bluuebunny/crossref_metadata_2025 huggingface dataset:
A numerical study of Marangoni flows in zone-refined silicon crystals
Authors: Kazarinoff Nicholas D. , Wilkowski Joseph S.
Published: July 2002

In zone refinement of silicon crystals, a molten zone of Si is held by surface tension between two solid, cylindrical rods. In a gravity-free environment the fluid Si bridge is subjected only to force generated by the temperature gradient on its free surface caused by the ring heater. This Marangoni flow is simulated numerically in an axially symmetric, initially cylindrical domain with a free lateral surface by solving the time-dependent Navier–Stokes–energy equations on this domain with appropriate boundary conditions. Asymmetric oscillations of the flow as well as the temperature of the fluid and the free surface were found for aspect ratios (length/radius) of 2.0, 1.5, 1.0, and 0.5.
Reynolds number and end-wall effects on a lid-driven cavity flow
Authors: Prasad Ajay K. , Koseff Jeffrey R.
Published: July 2002

A series of experiments has been conducted in a lid-driven cavity of square cross section (depth=width=150 mm) for Reynolds numbers (Re, based on lid speed and cavity width) between 3200 and 10 000, and spanwise aspect ratios (SAR) between 0.25:1 and 1:1. Flow visualization using polystyrene beads and two-dimensional laser-Doppler anemometer (LDA) measurements have shed new light on the momentum transfer processes within the cavity. This paper focuses on the variation, with Re and SAR, of the mean and the rms velocities profiles, as well as the ∼(U′V′) profile, along the horizontal and vertical centerlines in the symmetry plane. In addition, the contribution of the large-scale ‘‘organized structures,’’ and the high-frequency ‘‘turbulent’’ velocity fluctuations to the total rms is examined. At low Re, the organized structures account for most of the energy contained in the flow irrespective of SAR. As the Re increases, however, so does the energy content of the higher frequency fluctuations. This trend is not independent of SAR; a reduction in the SAR causes the ‘‘organized structures’’ to again become more evident.
Steady thermocapillary flows of thin liquid layers. II. Experiment
Authors: Burelbach J. P. , Bankoff S. G. , Davis S. H.
Published: July 2002

The steady thermocapillary flow of nonvolatile layers, nonuniformly heated from below, is examined. The interactions among viscous forces, thermocapillarity, and hydrostatic effects give rise to the steady-state dimpling of the interface. The steady dimpling of nonuniformly heated silicone–oil layers with mean thicknesses ranging from 0.125 to 1.684 mm is studied experimentally. The temperature distribution in the substrate is monitored by thermocouples and the interface shapes by a mechanical impedance probe. Measured steady shapes and theoretical predictions agree within 20% for moderate heating when the film is not close to rupture. When the heating rate causes the film to ‘‘dry out’’ above the hottest point on the substrate, the long-wave theory delivers a parametric index, involving thermocapillary and hydrostatic effects, which is an excellent predictor of rupture. Nonlinear long-wave theories of the type discussed here have never been tested experimentally, until now. The confirmation of this thermocapillary theory is suggestive of the validity of the previous long-wave analysis [Phys. Fluids A 2, 313 (1990)] of unsteady, evaporating/condensing liquid layers.
Bifurcation analysis of solutal convection during directional solidification
Authors: Impey M. D. , Riley D. S. , Wheeler A. A. , Winters K. H.
Published: July 2002

Techniques of bifurcation theory are used to analyze the possible forms of steady, two-dimensional, buoyancy-driven flow present during the vertical directional solidification of a dilute binary mixture. Morphological instabilities of the crystal–melt interface are ignored and the interface is assumed to be planar. The focus of the study concerns the effect of lateral confinement on the flow patterns observable in this simple model system. The use of a time-dependent numerical scheme by McFadden and Coriell [Proceedings of the First National Fluid Dynamics Congress, Cincinnati (AIAA, Washington, DC, 1988), p. 1572] to investigate this same problem resulted in gaps in the bifurcation structure, because unstable steady states exist that cannot be computed by their method. The present work extends and completes the description of the possible steady states. In particular, the complex modal exchanges that occur as the separation between the lateral walls varies are elucidated, and stable flow regimes and the sensitivity of the results to the closure condition at the upper boundary are determined.
Stretching in duct flows
Authors: Franjione J. G. , Ottino J. M.
Published: July 2002

Duct flows are steady three-dimensional isochoric velocity fields composed of a recirculating two-dimensional cross-sectional flow and a unidirectional axial flow, both flows being independent of the axial distance. It is shown that lineal stretch in such flows increases linearly in time. In particular, length stretch in bounded steady two-dimensional flows is linear as well.
The evolution and nature of large-scale structures in the turbulent jet
Authors: Yoda M. , Hesselink L. , Mungal M. G.
Published: July 2002

The structure and evolution of natural, circularly and axially forced turbulent round jets in the far field are investigated. A three-dimensional insovalue surface, which compactly shows the global evolution of the large-scale vortical structures, is extracted from x-y-t laser-induced fluorescence data. Correlation techniques are used to determine whether these structures are helical or axisymmetric. The present results suggest that both the helical and axisymmetric instability modes are present in the natural jet, while the helical mode is dominant in both types of forced jets. Circular forcing increases the spreading rate of the jet.
Stochastic particle dispersion modeling and the tracer-particle limit
Authors: MacInnes J. M. , Bracco F. V.
Published: July 2002

