bluuebunny/crossref_metadata_2025 huggingface dataset:
Integrable four vortex motion
Authors: Eckhardt Bruno
Published: July 2002

It follows from the Poisson brackets between constants of motion that the motion of four vortices of zero net vorticity is integrable if the total momentum vanishes. The phase space motion of this integrable case is analyzed. One stable and several unstable uniformly rotating configurations are identified.
Rectified flow of a rotating fluid along a vertical sidewall
Authors: Zhang Xiuzhang , Boyer Don L. , d’Hières Gabriel Chabert , Aelbrecht Denis
Published: July 2002

The motion field resulting from an oscillatory, rotating flow parallel to a vertical wall and bounded from below by a horizontal plane along which there is no slip and from above by a horizontal frictionless lid is investigated numerically by using primitive equations. The model is barotropic and forced by oscillatory, spatially uniform, along-wall, and lateral pressure gradients. The pertinent parameters are the Rossby, temporal Rossby, and Ekman numbers. By means of simulated particle tracking, including a statistical analysis, and a consideration of momentum balances, the physical mechanisms leading to flow rectification are identified; i.e., the exchange of along-wall momentum of fluid parcels communicating between the bottom Ekman layer, the vertical shear layer, and the fluid interior. A rectified flow is generated along the wall for all subinertial, inertial, and superinertial oscillation frequencies investigated. The direction of the rectified current is such that the sidewall is on the right, facing downstream, for a vertically upward or Northern Hemisphere rotation. The mean transports and widths of the rectified currents are determined as functions of the appropriate system parameters. The current width is much larger than the classical E1/4 Stewartson layer thickness. The numerical results are in good agreement with recent laboratory experiments.
Observations regarding ‘‘Coherence and chaos in a model of turbulent boundary layer’’ by X. Zhou and L. Sirovich [Phys. Fluids A 4, 2855 (1992)]
Authors: Berkooz G. , Holmes P. , Lumley J. L. , Aubry N. , Stone E.
Published: July 2002

In the following, the present authors comment on a paper by Zhou and Sirovich (ZS) [Phys. Fluids A 4, 2855 (1992)] which contained a critical appraisal of the models developed by Aubry et al. (AHLS) [J. Fluid Mech. 192, 115 (1988)]. It is found that ZS’s suggestion to use ‘‘a full channel interpretation of wall eigenfunctions,’’ thereby avoiding boundary terms, while attractive mathematically, is questionable in fluid mechanical terms. A major point of AHLS’s study was precisely to isolate the wall region and use the boundary terms to investigate the interaction with the outer flow. Also, it is demonstrated that certain instances of ‘‘irregular’’ bursting, as reported by ZS, are probably numerical effects.
Moderate Reynolds number entry flow and boundary-layer approximations for a viscoelastic fluid
Authors: Eggleton C. D. , Ferziger J. H. , Pulliam T. H.
Published: July 2002

The steady-state entry flow of an Oldroyd B fluid in a plane channel is treated by perturbation analysis. The model predicts entrance lengths shorter than those of a Newtonian fluid at moderate Reynolds and small elasticity parameter. Previously proposed boundary-layer approximations produce significant errors, so new boundary-layer approximations are proposed and are shown to agree with predictions based on the full governing equations at moderate Reynolds numbers. The viscoelastic stresses grow in magnitude as the elasticity parameter increases and become singular at a finite value of the elasticity parameter, due to a breakdown of the Oldroyd B model.
The response of anisotropic turbulence to rapid homogeneous one-dimensional compression
Authors: Mahesh Krishnan , Lele Sanjiva K. , Moin Parviz
Published: July 2002

Homogeneous rapid distortion theory is used to study the response of shear flows and axisymmetric turbulence to rapid one-dimensional compression. In the shear flow problem, both normal and oblique compressions are considered. The response of these anisotropic flows to compression is found to be quite different from that of isotropic turbulence. Upon normal compression, the amplification of the streamwise component of kinetic energy and the total kinetic energy in shear flows is higher than that in isotropic turbulence. Also, normal compression decreases the magnitude of the Reynolds shear stress by amplifying the pressure–strain correlation in the shear stress equation. Obliquity of compression (defined as the angle between the directions of shear and compression) is seen to significantly affect the evolution of the Reynolds stresses. For a range of oblique angles from −60° to 60°, the amplification of streamwise kinetic energy and total kinetic energy decrease with increasing magnitude of the oblique angle. Also, the tendency of the shear stress to decrease in magnitude is diminished upon increasing the oblique angle; for large oblique angles the shear stress amplifies. Upon compression along the axis of axisymmetry, the amplification of the streamwise component of kinetic energy is higher for contracted turbulence than for isotropic turbulence, while the amplification of the total kinetic energy is lower. The above results are interpreted in a more general framework. It is shown that the amplification of the streamwise component of kinetic energy is determined by the initial E11(κ1) (x1 is the direction of compression). Flows with u1 at lower κ1 have a lower effect of pressure during compression and hence, higher amplification of u21. The amplification of the total kinetic energy is determined by the initial fraction of energy along the direction of compression (u21/q2) and the initial E11(κ1). Flows with higher initial u21/q2 and with u1 at lower κ1 have a larger amplification of q2.
Flow structure from an oscillating nonuniform cylinder: Generation of patterned vorticity concentrations
Authors: Towfighi J. , Rockwell D.
Published: July 2002

