bluuebunny/crossref_metadata_2025 huggingface dataset:
Stability of bubbles in a Hele–Shaw cell
Authors: Tanveer S. , Saffman P. G.
Published: July 2002

The linear stability of steadily moving bubbles in a Hele–Shaw cell is investigated. It is shown analytically that without the effect of surface tension, the bubbles are linearly unstable with the stability operator having a continuous spectrum. For small bubbles that are circular, analytical calculations also show that any amount of surface tension stabilizes a bubble. Numerical calculations suggest that the branch of bubble solutions that, in the limit of large area, corresponds to the McLean–Saffman finger is stable for any nonzero surface tension. However, the decay rate of disturbances on the McLean–Saffman branch depends appreciably on the bubble size even for large bubbles. This suggests that the stability results on this branch cannot be immediately extrapolated to the McLean–Saffman fingers. For another branch of bubble solution, which in the limit or large area corresponds to the first of the Romero–Vanden-Broeck finger solutions, numerical evidence suggests that it is unstable to one symmetric and one antisymmetric mode for any surface tension. The symmetric unstable mode tends to break the tip of the bubble and the growth rate of this mode is unaffected by further increase in bubble size, once the bubble is large enough. This suggests that there is an analogous instability for the finger, and this agrees with the numerical findings of Kessler and Levine [Phys. Rev. A 33, 2632 (1986)]. Agreement is noted in the quantitative comparison of the growth rate with the predictions [Tanveer, Phys. Fluids 30, xxxx (1987)] on the limiting growth rate for the symmetric unstable mode for the first Romero–Vanden-Broeck branch of finger solution.
Optimal excitation of perturbations in viscous shear flow
Authors: Farrell Brian F.
Published: July 2002

Evidence, both theoretical and experimental, is accumulating to support a mechanism for transition to turbulence in shear flow based on the 3-D secondary instability of finite 2-D departures from plane parallelism. It is of central importance for using this mechanism to understand how the finite amplitude 2-D disturbances arise. To be sure, it is possible that in many experiments the disturbance is produced by the intervention of a mechanism that directly injects the requisite disturbance energy without calling on the store of kinetic energy inherent in the shear flow. It is shown here that it is also possible to tap the mean shear energy using properly configured perturbations that develop into the required primary disturbance on time scales comparable to those associated with the secondary instabilities even though the shear flow is stable or supports, at most, weak exponential instability.
Exact resonance broadening theory of diffusion in random electric fields
Authors: Salat A.
Published: July 2002

Particle motion in random electric fields is considered on the assumption that orbit stochasticity causes the velocity increments at different times to be independent random events with Gaussian probabilities (Wiener process). The resulting resonance broadening term is substantially different from the one derived by Dupree and others [Phys. Fluids 9, 1773 (1966); 11, 1977 (1968); 15, 1496 (1972); Long Time Prediction in Dynamics (Wiley, New York, 1983), p. 319], and describes the continuous loss of particles from the resonance region. The diffusion coefficient D is time dependent, being quasilinear for t≪td (=diffusion time across resonance region). The validity of D∼(〈E2〉)3/4 in the high-amplitude case of previous theories is questioned.
Generalized parallel heat transport equations in collisional to weakly collisional plasmas
Authors: Zawaideh Emad , Kim N. S. , Najmabadi Farrokh
Published: July 2002

A new set of two-fluid heat transport equations that is valid from collisional to weakly collisional limits is derived. Starting from gyrokinetic equations in flux coordinates, a set of moment equations describing plasma energy transport along the field lines of a space- and time-dependent magnetic field is derived. No restrictions on the anisotropy of the ion distribution function or collisionality are imposed. In the highly collisional limit, these equations reduce to the classical heat conduction equation (e.g., Spitzer and Härm or Braginskii), while in the weakly collisional limit, they describe a saturated heat flux (flux limited). Numerical examples comparing these equations with conventional heat transport equations show that in the limit where the ratio of the mean free path λ to the scale length of the temperature gradient LT approaches zero, there is no significant difference between the solutions of the new and conventional heat transport equations. As λ/LT→1, the conventional heat conduction equation contains a significantly larger error than (λ/LT)2. The error is found to be O(λ/L)2, where L is the smallest of the scale lengths of the gradient in the magnetic field, or the macroscopic plasma parameters (e.g., velocity scale length, temperature scale length, and density scale length). The accuracy of the flux-limited model depends significantly on the value of the flux limit parameter which, in general, is not known. The new set of equations shows that the flux-limited parameter is a function of the magnetic field and plasma parameter profiles.
Deformation and orientation of an elastic slender body sedimenting in a viscous liquid
Authors: Xu Xianghua , Nadim Ali
Published: July 2002

