flow, do not exhibit standing wave instability for (plasma beta)≤1, for the isotropic vortex sheet.
Hamiltonian theory of relativistic magnetohydrodynamics with anisotropic pressure
Authors: Holm Darryl D. , Kupershmidt Boris A.
Published: July 2002

This Brief Communication introduces a special relativistic extension of ideal magnetohydrodynamics having anisotropic pressure, and provides its Hamiltonian formulation in a fixed inertial frame. The nonrelativistic limit of this theory recovers the ‘‘double adiabatic’’ hydromagnetic equations of Chew, Goldberger, and Low [Proc. R. Soc. London Ser. A 236, 112 (1956)]. For isotropic pressure distribution the equations and Hamiltonian structure reduce to the usual theory of relativistic magnetohydrodynamics. The Poisson bracket for the system is not symplectic. Rather, it is dual to a Lie algebra of semidirect-product type.
Self-consistent plasma heating and acceleration by strong magnetosonic waves for θ=90 °. Part I: Basic mechanisms
Authors: Lembege B. , Dawson J. M.
Published: July 2002

The behavior of strong magnetosonic waves propagating perpendicular to a static field B0 is investigated within the frequency range ωci<ω<ωlh; ωci,ω, and ωlh are, respectively, the ion cyclotron, the pump wave, and the lower-hybrid frequencies. A one-dimensional, relativistic, fully electromagnetic, particle simulation code (for both electrons and ions) is used, where self-consistent effects are totally included. During the buildup phase, a longitudinal electric field develops and attains a nonlinear level which strongly distorts its shape so that many harmonics are produced. This is followed shortly by ion trapping, which simultaneously enhances the wave overtaking (the wave crests overtaking the wave troughs) and produced a strong wave damping. A very large ion acceleration accompanied by a strong heating (mainly nonstochastic) perpendicular to B0 results; the electrons exhibit only poor heating associated with their adiabatic compression. The dynamics of both particle species, the consequences of the wave–particle energy transfer and the particle viscosities, are studied in detail. Competitive and self-consistent effects such as space-charge effects, wave overtaking, ion trapping, and wave damping are investigated and compared with previous models; the mechanisms by which these various phenomena interact on each other are analyzed. Characteristics of nonstochastic and stochastic ion heating are also discussed. Our computations show that if sufficient intensity is reached, one is not constrained to use lower-hybrid waves or cyclotron harmonic waves to heat a plasma efficiently and that any frequency below ωlh can be used.
Compact dispersion relations for parametric instabilities of electromagnetic waves in magnetized plasmas
Authors: Cohen Bruce I.
Published: July 2002

The existence of compact dispersion relations for parametric instabilities of coherent electromagnetic waves in magnetized plasmas is addressed here. In general, comprehensive dispersion relations for parametric instabilities in unmagnetized plasmas become more complicated in the presence of an applied time-independent magnetic field. This is demonstrated with a fluid perturbation theory. A compact dispersion relation for parametric instabilities in unmagnetized plasma is heuristically extended here to the case of a magnetized plasma. This dispersion relation gives the correct results in a variety of circumstances of interest in considering electron cyclotron heating applications.
Numerical observations of dynamic behavior in two-dimensional compressible convection
Authors: Ginet G. P. , Sudan R. N.
Published: July 2002

Using numerical simulations of the anelastic partial differential equations, convective flow in a two-dimensional polytropic atmosphere is investigated. Fixing the aspect ratio at unity and choosing the viscosity as the order parameter, the numerical solutions have indicated a variety of dynamic behavior including (i) oscillatory motion with a period of order the eddy turnover time, (ii) quasiperiodic motion with a long period much longer than an eddy turnover time, and (iii) at least two branches of solutions in certain regimes.
Numerical study of the dynamics of a forced shear layer
Authors: Ghoniem Ahmed F. , Ng Kenneth K.
Published: July 2002

