bluuebunny/crossref_metadata_2025 huggingface dataset:
Large-scale three-dimensional Langmuir circulation
Authors: Cox Stephen M. , Leibovich Sidney
Published: July 2002

A reduced equation set in two space dimensions capable of describing three-dimensional Langmuir circulation in a layer of unstratified water is derived. The reduced description is valid for circulations having large horizontal scales compared to vertical scales, and should be useful for pattern formation studies when this condition is met. Windrow patterns on the surface are found from numerical simulations of the reduced equation set, guided by secondary instability theory.
Crude closure dynamics through large scale statistical theories
Authors: Grote Marcus J. , Majda Andrew J.
Published: July 2002

Crude closure algorithms based on equilibrium large scale statistical theories involving only a few constraints are developed here. These algorithms involve the nonlinear evolution of either a single parameter, the energy, for dynamic closure based on equilibrium energy-enstrophy statistical theory, or two parameters, the energy and circulation, for crude dynamic closure based on the equilibrium point vortex statistical theory. The crude closure algorithms are tested systematically through numerical experiments with the Navier–Stokes equations in two dimensions on a rectangular domain with stress-free boundary conditions and strong small scale forcing at moderately large Reynolds numbers. A series of successively more stringent tests is devised with conditions ranging from freely decaying flows to spin-up from rest by random forcing with like signed vortices, and finally to random forcing by vortices with alternating or opposite signs. Comparison of standard spectral simulations with crude dynamic closure based on the two-parameter theory yields at most 5% velocity errors for all of these examples. The velocity errors can be as large as 10% for the one-parameter closure theory but are often comparable to those obtained with the two-parameter closure. The results of numerical experiments with Ekman drag are also discussed here.
Front dynamics in turbulent media
Authors: Martí A. C. , Sagués F. , Sancho J. M.
Published: July 2002

A study of a stable front propagating in a turbulent medium is presented. The front is generated through a reaction-diffusion equation, and the turbulent medium is statistically modeled using a Langevin equation. Numerical simulations indicate the presence of two different dynamical regimes. These regimes appear when the turbulent flow either wrinkles a still rather sharp propagating interfase or broadens it. Specific dependences of the propagating velocities on stirring intensities appropriate to each case are found and fitted when possible according to theoretically predicted laws. Different turbulent spectra are considered.
The approach to self-preservation of scalar fluctuations decay in isotropic turbulence
Authors: Gonzalez M. , Fall A.
Published: July 2002

An analytical study of isotropic scalar fluctuations decay in isotropic turbulence is undertaken. From a fixed-point analysis, the existence of two complete self-preserving regimes is demonstrated. One of them relates to the final period of decay whereas the other one corresponds to the decay at large Reynolds and Péclet numbers. In both cases, the scalar-to-velocity timescale ratio is constant. In the final period, its asymptotic value is determined by the values of the coefficients of velocity and scalar enstrophy destruction. At large Reynolds and Péclet numbers, it depends on the latter as well as on the values of the mixed-derivative and velocity derivative skewness coefficients. A model for the approach to full self-preservation of scalar fluctuations decay is proposed. This model accounts for non-equilibrium resulting from initial unbalanced vortex stretching. In the conditions of experiments on temperature fluctuations decay in grid-turbulence, it displays a transient regime, extending over the region of measurements, during which the decay exponent is not constant but slowly varying.
Nonlinear oscillations of drops with internal circulation
Authors: Mashayek F. , Ashgriz N.
Published: July 2002

Nonlinear oscillations of viscous liquid drops with and without initial internal circulation are investigated. The full Navier–Stokes equations are solved for a liquid drop surrounded by a dynamically inactive ambient gas. The Galerkin/finite element technique along with the spine-flux method for the advection of the free boundaries are used. Internal circulations are generated by imposing a constant velocity at the surface of the drop and obtaining the steady state velocity field for a fixed drop shape. Oscillations of drops subject to small to large amplitude, and for the second-, third-, fourth-, and fifth-mode disturbances are considered. New data on the period and the decay factor of the oscillations are reported. The internal circulation in a drop released from an even-mode shape results in the transfer of energy mainly between the even modes. The internal circulation in a drop released from an odd-mode shape results in the transfer of energy between both odd and even modes. In general, the internal circulations generated by a constant surface velocity tend to transfer energy from any mode of drop oscillations to the second mode. This tendency increases as the strength of the internal circulation increases.
The effect of shape on the hydrodynamics of a hemispheroid projecting from a plate in irrotational fluid
Authors: Shatz Lisa F.
Published: July 2002