Simulations of spray and particle-laden flows have commonly relied on random walk models to represent dispersion of liquid or solid particles by turbulent motions in the carrier fluid. Particles respond, through a Lagrangian equation of motion, to the mean fluid velocity, computed simultaneously from an Eulerian solution, and to a random fluctuation velocity. In this paper the performance of available models for the case of tracer particles in dilute concentrations is tested. It is demonstrated that several models in wide use do not preserve the required divergence properties of the imposed mean flow. It is found that the method of sampling the fluctuation velocity in these models leads to a spurious component of mean velocity, causing particles to drift relative to the mean flow. Particles concentrate where the turbulence intensity is minimum (at shear layer edges), and are depleted from regions of high turbulence intensity (near the core of the shear layers). The particle concentration may be up more than six times the correct level at the layer edges and less than 40% of the correct level in the shear layer cores. An approximate correction is derived that is the same as that of Wilson et al. [Boundary-Layer Meteorol. 21, 423 (1981)], but with a slightly larger coefficient. It is shown that the effect of fluctuation acceleration has been left out of the model equations, and this leads to a precise correction. To broaden the scope of the work, some recent models that solve a stochastic differential equation for the Lagrangian flow velocity are also considered. One such model is found to give as good an account of the particle number distribution in the shear layers as do the corrected random walk models.
Complex demodulation applied to the transition to turbulence of the flow over a rotating disk
Authors: Le Gal Patrice
Published: July 2002

A complex demodulation technique based on the Hilbert transform is applied to hot-film velocity measurements of the flow over a rotating disk. As the cross-flow instability of the boundary layer of the disk sets in, finite bandwidth packets of Fourier modes appear and grow along the radius. These wave packets, giving strong amplitude and frequency modulations, allow the calculation of the envelope and instantaneous frequency of the signals. This decomposition in amplitude and frequency is used to determine different behaviors of the flow as the Reynolds number increases. Three concentric regions are accurately detected: a first one consisting of a linear growth of disturbances, a second zone where the flow becomes more organized, and finally a turbulent region. The transition to turbulence is also precisely determined and allows an interpretation in terms of defects (amplitude holes) occurring in the flow pattern.
A hybrid perturbation–Galerkin solution to a problem in selective withdrawal
Authors: Singler Timothy J. , Geer James F.
Published: July 2002

A model of selective withdrawal is considered in which a source is located above a gas–liquid interface in a gravitational field. The effects of surface tension are included, and the flow is assumed to be incompressible, inviscid, and irrotational. A perturbation solution is obtained for both the interfacial position and the velocity potential, and then improved using a Galerkin technique. The distortion of the interface by the source is found to be localized and nonmonotonic, and weakly modified by surface tension. An estimate for the stability of the interface is derived from the perturbation solution for the case of zero surface tension.
Energy stability of Taylor’s vortex array
Authors: Lin S. P.
Published: July 2002

A sufficient condition of the linear stability of Taylor’s two-dimensional decaying vortex array is obtained by use of the energy method.
Uniform mean scalar gradient in grid turbulence: Conditioned dissipation and production
Authors: Sahay Anupam , O’Brien Edward E.
Published: July 2002

The equation for the one-point probability distribution function (pdf), P(φ̂), of a passive scalar in incompressible turbulence contains two statistical functions, both conditioned on scalar value. The first is the much-studied (in homogeneous flows) conditioned expected value of scalar dissipation, χ, the second is the conditioned expected value of the velocity vector. Recent measurements in the grid configuration have shown that the tails of the scalar pdf are exponential rather than Gaussian and that χ is U shaped. For this field, χ has been solved for by assuming two forms of P(φ̂,x) (Gaussian and exponential) and taking the pdf of the velocity conditioned on φ̂ to be normal. The solutions χg and χe are shown to be similar in form, both U shaped, when the scalar (normalized by its variance)≤10. Comparison with experimental data confirms that advection by the mean velocity and production are dominant terms affecting the shape of χ. Gaussianity of P(φ̂,x) is not a sufficient condition for χ to be flat in this flow configuration.
The instability of rotating fluid columns subjected to a weak external Coriolis force
Authors: Mahalov A.
Published: July 2002

