bluuebunny/crossref_metadata_2025 huggingface dataset:
The inverse boundary problem for the Rayleigh system
Authors: Beals Richard , Henkin G. M. , Novikova N. N.
Published: July 2002

The inverse matrix Sturm–Liouville problem associated to the classical Rayleigh system is studied. This problem differs from previously investigated ones in several ways: the matrix potential is not Hermitian, the spectral parameter occurs also in the boundary condition, and both the potential and boundary condition depend also on a frequency parameter. We characterize all symmetries and identities satisfied by the corresponding scattering data and deduce an integral equation of the Gelfand–Levitan type that solves the inverse Rayleigh boundary problem. On the basis of these results we propose to study the interesting asymptotic properties of the Rayleigh boundary problem for large values of the frequency ω.
Diffusion through a slab
Authors: Mahan G. D.
Published: July 2002

Boltzmann’s equation is solved for the diffusion of nonabsorbing particles through a thick slab. The dimensionless thickness D=dμs, where d is the thickness and μs is the rate of scattering. Our solution neglects terms of order O(e−D) and is exact in the limit that D≫1. Simple expressions are obtained for the reflection and transmission coefficients, as well as for the angular distributions on the front and back sides of the slab.
On Poisson–Lie structure on the external algebra of the classical Lie groups
Authors: Arutyunov G. E. , Medvedev P. B.
Published: July 2002

The general expression for the bicovariant bracket for odd generators of the external algebra on a Poisson–Lie group is given. The graded Poisson–Lie structures derived before for GL(N) and SL(N) are shown to be the special cases of this bracket. The formula is universal and can be applied to any matrix Lie group.
On the convergence of the inverse diffraction transform kernel using Cesàro summability
Authors: Pallotta M.
Published: July 2002

In diffraction tomography, optical information processing, and, more generally, Fourier optics, the diffraction transform solves both the direct and the inverse boundary value propagation problem for the Helmholtz equation. Its kernel is itself an integral. It is the representation of the evolution operator associated with translations of a constrained Cartesian coordinate. This fact threatens the inverse scattering problem with a divergence if the transform kernel is understood as a Cauchy integral. The kernel is, however, everywhere convergent if its integral representation is interpreted as a summable integral.
Higher-dimensional algebra and topological quantum field theory
Authors: Baez John C. , Dolan James
Published: July 2002

The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of n-category suited for this purpose, and outline a program in which n-dimensional topological quantum field theories (TQFTs) are to be described as n-category representations. First we describe a ‘‘suspension’’ operation on n-categories, and hypothesize that the k-fold suspension of a weak n-category stabilizes for k≥n+2. We give evidence for this hypothesis and describe its relation to stable homotopy theory. We then propose a description of n-dimensional unitary extended TQFTs as weak n-functors from the ‘‘free stable weak n-category with duals on one object’’ to the n-category of ‘‘n-Hilbert spaces.’’ We conclude by describing n-categorical generalizations of deformation quantization and the quantum double construction.
Classification of unitary and grade star irreps for U
q
(osp(2‖2n))
Authors: Links J. R. , Gould M. D.
Published: July 2002

All the unitary and grade star irreps of the quantum supergroup Uq(osp(2‖2n)) are classified in terms of their highest weight labels.
Topological Yang–Mills theory with scalar and vector fields in two and three dimensions
Authors: Hwang Dae Sung , Lee Chang-Yeong
Published: July 2002

We study the topological Yang–Mills theory of scalar and vector fields in two and three dimensions in the superconnection framework. We modify the horizontality condition in such a way that we can take care of the topological symmetry of the δAμ=βμ type, as well as the usual gauge symmetry of the δAμ=Dμc type. We then obtain a complete set of BRST and anti-BRST transformation rules of the component fields in a systematic way.
Structure of matrix manifolds and a particle model
Authors: Kocik Jerzy , Rzewuski Jan
Published: July 2002

The decomposition of matrix manifolds into homogeneous spaces of certain groups is studied in some detail. The results are applied to the derivation of the internal structure of SU(2,2)×SU(m)- and P4×SU(m)-invariant particle models where the first (second) factor in the direct product represents external (internal) symmetry.
The identities of the algebraic invariants of the four-dimensional Riemann tensor
Authors: Sneddon G. E.
Published: July 2002

It is well known that there are fourteen independent algebraic invariants of the four-dimensional Riemann tensor. Several authors have written down a set of fourteen independent invariants, but it is still not known how other invariants can be expressed in terms of these sets. This paper investigates this problem by looking for relationships between invariants of the Riemann tensor. Essentially the problem turns out to be analogous to finding relationships between the invariants of two 3×3 matrices, one of which is symmetric and trace-free and the other Hermitian. A number of identities between the invariants can be obtained simply by using a generalization of the Cayley–Hamilton theorem but others, which depend on the symmetry of the matrices, are considerably more complex.
On the solutions of the CP1 model in (2+1) dimensions
Authors: Grundland A. M. , Winternitz P. , Zakrzewski W. J.
Published: July 2002