Forced oscillation of a mildly nonuniform cylinder generates patterns of vorticity concentrations oriented orthogonally to its axis. These complex, but ordered, patterns are repeatable at subharmonics of the cylinder oscillation frequency; they therefore provide a means of identifying the first and second period-doubled states of the wake response.
Observations of secondary flows generated by a torsionally oscillating sphere in linearly stratified fluids
Authors: Folse R. F.
Published: July 2002

Observations have been made of a cellular flow pattern in the secondary flow field generated by a sphere, 2.52 cm in radius, torsionally oscillating in linearly stratified fluids (Brunt–Väisälä frequencies, N, between 0.9 and 2.1 rad/s). Shadowgraphs were made of the secondary flow for frequencies of oscillation in the range 2.0 rad/s≤ω≤13.5 rad/s, and amplitudes of oscillation θ≤1 rad. The size and number of flow cells were determined for fixed values of the parameter (ω/N)θ2, and bifurcation-like transitions occurred during continuous variations of this parameter. Flow cells were mapped using a laser-Doppler velocimeter and compared to the secondary flow for homogeneous fluids. A phase diagram is presented to show the range of critical values of parameters where flow transitions occur.
Maximum entropy states for rotating vortex patches
Authors: Whitaker Nathaniel , Turkington Bruce
Published: July 2002

The statistical equilibrium theory of coherent structures in two-dimensional turbulence is used to study the coalescence and symmetrization of rotating vortex patches. In this theory, most probable states, which are local probability distributions on the fluctuating vorticity field, are characterized by maximizing entropy subject to constraints derived from the conserved quantities for the Euler equations. The merger of a symmetric pair of patches and the axisymmetrization of an elliptical patch are computed by solving the constrained maximum entropy problem. In this way, these generic phenomena, which are usually simulated by direct time integration, are shown to be equilibration processes for the statistical mechanics model. Moreover, macroscopic features of the filamentation generated in these processes are captured by the statistical equilibrium theory. Namely, the delicate balance between the coalescence into a vortex core and the migration of filamentary vorticity away from the core, which is dictated by the conservation of angular impulse, is exhibited by the equilibrium solutions.
On the symmetry of self-organized structures in two-dimensional turbulence
Authors: Jüttner B. , Thess A. , Sommeria J.
Published: July 2002

We report a systematic investigation of equilibrium states predicted by the statistical theory of vortex patches in a square box, in a channel, and in a square with doubly periodic boundary conditions. The study is limited to initial conditions containing negative and positive vortex patches with equal strength and area. It is demonstrated that the symmetry between positive and negative vorticity is, in general, broken by the self-organized states. Direct numerical simulations support the predictions of the vortex patch statistics, but agree with point vortex statistics only in the limiting case of small area vortex patches.
Vorticity transport in modeling three-dimensional unsteady shear flows
Authors: Karniadakis George Em , Brown Garry L.
Published: July 2002

This Letter examines how intrinsic three-dimensionality influences the flow structure of unsteady shear flows, and models its effects by considering spanwise averages of vorticity fluctuations. In particular, uniform flow past a half-cylinder is considered: the two-dimensional wake is very different from its three-dimensional counterpart and the evolution equation for the spanwise spatially averaged vorticity is analyzed. It is shown that the vector flux which transports spanwise vorticity due to spatial vorticity fluctuations is of considerable magnitude (large in comparison with molecular diffusion) and is far from co-linear with the gradient of the spanwise averaged vorticity. Modeling this flux using classical eddy viscosity ideas would therefore seem inappropriate.
A dynamical model for turbulence. II. Shear-driven flows
Authors: Canuto V. M. , Dubovikov M. S.
Published: July 2002

Using the formalism developed in paper I, we treat the case of shear-driven flows. First, we derive the dynamic equations for the Reynolds stress. The equations are expressed in both tensorial and scalar forms, that is, as a set of coupled differential equations for the functions that enter the expansion of the Reynolds stress in terms of basic tensors. We specialize the general results to (a) axisymmetric contraction, (b) plane strain, and (c) homogeneous shear, for which there is a wealth of DNS, LES, and laboratory data to test the predictions of our model. Second, for homogeneous shear, in the inertial range, the equations for the Reynolds stress spectral function can be solved analytically, E12(k)=−Cε1/3Sk−7/3, which is in excellent agreement with recent data. Since the model has no free parameters, we stress that the model yields a numerical coefficient C, which is also in agreement with the data. Third, we derive the general expressions for the rapid and slow parts of the pressure–strain correlation tensors Πrij and Πsij. Within the second-order closure models, the closure of Πsij (third-order moment) in terms of second-order moments continues to be particularly difficult. The general expression for Πij are then specialized to the three flows discussed above. When Πsij is written in the form first suggested by Rotta, we show that the Rotta constant is a nonconstant tensor. Fourth, we discuss the dissipation tensor εij. In standard turbulence models, one not only assumes that εij=2/3εδij+f(uiuj), where f(x) is a empirical function of the one-point Reynolds stress uiuj, but, in addition, one employs a highly parametrized equation for ε. In the present model, neither of the two assumptions is required nor adjustable parameters are needed since εij is computed directly. The model provides the k-dependent Rij(k) as one of the primary quantities.
Magnetic damping of buoyant convection during semiconductor crystal growth in microgravity. Continuous random g-jitters
Authors: Ma Nancy , Walker John S.
Published: July 2002

