bluuebunny/crossref_metadata_2025 huggingface dataset:
On linear evolution of unstable disturbances in a plane turbulent wake
Authors: Marasli B. , Champagne F. H. , Wygnanski I. J.
Published: July 2002

The evolution of sinuous perturbation waves in the turbulent wake of a flat plate is investigated. The Strouhal number of the perturbations is chosen so that the waves remain amplified over the entire range of measurements. Detailed comparisons between linear stability theory and the phase-averaged measurements of the coherent velocity field are presented. Initially, before significant amplification of the perturbation amplitude occurs, the agreement between the linear theory and the measurements is good. The measured amplitude and phase distributions of the streamwise and lateral components of the coherent or wave-induced velocity field as well as the coherent Reynolds stress show excellent agreement with their linear theory counterparts. The coherent Reynolds stress, which is generated through a nonlinear interaction between the fundamental mode and the mean flow, augments the turbulent Reynolds stress causing the spreading rate of the wake to increase. However, this nonlinear interaction does not affect the shape of the mean velocity profile in the early stages of amplification. The linear theory predictions deteriorate with increasing downstream distance because of nonlinearity and the stronger interaction with the turbulent field as the neutral point of the perturbation is approached. For the unforced flow, the peak in the measured spectrum of the cross-stream (turbulent) velocity fluctuations at any downstream location (in the far wake) corresponds to the local neutral frequency from linear, spatial stability theory for inviscid, parallel flow.
Onset of wavy vortices in the finite-length Couette–Taylor problem
Authors: Edwards W. S. , Beane S. R. , Varma S.
Published: July 2002

The transition from Taylor vortex flow to wavy vortex flow in the Couette–Taylor problem, for finite annulus lengths, is studied. Using an accurate, fully resolved numerical code, infinite-cylinder nonlinear axisymmetric Taylor vortices are computed and their stability with respect to nonaxisymmetric disturbances corresponding to wavy vortices is determined. The present method computes leading eigenmodes and eigenvalues for arbitrary axial Floquet exponents k and arbitrary azimuthal wave numbers m, so that the full complex dispersion relation ω=ω(k,m) is obtained. The linear coefficients appearing in the Ginzburg–Landau equation are calculated and compared to previous experimental results. It is found that for aspect ratios (length to gap width) less than 30, the Ginzburg–Landau predictions are not reliable; for these aspect ratios the transition is modeled as the superposition of two Floquet modes with k=±π/L, where L is the length of the annulus. This model is verified via a detailed numerical and experimental study at aspect ratios between 8 and 34, for radius ratio 0.87, obtaining good agreement for the critical Reynolds numbers, azimuthal wave numbers and wave speeds over the entire aspect-ratio range.
Experiments on instabilities in curved channel flow
Authors: Matsson O. John E. , Alfredsson P. Henrik
Published: July 2002

Experimental results are reported from hot-wire measurements in a narrow gap, curved air channel with a spanwise aspect ratio of 29. The Reynolds numbers (Re) covered a range from 2 to 6.5 times the critical Re, i.e., the Re for which the flow becomes centrifugally unstable according to linear stability theory. For the lowest Re studied, the measurements showed a regular flow pattern of streamwise vortices, whereas at higher Re interaction occurred between vortex pairs. The streamwise disturbance velocity increased rapidly near the inlet section, thereafter the disturbance amplitude overshot before it finally reached a saturated level of the nonlinear stage. At even higher Re a secondary instability in the form of traveling waves appeared on top of the primary instability and was found to be localized between one pair of vortices at the inflow region from the concave wall.
Relaxation of discrete rotational energy distributions using a Monte Carlo method
Authors: Boyd Iain D.
Published: July 2002

A new model is presented for simulating rotational energy relaxation in the direct simulation Monte Carlo method (DSMC) using discrete distributions. The method extends the phenomenological approach generally employed that simulates the distribution as a continuum. The discrete approach simulates the mechanics of relaxation for the rigid rotor model. The theory is developed and combined for use with an existing model for simulating the rate of rotational relaxation. A number of test problems are then considered. Each set of flow conditions is chosen because of the availability of experimental data. Some of the experimental measurements provide rotational energy distributions thus allowing detailed comparison with the numerical simulations. Generally, the comparisons are quite favorable, although it is indicated that more sophisticated models are required to simulate some of the detailed structure of the energy distributions observed experimentally.
Fractal properties of isovelocity surfaces in high Reynolds number laboratory shear flows
Authors: Praskovsky Alexander A. , Foss John F. , Kleis Stanley J. , Karyakin Mikhail Yu.
Published: July 2002

The fractal properties of isovelocity surfaces are studied in three high Reynolds number (Rλ≊2.0×102–3.2×103) laboratory shear flows using the standard box-counting method. The fractal dimension D=−d(log Nr)/d(log r) was estimated within the range of box sizes r from several Kolmogorov scales up to several integral scales (Nr is the number of boxes with size r required to cover the line intersection of an isovelocity surface). The inertial subrange was of particular interest in this investigation. Measurements were carried out for external intermittency factors γ≊0.6–1.0. The data were processed using threshold levels U±2.5u′ (U and u′ denote mean and rms values of longitudinal velocity). Over the parameters studied, no wide range of constant fractal dimension was found. On the other hand, the accuracy of constant fractal dimension approximation with D≊0.4 over the inertial subranges was shown to be similar to that of the Kolmogorov [Dokl. Akad. Nauk SSSR 30, 301 (1941)] ‘‘two-thirds law.’’
Goertler vortices with system rotation: Linear theory
Authors: Zebib Abdelfattah , Bottaro Alessandro
Published: July 2002

