bluuebunny/crossref_metadata_2025 huggingface dataset:
Point and line boundaries in scalar Casimir theory
Authors: Actor Alfred
Published: July 2002

A simple image-charge construction enables one to insert point or line boundaries (or planar or hyperplanar boundaries when sufficiently many spatial dimensions are available) at or into the central point, line, plane etc., of a great range of spatial backgrounds in quantum field theory which have appropriate symmetry. This nontrivial construction (which provides among other things the exact vacuum stress tensor Tμν of the quantum field if Tμν can be computed for the original background prior to point, line,…, insertion) works if all directions xi perpendicular to the inserted object are symmetric under xi→−xi. In other respects the symmetric spatial background can be quite arbitrary. While the inserted object experiences (by symmetry) no net Casimir force from the background, it does exert Casimir forces throughout this background which were originally not present. In addition to general theory, detailed examples are given (which include exact field Tμν’s and exact Casimir force densities) for arbitrary spatial dimension. First: point and line boundaries in otherwise empty space; then a planar boundary with a semi-infinite line extending from one side; finally, parallel planar boundaries with a point boundary halfway between them. Only scalar quantum fields are analyzed here; however the extension to the electromagnetic Casimir effect is discussed qualitatively.
Exact solutions of Dirac equation for neutrinos in presence of external fields
Authors: Hounkonnou M. N. , Mendy J. E. B.
Published: July 2002

Exact solutions of the Dirac equation in a chiral representation for neutrinos in the presence of external stresses are investigated in terms of special functions, using the algebraic method of the separation of variables in Cartesian, cylindrical, and spherical coordinates.
Degeneracy and para-supersymmetry of Dirac Hamiltonian in (2+1)-space–time
Authors: Jafarizadeh M. A. , Moayedi S. K.
Published: July 2002

The quantum mechanics of a spin 12 particle on a locally spatial constant curvature part of a (2+1)-space–time in the presence of a constant magnetic field of a magnetic monopole has been investigated. It has been shown that these two-dimensional Hamiltonians have the degeneracy group of SL(2,c), and para-supersymmetry of arbitrary order or shape invariance. Using this symmetry we have obtained its spectrum algebraically. The Dirac’s quantization condition has been obtained from the representation theory. Also, it is shown that the presence of angular deficit suppresses both the degeneracy and shape invariance.
Exact solution of the Herrera equation of motion in classical electrodynamics
Authors: Ares de Parga G. , Mares R.
Published: July 2002

The Landau–Lifshitz equation is derived as a first-order iteration of the Lorentz–Dirac equation for the charged particle. In those cases with null electromagnetic field’s gradient, the Landau-Lifshitz gives the so named Herrera equation. A general method for the solution of the latter equation is presented and applied to the motion of a particle in a uniform electromagnetic field.
On the differentiability of Cauchy horizons
Authors: Budzyński Robert J. , Kondracki Witold , Królak Andrzej
Published: July 2002

Chruściel and Galloway constructed a Cauchy horizon that is nondifferentiable on a dense set. We prove that in a certain class of Cauchy horizons densely nondifferentiable Cauchy horizons form a dense set. We show that our class of densely nondifferentiable Cauchy horizons implies the existence of densely nondifferentiable Cauchy horizons arising from partial Cauchy surfaces and also the existence of densely nondifferentiable black hole event horizons.
Calculation of the level splitting of energy and the decay rate of some one-dimensional potentials by instantons method
Authors: Jafarizadeh M. A. , Jalalzadeh S.
Published: July 2002

Using the popular Langer–Polyakov–Coleman instanton method, the decay rate of metastable states and the level splitting of energy, due to tunneling of some one-dimensional potentials have been calculated. The operators appearing in the prefactor of the decay rate or the level splitting of energy of these kinds of potentials possess the shape invariance symmetry, hence using this property, the determinant of these operators have been calculated analytically via heat kernel method.
Thermal conductivity and electrical resistivity of the layered compound Nb1−xSnxSe2
Authors: Beletskii V. I. , Gavrenko O. A. , Merisov B. A. , Obolenskii M. A. , Sologubenko A. V. , Khadjai G. Ya. , Chashka Kh. B.
Published: July 2002

The thermal conductivity λ(x=0,0.15,0.3,0.6;T=2–200 K) and electrical resistivity ρ(0⩽x⩽0.5;T=6–300 K) of layered crystals Nb1−xSnxSe2 are measured in the ab plane. The metal– semiconductor transition is observed at x≈0.5. The magnitude of the resistivity anomaly observed at 33 K and associated with a transition to the charge density wave phase increases with increasing x for x>0.15. The thermal conductivity of the metallic samples (x<0.5) increases with temperature at T>90K, which is in accord with the nonlinearity of the ρ(T) dependence. The absence of such an increase in λ(T) for a semiconducting sample indicates that this singularity is connected with the electronic subsystem. The observed nonmonotonicity of the ρ(x) dependence may be associated with the existence of a sharp peak in the electron density of states near the Fermi level. Approximation of the λ(T) dependence reveals the existence of a phonon scattering mechanism with a relaxation rate proportional to the square of the frequency.
Peculiarities of dynamics of one-dimensional discrete systems with interaction extending beyond nearest neighbors, and the role of higher dispersion in soliton dynamics
Authors: Kosevich A. M. , Savotchenko S. E.
Published: July 2002