Vortex simulation is used to study a confined two-dimensional, two-stream, spatially developing shear layer, focusing on the effect of upstream forcing on the development of the vorticity field and the entrainment of irrotational fluid into the mixing zone. In the unforced case, the layer rolls up at the most amplified mode as determined from the linear theory, forming eddies that equilibrate to the neutrally stable mode by increasing the local thickness. Subharmonic perturbation returns the state to the most amplified frequency and pairing starts, repeating the sequence of events and leading to the observed self-similarity. In the forced case, eddy interactions follow several stages. First, the layer rolls up at the harmonic of the forcing frequency closest to the most amplified mode. A process of accelerated pairing follows yielding eddies in tune with the forcing frequency. Pairing among resonant eddies, which represent the neutrally stable mode, is disabled and the growth of the vorticity layer is impaired. Finally, the effect of forcing diminishes and pseudorandom pairing is resumed. Velocity fluctuations are strongly affected by forcing, and the sign of Reynolds stresses is reversed following pairing. Entrainment of passive particles is commensurate with the development of the vorticity layer.
The influence of damping on the ion hose instability
Authors: Bosch R. A. , Gilgenbach R. M.
Published: July 2002

The ion hose instability in the ion-focused regime is analyzed using a rigid beam model with phenomenological damping terms. Values of the instability wavelength, e-folding length, and group velocity are calculated and compared with numerical results. The impulse response function for this model is also obtained.
Structure of rough-wall turbulent boundary layers
Authors: Bandyopadhyay Promode R. , Watson Ralph D.
Published: July 2002

Recent experiments have shown that, in rough-wall turbulent boundary layers, drag varies systematically with the spanwise aspect ratio λz (span/height) of roughness elements. In this paper, the effect of λz on turbulence structure has been examined. Based on λz, the roughness in a transversely grooved surface (λz≫1) is the opposite extreme of model plant canopies (λz≪1) studied in wind tunnels, whereas sandgrain is an intermediate type [λz=O(1)]. Second-, third-, and fourth-order turbulence moments have been measured in turbulent boundary layers over transversely grooved and smooth surfaces and compared with available turbulence structure measurements over other types of surfaces. The near-wall turbulence structure is found to vary with λz. The instantaneous motions involved in the flux of shear stress near the wall in smooth and transversely grooved surfaces are opposite in sign to those in three-dimensional roughness. The former is explained in terms of hairpin vortices alone while the latter group is modeled to have an additional vortex, viz., the so-called necklace vortex which straddles a three-dimensional roughness element near its base.
Evolution of high current, cold cathode diodes to steady state
Authors: Shefer R. E. , Friedland L. , Klinkowstein R. E.
Published: July 2002

A theoretical model of cathode plasma behavior in a planar, high current, space-charge limited diode is presented. The model predicts the evolution of the cathode plasma to steady state when certain diode conditions are satisfied. This steady state corresponds to current extraction from a stationary plasma boundary with no diode impedance collapse. In order for the equilibrium to be achieved, the driving impedance of the external power supply circuit must be smaller than a critical value that depends only on diode voltage, gap spacing, and plasma electron temperature. The temporal evolution of the cathode plasma is described using both a discrete numerical simulation model and an approximate analytical solution to the transport equations. The dependence on plasma temperature, neutral gas density and composition, diode voltage, gap spacing, and extracted current density are investigated.
Transport simulations of a density limit in radiation-dominated tokamak discharges—profile effects
Authors: Stotler D. P.
Published: July 2002

The density limit observed in tokamak experiments is thought to be due to a radiative collapse of the current channel. A transport code coupled with a magnetohydrodynamic (MHD) equilibrium routine is used to determine the detailed, self-consistent evolution of the plasma profiles in tokamak discharges with radiated power close to or equaling the input power. The present work is confined to Ohmic discharges in steady state. It is found that the shape of the density profile can have a significant impact on the variation of the maximum electron density with plasma current. Analytic calculations confirm this result.
Stability of Taylor–Couette flow in superfluid helium in the presence of superfluid vortex lines
Authors: Bielert F. , Stamm G.
Published: July 2002