This paper treats the buoyant convection of a liquid metal in a circular cylinder with a uniform, steady, axial magnetic field and with the random residual accelerations encountered on earth-orbiting vehicles. The objective is to model the magnetic damping of the melt motion during semiconductor crystal growth by the Bridgman process in space. For a typical process with a magnetic flux density of 0.2 T, the convective heat transfer and the nonlinear inertial effects are negligible, so that the governing equations are linear. Therefore, for residual accelerations or ‘‘g-jitters’’ whose directions are random functions of time, the buoyant convection is given by a superposition of the convections for two unidirectional accelerations: an axial acceleration which is parallel to the cylinder’s axis and a transverse acceleration which is perpendicular to this axis. Similarly, the response to accelerations whose amplitudes are random functions of time is given by a Fourier-transform superposition of the buoyant convections for sinusoidally periodic accelerations for all frequencies. Since the temperature gradient in the Bridgman process is primarily axial, the magnitude of the three-dimensional buoyant convection for the transverse acceleration is much larger than the magnitude of the axisymmetric convection for the axial acceleration. At a low frequency, only the magnetic damping limits the magnitude of the buoyant convection. As the frequency is increased, linear inertial effects augment the magnetic damping, so that the magnitude of the convection decreases, and its phase shifts to a quarter-period lag after the acceleration.
Analytical theory of the destruction terms in dissipation rate transport equations
Authors: Rubinstein Robert , Zhou Ye
Published: July 2002

Modeled dissipation rate transport equations are often derived by invoking various hypotheses to close correlations in the corresponding exact equations. D. C. Leslie [Modern Developments in the Theory of Turbulence (Oxford University, Oxford, 1972)] suggested that these models might be derived instead from Kraichnan’s [J. Fluid Mech. 47 (1971)] wavenumber space integrals for inertial range transport power. This suggestion is applied to the destruction terms in the dissipation rate equations for incompressible turbulence, buoyant turbulence, rotating incompressible turbulence, and rotating buoyant turbulence. Model constants like Cε2 are expressed as integrals; convergence of these integrals implies the absence of Reynolds number dependence in the corresponding destruction term. The dependence of Cε2 on rotation rate emerges naturally; sensitization of the modeled dissipation rate equation to rotation is not required. A buoyancy related effect which is absent in the exact transport equation for temperature variance dissipation, but which sometimes improves computational predictions, also arises naturally. The time scale in the modeled transport equation depends on whether Bolgiano or Kolmogorov inertial range scaling applies. A simple extension of these methods leads to a preliminary dissipation rate equation for rotating buoyant turbulence.
Modeling of compressible effects on the Reynolds stress using a Markovianized two-scale method
Authors: Yoshizawa Akira , Liou William W. , Yokoi Nobumitsu , Shih Tsan-Hsing
Published: July 2002

Compressibility effects on the Reynolds stress are modeled using a Markovianized two-scale method. These effects occur twofold. One is the effect on the turbulent viscosity, which is expressed in terms of the ratio of the normalized density variance to the squared turbulent Mach number. Another comes from the deviation of the Reynolds stress from a turbulent-viscosity representation, which is written using the Langrange derivative of the mean velocity and the spatial derivatives of the mean density and internal energy. A simple model with the former compressibility effect incorporated is applied to fully developed free-shear layers and is shown to capture the steep decrease in the growth rate with the increasing convective Mach number.
The Bénard problem for a rarefied gas: Formation of steady flow patterns and stability of array of rolls
Authors: Sone Yoshio , Aoki Kazuo , Sugimoto Hiroshi
Published: July 2002

The two-dimensional Bénard problem for a rarefied gas in a rectangular domain is studied numerically on the basis of kinetic theory. To be more specific, the instability of a stationary stratified gas is investigated by a finite-difference analysis of the Boltzmann–Krook–Welander equation (the so-called BGK model) with the diffuse reflection condition on the top (cooled) and bottom (heated) boundaries and the specular reflection condition on the side boundaries. The study is a continuation of the previous paper by the present authors with H. Motohashi [in Rarefied Gas Dynamics, edited by J. Harvey and G. Lord (Oxford U.P., Oxford, 1995), Vol. 1, p. 135], where the parameter range for which a steady convection exists was clarified, and some examples of steady flow patterns as well as those of flow bifurcation were presented. In the present paper, the attention is focused on the formation of steady flow patterns and the stability of an array of rolls. In particular, the effects of the initial condition and the aspect ratio of the domain on the types of steady convection as well as on the process of its formation and the stability of the double-roll solutions are investigated closely. The existence range of a steady convection is also discussed with some new examples of flow patterns supplementing the previous paper.
On the evolution of unsteady disturbances in continuous strip casting processes
Authors: Kluwick A. , Scheichl St.
Published: July 2002