In the analysis of dynamics of an ideal system as well as a system with point defects, the role of interaction is considered not only for the nearest neighbors. The Green’s function is constructed for steady-state vibrations of a chain at all possible frequencies. It is shown that, if the interaction with the next-to-nearest neighbors is taken into account, the Green’s function inevitably becomes double partial, the nature of its two components depending significantly on its eigenfrequency. It is found that the Green’s function for frequencies of the continuous spectrum of small vibrations has one component of the plane wave type, while the other component is localized near the source of perturbations. Such a Green’s function describes the so-called quasilocal vibrations. At certain discrete frequencies falling in the continuous spectrum, the quasilocal vibration is transformed into local vibration (that does not propagate to infinity). The conditions of applicability of differential equations with fourth spatial derivative are analyzed for describing the longwave vibrations of the atomic chain. Relations between parameters of atomic interactions permitting the use of such equations are formulated. Asymptotic forms of soliton fields in a nonlinear medium with spatial dispersion are discussed. It is shown that most of the soliton parameters are determined by the dispersion relation for the linearized equation.
Lattice-gas automata: A model for the simulation of dispersion phenomena
Authors: Baudet C. , Hulin J. P. , Lallemand P. , d’Humières D.
Published: July 2002

The dispersion of a tracer in two-dimensional (2-D) parallel flow between two parallel plates has been studied numerically using a lattice-gas model with two different species of particles. After a stepwise change of concentration at one end of the model, the tracer distribution in the flow evolves theoretically, as predicted, toward a Gaussian profile in a time lapse in agreement with the predictions of the Taylor model. The mean square width of the front increases linearly with time after the stabilization period, as required for a diffusive spreading process. The longitudinal dispersion coefficient D∥ has been determined in a range of Peclet number values Pe between 4.3 and 35.4. It varies as the square of the velocity, in agreement with the Taylor–Aris model; the molecular diffusion coefficient value (Dm=0.62 in lattice and simulation step units) obtained from the proportionality coefficient is in good agreement with the values obtained by other independent methods.
Small amplitude thermocapillary flow and surface deformations in a liquid bridge
Authors: Kuhlmann H.
Published: July 2002

A cylindrical liquid bridge under asymmetric heating is investigated for small Reynolds, Prandtl, and capillary numbers. Flow field and surface deformation are calculated in terms of a Papkovich–Fadle series. The present analytical solution is in very good agreement with recent numerical results. A comparison with numerical simulations of the full Navier–Stokes equations without surface deformations is made.
Oscillatory three-dimensional convection in rectangular cavities and enclosures
Authors: Afrid M. , Zebib A.
Published: July 2002

Numerical experiments of natural convection of a zero Prandtl (Pr) number fluid in 4×1×2 (length to height to width) and 4×1×1 rectangular cavities (with a free top surface) and enclosures (having a solid top surface) are performed. The cavities are referred to as R-F (rigid-free) while enclosures are referred to as R–R (rigid–rigid). The objective of this study is to establish the pattern of three-dimensional convection and to determine the value of the critical Grashof number, Grcrit, at which the flow becomes time dependent. A three-dimensional laminar flow model of a constant property fluid is used. The model equations are solved numerically by a finite volume method. The flow field is steady at relatively low Grashof number (Gr), and is represented by one cell, unlike the multicellular flow predicted by two-dimensional studies. When Gr reaches Grcrit, the flow becomes oscillatory. Transition to time dependence is a function of the geometry and the type of top surface (rigid or free). The R–R flow is more stable than that of the R-F case, for both widths considered (one and two). The width of cavity and/or enclosure has an important effect on transition to oscillatory convection, for it is found that reducing the width from two to one, leads to a much higher Grcrit, making the results of two-dimensional numerical simulations completely inadequate.
Energy stability of thermocapillary convection in a model of the float-zone crystal-growth process. II: Nonaxisymmetric disturbances
Authors: Neitzel G. P. , Law C. C. , Jankowski D. F. , Mittelmann H. D.
Published: July 2002

Energy-stability theory has been applied to investigate the stability properties of thermocapillary convection in a half-zone model of the float-zone crystal-growth process. An earlier axisymmetric model has been extended to permit nonaxisymmetric disturbances, thus determining sufficient conditions for stability to disturbances of arbitrary amplitude. The results for nonaxisymmetric disturbances are compared with earlier axisymmetric results, with linear-stability results for a geometry with an infinitely long aspect ratio and with stability boundaries from recent laboratory experiments.
Reynolds number dependence of scalar fluctuations in a high Schmidt number turbulent jet
Authors: Miller Paul L. , Dimotakis Paul E.
Published: July 2002