The equations which describe a boundary layer on a curved wall in a rotating system are derived and a linear stability analysis of a basic Blasius velocity profile is performed. Rotation can be either stabilizing or destabilizing corresponding to whether a rotation number is negative or positive, respectively. The stability boundaries at different rotation numbers and curves of constant positive growth rates are presented. It is shown that the flow is completely stabilized when the rotation number is ≤−1 in agreement with an inviscid Rayleigh-type analysis. For the cases examined growth rates increase linearly, in the initial phase, with streamwise distance.
The flow of suspensions in channels: Single files of drops
Authors: Zhou Hua , Pozrikidis C.
Published: July 2002

The flow of a periodic suspension of two-dimensional viscous drops between two parallel plane walls is considered, and a framework for performing dynamic simulations with suspensions of increasingly complex structure is developed. The computations are based on an improved implementation of the boundary integral method which is coined the method of interfacial dynamics. An elementary configuration is considered in detail in which the suspension is composed of a periodic array of suspended drops arranged on a single file, and the flow is driven by the relative motion of the two walls. The motion is studied as a function of the capillary number, the viscosities of the fluids, and the drop size. The transition from the small-drop behavior, where the effects of the walls are insignificant, to the large-drop behavior, where the drops occupy almost the whole of the clearance between the walls, is illustrated. It is found that, in all cases, the suspension exhibits a shear-thinning behavior and some type of elasticity. The single-file arrangement is unstable to subharmonic perturbations in which the drops are displaced in an alternating fashion across the centerline of the channel. The evolution of the perturbed array may lead to oscillatory motions including orbiting and bypassing, or to formation of a double file of nearly stationary drops. The effects of drop interactions on the effective properties of the suspension are discussed.
Wave energy flow conservation for propagation in inhomogeneous Vlasov–Maxwell equilibria
Authors: Kull H. J. , Berk H. L. , Morrison P. J.
Published: July 2002

Wave energy flow conservation is demonstrated for Hermitian differential operators that arise in the Vlasov–Maxwell theory for propagation perpendicular to a magnetic field. The energy flow can be related to the bilinear concomitant, for a solution and its complex conjugate, by using the Lagrange identity of the operator. This bilinear form obeys a conservation law and is shown to describe the usual Wentzel–Kramers–Brillouin (WKB) energy flow for asymptotically homogeneous regions. The additivity and lack of uniqueness of the energy flow expression is discussed for a general superposition of waves with real and complex wave-numbers. Furthermore, a global energy conservation theorem is demonstrated for an inhomogeneity in one dimension and generalized reflection and transmission coefficients are thereby obtained.
Structure and evolution of small-amplitude intermediate shock waves
Authors: Kennel C. F. , Blandford R. D. , Wu C. C.
Published: July 2002

A simplified set of equations is derived that approximates the magnetohydrodynamic (MHD) Navier–Stokes equations for weakly nonlinear disturbances whose speeds are close to the MHD intermediate speed. Its shock structure solutions are then examined. The fast and slow shock solutions are uniquely specified by their Rankine–Hugoniot relations. However, the intermediate shock solutions, which are not unique, are characterized by the integral through the shock of the noncoplanar component of the magnetic field. For situations in which this integral is conserved, the Riemann problem is well defined and predicts the evolution of intermediate shocks. This analysis is substantiated by numerical computations.
The mechanism of sawtooth precursors and sawtooth relaxations
Authors: Rogister André , Kaleck Armin , Psimopoulos Michalis , Hasselberg Günter
Published: July 2002

It is shown that certain specific properties are requested from the current density profile in order to arrive at a coherent theoretical explanation of the sawtooth phenomenon in tokamaks: (1) the shear ŝ must be small at the q=1 surface (hence the current density profile has a plateau or shoulder in the neighborhood of q=1); (2) J′ varies abruptly not far away from q=1 (in particular, the outer edge of the plateau is close to q=1). Indeed, when these conditions are satisfied, the contribution to the jump of the derivative of the magnetohydrodynamic (MHD) solution ([Ψ′]r1) from those terms that are proportional to ε2 (ε is the inverse aspect ratio) is not negligible. It is, moreover, opposite in sign to the usual contribution ([Ψ(0)′]r1∝ŝ1) so that the inverse of the logarithmic jump 1/Δ′∝Ψr1/[Ψ′]r1 can now take on either positive values (ŝ1>ŝ1,c), or negative ones (ŝ1<ŝ1,c), or can ‘‘diverge’’ (1/Δ′→±∞ for ŝ1→ŝ1,c).