Continuous solidification processes in thin layers of molten metal are of central importance in many fields of modern metallurgical engineering. This paper deals with unsteady disturbances possibly emerging at the free surface or the phase boundary within the solidification zone of a horizontal strip casting process. Assuming that the wave lengths of the disturbances are large compared to the characteristic depth of the melt, we can apply governing equations for one-dimensional flow. Furthermore, we assume the amplitudes of the disturbances to be so small that their evolution can be regarded as weakly nonlinear. Since unsteady wave propagation phenomena can arise from temperature variations as well as from the excitation of waves at the free surface or the solidification front, both mechanisms will be studied in the following. In the latter case the disturbances at the surface are found to be governed by the inviscid Burgers equations with varying coefficients and will then, in general, develop shock discontinuities.
Active control of vortex–wall interactions
Authors: Koumoutsakos Petros
Published: July 2002

A new simple and efficient methodology is presented for the active control of vortical wall bounded flows. The method is based on sensing of the wall pressure and the calculation of the wall vorticity flux. This information is used to determine explicitly the amount of unsteady, spatially varying mass transpiration, used as an actuating mechanism, necessary to achieve a desired wall vorticity flux. The present scheme is based on the physical mechanism of vorticity generation at solid boundaries. It has the advantage of implementing quantities that can be measured and manipulated at the wall, in computations as well as in experiments. It is shown to reproduce efficiently phenomena previously attained using off-wall information. An active control methodology is outlined and the practical implementation of the present scheme is discussed.
Mean flow effects on the linear stability of compressible planar jets
Authors: Kennedy Christopher A. , Chen Jacqueline H.
Published: July 2002

An analytical solution is derived for the two-dimensional, laminar, compressible, planar free jet. The solution assumes constant pressure, specific heats, and unity Prandtl number and accounts for the effects of heat conduction and viscous dissipation in a self-consistent fashion. Exact closed-form expressions are provided for the streamwise and transverse velocities, temperature, vorticity, and dilatation. Temporal instability analyses of these high Reynolds number mean flows indicate that jet-to-ambient temperature ratio exerts a far greater effect on instability growth rates than compressibility. Relative to isothermal conditions, a hot jet flowing into cold ambient fluid is an order of magnitude more unstable and is unstable over a far greater range of wavenumbers. For this hot jet both symmetric and antisymmetric modes are equally amplified whereas isothermal jets have relatively stronger amplification of their antisymmetric modes. A cold jet issuing into a hot fluid is very stable relative to isothermal conditions. Increasing compressibility suppresses instability growth rates for all temperature ratios. All modes found were two-dimensional. Comparison of the instability analysis and the mean vorticity transport equation indicates that the relative instability growth rates of these jets is qualitatively predicted by the mean inertial vorticity generation term, −ωθ. Jets exhibiting the greatest mean vorticity generation rate inside of the jet half-thickness are the most unstable.
Chaotic transitions in magnetic fluids
Authors: Khosla H. K. , Malik S. K.
Published: July 2002

Parametric excitation of surface waves in a magnetic fluid container is investigated under the influence of an externally applied magnetic field. With a view to explain the experimental observation the dynamical equations governing the evolution of the amplitude of instability are obtained using asymptotic methods. The solution of dynamical equations yields a period doubling sequence, orbits of odd periods, and windows of chaos. Also observed is the phenomenon of strange attractor.
Wick action at moderate Peclet number
Authors: Puyate Y. T. , Lawrence C. J.
Published: July 2002

An approximate analytical model describing transport of chloride in a concrete wall from a wet face in contact with salt solution to an internal liquid/gas interface located near a drying face (wick action) is presented. A constant concentration of the solution is assumed for the wet face of the concrete, and continuity of fluxes is assumed at the interface. The model is shown to be reasonably accurate over a practical range of the Peclet number, a transport parameter which shows the balance between convection and diffusion. Predictions of the model are compared with experimental data, a numerical solution, and an asymptotic solution, and good agreement is obtained.
Natural convection flow due to a heat source under an infinite horizontal surface
Authors: Higuera F. J.
Published: July 2002

An analysis is presented of the two-dimensional natural convection flow induced under an adiabatic unbounded horizontal surface by an embedded constant strength line heat source that is switched on at a certain initial time. After a sufficiently long time, the flow takes on an asymptotic boundary layer form in most of the warm fluid, with all the variables scaling as powers of time. This boundary layer includes a region of reverse flow and a sublayer of high temperature near the source. In addition, the limiting solution displays two small nonslender regions around the source and the front of the spreading layer. The analogous flow in a starting vertical plume is also discussed.
Solitary surface-wave deformation of a plasma boundary
Authors: Stenflo L. , Gradov O. M.
Published: July 2002

The theory for nonlinear electrostatic surface waves on a cold semi-infinite plasma is generalized. The deformation of the plasma surface due to the presence of a solitary wave is then determined.
Linear ray-optics theory of the radiation-driven ion-acoustic decay instability in flowing, inhomogeneous plasmas
Authors: Drake R. P. , Goldman M. V. , DeGroot J. S.
Published: July 2002