Taylor–Couette flow between two coaxial cylinders with a rotating inner cylinder and a fixed outer cylinder has been investigated in the temperature range from 1.45 to 2.15 K. The density of quantized vortex lines in the gap between the cylinders was measured by analyzing the damping of azimuthal second-sound resonances. Increasing the angular velocity of the inner cylinder the first appearance of quantized vortices was detected at a critical angular velocity of Ω0. The onset of the Taylor instability occurred at a critical Reynolds number Rec which appeared to be temperature dependent. In agreement with theoretical predictions the experimental results show that the presence of quantized vortex lines strongly influences the stability of the flow field.
Thermomechanical and magnetohydrodynamic stability of elongating plastic jets
Authors: Littlefield David L.
Published: July 2002

In this study the stability characteristics of uniformly elongating plastic jets exposed to axial electric currents are investigated. The objective of this study is to expand the results of previous analyses by Littlefield [‘‘The effect of electromagnetic fields on the stability of a uniformly elongating plastic jet,’’ Phys. Fluids A 2, 2240 (1990); ‘‘Finite conductivity effects on the MHD instabilities in uniformly elongating plastic jets,’’ ibid. 3, 166 (1991); ‘‘Enhancement of stability in uniformly elongating plastic jets with electromagnetic fields,’’ ibid. 3, 2927 (1991)] to include high levels of electric current, where thermal energy effects must be included. Coupling of the magnetohydrodynamic and thermal characteristics of the flow is accomplished through the variation of mechanical, thermal, and electrical properties with temperature. Phase change effects are also considered. The jet is assumed incompressible and perfectly plastic, with the Levy–von Mises criterion imposed to limit the effective stress. Solutions to the appropriate base flow are subjected to small axisymmetric disturbances, and linear perturbation theory is employed to determine the time evolution of these disturbances. Perturbations that grow the fastest in magnitude as time progresses are identified as the most unstable. Results of the analysis indicate that thermal effects can dramatically alter both the base and perturbed flow fields, as well as the growth rate of perturbations.
Mean flow distortion due to finite-amplitude instability waves in a plane turbulent wake
Authors: Marasli B. , Cohen J. , Levinski V.
Published: July 2002

The nonlinear interaction between the mean flow and a coherent disturbance in a two-dimensional (2-D) turbulent wake is investigated. Based on considerations from stability theory, a model that assumes a quasiparallel mean flow and constant eddy viscosity is developed. Detailed comparisons between the model and experimental results are made. It is found that for downstream distances, where the wave is still being amplified according to the linear stability theory, the model predicts very well the modification of the mean velocity profile and the spatial growth of both the forced wake and the disturbance amplitude.
An exact solution for axial flow in cylindrically symmetric, steady-state detonation in polytropic explosive with an arbitrary rate of decomposition
Authors: Cowperthwaite M.
Published: July 2002

Methods of differential geometry and Bernoulli’s equation, written as B=0, are used to develop a new approach for constructing an exact solution for axial flow in a classical, two-dimensional, ZND detonation wave in a polytropic explosive with an arbitrary rate of decomposition. This geometric approach is fundamentally different from the traditional approaches to this axial flow problem formulated by Wood and Kirkwood (WK) and Fickett and Davis (FD), and gives equations for the axial particle velocity (u), the sound speed (c), the pressure (p), and the density (ρ), that are expressed in terms of the detonation velocity (D), the extent of decomposition (λ), the polytropic index (K), and two nonideal parameters ε3 and ε1, and reduce to the equations for steady-state, one-dimensional detonation as ε3 and ε1 approach zero. In contrast to the FD approach, the equations for u and c are obtained from first integrals of a tangent vector Ã on (u,c,λ) space, and the invariant condition, ÃB=aB=0, bypasses the FD eigenvalue problem by defining ε3 in terms of the detonation velocity deficit D/D∞ and K. In contrast to the WK approach, the equations for p and ρ are obtained from equations expressing the conservation of axial momentum and energy. Because the equations for these flow variables are derived without using the conservation of mass, the axial radial particle velocity gradient (war) associated with the flow can be obtained from the continuity equation without making approximations.

