bluuebunny/crossref_metadata_2025 huggingface dataset:
Kinetic and transport theories of turbulent, axisymmetric, low-collisionality plasmas and turbulence constraints
Authors: Rogister André , Li Ding
Published: July 2002

The kinetic equations describing the evolution of the macroscopic distribution functions of electrons and ions in turbulent, axisymmetric, low-collisionality plasmas are derived in a systematic fashion. The first irreversible time scales are those of electron and ion classical collisions on which the distributions relax, in their lowest order, to Maxwellians. These results are sufficient to derive the nonlinear equations that describe the evolution of the ‘‘low-frequency’’ microturbulence. This turbulence controls the evolution of the Maxwellians on longer time scales and also influences the higher-order equilibrium distribution functions. By taking moments of the kinetic equations obtained on the diffusion time scale, (i) the equations of evolution of the density and pressures of the lowest-order Maxwellians, (ii) an expression for the macroscopic toroidal current driven from the passing electrons by the autocorrelation of the turbulent electric field parallel to B with the turbulent density, and (iii) a ‘‘constraint’’ equation telling that the anomalous sources and sinks of ion parallel momentum must be balanced by the divergence of the anomalous radial flux of the same momentum are thus obtained. It is noted that the transport is automatically ambipolar, that ion and electron anomalous heat transport are of the same order, that magnetic aspects of the turbulence are considered, although via a low-beta expansion scheme: They contribute to the anomalous bootstrap current which is estimated to be possibly of the order of 15% of the Ohmic current; and that the constraint, a consequence of ion momentum conservation, is automatically satisfied for weak turbulence in the ‘‘random phase’’ approximation if the plasma has up–down symmetry.
Nonlinear interactions of tearing modes in the presence of shear flow
Authors: Chen X. L. , Morrison P. J.
Published: July 2002

The interaction of two near-marginal tearing modes in the presence of shear flow is studied. To find the time asymptotic states, the resistive magnetohydrodynamic (MHD) equations are reduced to four amplitude equations, using center manifold reduction. These amplitude equations are subject to the constraints due to the symmetries of the physical problem. For the case without flow, the model that is adopted has translation and reflection symmetries. Presence of flow breaks the reflection symmetry, while the translation symmetry is preserved, and hence flow allows the coefficients of the amplitude equations to be complex. Bifurcation analysis is employed to find various possible time asymptotic states. In particular, the oscillating magnetic island states discovered numerically by Persson and Bondeson [Phys. Fluids 29, 2997 (1986)] are discussed. It is found that the flow-introduced parameters (imaginary part of the coefficients) play an important role in driving these oscillating islands.
Point vortex model of a modon solution
Authors: Matsuoka Chihiro , Nozaki Kazuhiro
Published: July 2002

An exact point vortex solution corresponding to the modon solution of the Hasegawa–Mima equation is presented and a new modulated point vortex model is introduced. In the framework of this model, the linear stability of a modon and modon–modon collisions are analyzed, and the frequency and position shift before and after the collision are estimated.
Ion heating by kinetic cross-field streaming instability due to reflected ions at a quasiperpendicular shock
Authors: Yoon Peter H. , Wu C. S. , Mandt M. E.
Published: July 2002

The present paper shows that the reflected ion at a supercritical quasiperpendicular shock wave can excite a purely growing m9de propagating parallel to the ambient magnetic field (k∥B0). To discuss the ion heating by such an unstable mode, the self-consistent quasilinear kinetic equation is solved with the assumption that the present purely growing mode is the dominant unstable mode in the system. In the quasilinear analysis of the instability, two particular cases are considered—the case of low initial ion beta [βi(0)=0.1] and that of a high initial ion beta [βi(0)=1]. For each case of low and high initial betas, two values of initial turbulence level are used. One corresponds to δB2(0)/B20=0.1 and the other corresponding to δB2(0)/B20 =0.1. It is shown that for both low and high beta cases, the ion heating at the shock becomes more efficient for a higher value of δB2(0)/B20.
Linear waves in a resistive plasma with Hall current
Authors: Almaguer J. A.
Published: July 2002

Dispersion relations for the case of a magnetized plasma are determined taking into account the Hall current and a constant resistivity, η, in Ohm’s law. It is found that the Hall effect is relevant only for parallel (to the equilibrium magnetic field) wave numbers in the case of uniform plasmas, giving place to a dispersive behavior. In particular, the cases of η→0 and small (nonzero) resistivity are discussed.
Experiments on whistler mode electron-cyclotron resonance plasma startup and heating in an axisymmetric magnetic mirror
Authors: Booske J. H. , Getty W. D. , Gilgenbach R. M. , Jong R. A.
Published: July 2002

Whistler mode electron-cyclotron resonance heating (ECRH) has been performed simultaneously with whistler mode electron-cyclotron emission measurements on an axisymmetric magnetic mirror plasma. Results presented include a study of the early plasma startup phase and two instability phases, one believed to be caused by a whistler instability and another by magnetohydrodynamic (MHD) flute instability. Enhanced microwave emission at frequencies below the midplane electron-cyclotron frequency has been correlated with enhanced electron endloss during the whistler instability. Cyclotron emission spectra during the startup phase match predictions for a ‘‘sloshing electron’’ type distribution based on numerical modeling. This distribution also agrees with anisotropic distributions resulting from electron-cyclotron heating as predicted by Fokker–Planck computer simulations. Experimentally measured heating rates show good agreement with simplified analytical models based on stochastic heating.
Double layer formation caused by contact between different temperature plasmas
Authors: Ishiguro Seiji , Kamimura Tetsuo , Sato Tetsuya
Published: July 2002