In this paper, we examine the problem of hemispheroid that is compliantly hinged to a plate oscillating with infinitesimal motions in fluid that can be modeled as irrotational. We use this model to understand the effect of the size and shape of hair bundles of sensory cells in the inner ear on hair bundle hydrodynamics at high frequencies. In response to the oscillating plate, the hemispheroid translates and rotates in the plane of the oscillation. Since the equations of motion are linear, the solution can be described as the superposition of the response due to translation of the hemispheroid and the plate, and the response due to rotation of the hemispheroid. The solution can be found by solving Laplace’s equation in prolate and oblate spheroidal coordinates. The response due to translational motion is the same as that derived in Hydrodynamics, 6th ed. (Dover, New York, 1945) for a full spheroid undergoing translational motion. The response due to rotational motion of the hemispheroid about its hinge has not been previously derived. The hydrodynamic pressure, torque, and drag on the hemispheroid as a function of hemispheroidal shape are presented. A good match was obtained for results of the model and measurements of a neural tuning curve of the alligator lizard.
High-order azimuthal instabilities on a cylindrical liquid jet driven by temporal and spatial perturbations
Authors: Dressler John L.
Published: July 2002

A method has been developed to drive a cylindrical liquid jet unstable for deformations with axial wavelengths shorter than the circumference of the jet and azimuthal mode numbers greater than 0. The benefit of this method is that a cylindrical liquid jet can be broken into a spray with an average diameter smaller than the diameter of the initial jet. The higher-order instabilities were created by establishing initial conditions for the jet in space and time at the nozzle. An electromechanical transducer creates the applied temporal initial condition which is a sinusoidally varying velocity perturbation added to the steady velocity of the jet. The amplitude of the velocity perturbation can be as large as the jet’s steady velocity and the energy in the applied velocity perturbation drives the instability. The spatial perturbation is created by placing perturbations in the circumference of the nozzle. As the velocity perturbation travels on the jet, its leading edge steepens and the trailing edge broadens in a manner analogous to the steepening of a pressure pulse in a compressible gas. If the driven velocity perturbation is sufficiently large, a shock or jump forms on the leading edge of the velocity pulse and the jet may break up into higher-order modes. A theoretical analysis of the breakup process, based on an adaptation of compressible fluid shock theory, is used to derive a fundamental lower bound on the spray’s Sauter mean diameter as a function of the velocity perturbation amplitude. Techniques for approaching the theoretical minimum spray diameter by using the higher-order modes to atomize liquid jets are discussed.
Finite amplitude stability of attachment line boundary layers
Authors: Balakumar P. , Trivedi Prakash A.
Published: July 2002

Two-dimensional nonlinear equilibrium solutions for the swept Hiemenz flow attachment line boundary layer are directly computed by solving the full Navier-Stokes equations as a nonlinear eigenvalue problem. The equations are discretized using the two-point fourth order compact scheme and the resulting nonlinear homogeneous equations are solved using the Newton-Raphson iteration technique. It is found that for Reynolds numbers larger than the linear critical Reynolds number of 583, the nonlinear neutral surfaces form open curves. The results showed that the subcritical instability exists near the upper branch neutral curve and supercritical equilibrium solutions exist near the lower branch. These conclusions are in agreement with the weakly nonlinear theory. However, at higher amplitudes away from the linear neutral points the nonlinear neutral surfaces show subcritical instability at lower and higher wave number regions. At Reynolds numbers lower than the critical value, the nonlinear neutral surfaces form closed loops. By reducing the Reynolds number, we found that the nonlinear critical point occurs at a Reynolds number of 511.3, below which all the two-dimensional disturbances will decay. The secondary instability of these equilibrium solutions is investigated using the Floquet theory. The results showed that these two-dimensional finite amplitude neutral solutions are unstable to three-dimensional disturbances.
Transient states during spin-up of a Rayleigh–Bénard cell
Authors: Vorobieff P. , Ecke R. E.
Published: July 2002

The influence of impulsive spin-up on Rayleigh–Bénard convection in a cylindrical cell with radius-to-height ratio Γ=0.5 is investigated. Velocity and temperature fields in the thin layer adjacent to the top of the cell are measured by means of particle image velocimetry and thermochromic liquid crystal visualization. The cell, initially in steady nonrotating convection, is rapidly accelerated to steady rotation about its vertical axis with dimensionless rotation rates 4×103⩽Ω⩽8×104. Rayleigh numbers Ra vary from 5×107 to 5×108. In a large part of this domain of the parameter space, axisymmetric structures appear near the top of the cell. In most cases, a single ring forms with a radius close to 3/4 of the radius of the cell. The same experiment without heating produces typical Ekman spin-up devoid of ring structures. The ring is characterized by a local decrease in temperature and azimuthal velocity. As the flow evolves, an azimuthal velocity gradient forming across the ring causes shear instability and leads to the emergence of Kelvin–Helmholz vortices.
On equilibrium modes and their stability in the small-gap Taylor problem by a new method
Authors: Eagles P. M.
Published: July 2002

