bluuebunny/crossref_metadata_2025 huggingface dataset:
Two-level solitary waves as generalized solutions of the KdV equation
Authors: Izrar B. , Lusseyran F. , Miroshnikov V.
Published: July 2002

An analytical class of standing wave solutions to the Korteweg–de Vries (KdV) equation is obtained in the framework of continuous finite generalized functions. This paper shows how this class can be used to describe a great variety of wave shapes, especially bores and jumps. These new solutions are built by appropriately combining parts of two ordinary KdV waves. These represent a system with a steep transition between different energy levels of two potential wells. A number of specific cases of the generalized solutions are identical to those obtained recently within the theory of the KdV equation forced by a Dirac delta function. Numerical simulations of both stationary and transient KdV equations are carried out in a few cases. The weak formulation used in the numerical scheme is equivalent to the analytical generalized functions approach. Simulations of initially perturbed wave fronts prove the high degree of stability of many of these solutions.
Mixing properties of three-dimensional (3-D) stationary convection
Authors: Schmalzl J. , Houseman G. A. , Hansen U.
Published: July 2002

Passive tracers in steady-state three-dimensional (3-D) convective flows with infinite Prandtl number, which is relevant for the Earth’s mantle, show a remarkable flow structure. Individual flowlines as shown by Poincare sections of the tracer paths lie on a two-dimensional (2-D) surface with distorted toroidal topology. Furthermore, the space occupied by the convecting fluid is filled by a set of these toroidal surfaces nested one within another. The small radius of the innermost toroidal surface approaches zero, defining a closed streamline whose location we have determined in specific cases using numerical solutions. The outermost of the toroidal surfaces coincides with the upper and lower surfaces of the layer and with vertical symmetry planes which separate the flow between neighboring cells. Both square and hexagonal convection planforms show a triangular cellular structure with triangles defined by (π/2,π/4,π/4) and (π/2,π/6,π/3), respectively. The outer toroidal surface is closed by a horizontal flow line through the middle of the cell. The numerical experiments suggest that streamlines are not generally closed in any small number of orbits. Instead the toroidal surface appears to be progressively filled in by the trace of a single streamline which, in successive orbits, is displaced across the surface without returning to the same path. This flow structure ensures that, while extreme shear strains can occur, particularly in the vicinity of the cell separatrices, mixing of the material only occurs in 2D. Tracers initially on one toroidal surface remain on that surface indefinitely. Like for 2-D convective flow, time dependence of the solution appears to be a necessary prerequisite for thorough spatial mixing to occur.
Three-dimensional instability of Kirchhoff’s elliptic vortex
Authors: Miyazaki Takeshi , Imai Takeshi , Fukumoto Yasuhide
Published: July 2002

The three-dimensional linear instability of Kirchhoff’s elliptic vortex in an inviscid incompressible fluid is investigated numerically. Any elliptic vortex is shown to be unstable to an infinite number of short-wave bending modes, with azimuthal wave number m=1. In the limit of small ellipticity, the axial wave number of each unstable mode approaches the value obtained by the asymptotic theory of Vladimirov and Il’in, indicating that the instability is caused by a resonance phenomena. As the ellipticity increases, the bandwidth broadens and neighboring bands overlap each other. The maximum growth rate of each mode, except for that of the longest one, agrees fairly with that of the elliptical instability modified by the influence of a Coriolis force. The growth rate of these three-dimensional modes are larger than those of the two-dimensional modes when ellipticity is smaller than a certain value.
A physical model for merging in two-dimensional decaying turbulence
Authors: Riccardi G. , Piva R. , Benzi R.
Published: July 2002

Some aspects of the simulation by point vortices of two-dimensional decaying turbulence are discussed, together with their most relevant consequences for the decay of the number of vortices. Two different merging models are proposed to simulate dissipative interactions between corotating vorticity structures within a point vortex simulation. Both models are based on a statistical approach to assign the number of vortices resulting from the merging of two vortices of different size. Probability distributions are defined for the production of one, two, or three vortices, and they are assigned as functions of the circulation ratio for the two interacting vortices. These functions are determined by performing a large number of Contour Dynamics simulations of vortex interactions, each under a given strain field. A simple rule to reset the vorticity field, at the end of the merging process, is discussed in terms of conserved quantities for the formation of one or three vortices. To complete the merging model, a criterion that indicates the onset of a merging event between two close vortices of like sign is required. The first model is defined by adopting a critical distance as merging criterion. In this way, the effect of the strain on the merging process is taken into account only in a statistical manner, i.e., by the probability law for the merging products. The use of this merging model into a point vortex simulation gives a surprisingly good agreement with the results for the vortex number decay obtained by Dritschel via Contour Surgery.