The relationship between ε1 and ε3 that closes the solution is obtained from equations expressing constraints imposed on the axial flow at the shock front by the axial and radial momentum equations, the curved shock and the decomposition rate law, and a particular solution is constructed from the ε1–ε3 relationship determined by a prescribed rate law and value of K. Properties of particular solutions are presented to provide a better understanding of two-dimensional detonation, and a new axial condition for detonation failure is used to show that detonation failure can occur before the curve relating D/D∞ to the axial radius of curvature of the shock (Sa) becomes infinite.
Long-wave motions in turbulent shear flows
Authors: Priymak V. G. , Miyazaki T.
Published: July 2002

Direct Navier–Stokes simulation of the fully developed turbulent viscous incompressible fluid flows in an infinite circular pipe is performed. Calculations were carried out at Reynolds number Re=Ū2R/ν=4000, based on the mean velocity and pipe diameter. Numerical Navier–Stokes solutions obtained belong to the class of streamwise periodic solutions with large periods λmax=16πR≂7460ν/uτ, where uτ is the friction velocity. It is demonstrated that the most energetic Fourier components of velocity fluctuations correspond to very low nonzero longitudinal wave number α=2π/(0.5λmax)=0.25R−1≂1.7×10−3uτ/ν. These long-wavelength motions were not resolved before in numerous channel and pipe flow simulations carried out with periodicity lengths λmax<2500ν/uτ. Space–time structure of the turbulent flow as well as associated wave-like motions are investigated. The possibility and accuracy of the velocity field approximation by the superposition of traveling and standing waves is analyzed. It is shown that the parameters of such a representation (wave amplitudes, phase velocities, the position of wave front, etc.) are strongly dependent on the inclusion of low longitudinal wave numbers in the Navier–Stokes simulation.
Hysteresis in forced oscillations of pendant drops
Authors: DePaoli D. W. , Feng J. Q. , Basaran O. A. , Scott T. C.
Published: July 2002

A hysteresis phenomenon has been revealed through experiments conducted with large-amplitude forced oscillations of pendant drops in air. Under strong excitation, the frequency response of a drop forced at constant amplitude exhibits jump behavior; a larger peak response amplitude ε↓ appears at a lower frequency ω↓ during a downward (↓) variation of forcing frequency than during an upward (↑) variation, viz. ε↓≳ε↑ and ω↓<ω↑. Similar results are obtained when forcing amplitude is varied at constant frequency. This behavior is characteristic of a system with a soft nonlinearity. These findings indicate that oscillating pendant drops constitute a convenient system for studying nonlinear dynamics.
Resonance phenomena in viscous fluids inside partially filled spinning and nutating cylinders
Authors: Selmi Mohamed , Herbert Thorwald
Published: July 2002

Spin-stabilized projectiles with liquid payloads may experience different types of flight instabilities caused by the fluid motion in the payload cylinder. The first type is known to occur in low-viscosity fluids, i.e., at high Reynolds numbers, owing to resonance with inertial waves at critical frequencies. The second type originates from a forced secondary flow at arbitrary frequency, and is most pronounced for fluids of high viscosity, i.e., relatively low Reynolds numbers. For cylinders completely filled with a single fluid, these instabilities were analyzed by eigenfunction expansion developed by Selmi, Li, and Herbert [Phys. Fluids A 4, 1998 (1992)]. The method permits unified analysis of both types of instability, since it can be used for flows at moderate as well as high Reynolds numbers. Often in practice, cylinders are made to include a central rod to alter resonance properties or are partially filled during production, to ensure safety as the liquid payload may expand under different conditions. In this paper, the eigenfunction approach is extended to analyze the moments caused by the flow in a spinning and nutating cylinder, containing a partial fill or a central rod. The analysis shows that the fill ratio (defined as the ratio of the volume of the fluid to the volume of the cylinder) affects resonance with inertial waves. The inviscid flow equations are solved analytically to provide criteria for the onset of resonance in the two configurations.
Wetting front instability in randomly stratified soils
Authors: Chen Guoliang , Neuman Shlomo P.
Published: July 2002