The scalar rms fluctuations in a turbulent jet were investigated experimentally, using high-resolution, laser-induced fluorescence techniques. The experiments were conducted in a high Schmidt number fluid (water), on the jet centerline, over a jet Reynolds number range of 3000≤Re≤24 000. It was found that the normalized scalar rms fluctuations c′/ c̄ decrease with increasing flow Reynolds number, at least for the range of Reynolds numbers investigated. Since c′/ c̄ is a measure of the inhomogeneity of the scalar field, this implies that high Schmidt number turbulent jets become more homogeneous, or better mixed, with increasing Re. These findings need to be assessed in the context of the documented Reynolds number independence of flame length for Re>3000 or 6500.
Simulation of the inertial–conductive subrange
Authors: Chasnov Jeffrey R.
Published: July 2002

The inertial–conductive subrange spectrum of a passive temperature field of a fluid of small Prandtl number is determined by large-eddy simulation. Results for simulations of both freely decaying and forced turbulence are presented. In the simulations of freely decaying turbulence, a subgrid model is used to simulate a decaying turbulent velocity field with a k−5/3 inertial subrange energy spectrum convecting eight different decaying temperature fields with well-resolved conductive subranges. In the simulations of forced turbulence, a subgrid model is again used to simulate an inertial subrange velocity field; however, the velocity field is now forced at the lowest wave numbers of the simulation, and an external uniform mean temperature gradient is imposed. Statistically stationary velocity and temperature fluctuations are generated. The results of the decaying and forced simulations are in excellent agreement with the Batchelor, Howells, and Townsend (BHT) [J. Fluid Mech. 5, 134 (1959)] k−17/3 spectrum in the far inertial–conductive subrange, whereas significant departures from the BHT spectrum are observed in the near inertial–conductive subrange.
Interactions and collisions of bubbles in thermocapillary motion
Authors: Satrape J. V.
Published: July 2002

A calculation of the motion of two bubbles in a constant temperature gradient is presented for the limit of creeping flow and vanishing Péclet number. The results are valid for undeforming, spherical bubbles of arbitrary size and orientation with respect to the temperature gradient, and for separations up to near touching. Trajectories of two bubbles, as they approach one another in an infinite fluid, are then determined from these instantaneous velocity calculations. The limiting trajectories, where the bubbles ‘‘just miss’’ each other, are used to tabulate collision efficiencies over a wide range of bubble size ratios. On the basis of the two-bubble results, a model for the evolution of a statistically homogeneous cloud of bubbles with a given initial size distribution is formulated in terms of a discrete stochastic collection equation. Using this simple model, the dependence of the rate of coalescence in a bubble cloud upon material properties, the bubble volume fraction, the average temperature gradient, and other characteristics of the system, is demonstrated. A significant conclusion is that the bubble collision rate increases with the standard deviation of the bubble size distribution.
Effect of surface tension on the onset of convection in a double-diffusive layer
Authors: Chen C. F. , Su T. F.
Published: July 2002

The effect of surface tension on the stability of a double-diffusive layer is considered using linear stability analysis. The surface tension is assumed to vary linearly with temperature and solute concentration. The eigenvalue problem is solved by the Galerkin method. Results show that the predicted stability boundary based on Marangoni effects alone is completely altered in the presence of buoyancy effects induced by low gravity levels (∼10−5 g). At reduced gravity levels, salt-finger instability may onset in the overstable mode due to the stabilizing effect of surface tension. Fluid properties in terms of the Prandtl and the Lewis numbers have a profound effect on the stability conditions; opposite stability characteristics are found in salt solutions and in molten metals. In the diffusive case, the competition between the surface-tension and the double-diffusive effects can generate bimodal marginal stability curves, thus resulting in the simultaneous occurrence of two instability modes with different wave numbers and oscillation frequencies.
Numerical simulation of miscible displacement processes in porous media flows under gravity
Authors: Rogerson A. , Meiburg E.
Published: July 2002

The nonlinear evolution of the interface between two miscible fluids of different densities and viscosities is simulated numerically for flow in a two-dimensional porous medium in which gravity is directed at various angles to the interface. Global velocities tangential to the interface are included in the analysis in addition to a normal displacing velocity. In unstable configurations, the viscous fingers that result translate as they amplify when nonzero tangential velocities are present. The increased stabilization by tangential shearing velocities reported in [A. Rogerson and E. Meiburg, Phys. Fluids A 5, 1344 (1993)] affects the growth and wavelength selection of the emerging fingers. Tangential shearing also breaks the symmetry in the shape and concentration distribution of emerging fingers. In addition to the fingering mechanisms reported in previous studies, new mechanisms of diagonal fingering, trailing-lobe detachment, and secondary side-finger instability, resulting from the presence of gravity and tangential velocities, have been identified. These phenomena are reflected in one-dimensional averaged profiles of the concentration field. Also, how different density–concentration relations influence the interfacial evolution is investigated. When the dependence of viscosity and density on the concentration has different functional forms, the region of instability may be localized. The nature of the interfacial development is altered by varying the density relation and thereby changing the region of instability, suggesting that careful modeling of the density and viscosity relations is warranted.
Experimental investigation into a turbulent jet with negative buoyancy
Authors: Cresswell R. W. , Szczepura R. T.
Published: July 2002