Instabilities in rotating fluid columns subjected to a weak external Coriolis force are studied. External Coriolis force alters the base flow distorting circular streamlines of the unperturbed columns. The inviscid part of the modified flow (0,r,−2εr sin φ) is an exact solution of Euler equations. Here ε is the strength (nondimensional) of imposed Coriolis force. It is shown that this distortion leads to three-dimensional instabilities. The instability mechanism is generic. It occurs in many flows having circular streamlines distorted by a spectrum of modes cos mφ, sin mφ (m=2 corresponds to elliptical instability). The instabilities occur for wavelengths and frequencies at the intersection points of dispersion curves for the unperturbed columns. Moreover, the instabilities occur at the points of intersection for which modes are coupled with the external Coriolis mode. Here a case is studied where axisymmetric and helical modes are involved in interactions leading to fully three-dimensional flows. It is shown that rotating fluid columns are unstable to disturbances whose axial wavelengths lie in a band, whose width is proportional to the strength ε of imposed Coriolis force. Parametric resonance between a pair of inertial waves (natural modes of oscillation) and the external Coriolis mode is the physical explanation for the instabilities. Numerical results are presented on growth rates of mixed modes and on widths of unstable regions. The growth rates depend linearly on the strength of external Coriolis force. It is shown that viscosity shifts the instability tongues to positive values of ‖ε‖. The results of small-amplitude perturbation analysis are compared with full numerical simulations of the Navier–Stokes equations. Comments are made on competition between centrifugal and parametric instabilities in Taylor–Couette systems subjected to an external Coriolis force studied in Wiener et al. [J. Stat. Phys. 64, 913 (1991)] and Ning et al. [J. Stat. Phys. 64, 927 (1991)].
The effect of axial pressure gradient on axisymmetrical and helical vortex waves
Authors: Marshall J. S.
Published: July 2002

The effect of axial pressure gradient in producing gradual changes in amplitude and wavelength of both axisymmetrical and helical waves on a vortex core is studied analytically using an idealized model of a vortex with uniform axial vorticity across the core in an unbounded space. Possible implications of the findings on the vortex breakdown phenomenon are also considered. In agreement with previous literature on the subject, the steady solution for a supercritical vortex flow in an adverse pressure gradient is found to become complex (and hence break down) at a certain critical point. The axisymmetric waves on the core obey a hyperbolic system of equations. An explicit solution of these equations for small-amplitude axisymmetric waves indicates that the wave amplitude becomes unbounded at the critical point in the linear theory. An implicit nonlinear solution of these equations shows the formation of ‘‘shocks’’ along the core considerably upstream of the critical point, which seem to correspond to formation of bubble-type vortex breakdowns. A solution is also obtained for evolution of long helical waves on a vortex core in the presence of an axial pressure gradient, and this solution is used to suggest an explanation for why the vortex breakdown at times adopts a bubble form while at other times it adopts a spiral form.
A hybrid one- and two-point approach for isothermal reacting flows in homogeneous turbulence
Authors: Tsai Kuochen , O’Brien Edward E.
Published: July 2002

A procedure that combines a one-point probability density function (pdf) and two-point correlation functions (TPCF’s) is introduced to simulate the multispecies chemical reactions carried by a homogeneous turbulence field. In this procedure, the pdf equation and the evolution of TPCF’s are treated in parallel using time splitting. The one-point pdf equation requires closure of only the molecular diffusion terms. At any instant the time scale for the linear mean square estimate closure is obtained from the parallel solutions of the equations for TPCF’s, using a physical-space EDQNM (eddy damped quasinormal Markovian) closure for the advection terms and a similarity assumption for the reaction terms. With this procedure, a study of chemical reactions with four or five species is possible. The model’s predictions are in good agreement with DNS data and a fully two-point pdf description of simpler kinetic schemes. Results for a range of Damköhler numbers, Schmidt numbers, and Reynolds numbers that are beyond the reach of DNS are also shown.
On the stability of nonisothermal circular Couette flow
Authors: Kolyshkin A. A. , Vaillancourt Rémi
Published: July 2002

The stability of a circular Couette flow with internal heat generation is studied in the region between two coaxial cylinders. The inner cylinder is rotating with constant velocity while the outer one is kept at rest. The investigation is carried out for wide ranges of the Prandtl number and radius ratio R, for the axisymmetric mode (n=0) and the first two asymmetric modes (n=1,2), respectively. For small to large gaps (R=0.95, 0.7, 0.4), axisymmetric perturbations are the single main cause of instability. The growths of the Prandtl and Taylor numbers lead to a decrease of the critical Grashof number. Stabilization of the Couette flow is possible for very large gaps (R=0.1), but the region of stabilization decreases for large Prandtl numbers. The stability boundary is determined by the concurrence of axisymmetric (n=0) and spiral (n=1) modes in the case of very large gaps.
Derivation of amplitude equations and analysis of sideband instabilities in two-layer flows
Authors: Renardy Michael , Renardy Yuriko
Published: July 2002

Sideband instabilities following the onset of traveling interfacial waves in two-layer Couette–Poiseuille flow are considered. The usual Ginzburg–Landau equation does not apply to this problem due to the presence of a long-wave mode for which the decay rate tends to zero in the limit of infinite wavelength. Instead of the Ginzburg–Landau equation, a coupled set of equations for three amplitude factors is derived. The first corresponds to an amplitude of a traveling wave, the second to a long-wave modulation of the interface height, and the third results from the pressure. The criteria which determine the stability of the primary traveling wave to sideband perturbations are presented. This scenario raises the possibility that as a result of sideband instability of a primary traveling wave, the flow may eventually be dominated by a long-wave mode. Experimental data on a gas–liquid flow are analyzed and models for air–water waves are discussed. Finally, it is noted that the amplitude equations allow for possibilities other than periodically modulated waves. In the concluding section, the presence of homoclinic and heteroclinic orbits is investigated. These correspond to solutions which approach either a flat interface or periodic waves at infinity.
End effects for the falling cylinder viscometer
Authors: Wehbeh Elias G. , Ui T. J. , Hussey R. G.
Published: July 2002

