bluuebunny/crossref_metadata_2025 huggingface dataset:
Yang–Mills–Higgs theory on a compact Riemann surface
Authors: Noguchi Mitsunori
Published: July 2002

Jaffe and Taubes [Vortices and Monopoles (Birkhauser, Boston, 1980)] have shown the existence and uniqueness of n-vortex solutions on the complex plane. In this paper, their results are generalized to an arbitrary U(1) bundle over a compact Riemann surface with a Hermitian metric. Berger’s ‘‘nonlinear analysis’’ [Nonlinearity and Functional Analysis (Academic, New York, 1977)] has provided an effective method to prove the existence part of the main theorem of this paper.
Fractional diffusion and wave equations
Authors: Schneider W. R. , Wyss W.
Published: July 2002

Diffusion and wave equations together with appropriate initial condition(s) are rewritten as integrodifferential equations with time derivatives replaced by convolution with tα−1/Γ(α), α=1,2, respectively. Fractional diffusion and wave equations are obtained by letting α vary in (0,1) and (1,2), respectively. The corresponding Green’s functions are obtained in closed form for arbitrary space dimensions in terms of Fox functions and their properties are exhibited. In particular, it is shown that the Green’s function of fractional diffusion is a probability density.
Heisenberg and interaction representations in thermo field dynamics
Authors: Evans T. S. , Hardman I. , Umezawa H. , Yamanaka Y.
Published: July 2002

In this paper the so-called α degree of freedom appearing in thermal quantum field theory is discussed, using thermo field dynamics (TFD). This paper is confined to stationary thermal situations, both nonequilibrium and equilibrium. The main result is that when the stationary number distribution differs from the equilibrium one the use of time ordered and antitime ordered formalisms picks up α=1 and α=0, in contrast to the general belief that the Feynman diagram method is usable for any other α as well. This situation in TFD will be compared with the other approaches. The reason why the Feynman diagram method becomes available for any α in the case of the equilibrium distributions is also studied.
Topological structure of Gauss–Bonnet–Chern density and its topological current
Authors: Duan Yishi , Meng Xinhe
Published: July 2002

The decomposition of spin connection on the sphere bundle of a compact and oriented even-dimensional Riemannian manifold is detailed. It is shown that the Gauss–Bonnet–Chern form can be expressed in terms of a smooth vector field Φ and taken the form of the δ function δ(Φ). The topological current of the Gauss–Bonnet–Chern theorem and its topological structure are discussed.
Finite dimensional irreducible representations of the quantum supergroup Uq
(gl(m/n))
Authors: Zhang R. B.
Published: July 2002

Finite dimensional irreducible representations of the quantum supergroup Uq(gl(m/n)) at both generic q and q being a root of unity are investigated systematically within the framework of the induced module construction. The representation theory is rather similar to that of gl(m/n) at generic q, but drastically different when q is a root of unity. In the latter case, atypicality conditions of highest weight irreducible representations (irreps) are substantially altered, and such finite-dimensional irreps arise that do not have highest weight and/or lowest weight vectors. As concrete examples, the irreps of Uq(gl(2/1)) are classified.
Four-dimensional topological quantum field theory, Hopf categories, and the canonical bases
Authors: Crane Louis , Frenkel Igor B.
Published: July 2002

A new combinatorial method of constructing four-dimensional topological quantum field theories is proposed. The method uses a new type of algebraic structure called a Hopf category. The construction of a family of Hopf categories related to the quantum groups and their canonical bases is also outlined.
Q-analytic functions on quantum spaces
Authors: Abad A. Shafei Deh , Milani V.
Published: July 2002

In this article a different interpretation is given of the quantum plane introduced by Manin and the Q-analytic functions on its two-intervals are characterized. The A1(q) modules of Q-analytic functions defined in this article are in fact noncommutative associative algebras with unity, which can be considered as the deformations of the algebras of analytic functions on the two intervals of R2. Some results obtained by this approach are briefly mentioned.
Eigenvalue problems of Ginzburg–Landau operator in bounded domains
Authors: Lu Kening , Pan Xing-Bin
Published: July 2002

In this paper we study the eigenvalue problems for the Ginzburg–Landau operator with a large parameter in bounded domains in R2 under gauge invariant boundary conditions. The estimates for the eigenvalues are obtained and the asymptotic behavior of the associated eigenfunctions is discussed. These results play a key role in estimating the critical magnetic field in the mathematical theory of superconductivity.
A construction of Killing spinors on Sn
Authors: Lü H. , Pope C. N. , Rahmfeld J.
Published: July 2002

We derive simple general expressions for the explicit Killing spinors on the n-sphere, for arbitrary n. Using these results we also construct the Killing spinors on various AdS×Sphere supergravity backgrounds, including AdS5×S5, AdS4×S7, and AdS7×S4. In addition, we extend previous results to obtain the Killing spinors on the hyperbolic spaces Hn.
Absence of a wetting transition for a pinned harmonic crystal in dimensions three and larger
Authors: Bolthausen Erwin , Deuschel Jean Dominique , Zeitouni Ofer
Published: July 2002

