bluuebunny/crossref_metadata_2025 huggingface dataset:
The function-series method and the coupled Boussinesq-like equations
Authors: Wu Juhao , Wang Kelin
Published: July 2002

The exact solution of a set of coupled Boussinesq-like equations is obtained procedurally by the function-series (FS) method without any ansatz. Meanwhile, the FS method itself is systematized into a universal approach to soliton-bearing nonlinear equation by introducing the convergence criterion.
Geodesic motion and confinement in van Stockum space–time
Authors: Opher Reuven , Santos Nilton O. , Wang Anzhong
Published: July 2002

Geodesic motion of test particles in van Stockum space–time, which represents the internal gravitational field produced by a rigidly rotating dust cylinder, is studied. In particular, it is found that confinement occurs quite generally in the radial direction, while the motion in the axial direction is free. The possible relevance of the confinement to the extragalactic jet formation is pointed out.
Surface-embeddability approach to the dynamics of the inhomogeneous Heisenberg spin chain
Authors: Balakrishnan Radha , Guha Partha
Published: July 2002

The surface-embeddability approach of Lund and Regge is applied to the classical, inhomogeneous Heisenberg spin chain to study the class of inhomogeneity functions f for which the spin evolution equation and its gauge-equivalent generalized nonlinear Schrödinger equation (GNLSE) are exactly solvable. Writing the spin vector S(x,t) as ∂xr and identifying r(x,t) with a position vector generating a surface, we show that the kinematic equation satisfied by r implies certain constraints on the admissible geometries of this surface. These constraints, together with the Gauss–Mainardi–Codazzi equations, enable us to express the coefficient of the second fundamental form as well as f in terms of the metric coefficients G and its derivatives, for arbitrary time-independent G. Explicit solutions for the GNLSE can also be found in terms of the same quantities. Of the admissible surfaces generated by r, a special class that emerges naturally is that of surfaces of revolution: Explicit solutions for r and S are found and discussed for this class of surfaces.
Singular continuous spectra and discrete wave packet dynamics
Authors: Guarneri Italo
Published: July 2002

Asymptotic estimates which relate the diffusion of wave packets on discrete lattices to Hausdorff dimensions of the local density of states are discussed.
Soliton curvatures of surfaces and spaces
Authors: Konopelchenko B. G.
Published: July 2002

An intrinsic geometry of surfaces and three-dimensional Riemann spaces is discussed. In the geodesic coordinates the Gauss equation for two-dimensional Riemann spaces (surfaces) is reduced to the one-dimensional Schrödinger equation, where the Gaussian curvature plays a role of potential. The use of this fact provides an infinite set of explicit expressions for curvature and metric of surface. A special case is governed by the KdV equation for the Gaussian curvature. Integrable dynamics of curvature via the KdV equation, higher KdV equations, and 2+1-dimensional integrable equations with breaking solitons is considered. For a special class of three-dimensional Riemann spaces the relation between metric and scalar curvature is given by the two-dimensional stationary Schrödinger or perturbed string equations. This provides us an infinite family of Riemann spaces with explicit scalar curvature and metric. Particular class of spaces and their integrable evolutions are described by the Nizhnik–Veselov–Novikov equation and its higher analogs. Surfaces and three-dimensional Riemann spaces with large curvature and slow dependence on the variable are considered. They are associated with the Burgers and Kadomtsev–Petviashvili equations, respectively.
Propagation of light in the stationary field of multipole gravitational lens
Authors: Kopeikin S. M.
Published: July 2002

A rigorous mathematical formalism for calculating the propagation of light rays in the stationary post-Newtonian field of an isolated celestial body (or system of bodies) considered as a gravitational lens having a complex multipole structure is developed. Symmetric trace-free tensors are used in the definition of gravitational multipoles instead of the less convenient (in general situations) scalar and vector spherical harmonics. Two types of perturbations of light rays, caused correspondingly by the mass and spin multipoles, are analyzed in full detail. A new simple method of integration for the equations of light propagation is proposed. This method enables us for the first time to obtain complete expressions both for the relativistic time delay and for the angle of the total deflection of light in any order of multipole perturbations without restriction. The results thus obtained can be applied to the interpretation of the secondary weak gravitational lens effects produced by the solar system bodies, stars, binary pulsars, and galaxies where the influence of higher-order multipoles on the propagation of null rays may be important and measurable. The methods developed in the paper can be also applied to physical optics of multipole electromagnetic lenses and for calculation of propagation of gravitational waves through the curved space–time. As a particular application of the method the generalized equation for a multipole gravitational lens is derived using Cartesian coordinates and symmetric transverse-traceless tensors.
Incorporation of space–time symmetries in Einstein’s field equations
Authors: Zafiris Elias
Published: July 2002

In the search for exact solutions to Einstein’s field equations the main simplification tool is the introduction of space–time symmetries. Motivated by this fact, we develop a method to write the field equations for general matter in a form that fully incorporates the character of the symmetry. The method is being expressed in a covariant formalism using the framework of a double congruence. The basic notion on which it is based is that of the geometrization of a general symmetry. As a special application of our general method we consider the case of a space-like conformal Killing vector field on the space–time manifold regarding special types of matter fields. New perspectives in General Relativity are discussed.
The Weierstrass–Enneper system for constant mean curvature surfaces and the completely integrable sigma model
Authors: Bracken P. , Grundland A. M. , Martina L.
Published: July 2002