Experimental results are presented for the Stokes velocity of a circular cylinder of radius a and length L moving axially through a viscous fluid contained within a coaxial closed cylindrical tube of radius b and length H. The results cover the intermediate range 0.21 ≤a/b≤0.70 and are found to be consistent with theoretical results for the narrow gap case (a≂b) and with previous experimental results for the wide gap case (a≪b). The fractional difference between the observed drag and the theoretical drag is represented well by 1.67x−0.017, where x=(b−a)(a/b)1/2/L. The negative term is interpreted as representing an effective cylinder length of 0.983L, and the 1.67x term is interpreted qualitatively as a measure of the degree to which the fluid is displaced radially by the falling cylinder. The limitations of our expression for end effects are explored experimentally. Additional experimental results are presented for two cases in which the ends of the cylindrical tube are not closed.
Motion of an expanding, spherical gas bubble in a viscous liquid under gravity
Authors: Chakraborty B. B. , Tuteja G. S.
Published: July 2002

An expanding spherical gas bubble moves in an incompressible, viscous fluid under gravity. The nonlinear equations of motion are solved numerically. The growth of the radius of the bubble, the velocity of its center, and the drag experienced by the bubble are obtained with the progress of time. The gravity is found to influence the results significantly.
An assessment of pressure-strain models for rotating flows
Authors: Salhi A. , Lili T. , Sini J.-F.
Published: July 2002

The plane turbulent boundary layer tied up with rotation normal to the mean shear plane and the rotating cylinder turbulent boundary layer are associated with transport equations that exhibit a formal analogy between the expressions of Coriolis and centrifugal forces. The traceless vorticity tensor and the production tensor (associated with the symmetric part of the mean velocity gradient) that appear in the Reynolds stress transport equation also exhibit a striking analogy between the rotation number and the curvature parameter. Due to the fact that in these flows rotation or streamline curvature do not affect the (convective and diffusive) transport terms it is shown that pressure-strain correlations comply with this formal analogy. The idea that convection and vorticity should have the same functional contribution in the models of the linear part of the pressure-strain term is shown to be consistent with a typical result of the rapid distortion theory, i.e., the most energetic state of turbulence is associated to the value of the rotation number R=−1/4. A few second-order closure models are tested with regard to the analogy criterion. Particularly, the Launder, Reece, and Rodi model [J. Fluid. Mech. 68, 537 (1975)], its variants, and the algebraic stress model of Rodi (Ph.D. thesis, University of London, 1972) are examined with respect to their deviations from Richardson number similarity. The results of these models are compared with previous experiments and numerical simulations of rotating homogeneous turbulent shear flows and inhomogeneous turbulent flows generated by a rotating cylinder in a quiescent fluid.
Collective effects of temperature gradients and gravity on droplet coalescence
Authors: Zhang Xiaoguang , Wang Hua , Davis Robert H.
Published: July 2002

The interaction and coalescence of small spherical drops in dilute, homogeneous dispersions are considered theoretically under conditions, where drop motion results from gravity settling and thermocapillary migration acting simultaneously. A trajectory analysis is used to predict pairwise collision rates, and population dynamics equations are solved to predict the time evolution of the droplet size distribution. The rate of droplet collisions and growth may be reduced dramatically by antiparallel alignment of the gravitational and thermocapillary velocities. For such antiparallel alignment with the gravitational relative velocity exceeding the thermocapillary relative velocity for two widely separated drops, there is a ‘‘collision-forbidden region’’ in parameter space. This occurs because the gravitational relative velocity decays more rapidly with decreasing separation distance between the drops than does the thermocapillary relative velocity, and so the resultant relative velocity along the line-of-centers from these two sources combined becomes zero at a finite separation and the drops are unable to collide. As a result, small drops which initially collide and coalesce due to thermocapillary motion will only grow until they reach a critical size for which the oppositely directed gravitational motion balances the thermocapillary motion.
Behavior of streamwise rib vortices in a three-dimensional mixing layer
Authors: Lopez J. M. , Bulbeck C. J.
Published: July 2002

The structure and behavior of a streamwise rib vortex in a direct numerical simulation of a time-developing three-dimensional incompressible plane mixing layer is examined. Where the rib vortex is being stretched, the vorticity vector is primarily directed in the vortex axial direction and the radial and azimuthal velocity distribution is similar to that of a Burgers vortex. In the region where the vortex stretching is negative, there is a change in the local topology of the vortex. The axial flow is decelerated and a negative azimuthal component of vorticity is induced. These features are characteristic of vortex breakdown. The temporal evolution of the rib vortex is similar to the evolution of an axisymmetric vortex in the early stages of vortex breakdown. The effect of vortex breakdown on other parts of the flow is, however, not as significant as the interaction between the rib vortex and other vortical structures.
Comments on ‘‘A fully toroidal fluid analysis of the magnetohydrodynamic ballooning mode branch in tokamaks’’ [Phys. Fluids 3
1, 359 (1988)]
Authors: Hirose A.
Published: July 2002