The growth rate reaches very large values when 1/Δ′→−∞ (i.e., [Ψ′]r1→0−) and its rapid acceleration observed shortly before the crash can now be explained: The ontology of the sawtooth rise and crash requires indeed that ŝ1 always be smaller than ŝ1,c (hence, 1/Δ′<0 opposite to conventional wisdom!) and approach this value from below at the onset of the collapse. Current density [Plasma Physics and Controlled Nuclear Fusion Research 1986 (IAEA, Vienna, 1987), Vol. 1, p. 263] as well as density [Controlled Fusion and Plasma Physics 1989 (EPS, Geneva, 1989), Vol. 13 B, II-565] plateaus and shoulders have been observed in TEXTOR discharges. This and other comparisons with experiment, including the acceleration rate of the perturbation, are discussed. Analysis of the particle trajectories in the perturbed magnetic structure yields an amplitude criterion for the onset of collapse that agrees well with observations on TEXTOR. The ontology of the crash phase requires an ambipolar electric field to build up inside the q=1 surface so that only suprathermal electrons are lost. This enables the calculation of ratios of the density, current density, and electron temperature crashes; these are found to agree with the measured ratios. Theory finally suggests that the sawtooth limitation of the central temperature is not unavoidable.
Nonlinear absorption of intense laser light by collective plasma excitations
Authors: Rae Stuart C. , Burnett Keith
Published: July 2002

The absorption of high-intensity laser light in a plasma has been studied with the aim of calculating the collective contribution to the inverse bremsstrahlung process. This contribution arises from the electron cloud oscillating, at the laser frequency, through the almost stationary distribution of ions. Plasma waves can be excited and their energy dissipated through subsequent collisions. The calculation is performed in a frame where the electrons are stationary and the oscillatory motion is transferred to the ions. The expression derived for collective absorption involves a sum over multiphoton terms, and shows resonances whenever the plasma frequency is an exact multiple of the laser frequency. When compared with the standard inverse bremsstrahlung expression, it shows that collective effects only become significant in the extreme intensity limit.
The theory of final focusing of intense light ion beams
Authors: Watrous J. , Ottinger P. F. , Mosher D.
Published: July 2002

Efficient transport of the high-power light ion beams of interest to inertial confinement fusion (ICF) experiments may require the use of large radius transport channels. The mismatch in the radii of the transported ion beam and the ICF target requires that the beam be focused following transport. A theoretical description of intense light ion beam focusing with a z-discharge plasma is presented. The theory is based on a Vlasov equation description of a fully charge- and current-neutralized ion beam, neglecting any angular momentum of the beam ions. An initial ion beam phase-space distribution with adjustable parameters is considered so that its effect upon the phase-space distribution at the focal plane can be analyzed. A numerical code is used to analyze the effect of angular momentum on the focusing properties of the final focusing cell. The theoretical analysis gives expressions for the focal length, for the discharge current required to produce a given degree of focusing, and for the radial number density profiles at the focal plane. The analysis of angular momentum indicates that the focal length and focusing current are not strongly affected even when beam ions have a significant amount of angular momentum.
Kinetic double layers in a two electron temperature multi-ion plasma
Authors: Baboolal S. , Bharuthram R. , Hellberg M. A.
Published: July 2002

A recent large-amplitude fluid theory of electrostatic ion-acoustic double layers [J. Plasma Phys. 40, 163 (1988)] is shown to be adaptable to the case of stationary double layers in a two-ion plasma with kinetically determined ions. The influence of ion temperature and light-ion concentration on the double-layer structure is studied and directly compared with fluid theory predictions. The role of the ion trapping parameter is examined. It is found that departure from fluid theory can be explained as being due to the influence of ion Landau damping and/or ion trapping. Extension of the theory to multielectron and multi-ion plasmas is pointed out.
Generation of efficient ultrafast laser-plasma x-ray sources
Authors: Murnane Margaret M. , Kapteyn Henry C. , Falcone Roger W.
Published: July 2002

When a subpicosecond laser is focused onto the surface of a solid, a high-density, short-lived plasma is created. Experimental observations demonstrate that subpicosecond laser-produced plasmas can generate subpicosecond x-ray pulses under the right conditions. The plasma x-ray emission extends over a broad spectral bandwidth and arises mainly from continuum emissions in the high-density plasma. Such a plasma source can be very efficient because almost 90% of the excitation laser energy can be coupled into the solid target and used to heat the target electrons to high temperature.
Skin size electromagnetic drift mode and anomalous transport
Authors: Hirose A.
Published: July 2002

A low-β tokamak discharge is unstable against skin size electromagnetic drift modes. The growth rate peaks at k⊥≂ωpe/c with a maximum growth rate of the order of the ion acoustic transit frequency. The quasilinear particle flux is radially inward (anomalous pinch) if η (the temperature gradient) ≳1. The proposed anomalous electron thermal diffusivity exhibits a good agreement with those inferred from several tokamaks both in magnitude and in reproducing the radial profile, and predicts that the energy confinement time should improve in discharges with heavier ions (the isotope effect).
Harmonic generation and departure from quasineutrality in ion sound and Langmuir wave coupling
Authors: Mounaix Philippe , Laval Guy , Mora Patrick , Pesme Denis
Published: July 2002