The formation of an electrical potential difference between hot and cold plasmas is studied by means of a particle simulation. It is found that a double layer structure is formed on the hot-plasma side of the contact surface between the cold and hot plasmas. The potential difference is given approximately by φDL∼Teh/2e, where Teh and e are the hot-electron temperature and the electronic charge, respectively. The double layer is accompanied by a negative potential dip on the low potential side (cold plasma) of the double layer, the depth of which is φdip∼2Tec/e, where Tec is the cold-electron temperature. Interestingly, however, the positive potential difference and the negative potential dip are created independently.
The Lagrangian–Eulerian probability relations and the random force method for nonhomogeneous turbulence
Authors: Novikov E. A.
Published: July 2002

The relations between Lagrangian and Eulerian probabilities are obtained for the case of variable density of fluid. The general stochastic model for trajectories in nonhomogeneous turbulence is considered, and probability for Lagrangian forcing is expressed in terms of Eulerian distribution. The criterion of the influence of boundaries on the asymptotic behavior of trajectories is presented.
The helical magnetic instability of arcs in an axial magnetic field treated by a linear time dependent perturbation theory
Authors: Hülsmann H. G. , Mentel J.
Published: July 2002

A straight arc column operated in a cylindrical tube changes its shape into a helical form if the strength of the arc current, the gas pressure, or a superimposed axial magnetic field exceed marginal values. The helical arc is described by the electromagnetic equations in an electrostatic approximation and by the balances of mass, momentum, and energy. The critical nonlinear term is the Lorentz force. The equations are solved by linear perturbation theory. A first order differential equation is deduced for the helix amplitude from which the stability limit of the cylindrical arc and the growth rate of the helical instability can be evaluated. The ratio of the destabilizing and stabilizing terms in the equation is determined by a dimensionless number, the Maecker number, which comprises integral properties of the arc and properties of the gas.
The limits of lubrication theory for a disk approaching a parallel plane wall
Authors: Trahan Jeffrey F. , Wehbeh Elias G. , Hussey R. G.
Published: July 2002

Measurements have been made of the velocity of a thin circular disk of radius r, as it falls with its axis vertical, through a viscous liquid toward a horizontal plane boundary. The distance from the fixed plane to the bottom surface of the disk is denoted by h. For h<0.032r the results agree with the squeeze film expression from lubrication theory. For h>3r the results agree with the far-field boundary effect formula derived by Brenner [J. Fluid Mech. 12, 35 (1962)]. An empirical expression is proposed for intermediate values of h. The squeeze film solutions for both a circular cylinder and a sphere approaching a plane are compared with the exact solutions for a cylinder [D. J. Jeffrey and Y. Onishi, Q. J. Mech. Appl. Math. 34, 129 (1981)] and a sphere [H. Brenner, Chem. Eng. Sci. 16, 242 (1961)] and empirical formulas are proposed for the departure from lubrication theory in these two cases.
The thermophoretic force in the Knudsen regime near a wall
Authors: Williams M. M. R.
Published: July 2002

The thermophoretic forces acting on a Small Knudsen particle in the neighborhood of a boundary have been investigated. The applied temperature gradient is constant, but it is not normal to the wall, thereby leading to thermophoretic forces both normal to and parallel with the wall. Using the velocity distribution of the gas atoms for this problem it has been possible to obtain the variation of the thermophoretic force as a function of distance from the boundary. It is noted, that for equal temperature gradients, the force is greater in the direction normal to the wall than along it. In addition, it is observed that the velocity dependence of the mean free path has a significant effect on the force in the neighborhood of the wall. In contrast to the normal force, which is in the direction of decreasing temperature, the mass flow induced by thermal creep along the wall leads to a parallel wall force that moves the particle in the direction of increasing temperature. When these two forces are compounded they indicate that particles can move in curved paths en route to the wall surface. As a by-product of the calculation, an exact expression for the thermal creep velocity as a function of distance from the wall for the case of constant collision cross-section is presented.
Axisymmetric interaction between a vortex ring and a free surface
Authors: Tyvand Peder A. , Miloh Touvia
Published: July 2002

The initial motion of a horizontal vortex ring with upwelling flow in its center is studied analytically by a small-time expansion. The toroidal vortex ring is put impulsively into an inviscid fluid near a free surface. The vortex coordinates and surface elevation are calculated up to third order in time, including the leading gravitational effects. The first-order problem is solved exactly, whereas the higher-order problems are covered only in the limits of small and large radius-to-depth ratio. The leading-order effects of the nonlinear interaction with the free surface are analogous to the case of a two-dimensional vortex pair. To the leading order, vortex stretching tends to move the vortex ring inwards and upwards.
Hydrodynamic diffusion in a suspension of sedimenting point particles with periodic boundary conditions
Authors: Koch Donald L.
Published: July 2002