We consider a free lattice field (a harmonic crystal) with a hard wall condition and a weak pinning to the wall. We prove that in a weak sense the pinning always dominates the entropic repulsion of the hard wall condition when the dimension is a least three. This contrasts with the situation in dimension one, where there is a so-called wetting transition, as has been observed by Michael Fisher. The existence of a wetting transition in the delicate two-dimensional case was recently proved by Caputo and Velenik.
Time-dependent Schrödinger equations having isomorphic symmetry algebras. I. Classes of interrelated equations
Authors: Nieto Michael Martin , Truax D. Rodney
Published: July 2002

In this paper, we focus on a general class of Schrödinger equations that are time dependent and quadratic in X and P. We transform Schrödinger equations in this class, via a class of time-dependent mass equations, to a class of solvable time-dependent oscillator equations. This transformation consists of a unitary transformation and a change in the “time” variable. We derive mathematical constraints for the transformation and introduce two examples.
Inverse scattering for inhomogeneous viscoelastic media
Authors: Cheng Chang-jun , Chen Xian-yao
Published: July 2002

In this paper, the inverse scattering problems for the full inhomogeneous viscoelastic medium are studied via the invariant imbedding technique. Special attention is paid to the propagation operators of the viscoelastic medium and the imbedding equations for these operators are derived. For the inverse scattering problems, it is shown that the reflection data can be extended from one round trip through the iscoelastic slab to arbitrary time with the help of the propagation operators, hence the reconstruction of the relaxation modulus is sufficient to be considered only in one round trip. It is also shown that only one-side measurement reflection data are not sufficient to reconstruct the relaxation modulus and the density of the medium simultaneously. The corresponding numerical examples are presented. For the case that the relaxation modulus of the medium is modeled by two independent functions, an iterative inversion procedure is proposed to recover the relaxation modulus and the density simultaneously with the input two-side normally reflection data.
Turaev–Viro invariant and 3nj symbols
Authors: Carbone Gaspare
Published: July 2002

We propose in this work a new method to construct the Turaev–Viro state sums, using a diagrammatic presentation describing surgery operation as Heegaard splittings. The resulting invariants can be connected with suitable 3nj symbols, and we evaluate them for the lens spaces.
A dominated-type convergence theorem for the Feynman integral
Authors: Johnson G. W. , Kim J. G.
Published: July 2002

A dominated-type convergence theorem is proved for the operator-valued Feynman integral defined via the Trotter product formula. This definition is intimately related to the one of Feynman and the physical setting is the same as in his original paper. The convergence result given here provides the final piece of a unifying and rather satisfactory picture of three approaches to the Feynman integral.
The contraction of SUμ(2) and its differential structures to Eκ(2)
Authors: Kosiński Piotr , Maślanka Paweł
Published: July 2002

The deformed double covering of the E(2) group, denoted by Ẽκ(2), is obtained by contraction from the SUμ(2). The contraction procedure is then used for producing new examples of differential calculi: three-dimensional left covariant calculus on both Ẽκ(2) and the deformed Euclidean group Eκ(2) and two different four-dimensional (4D)-bicovariant calculi on Ẽκ(2) which correspond to the one 4D-bicovariant calculi on Eκ(2) described by Giller et al. [Acta Phys. Pol. B 28, 1121 (1997)].
Some aspects of the classical three-body problem that are close or foreign to physical intuition
Authors: Posch H. A. , Thirring W.
Published: July 2002

We propose a simple oscillator model for the reduced three-body problem to understand the stability of orbits with small eccentricity of a light planet. It models the main short-time features for small mass ratios of the other bodies. These results are confronted with the exact mathematical analysis for stability for all times, and with computer simulation results for bigger mass ratios, where chaotic features emerge.
The quest for understanding in relativistic quantum physics
Authors: Buchholz Detlev , Haag Rudolf
Published: July 2002

We discuss the status and some perspectives of relativistic quantum physics.
Particle physics and quantum field theory at the turn of the century: Old principles with new concepts
Authors: Schroer Bert
Published: July 2002

The present state of quantum field theory (QFT) is analyzed from a new viewpoint whose mathematical basis is the modular theory of von Neumann algebras. Its physical consequences suggest new ways of dealing with interactions, symmetries, Hawking–Unruh thermal properties and possibly also extensions of the scheme of renormalized perturbation theory. Interactions are incorporated by using the fact that the S matrix is a relative modular invariant of the interacting—relative to the incoming—net of wedge algebras. This new point of view allows many interesting comparisions with the standard quantization approach to QFT and is shown to be firmly rooted in the history of QFT. Its radical “change of paradigm” aspect becomes particularly visible in the quantum measurement problem.
Some recent progress in classical general relativity
Authors: Finster Felix , Smoller Joel , Yau Shing-Tung
Published: July 2002

In this short survey paper, we shall discuss certain recent results in classical gravity. Our main attention will be restricted to two topics in which we have been involved; the positive mass conjecture and its extensions to the case with horizons, including the Penrose conjecture (Part I), and the interaction of gravity with other force fields and quantum-mechanical particles (Part II).
Temperature singularities in reflection spectra of YBaCuO superconducting films in the infrared frequency range
Authors: Fugol I. Ya. , Svishchev V. N. , Libin M. Yu.
Published: July 2002