The integrability of a system which describes constant mean curvature surfaces by means of the adapted Weierstrass–Enneper inducing formula is studied. This is carried out by using a specific transformation which reduces the initial system to the completely integrable two-dimensional Euclidean nonlinear sigma model. Through the use of the apparatus of differential forms and Cartan theory of systems in involution, it is demonstrated that the general analytic solutions of both systems possess the same degree of freedom. Furthermore, a new linear spectral problem equivalent to the initial Weierstrass–Enneper system is derived via the method of differential constraints. A new procedure for constructing solutions to this system is proposed and illustrated by several elementary examples, including a multi-soliton solution.
Dynamical electromagnetic modes for an expanding sphere
Authors: Mkrtchian V. E. , Baltz R. v.
Published: July 2002

The problem of dynamical modes for an expanding–contracting spherical cavity with metallic boundary conditions is considered, which is exactly solvable if the cavity surface is growing–decreasing with constant velocity. Explicit results are given for the normalized modes inside and outside the cavity.
Interaction of electromagnetic waves in a hard superconducting plate with unilateral excitation
Authors: Lyubimova I. O. , Baltaga I. V. , Kats A. A. , Yampolskii V. A. , Perez-Rodriguez F.
Published: July 2002

The nonlinear interaction of radiowaves with different frequencies in a superconducting plate under unilateral excitation is studied theoretically. The analysis of wave interaction is carried out in the framework of the critical state model. It is shown that the nonlinear nature of this model leads to a peculiar phenomenon in the wave interaction, namely, to jumps in the time dependence of electric field at the sample surface. The necessary conditions for the existence of these jumps are formulated. The role of dielectric properties of the substrate in the predicted phenomenon is formulated.
The film formation dynamics in spin coating
Authors: Ohara Taku , Matsumoto Yoichiro , Ohashi Hideo
Published: July 2002

Thin film formation using the process of spin coating is investigated. The liquid film and surrounding gas phase two-dimensional (2-D) full governing equations with applicable boundary conditions are formulated. The heat and mass transfer that occurs in the gas and liquid phase and across the free surface, including the evaporation of solvent, are taken into account. The governing equations and boundary conditions are then reduced to a 1-D case based on the variables radial dependency. The detailed film formation process that commences at the start of the spinning and ends with the dry-up of the coated film is numerically simulated by utilizing the 1-D governing equations. The complex effects of various process parameters, e.g., spinning speed, initial solute concentration, and disk heating, are clarified by the present numerical analysis. It was found that the final film thickness is mainly determined at the time when the film thinning rate resulting from radial convection has the same order as the film thinning rate resulting from solvent evaporation.
The fine structure in the Strouhal–Reynolds number relationship of the laminar wake of a circular cylinder
Authors: König Michael , Eisenlohr Holger , Eckelmann Helmut
Published: July 2002

There is experimental evidence that at least three discontinuities in the Strouhal number–Reynolds number relationship in the Reynolds number range 50–160 may exist under certain conditions. The appearance of discontinuities depends on how the cylinder is bounded at both ends, the aspect ratio, and the turbulence level of the oncoming flow. The discontinuity at Re≊90 observed by Tritton [J. Fluid Mech. 6, 547 (1959)] is therefore a three-dimensional effect. The discontinuities in the shedding frequency are accompanied by sudden changes in the shedding angle. Parallel vortex shedding results in the highest possible shedding frequency.
On the flow in the unobstructed space between shrouded corotating disks
Authors: Schuler C. A. , Usry W. , Weber B. , Humphrey J. A. C. , Greif R.
Published: July 2002

A model of a computer hard disk drive was constructed and measurements of the air flow in the unobstructed space between a pair of disks were obtained. The disks were centrally clamped to a common hub, and rotated within an axisymmetric (cylindrical) enclosure or shroud. Measurements of the circumferential velocity component were made at five radial locations and three rotation rates (Ω=300, 1200, and 3600 rpm) using a laser-Doppler velocimeter. The resulting mean and rms circumferential velocity profiles are presented and discussed. The data show that the circumferential velocity component profiles are fairly uniform in the axial direction in the space between the disks, except near the shroud where the flow is strongly sheared. The circumferential velocity peaks at a critical radius. Between the hub and the critical radius location the flow is in solid body rotation. Between the critical radius and the shroud the circumferential velocity decreases to zero, gradually at first and then very quickly as the shroud is approached. Analysis based on simplified force balance considerations facilitates the interpretation of the experimental observations and leads to improved understanding of the complex flow phenomena. Numerical calculations of the present configuration assuming axisymmetric steady flow were performed by Chang et al. (submitted to Int. J. Heat Mass Transfer). These calculations show reasonable agreement with the averaged velocity data but, for the reasons discussed, fail to reproduce features of the rms distribution associated with nonturbulent flow unsteadiness.
A model for the formation of oblique shedding and ‘‘chevron’’ patterns in cylinder wakes
Authors: Albarède Pierre , Monkewitz Peter A.
Published: July 2002