The linear Wentzel–Kramers–Brillouin (WKB) or ray-optics theory of the ion-acoustic decay instability is developed for flowing inhomogeneous, fluid plasmas of arbitrary ionic charge, as is needed in the planning and analysis of experiments. Equations are developed for the instability threshold in a homogeneous plasma and for the amplification in plasmas that may be inhomogeneous in more than one spatial direction and/or in time. These equations are formulated so that prior WKB theory of three-wave parametric instabilities may be directly applied to this problem. The results are compared with prior work on this instability, and are applied to several circumstances of practical interest. One finds that, for typical conditions, large amplification is possible over a wide range of angles. In addition, the flow properties of the plasma are found to be crucial in determining the angular distribution of the amplification produced by the instability. In particular, the magnitude of the plasma flow, when the flow is subsonic, directly controls the angle of maximum WKB amplification.
The influence of multiple ion species on Alfvén wave dispersion and Alfvén wave plasma heating
Authors: Elfimov A. G. , Tataronis J. A. , Hershkowitz N.
Published: July 2002

In this paper, the effects of light impurities, such as deuterium, helium, or carbon, on Alfvén wave dispersion characteristics are explored. It is shown that a small population of light impurities in a hydrogen plasma modify the dispersion of the global Alfvén waves and the Alfvén continuum in such a way that the wave frequency depends weakly on the toroidal wave number. It is also shown that the global Alfvén wave enters into the Alfvén continuum. Under these conditions, it is possible to heat plasma efficiently by employing an antenna with a broad toroidal wavelength spectrum. The relationship between impurity concentration and the efficiency of Alfvén wave heating is explored. Under appropriate conditions, the results indicate that in the presence of impurities, Alfvén waves can heat electrons predominantly in the central part of the plasma. This effect is explored via a series of numerical calculations of the heating specifically for the Phaedrus-T Alfvén wave heating experiment [Phys. Fluids B 5, 2506 (1993)].
Influence of radial electric field on Alfvén-type instabilities
Authors: Hahm T. S. , Tang W. M.
Published: July 2002

The influence of the large-scale radial electric field, E(0)r on the frequency of shear-Alfvén-type instability is analyzed. A frozen-in-flux constraint and the moderate-β ion gyrokinetic equation are used in the derivation. The present analysis indicates that the frequency predicted by a theory without E(0)r effect should be Doppler shifted by k⋅VE for comparison to the experimentally observed frequency. A specific example of the practical relevance of the result is given regarding possible identification of the edge-localized-mode-associated magnetic activity recently observed in PBX-M [Plasma Physics and Controlled Nuclear Fusion Research (International Atomic Energy Agency, Vienna, 1989), Vol. 1, p. 97] tokamak experiment.
Finite ion velocity effects on the stability of Pierce-like diodes
Authors: Kolinsky Heidrun , Schamel Hans
Published: July 2002

The stability of Pierce-like plasma diodes is investigated for arbitrary ion injection velocities. A recently developed integral formalism that accounts for ion dynamical effects is applied to derive a generalized dispersion relation for electrostatic perturbations. Its evaluation exhibits several new features, such as the appearance of growing oscillatory modes, which become Pierce–Buneman modes in the limit of initially resting ions, and of weakly damped oscillatory modes, which become undamped ion plasma oscillations in this limit. The stability of this bounded plasma system is shown to be controlled by the new control parameter α̂=α(1+μ̂)1/2, where α is the Pierce parameter and μ̂≡mev2e0/miv2i0 the ratio of electron and ion kinetic energy at the emitter.
Energy transport in plasmas produced by a high brightness krypton fluoride laser focused to a line
Authors: Al-Hadithi Y. , Tallents G. J. , Zhang J. , Key M. H. , Norreys P. A. , Kodama R.
Published: July 2002

A high brightness krypton fluoride Raman laser (wavelength 0.268 μm) generating 0.3 TW, 12 ps pulses with 20 μrad beam divergence and a prepulse of less than 10−10 has been focused to produce a 10 μm wide line focus (irradiances ∼0.8–4×1015 W cm−2) on plastic targets with a diagnostic sodium fluoride (NaF) layer buried within the target. Axial and lateral transport of energy has been measured by analysis of x-ray images of the line focus and from x-ray spectra emitted by the layer of NaF with varying overlay thicknesses. It is shown that the ratio of the distance between the critical density surface and the ablation surface to the laser focal width controls lateral transport in a similar manner as for previous spot focus experiments. The measured axial energy transport is compared to medusa [J. P. Christiansen, D. E. T. F. Ashby, and K. V. Roberts, Comput. Phys. Commun. 7, 271 (1974)] one-dimensional hydrodynamic code simulations with an average atom post-processor for predicting spectral line intensities. An energy absorption of ∼10% in the code gives agreement with the experimental axial penetration. Various measured line ratios of hydrogen- and helium-like Na and F are investigated as temperature diagnostics in the NaF layer using the ration [R. W. Lee, B. L. Whitten, and R. E. Strout, J. Quant. Spectrosc. Radiat. Transfer 32, 91 (1984)] code.
Impurity transport studies in the Texas Experimental Tokamak (TEXT)
Authors: Horton W. , Rowan W.
Published: July 2002