Nevertheless, a merging criterion based on the critical distance appears questionable, since it disregards the effect of the strain on the merging conditions. To this aim, we introduce a more sophisticated merging model that uses the dynamics of elliptical patches under a given strain field to select the merging events. This second model accounts also directly, and not only in a statistical sense, for the strain influence over the merging conditions, revising thoroughly the critical distance concept. The results show that the vortex number decay is not strongly sensitive to a detailed description of each individual merging process and, if the interest is focused on the vortex number decay, further improvements of the merging model are not strictly required.
Simple model for the turbulent mixing width at an ablating surface
Authors: Cherfils Catherine , Mikaelian Karnig O.
Published: July 2002

A diffusion model is applied to calculate the turbulent mixing width at an ablating surface. It is proposed that the general model be tested first on well-determined and easily accessible stabilizing mechanisms such as surface tension, viscosity, density gradient, or finite thickness. In this model the turbulent mixing width h is directly correlated with the growth rate γ of the perturbations in the presence of stabilizing mechanisms: h/hclass=(γ/γclass)1/2, where hclass=0.07 Agτ2 and γclass=√Agk (where A is the Atwood number, g is the acceleration, τ is the time, and k =2π/λ =2π/(ωhclass), ω being a dimensionless constant in the model). The method is illustrated with several examples for hablation, each based on a different γablation. Direct numerical simulations are presented comparing h with and without density gradients. In addition to mixing due to the Rayleigh–Taylor instability, the diffusion model is applied to the Kelvin–Helmholtz and the Richtmyer–Meshkov mixing layers.
Suppression of coalescence by shear and temperature gradients
Authors: Dell’Aversana Pasquale , Banavar Jayanth R. , Koplik Joel
Published: July 2002

We describe laboratory experiments on millimeter-sized drops of liquid in air which indicate that both thermocapillary and isothermal shear flows are able to prevent the coalescence of bodies of liquid which would occur readily in the absence of such flows. We have also carried out molecular dynamics computer simulations of nanometer-sized drops, which show the same qualitative behavior in the case of an applied shear. At the other extreme, persistent non-coalescence of larger drops was observed in microgravity conditions in a space shuttle experiment. We give an explanation of the experimental observations based upon lubrication theory and simple continuum hydrodynamics arguments, along with complementary microscopic insight obtained from the molecular simulations.
Investigations of boundary layer transition via Galerkin projections on empirical eigenfunctions
Authors: Rempfer D.
Published: July 2002

In this paper, Galerkin projections on eigenfunctions as obtained by proper orthogonal decomposition of numerically computed flow fields are used to derive dynamical models for different regions of a transitional boundary layer. The regions investigated cover the stages of the transition process from the evolution of low-amplitude Tollmien-Schlichting waves up to the final stages of transition, right at the onset of turbulence. In a first part of the paper, the possibilities and limitations of the approach chosen are investigated in detail, and in a second part the application of the techniques developed before is demonstrated for the case of a spatially evolving boundary layer that is inhomogeneous in all spatial directions. The focus of this work is mainly on how characteristic properties of the dynamics change as transition evolves in the streamwise direction.
Turbulence suppression by active control
Authors: Farrell Brian F. , Ioannou Petros J.
Published: July 2002

It has recently been recognized that the non-normality of the dynamical operator obtained by the linearization of the equations of motion about the strongly sheared background flow plays a central role in the dynamics of both fully developed turbulence and laminar/turbulent transition. This advance has led to the development of a deterministic theory for the role of coherent structures in shear turbulence as well as a stochastic theory for the maintenance of the turbulent state. In this work the theory of stochastically forced non-normal dynamical systems is extended to explore the possibility of controlling the transition process and of suppressing fully developed shear turbulence. Modeling turbulence as a stochastically forced non-normal dynamical system allows a great variety of control strategies to be explored and their physical mechanism understood. Two distinct active control mechanisms have been found to produce suppression of turbulent energy by up to 70%. A physical explanation of these effective control mechanisms is given and possible applications are discussed.
Linear and nonlinear evolution of boundary layer instabilities generated by acoustic-receptivity mechanisms
Authors: Breuer Kenneth S. , Dzenitis Elizabeth G. , Gunnarsson Jonas , Ullmar Mats
Published: July 2002

Experimental results are presented concerning the evolution of instabilities generated by the interaction between low-level broad-band acoustic waves and small two-dimensional roughness elements. Streamwise perturbation velocity spectra are measured and it is found that on the smooth plate, naturally-occurring Tollmien-Schlicting (T-S) waves grow in a manner consistent with a resonant subharmonic wave interaction. However, in the presence of small two-dimensional roughness elements, a strong primary T-S mode is forced by an interaction with the background acoustic field. This leads to a K-type of nonlinear interaction characterized by the generation of harmonics (up to six harmonics are observed) at the expense of the subharmonic. The scaling of the T-S waves and their harmonics with the number and amplitude of the wall roughness is also considered.
The excitation of ducted modes by passing internal waves
Authors: Chimonas George , Hauser Heather M. , Bennett Richard D.
Published: July 2002

A local peak in the atmospheric wind or stability profile supports ducted (vertically trapped) modes. If the duct is rather high in the atmosphere it cannot be directly excited by the major atmospheric sources such as convection, but an internal gravity wave radiating out of such sources transfers energy to the duct via nonlinear processes related to the resonance triad interaction. The amplitude of such a transfer is computed. The modal excitations remain after the internal wave has left the region, and while each passing wave adds only a small amount of activity to the duct such contributions are cumulative and drive the modal activity up to a level where it is limited by local dissipation. This suggests the possibility of monitoring the mean flux of internal waves through the region by measuring activity within elevated ducts, a procedure that offers several advantages over monitoring the wave flux directly.
Experimental investigation of Richtmyer–Meshkov instability before and after the reflected shock compression
Authors: Jourdan G. , Houas L.
Published: July 2002