An experimental investigation of a steady-state negatively buoyant jet has been performed using a hot water jet projected vertically downwards from a 7.5 mm radius inlet pipe into a cold ambient. The Richardson number was 0.1 based on inlet pipe radius and the Reynolds number was 5000. Mean and fluctuating velocities and temperatures, triple velocity correlations and velocity–temperature correlations were measured for the jet in a constant temperature ambient. Correlations between orthogonal velocity components were also measured. Velocity measurements were performed using laser Doppler anemometry (LDA), and errors associated with beam movement (due to refractive index fluctuations) were experimentally quantified. Temperatures were measured with fast response thermocouples. The two techniques were used in conjunction to provide velocity–temperature correlations. The intermittency factors around the edge of the flow were measured optically, employing refractive index as a tracer. The normal stresses were found to be high in the shear region at the jet-flow/reverse-flow interface and in the region of large-scale fluid reversal. The contribution from the intermittency at the boundary of the flow was evident in the velocity and temperature fluctuations. The triple velocity products were interpreted as fluxes of the Reynolds stresses and in general exhibited net fluxes away from the regions of high stress intensity. Balances of the terms in the axial momentum and turbulent kinetic energy equations showed that the main contribution from buoyancy was in the mean motion, with very little direct input to the turbulence field.
Alpha particle confinement in tokamaks
Authors: White R. B. , Mynick H. E.
Published: July 2002

An assessment of diffusive tokamak transport mechanisms of concern for alpha particles indicates that the ‘‘stochastic regime’’ is the only one that appears to pose a real danger for adequate alpha confinement. This fact, in conjunction with the threshold character of that mechanism, allows one to decide whether an alpha born at a given location will be lost or confined, according to a very simple criterion. Implementing this criterion numerically results in a new code for the assessment of alpha confinement, which is orders of magnitude faster than earlier codes used for this purpose.
Laser-induced fluorescence characterization of a multidipole filament plasma
Authors: Goeckner M. J. , Goree J. , Sheridan T. E.
Published: July 2002

A multidipole filament discharge was characterized using sub-Doppler laser-induced fluorescence (LIF). The ion temperature was found to be Ti=0.028±0.007 eV, measured in the center of an argon discharge. This stands in contrast to the much higher ion temperatures, 0.2<Ti<0.5 eV, reported by researchers using gridded electrostatic energy analyzers. The discrepancy is attributed to the energy resolution of the detectors, with the LIF providing more accurate measurements. In another result, the metastable excited-state ion density was found to scale linearly with the electron density and the discharge current under most conditions. This experiment also demonstrates that LIF can be used for basic plasma physics research in multidipole discharges.
Instability of fluid vortices and generation of sheared flow
Authors: Finn J. M. , Drake J. F. , Guzdar P. N.
Published: July 2002

A fluid equilibrium consisting of a periodic array of counter-rotating vortices is found to be unstable to the generation of one-dimensional sheared flow along the direction of periodicity. This instability is inviscid (exists for zero viscosity μ) or viscous (with growth rate γ∼μ3/4) depending on the elongation of the vortices. Nonlinearly, the instability goes through a vortex reconnection or ‘‘peeling’’ phase in which one of the vortices per period is destroyed, leading to a state with a chain of islands. Without a source, the flow evolves to pure one-dimensional shear flow, which decays because of viscosity on a much longer time scale. In the presence of a source driving the initial vortices, the flow evolves to an equilibrium having vortex flow plus shear flow and, for sufficiently high Reynolds number, having only one vortex per periodicity length rather than two, i.e., with islands.
Peeling of convection cells and the generation of sheared flow
Authors: Drake J. F. , Finn J. M. , Guzdar P. , Shapiro V. , Shevchenko V. , Waelbroeck F. , Hassam A. B. , Liu C. S. , Sagdeev R.
Published: July 2002

A periodic array of convection cells is subject to a ‘‘shear flow’’ instability. The generation of the sheared flow is a consequence of ‘‘peeling’’ of the convection cells. Fluid simulations demonstrate that the efficiency of shear flow generation is high. Implications for understanding poloidal rotation in tokamaks are discussed.
Magnetohydrodynamic instabilities in developed small-scale turbulence
Authors: Kleeorin N. , Mond M. , Rogachevskii I.
Published: July 2002

Modification of the magnetic force by a developed small-scale magnetohydrodynamic (MHD) turbulence can result in the sign reversal of the effective magnetic pressure. It is due to negative contribution of the MHD turbulence, to the large-scale magnetic force. It can significantly lower the elasticity of the large-scale magnetic field [ Sov. Phys. JETP 70, 878 (1990)]. This effect excites instabilities of the large-scale magnetic field due to the energy transfer from the turbulent pulsations to the latter. The nonturbulent stability criteria are modified due to the effective negative magnetic pressure. These instabilities may provide a mechanism of the large-scale magnetic ropes formation in the solar convective zone and spiral galaxies. In addition, the instabilities can excite the short-period solar oscillations.
A renormalization group analysis of two-dimensional magnetohydrodynamic turbulence
Authors: Liang Wenli Z. , Diamond P. H.
Published: July 2002