We consider small disturbances to the steady viscous flow between concentric rotating circular cylinders. It is shown that as the dimensionless gap width δ approaches zero the terms from ∂/∂θ in the governing equations are O(δ1/2) and so do not appear in the first approximation. This is in contrast to the classical small-gap approximation, in which terms from ∂/∂θ do appear in the first approximation. Here θ is the usual azimuthal angle. Let ε be a measure of the size of the small perturbation. In Sec. III it is argued that the asymptotic relation ε∼δ2 is needed to obtain a correct approximation to weakly nonlinear axisymmetric (Taylor-vortex) equilibrium flow for small values of δ. We use this relation between ε and δ to obtain a unified amplitude equation to describe both axisymmetric modes and those with a general dependence on the azimuthal angle, taking into account weakly nonlinear effects. This allows a description of single-mode equilibrium states and of their stability. Some unexpected results are obtained about the stability of these modes. The mode with m=0 is shown to be stable for all relevant values of the Taylor number T. This is to be expected under the particular limiting process used. However the modes with m=1, 2, and 3 are shown to become stable for successively higher values of T. It is also shown that these nonaxisymmetric equilibrium states may be obtained by the solution of some initial value problems, thus leaving open the possibility of attaining wavy disturbances by a different method than the usual one of instability of Taylor vortices.
Stability analysis of a Taylor–Couette flow of insulating fluid subjected to radial unipolar injection of charge
Authors: Lara Juan L. , Pontiga Francisco , Castellanos Antonio
Published: July 2002

The linear stability of a dielectric fluid filling a cylindrical capacitor is analyzed. The outer or the inner cylinders forming the capacitor may rotate with fixed angular velocities, thus generating a Taylor-Couette flow inside the fluid. A weak, moderate or strong injection of charge is assumed to occur at the anode when a high voltage is applied to the electrodes. The physical mechanisms associated to the instability of the steady flow are discussed. Special attention is paid to the case when the mobility of ions is similar to or smaller than the hydrodynamic mobility of the fluid.
Numerical study of the effective viscosity and pressure in perturbed turbulent flows
Authors: Panis Jean-François , Pérault Michel
Published: July 2002

We present a numerical investigation of the linear response of a turbulent flow to a perturbation at large scale. In the incompressible case, we show that part of the small scale action corresponds to the standard turbulent viscosity, but that there are also other terms which are important for the system dynamics and which do not reduce to a simple turbulent viscous effect. In the compressible case, we show that the small scales of the turbulent flow create a turbulent pressure force which resists compression. An adiabatic index is estimated for this pressure and is found to decrease with time scale, from a strongly adiabatic behavior down to a subisothermal behavior.
The influence of interface profile on the onset of long-wavelength Marangoni convection
Authors: Becerril Ricardo , Van Hook Stephen J. , Swift J. B.
Published: July 2002

Recent experimental results [J. Fluid Mech. 345, 45 (1997)] for long-wavelength surface-tension-driven rupture of thin liquid layers (∼0.01 cm) found the onset for significantly smaller imposed temperature gradients than predicted by linear stability analyses that assume an initially flat interface with periodic boundary conditions. The presence of sidewalls and other aspects of the experiment, however, led to deformed interfaces even with no imposed temperature gradient. These sidewall effects were not due to a small system size since experiments with aspect ratios as large as 450 were significantly affected. The stability analysis presented here takes into account the effects of the deformed interface profile and shows that these effects account for some of the disagreement between experiment and theory. In addition, deviations from standard linear stability theory caused by these effects have the same qualitative behavior as the deviations seen in the experiments.
Instantaneous, quantitative measurements of molecular mixing in the axisymmetric jet near field
Authors: King G. F. , Dutton J. C. , Lucht R. P.
Published: July 2002

Results from a dual-tracer planar laser-induced fluorescence (PLIF) technique for making instantaneous, quantitative measurements of molecularly mixed fluid fraction are presented for an axisymmetric jet in a slow co-flow. The two-camera, two-laser technique uses PLIF of nitric oxide seeded in a nitrogen jet to mark the unmixed jet fluid fraction, while PLIF of acetone seeded into the low velocity air co-flow marks the total co-flow fluid fraction. By combining data from these two simultaneous images, quantitative measurements of molecularly mixed jet fluid fraction can be made on a pixel-by-pixel basis, while simultaneously allowing visualizations of large-structure behavior and regions of subresolution stirring. Instantaneous images of molecularly mixed jet fluid fraction and jet fluid mixing efficiency, probability density functions (PDFs) of mixed jet fluid fraction, and associated statistics are presented for Rejet=1000, 5000, 10,000, 50,000, and 100,000. For fully turbulent conditions (Rejet⩾30,000), stirring at subresolution scales is detected primarily on the jet side of the mixing layer. This creates a hybrid PDF behavior (stationary on the jet side of the mixing layer, marching on the co-flow side) that is not shown by passive scalar methods at equivalent image resolution.
Dynamic generation of capillary waves
Authors: Ceniceros Hector D. , Hou Thomas Y.
Published: July 2002