It is demonstrated that many features of flow visualizations involving oblique vortex shedding from two-dimensional bluff bodies, cylinders in particular, are qualitatively well described by a one-dimensional model, which represents diffusively coupled oscillators arranged along a line parallel to the cylinder. In mathematical terms, the idealized model consists of a transverse Ginzburg–Landau equation, in which the coefficients are determined experimentally. In physical terms, the model describes the formation of a pattern of tracer particles (e.g., smoke) over a very short streamwise interval which is subsequently only convected downstream. It is shown that, as in impulsively started experiments, ‘‘vortex shedding’’ in the model starts parallel to the cylinder. Regions of oblique shedding then develop from the cylinder ends and lead to steady-state chevrons for symmetric end conditions. Selection rules for the shedding angle as a function of Reynolds number are derived from the model and compared to experiments.
Collisionless tearing instability of a bi-Maxwellian neutral sheet: An integrodifferential treatment with exact particle orbits
Authors: Burkhart G. R. , Chen J.
Published: July 2002

The integrodifferential equation describing the linear tearing instability in the bi-Maxwellian neutral sheet is solved without approximating the particle orbits or the eigenfunction ψ. Results of this calculation are presented. Comparison between the exact solution and the three-region approximation [Phys. Fluids 27, 1198 (1984)] motivates the piecewise-straight-line approximation, a simplification that allows faster solution of the integrodifferential equation, yet retains the important features of the exact solution.
Mode competition and suppression in free electron laser oscillators
Authors: Antonsen T. M. , Levush B.
Published: July 2002

The stability of single-mode operation of free electron laser (FEL) oscillators is investigated. Two models of an untapered FEL oscillator are considered. The first model is called the klystron model. In the klystron model the FEL interaction occurs at two points: a prebunching point and an energy extraction point. In this model the nonlinear electron dynamics are solvable exactly, leading to a complex delay equation for the wave fields. The stability of single-mode operation can then be determined easily as a function of a single-pass gain, energy mismatch–frequency, and the difference between the group velocity of the radiation and the beam velocity. The second, more realistic model has a distributed interaction region of finite length: Stability of single-mode operation in this device must be determined numerically. The results of the models in the low gain regime are compared and the parameter regimes where stable single-mode operation is possible are determined. It is found that the time to reach a single-mode state can be extremely long.
Influence of the trapped-electron distribution on the sideband instability in a helical wiggler free-electron laser
Authors: Yang T.-Y. Brian , Davidson Ronald C.
Published: July 2002

Use is made of the Vlasov–Maxwell equations to investigate detailed properties of the sideband instability for a helical wiggler free-electron laser with wiggler wavelength λw=2π/k0=const and normalized wiggler amplitude aw=eB̂w/mc2k0=const. The model describes the nonlinear evolution of a right circularly polarized primary electromagnetic wave with frequency ωs, wave number ks, and slowly varying amplitude âs(z,t) and phase δs(z,t) (eikonal approximation). The coupled Vlasov and field-evolution equations are analyzed in the ponderomotive frame (‘‘primed’’ variables) moving with velocity vp=ωs/(ks+k0) relative to the laboratory. Detailed properties of the sideband instability are investigated for small-amplitude perturbations about a quasi-steady state characterized by an equilibrium electron distribution f0(γ′0) and a primary electromagnetic wave with constant amplitude â0s=const (independent of z′ and t′) and slowly varying phase δ0s(z′). A formal dispersion relation is derived for perturbations about a general equilibrium distribution f0(γ0) that may include both trapped and untrapped electrons. For the case where only trapped electrons are present, the dispersion relation is reduced to a simple analytical form. Detailed properties of the sideband instability are investigated for the case where the trapped electrons uniformly populate the ponderomotive potential up to an energy γ′M≤γ̂+, where γ̂′+ is the energy at the separatrix. Analysis of the dispersion relation shows that the maximum energy of the trapped-electron population (γM) significantly affects detailed stability properties in the strong-pump and intermediate-pump regimes.
Nonlinear dynamics of field maintenance and quasiperiodic relaxation in reversed-field pinches
Authors: Ho Y. L. , Craddock G. G.
Published: July 2002

The detailed dynamics underlying the self-generation of magnetic flux (‘‘dynamo’’) in reversed-field pinches (RFPs) is investigated with a three-dimensional magnetohydrodynamic code. A novel energy diagnostic is used to identify the path taken in Fourier space by the poloidal magnetic field energy as it is converted to axial magnetic field energy by the dynamo. At high values of the pinch parameter, Θ, and Lundquist number, S, the dynamo can be alternatingly dominated by quasilinear and nonlinear processes in a quasiperiodic fashion. Quasilinearly, the m=1 modes can reverse the axial field by themselves. However, m=0 modes are crucial to produce the nonlinear dynamo that triggers quasiperiodic relaxations. The same causal mechanism is likely to be responsible for the experimentally observed sawteeth.
Ion-temperature-gradient-driven transport in a density modification experiment on the Tokamak Fusion Test Reactor
Authors: Horton W. , Lindberg D. , Kim J. Y. , Dong J. Q. , Hammett G. W. , Scott S. D. , Zarnstorff M. C. , Hamaguchi S.
Published: July 2002