The renormalization group (RNG) method is used to study the physics of two-dimensional (2-D) magnetohydrodynamic (MHD) turbulence. It is shown that, for a turbulent magnetofluid in two dimensions, no RNG transformation fixed point exists on account of the coexistence of energy transfer to small scales and mean-square magnetic flux transfer to large scales. The absence of a fixed point renders the RNG method incapable of describing the 2-D MHD system. A similar conclusion is reached for 2-D hydrodynamics, where enstrophy flows to small scales and energy to large scales. These analyses suggest that the applicability of the RNG method to turbulent systems is intrinsically limited, especially in the case of systems with dual-direction transfer.
Velocity-space particle loss in field-reversed configurations
Authors: Hsiao Ming-Yuan , Miley George H.
Published: July 2002

From particle confinement criteria for field-reversed configurations it is found that only a portion of (H,Pθ) space, or equivalently, of velocity space, provides confinement. A loss region in velocity space is found. The effects of this loss region in velocity space are investigated. The velocity-space particle loss, i.e., particle loss caused by the existence of a loss region in velocity space, because of collisions is calculated from the Fokker–Planck equation. The corresponding scaling law for particle confinement is obtained. In collisional equilibrium, a simple analytical expression is verified to be a good representation of the actual velocity distribution in the presence of the loss region in velocity space. It is shown that velocity-space particle loss in field-reversed configurations is an important mechanism for particle loss, as well as the occurrence and spin-up of plasma rotation.
Electrostatic ion-cyclotron instability caused by a nonuniform electric field perpendicular to the external magnetic field
Authors: Ganguli G. , Lee Y. C. , Palmadesso P.
Published: July 2002

A new mechanism that can destabilize kinetic ion-cyclotron waves in the presence of a nonuniform electric field perpendicular to the uniform ambient magnetic field is given. In the absence of the electric field, the mode energy is positive, while in the presence of a uniform electric field the mode energy could be negative. However, when the electric field is nonuniform, it is possible for a finite region to be a negative wave energy surrounded by regions of positive wave energy. A nonlocal wave packet couples the two regions so that a flow of energy from the region of negative wave energy to the region of positive wave energy will cause the mode to brow. This gives rise to the instability.
Radio frequency heating in the ion-cyclotron range of frequencies
Authors: Swanson D. G.
Published: July 2002

Both the theory of the absorption process in the ion-cyclotron range of frequencies and some of the experiments which slow the promise and problems with radio frequency plasma heating in this range are discussed. It is shown that mode conversion is invariably involved in the process and so an extensive review of mode conversion theory, expecially as it applies to problems with back-to-back cutoff-resonance pairs, is included. This includes a discussion of the tunneling equation with and without absorption effects and with and without energy conservation. The general theory is applied to various ion-cyclotron harmonics, the two-ion hybrid resonance, and to a case where a wave converts to a Bernstein mode at the plasma edge. The results are given analytically for a variety of cases without absorption, and empirical formulas are given for the second and third harmonics of the ion-cyclotron frequency, which include effects of absorption. Various problem areas in the theory are also discussed with some of the limitations caused by the approximations involved. A number of experiments are also discussed which show effective heating, and some show the features of the mode conversion process, indicating that the general processes of absorption are reasonably well understood. Areas where further work is necessary, both in fundamental theory and in comparing theory with experiment, are also discussed.
The dispersion functional for multidimensional equilibria
Authors: Lewis H. Ralph , Barnes Daniel C. , Schwarzmeier James L. , Seyler Charles E.
Published: July 2002

Numerical study of the linear stability of plasmas is very difficult when one or more of the plasma species is collisionless and the equilibrium is multidimensional, that is, characterized by two or more nonignorable spatial coordinates. The problem arises, for example, in evaluating kinetic stabilizing effects on the internal tilting mode (an n=1 ballooning mode) in field-reversed configurations. In this paper, the Laplace transform of the perturbation distribution function for a collisionless species is derived for all classes of phase-space trajectories and used to construct the dispersion functional for multidimensional equilibria. The kinetic part of the dispersion functional is expressed in terms of the Laplace transform of autocorrelation functions with respect to a certain delay time. It is shown how to obtain the same result formally by using Liouville eigenfunctions. For the case of the Vlasov-fluid model, the dispersion functional is transformed in a way that is particularly appropriate for computation of the kinetic stability of field-reversed configurations to the internal tilting mode.
The long-time evolution approximation for a quasi-one-dimensional plasma system
Authors: Caramana E. J.
Published: July 2002

The long-time evolution of a plasma through a series of equilibrium states for the case of the field-reversed configuration (FRC) is considered. A formulation of the transport model in magnetic flux variables is given for the approximate geometry where the magnetic field lines are straight. Thus a complicated two-dimensional elliptic differential equation amenable only to numerical solution is avoided. Radial force balance is enforced pointwise while axial force balance is enforced only globally. The equations formulated in this manner are relatively simple; some of their salient features are discussed. Although a particular plasma–magnetic field configuration is considered, the type of analytical method presented is more general and applies to other coupled initial-boundary value problems. The absence of complicated geometry and flux surface averaging involved for other systems makes the essential aspects of the transformations employed transparent.
Reconnection studies in field-reversed configurations
Authors: Sevillano E. , Ribe F. L.
Published: July 2002