A probabilistic criterion is derived for the onset of wetting front instability during surface water infiltration into a randomly stratified soil. It is based on the common assumption that the natural log hydraulic conductivity of the soil is a random, multivariate Gaussian function of space. Whereas the mean (expectation) of this function may exhibit a drift, its fluctuations about the mean are statistically homogeneous with constant variance and autocorrelation scale. The wetting front is taken to form a sharp boundary. Closed-form expressions for the probability of instability, and for the mean critical wave number, are obtained either directly or via a first-order reliability method. Monte Carlo simulations are used to verify these analytical solutions as well as to determine the mean maximum rate of incipient finger growth and corresponding mean wave number. The effects of applied pressure gradient, capillary pressure head at the wetting front, and statistical parameters of the hydraulic conductivity field on instability and incipient finger growth are investigated for a wide range of these variables.
The effect of thermal expansion on nonlinear first and second sound in the whole temperature region of He II
Authors: Braun S. , Kluwick A. , Cramer M. S.
Published: July 2002

We consider one-dimensional, weakly nonlinear first and second sound waves in He II. The first correction to the shock speed is computed for each sound mode. The expressions obtained are exact with respect to the coefficient of thermal expansion β. It is shown that the commonly made assumption of negligible β can lead to significant error in the shock speeds for first sound away from the lambda-line. This contrasts with the calculation of the linear sound speeds and the shock speed for second sound where the β=0 approximation yields accurate results. Near the lambda-line, the exact expressions for both modes are seen to contain fundamentally different singularities than those found in the commonly employed β=0 theory.
Transition of separated shear layer from order to chaos
Authors: Dong Y. F. , Wei Z. L. , Xu C.
Published: July 2002

Transition of the separated shear layer has been experimentally investigated for the Reynolds numbers (based on the diameter) ranging from 2.4×103 to 2.0×104. The degree of chaotic behavior of the separated shear layer is verified by applying ideas from nonlinear dynamics (such as Lyapunov exponents, correlation dimension and entropy) to the experimental data, thus relating the evolution of the separated shear layer from the laminar to the weak turbulence to the concept of chaos. The results demonstrate that the transition of the separated shear layer from order to chaos is through one Hopf bifurcation and the periodic bifurcation.
Superfluid vortex lines in a model of turbulent flow
Authors: Barenghi Carlo F. , Samuels David C. , Bauer Gregory H. , Donnelly Russell J.
Published: July 2002

Recent experiments have shown that the high Reynolds number turbulent flow of superfluid helium is similar to classical turbulence. To understand this evidence we have developed an idealized model of normal fluid turbulence which is based on vorticity tubes and we have studied numerically the behavior of superfluid quantized vortex lines in this model of turbulent normal flow. We have found that the vortex lines form ordered superfluid vortex bundles in regions of high normal fluid vorticity. A vortex wave instability and mutual friction are responsible for generating a high density of vortex lines such that the resulting macroscopic superfluid vorticity and the driving normal fluid vorticity patterns match. The results are discussed from the point of view of the idea, put forward to explain experiments, that in the isothermal, turbulent flow of He II a high density of vortex lines locks the two fluid components together and the resulting turbulent flow is that of a classical Navier–Stokes fluid.
Towards modeling inhomogeneous compressible turbulence using a two-scale statistical theory
Authors: Hamba Fujihiro , Blaisdell Gregory A.
Published: July 2002

Turbulence models for compressible flows are investigated using a statistical theory called the two-scale direct-interaction approximation. Inertial-range spectra for velocity and density variances are assumed to derive models for several correlations systematically; they include the dilatation dissipation, mass flux, Reynolds stress, and pressure–dilatation correlation. Model expressions are shown to contain two important parameters: the turbulent Mach number and the density variance normalized by the mean density. Typical terms are material derivatives of the turbulent kinetic energy and its dissipation rate as well as the mean velocity divergence. The statistical theory is also applied to a two-time velocity correlation to derive a transport equation for the eddy viscosity. The equation is combined with the turbulent kinetic energy equation to derive a model equation for the dissipation rate. Direct numerical simulation data of isotropic and homogeneous shear turbulence are used to examine models for the dilatation dissipation and the pressure dilatation. The normalized density variance is shown to be useful to explain results from two runs of isotropic turbulence with different initial conditions.
Finite-amplitude topographic Rossby waves in a channel
Authors: Clarke S. R. , Johnson E. R.
Published: July 2002