Results of an experimental investigation on the Richtmyer–Meshkov instability of a He–CO2 interface are reported. A simultaneous three-directional laser absorption technique is used to follow, at a single abscissa, the evolution of the created mixing zone before and after the interaction with the reflected shock, during the same run. CO2 density profiles have been determined within both the incident and the compressed mixing zones. However, near the pure CO2, the wall boundary layer reflected shock interaction perturbs measurements and does not allow objective conclusions.
Correlation between experimental results and numerical solutions of the Navier–Stokes problem for noncoalescing liquid drops with Marangoni effects
Authors: Monti Rodolfo , Savino Raffaele
Published: July 2002

Experiments show that, when two drops are brought in contact and pushed toward each other in the presence of temperature differences, coalescence is inhibited. Axisymmetric numerical solutions of the Navier–Stokes problem have been obtained to give an explanation of the phenomenon, assuming that a thin air film exists between the contacting drops and that, provided that well-defined dynamic conditions prevail on the liquid surfaces, the film experiences a suitable pressure that balances the pressure in the drops. The numerical results agree with the experimental ones, qualitatively explain why an air film between the drops could be created by Marangoni effects and show that the suppression of coalescence is obtained as long as films sufficiently large exhibit excess pressures of the same order of magnitude of the pressure needed to deform the drops.
Growth of non-modal transient structures during the spreading of surfactant coated films
Authors: Matar Omar K. , Troian Sandra M.
Published: July 2002

The spreading of surfactant coated thin liquid films is often accompanied by an instability producing significant film corrugation, fingering and branching. Marangoni stresses, responsible for the rapid and spontaneous spreading, are suspected as the main cause of unstable flow. Traditional eigenvalue analysis of a self-similar solution describing Marangoni driven spreading has predicted only stable modes. We present results of a transient growth study which reveals enormous amplification of initially infinitesimal disturbances in the film thickness. This analysis provides, for the first time, evidence of an instability resembling experimental patterns.
Steady-state Burgers turbulence with large-scale forcing
Authors: Gotoh Toshiyuki , Kraichnan Robert H.
Published: July 2002

Steady-state Burgers turbulence supported by white-in-time random forcing at low wave numbers is studied analytically and by computer simulation. The peak of the probability distribution function (pdf) Q(ξ) of velocity gradient ξ is at ξ=O(ξf), where ξf is a forcing parameter. It is concluded that Q(ξ) displays four asymptotic regimes at Reynolds number R≫1: (A) Q(ξ)∼ξf−2ξexp(−ξ3/3ξf3) for ξ≫ξf (reduction of large positive ξ by stretching); (B) Q(ξ)∼ξf2|ξ|−3 for ξf≪−ξ≪R1/2ξf (transient inviscid steepening of negative ξ); (C) Q(ξ)∼|Rξ|−1 for R1/2ξf≪−ξ≪Rξf (shoulders of mature shocks); (D) very rapid decay of Q for −ξ⩾O(Rξf) (interior of mature shocks). The typical shock width is O(1/Rkf). If R−1/2≫rkf≫R−1, the pdf of velocity difference across an interval r is found to be P(Δu,r)∝r−1Q(Δu/r) throughout regimes A and B and into the middle of C.
Tumbling cards
Authors: Mahadevan L. , Ryu William S. , Samuel Aravinthan D. T.
Published: July 2002

When a stiff rectangular card is dropped in still air with its long axis horizontal, it often settles into a regular mode of motion; while revolving around its long axis it descends along a path that is inclined to the vertical at a nearly constant angle. We show experimentally that the tumbling frequency Ω of a card of length l, width w and thickness d (l≫w≫d) scales as Ω∼d1/2w−1, consistent with a simple dimensional argument that balances the drag against gravity.
A dynamical model for turbulence. VII. Complete system of five orthogonal tensors for shear-driven flows
Authors: Canuto V. M. , Dubovikov M. S.
Published: July 2002

The one-point Reynolds stresses have been traditionally expressed in terms of ten tensors. It is, however, known that the independent tensors are only five. We construct a complete set of five orthogonal, traceless, and symmetric second rank tensors in terms of mean strain and vorticity. The system is used to express the one-point Reynolds stresses. The coefficients of the expansion are evaluated in papers VIII and IX.
Miscible quarter five-spot displacements in a Hele-Shaw cell and the role of flow-induced dispersion
Authors: Petitjeans Philippe , Chen Ching-Yao , Meiburg Eckart , Maxworthy Tony
Published: July 2002