The hydrodynamic diffusivity tensor is determined for a monodisperse suspension of non-Brownian sedimenting particles in the point-particle approximation using both theoretical and simulation approaches. The diffusion is dominated by convective motions occurring on the length scale of the box size H. The diffusivity is proportional to the product of the root-mean-square velocity and H or to fN1/2, where N is the number of particles in the unit cell and f is the ratio of the magnitude of the buoyancy force acting on a particle to the fluid viscosity. The ratio of the diffusivity in the vertical to that in the horizontal direction is a strong function of the shape of the periodic box and becomes smaller as the aspect ratio (vertical over horizontal length) is increased.
Linear instability of a two-layer flow with differential particle loading
Authors: Wen Feng , Evans John
Published: July 2002

The linear instability of an unbounded, two-layer particle-laden flow subjected to infinitesimal perturbations was investigated. The two-phase flow model employed in this study is dissipative because of a viscous mechanism through which momentum is transferred between the perturbed interstitial fluid and the suspended particles. The momentum interchange was found to depend critically on the ratio of the particle response time and the time scales of the perturbation. The dispersion equation for a flow system of large time scale ratio was solved analytically. Two unstable modes were found to coexist. The effects of three nondimensional parameters, a mean particle loading parameter, a differential loading parameter, and a relative offset between shear and the two layer interface, on two unstable modes were examined. In particular, if the velocity boundary layer is shifted toward the layer of low particle loading and the mean particle loading parameter increases, the most unstable mode ‘‘switches’’ from a long-wave instability to a short-wave instability.
Evaporation of a rarefied gas from a cylindrical condensed phase into a vacuum
Authors: Sone Yoshio , Sugimoto Hiroshi
Published: July 2002

Steady evaporating flows from a cylindrical condensed phase into a vacuum are studied on the basis of kinetic theory. The behavior of the gas (the velocity distribution function as well as the density, velocity, and temperature) is analyzed numerically in detail for the whole range of the Knudsen number defined by the condition of the condensed phase. The discontinuity of the velocity distribution function in the gas, a typical behavior of the gas around a convex body, is analyzed accurately. The flow is highly in nonequilibrium over the whole field except for very small Knudsen numbers. The behavior of the far field from the cylinder, proper to each Knudsen number, differs markedly from that of corresponding flow [Phys. Fluids A 5, 1491 (1993)] from a spherical condensed phase, universally of free molecular type. The height of the velocity distribution function and the temperature of the gas vanish at infinity, without freezing at finite values, except in the free molecular flow.
A family of large eddy simulation (LES) filters with nonuniform filter widths
Authors: van der Ven Harmen
Published: July 2002

In this Brief Communication a family of filters for large eddy simulation (LES) with nonuniform filter widths is constructed that commute with differentiation up to any given order.
Instability of wake-dominated compressible mixing layers
Authors: Zhuang Mei , Dimotakis Paul E.
Published: July 2002

The instability of supersonic mixing layers, with velocity profiles possessing a wake component, is investigated using linear, inviscid, spatial theory. The mean-velocity profile is represented by a hyperbolic-tangent profile plus a wake component. Such profiles are encountered in the initial region of experimental supersonic shear-layer flows, as well as in envisaged hypersonic propulsion systems in which ingested boundary layers generate substantial wake components. Shear-layer and wake instability modes previously found in incompressible mixing layers are also found in compressible mixing layers. The existence of a wake component in the velocity profile renders the mixing layer more unstable at all free-stream Mach numbers. For convective Mach numbers exceeding unity, the shear-layer mode splits into two supersonic modes, and the mixing layer becoming more unstable with increasing wake deficit. The wake mode becomes less unstable and eventually stable with increasing compressibility, i.e., increasing convective Mach numbers.
A nonlinear return-to-isotropy model with Reynolds number and anisotropy dependency
Authors: Chung Myung Kyoon , Kim Soong Kee
Published: July 2002

A new computational model for the return to isotropy is presented. In order to reproduce the significant role of the third invariant IIIb(=bijbjkbki) of the Reynolds stress anisotropy bij[=uiuj/(2k)−(1/3)δij] in the return-to-isotropy process, a nonlinear return-to-isotropy model is formulated by a Taylor series expansion up to fifth power of bij. Then the strong realizability condition for non-negativity of the component energies is utilized to reduce the number of model constants produced. Correction for the low Reynolds number effect is then included by investigating an energy-weighted average time scale of eddies over the three-dimensional energy spectrum. Superiority of the proposed model performance is exemplified by a number of test computations of homogeneous relaxing turbulence in a wide range of turbulence Reynolds number and IIIb.
Prandtl number of lattice Bhatnagar–Gross–Krook fluid
Authors: Chen Y. , Ohashi H. , Akiyama M.
Published: July 2002

The lattice Bhatnagar–Gross–Krook modeled fluid has an unchangeable unit Prandtl number. A simple method is introduced in this report to formulate a flexible Prandtl number for the modeled fluid. The effectiveness of this method was demonstrated by numerical simulation of the Couette flow.
Thermocapillary instabilities with system rotation
Authors: Zebib Abdelfattah
Published: July 2002