The sedimentation of a flexible slender particle within an otherwise quiescent viscous fluid is considered. The resulting distributed force along the body is shown to cause the deformation of the slender particle. An analytic solution describing this phenomenon is provided for the case of small deformation amplitudes. The effect of particle elasticity on determining its preferred orientation during sedimentation is also examined. One finds that, as a result of its deformation, the particle experiences a torque which tends to orient it toward a horizontal state, in which the long axis is perpendicular to the direction of settling.
Closure theories with non-Gaussian restarts for truncated two-dimensional turbulence
Authors: Frederiksen J. S. , Davies A. G. , Bell R. C.
Published: July 2002

NonMarkovian closure theories, with and without non-Gaussian restarts, are compared with ensemble averaged direct numerical simulations (DNS) for severely truncated two-dimensional Navier–Stokes flows. Both the closures and DNS are formulated for discrete spectra relevant to flows on the doubly periodic domain allowing unambiguous comparisons between the closure and DNS results. We examine the performance of the direct interaction approximation (DIA), self-consistent field theory (SCFT) and local energy-transfer theory (LET) closures and are particularly interested in the reliability of cumulant update versions of these closures (CUDIA, CUSCFT, and CULET). In the latter, the potentially long time-history integrals are periodically truncated and the closures are restarted using a three-point cumulant as the new non-Gaussian initial conditions, thus yielding computationally much more efficient closures. In 80-day integrations, the DIA replicates the DNS results most faithfully in inviscid, viscous decay and forced dissipative experiments. With an update time of T=10 days, the CUDIA is particularly promising performing nearly as well but with some extra oscillations at intermediate times. The SCFT and particularly LET, have spurious oscillations in inviscid and viscous decay experiments; this is also the case, but to a greater degree, for the CUSCFT and CULET closures.
Linear instability of curved free shear layers
Authors: Liou William W.
Published: July 2002

The linear inviscid hydrodynamic stability of slightly curved free mixing layers is studied in this paper. The disturbance equation is solved numerically using a shooting technique. Two mean velocity profiles that represent stably and unstably curved free mixing layers are considered. Results are shown for cases of five curvature Richardson numbers. The stability characteristics of the shear layer are found to vary significantly with the introduction of the curvature effects. The results also indicate that, in a manner similar to the Görtler vortices observed in a boundary layer along a concave wall, instability modes of spatially developing streamwise vortex pairs may appear in centrifugally unstable curved mixing layers.
Translational velocity oscillations of piston generated vortex rings
Authors: Kumar Manoj , Arakeri J. H. , Shankar P. N.
Published: July 2002

Experimental results are presented that show that the translational velocities of piston generated vortex rings often undergo oscillations, similar to those recently discovered for drop generated rings. An attempt has been made to minimize uncertainties by utilizing both dye and hydrogen bubbles for visualization and carefully repeating measurements on the same ring and on different realizations under the same nominal piston conditions. The results unambiguously show that under most conditions, both for laminar and turbulent rings and for rings generated from pipes and orifices, the oscillations are present. The present results, together with the earlier results on drop generated rings, give support to the view that translational velocity oscillations are probably an inherent feature of translating vortex ring fields.
Transition in shear flows. Nonlinear normality versus non-normal linearity
Authors: Waleffe Fabian
Published: July 2002

A critique is presented of recent works promoting the concept of non-normal operators and transient growth as the key to understanding transition to turbulence in shear flows. The focus is in particular on a simple model [Baggett et al., Phys. Fluids 7, 883 (1995)] illustrating that view. It is argued that the question of transition is really a question of existence and basin of attraction of nonlinear self-sustaining solutions that have little contact with the non-normal linear problem. An alternative nonlinear point of view [Hamilton et al., J. Fluid Mech. 287, 317 (1995)] that seeks to isolate a self-sustaining nonlinear process, and the critical Reynolds number below which it ceases to exist, is discussed and illustrated by a simple model. Connections with the Navier–Stokes equations and observations are highlighted throughout.
Rapid distortion theory for compressible homogeneous turbulence under isotropic mean strain
Authors: Blaisdell G. A. , Coleman G. N. , Mansour N. N.
Published: July 2002