We investigate the dynamic generation of capillary waves in two-dimensional, inviscid, and irrotational water waves with surface tension. It is well known that short capillary waves appear in the forward front of steep water waves. Although various experimental and analytical studies have contributed to the understanding of this physical phenomenon, the precise mechanism that generates the dynamic formation of capillary waves is still not well understood. Using a numerically stable and spectrally accurate boundary integral method, we perform a systematic study of the time evolution of breaking waves in the presence of surface tension. We find that the capillary waves originate near the crest in a neighborhood, where both the curvature and its derivative are maximum. For fixed but small surface tension, the maximum of curvature increases in time and the interface develops an oscillatory train of capillary waves in the forward front of the crest. Our numerical experiments also show that, as time increases, the interface tends to a possible formation of trapped bubbles through self-intersection. On the other hand, for a fixed time, as the surface tension coefficient τ is reduced, both the capillary wavelength and its amplitude decrease nonlinearly. The interface solutions approach the τ=0 profile. At the onset of the capillaries, the derivative of the convection is comparable to that of the gravity term in the dynamic boundary condition and the surface tension becomes appreciable with respect to these two terms. We find that, based on the τ=0 wave, it is possible to estimate a threshold value τ0 such that if τ⩽τ0 then no capillary waves arise. On the other hand, for τ sufficiently large, breaking is inhibited and pure capillary motion is observed. The limiting behavior is very similar to that in the classical KdV equation. We also investigate the effect of viscosity on the generation of capillary waves. We find that the capillary waves still persist as long as the viscosity is not significantly greater than surface tension.
Development of a turbulence model based on the energy spectrum for flows involving rotation
Authors: Thangam Siva , Wang Xiao-Hua , Zhou Ye
Published: July 2002

A generalized eddy viscosity model is formulated by using the rotation modified energy spectrum. Rotation and mean shear effects are directly included in the eddy viscosity without the use of the local equilibrium assumption. The formulation also includes the modeling of vortex stretching and viscous destruction terms of the dissipation rate equation based on the limit of rotating isotropic turbulence at high Reynolds numbers. The rotation modified energy spectrum includes the contribution of rotation effects on the dissipation and structure of turbulence. The model is shown to reproduce the dominant effects of rotation on turbulence in rotating homogeneous shear flows and turbulent channel flows subject to spanwise rotation. The general applicability of the model and its implications are also addressed.
Passive advection in nonlinear medium
Authors: Chertkov Michael
Published: July 2002

Forced advection of passive tracer in nonlinear medium by a smooth flow is considered. Effective theory for small scale scalar fluctuations is shown to be linear (asymptotic free) and universal. Structure functions demonstrate an extremely anomalous, intermittent behavior while the dissipative anomaly is absent in the problem.
Another note on forced burgers turbulence
Authors: E Weinan , Vanden Eijnden Eric
Published: July 2002

The power law range for the velocity gradient probability density function in forced Burgers turbulence has been an issue of intense discussion recently. It is shown in E and Vanden Eijnden, Phys. Rev. Lett. 83, 2572 (1999) that the negative exponent in the assumed power law range has to be strictly larger than 3. Here we give another direct argument for that result, working with finite viscosity. At the same time we discuss viscous corrections to the power law range. This should answer the questions raised in Kraichnan, Phys. Fluids 11, 3738 (1999) regarding the results of E and Vanden Eijnden, Phys. Rev. Lett. 83 2572 (1999).
Solving the kinetic equation for all Knudsen numbers
Authors: Beylich Alfred E.
Published: July 2002

Starting from the Boltzmann kinetic equation, a system is constructed which allows one to calculate flow fields with strong deviation from equilibrium and for Knudsen numbers 0<Kn0<∞. This is achieved by interlacing the path-integral form of the kinetic equation with the equations of conservation (the first five moments of the equation of transfer). Thus, at the lower level, we maintain the ability of the drifting part of the kinetic equation to drive the state toward nonequilibrium and, at the upper level, we keep the properties of the hydrodynamic (collisional) system to transport information on the grid system in physical (r) space in a nonmaterial way by waves. The distribution function fr,c,t is defined on an equally spaced Cartesian grid in r space and in velocity (c) space. An important step in the construction of the interlaced system is to interpolate the distribution function fr,c,t at interstitial points in r,c space. Approximations of the path-integral equation and different levels of approximation of the gain function (collision term) allow an adequate and efficient description of flows at any degree of deviation from equilibrium. Introducing a phase function in c space allows one to select those collisions that contribute to the gain function. The determination of collision terms then becomes very efficient, and calculating a time step is reduced by orders of magnitude. The problem of maintaining conservation of the lower moments, generally arising when the gain collision integral is to be determined at interstitial points, is solved by imposing on f a set of integral constraints. The system was developed and tested using the Riemann problem and steady planar Couette flow. Results demonstrate that the system is able to maintain conservation, describe nonequilibrium over a large range of Knudsen numbers and over orders of magnitude of density change. In the example of Couette flow, the system was tested for 0.0001<Kn0<50 and wall Mach numbers Maw⩽3.
On the stability limits of long nonaxisymmetric cylindrical liquid bridges
Authors: Zayas F. , Alexander J. I. D. , Meseguer J. , Ramus J.-F.
Published: July 2002

There is a self-similar solution for the stability limits of long, almost cylindrical liquid bridges between equal disks subjected to both axial and lateral accelerations. The stability limits depend on only two variables; the so-called reduced axial, and lateral Bond numbers. A novel experimental setup that involved rotating a horizontal cylindrical liquid bridge about a vertical axis of rotation was designed to test the stability limits predicted by the self-similar solution. Analytical predictions compared well with both numerical and experimental results.
A closure method for random advection of a passive scalar
Authors: Gleeson James P.
Published: July 2002