Influence of rotation on thermocapillary instabilities is demonstrated from linear stability analysis of a parallel flow model relevant to crystal growth. It is shown that system rotation has a dramatic influence on transitions at parameter values typical of the microgravity environment of an orbiting space laboratory. Thus the Coriolis force must be included in the design of future space experiments.
Experimental measurement of dispersion processes at short times using a pulsed field gradient NMR technique
Authors: Lebon L. , Leblond J. , Hulin J. P.
Published: July 2002

Dispersion at short times is studied using a PFG-NMR (pulsed field gradient NMR) technique inside a fixed bed of nonconsolidated spherical beads saturated with water flowing at a constant velocity. This allows measurement of the probability distribution of the displacement of water molecules along the magnetic field gradient during a preset measurement time Δ: the mean displacement of the water molecules is varied between 0.1 and 7.3 times the bead diameter by varying Δ between 20 and 100 ms and the bead diameter between 800 and 81 μm. At short times, the displacement of the molecules is small enough so that the local displacement is proportional to the local velocity component along the magnetic field gradient. At mean displacements larger than 5 bead diameters, the displacement distribution is Gaussian and centered about the mean displacement; the width of the distribution corresponds to the macroscopic dispersion coefficient as measured by other techniques. At intermediate displacements, this distribution displays two peaks corresponding to a combination of the two processes. The main features of this transition can be reproduced by a simple Monte-Carlo simulation modeling the porous medium as a set of finite length tubes with random orientations.
A simple experimental equation for the bursting cycle
Authors: Perona Paolo , Porporato Amilcare , Ridolfi Luca
Published: July 2002

This Brief Communication presents a simple second-order differential equation extracted from experimental data, which can mimic the velocity fluctuations that are typical of bursting. The starting time series concerns the longitudinal component of turbulent velocity measured near the wall in a hydraulically smooth pipe flow. By means of standard conditional sampling techniques, we found the typical behavior of velocity fluctuations during the bursting events, to which we then applied the trajectory method in order to extract the equation of motion. The resulting equation, containing quadratic and cubic nonlinearities, follows the original time series very well, and may represent a useful starting point for the construction of more complex models of this phenomenon.
Moment realizability and the validity of the Navier–Stokes equations for rarefied gas dynamics
Authors: Levermore C. David , Morokoff William J. , Nadiga B. T.
Published: July 2002

We present criteria for monitoring the validity of the Navier–Stokes approximation during the simulation of a rarefied gas. Our approach is based on an underlying kinetic formulation through which one can construct nondimensional non-negative definite matrices from moments of the molecular distribution. We then identify one such 3×3 matrix that can be evaluated intrinsically in the Navier–Stokes approximation. Our criteria are based on deviations of the eigenvalues of this matrix from their equilibrium value of unity. Not being tied to a particular benchmark problem, the resulting criteria are portable and may be applied to any Navier–Stokes simulation. We study its utility here by comparing stationary planar shock profiles computed using the Navier–Stokes equations with those computed using Monte Carlo simulations.
Transient critical-level effect for internal gravity waves in a stably stratified shear flow with thermal forcing
Authors: Baik Jong-Jin , Hwang Hong-Sub , Chun Hye-Yeong
Published: July 2002

We have examined the transient critical-level effect for internal gravity waves produced by thermal forcing in a stably stratified shear flow. For this, we have solved analytically the equations governing small-amplitude perturbations in a two-dimensional, hydrostatic, nonrotating, inviscid, and Boussinesq flow system. In the case of the point pulse forcing, there is only one transient critical-level line at any time and every internal gravity wave passing through the critical level is attenuated by a factor of e−πμ [μ=(Ri−1/4)1/2, Ri: Richardson number (=N2/α2, where N is the buoyancy frequency and α the vertical shear of the basic-state horizontal velocity)]. In the case of the line-type pulse forcing (bell-shaped in the horizontal), there are an infinite number of transient critical-level lines at any time. The attenuation factor for internal gravity waves is a function of space and time. This is because internal gravity waves passing through any point at any time consist of internal gravity waves which have already experienced the transient critical-level effect and those which have not experienced the effect yet.
Pushing a non-Newtonian fluid in a Hele-Shaw cell: From fingers to needles
Authors: Ben Amar Martine , Corvera Poiré Eugenia
Published: July 2002

We make a theoretical study of the finger behavior of a simple fluid displacing a non-Newtonian fluid confined in a Hele–Shaw cell. We study the Saffman–Taylor instability when the viscosity of the displaced fluid changes with shear. Our results predict a decrease of the finger width that goes to zero for large values of the velocity. An analytical treatment allows the predictions of the dynamics in radial growth.
The formation of thick borders on an initially stationary fluid sheet
Authors: Song Museok , Tryggvason Grétar
Published: July 2002