The validity conditions of the Zakharov equations are reconsidered by investigating the linear stability analysis of a dipolar Langmuir wave. It is shown that the corresponding dispersion relation has a wider range of applicability, W/NT<(kλD)−2, than the usual domain of validity of the Zakharov equations, W/NT<1 (W/NT is the ratio of the Langmuir wave energy to the particle thermal energy, k is the characteristic wave number of the low-frequency perturbation). This result follows from an exact cancellation between the corrections as a result of the departure from quasineutrality and the contributions from the harmonics of the Langmuir wave. Such a cancellation is interpreted in terms of absence of nonlinear frequency shift caused by a dipolar pump wave in the dispersion relation of the Langmuir waves. The next-order corrections to the linearized Zakharov equations are computed; the proper renormalization of the low-frequency part of the dispersion relation is shown to result from the slow time variation and finite temperature corrections in the coupling constants.
Nonlocal theory of lower-hybrid drift instability for a plasma shell expanding into a magnetic field
Authors: Gladd N. T. , Brecht Stephen H.
Published: July 2002

A two-fluid, nonlocal theory of the lower-hybrid drift instability is developed for a plasma shell expanding into a magnetic field. The plasma is assumed cold and the induced cross-field current is entirely due to the deceleration of the plasma by the magnetic field. Attention is focused on physically realistic cases where the cross-field electron velocity has a single-jet or double-jet profile. Lower-hybrid drift eigenmodes are found to be localized where the transverse wave velocity is resonant with the cross-field electron velocity. This is markedly different from previously analyzed cases where the cross-field velocity is constant and eigenmode localization is near the maximum of ‖d ln n(x)/dx‖. For double-jet cross-field velocity profiles there is a rich set of eigenmodes associated with the double-well localizing structure. Despite the different localizing mechanism and more complicated nature of eigenmodes, the parametric dependencies of the frequency and growth rate are quite similar to those obtained for constant cross-field velocity profiles. Specifically, it is found that the transverse wave number of the most rapidly growing eigenmode generally scales as kmax∼V−1/2, where V is a measure of the magnitude of the cross-field electron velocity. This scaling is approximately the same for constant, as well as single and double-jet cross-field velocity profiles. The robustness of this weak scaling of kmax with V implies that the long wavelength structures experimentally observed on expanding plasma shells are not likely to be explained by including realistic geometry effects within linear lower-hybrid drift instability theory.
Point vortex description of drift wave vortices: Dynamics and transport
Authors: Kono M. , Horton W.
Published: July 2002

A point vortex description for drift wave vortices is formulated based on the Hasegawa–Mima equation to study elementary processes for the interactions of vortices as well as statistical properties like vortex diffusion. Dynamical properties of drift wave vortices known by numerical experiments are recovered. Furthermore, an empirical expression for the vortex diffusion given by Horton [Phys. Fluids B 31, 524 (1989)] based on numerical simulations is shown to be analytically obtained. A variety of phenomena arising from the short-range nature of the interaction force of point vortices are suggested.
Characteristics of a Z-pinch produced from a glass optical fiber
Authors: Figura E. S. , McCall G. H. , Dangor A. E.
Published: July 2002

A Z-pinch discharge in a quartz fiber (20–125 μm diameter) driven by a 150 kA current with a rise time of 50 nsec has been investigated. The pinch was found to develop an m=0 instability during the time of current rise and before the whole fiber had been formed into a plasma. No anomalously stable behavior was seen. The bright spots associated with the instability expanded radially and moved in the axial direction with typical velocities of a few 106 cm sec−1. A coronal plasma was found to exist with density 1016 cm−3 at a radius 500 μm. There was evidence of an energetic (20 keV) electron beam. The observed plasma expansion and ionization agreed well with a one-dimensional magnetohydrodynamic simulation. The simulation showed that the light which was observed to be generated in the core of the optical fiber was due to shock heating. The predicted temperature of the surface of the plasma was also in good agreement with an estimate of the temperature (25±8 eV) obtained by assuming that the light emission was blackbody.
On the definition of Pfirsch–Schlüter and bootstrap currents in toroidal systems
Authors: Coronado M. , Wobig H.
Published: July 2002

In the plasma physics literature there appear two different definitions of Pfirsch–Schlüter current. One of them is predominantly used in equilibrium calculations and satisfies the condition IT=0. The other definition appears commonly in transport calculations and requires that the surface average of the dot product of the Pfirsch–Schlüter current density with the magnetic field vanish, i.e., 〈JPS⋅B〉=0. The difference between the definitions is a surface function. Within the framework of the moment equation approach, the total parallel current is completely determined through a surface average of Ohm’s law; thus different definitions of Pfirsch–Schlüter current imply different expressions for the bootstrap current. Understanding the different implications of these two definitions is of particular importance when designing toroidal devices with minimized Pfirsch–Schlüter current or studying tokamaks with optimized bootstrap current. In this paper the definitions of Pfirsch–Schlüter and bootstrap current, as well as the expressions for the corresponding Pfirsch–Schlüter diffusion flux, are analyzed and discussed for the case of axisymmetric and nonaxisymmetric plasmas. Although in cases like a current-free stellarator or a large-aspect-ratio tokamak both definitions are equivalent, they are in general different, and in order to avoid misunderstandings it is therefore important to use only one. The most appropriate definition is IT=0. In this paper the equations for determining the bootstrap current within the framework of the fluid equations are also analyzed.
Nonlinear relativistic interaction of an ultrashort laser pulse with a cold plasma
Authors: Rax J. M. , Fisch N. J.
Published: July 2002