The results of impurity transport experiments in the Texas Experimental Tokamak (TEXT) [Nucl. Technol./Fusion 1, 479 (1981)] are compared with the predictions of a turbulence-based transport model. In the experiments, Sc was injected into the plasma using laser ablation and the time-resolved profiles of critical Sc ionization stages were measured along with the potential fluctuation profile. The experiment was simulated using a one-dimensional (1-D) radial transport code with the standard transport flux Γ=−D(∂n/∂r)+nV. The diffusion coefficient D and convective velocity V parameters were varied until the time-dependent 1-D simulations reproduce the data. This representation for the empirical impurity transport is compared with the E×B turbulent diffusivities and mobility based on the fluctuation data and the measured radial electric field. The agreement is best with the E×B diffusivity taken in the strong turbulence regime, where D=cD(φ̃/BT), while the comparison with the weak turbulence diffusivity and the collisional (no fluctuations) diffusivity results in qualitative disagreements. The percolation theory diffusivity (φ̃/BT)7/10(Δω/k2⊥)3/10 is also briefly discussed.
Shear flow generation by Reynolds stress and suppression of resistive g modes
Authors: Sugama H. , Horton W.
Published: July 2002

Suppression of resistive g-mode turbulence by background shear flow generated from a small external flow source and amplified by the fluctuation-induced Reynolds stress is demonstrated and analyzed. The model leads to a paradigm for the low-to-high (L–H) confinement mode transition. To demonstrate the L–H transition model, single-helicity nonlinear fluid simulations using the vorticity equation for the electrostatic potential, the pressure fluctuation equation, and the background poloidal flow equation are used in the sheared slab configuration. The relative efficiency of the external flow and the Reynolds stress for producing shear flow depends on the poloidal flow damping parameter ν, which is given by neoclassical theory. For large ν, the external flow is a dominant contribution to the total background poloidal shear flow and its strength predicted by the neoclassical theory is not enough to suppress the turbulence significantly. In contrast, for small ν, it is shown that the fluctuations drive a Reynolds stress that becomes large and suddenly, at some critical point in time, shear flow much larger than the external flow is generated and leads to an abrupt, order unity reduction of the turbulent transport just like that of the L–H transition in tokamak experiments. It is also found that, even in the case of no external flow, the shear flow generation due to the Reynolds stress occurs through the nonlinear interaction of the resistive g modes and reduces the transport. To supplement the numerical solutions, the Landau equation for the mode amplitude of the resistive g mode is derived, taking into account the fluctuation-induced shear flow and the opposite action of the Reynolds stress in the resistive g turbulence compared with the classical shear flow Kelvin–Helmholtz (KH) driven turbulence is analyzed.
Direct measurement of velocity space transport in a plasma
Authors: Bowles Jeffrey , McWilliams Roger , Rynn Nathan
Published: July 2002

The direct measurement of the velocity space transport of ions in a plasma is reported. Measured diffusion and convection coefficients are compared to the calculated Fokker–Planck coefficients for a fully ionized plasma. The measurements were made in a Q-machine barium plasma (Ti=Te= 0.17 eV, 5×108≤n≤8×109 cm−3) with both high and low fluctuation levels. At low fluctuation levels the measured coefficients agree with classical collision theory. Coefficients measured in the presence of large amplitude fluctuations generally are larger and have different velocity dependences. Test particle distributions are created and interrogated using the technique of optical tagging. The short-time (≪90° collision time) relaxation of the test particle distribution function was measured as a function of density and temperature of the background plasma and as a function of the velocity of the test particle distribution. The values of the convection and diffusion coefficients were extracted from these measurements. Longer time relaxations (∼90° time) also were measured.
Nonlinear vortex chain associated with tearing mode
Authors: Jovanović D. , Vranješ J.
Published: July 2002

A nonlinear stage in the development of the tearing mode instability is studied analytically using a two-fluid plasma description. A coherent nonlinear solution is constructed in the form of a moving single chain of magnetic islands, coupled with a double chain of hydrodynamic vortices. The adiabatic theory of the chain evolution in the presence of finite electron viscosity indicates its finite lifetime and the possibility of intermittency, which provides a new mechanism for the magnetic field stochastization within a layer of a collisionless skin depth scale. This process occurs before the magnetic island overlapping and the global stochastization takes place.
Relativistic harmonic generation by intense laser in plasmas
Authors: Shen Baifei , Yu Wei , Zeng Guihua , Xu Zhizhan
Published: July 2002

Starting from the nonlinear equations describing intense laser plasma interaction, without the supposition of tenuous plasma, weak relativity and a priori assumption φf≪1+φs, slowly varying part and rapidly varying part of scalar potential φ, and ratio of third harmonic and pumping laser a3/a1 in plasmas pumped by intense laser (≥1018 W/cm2) are obtained. Plasma and laser parameters suitable to generation of harmonic are discussed.
A full mode set electromagnetic stability analysis of magnetically insulated ion diodes
Authors: Lemke R. W. , Slutz S. A.
Published: July 2002

An analysis of the stability of magnetically insulated ion diodes is presented that includes electromagnetic perturbations both parallel and perpendicular to the applied magnetic field, and is fully relativistic. The theory represents a generalization of previous work, which is either electrostatic or excludes wave motion parallel to the applied magnetic field. The analysis reveals a fast growing, low-phase velocity mode that is identified as a modified two-stream instability. This mode is similar to the low frequency mode observed in three-dimensional (3-D) particle simulations, and may be a major cause of ion divergence. It is shown that allowing diode electrons to respond to perturbations in the direction of the applied magnetic field introduces a new set of electron space-charge waves that cause ion modes to become unstable at low frequency and phase velocity. Furthermore, it is shown that these electron space-charge waves are significantly influenced by electromagnetic effects, which therefore cannot be ignored.
Numerical simulation of bump-on-tail instability with source and sink
Authors: Berk H. L. , Breizman B. N. , Pekker M.
Published: July 2002