The reflection spectra of YBaCuO superconducting films with moderate and optimal doping are measured in the IR region (2500–10000 cm−1) by varying temperature in the interval 5–200 K. The experimental results convincingly confirm an optical response to the superconducting transition occurring at the point T=Tc and the sensitivity of optical IR spectra to the phase ordering temperature T=T*>Tc. It is found that samples with optimal doping display reproducible temperature changes at T*>Tc. It is shown that the two-component model of carriers, including light fermions and heavy bosons, is most adequate for a description of the entire body of optical data. Optical data are used for reconstructing the phase diagram for YBa2Cu3O6+x in the T vs. x coordinates.
Dynamics of electronic excitations in YBCO at low temperatures
Authors: Fugol I. Ya. , Samovarov V. N. , Libin M. Yu.
Published: July 2002

We present the results of low-temperature optical experiments (absorption and reflection) in visible and middle infrared frequency regions with epitaxial films of copper oxide materials like a Y1Ba2Cu3O6+x. Based on our data and reference data, we consider the anomalous spectral effects in HTSC having no analogy with conventional BCS superconductors: (1) the optical response to superconducting transition at Tc; (2) the spectral weight redistribution induced by chemical doping and temperature; (3) the drastic enhancement of low-temperature photodoping; (4) the long spin-structure relaxation via temperature variations seen in the optical spectra. The thorough analysis of the results obtained is fully compatible with the concept of two-component system of light and heavy carriers (holes), being in dynamical coexistence with each other. The dynamical coexistence of the intraband carriers occurs on the background of strongly correlation interrelation of the heavy quasiparticles with the optical interband (charge transfer) excitations.
Three-phonon interactions and initial stage of phonon pulse evolution in He II
Authors: Tucker M. A. H. , Wyatt A. F. G. , Adamenko I. M. , Zhukov A. V. , Nemchenko K. E.
Published: July 2002

An expression for the characteristic rate of three-phonon processes in superfluid He4, which is valid in the entire range of phonon energies where three-phonon processes are allowed is derived proceeding from the hydrodynamic Landau Hamiltonian. Possible limiting cases are analyzed and compared with the results of previous investigations. It is found that three-phonon processes completely govern the initial relaxation of a phonon pulse injected into He II by a heated solid. As a result, the equilibrium form of phonon distribution is established in the anomalous region of phonon dispersion over a time interval of the order of 10−10 s.
Field, temperature, and concentration dependences of the magnetic susceptibility of bismuth–antimony alloys
Authors: Mikitik G. P. , Sharlaı̆ Yu. V.
Published: July 2002

In the framework of the McClure model, which describes the electronic energy spectrum of bismuth and its alloys in the neighborhood of the L point of the Brillouin zone, an expression is obtained for the electron energy levels in a magnetic field. This expression is used to calculate the magnetic susceptibility of bismuth alloys at arbitrary magnetic fields. It is shown that the theoretical results are in good agreement with the entire set of published experimental data on the field, temperature, and concentration dependences of the magnetic susceptibility of bismuth–antimony alloys.
An equation of surface dynamics modeling flame fronts as density discontinuities in potential flows
Authors: Frankel M. L.
Published: July 2002

A coordinate-free equation modeling the flame front dynamics as propagation of density discontinuity within the framework of the Darreus–Landau hydrodynamical model is derived under the assumption of potential flow. The assumption is based on the observation that for slightly perturbed plane configurations the flow is irrotational if the thermal expansion of the gas is weak. A relationship with an equation obtained earlier for a slightly perturbed plane flame front is established in the case of weak thermal expansion. An invariant equation simultaneously modeling the thermal-diffusional and the hydrodynamical instabilities is suggested, which also can be reduced to earlier results in appropriate limits.
Relation between universal constants of turbulence
Authors: Qian J.
Published: July 2002

The Yakhot–Orszag relation between the turbulent Prandtl number Pt, the Kolmogorov constant Ko, and the Batchelor constant Ba [Phys. Fluids 30, 3 (1987)] should be revised to be Ba=C Ko Pt, with C=1 or 2 corresponding to two different definitions of Ba, and the experimental data of Ba is 0.5–0.8 for C=1 and 1.0–1.6 for C=2. Hence the Yakhot–Orszag prediction Ba=1.161 for C=1 [Phys. Rev. Lett. 57, 1722 (1986)] is not in agreement with experimental data.
Viscous–inviscid interaction due to the freezing of a liquid flowing on a flat plate
Authors: Higuera Francisco J.
Published: July 2002

The solidification of a liquid flowing along a flat plate whose temperature presents a step reduction from a value above to a value below the melting temperature of the liquid is shown to promote a viscous–inviscid interaction region. The structure of the flow in this region and the growth of the solid phase crust above the plate are described in the limit of high Reynolds numbers using triple-deck theory. Boundary-layer separation, which is a regular process in the framework of triple-deck theory, is shown to occur under appropriate conditions, namely for severe plate temperature reductions leading to thick solid crusts. A simplified approximate method is introduced to deal with these separated flows.
A note on the asymmetry of rotating, stratified flow past a shallow ridge
Authors: Chilakamarri Kiran B. , Foster M. R. , Hamburger Peter
Published: July 2002