The formation of thick borders on an initially stationary two-dimensional fluid sheet surrounded by another fluid is examined by numerical simulations. The process is controlled by the density and the viscosity ratios, and the Ohnesorge number [Oh=μ/(ρdσ)0.5]. The main focus here is on the variation with Oh. The edge of the sheet is pulled back into the sheet due to the surface tension and a thick blob is formed at the edge. In the limits of high and low Oh, the receding speed of the edge is independent of Oh. Different scaling laws, however, apply for the different limits. The speed scales as V∼(σ/ρd)0.5 in the low Oh limit as proposed by Taylor [Proc. R. Soc. London, Ser. A 253, 13 (1959)] and as V∼σ/μ in the high Oh limit. For low enough Oh, the edge forms a two-dimensional drop that is connected to the rest of the sheet by a thin neck and capillary waves propagate into the undisturbed sheet. The thickness of the neck reaches an approximately constant value that decreases with Oh, suggesting that the blob may “pinch-off” in the inviscid limit.
The geometry and statistics of mixing in aperiodic flows
Authors: Poje A. C. , Haller G. , Mezić I.
Published: July 2002

The relationship between statistical and geometric properties of particle motion in aperiodic, two-dimensional flows is examined. Finite-time-invariant manifolds associated with transient hyperbolic trajectories are shown to divide the flow into distinct regions with similar statistical behavior. In particular, numerical simulations of simple, eddy-resolving barotropic flows indicate that there exists a close correlation between such geometric structures and patchiness plots that describe the distribution of Lagrangian average velocity over initial conditions. For barotropic turbulence, we find that Eulerian velocity correlation time scales are significantly longer than their Lagrangian counterparts indicating the existence of well-defined Lagrangian structures. Identification of such structures shows a similar, close relationship between the invariant manifold geometry and patchiness calculations at intermediate time scales, where anomalous dispersion rates are found.
Measurements of the flow structure and turbulence within a ship bow wave
Authors: Roth Gary I. , Mascenik Daniel T. , Katz Joseph
Published: July 2002

Particle image velocimetry measurements around a 7-m-long ship model focus on the flow within the attached liquid sheet, upstream of the point at which the bow wave separates from the model. Performed in a towing basin at a Reynolds number of 1.6×107 and a Froude number of 0.30 (both based on ship length L), these measurements expand upon previous work by examining the bow wave flow at a higher Reynolds number than before. Further, the increased scale of the model and the flow allows finer observation of the flow structure. Individual vector maps show a growing region of negative vorticity originating at the toe of the wave. This shear layer, which first appears at X/L=0.0619, penetrates further into the wave as X/L increases but curves upward to remain close to the forward face. Positive vorticity appears on the top of the wave and at the ship boundary. Repeated runs at X/L=0.0690 produce mean flow and turbulent stress data for this three-dimensional spilling wave. Normal and shear Reynolds stresses are concentrated at the forward face of the wave in the same region as the negative vorticity. The magnitudes of the Reynolds stresses are consistent with theoretical expectations, with maximum vrms′ and wrms′ attaining 16% and 11% of the local fluid speed, respectively. The correlation coefficient of −v′w′ is between 0.5 and 0.7 in the turbulent region, indicating the presence of coherent structures. Although the Reynolds stresses penetrate deeply into the bow wave, turbulent production is concentrated in a small region at the toe. Changing from a fixed coordinate system to a system that shifts with the free surface causes the Reynolds stresses and turbulent production to form thinner regions closer to the free surface with no reduction in intensity. Calculations of the three-dimensional velocity on the free surface in the ship frame of reference indicate that it turns sharply at the toe of the bow wave and that the forward face forms a three-dimensional region of separated flow. Energy losses of 30% are experienced at the toe.
Numerical investigation of boundary conditions for moving contact line problems
Authors: Somalinga Sandesh , Bose Arijit
Published: July 2002

When boundary conditions arising from the usual hydrodynamic assumptions are applied, analyses of dynamic wetting processes lead to a well-known nonintegrable stress singularity at the dynamic contact line, necessitating new ways to model this problem. In this paper, numerical simulations for a set of representative problems are used to explore the possibility of providing material boundary conditions for predictive models of inertialess moving contact line processes. The calculations reveal that up to Capillary number Ca=0.15, the velocity along an arc of radius 10Li (Li is an inner, microscopic length scale) from the dynamic contact line is independent of the macroscopic length scale a for a>103Li, and compares well to the leading order analytical “modulated-wedge” flow field [R. G. Cox, J. Fluid Mech. 168, 169 (1986)] for Capillary number Ca<0.1. Systematic deviations between the numerical and analytical velocity field occur for 0.1<Ca<0.15, caused by the inadequacy of the leading order analytical solution over this range of Ca. Meniscus shapes produced from calculations in a truncated domain, where the modulated-wedge velocity field [R. G. Cox, J. Fluid Mech. 168, 169 (1986)] is used as a boundary condition along an arc of radius R=10−2a from the dynamic contact line, agree well with those using two inner slip models for Ca<0.1, with a breakdown at higher Ca. Computations in a cylindrical geometry reveal the role of azimuthal curvature effects on velocity profiles in the vicinity of dynamic contact lines. These calculations show that over an appropriate range of Ca, the velocity field and the meniscus slope in a geometry-independent region can potentially serve as material boundary conditions for models of processes containing dynamic contact lines.
Radial plasma transport and toroidal current driven by nonresonant ponderomotive forces
Authors: Elfimov A. G. , Petržílka V. , Tataronis J. A.
Published: July 2002