Tokamak Fusion Test Reactor (TFTR) profiles from a supershot density-modification experiment [Zarnstorff et al., Plasma Physics and Controlled Nuclear Fusion Research, 1990, Proceedings of the 12th International Conference, Washington (IAEA, Vienna, 1991), Vol. I, p. 109] are analyzed for their local and ballooning stability to toroidal ηi modes in order to understand the initially puzzling results showing no increase in χi when a pellet is used to produce an abrupt and large increase in the ηi parameter. The local stability analysis assumes that k∥=1/qR and ignores the effects of shear, but makes no assumption on the magnitude of k∥vti/ω. The ballooning stability analysis determines a self-consistent linear spectrum of k∥’s including the effect of shear and toroidicity, but it expands in k∥vti/ω≤1, which is a marginal assumption for this experiment. Nevertheless, the two approaches agree well and show that the mixing length estimate of the transport rate does not change appreciably during the density modification and has a value close to or less than the observed χi, in contrast to most previous theories, which predicted χi’s that were over an order-of-magnitude too large. However, still to be explained is the observed increase of χi(r) with minor radius by adding the effects of (i) the finite-beta drift wave—magnetohydrodynamic (MHD) mode coupling, (ii) the slablike mode, or (iii) the trapped-electron response. The experimental tracking 0.2<χe/χi<0.7 suggests that both grad Ti and trapped-electron driving mechanisms are operating.
Kinetic modeling of the α to γ transition in radio frequency discharges
Authors: Parker G. J. , Hitchon W. N. G. , Lawler J. E.
Published: July 2002

An accurate and comprehensive self-consistent kinetic model is applied to a helium radio frequency (rf) discharge which in experiments exhibits an ‘‘α to γ’’ transition. The main conclusions are (i) there is good agreement (factor of 2) between the experiment and simulation in plasma density, power density, and current density across two orders of magnitude of the applied voltage. (ii) The bulk electron temperature exhibits a transition from high at low driving voltages to low at high voltages. The low-voltage regime exhibits a larger bulk electric field in the simulation. (iii) Multistep ionization is important under all conditions studied.
Plasma-screening effects on the electron-impact excitation of hydrogenic ions in dense plasmas
Authors: Jung Young-Dae
Published: July 2002

Plasma-screening effects are investigated on electron-impact excitation of hydrogenic ions in dense plasmas. Scaled cross sections Z4⋅σ for 1s→2s and 1s→2p are obtained for a Debye–Hückel model of the screened Coulomb interaction. Ground and excited bound wave functions are modified in the screened Coulomb potential (Debye–Hückel model) using the Ritz variation method. The resulting atomic wave functions and their eigenenergies agree well with the numerical and high-order perturbation theory calculations for the interesting domain of the Debye length Λ/aZ≥10. The Born approximation is used to describe the continuum states of the projectile electron. Plasma screening effects on the atomic electrons cannot be neglected in the high-density cases. Including these effects, the cross sections are appreciably increased for 1s→2s transitions and decreased for 1s→2p transitions.
Coronal mass ejections: The link between solar and geomagnetic activity*
Authors: Gosling J. T.
Published: July 2002

Coronal mass ejections are spectacular manifestations of solar activity in which 10+15–10+16 g of solar material are propelled outward into interplanetary space. Recent work has demonstrated that these events are the prime link between solar activity and large, nonrecurrent geomagnetic storms, closing a loop in a body of research extending back more than 130 years.
Renormalized geometric optics description of mode conversion in weakly inhomogeneous plasmas
Authors: Friedland L.
Published: July 2002

Conventional mode conversion theory in inhomogeneous plasmas starts with a local dispersion relation, which serves as a base for constructing a differential equation describing the waves in nearly degenerate plasma regions, where the mode conversion can take place. It will be shown, however, that the usual geometric optics perturbation scheme, which in the zero order leads to the aforementioned dispersion relation, predicts either rapid variations of the local wave vector and amplitude of the wave, or large first-order corrections to the amplitude in nearly degenerate plasma regions. A novel, general, renormalized perturbation scheme will be suggested in order to remove this singular behavior. The new method is formulated in terms of the conventional, general plasma dielectric tensor and yields two coupled, energy-conserving differential equations describing the mode conversion. Simple asymptotic solutions of these equations exist if the mode coupling is localized and weak. The method is applied to the classical problem of transformation of the extraordinary mode propagating in a cold magnetized plasma at small angles to the magnetic field. Generalization of the method to the case of an unreduced, multicomponent wave propagation problem is discussed.
Linear stability of tearing modes
Authors: Cowley S. C. , Kulsrud R. M. , Hahm T. S.
Published: July 2002