Streamline patterns in experiments of Boyer and Biolley [Philos. Trans. R. Soc. London Ser. A 318, 411 (1986)] on flow past a shallow ridge on the floor of a channel in a rotating, stratified fluid exhibit a clear upstream/downstream asymmetry. In this note this question is considered and also a condition for the existence of an eddy in such flows is derived by examining the mathematical properties of the solution.
Energy transport by a turbulent plasma flow
Authors: Kleva Robert G.
Published: July 2002

The transport of energy in a magnetically confined plasma by the E×B flow generated by a spectrum of electrostatic waves is calculated. When the potential amplitude φ0 of the wave spectrum exceeds a collision-frequency-dependent threshold, eφ0/T>νi/Ωi (where νi is the ion collision frequency, Ωi is the ion cyclotron frequency, and νi/Ωi≪1), then the thermal conductivity is much larger than the classical collisional thermal conductivity. Importantly, there is no change in the character of the transport at the transition to stochasticity. The flow need not be turbulent or stochastic to affect energy confinement. Energy confinement is degraded by nonstochastic flows in which the collisionless single-particle orbits are bounded and confined, as well as by stochastic flows. Collisions always play an important role in the physics of the transport, even when the collision frequency is very small and the thermal conductivity is much larger than the classical collisional thermal conductivity. For stochastic flows, collisions act to reduce the transport rate below the collisionless rate.
The effect of bandwidth on the convective Raman instability in inhomogeneous plasmas
Authors: Guzdar P. N. , Liu C. S. , Lehmberg R. H.
Published: July 2002

The effect of bandwidth on the convective amplification of the Raman instability in the underdense, inhomogeneous plasma is investigated. For the case when the homogeneous growth rate γ0≪Δω, where Δω is the bandwidth, it is shown both analytically and numerically that there is no effect of bandwidth on the convective amplification. The reduction in the homogeneous growth rate due to the bandwidth is compensated for by an increase in the interaction region such that the convective amplification is unaffected. For γ0≳Δω there is a statistical enhancement in the amplification factor.
Large growth, planar Rayleigh–Taylor experiments on Nova
Authors: Remington B. A. , Haan S. W. , Glendinning S. G. , Kilkenny J. D. , Munro D. H. , Wallace R. J.
Published: July 2002

A set of indirect-drive experiments to study large growth Rayleigh–Taylor instability using shaped laser pulses at the Nova laser facility has been conducted. Planar foils of fluorosilicone were accelerated by x-ray ablation. The foil trajectory was measured using edge-on radiography. In separate experiments using face-on radiography, contrast in optical depth was measured as a function of time, from which the evolution of 50 μm wavelength initially sinusoidal surface perturbations was deduced. Holding other parameters fixed, the amplitude of the initial perturbation was varied by up to a factor of 30 in separate shots. The foils with the smallest initial perturbation exhibited growth factors of 75 in contrast. Foils with large initial amplitude perturbation gave growth factors of 6 or less, and displayed the ‘‘bubble-and-spike’’ shape characteristic of the nonlinear Rayleigh–Taylor instability. Comparisons of two-dimensional computer simulations with both the measured foil trajectory and the perturbation growth show good agreement, provided that a suitable opacity model is chosen. In the linear regime the observed growth rates are 60%–75% of classical, the reduction attributed primarily to ablative stabilization. The observed onset of harmonic generation, signaling the transition into the nonlinear regime, is well predicted by third-order theory.
Dusty plasma near a conducting boundary
Authors: Yu M. Y. , Saleem H. , Luo H.
Published: July 2002

The effect of dust particles or impurity ions on plasma–wall interaction is investigated using simple fluid models. It is shown that the behavior of the electrostatic potential as well as the particle densities can be considerably different from that of a two-component plasma.
Theory of continuum damping of toroidal Alfvén eigenmodes in finite-β tokamaks
Authors: Zonca Fulvio , Chen Liu
Published: July 2002

A general theoretical approach has been formulated for analyzing two-dimensional structures of high-n toroidal Alfvén eigenmodes (TAE) in large aspect-ratio, finite-β tokamaks. Here, n is the toroidal wave number and β is the ratio between plasma and magnetic pressures. The present approach generalizes the standard ballooning-mode formalism and is capable of treating eigenmodes with extended global radial structures, as well as finite coupling between discrete and continuous spectra. Employing the well-known (s,α) model equilibrium and assuming a linear equilibrium profile, the present approach has been applied to the calculation of the resonant continuum damping rate of TAE modes. Here, s and α denote, respectively, the strengths of magnetic shear and pressure gradients. In particular, it is found that there exists a critical α value, αc(s), such that, as α→αc, the continuum damping rate is significantly enhanced and, thus, could suppress the potential TAE instability.
A simple model for lower-hybrid current drive in tokamaks
Authors: Andrews P. L. , Chan V. S. , Liu C. S.
Published: July 2002