Miscible quarter five-spot displacements in a Hele-Shaw cell are investigated by means of experimental measurements and numerical simulations. The experiments record both the volumetric as well as the surface efficiency at breakthrough as a function of the dimensionless flow rate in the form of a Peclet number and the viscosity contrast. For small flow rates, both of these efficiency measures decrease uniformly with increasing Peclet numbers. At large flow rates, an asymptotic state is reached where the efficiencies no longer depend on the Peclet number. Up to Atwood numbers of approximately 0.5, the less viscous fluid occupies close to 23 of the gap width, which indicates a near-parabolic velocity profile across the gap. Consequently, in this parameter range a Taylor dispersion approach should be well suited to account for flow-induced dispersion effects. For larger viscosity contrasts, accompanying two-dimensional numerical simulations based on Taylor dispersion predict an increased stabilization for high flow rates, which is not confirmed by the experiments. This suggests that, in order to extend the range of applicability to larger viscosity contrasts, the components of the dispersion tensor will have to be amended in order to account for the presence of quasi-steady fingers.
On the validity of a nonlocal approach for MHD turbulence
Authors: Gomez T. , Politano H. , Pouquet A.
Published: July 2002

The phenomenology of magnetohydrodynamic (MHD) turbulence proposed by R. H. Kraichnan, and its consequences for energy spectra and energy decay laws in the high Reynolds number self-similar regime, are first reviewed. After recalling the exact relationships for MHD derived in the spirit of the so-called “4/5” law of Kolmogorov, such laws are used to compute intermittency exponents for statistically steady MHD flows in two space dimensions. These exponents are evaluated both for the structure functions of order p built on the physical variables—velocity v and magnetic field b, or their combination, through the Elsässer variables z±=v±b—and for the flux variables Yp±(r)≡〈[δzL∓(r)(δzi±(r))2]p/3〉, where L denotes the longitudinal components of the fields. There are indications that these nonlinear fluxes scale in a manner similar to that of nonconducting fluids, whereas the physical v, b, z± fields are more intermittent than in the neutral fluid case.
Axisymmetric thermal wake interaction of two bubbles in a uniform temperature gradient at large Reynolds and Marangoni numbers
Authors: Balasubramaniam R. , Subramanian R. Shankar
Published: July 2002

An analysis is performed on the thermocapillary motion of two bubbles in a continuous phase in which a linear temperature field is imposed in the undisturbed state. The bubbles are moving in the direction of the temperature gradient and are assumed to interact axisymmetrically via the influence of the thermal wake of the leading bubble on the trailing bubble. The flow-field interaction of the bubbles is neglected. The Reynolds number of the motion is assumed to be sufficiently large that a potential flow field prevails around each bubble. The energy equation for the temperature field around the trailing bubble is solved by matched asymptotic expansions for large values of the Marangoni number. It is shown that the thermal wake of the leading bubble induces a nonmonotonic temperature field on the surface of the trailing bubble. The effective temperature gradient on the trailing bubble is weakened. Hence its migration speed is reduced compared to the case when it is isolated. This result is in qualitative agreement with experimental results for a pair of interacting drops obtained from a space flight experiment that has been reported in the literature.
Collisionless kinetic ballooning equations in the comparable frequency regime
Authors: Zheng L.-J. , Tessarotto M.
Published: July 2002

The collisionless kinetic ballooning mode equations are obtained from the gyrokinetic and Maxwell equations for the comparable frequency regime (i.e., for frequency of the modes comparable with the ion acoustic frequency along the field lines). A two length-scale analysis is made to reduce the kinetic ballooning mode equations to a fluid-like one. The finite Larmor radius (FLR) effect and particle–wave resonance (Landau damping) are taken into account. The trapped-particle effect is proven to be negligible in the ordering scheme adopted in this paper. It is emphasized that the non-FLR kinetic effects, especially the parallel electric field effect, are significant in the comparable frequency regime rather than the intermediate one. The non-FLR kinetic effects are found to be coupled to the vorticity equation through the apparent mass term, which suggests that the toroidal effect is essential to the kinetic mechanism in the singular layer (i.e., the outer region of ballooning mode representation space). The applications of the equations are discussed. The comparison with ideal magnetohydrodynamic (MHD) theory is made.
Numerical simulation of drift waves and trapped ion modes
Authors: Kingsbury O. T. , Waltz R. E.
Published: July 2002

Two-dimensional numerical simulations are used to study the interaction of trapped electron drift waves (DW) and trapped ion modes (TIM). Wave-number (k) space is divided into long and short wave regions at a poloidal wave number corresponding to the ion bounce frequency. Two field models are used to describe trapped electron drift wave dynamics at short waves and trapped ion mode dynamics for long waves. The standard case has curvature effects and collisionality. The nonlinearity that couples the two regions includes a trapped ion banana width effect analogous to finite Larmor radius (FLR) polarization drift. The principal result of this study is that the TIM do not contribute to the diffusion significantly, regardless of the model for the nonlinear coupling to the DW. This conclusion is supported by a more general four field model that includes pressure dynamics and which allows ion temperature gradient (ITG) driven drift modes. When the collisionality is varied, the diffusion deviates from the γ/k2x form and tends to vanish towards the collisionless limit even though the system is strongly unstable linearly.
Two-dimensional simulation studies of the electron beam-plasma instability
Authors: Dum C. T. , Nishikawa K.-I.
Published: July 2002