The nonlinear, relativistic dynamics that results when intense (1018 W/cm2 and above) and ultrashort (one plasma period or shorter) laser pulse travels through a cold underdense plasma is investigated. Using a Lagrangian analysis of the plasma response, it can be demonstrated that the nonlinear wake, the collective dissipation, the nonlinear Compton losses, and the harmonic generation, are all determined by a finite set of integrated scalar quantities. This result holds for one-dimensional, short pulses of arbitrary amplitude, shape, and polarization, so that these very short intense laser pulses in a plasma can be viewed essentially as a quasiparticle characterized by a small set of global parameters.
Energetic particle modified Mercier criterion
Authors: Zheng Lin-jin , Tsai Shih-tung
Published: July 2002

The Mercier criterion is obtained from the ballooning mode equation resulting from the generalized kinetic energy principle. Drift nonreversal of the energetic particles is assumed in order to obtain a sufficient stability criterion. The criterion is valid for three-dimensional configurations. Contributions of the energetic component are recovered and in several interesting cases our result gives stabilizing effects additional to the rigid model result.
Self-similar magnetic field penetration of a homogeneous collisionless plasma due to electron velocity advection
Authors: Oliver B. V. , Rudakov L. I. , Mason R. J. , Auer P. L.
Published: July 2002

The velocity advection, me(ve⋅∇)ve, terms in the momentum equation for electrons in a collisionless plasma are shown to introduce an effective resistivity on the currents drawn from a bounding cathode. This leads to nonlinear diffusive penetration of an externally driven magnetic field, which at time t and height y above the cathode, penetrates to a depth δ obeying the scaling δ∼(t/y)1/3.
Linear theory of non-neutral plasma equilibrium in a tilted magnetic field
Authors: Spencer R. L. , Hart G. W.
Published: July 2002

A linear perturbation expansion has been found that allows the rapid and accurate calculation of the response of a non-neutral plasma to a tilted magnetic field. The results of the calculation have been found to agree with previous three-dimensional equilibrium calculations, and also to agree with Keinigs’ [Phys. Fluids 24, 860 (1981)] calculation of zero-frequency resonances caused by magnetic field errors. This expansion also allows the perturbed velocity to be calculated. It is speculated that this perturbed flow may be related to the enhanced radial transport in a non-neutral plasma with a tilted magnetic field.
Electric field in the edge layer of field-reversed configurations
Authors: Chiang Pi-Ren , Hsiao Ming-Yuan
Published: July 2002

A particle-tracing routine is used to find the boundary surface of the confinement region in velocity space. This numerical boundary surface is then imposed on the distribution function to calculate the electric potential profile around the X point in field-reversed configurations (FRC’s). The model eliminates the original assumptions of the fast loss of the unconfined particles and free end-throat electric field in deriving the analytical confinement criteria in the velocity-space particle loss (VSPL) model. Electric potential profiles over the whole region with different particle-tracing times are presented. According to the calculated results, a new hypothetical electrostatic confinement in the edge layer is proposed. Effects resulting from this electrostatic confinement are investigated. It is found that several physical issues in the edge layer can be explained by this hypothetical electrostatic confinement.
Theory of drift-thermal instability-induced turbulence
Authors: Ware A. S. , Diamond P. H. , Carreras B. A. , Leboeuf J.-N. , Lee D. K.
Published: July 2002

A simple model for drift-thermal instability-induced turbulence is derived and studied both analytically and numerically. Both nonlocal, nonlinear analytical calculations and three-dimensional computations are used. Potential and temperature fluctuation levels and radial correlation lengths are calculated and compared to numerical results. The saturation mechanism and the role of a fluctuation-generated shear flow are elucidated. The numerical calculations are used to obtain spectra and correlation lengths. A detailed comparison of analytical and numerical results is given.
An experimental study of magnetic islands as Hamiltonian systems
Authors: Gandy R. F. , Hartwell G. J. , Hanson J. D. , Knowlton S. F. , Lin H.
Published: July 2002

Magnetic islands play an important role in determining plasma transport in toroidal magnetic confinement systems. The magnetic error fields and the associated islands can be theoretically described by a Hamiltonian approach. Experiments have been conducted on the Compact Auburn Torsatron [Fusion Technol. 18, 281 (1990)] to test the applicability and limits of the first-order Hamiltonian theory to magnetic islands. A novel set of helical trim coils with the same spatial periodicity as an ι– = 1/2 magnetic island were used to create a perturbation field of variable magnitude and phase. Extensive experimental parametric studies of the magnetic island were conducted and compared with theory. It was found that the first-order Hamiltonian theory is applicable for the complete range of experimental error fields.
Long-wavelength microinstabilities in toroidal plasmas*
Authors: Tang W. M. , Rewoldt G.
Published: July 2002