A numerical procedure has been developed for the self-consistent simulation of the nonlinear interaction of energetic particles with discrete collective modes in the presence of a particle source and dissipation. A bump-on-tail instability model is chosen for these simulations. The model presents a kinetic nonlinear treatment of the wave–particle interaction within a Hamiltonian formalism. A mapping technique has been used in this model in order to assess the long time behavior of the system. Depending on the parameter range, the model shows either a steady-state mode saturation or quasiperiodic nonlinear bursts of the wave energy. It is demonstrated that the mode saturation level as well as the burst parameters scale with the drive in accordance with the analytical predictions. The threshold for the resonance overlap condition and particle global diffusion in the phase space are quantified. For the pulsating regime, it is shown that when γL≳0.16 ΔΩ, where γL is the linear growth rate for the unperturbed system and ΔΩ is the frequency separation of neighboring resonances, overlap occurs together with an amplification of the free energy release compared to what is expected with the saturation of nonoverlapping modes. The effect of particle losses on the wave excitation is included in the model, which illustrates in a qualitative way the bursting collective losses of fast ions/alpha particles due to Alfvén instabilities.
The role of symmetry in indirect-drive laser fusion
Authors: Hauer A. A. , Suter L. , Delamater N. , Ress D. , Powers L. , Magelssen G. , Harris D. , Landen O. , Lindmann E. , Hsing W. , Wilson D. , Amendt P. , Thiessen R. , Kopp R. , Phillion D. , Hammel B. , Baker D. , Wallace J. , Turner R. , Cray M. , Watt R. , Kilkenny J. , Mack J.
Published: July 2002

Good radiation drive symmetry will be crucial for achieving ignition in laboratory inertial fusion experiments. The indirect-drive inertial confinement fusion (ICF) method utilizes the soft x-ray field in a radiation-containing cavity, or hohlraum, to help achieve a high degree of symmetry. Achievement of the conditions necessary for ignition and gain will require experimental fine tuning of the drive symmetry. In order to make tuning possible, a significant effort has been devoted to developing symmetry measurement techniques. These techniques have been applied to a series of experiments that give a graphic picture of the symmetry conditions in the complex hohlraum environment. These experiments have been compared with detailed, fully integrated theoretical modeling. The ultimate goal of this work is the detailed understanding of symmetry conditions and the methods for their control. Comparison with experiments provides crucial benchmarking for the modeling—a key element in planning for ignition.
Modification of classical Spitzer ion–electron energy transfer rate for large ratios of ion to electron temperatures
Authors: Rider Todd H. , Catto Peter J.
Published: July 2002

Corrections to the classical Spitzer heat transfer rate between ions and electrons are calculated for the case when the ion temperature Ti is significantly higher than the electron temperature Te. It is found that slow electrons are partially depleted by their interactions with the ions, resulting in a decrease in the heat transfer in comparison with the Spitzer rate, which assumes perfectly Maxwellian electrons. The heat transfer steadily decreases from the classical value as Ti/Te increases; for Ti/Te values of several hundred, the heat transfer rate drops to around 60%–80% of the Spitzer result. A useful expression for the heat transfer correction factor in the case when all of the ion species are at the temperature Ti is found to be Pie/(Pie)Spitzer ≊[1+(me/mi)(Ti/Te)]3/2 exp{−[3.5∑i (Z2ini/ne)(me/mi) (Ti/Te)]2/3}. This expression is quite accurate for values of ∑i (Z2ini/ne)(mp/mi)(Ti/Te) less than about 50 (where mp is the proton mass), although it underestimates the heat transfer rate for larger values of Ti/Te, and one must resort to the more accurate but more complex analytical results derived in the paper. In the event that the ion distribution is non-Maxwellian, Ti in the correction factor should be replaced by 2〈Ei〉/3, where 〈Ei〉 is the mean ion energy.
Modeling and effects of nonlocal electron heat flow in planar shock waves
Authors: Vidal F. , Matte J. P. , Casanova M. , Larroche O.
Published: July 2002

Electron heat flow was computed in the context of a steadily propagating shock wave. Two problems were studied: a Mach 8 shock in hydrogen, simulated with an ion kinetic code, and a Mach 5 shock in lithium, simulated with an Eulerian hydrodynamic code. The electron heat flow was calculated with Spitzer–Härm classical conductivity, with and without a flux limit, and several nonlocal electron heat flow formulas published in the literature. To evaluate these, the shock’s density, velocity, and ion temperature profiles were fixed, and the electron temperature and heat flow were compared to those computed by an electron kinetic code. There were quantitative differences between the electron temperature profiles calculated with the various formulas. For the Mach 8 shock in hydrogen, the best agreement with the kinetic simulation was obtained with the Epperlein–Short delocalization formula [Phys. Fluids B 4, 2211 and 4190 (1992)], and the Luciani–Mora–Bendib formula [Phys. Rev. Lett. 55, 2421 (1985)] gave good agreement. For the Mach 5 shock in lithium, both of these gave good agreement. The earlier Luciani–Mora–Virmont formula [Phys. Rev. Lett. 51, 1664 (1983)] gave fair agreement, while that of San Martin et al. [Phys. Fluids B 4, 3579 (1992); 5, 1485 (1993)] was even further off than the classical Spitzer–Härm [Phys. Rev. 89, 977 (1953)] formula for thermal conduction. To assess the effect of nonlocal electron heat flow on the shock’s hydrodynamics and ion kinetics, each of the two problems was done with two different electron heat flow models: the classical Spitzer–Härm local heat conductivity, and the Epperlein–Short nonlocal electron heat-flow formula. In spite of the somewhat different electron temperature profiles, the effect on the shock dynamics was not important.
Kinetic theory of low-frequency cross-field instability in a weakly ionized plasma. I
Authors: Dimant Ya. S. , Sudan R. N.
Published: July 2002