A novel functional method is applied to calculate the statistics of a passive scalar in an isotropic turbulent velocity field. The method yields asymptotic series expansions for small velocity correlation time from which approximate closure equations are derived. The closure method admits a diagram expansion, and is implemented as a Mathematica program. Padé summation of the asymptotic series yields accurate values for the effective diffusivity and gives formulas expressing the Lagrangian correlation of the velocity in terms of the Eulerian correlation. The approximations compare very favorably with numerical simulations of advection by a Gaussian velocity field.
Orthogonal antisymmetry of deformation rates and scaling in turbulence
Authors: Novikov E. A.
Published: July 2002

It is shown that certain statistical-geometrical properties of deformation rates [orthogonal antisymmetry (4) and its generalizations due to intermittency, (1) and (15)] lead to corresponding power laws of turbulent velocity field.
Nonlinear surface waves in a plasma with a diffuse boundary
Authors: Brodin G. , Lundberg J.
Published: July 2002

The propagation of surface waves in a plasma with a diffuse boundary is considered. Three equations governing the evolution of the system are derived. If the excursion length of the electrons in the surface wave field is smaller than the width of the plasma–vacuum transition layer, it is found that typically the nonlinear density modifications in the boundary layer are more important than the previously investigated bulk nonlinearities.
Formation of positive radial electric field by electron cyclotron heating in compact helical system
Authors: Idei H. , Ida K. , Sanuki H. , Kubo S. , Yamada H. , Iguchi H. , Morita S. , Okamura S. , Akiyama R. , Arimoto H. , Matsuoka K. , Nishimura K. , Ohkubo K. , Takahashi C. , Takita Y. , Toi K. , Tsumori K. , Yamada I.
Published: July 2002

The radial electric field is driven to positive value by off-axis second harmonic electron cyclotron heating (ECH) in the Compact Helical System [Plasma Physics and Controlled Nuclear Fusion Research 1988, Nice (International Atomic Energy Agency, Vienna, 1989), Vol. II, p. 411]. The observed positive electric field is associated with the outward particle flux enhanced with ECH. The enhanced particle flux triggered by the production of the electrons accelerated perpendicularly to the magnetic field with ECH results in the change of the electric field.
Hamiltonian analysis of fast wave current drive in tokamak plasmas
Authors: Bécoulet A. , Fraboulet D. , Giruzzi G. , Moreau D. , Saoutic B. , Chinardet J.
Published: July 2002

The Hamiltonian formalism is used to address the problem of the direct resonant interaction between the fast magnetosonic wave and the electrons in a tokamak plasma. The intrinsic stochasticity of the electron trajectories in phase space is first derived. Together with extrinsic decorrelation processes, it assesses the validity of the quasilinear approximation for the kinetic studies of fast wave current drive (FWCD). A full-wave solution of the Maxwell–Vlasov set of equations provides the exact pattern of the wave fields in the tokamak geometry, consistent with a realistic antenna spectrum. The local quasilinear diffusion tensor is then derived from the wave fields and the driven current density profile, the power deposition profile and the current drive efficiency are computed, including possible nonlinear effects in the kinetic equation. Several applications of FWCD on existing and future machines are given, and the combination of FWCD with other noninductive current drive methods is investigated. Finally, an analytical expression for the current drive efficiency is derived in the moderate to high single-pass absorption regime.
A remark on the Hamiltonian form of the magnetic-field-line equations
Authors: Yoshida Z.
Published: July 2002

It is frequently assumed that a solenoidal vector field u in a simple toroid may be represented in the form of u=∇Ψ×∇φ+∇χ×∇θ with appropriate toroidal angle φ, poloidal angle θ, and two fluxes Ψ and χ. This expression allows one to write the field-line equations in a Hamiltonian form [Phys. Fluids 26, 1288 (1983)]. It is proved on a rigorous mathematical basis that every solenoidal field in an arbitrary smooth simple toroidal domain can be written in the above form.
Enhancement of Lyapunov exponents in one-dimensional, randomly phased waves
Authors: Stoltz Peter H. , Cary John R.
Published: July 2002

For a particle moving in the electric field of many, randomly phase waves, numerical measurements show that the Lyapunov exponent (1) asymptotes to a value of 0.4 times the resonance broadening frequency, in contrast with previous calculations, and (2) has a peak at intermediate values of the overlap parameter. This latter result indicates that the previously observed enhancement of the diffusion coefficient is not due to coherence effects near stable regions of phase space. These results provide further evidence that the standard model is an inadequate description of the turbulent electric field.
A study of the magnetic compression of energetic ion layers in conductive plasmas
Authors: Lyster P. M. , Sudan R. N.
Published: July 2002