The effects of scattering by density fluctuations on the single pass lower-hybrid propagation in tokamaks for current drive are analyzed in a cylindrical plasma model with sheared magnetic field. Even for the launched N∥ spectrum peaked around 2, the turbulent scattering and propagation in the sheared field significantly modifies the N∥ spectrum so that the waves can effectively couple to slower electrons. At low densities, a small amount of the incident energy experiences a large N∥ upshift and creates a high-energy electron tail which interacts with the main part of the wave energy. At higher densities, the bulk of the wave energy is shifted in N∥ before damping resulting in lower current drive efficiencies.
Drift-Alfvén modes in high current pinches
Authors: Chu Cheng , Bard W. , Moore R. , Lee Y. C.
Published: July 2002

A field-aligned current couples the accelerated and decelerated Alfvén modes together. When the coupling is strong enough, instability results. The coupling term is proportional to the deviation from Taylor’s state. Characteristics of this instability resemble experimental observations on reversed field pinches. In the appropriate limit, these instabilities reduce to the magnetohydrodynamic kink mode.
Oscillatory instability in a Bénard problem of two fluids
Authors: Renardy Yuriko , Joseph Daniel D.
Published: July 2002

A linear stability analysis for a Bénard problem with two layers is considered. The equations are not self-adjoint. The system can lose stability to time-periodic disturbances. For example, it is shown numerically that when the viscosities and coefficients of cubical expansion of the fluids are different, a Hopf bifurcation can occur, resulting in a pair of traveling waves or a standing wave. This may have application in the modeling of convection in the Earth’s mantle.
Turbulent spots in plane Poiseuille flow–flow visualization
Authors: Alavyoon Farid , Henningson Dan S. , Alfredsson P. Henrik
Published: July 2002

The structure and spreading of turbulent spots in plane Poiseuille flow were studied through flow visualization, in the Reynolds number range 1100 to 2200 (based on centerline velocity and channel half-height). The spot spreading half-angle varied from 6° for the lowest Re to 12° for the highest Re. The propagation velocity of the rear laminar–turbulent interface was slightly above 50% of the centerline velocity. Spotsplitting, as reported in earlier studies, seems to occur only at low Re.
Experimental study of neoclassical currents
Authors: Zarnstorff M. C. , Prager S. C.
Published: July 2002

A detailed experimental study of the bootstrap and Pfirsch–Schlüter currents that are predicted by neoclassical transport theory is presented. In a toroidal octupole, on magnetic surfaces within the separatrix, the observed parallel plasma currents are in excellent quantitative agreement with neoclassical theory with regard to the spatial structure (along a magnetic surface), collisionality dependence, and toroidal magnetic field dependence. On magnetic surfaces outside the separatrix, the ion portion of the parallel current is in agreement with neoclassical theory, but the electron parallel current is observed to obtain a unidirectional component that deviates from and exceeds the theoretical prediction.
Nonlocal effects on the drift cyclotron loss cone dispersion relation in cylindrical geometry
Authors: Ferraro R. D. , Littlejohn R. G. , Sanuki H. , Fried B. D.
Published: July 2002

In carrying out a nonlocal analysis of drift cyclotron loss cone (DCLC) modes in a cylindrically symmetric plasma, a new dispersion relation branch not described by local theories has been found. The model assumes a low-β plasma column with a Gaussian density profile in a uniform magnetic field. The exact k-space integral equation is solved using a Laguerre polynomial decomposition of the eigenfunctions. It is these new modes that couple with the diamagnetic drift wave to form unstable DCLC modes, a phenomenon not predicted by local theory. The existence of these modes requires a proper treatment of the spatial variation of the equilibrium distribution function describing the ions.
The fast crash of the central temperature during sawteeth in tokamaks
Authors: Kleva Robert G. , Drake J. F. , Denton Richard E.
Published: July 2002

A simple model of the crash phase of sawteeth in tokamaks is presented, which explains many of the significant experimental observations: small oscillations in the electron temperature prior to the crash (precursor), a short crash time, and large long-lived oscillations in the electron temperature following the crash (successor). In tokamak discharges with good central confinement the temperature profile across the center of the discharge remains rather flat. In such profiles skin currents form that cause the safety factor q to fall below one at a finite radius rs while q(r=0)≂1. The sawtooth crash is caused by the m=n=1 tearing mode growing on such a profile. For a profile in which q falls below one by an amount Δq, the crash time is given by the helical Alfvén time τA/Δq, independent of the resisitivity. The size of the magnetic island of the precursor can be a small fraction of rs. In contrast, a remnant magnetic island of the order of rs survives the crash and causes the successor oscillation. Estimates of the decay time of the successor are given.
Magnetic field line ergodicity in the edge plasma due to an ion-Bernstein wave antenna
Authors: Myra J. R.
Published: July 2002

Large ponderomotive forces can occur near a high-power ion cyclotron range of frequency antenna, particularly for the parallel electric field polarization used to excite ion-Bernstein waves (IBW). The magnetohydrodynamic (MHD) equilibrium of the edge plasma is modified by these forces when the antenna is highly localized poloidally and toroidally. Magnetic islands develop at the edge, near q=m/n, where ‖m‖≤πa/wa and ‖n‖≤πR/la, with wa and la the width and length of the antenna, respectively. Ergodicity of the magnetic field lines may be expected when the islands overlap. Numerical calculations of the island overlap criteria are presented for two examples relevant to present day (IBW) heating experiments.
The high-frequency nonlinear plasma instability
Authors: Nambu Mitsuhiro
Published: July 2002