A consistent kinetic theory is developed for the description of electrons under conditions of a low-frequency two-stream E×B instability in collisionally dominated, weakly ionized plasmas. Starting from the Boltzmann collision integral, a simplified kinetic equation for the electron distribution function has been derived, which takes into account strong pitch-angle scattering of electrons by neutrals, velocity dependence of the electron–neutral collision frequency, etc. Linearized equations describing small oscillations of the electron distribution function and ion density are presented. For the asymptotic case of short waves, the dispersion relation of the E×B instability has been obtained and analyzed under conditions typical for the lower ionosphere. Under certain conditions, the rigorous kinetic consideration yields substantial changes in results compared to previous theories. The general approach may be applied to other linear and nonlinear low-frequency processes in a weakly ionized plasma.
New unstable branch of drift resistive ballooning modes in tokamaks
Authors: Novakovskii S. V. , Guzdar P. N. , Drake J. F. , Liu C. S. , Waelbroeck F. L.
Published: July 2002

Drift resistive ballooning modes (DRBM) are studied for present-day tokamak edge plasmas. A ballooning equation has been derived for DRBM, corresponding to an ‘‘optimal ordering,’’ i.e., such a choice of the length and time normalizing units that make the three terms in the vorticity equation to be of the same order. A simple criterion to distinguish strong and weak ballooning regimes for DRBM has been obtained. The DRBM in the strong ballooning regime have been studied and it has been found that they are robustly unstable with an ideal growth rate γ∝cs/(RLn)1/2. The weak ballooning regime also has been studied. It has been found that there exist two different unstable branches in this case. The first one has been identified as a conventional DRBM studied earlier. It has been shown, however, that this solution is stabilized when magnetic shear ŝ=aq′/q is order of 1. The other branch has a stronger ballooning structure compared to the conventional DRBM branch and is localized on the outside of the torus. It is less unstable for a weak shear, but is the only one that is robustly unstable for ŝ∼1. A numerical simulation has shown that this branch matches the strong ballooning solution.
Collisional regimes of radiation-driven Langmuir turbulence
Authors: Goldman M. V. , Newman D. L. , Russell D. , DuBois D. F. , Rose Harvey A. , Drake R. P. , Rubenchik A. M.
Published: July 2002

Numerical solutions of the Zakharov equations for a plasma driven above the electron plasma frequency by a long-wavelength radiation pump can be applied to both ionospheric modification experiments and laboratory laser-plasma interactions. A key difference between these two environments is the much larger collisional damping of Langmuir waves near the critical density in laser plasmas. Zakharov equation simulations in one and two dimensions reveal a significant change in the character of the saturated turbulence state of the electromagnetic ion-acoustic decay instability for pump strengths near threshold as the collisional damping is increased to values appropriate to certain (low-intensity) laboratory laser-plasma experiments [Phys. Fluids B 3, 1983 (1991)]. The linear-instability is then characterized by the coupling of the up- and downshifted Langmuir decay modes. A new turbulence regime differing from existing models of both weak and strong turbulence is found, which is characterized by a sequence of narrow peaks in the Langmuir frequency spectrum and a nonlinearly broadened wave-vector spectrum centered near the linearly most unstable modes. Results in this regime may be relevant to second harmonic emission experiments [Phys. Fluids B 3, 1983 (1991)].
Nonlinear theory of a high efficiency E×B drifting electron laser
Authors: Riyopoulos Spilios
Published: July 2002

In a drifting electron laser (DEL), powered by a relativistic beam of E×B drifting electrons in crossed, spatially modulated electric and magnetic fields, the emitted radiation energy and momentum come, respectively, from the change in the electrostatic energy eE0δX and vector potential eB0δX of the electron, δX being the recoil of the guiding center location perpendicular to the drift direction. Since the average drift velocity and the resonance condition are energy-independent one avoids the low efficiency limit η≤1/2Nw placed on free electron lasers (FELs) from energy detuning; in particular there is no inverse relation between per-pass gain and efficiency. In the large radiation amplitude and spot size limit it is shown that the trapped particles do not ‘‘turn around the bucket’’ but keep converting potential energy to radiation until they exit the interaction space, yielding typical DEL efficiency 30%–40% independent of the wiggler length. In addition DELs exhibit much higher tolerance to thermal beam spreads than FELs. In the case of small radiation spot size, gain saturation via the off-axis walk of the emitting electrons is avoided and overlap between the beam and the radiation is maintained by a small tilt of the resonator axis relative to the E×B drift direction.