Isotropic compressible turbulence subjected to rapid isotropic compression is studied using inviscid rapid distortion theory (RDT) and direct numerical simulation. An exact solution to the rapid distortion problem is given. Comparisons are made between the simulation results and the RDT solution, as well as previously studied limiting cases of the RDT solution. The comparisons illustrate the range of applicability of the RDT solutions. Implications for the use of RDT results in modeling compressible turbulent flows are briefly discussed.
Drag reduction by dc corona discharge along an electrically conductive flat plate for small Reynolds number flow
Authors: El-Khabiry S. , Colver G. M.
Published: July 2002

Corona-induced drag reduction was studied numerically over a finite region of a semi-infinite flat plate having small Ohmic surface conductivity for low Reynolds number flow (<100 000, based on the farthest downstream electrode distance). The model simulates a corona discharge along a surface from two parallel wire electrodes of infinite length immersed flush on the surface and oriented perpendicular to the flow. Charge deposition and removal with the conducting surface are included as possible charge transfer mechanisms. The analysis is limited to ions of positive charge. Five coupled partial differential equations govern the numerical model including continuity, momentum, gas phase conservation of charge, Poisson’s equation of electrostatics, and conservation of charge at the solid interface. The governing equations together with empirical breakdown and current–voltage relationships (Φ–I characteristic) were evaluated by finite differencing schemes. The calculated results predict “corona thinning” of the boundary layer for a downstream ion flow and a corresponding reduction in drag, in agreement with previous theoretical studies. Various parameters of flow, electricity, and geometry, relating to corona-induced drag, are investigated.
Forced oscillations of pendant (sessile) drops
Authors: Wilkes Edward D. , Basaran Osman A.
Published: July 2002

Oscillations of supported liquid drops are the subject of wide scientific interest, with applications in areas as diverse as liquid–liquid extraction, synthesis of ceramic powders, growing of pure crystals in low gravity, and measurement of dynamic surface tension. In this study, axisymmetric forced oscillations of arbitrary amplitude of a viscous liquid drop of fixed volume which is pendant from or sessile on a rod with a fixed contact line and surrounded by an inviscid ambient gas are induced by moving the rod in the vertical direction sinusoidally in time. This nonlinear free boundary problem is solved by a method of lines using Galerkin/finite element analysis for discretization in space and an implicit, adaptive finite difference technique for discretization in time. The variation of the drop response over a wide range of the governing parameters (Reynolds number Re, gravitational Bond number G, volume, and forcing frequency and amplitude) is analyzed. The results show that as the forcing frequency is increased, a sequence of oscillation modes is observed, each with its own resonance frequency ωrn, n=1,2,…, at which drop response amplitude reaches a local maximum. While resonance frequencies depend strongly on drop size and on forcing amplitude, the effect of Reynolds number on ωrn is large when Re is small and diminishes when Re is large, in accord with observations for free oscillations. At high Re, a sharp increase in drop deformation can occur for drops forced to oscillate in the vicinity of their resonance frequencies, indicating the incipience of hysteresis. The maximum observed drop deformations increase with Re, G, and forcing amplitude, while the value of the drop deformation as a function of drop size is determined by a balance between the magnitude of the viscous shear stress imposed on the drop liquid by the solid rod relative to the capillary pressure due to surface tension acting on the fluid interface. The effects of viscous dissipation are also seen in the damping of various oscillation modes and in the creation, evolution in time, and disappearance of zones of fluid recirculation within the drop.
Log laws or power laws: The scaling in the overlap region
Authors: Zagarola M. V. , Perry A. E. , Smits A. J.
Published: July 2002