A simple derivation of the Langmuir wave growth rate in the presence of a coherent ion sound wave is shown, based on high-frequency nonlinear force. The new energy up-conversion process (plasma–maser) may play an important role in space and laboratory plasmas with enhanced low-frequency fluctuations.
A model of bubble dynamics in a Hele–Shaw cell
Authors: Pumir Alain , Aref Hassan
Published: July 2002

A model of the interaction of small, well-separated bubbles of one fluid propagating through another ‘‘resident’’ fluid in a Hele–Shaw cell is introduced and studied. In the model each bubble acts on the others by setting up a velocity field of the dipole type. A system of ordinary differential equations is developed for the bubble positions. The system is solved completely for the two-bubble problem. The three-bubble problem is addressed by numerical simulations. A set of self-similar motions are also found analytically. The dynamics of rows of bubbles is investigated analytically and via numerical simulations. Although clearly an extreme idealization, the model appears to shed considerable light on what to expect in laboratory experiments.
The vortex shedding of a streamwise-oscillating sphere translating through a linearly stratified fluid
Authors: Lin Qiang , Boyer Don L. , Fernando Harindra J. S.
Published: July 2002

The flow past a horizontally translating, streamwise oscillating sphere through a linearly stratified fluid is investigated in a series of laboratory experiments. The pertinent governing parameters are shown to be the internal Froude number Fi, the Reynolds number Re, the Keulegan–Carpenter number KC, and the normalized forcing frequency Sf. A KC against Sf regime diagram for flows at Fi=0.07 and Re=190 is developed; for these parameters the flow is approximately two dimensional in the horizontal zone, −1/2≲z/D≲1/2, where z is the vertical coordinate and D is the sphere diameter. Numerous flow regimes are delineated, and it is shown that the regime boundaries approximate the lines of constant u1/u0=2π(KC)(Sf), where u1 is the amplitude of the sphere oscillation and u0 is the magnitude of the mean background flow. Vortex shedding occurs for the entire range of experiments at these Fi, Re values. Lock-on of the shedding frequency to the sphere oscillation frequency occurs for u1/u0≳0.1. Flows at large Fi are shown to exhibit three-dimensional motions in the near wake, and, owing to stratification, exhibit vertical collapse at a certain distance downstream. The far wake develops into a horizontal vortex street pattern for all flows when stratification is present. At large Fi, Re combinations, turbulent patches are found in the wake. The inverse normalized streamwise distance between shed vortices (an effective Strouhal number) is shown to scale as Sf, independent of KC. Measurements of the horizontal separation angles and times for the collapse of the vertical structure are also presented.
Characterization of the low-pressure filaments in a three-dimensional turbulent shear flow
Authors: Cadot O. , Douady S. , Couder Y.
Published: July 2002

In this paper results on the low-pressure filaments that appear spontaneously in three-dimensional turbulent flows are presented. An individual characterization of the filaments is first obtained by studying the correlations between the flow visualization and local measurements of the pressure and the velocity. Then, a statistical study of the time recordings of the pressure that exhibits intermittent short and deep depressions is presented. It is shown that the pressure histograms depend only on the square of the injection velocity, and that the rate of production of strong depressions is independent of the Reynolds number. These results impose severe constraints on the possible mechanisms of formation of the filaments; they are consistent with a simple model, in which the formation of the filaments results primarily from the partial rollup of stretched shear layers. In this model there is a difference between the hierarchies of pressure and vorticity filaments: the filaments with the largest depression are the thickest (and the longest), while the filaments with the strongest vorticity are likely to be the thinnest (and shortest).
An experimental investigation of the instability of a shear flow with multilayered density stratification
Authors: Caulfield C. P. , Peltier W. R. , Yoshida Shizuo , Ohtani Morimasa
Published: July 2002

The evolution of stratified shear flows with multilayer density distributions is discussed briefly from a theoretical perspective, generalizing the results of Caulfield [J. Fluid Mech. 258, 255 (1994)] to allow for asymmetry. Three distinct types of instability are predicted to occur according to linear theory. In the laboratory, we measure the density profile and the velocity profile continuously, and so are able to identify the flow characteristics that are applicable when each of the different instabilities grow. Knowledge of the bulk Richardson number is insufficient to predict the observed properties of the instabilities of the flow. The parameter that is most determinant of the selection of a particular type of instability is found to be the ratio R of the depth of the intermediate density layer to the depth over which the velocity varies, though any asymmetry in the flow (either in the velocity or density fields) also plays a role. If R is close to 1, and hence the layer of intermediate density occupies a significant portion of the shear layer, overturnings appear in the intermediate layer, which are long lived, and strongly two dimensional. These overturnings are the three layer stratified generalization of the Kelvin–Helmholtz instability first discussed by Taylor [Proc. R. Soc. London Ser. A 132, 499 (1931)]. Such modes inefficiently mix the background flow, and the major mixing mechanisms are found to consist of overturnings in the lower fluid layer (and, to a lesser extent, the upper layer). These overturnings are clearly manifestations of an (asymmetric) three layer generalization of the Holmboe [Geophys. Publ. 24, 67 (1962)] instability. In general, all three instabilities can be observed simultaneously at markedly different wavelengths and phase speeds for extended periods of time, even though linear theory may predict significantly different growth rates.
Pinching threads, singularities and the number 0.0304...
Authors: Brenner Michael P. , Lister John R. , Stone Howard A.
Published: July 2002