A general form of the time-averaged ponderomotive force produced by radio frequency waves in magnetized plasma configurations is treated. Included in the ponderomotive force are components that result from plasma flow, the dynamo effect, and wave helicity. A detailed description of effects of individual components in the ponderomotive force on radio frequency (RF) driven transport and current is given.
Critique of atomic physics instability mechanisms: Ionization-driven and radiative microinstabilities in the tokamak edge plasma
Authors: Ross David W.
Published: July 2002

The theory of atomic-process driven microinstabilities in the tokamak edge plasma is reexamined. It is found that these instabilities, as they are usually presented, do not exist. This assertion applies both to ionization-driven modes and to radiative condensation, or thermal-driven modes. The problem is that there exists no separation of time scales between the approach to equilibrium and the growth rate of the purported instabilities. Therefore, to describe the perturbation of an inhomogeneous plasma, it is essential either to establish an equilibrium that includes both perpendicular transport and the proposed source, or, alternatively, to follow the background evolution simultaneously with the growth of the modes. Neither has been done in theoretical or numerical studies of microinstabilities driven by atomic effects in tokamaks. Very near the density limit, macroscopic modes may be unstable, leading to marfes or disruptions, but perturbations of the equilibrium transport fluxes, when taken into account, are sufficient to stabilize the microscopic modes. If the equilibrium fluxes are not included a priori, the ordering breakdown persists into the nonlinear regime. Since the atomic driving terms are the same as in the linear limit, radial decorrelation lengths would have to approach background scale lengths to yield transport of significant magnitude. Under ordinary tokamak conditions, therefore, atomic processes are unlikely to provide an important driving mechanism for the microturbulence that is presumed to cause anomalous transport.
Coherent synchrotron radiation in a cylindrical waveguide with a helical wiggler
Authors: Hartemann F. V. , Le Sage G. P. , McDermott D. B. , Luhmann N. C.
Published: July 2002

The spectral and temporal radiation characteristics of an axially extended (finite-size), transversally accelerated, charge distribution propagating on fixed helical trajectories through a wiggler are derived both in free-space and in a cylindrical waveguide. If the charge distribution scale length is short compared to the radiation wavelength, the electron bunch essentially behaves as an accelerated point charge, and coherently radiates spontaneous synchrotron radiation. In a waveguide, two very different radiation processes are possible. At grazing, where the axial bunch velocity matches the electromagnetic wave group velocity, the single output radiation pulse is extremely short, and chirped over the full interaction bandwidth; the pulse duration is determined by group velocity dispersion. In the free-space limit, the widths of the Doppler upshifted and downshifted radiation pulses are determined by slippage. At grazing, the radiation power level is considerably higher than that expected from the conventional coherent synchrotron scaling.
Analytic model for the runaway distribution function in the presence of spatial diffusion
Authors: Catto Peter J. , Myra J. R. , Wootton A. J.
Published: July 2002

A steady-state kinetic model for runaway electrons in the presence of radial diffusion in a stochastic magnetic field is adopted and solved for a constant magnetic diffusivity. The model is constructed to recover the correct runaway production rate in the absence of spatial diffusion. The parallel energetic electron distribution function f is found by matching the solutions from three regions in parallel velocity space and is employed to form moments of f. Upper and lower bounds on the spatial diffusion are obtained by using these moments and the model exhibits the strong sensitivity to collisionality needed to explain the difference between similar plasmas with little or no hard x-ray signal and those with significant hard x-ray signals.
Phenomenological modeling of turbulence in Z-pinch implosions
Authors: Thornhill J. W. , Whitney K. G. , Deeney C. , LePell P. D.
Published: July 2002

A phenomenological investigation into the effects of magnetohydrodynamic (MHD) turbulence on the initial stagnation dynamics of aluminum wire array and argon gas puff Z-pinch implosions is performed. The increases that turbulence produces in the plasma viscosity, heat conductivity, and electrical resistivity are modeled by using multipliers for these quantities in one-dimensional (1-D) MHD calculations. The major effect of these increases is to soften the 1-D implosions by decreasing the densities that are achieved on axis at stagnation. As a consequence, a set of multipliers can be found that reasonably duplicates the average electron temperatures, ion densities, and mass of the K-shell emission region that were measured at stagnation for a variety of Physics International aluminum wire array and argon gas puff experiments. It is determined that the dependence of these measured quantities on the multipliers is weak once a level of enhancement is reached, where agreement between calculations and experiments is attained. The scaling of K-shell yield with load mass for a fixed implosion velocity is then reexamined, and the minimum load mass needed to efficiently produce K-shell emission by thermalization of kinetic energy is calculated for aluminum and argon using this phenomenological soft implosion modeling. The results show an upward shift in the minimum mass by a factor of 6 when compared to the original nonturbulent hard implosion calculations.
Dynamics of spatiotemporally propagating transport barriers
Authors: Diamond P. H. , Lebedev V. B. , Newman D. E. , Carreras B. A.
Published: July 2002