Internal magnetic field measurements are used to study the reconnection process near the ends of a low-compression field-reversed theta pinch. The measurements indicate that the addition of independently driven magnetic mirror coils at the ends are effective in inducing rapid reconnection and in minimizing plasma losses out the ends. Fast reconnection leading to the formation of a chain of magnetic islands along the length of the coil is observed on a time scale of a 100 nsec. These islands coalesce on a time scale of 1–2 μsec. Measured values of the resistivity are two orders of magnitude greater than classical during the implosion phase. The resistivity during the equilibrium phase is four times the classical value. Axial contraction and the n=2 rotational instability are not observed to occur in these experiments. Sudden termination of the configurations is thought to be caused by rapid loss of the internal field. This flux dissipation may be a consequence of electron cooling by the crossing of a radiation barrier. An oxygen impurity concentration of 2% is enough to account for the power dissipated during the collapse.
Magnetic reconnection via current sheets
Authors: Biskamp D.
Published: July 2002

A general picture of magnetic reconnection in the framework of 2-D incompressible resistive magnetohydrodynamic theory is presented. Numerical studies of (quasi-) steady-state driven reconnection reveal current sheet formation for Mach numbers M=u/vA exceeding the Sweet–Parker reconnection rate MSP=(η/LvA)1/2. Since the thickness δ of the current sheet is found to be invariant to a change of the resistivity η, its length Δ increases rapidly with decreasing η or increasing M, which can be written in the form Δ∼(M/MSP)4, so that Δ reaches the global system size L within a short range of the parameter M/MSP. The results are rather insensitive to the particular choice of boundary conditions. Because of the presence of a current sheet, the overall reconnection process is quite slow. This picture essentially agrees with Syrovatsky’s [Sov. Phys. JETP 33, 933 (1971)] theory and disproves Petschek’s [AAS/NASA Symposium on the Physics of Solar Flares, (NASA, Washington, DC, 1964) p. 425] mechanism of fast magnetic reconnection. A theory of the solution in the external and in the diffusion region is developed and analytical expressions in agreement with the simulation results are obtained by means of a variational principle. For sufficiently long current sheets the tearing mode becomes unstable in spite of the stabilizing effect of the inhomogeneous flow. The tearing mode contributes to the overall reconnection process, but a general assessment of this effect in the asymptotic regime of almost vanishing η is difficult.
Isotropic forms of vorticity and velocity structure function equations in several turbulent shear flows
Authors: Shah D. A. , Antonia R. A.
Published: July 2002

Isotropic forms of the vorticity and velocity structure function equations are valid in the logarithmic regions of a fully developed turbulent duct flow and a boundary layer over a wide range of Reynolds numbers. These equations are also valid in a low Reynolds number turbulent wake and a high Reynolds number atmospheric surface layer. However, these equations are not satisfied in the near-wall region of duct and boundary layer flows where the production of vorticity is significantly larger than the dissipation. The appropriateness of the equations as indicators of local isotropy is discussed in the context of the present and other published measurements.
Vortex breakdown in spherical gap
Authors: Bar-Yoseph P. , Seelig S. , Solan A. , Roesner K. G.
Published: July 2002

A finite element solution of the flow between rotating spheres shows a vortex breakdown for Reynolds numbers exceeding a critical value. The result is in agreement with published results for a vortex breakdown in a cylindrical enclosure.
Kolmogorov’s constant and local interactions
Authors: Kraichnan Robert H.
Published: July 2002

Suppose that all the wave-vector triad interactions that involve no wavenumber ratio that exceeds β are removed from the Navier–Stokes equation. Within a class of closures, the paradoxical effect is to enhance energy cascade through the Kolmogorov inertial range for 1<β<βc, where βc may be as large as 8. This may have implications with regard to force-free structures in the true Navier–Stokes dynamics.
The onset of Alfvénic turbulence
Authors: Ghosh S. , Papadopoulos K.
Published: July 2002

An investigation is conducted on how low-frequency, ω<Ωi, magnetohydrodynamic oscillations in a warm plasma may undergo a transition from a coherent state to one of turbulence. A driven/dissipative derivative nonlinear Schrödinger (DNLS) equation is derived from the fluid equations. The time evolution of an arbitrary spectrum of waves is analyzed in the case where one k-mode is unstable, with the rest damped. It is found that the transition from order to chaos in the driven/dissipative system is correlated with the existence or absence of ‘‘breathing’’ solitons in the associated conservative system.
Nozzle flows of gas–particle mixtures
Authors: Ishii R. , Umeda Y. , Kawasaki K.
Published: July 2002

A numerical analysis of supersonic nozzle flows of gas–particle mixtures is described. A time-dependent technique is applied to solve a two-phase inviscid flow through an axially symmetric nozzle. The two-step MacCormack algorithm is used for the gas-phase flow and the method of characteristics is applied to the particle-phase flow. Attention is mainly focused on the location of the limiting particle streamline. The numerical results are compared with the theoretical results obtained previously and also with experiments.
Harmonic overlap in electron-cyclotron current drive at high T
e
Authors: Smith Gary R. , Cohen Ronald H. , Mau T. K.
Published: July 2002