We use the methods of group theory to reduce the equations of motion of the CP1 model in (2+1) dimensions to sets of two coupled ordinary differential equations. We decouple and solve many of these equations in terms of elementary functions, elliptic functions, and Painlevé transcendents. Some of the reduced equations do not have the Painlevé property. The existence of a Lax pair, making the model integrable, is hence very unlikely, even though it possesses many properties of integrable systems (such as stable ‘‘numerical solitons’’).
Wave scattering in one dimension with absorption
Authors: Aktosun Tuncay , Klaus Martin , van der Mee Cornelis
Published: July 2002

Wave scattering is analyzed in a one-dimensional nonconservative medium governed by the generalized Schrödinger equation d2ψ/dx2+k2ψ=[ikP(x)+Q(x)]ψ, where P(x) and Q(x) are real, integrable potentials with finite first moments. Various properties of the scattering solutions are obtained. The corresponding scattering matrix is analyzed, and its small-k and large-k asymptotics are established. The bound states, which correspond to the poles of the transmission coefficient in the upper-half complex plane, are studied in detail. When the medium is not purely absorptive, i.e., unless P(x)⩽0, it is shown that there may be bound states at complex energies, degenerate bound states, and singularities of the transmission coefficient imbedded in the continuous spectrum. Some explicit examples are provided illustrating the theory.
Heisenberg chain systems from compact manifolds into S2
Authors: Wang You-De
Published: July 2002

In this paper, it is shown that the initial value problems of Heisenberg Spin Chain Systems with external magnetic field from compact Riemannian manifolds into S2 admit global weak solutions.
Hamiltonian systems on k-cosymplectic manifolds
Authors: de León Manuel , Merino Eugenio , Oubiña José A. , Rodrigues Paulo R. , Salgado Modesto R.
Published: July 2002

The Hamiltonian framework on symplectic and cosymplectic manifolds is extended in order to consider classical field theories. To do this, the notion of k-cosymplectic manifold is introduced, and a suitable Hamiltonian formalism is developed so that the field equations for scalar and vector Hamiltonian functions are derived.
Brownian motion of quantum harmonic oscillators: Existence of a subdynamics
Authors: Lindblad Göran
Published: July 2002

The effects of system-environment correlations on the dynamics of an open quantum system are investigated for the standard model of a set of quantum harmonic oscillators interacting with a heat bath of oscillators. By definition, a subdynamics is described by transformations of the open system observables. It is shown that such a construction can reproduce the observable properties of the exact dynamics only when the states of system and environment are uncorrelated, while for classical systems there is always a subdynamics. A quantum subdynamics cannot have the properties we associate with thermal fluctuations; the KMS relation at a finite temperature for the open system implies that the system must be closed. The conditions for having a subdynamics as a good approximation to the exact closed dynamics are investigated, and so are the similar but stronger conditions for a Markovian dynamics. It is also shown that a subdynamics defines the response of the open system to some types of time dependent external forces.
Covariant phase observables in quantum mechanics
Authors: Lahti Pekka , Pellonpää Juha-Pekka
Published: July 2002

In this paper we characterize all the phase shift covariant normalized positive operator measures, i.e., phase observables, and we investigate some of their examples. We also characterize those phase observables which arise from the phase space observables as their polar coordinate angle margins.
New vacuum solutions of conformal Weyl gravity
Authors: Dzhunushaliev V. , Schmidt H.-J.
Published: July 2002

The Bach equation, i.e., the vacuum field equation following from the Lagrangian L=CijklCijkl, will be completely solved for the case that the metric is conformally related to the Cartesian product of two two-spaces; this covers the spherically and the plane symmetric space–times as special subcases. Contrary to other approaches, we make a covariant 2+2-decomposition of the field equation, and so we are able to apply results from two-dimensional gravity. Finally, some cosmological solutions will be presented and discussed.
The motion of droplets in a vertical temperature gradient
Authors: Hähnel Michael , Delitzsch Volkmar , Eckelmann Helmut
Published: July 2002

The thermocapillary migration of single water droplets in butyl benzoate was investigated using the Plateau configuration. The droplets were injected below the level of equal density in the stably stratified butyl benzoate. Because of buoyancy and Marangoni force, the droplets rise until these forces balance each other. For seven different temperature gradients the final position of four to eight single droplets was determined. The reciprocal diameter was found to be a linear function of the deflection from the height of equal density. A systematic deviation from the theory of Young, Goldstein, and Block [J. Fluid Mech. 6, 350 (1959)] was observed. This deviation was attributed to the convective heat transport inside and outside the droplet not covered by the theory. The experimental data could be fitted by introducing an effective temperature gradient that decreases with the square of the applied gradient.
A passive scalar convected by homogeneous axisymmetric turbulence
Authors: Nakauchi Norihiko , Oshima Hiroshi , Saito Yoshio
Published: July 2002

A passive scalar convected by homogeneous axisymmetric turbulence is studied using the eddy-damped quasinormal Markovian (EDQNM) approximation to obtain a determinate set of equations for scalar-variance and turbulence energy spectra. The study is confined to a turbulent field in which cross correlations between the scalar and velocity fluctuations are zero, so that scalar flux is absent. Our broad objective is to study the effect of anisotropy of homogeneous axisymmetric turbulence and the subsequent return toward isotropy for a passive scalar field. In particular, the dependence of the scalar decay rate on the anisotropy strength of turbulence and the invariant III is examined. Numerical results are shown for cases where the initial Reynolds number with respect to the Taylor microscale is Rλ(t=0)=107 and the Prandtl number Pr=1.
Organized motion in a very high Reynolds number jet
Authors: Mungal M. G. , Hollingsworth D. K.
Published: July 2002