A simple dynamic model of spatiotemporally propagating transport barriers and transition fronts from low (L) to high (H) confinement regimes is presented. The model introduces spatial coupling (via transport) into the coupled evolution equations for flow shear and fluctuation intensity, thus coupling the supercritical L to H bifurcation instability to turbulent transport. Hence, fast spatiotemporal front propagation and evolutionary behavior result. The theory yields expressions for the propagation velocity and termination point of an L–H transition front and transport barrier. When the evolution of the pressure gradient, ∇Pi, and the contribution of ∇Pi to sheared electric field, Er′, is included, the ambient pretransition pressure gradient acts as a local source term that drives the evolution of the poloidal velocity shear. The transition may then evolve either as a spatiotemporally propagating front or as a uniform (i.e., nonlocal) fluctuation reduction or quench. The precise route to transition adopted depends on the relative magnitudes of the front transit time, τT, and the fluctuation reduction time, τf, respectively. The relevance of spatiotemporally propagating L–H transition fronts to the very high confinement regime (VH mode) evolution in DIII-D [R. I. Pinsker and the DIII-D Team, Plasma Physics and Controlled Nuclear Fusion Research 1992 (International Atomic Energy Agency, Vienna, 1993), Vol. 1, p. 683] and in the Joint European Torus (JET) [Plasma Physics and Controlled Nuclear Fusion Research 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 27] is discussed.
A free-electron laser for cyclotron resonant heating in magnetic fusion reactors
Authors: Freund H. P. , Read M. E. , Jackson R. H. , Pershing D. E. , Taccetti J. M.
Published: July 2002

A G-band free-electron laser designed for plasma heating is described using a coaxial hybrid iron (CHI) wiggler formed by insertion into a solenoid of a central rod and an outer ring of alternating ferrite and nonferrite spacers positioned so that the central ferrite (nonferrite) spacers are opposite the outer nonferrite (ferrite) spacers. The CHI wiggler provides for enhanced beam focusing and the ability to handle intense beams and high-power continuous wave radiation. Simulations indicate that a power/efficiency of 3.5 MW/13% are possible using a 690 kV/40 A beam. No beam loss was found in simulation.
Motion of relativistic particles in axially symmetric and perturbed magnetic fields in a tokamak
Authors: de Rover Machiel , Lopes Cardozo Niek J. , Montvai Attila
Published: July 2002

An extensive comparison is given between an analytical theory for the computations of particle orbits of relativistic runaway electrons [M. de Rover et al., Phys. Plasmas 3, 4468 (1996)], and numerical simulations. A new numerical scheme is used for the computer simulations of guiding center orbits. Furthermore, simulations of the full particle motion, including the gyration are performed to check the guiding center approximation. The behavior of drift surfaces and particle orbits in axially symmetric magnetic fields, as predicted in the companion paper are confirmed. This includes the smaller minor radius of a drift surface compared to a magnetic flux surface with identical rotational transform, and the decrease of the minor radius of a drift surface with increasing particle energy. Magnetic islands and drift islands appear when the axial symmetry of the magnetic field is broken by harmonic perturbations. In the numerical simulations the amplitudes of the perturbations have been chosen to increase towards the plasma edge. The analytic theory gave predictions of the width of the drift islands that are in good agreement with the numerical simulations. When overlap of the magnetic perturbations introduces stochasticity, the Hamiltonian theory shows that drift islands can exist in the region of stochastic magnetic field lines, which is also confirmed by the numerical simulations.
Velocity–space asymmetry of the trapping boundary of charged particles at and near the magnetic axis of a tokamak
Authors: Chu T. K.
Published: July 2002

In tokamaks, the trajectory of a trapped particle has a pair of poloidal turning points where Vz reverses direction. They form a stagnation point when coalescing on the equatorial plane. The trajectories traversing the stagnation point, because of the finite Larmor radius and hence the banana width, have a threefold degeneracy: a pinch orbit and a kidney orbit of a trapped particle, and a loop orbit of a passing particle. When traversing the stagnation point from a pinch orbit, the trajectory of a negative-V∥ particle must change to a loop orbit and the particle becomes passing, and that of a positive-V∥ particle must change to a kidney orbit and the particle remains trapped. The trapping boundary is asymmetric in V∥. The percentage of trapped particles in a species in a local Maxwellian plasma depends on the radial distance r as well as on the Larmor radius of its thermal particle. At the axis the trapping ratio is finite and more ions than electrons are trapped; for typical parameters in Princeton Beta Experiment-Modification [Bell et al., Phys. Fluids B 2, 1271 (1990)], for example, 2.2% of electrons and 8.6% of deuterons are trapped. Up to a radial distance of ∼10 times the Larmor radius of a thermal particle, the trapping ratio increases as r2.
Lyapunov exponents and particle dispersion in drift wave turbulence
Authors: Pedersen Thomas Sunn , Michelsen Poul K. , Rasmussen Jens Juul
Published: July 2002

The Hasegawa-Wakatani model equations for resistive drift waves are solved numerically for a range of values of the coupling due to the parallel electron motion. The largest Lyapunov exponent, λ1, is calculated to quantify the unpredictability of the turbulent flow and compared to other characteristic inverse time scales of the turbulence such as the linear growth rate and Lagrangian inverse time scales obtained by tracking virtual fluid particles. The results show a correlation between λ1 and the relative dispersion exponent, λp, as well as to the inverse Lagrangian integral time scale τi−1. A decomposition of the flow into two distinct regions with different relative dispersion is recognized as the Weiss decomposition [J. Weiss, Physica D 48, 273 (1991)]. The regions in the turbulent flow which contribute to λ1 are found not to coincide with the regions which contribute most to the relative dispersion of particles.
Multifaceted asymmetric radiation from the edge impurity density limits in tokamaks with poloidal asymmetry and rotation
Authors: Stacey Weston M.
Published: July 2002