Two-dimensional simulations of the electron-beam plasma instability with large system size are carried out and are compared with recent one-dimensional simulations for plasma parameters appropriate to the electron foreshock. It is found that wave propagation and diffusion perpendicular to the beam drift are significant at all times. Because a plateau cannot be maintained in this case, the wave level decreases much more rapidly than in one-dimensional simulations. The nonlinear wave scattering process which occurs at late times also differs in that it generates a broad secondary spectrum rather than a condensate. The two-dimensional model, in addition, allows the investigation of the effects of increasing magnetic field strength (e.g., along auroral field lines). For intermediate magnetic fields Langmuir waves and a highly oblique spectrum belonging to the lower hybrid branch are simultaneously excited. The oblique wave spectrum for strong magnetic fields can be explained by mapping from the magnetic field direction.
Nonlinear destabilization of linearly stable tearing modes with multiple rational surfaces
Authors: Persson M. , Dewar R. L.
Published: July 2002

The stability of finite size magnetic islands is analyzed in configurations with multiple resonant magnetic surfaces. It is demonstrated that there are configurations that are linearly stable which can be unstable to finite size perturbations. Two different examples of single helicity double tearing are given for configurations with two q=2 surfaces. In the first case the destabilization is due to the extension of magnetic separatrices out to regions of destabilizng current gradients. For the second case the modes are linearly stabilized by the suppression of the linear coupling of the rational surfaces by differential plasma rotation, which essentially decouples the perturbations around the different rational surfaces. A finite size magnetic island will interact quasilinearly with initial plasma rotation. The plasma rotation is then equilibrated and the mode destabilized.
Construction of Monte Carlo operators in collisional transport theory
Authors: Tessarotto Massimo , White Roscoe B. , Zheng Lin-Jin
Published: July 2002

A Monte Carlo approach for investigating the dynamics of quiescent collisional magnetoplasmas is presented, based on the discretization of the gyrokinetic equation. The theory applies to a strongly rotating multispecies plasma, in a toroidally axisymmetric configuration. Expressions of the Monte Carlo collision operators are obtained for general v-space nonorthogonal coordinates systems, in terms of approximate solutions of the discretized gyrokinetic equation. Basic features of the Monte Carlo operators are that they fullfill all the required conservation laws, i.e., linear momentum and kinetic energy conservation, and in addition that they take into account correctly also off-diagonal diffusion coefficients. The present operators are thus potentially useful for describing the dynamics of a multispecies toroidal magnetoplasma. In particular, strict ambipolarity of particle fluxes is ensured automatically in the limit of small departures of the unperturbed particle trajectories from some initial axisymmetric toroidal magnetic surfaces.
Plasma flows and fluctuations in intense ion-beam diodes
Authors: Litwin C. , Maron Y. , Sarid E.
Published: July 2002

A possible source of electric field fluctuations in the anode plasma of a magnetically insulated ion diode which have been observed in recent experiments is discussed. It is suggested that these fluctuations are driven by the ion flow which destabilizes an electrostatic mode akin to two-stream instability. Evidence is presented for such a flow and its implications for the electric field polarization and magnitude are discussed.
Thermal and electric oscillation driven by orbit loss in helical systems
Authors: Itoh K. , Sanuki H. , Itoh S.-I.
Published: July 2002

Coupled oscillation of the radial electric field, the heating power, and the plasma temperature in helical systems is analyzed. This oscillation is caused by the influence of the radial electric field on the direct loss of injected fast ions. The damped oscillations of the radial electric field, temperature and fast-ion loss are predicted. Conditions for the occurrence of the mode and the oscillation frequency are discussed.
Dynamo effect and current drive by low-frequency waves
Authors: Litwin C.
Published: July 2002

The dynamo effect due to low-frequency oscillations and its application to the nonresonant current drive are examined. The relevant single particle forces are analyzed and the possibility of the dynamo effect enhancement by thermal effects is investigated. In the collisional two-fluid theory with isotropic pressure the flux-surface averaged parallel dynamo field is found to be solely due to frictional forces. In the collisionless, double-adiabatic approximation the previously reported steady-state collisionless α-effect is shown to be absent. The origin of this discrepancy is discussed.
Nonlinear Landau damping of resonantly excited fields in nonuniform plasmas
Authors: Srivastava S. , Morales G. J. , Maggs J. E.
Published: July 2002

In this study the resonant excitation of a nonuniform plasma by two electromagnetic waves at closely spaced frequencies ω1, ω2 with ω1≳ω2 is considered. Each of the pump waves excites a Langmuir wave at the point in the density profile, where plasma resonance is achieved. For profiles having scale lengths L large compared to the characteristic Airy scale length (i.e., kAL≫1) the linear Landau damping of the Langmuir waves is quite small close to their cutoff, hence the beat interaction with slow electrons plays an important role. The problem is formulated in terms of differential equations in configuration space for the waves at ω1, ω2, which are coupled to the idler field at ω1−ω2. The idler is described kinetically by a differential equation in Fourier space. The interaction is governed by the parameter ω̃3=(1−ω2/ω1)kAL and the scaled pump strength. For ω̃3≪1 the ponderomotive nonlinearity is recovered and a dissipative contribution is obtained. For ω̃3≳1 plasmon transfer from ω1 to ω2 causes strong depletion of the high-frequency wave before significant ponderomotive profile changes set in. The fractional power absorbed through the idler is smaller than the power transferred to ω2 by a factor of (1−ω2/ω1).
Radiation-driven turbulence at the plasma edge in toroidal devices
Authors: Charlton L. A. , Leboeuf J.-N. , Carreras B. A. , Lynch V. E.
Published: July 2002