Direct visual observations of a high Reynolds number jet are presented. The jet consists of the exhaust plume of a TITAN IV rocket motor, which was discharged upward during ground-based testing producing an estimated Reynolds number of about 2×108. An overall view of the first 2000 ft of the resulting plume is observed and discussed. Image processing is used to enhance the plume appearance and reveal significant events associated with the jet evolution. The most striking finding is the progression of organized structures up through the jet, similar to those observed in laboratory flows at Reynolds numbers of 104. Significant differences are also seen between the time-averaged scalar field, which appears more Gaussian, and the instantaneous scalar field, which appears more top hat. It is concluded that the organization is associated with inviscid instability mechanisms that are Reynolds number independent, and that large-scale organization is an integral part of the evolution of such flows, and not a remnant of transitional behavior.
Viscous interlayer structure and transport properties in von Kármán swirling flows
Authors: Zhang K. , Goddard J. D.
Published: July 2002

This paper is a discussion of the thin viscous regions that separate the nearly inviscid cellular domains arising at large Reynolds number in von Kármán swirling flow. A review and extension are given of previous analyses of the inviscid structure and the associated critical-layer structure that occurs in the regime of small positive radial pressure gradients. It is first shown that the inviscid perturbation analysis can be cast into an analytical closed form, from which an explicit expression for the first-order viscous correction at arbitrary pressure gradients is obtained. By then allowing for negative pressure gradients, of the kind associated with weakly stagnating flows, the present analysis serves to describe the transition from the Prandtl-layer structure characteristic of stagnation-dominated flows to a diffuse viscous damping associated with rotation-dominated flows. Finally, it is shown that, in a discretely stratified flow, the hydrodynamic transition to the critical-layer structure involves a hydrodynamic ‘‘freezing’’ of the interface, which is accompanied by an interesting transition in the interfacial mass-transport characteristics, with the asymptotic Nusselt number changing from (Pe)1/2 abruptly to (Pe)1/3 dependency on the Péclet number Pe.
The velocity-dissipation probability density function model for turbulent flows
Authors: Pope S. B. , Chen Y. L.
Published: July 2002

In probability density function (pdf) methods, statistics of inhomogeneous turbulent flow fields are calculated by solving a modeled transport equation for a one-point joint probability density function. The method based on the joint pdf of velocity and fluid compositions is particularly successful since the most important processes—convection and reaction—do not have to be modeled. However, this joint pdf contains no length-scale or time-scale information that can be used in the modeling of other processes. This deficiency can be remedied by considering the joint pdf of velocity, dissipation, and composition. In this paper, by reference to the known properties of homogeneous turbulence, a modeled equation for the joint pdf of velocity and dissipation is developed. This is achieved by constructing stochastic models for the velocity and dissipation following a fluid particle.
Influences of swirl on the structure and extinction of strained premixed flames. Part I: Moderate rates of rotation
Authors: Libby Paul A. , Williams Forman A. , Sivashinsky Gregory I.
Published: July 2002

The characteristics of isenthalpic planar premixed flames in counterflowing, high Reynolds number streams with counter- and corotating swirl are analyzed by activation energy asymptotics for a one-step Arrhenius reaction with small departures from unity Lewis numbers. Density changes resulting from heat release are fully taken into account. For moderate rates of rotation, the situation considered in the present study, there is only one stagnation plane that is coincident with the plane of symmetry separating the inviscid outer flows and that involves a viscous layer with an embedded flame in some circumstances. The analysis of a flame in the viscous layer is relevant to the experimentally observed variation of the lean flammability limit with the rotation rate. Comparison with the existing experimental data is carried out.
Dynamics of two-dimensional turbulence
Authors: Viecelli J. A.
Published: July 2002

Mixing of Lagrangian particles by a vortex singularity is shown to correspond to a continuous curdling process with the Lipschitz–Hölder exponent equal to (4)/(3) , demonstrating that Richardson’s l4/3 scaling is derivable from the two-dimensional kinematics of the vortex singularity. Scaling relationships describing the Lagrangian geometry of two-dimensional turbulence are linked to the rate of enhanced diffusion. The value of the two-dimensional intermittency exponent μ= (2)/(3) , derived from the author’s Lagrangian structure function theory [Phys. Fluids A 1, 1836 (1989)], when used in the Lévy flight theory of enhanced diffusion developed by Shlesinger et al. [Phys. Rev. Lett. 58, 1100 (1987)] predicts 〈R2〉∝t2.6 for the time rate of separation of labeled pairs of vortices in two dimensions. This is found to be in good agreement with the rate of dispersion measured in numerical simulations of inviscid two-dimensional turbulence. Kinetic theory arguments, supplemented by the previously derived Lagrangian structure relationships, yield an asymptotic P∝s−5/3 probability distribution function for path lengths s between vortex pair collisions. This result is consistent with path length distributions obtained from the two-dimensional simulations.
Modeling the rapid spherical compression of isotropic turbulence
Authors: Coleman Gary N. , Mansour Nagi N.
Published: July 2002