This paper describes Rossby waves propagating along a channel with a discontinuity in potential vorticity. A finite-amplitude, long-wave equation giving the displacement of the material interface separating two constant vorticity regions is derived and solved for both steady and unsteady finite-amplitude waves. Finite-amplitude Rossby waves that propagate in the opposite direction to infinitesimal waves are identified, and the mechanism for these waves is elucidated. The full parameter space of possible flows is described quantitatively. The weakly nonlinear limit of this finite-amplitude equation is also presented, including the novel case of kink solitons in an equation with only quadratic nonlinearity.
Flow visualization of Taylor-mode breakup of a viscous liquid jet
Authors: Tsai Shirley C. , Luu Patrick , Tam Patrick , Roski Gerald , Tsai Chen S.
Published: July 2002

We recently reported a new spray technique called ultrasound-modulated two-fluid (UMTF) atomization and the pertinent “resonant liquid capillary wave (RLCW) theory” based on linear models of Taylor-mode breakup of capillary waves. In this article, flow visualizations of liquid jets near the nozzle tip are presented to verify the central assumption of the RLCW theory that the resonant liquid capillary wave in UMTF atomization is initiated by the ultrasound at the nozzle tip. Specifically, a bright band beneath the nozzle tip was seen in ultrasonic and UMTF atomization separately, but not in two-fluid atomization. The bright band can be attributed to scattering of laser light sheet by the capillary waves generated by the ultrasound on the intact liquid jet. As the capillary wave travels downstream in the direction of airflow, it is amplified by the air blowing around it and eventually collapsed into drops. Therefore, the jet breakup time can be determined by dividing the measured band length with the capillary wave velocity. The breakup times thus determined for water and glycerol/water jets are twice the values predicted by the modified Taylor’s model with a sheltering parameter, and are one order of magnitude shorter than those in conventional two-fluid atomization. Furthermore, the images of the spray in the proximity of the nozzle tip obtained by 30 ns laser pulses are consistent with the drop sizes obtained 2.3–6 cm downstream from the nozzle tip by 13 s time average of continuous laser light. Also reported in this article is the good agreement between the measured viscosity effects on the drop-size and size distribution in UMTF atomization and those on the relative amplitude growth rates of capillary waves at different wavelengths predicted by Taylor’s model as a result of its inclusion of higher order terms other than the first in viscosity. These new findings have led to the conclusion that UMTF atomization occurs via Taylor-mode breakup of capillary waves; secondary atomization and drop coalescence are negligible. Further, UMTF atomization offers a means to control the drop-size and size distribution of two-fluid atomization for uniform drop formation.
Statistics of pressure and of pressure-velocity correlations in isotropic turbulence
Authors: Biferale L. , Gualtieri P. , Toschi F.
Published: July 2002

Some pressure and pressure-velocity correlations in a direct numerical simulations of a three-dimensional turbulent flow at moderate Reynolds numbers have been analyzed. We have identified a set of pressure-velocity correlations which possess a good scaling behavior. Such a class of pressure-velocity correlations is determined by looking at the energy-balance across any sub-volume of the flow. According to our analysis, pressure scaling is determined by the dimensional assumption that pressure behaves as a “velocity squared,” unless finite-Reynolds effects are overwhelming. The SO(3) decompositions of pressure structure functions has also been applied in order to investigate anisotropic effects on the pressure scaling.
Convective amplification of drift-acoustic waves in sheared flows
Authors: Waelbroeck F. L. , Dong J. Q. , Horton W. , Yushmanov P. N.
Published: July 2002