The radiation drives for plasma edge parameters are reexamined. By including the electron density gradient, the radiation drive through density fluctuations can be strongly destabilizing even in a parameter regime away from force balance. This results in the dominance of the magnitude of the radiation power (γn drive) over its derivative (γT drive) for plasma edge parameters of Ohmic tokamak discharges. This leads to instability over a range of poloidal mode numbers much broader than in the case of the γT drive and to temperature fluctuations of opposite phase to the density fluctuations. Nonlinear numerical calculations show that this opposite phase relationship persists nonlinearly. As a consequence, the fluctuations induce a heat flux that is observed to be inward, while the particle and energy fluxes that they generate are calculated to be outward.
Theoretical analysis of thermal dike supported by electron cyclotron resonance heating
Authors: Kiwamoto Y. , Tatematsu Y. , Saito T. , Katanuma I. , Yoshimura Y. , Tamano T.
Published: July 2002

Thermal dike is a new concept for controlling energy transport carried by electrons along open magnetic field lines by enhancing mirror-reflection with assistance of electron cyclotron resonance heating (ECRH). Quantitative analyses are made to evaluate merits of thermal dike and to clarify requirements for efficient use of it. Heating response function is applied for trajectory analyses of electrons streaming through the ECRH zone. Substantial power gain is obtained under a configuration with a high mirror ratio between the reflection point and the resonance point and with a large scale length of the magnetic gradient in the resonance zone. Thermal dike is shown to be beneficial both in tandem mirrors and in diverters in tori. Discussions are made also on a basic experiment program of thermal dike in the GAMMA 10 tandem mirror.
Rotational pumping and damping of the m=1 diocotron mode
Authors: Crooks S. M. , O’Neil T. M.
Published: July 2002

An effect called rotational pumping by the authors (by analogy with magnetic pumping) causes a slow damping of the m=1 diocotron mode in non-neutral plasmas. In a frame centered on the plasma and rotating at the diocotron mode frequency, the end confinement potentials are nonaxisymmetric. As a flux tube of plasma undergoes E×B drift rotation about the center of the column, the length of the tube oscillates about some mean value, and this produces a corresponding oscillation in T∥. In turn, the collisional relaxation of T∥ toward T⊥ produces a slow dissipation of electrostatic energy into heat and a consequent radial expansion (cross-field transport) of the plasma. Since the canonical angular momentum is conserved, the displacement of the column off axis must decrease as the plasma expands. In the limit where the axial bounce frequency of an electron is large compared to its E×B drift rotation frequency theory predicts the damping rate γ=−2κ2ν⊥,∥ (r2p/R2w)(λ2D/L20)/(1−r2p R2w), where κ is a numerical constant, λD is the Debye length, Rw is the radius of the cylindrical conducting wall, rp is the effective plasma radius, L0 is the mean length of the plasma, and ν⊥,∥ is the equipartition rate. A novel aspect of this theory is that the magnetic field strength enters only through ν⊥,∥. As the field strength is increased, the damping rate is nearly independent of the field strength until the regime of strong magnetization is reached [i.e., Ωc≳v̄/b=(kT)3/2/√me2], and then the damping rate drops off dramatically. This signature has been observed in recent experiments. For completeness, the theory is extended to the regime where the bounce frequency is comparable to the rotation frequency, and bounce-rotation resonances are included.
Growth rate reduction of the Rayleigh–Taylor instability by ablative convection
Authors: Wouchuk J. G. , Piriz A. R.
Published: July 2002

A simple model for the instability of a steady ablation front is presented. The model is based on the sharp boundary approximation, but it is considered that, as far as the Rayleigh–Taylor instability regards, the front thickness is of the order of the minimum scale length of the density gradient. The model yields a general analytical expression for the linear growth rate, which does not depend explicitly on the particular process of energy deposition, which drives the ablation. For the specific case of electronic thermal conduction the model is in good agreement with previously reported numerical calculations. The growth rate results to be well fitted by the so-called Takabe formula, and the coefficients in such a formula are analytically derived.
How fluctuations continue through an X point
Authors: Mattor Nathan , Cohen Ronald H.
Published: July 2002

The structure of waves around a magnetic X point is analyzed. A paradox is noted, in which theory implies that waves cannot propagate along the field past an X point, but experiment shows that they do anyway. The paradox may arise from the theoretical ‘‘eikonal in the perpendicular direction’’ ansatz, in which waves follow field lines to lowest order. This paper demonstrates that waves can encounter a boundary layer in which this ansatz is violated. Such waves can propagate around the X-point region, thus avoiding the large wave number increase from magnetic shear, allowing them to correlate through such a region. This result has some unexpected implications concerning mode structure in the edge and scrape-off layer of a diverted tokamak, and possibly for the core as well.
Stabilization of ideal plasma resistive wall modes in cylindrical geometry: The effect of resistive layers
Authors: Finn John M.
Published: July 2002