Rapid distortion analysis is used to modify the form of the closure model for the dissipation rate of the turbulent kinetic energy. The modification is such that the evolution of the dissipation rate during a rapid compression is predicted exactly; good agreement between the model prediction and direct simulation data is obtained. Previous closure proposals fail to properly predict the rapid compression case. The reason for the difference between the present and previous models is traced to the fact that previous workers neglected variations of kinematic viscosity.
Comparison of experiment with a new theory of the turbulence temperature structure function
Authors: Hill Reginald J.
Published: July 2002

The theory for the structure function of an advected scalar quantity in turbulent flow by Effinger and Grossman [Phys. Fluids A 1, 1021 (1989)], is compared with data. The theoretical structure function is transformed to a spatial power spectrum, which is found to have negative values. The theory does not agree with data for the spectrum. The theory has startling differences with Batchelor’s theory [J. Fluid Mech. 5, 113 (1959)] for the viscous-diffusive and viscous-convective ranges.
The length-scale dependence of scalar mixing
Authors: Mell William E. , Kosály George , Riley James J.
Published: July 2002

Direct numerical simulations were performed to investigate scalar mixing in decaying isotropic turbulence. The results are consistent with the laboratory experiments of Warhaft and Lumley [J. Fluid Mech. 88, 659 (1978)], which showed that the asymptotic scalar decay of the variance is dependent on the initial velocity-to-scalar length-scale ratio. The results indicate that the universal scalar decay found in the simulations of Eswaran and Pope [Phys. Fluids 31, 506 (1988)] is due to the forcing of the turbulence.
High-resolution calculations of reduced waveset two-dimensional turbulence
Authors: Vázquez-Semadeni Enrique , Scalo John M.
Published: July 2002

Motivated by the possible utility of studying turbulent astrophysical flows as dynamical systems, solutions to the incompressible two-dimensional Navier–Stokes equation in Fourier space are investigated employing a small subset of Fourier modes that span a range of nearly 3000:1 in size and that preserve the triadic nature of the nonlinear interactions. These solutions thus preserve the energy and enstrophy conservation properties of the full solutions. The statistical similarity of the reduced solutions to the full solutions is tested by comparing their respective energy spectra in the energy and enstrophy inertial ranges, as well as the energy and enstrophy cascade directions. The behavior of the reduced solutions is consistent with full solutions having similar physical conditions (rates of injection and dissipation of the energy and enstrophy), while providing a computational gain of about a factor ∼1000 for kmax∼104 in two dimensions (2D) and ∼106 at kmax∼103.5 in 3D. Also, the effect and importance of the forcing on the outcome of the calculations are discussed, namely the slope of the energy spectrum and the duration of the net energy and enstrophy transfer.
Nonlinear wave coupling and subharmonic resonance in planar jet shear layer transition
Authors: Thomas F. O. , Chu H. C.
Published: July 2002

An experimental investigation of the nonlinear spectral development associated with the transition of an initially laminar planar jet shear layer is presented. The local shear layer spectral dynamics are modeled as a nonlinear system containing both linear and quadratically nonlinear system elements. A novel digital signal processing technique is applied which allows the linear and quadratically nonlinear wave coupling coefficients that characterize the local spectral dynamics to be estimated directly from time-series velocity fluctuation data. The method utilized is noniterative and explicitly includes fourth-order spectral moments. From the linear coupling coefficient, the local spatial growth rate and dispersion relation may be obtained. Of particular interest in the work reported is the associated nonlinear wave coupling coefficient which provides a measure of the efficiency of local nonlinear three-wave coupling. These show that the jet shear layer exhibits a strong preference for difference mode interactions. With the estimation of the related nonlinear power transfer function, the total, linear, and quadratic nonlinear spectral energy transfer may be locally estimated. When these measures are used in conjunction with the local quadratic bicoherency and local linear–quadratic coupling bicoherency, the local nonlinear spectral dynamics of the flow may be completely and unambiguously quantified. Particular emphasis is placed upon discerning the mechanism which gives rise to subharmonic resonance with the fundamental. Results show that the amplification of the subharmonic occurs via a parametric resonance with the fundamental rather than by direct quadratic difference interaction. That is, the subharmonic is boosted by a weakly nonlinear mechanism involving a linear growth rate modification due to a resonant phase lock with the fundamental instability.
Shear fronts in slowly varying media
Authors: Clarke S. R.
Published: July 2002

Previous studies have assumed that the propagation of shear fronts, or internal undular bores, through slowly varying changes in depth and width are described by unidirectional, unimodal models. The propagation of shear fronts is considered in the linear, nondispersive limit to show that this assumption is only valid for small changes in width, while for a continuously stratified fluid it is not a valid approximation for changes in depth. It is also shown for waves of finite extent propagating over changes in depth, that unidirectional, unimodal models will only describe the evolution of an incident first mode wave.
Precise measurement of particle–wall hydrodynamic interactions at low Reynolds number using laser interferometry
Authors: Lecoq N. , Feuillebois F. , Anthore N. , Anthore R. , Bostel F. , Petipas C.
Published: July 2002