Results of a study of the magnetic compression of one-dimensional energetic ion layers in the presence of conductive background plasmas in cylindrical geometry are presented. For this, an updated hybrid (particle-ion and fluid-electron) computer model has been used. The first observation is that when the magnetic field at the wall is ramped quickly relative to the radial Alfvén wave transit time across the cylinder then a magnetic probe on axis would measure a larger field perturbation. When the wall field is ramped slowly, the layer energy increases proportionally with the external magnetic-field strength and, as expected, the layer self-field on axis does not change relative to external field. A study is also made of the effects of transient fluctuations on the layer energy when the field is ramped quickly. When the ramped field strength is small compared with the ambient field (the linear case), the average layer kinetic energy gained is not substantially different from the case where ramping is slow; however, the fluctuating energy is more than twice the average change. The interesting observation is made that the thermal spread in particle energy for a layer is not necessarily related to the strength of the self-field. This is explained in terms of the single particle motion in a self-potential well, and is different from the expected result for a two-dimensional ring.
The plasma properties of the solar upper atmosphere determined from high resolution observations and the nature of the physical processes sustaining it*
Authors: Feldman Uri
Published: July 2002

Half a century ago, it was established that the temperature of the ‘‘quiescent’’ solar corona is ≊106 K (≊100 eV). Wave theories have been used to explain the means by which the Sun keeps the corona about 200 times hotter than the 5000 K (≊0.5 eV) photosphere. In recent years, it has been suggested that a mechanism other than wave dissipation heats the ‘‘quiescent’’ corona and other transient phenomena that occur in the upper solar atmosphere. It is postulated by some that the solar upper atmosphere is heated by small bursts of energy resulting from magnetic reconnection. In this paper, the plasma properties of the upper solar atmosphere, a domain that, when flares are included, encompasses about three orders of magnitude in temperature (3×104–3×107 K) and four orders of magnitude in electron density (3×108—3×1012 cm−3), are described. It is shown that conventional scenarios based on magnetic reconnections may not adequately explain the observed plasma properties of the solar upper atmosphere. However, a model, consisting of electric currents flowing along magnetic field lines may have a better chance simulating the observed properties. For quiescent solar upper atmosphere phenomena, constant currents are needed to simulate the observations, while for flares, currents supplied by an exponentially decaying storage media are required.
Synchrotron radiation and its relevance on plasma diagnostics in next generation tokamaks
Authors: Fidone I. , Granata G.
Published: July 2002

Plasma diagnostics using synchrotron radiation in next generation large tokamaks is discussed. Is is first shown that for electron temperature on axis in excess of 20–25 keV, harmonic overlap invalidates the familiar second harmonic emission method for temperature measurements in the central plasma region. Next, it is shown that radiation measurements at arbitrary frequencies of the X-mode normal to the magnetic field in the horizontal and vertical directions yield a set of independent equations for deriving the plasma parameters characterizing the temperature and density profiles. The method and the salient features of the emitted radiation at arbitrary frequencies are illustrated for parameters being considered in the design of tokamak reactors.
High and very high modes from energy, particle, and momentum transport models
Authors: Staebler G. M. , Hinton F. L. , Wiley J. C. , Dominguez R. R. , Greenfield C. M. , Gohil P. , Kurki-Suonio T. K. , Osborne T. H.
Published: July 2002

Time-dependent simulations of energy, particle, and momentum transport are presented, which show improved confinement similar to the high mode (H mode). The transport model incorporates the suppression of turbulence by sheared flows, which are self-consistently calculated. Constraints on the turbulence model from the time evolution of the temperature, density, and velocity profiles are discussed. A regime similar to the very high confinement mode (VH mode) is found to result at higher heating power due to an increase in the width of the transport barrier. Coneutral beam injection lowers the power required for VH mode substantially due to the toroidal rotation shear. The possible role of edge momentum sources such as ion orbit loss is considered, and a comparison between biased probe-induced and heating-induced H modes is made.
Anomalous perturbative transport in tokamaks due to drift-wave turbulence
Authors: Thoul Anne A. , Similon P. L. , Sudan R. N.
Published: July 2002

A new method for calculating the anomalous transport in tokamak plasmas is presented. The renormalized nonlinear plasma response function is derived using the direct-interaction approximation (DIA). A complete calculation for the case of electrostatic drift-wave turbulence is presented. Explicit expressions for all coefficients of the anomalous transport matrix relating particle and heat fluxes to density and temperature gradients in the plasma are obtained. The anomalous transport matrix calculated using the DIA does not have the Onsager symmetry. As an example of application, the parameters of the Texas Experimental Tokamak (TEXT) [Nucl. Technol. Fusion 1, 479 (1981)] are used to evaluate all transport coefficients numerically, as well as the spectrum modulation. The relation between the theoretical results and the experimental data is discussed. Although this paper focuses on electron transport for simplicity, the method can also be used to calculate anomalous transport due to ion instabilities, such as the ion-temperature-gradient instability.
Space charge instabilities in gyrotron beams
Authors: Li H. , Antonsen T. M.
Published: July 2002

Space charge instabilities in gyrotron electron beams are studied via both the solution of the linear dispersion equation and by nonlinear particle simulation. The linear analysis addresses the stabilizing effects of energy spread in the beam and the inhomogeneity of the external magnetic field. The nonlinear multifrequency simulation demonstrates that for a uniform magnetic field, the energy spread induced by many unstable waves will be larger than the corresponding spread induced by a single unstable wave. This emphasizes the need to design electron guns that are stable to this mode.
Hamiltonian approach to the magnetostatic equilibrium problem
Authors: Tessarotto Massimo , Johnson John L. , Zheng Lin Jin
Published: July 2002