A linear stability analysis of two-dimensional, edge-localized thermal instabilities in tokamaks has been performed using a fluid model which incorporates the effects of large radial gradients and near-sonic rotation speeds. Sufficient stability requirements for fundamental (m=0) and harmonic (m≳0) poloidal modes are established and used to investigate the effects of rotation, poloidal asymmetry in the equilibrium solution, parallel current, and parallel momentum injection on impurity density limits. The higher density limits due to parallel heat conduction and parallel viscosity that are associated with the m≳0 modes, but that are absent for the m=0 mode, account for the onset and stability of MARFEs (multifaceted asymmetric radiation from the edge). Rotation and asymmetry in the equilibrium solution are significant in the determination of impurity density limits. The MARFE threshold density limit can be increased by driving current in the plasma edge counter to the magnetic field.
Self-focusing of ion-acoustic surface waves
Authors: Stenflo L. , Gradov O. M.
Published: July 2002

An electrostatic ion-acoustic surface wave propagating along the boundary of a semi-infinite plasma is considered. It is shown that a nonlinear Schrödinger equation can describe the development of the wave amplitude. The self-focusing length of a wave beam is estimated.
Theory of the collisional presheath in a magnetic field parallel to the wall
Authors: Schmitz H. , Riemann K.-U. , Daube Th.
Published: July 2002

In the limit of a small Debye length (λD→0) the plasma boundary layer in front of a negative absorbing wall is split up into a collision-free planar space charge sheath and a quasineutral presheath, where the ions are accelerated to fulfill the Bohm criterion. Apart from ion inertia, the mechanism of the presheath depends on an additional effect controlling the ion field acceleration. The present paper considers a stationary presheath dominated by the deflection of the ion orbits in a magnetic field parallel to the wall. The ion transport is provided by charge exchange collisions with cold neutrals. The potential profiles and ion distributions resulting from the self-consistent kinetic analysis are compared with expectations based on a previous hydrodynamic model. The transition from ‘‘closed’’ to ‘‘open’’ ion orbits results in typical deviations near the sheath edge. The kinetic Bohm criterion is found to be fulfilled marginally.
Pulse shaping for ignition and gain of an indirectly driven target
Authors: Djaoui A.
Published: July 2002

A detailed study of the problem of ignition of the intended indirectly driven ‘‘point design target’’ [J. Lindl, Phys. Plasmas 2, 3933 (1995)] for the U.S. National Ignition Facility is presented. First a multistep pressure pulse which ignites the target (without its ablator) is found and the effect of changing the timing of the different shocks on the target yield is analysed in detail. A radiation drive which nearly reproduces such a pressure pulse at the ablator/fuel interface is then constructed. The resulting radiation drive is similar to the one used by the U.S. workers but has a 3 percent higher peak value. An operating window of about 35 eV width is found around the optimum maximum drive temperature. Below this window the target fails because adequate implosion velocities are not achieved, while above it the main fuel is raised to high entropies resulting in low compressions, despite high implosion velocities. These calculations represent the first independent confirmation, outside the weapons laboratories, that ignition and gain can be achieved near the operating parameters for the above target.
Multifaceted asymmetric radiation from the edge suppression by external edge heating
Authors: Stacey Weston M.
Published: July 2002

A linear, fluid model stability analysis of a radiative plasma mantle reveals that the impurity density limit for the onset of multifaceted asymmetric radiation from the edge (MARFE) in tokamaks can be increased by external heating of the radiative mantle at the plasma edge. The required injected power is estimated to be a few MW for present experiments and a few tens of MW for future reactors.
The stability of advanced operational regimes on the Tokamak Fusion Test Reactor
Authors: Fredrickson E. D. , Sabbagh S. A. , Bell M. G. , Mansfield D. , Batha S. , Chang Z. , Levinton F. , McGuire K. M. , Okabayashi M. , Taylor G. , Takahashi H. , Hughes M. , Manickam J. , Phillips M. , Zakharov L.
Published: July 2002

The performance of the Tokamak Fusion Test Reactor [D. Meade and the TFTR Group, in Plasma Physics and Controlled Nuclear Fusion Research, Washington, D.C., 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. I, pp. 9–24], as defined by the maximum fusion power production, has been limited, not by confinement, but by stability to pressure-driven modes. Two classes of current profile modification have been investigated to overcome this limit. A new technique has been developed to increase the internal inductance of low-q (q≈4), high-current (Ip>2MA) plasmas. As was the case at higher edge q, the disruptive β limit has been found to increase roughly linearly with the internal inductance, li. Plasmas with hollow current profiles, i.e., reversed shear, are also predicted and experimentally observed to have increased stability in the negative shear region to ballooning and kink modes. However, performance of these plasmas is still limited by pressure-driven modes in the normal shear region.