This paper examines the stability of tearing modes in a sheared slab when the width of the tearing layer is much smaller than the ion Larmor radius. The ion response is nonlocal, and the quasineutrality retains its full integral form. An expansion procedure is introduced to solve the quasineutrality equation in powers of the width of the tearing layer over the ion Larmor radius. The expansion procedure is applied to the collisionless and semicollisional tearing modes. It is found that first-order terms in the expansion are strongly stabilizing. The physics of the mode and of the stabilization are discussed. Tearing modes are observed in experiments even though the slab theory predicts stability. It is proposed that these modes grow from an equilibrium with islands at the rational surfaces. If the equilibrium islands are wider than the ion Larmor radius, the mode is unstable when Δ′ is positive.
The resistive tearing mode in a weakly two-dimensional sheet pinch
Authors: Paris R. B.
Published: July 2002

The influence of a weak normal component of the magnetic field Bn on the resistive tearing mode in a sheet pinch is examined. The dispersion relation in the high conductivity limit is derived in closed analytical form and it is shown that the normal magnetic field exerts a stabilizing influence. For values of Bn scaling like η2/5, where η is the resistivity, the results obtained relate to recent numerical calculations of Nishikawa and Sakai [Phys. Fluids 25, 1384 (1982)] for finite Bn. In the very weak ordering with Bn scaling like η4/5, the previous analytical result of Janicke [Phys. Fluids 23, 1843 (1980)] is recovered.
Theory and simulation of electromagnetic beam modes and whistlers
Authors: Newman David L. , Winglee Robert M. , Goldman Martin V.
Published: July 2002

Using particle-in-cell simulations and analytical methods, a study of the nonlinear evolution of electromagnetic instabilities driven by an anisotropic electron beam (Tb⊥≫Tb∥) in an external magnetic field is performed. The unstable waves are either whistlerlike or beam-mode-like depending on the external field strength and beam velocity. The evolution of the particle distribution differs significantly in the two regimes. Even in the presence of a faster electrostatic instability, the electromagnetic waves grow to a significant amplitude. In certain cases, an energetic tail is formed, resulting in enhanced Čerenkov emission of electrostatic waves. The initial evolution of the particle distribution is explained in terms of the interaction of a given linearly unstable wave with the self-consistent perturbed distribution.
Nearly incompressible magnetohydrodynamics at low Mach number
Authors: Matthaeus William H. , Brown Michael R.
Published: July 2002

The dynamics of a compressible magnetofluid plasma with a polytropic equation of state are considered in the limit of low plasma frame acoustic Mach number. The relationship between the equations describing the low Mach number flow and the equations of idealized incompressible magnetohydrodynamics is investigated using a multiple time scale asymptotic expansion procedure, which is justified by appealing to several rigorous theorems concerning both hydrodynamics and magnetohydrodynamics. When appropriate assumptions are adopted concerning the degree of departure from incompressibility, the lowest-order behavior is that of incompressible magnetohydrodynamics, associated with order Mach number-squared ‘‘pseudosound’’ density fluctuations. The first corrections to incompressible flow take the form of magnetoacoustic fluctuations, with associated pressure fluctuations at the same order as the pseudosound pressure. Resumming the asymptotic series gives rise to a simple set of equations that describes ‘‘nearly incompressible magnetohydrodynamics.’’ The theory provides a justification for the turbulent density spectrum theory of Montgomery, Brown, and Matthaeus [J. Geophys. Res. 92, 282 (1987)] and clarifies several issues pertaining to Alfvén wave turbulence in the solar wind. The nearly incompressible description may also be useful in other theoretical contexts, particularly in extensions of incompressible magnetohydrodynamic turbulence theory, since it is expected to be valid for finite times (until possible shock structures form) when the global Mach number is sufficiently small.
Effects of curvature variations on the nonlinear evolution of Goertler vortices
Authors: Benmalek Ali , Saric William S.
Published: July 2002

The nonlinear development of Goertler vortices over walls of variable curvature is studied. The parabolized disturbance equations governing the problem for small curvature, high Reynolds number, and order unity Goertler number are integrated numerically. Cases with concave, convex, and zero curvatures are analyzed. The ‘‘mushroom-shaped’’ distributions of low-momentum fluid riding above high-momentum fluid that are subject to secondary instability are predicted. The results show significant stabilization of disturbances introduced from a concave into a convex region, where new sets of vortices are successively created with opposite rotation to the preceding set. The convex curvature tends to eliminate the inflection points from the spanwise and normal profiles of the streamwise velocity and, hence, suppresses the oscillatory secondary instability that leads to turbulence. Decay of Goertler vortices in a flat region is found to be less rapid than in a convex region.
Numerical study of bypass transition
Authors: Voke Peter R. , Yang Zhiyin
Published: July 2002

A large-eddy simulation has been performed of a flat-plate boundary layer undergoing transition to turbulence under free-stream turbulence at a level of 6%. The properties of the simulated transition match those found experimentally: not only is the position and length of transition in agreement with available data, but the mechanism of transition also appears to correspond closely, since disturbances seen in the laminar layer prior to transition are found in the simulation. Statistical data have been gathered that allow the computation of all terms in the derived equations for the Reynolds stresses at four x stations. Aspects of these balances are presented that allow new insights into the physical mechanisms at work. The importance of the wall-normal component of free-stream turbulence and the timing of the redistribution of energy into this component through the fluctuating pressure field are revealed.
Multiple, two-dimensional solutions in a rotating straight pipe
Authors: Sharma Ravi K. , Nandakumar K.
Published: July 2002