It is shown that, in the compressible limit considered by Andersson and Weiland, the magnetohydrodynamic ballooning mode disappears if εn (the pressure gradient inverse aspect ratio)≳0.14 irrespective of plasma pressure.
Computational treatment of collisional magnetic pumping
Authors: Laroussi M. , Roth J. Reece
Published: July 2002

When collisional magnetic pumping is applied to a plasma, the heating rate depends strongly on the nature of the waveform of the magnetic perturbation, whether sinusoidal, triangular, or sawtoothed in time. Numerical solutions to the energy transfer problem are obtained when these waveforms are applied to heat a plasma, and compared with previously obtained analytical results using small perturbation theory where these results are available. A specially written fortran program computes the numerical values of the parallel, perpendicular, and total energy at each time increment. The plasma heating rates and optimum heating conditions derived from this study are in good agreement with analytical limiting cases and available experimental data, except when the perturbation amplitude becomes large enough that the analytical results no longer hold.
Experimental verification of a simple, one-dimensional model for the hydrodynamic expansion of a laser-produced plasma into vacuum
Authors: Qi Niansheng , Krishnan Mahadevan
Published: July 2002

A one-dimensional, hydrodynamic model is described for a laser-produced plasma expanding into vacuum. Measurements of the absolute continuum emission from the laser-produced plasma are compared with the predictions of this model and yield density and temperature profiles for the expanding plasma. The agreement between theory and experiment is remarkably good, considering the simplicity of the model. Such a model might be useful as a quick, approximate solution of a variety of low-power, laser plasma expansions.
Stability thresholds of a disk-shaped Migma
Authors: Wong H. Vernon , Rosenbluth M. N. , Berk H. L.
Published: July 2002

The stability of a Migma disk is reexamined to determine the threshold to the interchange instability. It is shown that a previous calculation [Z. Naturforsch. Teil A 42, 1208 (1987)], which assumes a rigid mode eigenfunction, is inaccurate at the predicted particle number for marginal stability. As a result the integral equation for the system must be solved. A variational method of solution is developed and is shown to give good agreement with a direct numerical solution. The threshold for instability is found to be sensitive to the details of the distribution function. For highly focused systems, where all ions pass close to the axis, the threshold particle number (Nu1) for instability is substantially below that predicted by rigid mode theory (Nrigid) (by a factor ∼8ε2, where ε=r1/rL, r1 is the spread in the distance of closest approach to the axis, and rL the ion Larmor radius). At a higher density, a second band of stability appears that again destabilizes at yet a higher particle number (Nu2). If ε≪1, Nu2 is substantially below the rigid mode prediction, while for 0.2<ε<0.3, Nu2 is comparable to the rigid mode prediction. At moderate values of ε (ε≊0.3–0.4) the second stability band disappears and the instability particle number threshold varies from the rigid stability threshold by a factor of 0.4ε, when ε=0.4, to 0.7ε when ε is about unity. The stability criteria would be consistent with the observed particle storage number obtained in experimental configurations if the spread in ε is sufficiently large.
Measurements of the ponderomotive force including sideband mode coupling effects and damping rates
Authors: Meassick S. , Intrator T. , Hershkowitz N. , Browning J. , Majeski R.
Published: July 2002

Measurements of the interactions of waves in the ion cyclotron range of frequencies (ICRF) with flute interchange modes are presented. Interactions between the applied l=1 radio frequency (rf) wave and an m=−1 flute mode give rise to sidebands above and below the rf frequency with mode numbers of l=0 and l=+2, respectively. The contribution of the sideband terms to stability are shown to cancel 40% of the direct ponderomotive contribution. This is less than the 90% predicted by theory [Phys. Fluids 30, 148 (1987)] for an applied l=+1 rf wave above the ion cyclotron frequency with a large separation between the plasma and the vacuum vessel. Measurements of the linear growth and damping rate of the flute instability in the presence of rf are in good agreement with that calculated by considering only the curvature-driven instability and the ponderomotive force. The growth rate of the magnetohydrodynamic mode is consistent with the primary force acting on the plasma being the curvature force. This method allows a determination of the net stabilizing force on the plasma.
Numerical simulation of the reversed field pinch dynamo effect in the quasilinear, mean field equilibrium limit
Authors: Caramana E. J.
Published: July 2002

In this paper numerical simulations are presented of the reversed field pinch (RFP) dynamo effect utilizing the resistive magnetohydrodynamic (MHD) equations in the quasilinear approximation. In addition, a mean field equilibrium magnetic field configuration is constructed in cylindrical geometry by dropping inertia on the symmetric radial component of the velocity field. Results are obtained for a variety of operating conditions: flat-top current, current ramp-up, and ramp-down. It is found that the Alfvén time, although present in the equations describing the perturbed quantities, is not important on the long resistive run time; the result is a three-dimensional Ohmic equilibrium with symmetric mean toroidal magnetic field reversal. Using these results, and in view of recent RFP experimental data, a simple correspondence between global MHD behavior in the RFP and the tokamak is given.
Ion temperature gradient-driven turbulence in tokamaks with flat density profiles
Authors: Mattor N. , Diamond P. H.
Published: July 2002