The purpose of this paper is to investigate the classical scalar-pressure magnetostatic equilibrium problem for nonsymmetric configurations in the framework of a Hamiltonian approach. Requiring that the equilibrium admits locally a family of nested toroidal magnetic surfaces, the Hamiltonian equations describing the magnetic flux lines in such a subdomain are obtained for a general canonical curvilinear coordinate system. The properties of such a coordinate system are investigated and a representation of the magnetic field is obtained. Its basic feature is that the magnetic field must fulfill suitable periodicity constraints to be imposed on arbitrary rational magnetic surfaces for general nonsymmetric toroidal equilibria, i.e., it is quasisymmetric. Implications for the existence of magnetostatic equilibria are pointed out. In particular, it is proven that a generalized equilibrium equation exists for such quasisymmetric equilibria, which extends the Grad–Shafranov equation to fully three-dimensional configurations. As an application, a representation is obtained for generalized helically symmetric equilibrium, extending the definition given by Nührenberg and Zille [Phys. Lett. A 129, 113 (1988)]. Since the new representation overcomes the inconsistency exhibited by the previous representation near the magnetic axis, pointed out by Garren and Boozer [Phys. Fluids B 3, 2805, 2822 (1991)], it appears potentially useful to interpret the numerical findings of quasihelical equilibria obtained so far.
Analytical criteria for nonlinear instability of thermal structures
Authors: Ibañez S. Miguel H. , Rosenzweig Patricia
Published: July 2002

Analytical criteria for supercritical and asymptotic stability and for subcritical and superexponential instability are obtained for slab-like, spherical, and cylindrical thermal structures. It is assumed that both, the thermal conductivity κ(T) and the gain/loss function Q(T), can be written as continuous functions of the temperature and they have continuous derivatives. Conditions on κ and Q under which the symmetry of the structure determines the kind of instability (or stability) are obtained. Additionally, it is found that the response of the structure not only depends on the amplitude of the disturbance, but also on whether the disturbance increases or decreases the initial steady temperature. In particular, the threshold value for the amplitude of the disturbances beyond which a linearly stable configuration destabilizes, and explicit conditions for catastrophic heating or cooling are obtained. Applications to structures constituted by atomic and molecular gas are outlined.
Nonlinear instability and chaos in plasma wave–wave interactions. II. Numerical methods and results
Authors: Kueny C. S. , Morrison P. J.
Published: July 2002

In Part I of this work [Phys. Plasmas 2, 1926 (1995)], the behavior of linearly stable, integrable systems of waves in a simple plasma model was described using a Hamiltonian formulation. Explosive instability arose from nonlinear coupling between positive and negative energy modes, with well-defined threshold amplitudes depending on the physical parameters. In this concluding paper, the nonintegrable case is treated numerically. The time evolution is modeled with an explicit symplectic integrator derived using Lie algebraic methods. For amplitudes large enough to support two-wave decay interactions, strongly chaotic motion destroys the separatrix bounding the stable region in phase space. Diffusive growth then leads to explosive instability, effectively reducing the threshold amplitude. For initial amplitudes too small to drive decay instability, slow growth via Arnold diffusion might still lead to instability; however, this was not observed in numerical experiments. The diffusion rate is probably underestimated in this simple model.
Energy partitions in saturated compressible electron magnetoturbulence
Authors: Fernandez E. , Terry P. W. , Newman D. E.
Published: July 2002

The two-dimensional stationary turbulence of magnetic field and density fluctuations coupled through the compressibility of parallel electron motion is shown to possess three distinct stationary states under driving of the magnetic field by the time-dependent thermal force and damping by resistivity and collisional diffusivity. The three states are the equipartitioned magnetic state that occurs when short-wavelength fluctuations interact principally through the long-wavelength magnetic field fluctuation, a magnetic energy-dominated state induced by the decorrelation of nonlinear interactions by strong diamagnetic rotation, and an internal energy-dominated state possible when the dissipation of the density is weaker than the resistive diffusion. The equipartitioned and internal energy-dominated states can occur for identical parameters, making the driven/damped turbulent steady state nonunique.
Data and extended diffusion theories for neutral particle transport in tokamak divertors
Authors: Stacey W. M. , Thomas E. W. , Evans T. M.
Published: July 2002

A formalism is developed that incorporates the anisotropic effects on the neutral atom and molecule transport of collisions with plasma ions flowing toward the divertor into Legendre representations of the scattering, charge-exchange, and recombination processes. These anisotropic directed flow effects and the anisotropic effects of neutral particles recycling from the divertor plate or streaming across low-density regions are incorporated into a differential transport formalism, which retains the computational advantages of an extended diffusion theory. The available collision and wall reflection data that are needed for implementation of the model for deuterium are reviewed, and recommended reaction rates and reflection coefficients are presented. Model problem calculations illustrate the importance of these anisotropic effects.
Laser-driven shock stability in Al and shock compressibilities of Fe up to 0.8 TPa and SiO2 up to 0.4 TPa
Authors: Fu Sizu , Gu Yuan , Wu Jiang , Wang Shiji
Published: July 2002