The multiplicity features and the secondary flow structure of the fully developed, laminar flow of a Newtonian fluid in a straight pipe that is rotating about an axis perpendicular to the pipe axis are examined. The governing equations of motion are solved numerically using the control volume method and the SIMPLE algorithm. The solution structure is governed by two dynamical parameters, Ekman number, Ek=ν/D2Ω and Rossby number, Ro=U/DΩ, where D is the pipe diameter, ν is kinematic viscosity, Ω is rotational speed, and U is velocity scale. Results are presented for a fixed Ekman number of Ek=0.01 and a range of Rossby numbers between 0 to 20. The primary solution branch begins as a unique solution at low Rossby numbers. Its secondary flow structure consists of two-cells. At higher values of Ro a hitherto unknown solution with a four-cell flow structure appears, which coexists with the two-cell flow structure over a range of Ro up to 20. Transient, two-dimensional simulations were carried out to determine the stability of the solutions to two-dimensional perturbations. The two-cell flow structure is stable to both symmetric and asymmetric perturbations. Four-cell flow structure is stable to symmetric perturbations and unstable to asymmetric perturbations, where it breaks down to a two-cell flow structure.
Study of the von Kármán flow between coaxial corotating disks
Authors: Labbé R. , Pinton J.-F. , Fauve S.
Published: July 2002

We report an experimental study of the swirling flow generated in the gap between two coaxial corotating disks. We use a free geometry, i.e., unshrouded disks in air, with moderate to high Reynolds numbers. When the relative rotation rate is varied, transitions in the flow can be observed by global power measurement and are related to the geometry of the external recirculating flow. The mean flow is studied in details with hot-wire measurements using a boxcar-type averaging technique. It involves a single turbulent vortex undergoing a slow precession motion. We show that statistical properties of the turbulent fluctuations are affected by the dynamics of the mean flow, which also displays a correlation with the global power fluctuations.
On the effects of suction and injection on the absolute instability of the rotating-disk boundary layer
Authors: Lingwood R. J.
Published: July 2002

In this paper we are concerned with the theoretical behavior of the laminar von Kármán boundary-layer flow, extending the work presented by Lingwood [J. Fluid Mech. 299, 17 (1995); 314, 373 (1996)] to the flow with mass transfer at the surface of the disk. It is known that, within specific regions of the parameter space, the flow is absolutely unstable in the radial direction, i.e. disturbances grow in time at every radial location within these regions. Uniform suction through the disk is shown to delay the onset of absolute instability, while uniform injection promotes the onset. By comparing suction and injection velocities of the same magnitude, it is shown that suction has a greater stabilizing effect on the absolute instability than the destabilizing effect of injection. Suction is also strongly stabilizing to both stationary and travelling inviscidly unstable branch-1 modes; injection is destabilizing. Stationary viscously unstable branch-2 modes are strongly stabilized and destabilized by suction and injection, respectively, but travelling branch-2 modes are shown to be much less sensitive to mass transfer through the disk.
Measurement of the inertial lift on a moving sphere in contact with a plane wall in a shear flow
Authors: King Michael R. , Leighton, Jr. David T.
Published: July 2002

The translational and rotational velocities of a positively buoyant sphere suspended in a parallel plate device are measured, and related to the inertial lift of the sphere from the upper plate. The experimental results obtained agree well with the corrected theoretical predictions of Krishnan and Leighton [Phys. Fluids 7, 11 (1995)]. The motion of the sphere principally depends on the shear Reynolds number Re≡γ̇a2/ν, where γ̇ is the shear rate, a is the particle radius and ν the kinematic viscosity, and the sedimentation Reynolds number Res≡Usa/ν where Us is the Stokes sedimentation velocity of the sphere. The transition from translation without slip to translation with slip along the plane is observed to scale as Re/Res, and occurs at order 10−1. The separation of the sphere from the plane due to inertial lift at low Reynolds number is found to have the scaling Re2/Res, as predicted by theory. In experiments with two particles of diameter 1.5 and 2 mm in two glycerin/water solutions of different densities, the particles were found to lift off the plane at Re2/Res≈4. This value is consistent with measurements of the particle surface roughness.
Nusselt number for flow perpendicular to arrays of cylinders in the limit of small Reynolds and large Peclet numbers
Authors: Wang Wei , Sangani Ashok S.
Published: July 2002

The problem of determining the Nusselt number N, the nondimensional rate of heat or mass transfer, from an array of cylindrical particles to the surrounding fluid is examined in the limit of small Reynolds number Re and large Peclet number Pe. N in this limit can be determined from the details of flow in the immediate vicinity of the particles. These are determined accurately using a method of multipole expansions for both ordered and random arrays of cylinders. The results for N/Pe1/3 are presented for the complete range of the area fraction of cylinders. The results of numerical simulations for random arrays are compared with those predicted using effective-medium approximations, and a good agreement between the two is found. A simple formula is given for relating the Nusselt number and the Darcy permeability of the arrays. Although the formula is obtained by fitting the results of numerical simulations for arrays of cylindrical particles, it is shown to yield a surprisingly accurate relationship between the two even for the arrays of spherical particles for which several known results exist in the literature suggesting thereby that this relationship may be relatively insensitive to the shape of the particles.
Convective and absolute instability of a liquid jet in a longitudinal magnetic field
Authors: Shugai G. A. , Yakubenko P. A.
Published: July 2002