The scaling in the overlap region of turbulent wall-bounded flows has long been the source of controversy, and until recently this controversy could not be addressed because measurements did not span a sufficient range of Reynolds number. Mean velocity surveys performed in a new pipe flow experiment span a very large range of Reynolds numbers, 31×103 to 35×106 (based on average velocity and diameter). Here, these experimental data are used to evaluate theories on the scaling in the overlap region. At sufficiently high Reynolds numbers, the mean velocity profile in the overlap region is found to be better represented by a log law than a power law. These results suggest a theory of complete similarity instead of incomplete similarity, contradicting the theories recently developed by Barenblatt et al.
Dissipation due to particle/turbulence interaction in a two-phase, turbulent, shear layer
Authors: Kiger K. T. , Lasheras J. C.
Published: July 2002

Experimental measurements of particle velocity, size, concentration and gas velocity have enabled the calculation of additional carrier phase dissipation due to the Stokes disturbance flow generated by small, heavy droplets interacting with the coherent large-scale eddies of a turbulent shear layer. The flow field was generated by mixing a homogeneous, droplet-laden (volume fraction ∼10−5) high-speed air stream with the ambient atmosphere. Ensemble averaged measurements of the large-scale spanwise vortices through the first pairing event show that the additional dissipation is primarily concentrated into intense regions located beneath the core of the vortex and extends into the mixing layer close to the free stagnation point. The magnitude of the dissipation is typically on the order of 10% of the rate at which kinetic energy is transferred between the gas and the particles. A simple model based on the steady-state response of heavy particles to an oscillatory forcing qualitatively illustrate the evolution of the dissipation and kinetic energy transfer within the freestream outside the mixing layer. The comparison also indicates that improved results might be attained by accounting for the unsteady growth of the gas phase velocity fluctuation resulting from the evolution of the coherent structures. Estimates of the single-phase turbulent dissipation indicate that the additional dissipation due to the presence of the particles is approximately 1% of the single-phase dissipation. This is the same order of magnitude as the mass loading and is in agreement with numerical simulation estimates of the increased dissipation in homogeneous turbulent flows.
On the bursting of viscous films
Authors: Brenner Michael P. , Gueyffier Denis
Published: July 2002

In this Brief Communication we consider the shape of the rim of a very viscous film retracting with velocity U0 under surface tension. We demonstrate that the film has a growing rim if and only if the Stokes length ν/U0 is smaller than the radial extent of the film. If the Stokes length is larger than the radial extent of the film the retracting edge has no rim and the film is perfectly flat. These results are discussed in light of recent experiments on the bursting of viscoelastic films.
Experimental study of curvature-driven flute instability in the gas-dynamic trap*
Authors: Ivanov A. A. , Anikeev A. V. , Bagryansky P. A. , Bocharov V. N. , Deichuli P. P. , Karpushov A. N. , Maximov V. V. , Pod’minogin A. A. , Rogozin A. I. , Salikova T. V. , Tsidulko Yu. A.
Published: July 2002

A curvature-driven flute instability will be excited in the magnetized plasmas if the magnetic field lines curve toward the entire plasma boundary. Conditions under which it can be effectively stabilized in axisymmetric geometry have been experimentally studied in a gas-dynamic trap (GDT) at Novosibirsk. Flexible design of the experimental device and the availability of neutral beams and ion cyclotron heating enabled the pressure-weighted curvature to be varied over a wide range. The stability limits were thus measured and compared with those predicted by the modified Rosenbluth–Longmire criterion. Characteristics of unstable curvature-driven flute modes were also measured and found to conform to a theory including finite ion Larmor radius (FLR) effects. Stable operation during neutral beam injection was achieved with a cusp end cell, resulting in an increase in Te to 45 eV, limited by end losses rather than anomalous power losses.
Topological invariants of magnetic fields, and the effect of reconnections
Authors: Ruzmaikin Alexander , Akhmetiev Peter
Published: July 2002

Properties of the second-order topological invariant (the helicity) and the third-order topological invariant for ‘‘the Borromean rings’’ (three linked rings no two of which link each other) are discussed. A fourth-order topological invariant of ideal magnetohydrodynamics is constructed in an integral form. This invariant is determined by the properties of Seifert surfaces bounded by two coupled flux tubes. In particular, for the Whitehead link, it represents the fourth-order Sato–Levine invariant. The effect of reconnections on the topological invariants in the limit of small diffusivity is considered. In this limit the helicity is approximately conserved and the higher-order invariants decay rapidly under the action of diffusivity. The destruction of the higher-order invariants, however, creates helicity fluctuations.
Isotope scaling and ηi mode with impurities in tokamak plasmas
Authors: Dong J. Q. , Horton W. , Dorland W.
Published: July 2002