The motion of a spherical particle (with radius 1 to 6 mm) in a viscous fluid is measured using laser interferometry. The typical sensitivity on the measured displacement of the sphere is of the order of 50 nm. The particle is moving on the axis of a closed cylinder. The hydrodynamic interactions between the particle and the walls of the cylinder are compared with the theoretical result of Sano [J. Phys. Soc. Jpn. 56, 2713 (1987)] valid for a very small sphere. The agreement is excellent for the smallest sphere used in the experiment. The experiment also agrees with the result from the theory of lubrication when the sphere is close to a plane end wall. The effect of the particle roughness appears at small distances. Laser interferometry appears as a useful tool to study particle–wall hydrodynamic interactions when the geometry is cumbersome.
An asymptotic theory for the nonlinear instability of antiparallel pairs of vortex filaments
Authors: Klein Rupert , Majda Andrew J.
Published: July 2002

Simplified asymptotic equations describing the nonlinear dynamics of perturbed pairs of parallel vortex filaments are derived and analyzed here. The derivations are general enough to allow for vortices of unequal strength, but emphasis here is on the antiparallel vortex pair. The simplified asymptotic equations account for both the internal effects of self-induction and self-stretching for each filament and also the external effects of mutual induction that lead to a nontrivial coupling of the perturbations of the two filaments. When these nonlinear equations are linearized at the unperturbed filament pair, the linearized stability theory of Crow [AIAA J. 8, 2172 (1970)] is recovered in a systematic fashion. The asymptotic equations are derived in a novel singular limit at high Reynolds numbers through assumptions similar to the authors’ recent theories [Physica D 49, 323 (1991); ibid. 53, 267 (1991); Phys. Fluids A 4, 2271 (1992)] for the dynamics of a single perturbed vortex filament. Through the Hasimoto transform [J. Fluid Mech. 51, 477 (1972)], these equations become two coupled perturbed nonlinear Schrödinger equations for a pair of filament functions. A series of numerical solutions of the asymptotic equations exhibits several new phenomena in the nonlinear instability of pairs of antiparallel vortex filaments.
Electron energy transport by magnetic electron drift vortex waves
Authors: Shukla P. K. , Yu M. Y. , Stenflo L.
Published: July 2002

It is shown that magnetic electron drift vortex waves can cause electron energy transport in a nonuniform plasma. Using a quasilinear approach, an expression for the corresponding anomalous thermal conductivity is derived. The result may be relevant to the study of energy transport in laser-produced as well as other plasmas.
Sheath and presheath in a collisionless open-field plasma
Authors: Sato Kunihiro , Miyawaki Fujio , Fukui Wakumi
Published: July 2002

The plasma–sheath equation for a collisionless plasma with a finite-temperature particle source in a nonuniform open magnetic field is formulated. The plasma equation is solved analytically and the plasma–sheath equation is also solved numerically for various profiles of the magnetic field. The potential formed in the plasma depends considerably on the profile of the magnetic field strength; the potential drop in the presheath increases and the ion distribution function widens as the magnetic field strength decreases in the direction of the plasma flow. Application of the generalized Bohm criterion shows that the solution of the plasma equation always satisfies this criterion when the magnetic field monotonically decreases in the outside direction. The potential drop in the sheath is almost independent of the magnetic field profile, and the ion energy at a wall for a decreasing magnetic field is slightly large when compared with that for a uniform magnetic field.
Energetic particle effects on global magnetohydrodynamic modes
Authors: Cheng C. Z.
Published: July 2002

The effects of energetic particles on magnetohydrodynamic (MHD) type modes are studied using analytical theories and the nonvariational kinetic-MHD stability code (nova-k) [Workshop on Theory of Fusion Plasmas, (Societa Italiana di Fisica, Bologna, 1987), p. 185]. In particular, the problems of (1) the stabilization of ideal MHD internal kink modes and the excitation of resonant ‘‘fishbone’’ internal modes and (2) the alpha particle destabilization of toroidicity-induced Alfvén eigenmodes (TAE) via transit resonances are addressed. Analytical theories are presented to help explain the nova-k results. For energetic trapped particles generated by neutral beam injection or ion cyclotron resonant heating, a stability window for the n=1 internal kink mode in the hot particle beta space exists even in the absence of core ion finite Larmor radius effect. On the other hand, the trapped alpha particles are found to resonantly excite instability of the n=1 internal mode and can lower the critical beta threshold. The circulating alpha particles can strongly destabilize TAE modes via inverse Landau damping associated with the spatial gradient of the alpha-particle pressure.
Second stability in the ATF torsatron—Experiment and theory
Authors: Harris J. H. , Anabitarte E. , Bell G. L. , Bell J. D. , Bigelow T. S. , Carreras B. A. , Charlton L. A. , Colchin R. J. , Crume E. C. , Dominguez N. , Dunlap J. L. , Dyer G. R. , England A. C. , Gandy R. F. , Glowienka J. C. , Halliwell J. W. , Hanson G. R. , Hidalgo-Vera C. , Hillis D. L. , Hiroe S. , Horton L. D. , Howe H. C. , Isler R. C. , Jernigan T. C. , Kaneko H. , Leboeuf J. N. , Lee D. K. , Lynch V. E. , Lyon J. F. , Menon M. M. , Morris R. N. , Murakami M. , Neilson G. H. , Paré V. K. , Rasmussen D. A. , Thomas C. E. , Uckan T. , Wade M. R. , Wilgen J. B. , Wing W. R.
Published: July 2002