A circular jet of perfectly conductive inviscid liquid in a uniform longitudinal magnetic field can be absolutely or convectively unstable for different values of the flow parameters. Higher intensity of the field always reduces the domain of absolute instability. For both cases of absolute and convective instability, the corresponding jet of large but finite length is globally unstable if suitable boundary conditions hold at its beginning and end. The unstable global mode is based on a pair of waves that propagate in opposite directions and reflect from one into the other at the flow boundaries.
Theory for the off-diagonal element of dissipation in homogeneous shear turbulence
Authors: Weinstock J.
Published: July 2002

The off-diagonal element, ε12, of the energy dissipation rate tensor is calculated from straight-forward spectral considerations. The derivation is for homogeneous shear flows. Account is taken of the difference between energy spectra and stress spectra, and the dissipation range of the spectra is taken from recent high-resolution numerical simulations. Emphasized, is the theoretically derived power law describing the decrease of ε12/ε with increasing Reynolds number at large Reynolds number. For moderate Reynolds number, the theoretical ε12/ε is compared with numerical simulations. For large Reynolds number, the theory implies local isotropy.
Ionization and particle transfer in an expanding current-carrying plasma
Authors: Krinberg I. A.
Published: July 2002

A theory is developed for steady-state spherical expansion of a current-carrying plasma that is fully ionized at the transition point to supersonic flow. It is shown that there exists a small region of the initial part of plasma flow where the charge particle density has a maximum and the ions move in a direction opposite to the plasma. The appearance of such a counterstreaming ion current may be of interest when interpreting the plasma–cathode surface interaction in a vacuum arc discharge.
Far field sheaths from waves in the ion cyclotron range of frequencies
Authors: Myra J. R. , D’Ippolito D. A. , Bures M.
Published: July 2002

Experimental evidence suggests that unabsorbed wave energy in ion cyclotron range of frequency fast wave (FW) experiments can result in deleterious edge interactions. A model describing the formation of far field sheaths due to FW interaction with material surfaces is presented. Near conductors that do not conform to flux surfaces, an incoming FW causes the generation of a slow wave (SW) component. The E∥ of the SW drives an RF sheath, in a manner similar to what has been previously discussed for antenna (near field) sheaths. To assess the importance of the proposed mechanism, a heuristic scaling model of the resultant sheath voltage V is developed and compared with a numerical code. The model illustrates the important dependencies of V on the single pass absorption, edge density, FW frequency, FW cutoff location, and limiter/wall geometries and yields qualitative agreement with the experimental observations.
Numerical simulation of nonequilibrium effects in an argon plasma jet
Authors: Chang C. H. , Ramshaw J. D.
Published: July 2002

Departures from thermal (translational), ionization, and excitation equilibrium in an axisymmetric argon plasma jet have been studied by two-dimensional numerical simulations. Electrons, ions, and excited and ground states of neutral atoms are represented as separate chemical species in the mixture. Transitions between excited states, as well as ionization/recombination reactions due to both collisional and radiative processes, are treated as separate chemical reactions. Resonance radiation transport is represented using Holstein escape factors to simulate both the optically thin and optically thick limits. The optically thin calculation showed significant underpopulation of excited species in the upstream part of the jet core, whereas in the optically thick calculation this region remains close to local thermodynamic equilibrium, consistent with previous experimental observations. Resonance radiation absorption is therefore an important effect. The optically thick calculation results also show overpopulations (relative to equilibrium) of excited species and electron densities in the fringes and downstream part of the jet core. In these regions, however, the electrons and ions are essentially in partial local thermodynamic equilibrium with the excited state at the electron temperature, even though the ionized and excited states are no longer in equilibrium with the ground state. Departures from partial local thermodynamic equilibrium are observed in the outer fringes and far downstream part of the jet. These results are interpreted in terms of the local relative time scales for the various physical and chemical processes occurring in the plasma.
Development of a medium power, submillimeter wave gyrotron using a 17 T superconducting magnet
Authors: Idehara T. , Shimizu Y. , Ichikawa K. , Makino S. , Shibutani K. , Kurahashi K. , Tatsukawa T. , Ogawa I. , Okazaki Y. , Okamoto T.
Published: July 2002

GYROTRON FU IV, a frequency tunable gyrotron for spectroscopy in the submillimeter wavelength range using a 17 T superconducting magnet, has been designed and constructed. Simulations predict that the gyrotron will emit radiation at high frequencies up to 394 GHz (TE041 cavity mode) at the fundamental of the electron cyclotron frequency, up to 858 GHz (TE091 mode) at the second harmonic and up to 1301 GHz (TE8 11 1 mode) at the third harmonic. Preliminary experimental results have demonstrated operation from 158 to 443 GHz at the fundamental and from 336 to 838 GHz at the second harmonic. Output powers are several hundred watts and efficiencies several percent.
Reflection of modified Korteweg–de Vries solitons in a negative ion plasma
Authors: Yi Seungjun , Cooney Jamie L. , Kim Hyun-Soo , Amin Ali , El-Zein Yasser , Lonngren Karl E.
Published: July 2002