The ion temperature gradient- (ITG) driven instability, or ηi mode, is studied for discharges with hydrogen, deuterium, or tritium in a toroidal magnetic configuration. Impurity effects on the mode and the instability (impurity mode) driven by the presence of impurity ions with negative density gradient are studied. It is found that the maximum growth rate of the ηi mode scales as M−1/2i for pure hydrogenic plasmas, where Mi is the mass number of the working gas ion. With the inclusion of impurity ions, the growth rate of the ηi mode decreases in all three kinds of plasmas, with a hydrogen plasma still having the highest maximum growth rate, tritium the lowest, and deuterium in between. However, the isotope effects are weaker and scale as M−1/2eff with the presence of impurity ions, where the effective mass number, Meff=(1−fz)Mi+fzMz, with Mz and fz= Zn0z/n0e being the mass number and charge concentration of impurity ions, respectively. For the impurity mode, the scaling is similar to that of the ηi mode without impurity ions. The experimental database shows that the plasma energy confinement time scales as τE∝M1/2i for a wide range of clean plasmas. The correlation of the theoretical results with the experimental confinement scaling is discussed.
Gyrokinetic particle simulation of neoclassical transport
Authors: Lin Z. , Tang W. M. , Lee W. W.
Published: July 2002

A time varying weighting (δf ) scheme for gyrokinetic particle simulation is applied to a steady-state, multispecies simulation of neoclassical transport. Accurate collision operators conserving momentum and energy are developed and implemented. Simulation results using these operators are found to agree very well with neoclassical theory. For example, it is dynamically demonstrated that like-particle collisions produce no particle flux and that the neoclassical fluxes are ambipolar for an ion–electron plasma. An important physics feature of the present scheme is the introduction of toroidal flow to the simulations. Simulation results are in agreement with the existing analytical neoclassical theory. The poloidal electric field associated with toroidal mass flow is found to enhance density gradient-driven electron particle flux and the bootstrap current while reducing temperature gradient-driven flux and current. Finally, neoclassical theory in steep gradient profile relevant to the edge regime is examined by taking into account finite banana width effects. In general, in the present work a valuable new capability for studying important aspects of neoclassical transport inaccessible by conventional analytical calculation processes is demonstrated.
Self-consistent stability analysis of ablation fronts in inertial confinement fusion
Authors: Betti R. , Goncharov V. N. , McCrory R. L. , Sorotokin P. , Verdon C. P.
Published: July 2002

The linear stability analysis of accelerated ablation fronts is carried out self-consistently by retaining the effect of finite thermal conductivity. Its temperature dependence along with the density gradient scale length are adjusted to fit the density profiles obtained in the one-dimensional simulations. The effects of diffusive radiation transport are included through the nonlinear thermal conductivity (κ∼Tν). The growth rate is derived by using a boundary layer analysis for Fr≫1 (Fr is the Froude number) and a WKB approximation for Fr≪1. The self-consistent Atwood number depends on the mode wavelength and the power law index for thermal conduction. The analytic growth rate and cutoff wave number are in good agreement with the numerical solutions for arbitrary ν≳1.
Self-organization process of a magnetohydrodynamic plasma in the presence of thermal conduction
Authors: Zhu Shao-ping , Horiuchi Ritoku , Sato Tetsuya ,   the Complexity Simulation Group
Published: July 2002

A self-organization process of a magnetohydrodynamic (MHD) plasma with a finite thermal conductivity is investigated by means of a three-dimensional MHD simulation. With no thermal conduction a MHD system self-organizes to a non-Taylor state in which the electric current perpendicular to the magnetic field remains comparable to the parallel electric current. In the presence of thermal conductivity, the perpendicular component of electric current and the nonuniformity of thermal pressure generated by driven reconnection tend to be smoothed. Thus, the self-organized state approaches to a force-free minimum energy state under the influence of thermal conduction. Detailed energy conversion processes are also studied to find that the rapid decay of magnetic energy during the self-organization process is caused not only through Ohmic heating, but also through the work done by the j×B force.
Global ideal magnetohydrodynamic stability analysis for the configurational space of Wendelstein 7–X
Authors: Nührenberg Carolin
Published: July 2002