The theory of ion temperature gradient-driven turbulence in tokamaks is extended to the flat density regime. The values of ion and electron thermal conductivities, χi and χe, momentum diffusivity χφ, and particle flux Γr are also calculated. These formulas extend previous calculations, which were restricted to the regime Ln<(LsLT)1/2 [Phys. Fluids 29, 3291 (1986); Phys. Fluids 31, 1180 (1988)]. This allows an assessment of the role of ion temperature gradient turbulence in H modes, where the density gradient is often observed to be flattened in the plasma core.
Resistive convection in a current-carrying cylindrical plasma: An exact model
Authors: Gomberoff L.
Published: July 2002

In a previous paper [J. Plasma Phys. 34, 299 (1985)] it was shown that resistivity and thermal conductivity lead to large scale stationary convection in a current-carrying cylindrical plasma under the action of a shearless magnetic field. It was shown there that convection takes place when (η/κ)=8π/3, where η is the resistivity and κ the thermal conductivity. Convection occurs when either (Bθ/Bz) ≫1 or when (Bθ/Bz)≪1. In both cases the condition for convection, i.e., R>Rcrit, where R is the Rayleigh number, was shown to be the same. From this fact it was then conjectured that convection takes place for any Bθ/Bz. By solving the model in a closed form, it is shown that the conjecture is correct for large azimuthal wavenumbers, but, otherwise, convection takes place only in the limits mentioned above.
Modeling of high-pressure generation using the laser colliding foil technique
Authors: Fabbro R. , Faral B. , Virmont J. , Cottet F. , Romain J. P.
Published: July 2002

An analytical model describing the collision of two foils is presented and applied to the collision of laser-accelerated foils. Numerical simulations have been made to verify this model and to compare its results in the case of laser-accelerated foils. Scaling laws relating the different parameters (shock pressure, laser intensity, target material, etc.) have been established. The application of this technique to high-pressure equation of state experiments is then discussed.
Some parametric instabilities which arise during ion-Bernstein wave heating in fusion plasmas
Authors: Kumar A. , Sharma R. P.
Published: July 2002

In the present paper, the parametric decay instability of an ion-Bernstein wave (ωci<ω0≲2ωci) into a scattered ion-Bernstein wave and a low-frequency wave (either an ion-acoustic wave or a kinetic-Alfvén wave) has been examined. It has been demonstrated that this parametric process may be one of the possible sources of ion heating in tokamaks. In addition to this, the possibility of oscillating two-stream instability (OTSI) of an ion-Bernstein wave (ωci<ω0≲2ωci) or a cold plasma ion-Bernstein wave (ω0≲ωci) has also been discussed. The explicit expressions for threshold and convective threshold of the decay processes are given. For OTSI, the expressions for maximum growth rate have also been given explicitly.
Whistler instability in an electron-cyclotron-resonance-heated, mirror-confined plasma
Authors: Garner R. C. , Mauel M. E. , Hokin S. A. , Post R. S. , Smatlak D. L.
Published: July 2002

The warm-electron-driven (2 keV) whistler electron microinstability [Phys. Rev. Lett. 59, 1821 (1987)] of the Constance B electron-cyclotron-resonance-heated (ECRH), quadrupole mirror-confined plasma experiment has been studied. Experiments show (i) that the instability comes in fairly regular bursts on axis and continuously in time off axis due to the minimum-B geometry, (ii) a frequency spectrum that is insensitive to changes in the plasma parameters, and (iii) instability-induced power losses which are not greater than 10% of the ECRH power input for the regimes studied. A linear perturbation analysis of the relativistic Vlasov equation together with Maxwell’s equations has been made. Using the ECRH distribution function, a new distribution function well suited for describing ECRH, mirror-confined plasmas, the analysis shows the instability frequency spectrum to be insensitive to changes in cyclotron frequency, temperature, and density, in agreement with experimental results, and only sensitive to changes in ECRH frequency.
Three-dimensional transmission of the fast wave in ion cyclotron resonance plasma heating
Authors: Friedland L.
Published: July 2002

The transmission of the fast Alfvén wave in second harmonic ion cyclotron resonance heating of a deuterium–hydrogen (minority) plasma is analyzed in a general three-dimensional magnetogeometry. The approach is based on the congruent reduction of the Hermitian, anisotropic pressure fluid plasma model. The unreduced, 17th-order, slow-amplitude transport equation, characterizing the problem of interest, is systematically reduced to the fourth-order irreducible transport system describing the coupling of the fast wave to the resonant components of the anisotropic pressure plasma model. This system yields a compact expression for the fast wave transmission coefficient in a general geometry and arbitrary direction of propagation of the incident wave.
Photographic study of hot electrons generated by the two-plasmon decay instability
Authors: Meyer J. , Legault L. E.
Published: July 2002

Hot electrons generated by the two-plasmon decay instability in a CO2-laser irradiated underdense plasma are studied by photographic methods. For laser intensities less than 5×1013 W/cm2 the electrons are emitted in the plane of polarization. From the direction of their trajectories the wave vector distribution of the electron accelerating two-plasmon decay waves is determined. These wave vector measurements are in good agreement with values theoretically predicted for the fastest growing mode. For laser intensities large than 6×1013 W/cm2 space-charge effects become important and hot electrons are detected out of the plane of polarization.
Stability of magnetohydrodynamic cylindrical flows: Compressible modes
Authors: Corbelli Edvige , Torricelli-Ciamponi Guidetta
Published: July 2002