Access to the magnetohydrodynamic (MHD) second stability regime has been achieved in the Advanced Toroidal Facility (ATF) torsatron [Fusion Technol. 10, 179 (1986)]. Operation with a field error that reduced the plasma radius and edge rotational transform resulted in peaked pressure profiles and increased Shafranov shift that lowered the theoretical transition to ideal MHD second stability to β0≊1.3%; the experimental β values (β0≤3%) are well above this transition. The measured magnetic fluctuations decrease with increasing β, and the pressure profile broadens, consistent with the theoretical expectations for self-stabilization of resistive interchange modes. Initial results from experiments with the field error removed show that the pressure profile is now broader. These later discharges are characterized by a transition to improved (×2–3) confinement and a marked change in the edge density fluctuation spectrum, but the causal relationship of these changes is not yet clear.
Nonlocal heat transport in plasmas down steep temperature gradients
Authors: Minotti F. , Fontán C. Ferro
Published: July 2002

An analytic solution to the problem of nonlocal heat transport in plasmas by electrons whose range is not short compared to the temperature scale length is presented. The formalism extends the results of Albritton et al. [Phys. Rev. Lett. 57, 1887 (1986)] to an arbitrary ionization state Z. This simple transport scheme is checked against recent experiments in the AURORA device [Phys. Fluids B 1, 741 (1989)]. The agreement, both for the measured cold electron temperature profile and the plasma potential, is very good and comparable to the result of full kinetic calculations.
Is Onsager symmetry relevant in the transport equations for magnetically confined plasmas?
Authors: Balescu R.
Published: July 2002

A global, algebraic view of the transport processes in a magnetically confined plasma is developed. Both the neoclassical (banana) and the anomalous transport matrices are represented in a factorized form, thus separating the roles of the dynamics and of the geometric constraints. The self-adjointness of the collision operator (the sole condition for classical Onsager symmetry) is shown to be a necessary, but not sufficient condition for this symmetry in confined plasmas. The latter results for the banana transport matrix from a delicate relationship between dynamic and geometric components. This structure is not present in the anomalous transport matrix, and the Onsager symmetry is broken in this case. It is stressed that the symmetry breaking does not violate any general principles.
Can useful toroidal current be driven by classical viscoresistive Alfvén waves?
Authors: Bellan P. M. , Schalit M. A.
Published: July 2002

Simple, yet exact, analytic solutions for the shear and compressional Alfvén wave are obtained for helical magnetohydrodynamic (MHD) waves in cylindrical geometry with both resistivity and viscosity included. The current driven by all possible combinations of these waves is examined in the quasilinear regime (i.e., where the magnetic field produced by the driven current is not self-consistently included in the equilibrium where the wave equations are derived). It is found in all cases that it is not possible to drive significant bulk axial current with small amplitude wave fields. Thus, any useful low-frequency current drive scheme will have to be based on phenomena more complicated than those discussed here.
Runaway electrons as a diagnostic of magnetic fluctuations in the edge plasma of the Texas Experimental Tokamak
Authors: Myra J. R. , Catto Peter J. , Wootton A. J. , Bengtson Roger D. , Wang P. W.
Published: July 2002

Recent experimental and theoretical results are combined to explore the energy dependence of runaway and suprathermal electron diffusion. It is shown that a quasilinear theory containing both magnetic and electrostatic E×B-driven radial transport is consistent with the available experimental data, and supports the notion that magnetic turbulence dominates runaway diffusion but electrostatic turbulence dominates thermal diffusion in the edge plasma of the Texas Experimental Tokamak (TEXT) [Nucl. Technol./Fusion 1, 479 (1981)]. These observations further expand the possibilities for employing runaway or suprathermal electrons as a diagnostic of the underlying transport mechanisms in a tokamak plasma.
The effect of electron inertia on solitary waves in a plasma with an ion beam
Authors: Zhang C. Y. , Kuehl H. H.
Published: July 2002

The properties of solitary waves in a plasma with an ion beam are investigated. The two conditions for the existence of solitary-wave solutions are determined and presented graphically in parameter space. Electron inertia is shown to restrict the regime of the fast and slow beam solitary waves to beam velocities that are less than the electron thermal velocity.
Comment on ‘‘Peeling of convection cells and the generation of sheared flow’’ [Phys. Fluids B 4, 488 (1992)]
Authors: Montgomery David , Matthaeus William H.
Published: July 2002

The results of Drake et al.1 on conversion of a periodic array of Navier-Stokes vortices into shear flow are interpreted in an alternate context. Reservations are expressed concerning the computation. (AIP)
Nonresonant current drive and helicity injection by radio-frequency waves
Authors: Fukuyama A. , Itoh K. , Itoh S.-I. , Hamamatsu K.
Published: July 2002