The evolution of wave packets is investigated in a cold-ion plasma model with sheared magnetic and velocity fields. Wave packets may be amplified by the drift Kelvin–Helmholtz mechanism even when the velocity shear is such that normal modes are stable. It is shown that the logarithm of the convective amplification can be an order of magnitude greater than the logarithm of the steady-state amplification often taken as the measure of convective instability. For a given wave number, the maximum of either of these amplifications decreases only as the inverse of the perpendicular component of the velocity shear.
Mode coupling theory in ablative Rayleigh–Taylor instability
Authors: Hasegawa Susumu , Nishihara Katsunobu
Published: July 2002

The weakly nonlinear stage of the ablative Rayleigh–Taylor instability has been investigated by expanding the one-fluid and one-temperature equations to second order. Mode coupling of linear growing perturbations with wave numbers kA and kB and corresponding growth rates γA and γB excite a long-wavelength perturbation with wave number k0=kA−kB. Time evolution of the excited perturbation has been studied for two cases, the first having no initial perturbation with the wave number k0 and the second having a finite perturbation. In both cases, parts of the excited perturbation are initially convected out from an ablation surface toward the first and second sonic points. In the latter case, the perturbation grows initially with a linear growth rate and later with the growth rate γA+γB. Mass flows across an ablation surface, which determine deformation of the surface, are investigated in detail. Calculated mass flows to first and second order are found to be quite different.
Radial profile of diffusion-controlled He positive columns
Authors: Kimura T. , Kano A. , Ohe K.
Published: July 2002

The radial profile of electron temperature deduced from the measured electron energy distribution function (EEDF) is investigated in an axially homogeneous He positive column and compared with a theoretical one calculated from the electron energy balance equation. The radial shift of the measured EEDF can be explained by the effect of the ambipolar potential.
Interface localized instabilities in resistive magnetohydrodynamics
Authors: Lortz D. , Spies G. O.
Published: July 2002

Modes localized at a plasma–vacuum interface are studied in plane slab equilibria by using resistive magnetohydrodynamics. Such modes are unstable whenever the current density and the magnetic field are not perpendicular to each other in the interface. The perturbations have no radial nodes but large mode numbers in the other two directions. The instability occurs for a wide range of angles between the nodal lines and the magnetic field lines in the interface and does not depend on the presence of a mode resonant surface.
The stability of a stochastic plasma with respect to low frequency perturbations
Authors: Hurricane Omar A. , Pellat René , Coroniti Ferdinand V.
Published: July 2002

Following the suggestion that substorm breakup might be caused by an interchange or ballooning instability, several magnetohydrodynamic (MHD) and gyrokinetic stability analysis have been performed for plasma sheet magnetic field geometries. However, the stochastic ion dynamics in the highly stressed, thin high-β near earth plasma sheet violate the locality requirements of MHD and the invariance of the magnetic moment, μ, required by gyrokinetic theories. In this paper, a proper quadratic form energy principle (for low frequency modes ω<ωb, ωb being the bounce frequency) which includes the dynamics of stochastic ions is developed, and it is demonstrated that the stochastic plasma is less stable than the corresponding adiabatic plasma.
Nonlinear growth rate of Langmuir waves in the case of a wide spectrum
Authors: Ragot Brigitte R. , Shklyar David R.
Published: July 2002

A nonlinear equation for the evolution of a Langmuir harmonic in a wide spectrum is derived in a consistent manner. This equation substitutes the usual quasilinear growth rate of the weak plasma turbulence theory. The derivation is based on the determination of the resonant particle distribution through the solution of the exact nonlinear equations of motion in a given field, composed of all effectively acting harmonics. The method requires a slow variation of the harmonic amplitudes over the nonlinear characteristic time of resonant interaction, and small enough amplitudes for the averaging method to be applicable. Two nonlinear terms appear in this equation: one is proportional to the particular harmonic considered, the other is a contribution from the whole effective spectrum around this harmonic. From this last term, it follows that a wave with negligible initial amplitude can grow spontaneously through the nonlinear wave–particle interaction.
Chaotic particle motion and halo formation induced by charge nonuniformities in an intense ion beam propagating through a periodic quadrupole focusing field
Authors: Qian Qian , Davidson Ronald C. , Chen Chiping
Published: July 2002