The dynamics of capillary pinching of a fluid thread are described by similarity solutions of the Navier–Stokes equations. Eggers [Phys. Rev. Lett. 71, 3458 (1993)] recently proposed a single universal similarity solution for a viscous thread pinching with an inertial–viscous–capillary balance in an inviscid environment. In this paper it is shown that there is actually a countably infinite family of such similarity solutions which are each an asymptotic solution to the Navier–Stokes equations. The solutions all have axial scale t′1/2 and radial scale t′, where t′ is the time to pinching. The solution obtained by Eggers appears to be special in that it is selected by the dynamics for most initial conditions by virtue of being less susceptible to finite-amplitude instabilities. The analogous problem of a thread pinching in the absence of inertia is also investigated and it is shown that there is a countably infinite family of similarity solutions with axial scale t′β and radial scale t′, where each solution has a different exponent β.
Dynamics of baroclinic vortices in a rotating, stratified fluid: A numerical study
Authors: Verzicco R. , Lalli F. , Campana E.
Published: July 2002

This study deals with the instabilities that arise in the flow generated in a rotating tank by the evolution of a two-layer density stratified fluid. Numerical investigations have been performed by direct simulation of the Navier-Stokes equations for axisymmetric and fully three-dimensional flows. In the former case results have shown the attainment, in a very short time, of an equilibrium position and the formation of an anticyclonic structure in the upper light layer and a cyclonic one in the lower layer, consistently with the observation of Griffiths and Linden. In the long term, however, the Ekman layer at the bottom damps out the cyclone and a steady state with only an anticyclone in the upper layer is reached. In three-dimensions the flow is unstable to azimuthal disturbances and the steady state is no longer achieved. In particular a ring of cyclonic vorticity, surrounding the anticyclone, by the combined effects of baroclinic and barotropic processes, breaks, entrains vorticity from the anticyclone and eventually forms vortex pairs. As observed by Griffiths and Linden the azimuthal wave number (n*) of the instability depends on the Richardson number (Ri) and the ratio between the depth of the light fluid and the total depth (δ). However, since several modes, in addition to the most unstable, are amplified an initial perturbation whose energy is not equidistributed among the modes can lead to an instability with wave number different from the expected n*. Finally, the analysis of the equation for the energy of the instability has shown that the instability is initially driven by baroclinic effects, even for low values of δ. The barotropic source, in contrast, sets in only in the large-amplitude phase of the instability and its effect is larger when δ is small.
Reversing buoyancy of particle-driven gravity currents
Authors: Hogg Andrew J. , Huppert Herbert E. , Hallworth Mark A.
Published: July 2002

Particle-laden flows exhibit reversing buoyancy behavior if the density of the ambient through which they propagate is greater than that of the interstitial fluid, though less than the initial bulk density of the suspension. In this case a gravity current is initiated above the underlying boundary until sufficient particles have sedimented from the flow, at which time the particle-laden fluid becomes less dense than the surrounding ambient. The buoyancy of the residual suspension reverses and it lifts off the boundary to ascend through the ambient. Such phenomena are encountered in industrial and natural situations. This study presents a laboratory investigation of finite volume releases of particle-laden fluid which undergo reversing buoyancy. A simple box model theory is proposed to describe the flow and to predict the distance from the source at which lift-off occurs. The predictions of the model agree well with both our experiments and those of previous studies. Additionally, we investigate these flows using the shallow-water equations which are analyzed using asymptotic series. These reveal the structure of the internal dynamics within the currents and predict lift-off distances which verify the validity of those obtained from the less rigorous box model.
The influence of a radial electric field on neoclassical orbits and ion prompt losses from tokamak edge plasmas
Authors: Krasheninnikov S. I. , Yushmanov P. N.
Published: July 2002

The effect of the radial electric field on neoclassical orbits in a tokamak using the integrals of drift motion is considered. It is shown that for the most interesting case of high radial electric field shear, due to a dramatic change of the particle orbit topology at a distance of the order of one particle orbit width, it is not correct to apply local theory to describe neoclassical transport processes. For step-like electrostatic potentials typical for the tokamak plasma periphery in the high (H) mode, the trajectories of the particles can be either squeezed or expanded depending on the location of the potential jump with respect to the unperturbed particle trajectories. The widening of the orbits decreases the threshold energy of suprathermal particles which can be promptly lost and enhances the ion prompt losses which might increase the amplitude of the potential step. It is shown that these effects are more pronounced for a diverted tokamak with the X point located at the inner side of the torus. Simultaneous growth of prompt losses and potential magnitude might be the reason for the fast formation of the narrow electrostatic barrier during the ‘‘low’’–‘‘high’’ (L–H) transition. Toroidal plasma rotation induced by the radial electric field can strongly enhance the destabilizing effect of the step-like potential.
High harmonic fast waves in high beta plasmas
Authors: Ono Masayuki
Published: July 2002