The stability analysis of an ideal magnetohydrodynamic cylindrical configuration subject to compressible perturbations is carried out assuming smooth profiles for both the magnetic field and the mass flow. The adiabatic energy equation is assumed everywhere. Subsonic and transonic regimes up to flow speeds a few times the sound speed are analyzed for models with axial mass flow and for a variety of helical magnetic models. It is shown that compressibility increases the growth rates of pure ideal magnetic models while it lowers those of the Kelvin–Helmholtz instabilities. Beyond the transonic regime, the pinching mode (m=0) is stable for a range of magnetic models wider than that of the incompressible case. The case of uniform mass density is investigated more in detail but some results for models with a nonuniform mass density are also considered.
Linear interaction of electron cyclotron waves with a suprathermal electron tail
Authors: Farina Daniela , Pozzoli Roberto
Published: July 2002

The analysis of power absorption and current generation by electron cyclotron waves at the first cyclotron harmonic, interacting with a suprathermal tail, has been performed using the relativistic linear theory and the adjoint technique. A one-sided tail has been considered and the comparison between upshifted resonance conditions, corresponding to coinjection with respect to the tail, and downshifted (corresponding to counterinjection) has been made. The results are explained by means of the behavior, along the resonant curve, of the absorbed power density in momentum space and of the single-particle current drive efficiency. The ratio between the transverse linear dimension of the resonant curve and the transverse average momentum of the tail is found to play a determinant role in the interaction process. Upshifted resonance conditions are found to be generally more favorable than the downshifted with respect to both power absorption and current drive; this advantage tends to vanish as the perpendicular temperature of the tail is increased.
Comments on ‘‘Dynamics of decaying two-dimensional magnetohydrodynamic turbulence’’ [Phys. Fluids B 1, 1964 (1989)]
Authors: Diamond P. H. , Biskamp D.
Published: July 2002

In a recent simulation, Biskamp and Welter [Phys. Fluids B 1, 1964 (1989)] noted that the dissipation scale in two-dimensional magnetohydrodynamic turbulence appears to be ld=(l2Kλ)1/3, where lK is the Kolmogorov dissipation scale and λ the Taylor microscale. Here, it is shown that this result can be obtained from a simple scaling argument, and is not a consequence of intermittency.
Root-mean-square emittance increase in a nonlinear lens
Authors: Rhee M. J.
Published: July 2002

An exact derivation of the root-mean-square emittance increase when a beam of arbitrary distribution passes through a nonlinear lens system is presented. It is found that the emittance increase depends on the spherical aberration coefficient of the lens and characteristics of the beam distribution.
Alfvén-ion-cyclotron instability and absence of sawteeth in tokamaks
Authors: Litwin C.
Published: July 2002

Linear stability of the anisotropic energetic ion population, observed in recent experiments at the Joint European Torus [Phys. Rev. Lett. 60, 2148 (1988)], to Alfvén-ion cyclotron wave excitations is analyzed and the saturation mechanism is discussed. In the absence of external heating the anisotropic distribution lifetime is found comparable to the observed delay time in the monster sawtooth crash after the turn-off of the heating. It is suggested that the ponderomotive force of unstable waves is responsible for this delay. Saturated wave fields are found sufficiently large to stabilize the internal kink mode.
The effect of compressibility on magnetohydrodynamic instabilities in toroidal tokamak geometry
Authors: Charlton L. A. , Carreras B. A.
Published: July 2002

The effect of compressibility on the stability of ideal internal kink modes, ballooning modes, and infernal modes is studied. Most characteristics of these modes and their thresholds are not affected by compressibility. However, in general, the linear growth rates obtained from calculations that include compressibility are larger than those from calculations that do not. In the calculations with compressibility, the sound wave contribution to δW, Γ|∇⋅V|2, is negligible. The increase in the linear growth rate with compressibility is caused mainly by the change in the parallel component of the displacement vector.
Multiple helicity quasilinear ballooning modes
Authors: Riedel K. S.
Published: July 2002

The validity of the ballooning mode transformation in quasilinear calculations is examined. If the range of interacting helicities is too large, the equivalence of harmonics is destroyed. The criterion for the validity of the ballooning mode transformation is Lm δn δm≪n, where δm and δn are the spreads of excited poloidal and toroidal harmonics, respectively, and Lm is the number of harmonics necessary to represent the quasilinear pressure profile flattening. The quasilinear formalism of Riedel [Phys. Fluids B 1, 1780 (1989)] is generalized to the multiple toroidal helicity case.
Experimental measurements of competition between fundamental and second harmonic emission in a quasi-optical gyrotron
Authors: Alberti S. , Pedrozzi M. , Tran M. Q. , Hogge J. P. , Tran T. M. , Muggli P. , Jödicke B. , Mathews H. G.
Published: July 2002