A cylindrical model with finite beta having an external resonant ideal magnetohydrodynamic instability has been constructed. This resonant mode has a mode rational surface, where the safety factor q equals m/n, within the plasma. In this model, the perturbed radial magnetic field for the ideal mode is nonzero between the mode rational surface and the wall, even though it must vanish at the mode rational surface. This property of the mode is in common with the toroidal external kink. Results are presented showing that in the parameter range for which this ideal mode is stable with a conducting wall but unstable with the wall at infinity, a resistive wall mode persists. However, in the presence of plasma resistivity in a resistive layer about the mode rational surface, this resistive wall mode can be stabilized by a plasma rotation frequency of order a nominal resistive instability growth rate. Furthermore, the stabilization occurs in a large gap in wall position or beta. It is also shown that for the ideal resonant mode, as well as resistive plasma modes and nonresonant ideal plasma modes, there is a maximum value of plasma rotation above which there is no stability gap. Discussions are presented suggesting that these properties may hold for the toroidal external kink.
Parametric excitation of Bernstein modes in laser-produced plasma
Authors: Simon Albert
Published: July 2002

Parametric excitation of electron Bernstein modes in magnetized laser-produced plasma is studied. A dispersion relation is derived for the pump and scattered light wave vectors collinear and perpendicular to a uniform magnetic field in a uniform plasma and numerical solutions are obtained for the growth rate in collisionless plasma. These are then compared to an improved analytic approximation for the growth rate, and excellent agreement is obtained. Magnetic fields considered range from 10 to 1000 kG. Threshold pump intensities are estimated by including collisions or density inhomogeneity of the plasma. Ion-sound wave excitation (stimulated Brillouin scattering) is also seen and compared with the Bernstein mode results. In some regimes, the two thresholds are quite comparable. The numerical code also yields a nearly purely growing mode near the critical density. Numerical results are in good agreement with an analytic approximation, for this close cousin of the oscillating two stream instability.
A minimal dynamical model of edge localized mode phenomena
Authors: Lebedev V. B. , Diamond P. H. , Gruzinova I. , Carreras B. A.
Published: July 2002

A simple, low-dimensional model of edge localized mode (ELM) phenomena is presented. ELM dynamics are determined by the interaction of few basic processes at the edge of tokamak plasma; these include the evolution of magnetohydrodynamic (MHD) pressure gradient driven instabilities, the low–high (L–H) transition (mediated by electric field shear induced suppression and generation), the fueling of the edge by neutral particles, and edge heating by thermal flux from the core plasma. In the parameter regime characteristic of an H-mode plasma, the model exhibits a transition to stationary relaxation oscillations (i.e., stable limit cycle behavior) corresponding to ELMs. The dependence of ELM frequency, amplitude, etc. on the heating power Pin and other control parameters is studied. The transition from giant to grassy ELM behavior appears as a consequence of increasingly marginal stability to ideal ballooning as Pin increases. Several details of the dynamics of the ELM onset and behavior close to the L–H transition threshold are revealed, as well.
Scaling and transport analysis of divertor conditions on the Alcator C-Mod tokamak
Authors: LaBombard B. , Goetz J. , Kurz C. , Jablonski D. , Lipschultz B. , McCracken G. , Niemczewski A. , Boivin R. L. , Bombarda F. , Christensen C. , Fairfax S. , Fiore C. , Garnier D. , Graf M. , Golovato S. , Granetz R. , Greenwald M. , Horne S. , Hubbard A. , Hutchinson I. , Irby J. , Kesner J. , Luke T. , Marmar E. , May M. , O’Shea P. , Porkolab M. , Reardon J. , Rice J. , Schachter J. , Snipes J. , Stek P. , Takase Y. , Terry J. , Tinios G. , Watterson R. , Welch B. , Wolfe S.
Published: July 2002

Detailed measurements and transport analysis of divertor conditions in Alcator C-Mod [Phys. Plasmas 1, 1511 (1994)] are presented for a range of line-averaged densities, 0.7<n̄e<2.2×1020 m−3. Three parallel heat transport regimes are evident in the scrape-off layer: sheath-limited conduction, high-recycling divertor, and detached divertor, which can coexist in the same discharge. Local cross-field pressure gradients are found to scale simply with a local electron temperature. This scaling is consistent with classical electron parallel conduction being balanced by anomalous cross-field transport (χ⊥∼0.2 m2 s−1) proportional to the local pressure gradient. A 60%–80% of divertor power is radiated in attached discharges, approaching 100% in detached discharges. Detachment occurs when the heat flux to the plate is low and the plasma pressure is high (Te∼5 eV). High neutral pressures in the divertor are nearly always present (1–20 mTorr), sufficient to remove parallel momentum via ion–neutral collisions.
Alfvén wave current drive in the Phaedrus-T tokamak
Authors: Intrator T. , Probert P. , Wukitch S. , Vukovic M. , Brouchous D. , Diebold D. , Breun R. , Doczy M. , Edgell D. , Elfimov A. , Hershkowitz N. , Kishinevsky M. , Litwin C. , Moroz P. , Nonn P. , Winz G.
Published: July 2002