Using uniform illumination of a high-power laser on inclined plane targets and impedance-match targets, we have studied the shock stability in Al and measured the shock adiabats of Fe and SiO2 by recording the shock luminant signals from the back surface of the targets with an optical streak camera. Experiments show that the shock wave is steady in the thickness range of (20–40) μm in Al. The reliable shock adiabats of Fe and SiO2 were obtained in the pressure range of (0.35–0.82)TPa and (0.21–0.41)TPa, respectively.
Influence of parallel viscosity on tearing mode stability
Authors: Xie H. X. , Bondeson A.
Published: July 2002

The influence of parallel viscosity on the linear stability of tearing modes is analyzed. The parallel viscosity is introduced as a fluid approximation of ion Landau damping. Solution of the resistive layer equations shows that the toroidal stabilization resulting from favorable averaged curvature is rather robust and is only weakly reduced by the parallel viscosity.
Trapped ion mode in toroidally rotating plasmas
Authors: Artun M. , Tang W. M. , Rewoldt G.
Published: July 2002

The influence of radially sheared toroidal flows on the Trapped Ion Mode (TIM) is investigated using a two-dimensional eigenmode code. These radially extended toroidal microinstabilities could significantly influence the interpretation of confinement scaling trends and associated fluctuation properties observed in recent tokamak experiments. In the present analysis, the electrostatic drift kinetic equation is obtained from the general nonlinear gyrokinetic equation in rotating plasmas [M. Artun and W. M. Tang, Phys. Plasmas 1, 2682 (1994)]. In the long perpendicular wavelength limit krρbi≪1, where ρbi is the average trapped ion banana width, the resulting eigenmode equation becomes a coupled system of second order differential equations for the poloidal harmonics. These equations are solved using finite element methods. Numerical results from the analysis of low and medium toroidal mode number instabilities are presented using representative Low confinement mode (L-mode) experimental data followed by a discussion of numerical results.
Properties of a two-nonlinearity model for drift-wave turbulence
Authors: Naulin V. , Spatschek K. H. , Musher S. , Piterbarg L. I.
Published: July 2002

The physical and mathematical consequences of a two-nonlinearity equation for drift-wave turbulence are discussed. The one-field model contains the linear electron Landau damping, the ion polarization drift nonlinearity, and, due to the E×B convected phase shift between density and potential fluctuations, an additional E×B nonlinearity. The latter changes the behavior of the system significantly. It is proved that for the two-nonlinearity model canonical variables do not exist within a Hamiltonian description. Numerical simulations show that the self-organization into large vortices is suppressed, and for dominating E×B nonlinearity a tendency to a zonal flow-like state is favored.
The next large helical devices
Authors: Iiyoshi Atsuo , Yamazaki Kozo
Published: July 2002

Helical systems have the strong advantage of inherent steady-state operation for fusion reactors. Two large helical devices with fully superconducting coil systems are presently under design and construction. One is the LHD (Large Helical Device) [Fusion Technol. 17, 169 (1990)] with major radius=3.9 m and magnetic field=3–4 T, that is under construction during 1990–1997 at NIFS (National Institute for Fusion Science), Nagoya/Toki, Japan; it features continuous helical coils and a clean helical divertor focusing on edge configuration optimization. The other one in the W7-X (Wendelstein 7-X) [in Plasma Physics and Controlled Fusion Nuclear Research, 1990, (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 525] with major radius=5.5 m and magnetic field=3 T, that is under review at IPP (Max-Planck Institute for Plasma Physics), Garching, Germany; it has adopted a modular coil system after elaborate optimization studies. These two programs are complementary in promoting world helical fusion research and in extending the understanding of toroidal plasmas through comparisons with large tokamaks.
Three-dimensional multimode simulations of the ablative Rayleigh–Taylor instability
Authors: Dahlburg Jill P. , Fyfe David E. , Gardner John H. , Haan Steven W. , Bodner Stephen E. , Doolen Gary D.
Published: July 2002

Multimode simulations of the evolution of the laser-driven, ablative Rayleigh–Taylor instability on planar, plastic targets are performed in three dimensions, with FAST3D–CM. The initial mass density target perturbations are random, with a power law dependence of k−2, a RMS surface finish of 0.1 μm, and perturbation wave numbers ranging from 2π/dmax to √2×(12π/dmax), for dmax=128 μm. At early nonlinear times, the perturbations grow to tile the target with approximately hexagonal bubbles that are of the shortest, initially seeded wavelengths not stabilized by density gradients. This tiling occurs on a time scale that is comparable to the eddy turnover time of the dominant bubble wavelength. When the target thickness is large compared to the dominant, short wavelengths, the bubbles continue to burn into the target and to evolve to progressively longer spatial scales. Predictions from second-order mode coupling and saturation models are found to be consistent with the simulation results.