Reflection of modified Korteweg–de Vries solitons from the sheath in front of a negatively biased metal disk is experimentally investigated in a negative ion plasma. Both rarefactive and compressive solitons are reflected and the polarity of the reflected solitons is the same as that of the incident solitons. The points of reflection for the rarefactive and compressive solitons are at different locations. As the magnitude of the negative bias potential that is applied to the reflector is increased, the two reflection points move away from the reflector. An interpretation in terms of the sheath characteristics is presented.
Experimental analysis of drift waves destabilization in a toroidal plasma
Authors: Riccardi C. , Xuantong D. , Salierno M. , Gamberale L. , Fontanesi M.
Published: July 2002

This paper concerns the study of the development of turbulence in a toroidal magnetoplasma [C. Riccardi et al., Plasma Phys. 36, 1791 (1994)]. This analysis has been performed by evaluating wave number, frequency spectra, and bicoherence coefficients of density fluctuations associated to drift wave propagation. Plasma parameters have been changed over a wide range, in order to identify and characterize density fluctuations both in absence and in presence of nonlinear phenomena.
Dynamic screening effects on semiclassical ionization probabilities for electron–ion collisions in weakly coupled plasmas
Authors: Jung Young-Dae
Published: July 2002

In dense weakly coupled plasmas, dynamic screening effects on semiclassical ionization probabilities for electron-impact ionization of hydrogenic ions are investigated. The projectile–target interaction Hamiltonian is obtained by introduction of the longitudinal plasma dielectric function. The semiclassical approximation is applied to treat the projectile electron as a classical point particle with a well-defined straight-line trajectory R(t) and the bound electron is treated quantum mechanically. The semiclassical ionization probability is obtained as a function of the impact parameter, the projectile energy, and the Debye length. The semiclassical ionization probability including the dynamic screening effect is always greater than that, including the static screening effect described by the nonspherical Debye–Hückel model. When the projectile velocity is smaller than the electron thermal velocity, the dynamic screening effect turns out to be the static screening effect. However, when the projectile velocity is greater than the electron thermal velocity, the interaction Hamiltonian is almost unshielded. Unlike the electron capture processes, the difference between the dynamic and static screening effects are more significant for high-energy projectiles. The static interaction Hamiltonian always overestimates the plasma screening effect on the electron-impact ionization processes in dense weakly coupled plasmas.
Control of the chaotic regimes of nonlinear drift-waves in a magnetized laboratory plasma
Authors: Gravier E. , Caron X. , Bonhomme G. , Pierre Th.
Published: July 2002

Nonlinear drift-waves are experimentally studied in a cylindrical magnetized laboratory plasma. Low-dimensional chaotic regimes are controled using the time-delay autosynchronization method [K. Pyragas, Phys. Lett. A 170, 421 (1992)]. A significant reduction of spectral width in the power spectrum is obtained.
Liquid- and crystallike structures in strongly coupled dusty plasmas
Authors: Fortov Vladimir E. , Molotkov Vladimir I. , Nefedov Anatoli P. , Petrov Oleg F.
Published: July 2002

Dust particle ordering is discussed in various types of low-temperature plasma, such as thermal plasmas at atmospheric pressure, dc glow discharges, UV- and radioactivity induced plasmas. The investigations of UV-induced dusty plasma were made under microgravity conditions. Experimental data are presented. Properties of ordered structures are discussed and the conditions of formation considered.
Rapid frequency step-switching in submillimeter wave gyrotrons (Gyrotrons FU III and FU IV)
Authors: Idehara T. , Shimizu Y. , Ogawa I. , Tatsukawa T. , Brand G. F.
Published: July 2002

The rapid frequency step-switching between two nearby cyclotron fundamental modes achieved by switching beam energy is analyzed by a computer simulation and demonstrated experimentally. More dramatic frequency switching between a fundamental mode and a second harmonic mode is analyzed and demonstrated experimentally.
Investigation of rising-sun magnetrons operated at relativistic voltages using three-dimensional particle-in-cell simulation
Authors: Lemke R. W. , Genoni T. C. , Spencer T. A.
Published: July 2002

This work is an attempt to elucidate effects that may limit efficiency in magnetrons operated at relativistic voltages (V∼500 kV). Three-dimensional particle-in-cell simulation is used to investigate the behavior of 14 and 22 cavity, cylindrical, rising-sun magnetrons. Power is extracted radially through a single iris located at the end of every other cavity. Numerical results show that in general output power and efficiency increase approximately linearly with increasing iris width (decreasing vacuum Q) until the total Q becomes too low for stable oscillation in the π-mode to be maintained. Beyond this point mode competition and/or switching occur and efficiency decreases. Results reveal that the minimum value of Q (maximum efficiency) that can be achieved prior to the onset of mode competition is significantly affected by the magnitude of the 0-space-harmonic of the π-mode, a unique characteristic of rising suns, and by the magnitude of the electron current density (space-charge effects). By minimizing these effects, up to 3.7 GW output power has been produced at an efficiency of 40%.