A test-particle model is used to investigate the charged-particle dynamics in an intense matched ion beam with nonuniform density profile propagating through an alternating-gradient quadrupole focusing field in the space-charge-dominated regime. It is shown that self-field nonlinearities due to the transverse nonuniformity in the beam density profile not only can result in chaotic ion motion but also can cause halo formation by the ejection of particles from the beam core. The structure of the particle phase space is studied. It is shown that the process of halo formation can occur on a fast time scale—on the order of a few lattice periods. The halo size is found to be determined by a Kolmogorov–Arnold–Moser (KAM) surface on a time scale much shorter than that of Arnold diffusion.
Poloidal edge-plasma rotation driven by angular momentum transfer originating from charge exchange in the scrape-off layer of a tokamak
Authors: Vaessen P. H. M. , van Toledo W.
Published: July 2002

A possible new driving mechanism for poloidal plasma rotation in the scrape-off layer (SOL) of a tokamak is proposed. This driving mechanism results from charge exchange between ‘‘cold’’ hydrogen atoms from the wall and ‘‘hot’’ plasma ions in the SOL, where the consequent loss of microscopic angular momentum is compensated by an increase of the macroscopic rotation of the edge plasma. Balancing the increase by viscous damping, inherent to the toroidal geometry of the tokamak, gives values for the poloidal rotation velocity, which are in good agreement with experimental results.
Comment on ‘‘On the Alfvén resonance and its existence’’ [Phys. Plasmas 2, 340 (1995)]
Authors: Bellan P. M.
Published: July 2002

The validity of the Alfvén resonance concept in a real plasma is discussed since experiments are performed on real plasmas and not on MHD plasmas. (AIP)
Second harmonic electromagnetic emission via Langmuir wave coalescence
Authors: Willes A. J. , Robinson P. A. , Melrose D. B.
Published: July 2002

The coalescence of Langmuir waves to produce electromagnetic waves at twice the plasma frequency is considered. A simplified expression for the rate of production of second harmonic electromagnetic waves is obtained for a broad class of Langmuir spectra. In addition, two different analytic approximations are considered. The validity of the commonly used head-on approximation is explored, in which the two coalescing Langmuir waves are assumed to approach from opposite directions. This approximation breaks down at low Langmuir wavenumbers, and for narrow Langmuir wave spectra. A second, more general, approximation is introduced, called the narrow-spectrum approximation, which requires narrow spectral widths of the Langmuir spectra. The advantages of this approximation are that it does not break down at low Langmuir wavenumbers, and that it remains valid for relatively broad Langmuir wave spectra. Finally, the applicability of these approximations in treating harmonic radiation in type III solar radio bursts is discussed.
Self-consistent nonlinear theory of a premodulated electron beam propagating through a drift tube
Authors: Uhm Han S.
Published: July 2002

A self-consistent nonlinear theory of the current and energy modulations in an electron beam propagating through a grounded drift tube is developed. The theoretical analysis is based on the assumption that each beam segment has a prescribed current profile at the drift tube entrance. A closed integrodifferential equation for beam current is obtained in terms of time and propagation distance. Properties of the current and energy modulations are investigated from the integrodifferential equation for a broad range of system parameters. The current modulation amplitude decreases, reaches its minimum value, and increases as the beam propagates downstream. By linearizing the integrodifferential equation for beam current for small modulation, it is shown that the current modulation in the linear regime is a sum of the forward and backward density waves. On the other hand, the energy modulation in the linear regime is a difference between the forward and backward density waves. Several points are noteworthy from the current and energy modulations in the linear regime. First, the maximum current modulation occurs at the propagation distance, where the forward and backward density waves have the same intensity and sign. The corresponding energy modulation is zero. Second, the maximum energy modulation occurs at the propagation distance, where the forward and backward density waves almost cancel each other and where the corresponding current modulation is least. Third, wavelength of the amplitude oscillation in modulations increases with beam energy and decreases with beam intensity.