The relativistic wave–particle resonance condition imposes a harmonic-overlap constraint on electron-cyclotron current drive. Specifically, for fundamental cyclotron resonance the current-drive efficiency cannot be increased by raising the minimum resonant energy ε1 above about 115 keV. A limiting efficiency corresponding to an even lower ε1 follows for microwave beams with realistic width and angular divergence.
Nonlinear stability analysis of inviscid flows in three dimensions: Incompressible fluids and barotropic fluids
Authors: Abarbanel Henry D. I. , Holm Darryl D.
Published: July 2002

Using the energy-conserved quantity method developed by Arnol’d [Dokl. Mat. Nauk 162, 773 (1965); Am. Math. Soc. Trans. 19, 267 (1969)] a study was made of the nonlinear stability of two inviscid fluid flows in three dimensions: (1) flow of a homogeneous fluid and (2) flow of a fluid whose energy density depends on the mass density alone (a so-called barotropic fluid). In order to implement the Arnol’d technique one must identify the quantities conserved by the flow in addition to the total energy. In the case of the two flows considered, the conserved quantities cannot be expressed in terms of the usual Eulerian variables—fluid velocity and mass density—alone. Instead the introduction of the Lagrangian labels of the fluid elements is required. A complete description of these conserved quantities, in both Eulerian and Lagrangian specifications of the fluid, is provided. The phase space of the flow is the entire Hamiltonian phase space expressed in either canonical or noncanonical variables. The nature of the flows to which the Arnol’d method is applicable is discussed in some depth. It was discovered that only time independent Eulerian flows can be discussed by the method; this result is given a general Hamiltonian context. The allowed Eulerian equilibria are displayed in detail. Finally, having the formal structure of these flows well in hand, it is shown that they are not, in three dimensions, formally stable. This results from a particle vortex stretching mechanism which is identified. The nature of the indicated instability is not revealed by this work, but may well be a slowly evolving Arnol’d diffusion kind of breakdown of the equilibrium.
The relationship between Brownian motion and the random motion of small particles in a turbulent flow
Authors: Reeks M. W.
Published: July 2002

Previous works have used the fluctuation–dissipation theorem to evaluate the diffusion coefficient for particles in a turbulent flow which differs from the commonly accepted value. This calculation is reexamined and it is concluded that fluctuation–dissipation expressing energy equipartition is inappropriate for hydrodynamic turbulence.
A direct interaction approximation treatment of turbulence in a compressible fluid. I. Formalism
Authors: Hartke Gregory J. , Canuto V. M. , Alonso Carol T.
Published: July 2002

The direct interaction approximation (DIA) is used to treat turbulence in a compressible medium with constant mean gradients. The set of coupled nonlinear integrodifferential equations is derived that is satisfied by the transverse and longitudinal energy spectral functions, QT and QL, and by the transverse and longitudinal response functions, GT and GL. Finally, expressions for the average of the product of pairs of physically relevant fluctuating quantities (velocity, temperature, density) are derived in terms of QT and QL. The numerical solution of this set of equations will be presented in part II of this work.
Dependence of heat pulse propagation on transport mechanisms: Consequences of nonconstant transport coefficients
Authors: Gentle K. W.
Published: July 2002

The transport coefficients for particles and heat will certainly depend upon plasma parameters. Besides making the equilibrium equations nonlinear, this introduces a multitude of new terms in the set of linearized equations, which can be used to describe the effects of perturbations to the system. A general set of such equations is obtained that includes most physical dependences of the transport coefficients. If transport is driven by gradients in density or temperature, as would be expected from most turbulence theories, significant quantitative effects result. Perturbations no longer evolve at the equilibrium transport rates, and the density and temperature perturbations can be strongly coupled. Results are presented for several specific cases.
Multidimensional similarity models for exploding foils
Authors: Hunter James H. , London Richard A.
Published: July 2002

A general derivation of the Gaussian, isothermal similarity equations for multidimensional hydrodynamic expansions is presented. Analytical solutions for the cases of constant heating and adiabatic flow for planar, cylindrical, and spherical expansions are given. An energy integral is derived for general multidimensional adiabatic flows. For two-dimensional adiabatic expansions, a second invariant of the motion is demonstrated. It is shown that this invariant gives the asymptotic shape of a Gaussian object in terms of its initial shape. A simple model for laser heating of an exploding foil is described and the asymptotic form of the corresponding solutions are given for two and three dimensions. The similarity solutions are compared with two-dimensional numerical hydrodynamic simulations for an example of an exploding foil, designed to produce a recombination x-ray laser.
Landau damping of sound in a rarefied neutral gas
Authors: Stubbe Peter
Published: July 2002