Current drive via nonresonant interaction between radio-frequency (rf) waves and plasma is studied. The averaged force of rf waves acting on each species of a plasma can be divided into a resonant force and a nonresonant one. A part of the nonresonant force cannot be expressed by a gradient of a scalar potential and remains after integrating along the direction of the force. This force mainly acts as an internal force among plasma species and the net momentum input from the wave to the plasma is usually small. This process is not included in the conventional current drive schemes but is associated with the rf wave helicity injection. Quantitative analysis using a one-dimensional kinetic wave code is applied to waves in the ion cyclotron range of frequencies and low-frequency Alfvén waves in a large tokamak. The driven current is estimated taking account of the effect of the toroidally trapped particles. The spatial profile of the forces acting on electrons and ions as well as the driven current are obtained. The parameter dependence of the current drive efficiency on the wave number, the plasma density, the temperature, and the toroidal magnetic field is compared with the estimate based on a local analysis.
Confinement and divertor studies in Japan Tokamak JT-60U*
Authors: Hosogane N.
Published: July 2002

This paper presents confinement characteristics of H mode and high βP mode in Japan Tokamak JT-60U [Plasma Devices Operat. 1, 43 (1990)], effects of current profiles, pressure profiles and sawtooth oscillations on the operational limits and energy confinement, and divertor characteristics. The operational regime required for core plasma performance and divertor conditions is discussed on the basis of the experimental results. The main parameters achieved in confinement studies are Ti(0)=38 keV, nd(0)Ti(0)τglobalE ∼ 4.4×1020 m−3 sec keV, H factor {defined by τE/τITER89P L modeE [Nucl. Fusion 30, 1999 (1990)]}∼3 at εβP∼0.5 in high βP mode and nd(0)Ti(0)τglobalE ∼ 2.5 × 2020 m−3 sec keV in H-mode discharges with BT=4.2 T. Advantages of high q operation are suggested from studies on operational regime and confinement. The divertor study shows that a parameter ne qeff (qeff: effective safety factor) plays a role in characterizing divertor actions such as relaxing of heat flux profiles, radiation loss and deuterium recycling. High ne qeff operation is shown to be essential for the alleviation of heat load on the divertor.
Magnetic helicity and dynamos
Authors: Boozer Allen H.
Published: July 2002

A magnetic field that is maintained by the dynamo action of a conducting fluid must have a nonvanishing magnetic helicity. The constraint of helicity preservation implies that a dynamo is more easily produced if the electric potential varies in the surface of the dynamo. For the Earth the north–south potential variation should be of the order of a hundred volts. The energetics and thermodynamic efficiency of a heat-driven dynamo are also considered.
Effect of rigid toroidal rotation on the stability of a high-beta tokamak to external kink modes
Authors: Bhattacharyya S. N.
Published: July 2002

The effect of rigid toroidal rotation on the stability of a tokamak to external kink modes is examined. For simplicity a surface current model is assumed. For a high-β tokamak it is shown that to leading order the equations governing stability in the presence of rotation are identical to those for a static plasma with β replaced by β+S, where β is the plasma beta and S is a parameter which provides a measure of the rotation rate. For a circular cross-section tokamak the critical beta for stability to external kink modes in the presence of rigid toroidal rotation is given, to leading order in the inverse aspect ratio ε, by β=0.21ε−S. For an elliptical cross-section tokamak the largest critical beta is obtained for a vertical elongation of 2.2 and is given, to leading order in ε, by β=0.37ε−S. The lower limit on the kink safety factor q* or the Mercier q increases with increase in S. Quantitative estimates of this increase can be obtained from the stability boundaries for the static problem.
Wave structures in jets of arbitrary shape. I. Linear inviscid spatial instability analysis
Authors: Koshigoe Shozo , Tubis Arnold
Published: July 2002

Green function methods are used to give a practical form of the Rayleigh linear inviscid instability analysis for jets of arbitrary mean flow profile. Simple illustrations of the general methodology are given for vortex-sheet and continuous-velocity-profile shear layers. Some of the numerical results for elliptic jets are compared with those previously obtained from solutions of Mathieu’s equation in elliptic cylindrical coordinates.
The onset of eruptive processes in plasmas. I
Authors: Hesse M. , Kiessling M.
Published: July 2002

Bifurcation theory techniques are employed to compare two apparently similar models for the quasistatic evolution of isothermal current sheet equilibria in cosmic plasma structures. The limitations of the approximation of quasistatic evolution are discussed. In spite of the apparent similarity of the models the qualitative bifurcation behavior is entirely different. It is shown that one model necessarily gives a transition from quasistatic to dynamical evolution of the system, while the other is more likely to describe a slow structural transition to a neighboring stable equilibrium branch. The notion of stability employed here is based on the concept of available free energy. The results shed light on the generic properties of such models.
Stochasticity about a poloidal divertor separatrix
Authors: Skinner Darrell A. , Osborne T. H. , Prager S. C. , Park W.
Published: July 2002

The stochasticization of the magnetic separatrix caused by the presence of a helical perturbation in a poloidal divertor tokamak is illustrated by a numerical computation that traces magnetic field lines.
Effect of a strong-current ion ring on spheromak stability
Authors: Litwin C. , Sudan R. N.
Published: July 2002