High harmonic fast magnetosonic waves in high beta plasmas are investigated. In the high beta regime, a combination of reduced group velocity and a high beta enhancement of magnetic pumping lead to such large values of electron absorption that one can expect strong (≊100%) single pass absorption. In particular, by controlling the wave spectrum, the prospect of localized electron heating and current drive appears to be feasible in high beta low-aspect-ratio tokamak regimes. Inclusion of finite-Larmor-radius terms reveals an accessibility limit in the high ion beta regime (βi≊50% for a deuterium plasma) due to mode conversion into an ion-Bernstein-wave-like mode. No similar beta limit is expected for electrons. With increasing ion beta, the ion damping can increase significantly, particularly near the mode-conversion accessibility limit. The presence of an energetic ion component expected during intense neutral beam injection and α heating does not appear to modify the accessibility condition nor cause excessive wave absorption by the energetic ions.
Dynamics of non-neutral plasmas
Authors: Gould Roy W.
Published: July 2002

In this paper the focus is on the dynamics of two-dimensional cylindrical non-neutral plasmas. After reviewing some highlights of the non-neutral plasma dynamics, some recent two-dimensional results are described: vortex dynamics, diocotron instabilities of hollow profiles, collisionless damping of modes and fluid trapping by modes, fluid echoes, the cyclotron center of mass modes and warm plasma Bernstein modes, and temperature determination from fluctuation measurements. Attention is called to some unsolved problems.
Effect of edge neutrals on the low-to-high confinement transition threshold in the DIII-D tokamak
Authors: Carreras B. A. , Owen L. W. , Maingi R. , Mioduszewski P. K. , Carlstrom T. N. , Groebner R. J.
Published: July 2002

To study the effect of edge neutrals on the low-to-high confinement transition threshold, a broad range of plasma discharges has been analyzed. These discharges vary by gas puffing and pumping rates, position of the X point, and line-averaged density. It is shown that the determination of the neutral density (or neutral pressure) in the scrape-off layer (SOL) can give a misleading indication of the neutral population inside the separatrix. An increase of neutral density in the SOL creates an increase of plasma density that, in turn, increases the opacity to the neutrals and results in reduced neutral penetration. At a constant magnetic field, the transition power divided by the density appears to be a function of a single parameter measuring the neutrals effect. From this analysis, this parameter cannot be uniquely identified. For instance, it may be the radial decay length of the neutral profile or the charge-exchange damping rate at about r/a≈0.95. A similar correlation exists between these neutral parameters and local plasma parameters such as electron and ion temperature. This indicates that a missing parameter linked to the neutrals exists in the power threshold scaling laws.
Stabilized radiative Z-pinch loads with tailored density profiles
Authors: Velikovich A. L. , Cochran F. L. , Davis J. , Chong Y. K.
Published: July 2002

Mitigation of the Rayleigh–Taylor (RT) instability of Z-pinch loads imploded from large initial radii through tailoring initial load density profiles in radial and axial directions is studied numerically. These methods could be helpful for a variety of applications of high-power Z-pinches, from producing large amounts of K-shell radiation to imploding inertial confinement fusion pellets. Radial density tailoring is demonstrated to delay the onset of the RT instability development at the expense of reducing the energy available for conversion into radiation. Axial density tailoring can fully stabilize acceleration of a fraction of the initial load mass. For a better tradeoff between stability and radiative performance of the loads, the density profiles could be tailored in two dimensions, combining the advantages of both methods. Post-processing of the radiation-magnetohydrodynamic simulation results demonstrates that an appreciable K-shell argon radiation power could be generated with a stabilized argon load imploded by a 5 MA current from a ∼10 cm initial radius in about 0.5 μs.
Computational investigation of single mode vs multimode Rayleigh–Taylor seeding in Z-pinch implosions
Authors: Douglas M. R. , Deeney C. , Roderick N. F.
Published: July 2002

A series of two-dimensional magnetohydrodynamic calculations have been carried out to investigate single and multimode growth and mode coupling for magnetically-driven Rayleigh–Taylor instabilities in Z pinches. Wavelengths ranging from 5.0 mm down to 1.25 mm were considered. Such wavelengths are comparable to those observed at stagnation using a random density “seeding” method. The calculations show that wavelengths resolved by less than 10 cells exhibit an artificial decrease in initial Fourier spectrum amplitudes and a reduction in the corresponding amplitude growth. Single mode evolution exhibits linear exponential growth and the development of higher harmonics as the mode transitions into the nonlinear phase. The mode growth continues to exponentiate but at a slower rate than determined by linear hydrodynamic theory. In the two and three mode case, there is clear evidence of mode coupling and inverse cascade. In addition, distinct modal patterns are observed late in the implosion, resulting from finite shell thickness and magnetic field effects.