The first experimental evidence of Alfvén Wave Current Drive (AWCD) in a tokamak is shown. In a low-density experiment, an estimated 20–35 kA out of 65 kA total current, or 30%–55% of the total current has been driven. The estimated efficiency for current driven per unit RF input power is approximately ICD/PRF≊0.2 A/W, which is near the predicted efficiency, and corresponds to the commonly used figure of merit, neR0ICD/PRF≊0.4×1018 A m−2 W−1, where ne is plasma density and R0 is the major radius. The significant 30%–40% drop in loop voltage observed cannot be explained by any plausible increase in electron temperature Te, or decrease in inductive plasma energy, or changes in plasma resistivity. Independently measured loop voltage, Te, effective ionic charge Zeff, and plasma inductance and resistance are all consistent with this conclusion.
Stimulated Raman backscattering with and without optical fiber smoothing technique in 0.53 μm laser-created plasmas
Authors: Rousseaux C. , Meyer B. , Thiell G.
Published: July 2002

Backward stimulated Raman scattering (SRS) experiments have been performed using the optical fiber smoothing implemented on the high-power Phébus laser facility [Laser Part. Beams 4, 93 (1988)]. The interaction took place in low-Z plasmas presenting either exponential density profiles (solid targets) or Gaussian-type profiles. Raman instability was driven with 1.4 ns duration—0.53 μm laser pulses, containing an energy up to 1.8 kJ. Comparative and absolute measurements of SRS reflectivity are reported as a function of the incident laser intensity, both with and without beam smoothing. Near-backward time-resolved SRS spectra are also presented. Random phase plates are not used in these experiments. With or without smoothing, SRS reflectivities of the order of 10% have been measured. However, smoothing becomes effective in exponential profiles below 1015 W/cm2. Although the optical fiber efficiently reduces the contrast of the energy modulations in the focal spot, the spectral bandwidth may be insufficient to quench SRS development in these conditions. This last assumption is in agreement with theoretical predictions.
Streaming instabilities of a non-neutral plasma with turning points
Authors: Turner Leaf , Finn John M.
Published: July 2002

Streaming instabilities of a reflexing beam in a slab model of a beam Penning trap or an inertial electrostatic confinement device are studied. Particles may have turning points that may be between the walls. Linear theory is developed for the case in which the self-field cancels the external potential. If the electric field perturbation is odd about the center, these two-stream modes couple the slow waves on the two beams. Even modes consist of two classes: a class of two-stream modes and another class of complex-frequency modes, coupling the slow and fast waves on the same beam. The latter are unstable over a larger range than the two-stream modes. Thermal spread is stabilizing only when the thermal and streaming velocities are comparable. Numerical results for the general class of equilibria show both two-stream-like modes and oscillating modes.
Thermal equilibrium of bunched charged particle beams
Authors: Brown Nathan , Reiser Martin
Published: July 2002

The Maxwell–Boltzmann distribution of a bunched charged particle beam is the state toward which every other distribution will relax. For beams with lifetimes much shorter than the time required for relaxation to equilibrium, it is the distribution at injection that minimizes the emittance growth due to relaxation toward equilibrium. Three-dimensional thermal distributions are found numerically for the case of linear external focusing forces acting on an axially symmetric bunched beam in a conducting pipe. Equations are derived for current loss into the conducting channel due to particle thermal motion in the equilibrium distribution. Relations between parameters such as perveance, emittance, space-charge tune depression, bunch radius, and bunch length are given over a wide range of conditions from short to long bunches and from space-charge dominated to emittance-dominated beams. Comparison is made with previous results of radial density profiles for unbunched beams and line-charge density profiles for bunched beams [Phys. Rev. Lett. 71, 2911 (1993)].
The size and dynamics of magnetic flux structures in magnetohydrodynamic turbulence
Authors: Brandenburg Axel , Procaccia Itamar , Segel Daniel
Published: July 2002

The structures in magnetohydrodynamic (MHD) flow, flux tubes in particular, are investigated with respect to coherence in the direction of the magnetic field. A length scale, which is interpreted as the diameter of the tubes, is derived from the MHD equations. This scale implies that the tendency towards alignment of flux lines in tubes is a diffusion driven phenomenon. The dynamics of the tubes is also investigated; the major conclusion is that stronger tubes are expected to be straighter. These ideas are tested out on data from numerical simulations of turbulent MHD convection. It is also seen that alignment of flux lines increases with the strength of the tube. Possible reasons for this effect are discussed.
Inertial corrections to the matching condition for tearing modes
Authors: Greene J. M. , Miller R. L.
Published: July 2002

In the usual matching condition for resistive tearing modes between an inner resistive layer and an outer ideal region, the inertia of the outer region is ignored; that is, the growth rate Q is set equal to zero in the outer region. However, in the large growth rate limit of these modes, the inertia plays a significant role throughout the inner layer, and up to and through the transition between the inner and outer layers, so that the matching between the inner layer and outer region becomes more subtle. Either inertial effects must be retained in the outer region or they must be modified in the inner layer. Here, the latter course is taken by modifying the density in the inner layer so that it vanishes outside some region confined within the inner layer. This can result in a large difference for the inner region matching data Δ(Q), where Q is the normalized growth rate and Δ(Q)=Δ′ is the dispersion relation. Even the sign of Δ(Q) can be affected. The large growth rate limit is only one regime where inertial corrections are important. Regions of large pressure gradient and/or low magnetic shear are also shown to require inertial corrections. A final conclusion is that the above modifications extend the parameter range in which it is possible to treat finite-n ideal and resistive stability within a single formalism.