A quasi-optical gyrotron (QOG) designed for operation at the fundamental ( fce≂100 GHz) exhibits simultaneous emission at fce and 2fce (second harmonic). For a beam current of 4 A, 20% of the total rf power is emitted at the second harmonic. The experimental measurements show that the excitation of the second harmonic is only possible when the fundamental is present. The frequency of the second harmonic is locked by the frequency of the fundamental. Experimental evidence shows that when the second harmonic is not excited, total efficiency is enhanced.
A nearly one-and-one-half-dimensional confinement model for field-reversed configurations
Authors: Steinhauer Loren C.
Published: July 2002

A global confinement model is developed for a field-reversed configuration (FRC) using a quasistatic profile assumption and assuming a realistic two-dimensional equilibrium. Since the associated computational problem is modest, the model is useful as a fast tool for interpreting experimental results and extracting confinement trends. Its predictions compare well with a fully time-dependent 1 (1)/(2) -dimensional computation. The results are compared with results from a similar previous model that employed a crude ‘‘square-ends’’ equilibrium. Generic confinement relationships between resistivity and its profile, and the confinement of particles and poloidal flux are found.
Effect of asymmetric sources on tokamak neoclassical transport in the plateau regime
Authors: Solano E. R. , Hazeltine R. D.
Published: July 2002

A plasma source is present in the edge of tokamak plasmas that can modify neoclassical flows and fluxes, including the self-consistent value of the electric field. The usual neoclassical assumption of divergenceless flows yields well-known equilibrium rotation rates; equilibrium rotation in the presence of sources, however, can be very different. In order to study this problem when toroidal symmetry is broken a kinetic approach is necessary. Estimates from TEXT [Nucl. Technol./Fusion 1, 479 (1981)] indicate that the source term in the drift kinetic equation is of the same order as the guiding center drift frequency. The drift kinetic equation is solved in the plateau regime with toroidally and poloidally localized sources. A modification of the radial and parallel neoclassical flows is obtained. Possible implications for L–H transitions are studied.
Axially symmetric propagation of small-amplitude ion-acoustic waves
Authors: Herman Russell L.
Published: July 2002

In this paper a generalization of the Korteweg–de Vries equation, which may be applicable to the axially symmetric propagation of ion-acoustic waves from a conical mesh, is sought. In an appropriate limit the equation for propagation of axially symmetric waves in a cylindrical geometry is also obtained.
Chaotic evolution of the Buneman instability in the vicinity of the resonance
Authors: Hamamatsu Nobuyuki , Kono Mitsuo
Published: July 2002

A system of equations describing the evolution of the Buneman instability in the vicinity of the resonance is derived and solved numerically to show periodic and chaotic solutions depending on the system parameters, such as the magnitude of the resonance mismatch and the drift velocity. It is found that the chaotic behavior exhibits an intermittent development where solutions are characterized by long quiescent periods separated by short unpredictable jumps.
Rotating kink modes in a noncircular Z pinch
Authors: Wahlberg Christer
Published: July 2002

The free-boundary m=1 kink mode of a noncircular (square-shaped) Z pinch is investigated. Particular attention is paid to the exchange of angular momentum between the external coil system (providing the external transverse magnetic field which deforms the plasma cross section) and helical kink perturbations of the plasma column. Following the time development of an initial, arbitrary perturbation of the plasma it is found that a torque, in general, is exerted on the m=1 component, thus causing the kink modes to rotate. Damping effects of the m=3 and m=5 sidebands [excited by the first order m=4 (square) and m=1 interaction] are shown to slow down the rotational motion, resulting in a lifetime of the order of τL∼1/Γλ2 Alfvén times of the angular momentum (λ is the degree of noncircularity ΔRP/RP and Γ is the normalized damping decrement γm/ωm of the sidebands). The calculations are based on a surface current magnetohydrodynamic (MHD) description of the pinch with internal (Bi) as well as external (Be) axial magnetic fields included. The free-boundary m=1 dispersion relation ω(kz) is calculated analytically to leading order in the noncircularity, and various cases corresponding to different combinations of Bi and Be are illustrated. The results confirm previous pessimistic predictions about the linear MHD stability of the long m=1 kink mode in the straight Extrap [Fusion Technol. 16, 7 (1989)] configuration. The phenomenon of mode rotation may, however, open the possibility of dynamic stabilization of the long kink mode in the nonlinear regime.
Nonlinear evolution of ideal internal kink modes in tokamaks with nonmonotonic q profiles
Authors: Avinash K.
Published: July 2002

A calculation of the nonlinear state of the m=n=1 internal kink mode within the ideal magnetohydrodynamic approximation is presented. The nonlinear problem is divided into a layer around the q=1 surface and an outer region. An examination of the nonlinear terms from the two regions shows that within the optimal ordering of the linear theory, nonlinear terms from the outer region are formally bigger than the corresponding terms of the layer. However, because of the rigid shift nature of the linear radial displacement, these terms are actually weaker than the terms from the layer. The contribution from the nonlinear terms from the outer region has been calculated and it is shown that it produces a small correction in the final expression. This is essential for the calculation of Avinash et al. [Phys. Rev. Lett. 59, 2647 (1987)] and Bussac and Pellat [Phys. Rev. Lett. 59, 2650 (1987)] to be correct. Further, the case of arbitrary resonant q profiles has been considered and the relevance of these results to recently observed sawtooth activity in tokamaks is discussed.