Realistic kinetic toroidal eigenmode calculations have been carried out to support a proper assessment of the influence of long-wavelength microturbulence on transport in tokamak plasmas. In order to efficiently evaluate large-scale kinetic behavior extending over many rational surfaces, significant improvements have been made to a toroidal finite element code used to analyze the fully two-dimensional (r,θ) mode structures of trapped-ion and toroidal ion temperature gradient (ITG) instabilities. It is found that even at very long wavelengths, these eigenmodes exhibit a strong ballooning character with the associated radial structure relatively insensitive to ion Landau damping at the rational surfaces. In contrast to the long-accepted picture that the radial extent of trapped-ion instabilities is characterized by the ion-gyroradius-scale associated with strong localization between adjacent rational surfaces, present results demonstrate that under realistic conditions, the actual scale is governed by the large-scale variations in the equilibrium gradients. Applications to recent measurements of fluctuation properties in Tokamak Fusion Test Reactor (TFTR) [Plasma Phys. Controlled Nucl. Fusion Res. (International Atomic Energy Agency, Vienna, 1985), Vol. 1, p. 29] L-mode plasmas indicate that the theoretical trends appear consistent with spectral characteristics as well as rough heuristic estimates of the transport level. Benchmarking calculations in support of the development of a three-dimensional toroidal gyrokinetic code indicate reasonable agreement with respect to both the properties of the eigenfunctions and the magnitude of the eigenvalues during the linear phase of the simulations of toroidal ITG instabilities.
A theory of space-charge limiting current for a relativistic electron beam
Authors: Uhm Han S.
Published: July 2002

A theory of the space-charge limiting current is developed for a relativistic electron beam propagating through a grounded conducting cylinder. The beam electron density is assumed to be uniform. It is found that the propagating current depends very sensitively on the current density profile. Moreover, the self-consistently evaluated limiting current is considerably larger than the conventionally estimated value.
Particle simulation of the kinetic Kelvin–Helmholtz instability in a magnetoplasma
Authors: Cai D. , Storey L. R. O. , Itoh T.
Published: July 2002

The kinetic Kelvin–Helmholtz instability in a collisionless magnetoplasma is simulated numerically in cases where the ion gyroradius is comparable with or larger than the spatial scale of the cross-field shear. The approach consists of starting the simulation from a state close to equilibrium, then observing the linear growth of instabilities and their ultimate saturation. The initial quasiequilibrium state is set up by a newly developed particle loading method; the instabilities are excited by numerical noise. The simulation is performed in two dimensions, in the plane perpendicular to the magnetic field, using an electrostatic particle code. The results for the kinetic Kelvin–Helmholtz instability are similar to those predicted by a hydromagnetic model, except that they depend slightly on the sign of the shear. Other instabilities are observed also: when the ion gyroradius is small on the scale of the shear, there is an unidentified short-wavelength instability characterized by k Δx≥1, where k is the wave number in the flow direction and Δx is the spatial scale of the shear; when the ion gyroradius is large, Bernstein waves, both ionic and electronic, are excited in the flow direction.
The dynamics of spectral transfer in a model of drift wave turbulence with two nonlinearities
Authors: Newman D. E. , Terry P. W. , Diamond P. H. , Liang Y.-M.
Published: July 2002

The spectral transfer dynamics of two-dimensional (2-D) drift wave turbulence over a broad range incorporating long- and short-wavelength extremes is studied numerically in the context of dissipative trapped electron convective cell turbulence. The direction, locality, and isotropy of energy and enstrophy transfer in wave-number space are determined by examining energy and enstrophy transfer rates, the enstrophy generation rate, spectra, and the spectrum response to perturbative impulses. Energy transfer is characterized by two subranges, according to the dominant nonlinearity, and a dynamically complex crossover region dividing the subranges. In the long-wavelength E×B subrange, energy transfer is nonlocal and anisotropic, proceeding to shorter wavelengths with significant generation of enstrophy. In the short-wavelength polarization drift subrange, energy transfer is local and, in the absence of sources and sinks, is dominated by an inverse cascade, consistent with the near conservation of enstrophy on dynamical time scales. In the crossover region, there is isotropic nonlocal forward transfer, as well as cascading to long wavelength. A significant shift of the frequency spectrum peak in the crossover region is shown to result from the cross coupling of the two nonlinearities. The shift is in the electron diamagnetic direction and increases with increasing wave number, consistent with the behavior of the renormalized response function. The simulation model does not incorporate the effects of electron inertia, and therefore does not account for the feedback of the frequency shift on nonlinear mode stability. Nevertheless, the simulations provide numerical validation of many aspects of the accompanying analytical investigation [Liang et al., Phys. Fluids B 5, 1128 (1993)].
Skin current driven microinstabilities in a magnetized plasma
Authors: Farengo R. , Lee Y. C. , Guzdar P. N.
Published: July 2002

Currents flowing parallel to a magnetic field with a gradient in the perpendicular direction are present in many interesting situations in plasma physics. In Ohmic heated experiments the current gradient is accompanied by a temperature gradient, and it is shown that both gradients can drive unstable, low-frequency, localized modes. These modes are studied using various models for the electron and ion dynamics (including an integral formalism that retains finite ion gyroradius effects) and considering the effects of density gradients and collisions. A detailed numerical study of the parametric dependence of the mode frequency and structure and a mechanism for anomalous current penetration are presented.
Quasi-steady-state toroidal discharges
Authors: Bevir M. K. , Gimblett C. G. , Miller Guthrie
Published: July 2002