The stability of a spheromak with an energetic ion ring, carrying a current comparable to the plasma current, to the tilt mode is considered. For small departures from sphericity a perturbative approach is applied to an appropriate energy principle in order to calculate the lowest nontrivial kinetic contribution of the ion ring. An analytic stability criterion is obtained. It is seen that the prolate configuration becomes more stable while the oblate one is less stable than in the absence of the ring. The prolomak becomes stable when the ring kinetic energy exceeds the magnetic energy within the separatrix.
Ponderomotive stabilization of external kink modes in tokamaks
Authors: D’Ippolito D. A.
Published: July 2002

It is shown that external kink modes in tokamaks can be stabilized by applied radio frequency (rf) waves in the ion cyclotron range of frequencies. This stabilization results from the work done by the plasma against the ponderomotive force exerted by the rf field. For a strongly evanescent surface field (such as the near field of an ion Bernstein wave coupler), the ponderomotive layer is confined to the vicinity of the plasma surface and, if sufficiently strong, influences kink stability in the same way as a close-fitting conducting wall. This effect is illustrated by deriving an analytic condition for stabilizing a single (m,n) mode in the low-beta straight tokamak model by means of a cylindrically symmetric E∥ rf field. The effects of poloidally or toroidally nonuniform rf fields are examined in a two-mode coupling perturbation analysis. This stabilization mechanism may be useful in extending the beta limit of ion-Bernstein-wave-heated tokamaks against both ideal and resistive modes.
Transition of viscous fingering patterns in polymer solutions
Authors: Makino Kyoko , Kawaguchi Masami , Aoyama Koichi , Kato Tadaya
Published: July 2002

Viscous fingering patterns of aqueous hydroxypropyl methyl cellulose (HPMC) solutions pushed by air in the Hele–Shaw cell were observed as a function of isopropyl alcohol content under a constant pressure of 15 cm H2O. A morphological transition from side branching patterns to tip splitting ones with increasing isopropyl alcohol content, accompanied with a decrease in surface tension and an increase in viscosity is found. The observed morphology transition was correlated with the dimension of the fingering pattern, as well as the average tip velocity in the fingering.
High gradient phenomena in two-dimensional vortex interactions
Authors: Yao H. B. , Zabusky N. J. , Dritschel D. G.
Published: July 2002

Hyperdiffusion, a simple linear eddy diffusivity scheme, is commonly used in atmospheric and oceanic simulations because it increases the range of inertially behaving spatial scales for a given model resolution. Compared with molecular diffusion (which is utterly negligible in the atmosphere and oceans), hyperdiffusion more sharply confines the dissipation to the smallest scales of the numerical model. But is this all that hyperdiffusion does? In this paper, the inelastic interaction of two distributed vortices of unequal size is examined. Contour surgery (CS) simulations are compared with pseudospectral (PS) simulations employing hyperdiffusion or molecular diffusion. The example illustrates what is believed to be the most fundamental characteristic of two-dimensional (2-D) (and layerwise-2-D) vortex dynamics, namely, the formation of exceedingly high vorticity gradients. There is an excellent agreement between the hyperdiffusive PS and CS calculations at early times (i.e., for a few vortex rotation periods). Thereafter, significant discrepancies develop, beginning abruptly from the time when vorticity-gradient intensification is arrested by diffusion. A rapid inward erosion of the smaller of the two vortices then takes place. This erosion takes place under the joint action of (hyper) diffusion and stripping (the peeling of the vortex periphery by the external flow). With hyperdiffusion, the erosion is accompanied by a serious numerical artifact: a climb in the peak vorticity by 30% in this example. Eventually, the erosion reaches the vortex center and the vortex is sheared into a filament. In the CS calculation, there is no erosion, no climb in peak vorticity, and the vortex appears to last indefinitely.

In the PS calculations, the viscosity or hyperdiffusion is adjusted according to the resolution to give the largest possible inertial range while ensuring numerical stability. It is found that vortices that are spanned by fewer than 10–20 grid points are eroded away in only a few vortex rotation periods (a time scale that is very much shorter than one would estimate from pure viscous decay). These findings bring into question the results of many 2- turbulence simulations using hyperdiffusion, for hyperdiffusion simulates neither inviscid dynamics nor molecular-diffusive dynamics.
Experimental investigation of Richtmyer–Meshkov instability in shock tube
Authors: Houas L. , Chemouni I.
Published: July 2002

An experimental investigation of the Richtmyer–Meshkov instability is carried out in a shock tube. The purpose of this study is to obtain information on the growth in the thickness of the turbulent mixing zone, which is induced by the impulsive acceleration of the interface between two gases of different densities. The turbulent phase of the evolution of this instability is of interest here. The thickness of the turbulent mixing zone is inferred from two different diagnostic techniques: measurements of infrared emission of CO2 and black-and-white or color schlieren photographs. Following an assessment of the diagnostic techniques, discussions of the main experimental difficulties as the presence of membrane fragments and the disturbances induced by the wall boundary layers, are given. Comparisons of the thickness and the thickness growth rate of the turbulent mixing zones obtained in the present experiments, with both experimental and theoretical results, are made. A tentative picture of the evolution in time of the turbulent mixing zone thickness has been developed. Results fall between the predictions of the linear and the t2/3 power law theories, with a tendency toward the latter one.