It is shown that the damping of sound, as measured in highly rarefied neutral gases, can be quantitatively described in terms of Landau damping. The theoretical method is based on determining the unknown pressure tensor gradient in the equation of motion by using the solution of the linearized kinetic equation, treating the occurring integrals over velocity space by Landau’s integration prescription. Collisions are taken into account by means of a relaxation model that meets all conservation requirements. The resulting equation of motion is formulated such that the entirety of linear kinetic effects is encapsulated in two coefficients, γ and Γ, which do not depend on particle charge, and are thus applicable to plasmas and neutral gases alike. The only occurrence of charges and electric fields in the equation of motion is in the form of a cold plasma force term. The coefficients γ and Γ are, in general, nonlocal in time and space, but become constants in certain limits. Application of the theory to neutral sound absorption leads to a good agreement with experimental data (Meyer and Sessler [Z. Phys. 149, 15 (1957)]) over the entire range of experimental parameters, from the near-collisionless to the collision-dominated limit.
A numerical study of local isotropy of turbulence
Authors: Antonia R. A. , Kim J.
Published: July 2002

The degree to which local isotropy applies is examined using databases obtained from numerical simulations of a variety of turbulent flows at low Reynolds numbers. Simulations of a turbulent channel flow were used to obtain most of the results but simulations of other flows, e.g. homogeneous isotropic turbulence, a homogeneous shear flow, and a turbulent mixing layer, have also been considered. Attention is mainly given to the high wave number part of the vorticity and temperature derivative spectra. The ratio of these spectra and their isotropic values depends on the particular quantity considered, the departure from isotropy being more pronounced for the temperature derivative than for the vorticity. When the Kolmogorov-normalized wave number is sufficiently large, isotropy is approximately satisfied provided the (Kolmogorov-normalized) mean strain rate is sufficiently small. This result appears to be independent of the quantity considered and of the Reynolds number.
Small-scale properties of scalar and velocity differences in three-dimensional turbulence
Authors: Pumir Alain
Published: July 2002

Turbulent flows are known to concentrate strong vorticity in vortex tubes, giving rise to large velocity jumps across the tubes. When a passive scalar is advected by the flow, very steep scalar fronts separate well-mixed regions, and result in large scalar differences. The properties of these large jumps are investigated by studying the probability distribution functions of velocity, scalar differences as a function of the separation between the points, of the Reynolds and of the Prandtl number. Over the range of parameters covered by the direct numerical simulations reported here (20≤Rλ≤90 and 1/32≤Pr≤1), it is found that the widths of the velocity (respectively, the scalar) jumps scale like the Kolmogorov length (respectively, like the Batchelor length). For both the scalar and the velocity, the large differences over small distance become rarer as the Reynolds number increases.
Bifurcation diagrams of axisymmetric liquid bridges subjected to axial electric fields
Authors: Ramos Antonio , González Heliodoro , Castellanos Antonio
Published: July 2002

The stability of dielectric liquid bridges between plane parallel electrodes when an electric potential difference is applied between them is studied for an axisymmetric configuration regarding arbitrary volume, axial gravity, and unequal coaxial anchoring disks attached to the electrodes. The stability is determined from the bifurcation diagrams related to the static problem. Two mathematical approaches are presented which are different in scope. First, the Lyapunov–Schmidt projection technique is applied to give the liquid bridge bifurcation diagrams for the bridge considered as an imperfect cylindrical one. The imperfection parameters, i.e., the relative difference of radii to the mean diameter, the deviation from the cylindrical volume, and the gravitational Bond number, are assumed to be small. Second, a Galerkin/finite element technique is used to obtain numerically bifurcation diagrams for arbitrary values of all the parameters. Agreement between both methods is good for small enough values of the imperfection parameters. The effect of the polarization charges existing at the free surface is highlighted. As in the absence of applied electric field, the gravitational Bond number and the relative difference of radii separately decrease the stability of the liquid column, but both effects conveniently combined may cancel out.
An investigation of recirculating flow in a driven cavity
Authors: Vynnycky Michael , Kimura Shigeo
Published: July 2002

The problem of steady incompressible laminar shear-driven flow in a two-dimensional quarter-circular cavity is discussed. An analytical solution is presented to the continuity and momentum equations at leading order for the case when the Reynolds number (Re) is much smaller than one. In addition, the O(Re) correction is computed numerically, and comparison of the two-term expansion for the streamfunction with a full numerical computation of the Navier–Stokes equations yields good agreement for a nominal value of Re as large as 100. Solutions for Re≫1 are also presented; these indicate several extra features that are not present in the classical driven-cavity problem, pertaining in particular to the flow direction and to the manner in which the governing equations should be correctly scaled.
Fractal properties of propagating fronts in a strongly stirred fluid
Authors: Haslam B. D. , Ronney P. D.
Published: July 2002

The fractal properties of propagating aqueous autocatalytic chemical reaction fronts are measured in a capillary-wave (CW) flow at values of the ratio of the RMS intensity of the fluid velocity fluctuation (u′) to the laminar propagation rate of the front (SL) up to 220. The images of the fronts are found to exhibit fractal behavior with a fractal dimension (d) of 1.31±0.06, which is very similar to some measurements in gaseous flame fronts, as well as isoscalar contours of passive dyes in CW and other randomly stirred flows. These results suggest that u′/SL, thermal expansion, variations of viscosity and diffusivity across the flame front, and the turbulence spectrum do not significantly affect d in randomly stirred flows.