A method for maintaining toroidal current in toroidal plasmas is discussed. The method requires application of suitably phased oscillating toroidal and poloidal voltages to the plasma resulting in a magnetic field configuration with small oscillations around some mean state. In such quasi-steady states the usual v sec limitation on discharge duration is eliminated. The current drive effect is caused by a nonlinear interaction between the toroidal and poloidal circuits that can be understood in general terms from symmetry considerations. Specific calculations of the effect are made using two models: (1) a zero-dimensional relaxation model, relevant to the reversed-field pinch, and (2) a one-dimensional resistive diffusion model (assuming slab geometry). The results for the relaxation model indicate a useful current drive effect that may be of importance for the reversed-field-pinch program.
Simulation of the ion-beam-driven drift instability in a magnetic trap. I
Authors: Thomas V. A. , Nevins W. M. , Chen Y. J.
Published: July 2002

Recent experiments on the TMX-U device, at the Lawrence Livermore National Laboratory have indicated the possibility of a drift wave being driven unstable by the injection of neutral beams in the thermal barrier region. A review of linear theory is presented in the local approximation. In addition, particle simulations are used to understand the nonlinear characteristics of this instability. The particle simulations are performed using 1d-3v and 2d-3v electrostatic particle simulation codes. The instability is shown to saturate by beam trapping, nonlinear electron effects, and nonlinear motion parallel to the density gradient. Resonant E×B motion is a significant process for some of the beam particles. This process is closely associated with the trapping of beam ions. Harmonic generation is also observed, as appears in some of the experimental data. Qualitative nonlinear theory is presented in support of the particle simulations.
The possibility of a resonance mechanism in the developing two-dimensional jet
Authors: Thomas F. O. , Goldschmidt V. W.
Published: July 2002

An experimental investigation of a developing planar turbulent jet discharging into a quiescent environment was undertaken. The measurements now reported suggest that the pressure field associated with the large-scale flow structures occurring downstream excite the nascent jet shear layers near the jet exit. Such structures are characterized by the formation of an antisymmetric structural array near the end of the potential core and extending far into the similarity region. The results suggest that coupling or feedback between downstream coherent structures and the initial region may be important in the development of the flow.
Instability at the interface between two shearing fluids in a channel
Authors: Renardy Yuriko
Published: July 2002

The linear stability of plane Couette flow composed of two immiscible fluids in layers is considered. The fluids have different viscosities and densities. For the case of equal densities, there is a critical Reynolds number above which the interfacial mode of the bounded problem is approximated by that of the unbounded problem for wavelengths that are not short enough to be in the asymptotic short-wavelength range, as well as for short waves. The full linear analysis reveals unstable situations missed out by the long- and short-wavelength asymptotic analyses, but which have comparable orders of magnitudes for the growth rates. For the case of unequal densities, it is found that the arrangement with the heavier fluid on top can be linearly stable if the viscosity stratification, volume ratio, surface tension, Reynolds number, and Froude number are favorable.
Quadratic resonance in the three-dimensional oscillations of inviscid drops with surface tension
Authors: Natarajan Ramesh , Brown Robert A.
Published: July 2002

The moderate-amplitude, three-dimensional oscillations of an inviscid drop are described in terms of spherical harmonics. Specific oscillation modes are resonantly coupled by quadratic nonlinearities caused by inertia, capillarity, and drop deformation. The equations describing the interactions of these modes are derived from the variational principle for the appropriate Lagrangian by expressing the modal amplitudes to be functions of a slow time scale and by preaveraging the Lagrangian over the time scale of the primary oscillations. The equations describing the motion of axisymmetric resonant modes are integrable. Stochastic motions are predicted for nonaxisymmetric deformations starting from most initial conditions, even those arbitrarily close to the axisymmetric shapes. The stochasticity is characterized by a redistribution of the energy contained in the initial deformation over all the degrees of freedom of the interacting modes.
Almost two-dimensional strong turbulence in a magnetized plasma
Authors: Rosenbluth M. N. , Sudan R. N.
Published: July 2002

From the direct interaction approximation (DIA) equations for strong turbulence it is shown that low-frequency fluctuations constituting two-dimensional strong turbulence in a magnetized plasma scatter off each other to develop a finite spread in wave vectors along the magnetic field and are thereby Landau-damped. A transport equation in (k⊥,k∥) space is developed that determines the wave spectrum under these conditions.
Onset and decay of two-dimensional magnetohydrodynamic turbulence with velocity–magnetic field correlation
Authors: Grappin R.
Published: July 2002

Direct numerical simulations of two-dimensional magnetohydrodynamic (MHD) flows propagating in a mean uniform magnetic field, with correlated velocity and magnetic fields are discussed. A high correlation inhibits the amount of excitation transferred to small scales, showing steeper spectral slopes at very high correlation, as in previous closure calculations. The growth of the correlation coefficient between kinetic and magnetic fields is attributed to the nondefinite positiveness of the cross correlation, which reverses its sign at small scales, because of nonlinear interactions between large and small scales in the MHD equations.
Ion-acoustic solitary waves in two-temperature electron plasmas
Authors: Das G. C. , Paul S. N. , Karmakar B.
Published: July 2002

By using the reductive perturbation technique, a modified Korteweg–deVries (KdV) equation aids in the study of the solitary wave solution in a nonisothermal two-temperature electron plasma. The results indicate the solitary wave solution in the plasma with isothermal electrons, and finally a link with the solitons existing in both cases is made. Moreover, general comparisons and conclusions are made on the ion-acoustic waves in the plasma with several ionic species and multiple electrons.
Application of unsteady aerodynamics to large-eddy breakup devices in a turbulent flow
Authors: Balakumar Ponnampalam , Widnall Sheila E.
Published: July 2002

The modifications to the vertical velocity of a turbulent flow by the large-eddy breakup devices (LEBU) were analyzed using linear three-dimensional unsteady aerodynamics. A Fourier component of the input turbulence convected over these devices was considered and the modified vertical velocity in the far downstream wake was solved. It is shown that the amplitude of the vertical velocity behind the device is reduced, the effect increasing with increasing stream and spanwise wavenumber. Two plates placed far apart in series produce a reduction that is the square of that for a single plate. The presence of the ground plane decreases the effectiveness of the LEBU in reducing the amplitude of the vertical velocity in the far wake.
Large amplitude ion holes
Authors: Dupree Thomas H.
Published: July 2002

Earlier work [Phys. Fluids 25, 277 (1982); Phys. Fluids 26, 2460 (1983)] on the structure and growth of phase space density holes for ψ=−qiφ/Ti<1 is extended to ψ>1. As in the ψ<1 case, it is found that reflecting electrons cause the ion holes to decelerate and grow, although the details are quite different. The reflected electrons cause the formation of a so-called ‘‘double layer.’’ It is shown that isolated (intermittent) ion holes or wave packets can grow to much larger amplitudes than that predicted by the conventional quasilinear plateau limitation or Manheimer’s [Phys. Fluids 14, 579 (1971)] trapping criteria.
Ambipolarons: Solitary wave solutions for the radial electric field in a plasma
Authors: Hastings D. E. , Hazeltine R. D. , Morrison P. J.
Published: July 2002

The ambipolar radial electric field in a nonaxisymmetric plasma can be described by a nonlinear diffusion equation. This equation is shown to possess solitary wave solutions. A model nonlinear diffusion equation with a cubic nonlinearity is studied. An explicit analytic step-like form for the solitary wave is found. It is shown that the solitary wave solutions are linearly stable against all but translational perturbations. Collisions of these solitary waves are studied and three possible final states are found: two diverging solitary waves, two stationary solitary waves, or two converging solitary waves leading to annihilation.
The dielectric function for the Balescu–Lenard–Poisson kinetic equations
Authors: Jasperse J. R. , Basu B.
Published: July 2002

By using the propagator expansion method applied to an electon–ion plasma near thermal equilibrium, a closed-form solution is found for the high-frequency, collisional dielectric function in the electrostatic approximation to the first order in the plasma parameter when the Balescu–Lenard collision operator [Phys. Fluids 3, 52 (1960); Ann. Phys. (N.Y.) 3, 390 (1960)] is used to describe electron–electron and electron–ion collisions. The Balescu–Lenard dielectric function is shown to be an entire function of the complex frequency variable ω. Since an exact solution for the collisional propagator for the Balescu–Lenard problem is probably impossible, these results illustrate the usefulness of the propagator expansion method as a way of obtaining the dielectric function for collisional plasmas. A comparison is made between the Balescu–Lenard result for the plasma conductivity as the wave vector k → 0 and the Guernsey result, obtained by Oberman, Ron, and Dawson [Phys. Fluids 5, 1514 (1962)]. By solving the Balescu–Lenard dispersion relation in the long wavelength approximation, a formula is obtained for the total damping rate for Langmuir waves Γk, which is the sum of the collisionless (Landau) part γLk and the collisional part γνk. A numerical solution of the Balescu–Lenard dispersion relation has also been performed, and the analytical and numerical results for the damping rates are compared at long wavelengths. Comparisons of the Balescu–Lenard damping rate to the quantum mechanical result obtained by Dubois, Gilinsky, and Kivelson [Phys. Rev. Lett. 8, 419 (1962)] and to other results are also made.
Symmetry properties of a multidimensional dispersion functional
Authors: Schwarzmeier J. L. , Barnes D. C. , Lewis H. R. , Seyler C. E.
Published: July 2002

Symmetry properties are presented for a multidimensional dispersion functional. If the system of linearized Vlasov-field equations is ‘‘completely Hamiltonian,’’ the dispersion operator satisfies a certain formal self-adjointness property as a function of omega. For appropriate boundary conditions this implies a relation between an eigenfunction and its dual. If the equilibrium admits ‘‘conjugate orbits’’ for a completely Hamiltonian system and if the ‘‘conjugate-orbit parity condition’’ is satisfied, then the kinetic part of the dispersion matrix is symmetric. For this case and for appropriate boundary conditions the entire dispersion matrix for the multispecies Vlasov or Vlasov-fluid models is symmetric. It then follows that the complex conjugate of the dual eigenfunction is proportional to the eigenfunction itself. The analytic continuation of the dispersion functional of the linearized Vlasov-field equations into the lower half of the frequency plane is derived.