A survey of the magnetohydrodynamic (MHD) stability properties of three-dimensional (3-D) MHD configurations representing the Wendelstein 7–X (W7–X) stellarator experiment [ G. Grieger et al., Plasma Physics and Controlled Nuclear Fusion Research, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 525] was performed with the Code for the Analysis for the Stability of 3-D Equilibria (CAS3D) [C. Schwab, Phys. Fluids B 5, 3195 (1993)] . This study confirms and elaborates previous indications on the structural characteristics of global MHD modes in stellarators. In particular these characteristics pertain to the compressibility of these modes, the equivalence of the decoupled stability problems for the modes with different parities, and the separability of global from fine-scale perturbations within the same mode family. As to the W7–X stellarator experiment, the envisaged configurational class—providing the intended experimental flexibility—appears to offer scenarios of safely stable operation.
Properties of an argon plasma free jet generated from a continuous optical discharge
Authors: Lebéhot A. , Campargue R.
Published: July 2002

The expansion of a supersonic free jet generated from a laser-sustained argon plasma is studied experimentally by using two techniques: (i) the time-of-flight analysis of velocity distributions of the atom beam skimmed from the free jet, leading to the conclusion that the translational relaxation of the heavy particles (neutral atoms and ions) follows very accurately the classical isentropic laws; (ii) the fluorescence technique for studying the internal state relaxation process by local analysis of the radiation emitted spontaneously from the plasma free jet. Only the electronic states excited above 14.5 eV are found to be in a Boltzmann equilibrium, defining a local temperature Texcit in the structure of the free jet. The axial electronic temperature, calculated using a simple one-dimension thermodynamic model, follows fairly well the experimental values of Texcit, while the translational temperature of the heavy particles decreases much lower, in agreement with the asymptotic value deduced from the velocity distributions of the atom beam. Thus appears the uncoupling between the electronic excitation process, governed by the electronic collisions, and the translational cooling of the heavy particles, governed by the collisions between the heavy particles. A more detailed analysis of the excitation process is obtained through the calculation of the state population densities with a collisional-radiative model. The agreement with the experimental measurements is rather good for most of the states investigated.
Wake potential of a dust grain in a plasma with ion flow
Authors: Ishihara Osamu , Vladimirov Sergey V.
Published: July 2002

Debye screening potential and wake potential for a moving dust grain in a collisionless plasma with ion flow is studied. When a relative velocity of the dust grain exceeds the ion acoustic velocity, the oscillatory wake potential is formed in a circular cone behind the particle and produces potential minima in a periodic manner. The ion acoustic collective effects on dust particles contribute to the formation of the periodic structure. The characteristic spacing between the potential minima are several times of Debye wavelength in height and in radius. Such a periodic structure may be relevant to the formation of Coulomb quasilattices (plasma crystals) observed in the dusty plasma laboratory experiments.
Statistical theory of resistive drift-wave turbulence and transport
Authors: Hu Genze , Krommes John A. , Bowman John C.
Published: July 2002

Resistive drift-wave turbulence in a slab geometry is studied by statistical closure methods and direct numerical simulations. The two-field Hasegawa–Wakatani (HW) fluid model, which evolves the electrostatic potential and plasma density self-consistently, is a paradigm for understanding the generic nonlinear behavior of multiple-field plasma turbulence. A gyrokinetic derivation of the HW model is sketched. The recently developed Realizable Markovian Closure (RMC) is applied to the HW model; spectral properties, nonlinear energy transfers, and turbulent transport calculations are discussed. The closure results are also compared to direct numerical simulation results; excellent agreement is found. The transport scaling with the adiabaticity parameter, which measures the strength of the parallel electron resistivity, is analytically derived and understood through weak- and strong-turbulence analyses. No evidence is found to support previous suggestions that coherent structures cause a large depression of saturated transport from its quasilinear value in the hydrodynamic regime of the HW model. Instead, the depression of transport is well explained by the spectral balance equation of the (second-order) statistical closure when account is taken of incoherent noise.
The relation of edge confinement to global confinement in ASDEX Upgrade (Axially Symmetric Divertor Experiment)
Authors: Pitcher C. S. , Boozer A. H. , Murmann H. , Schweinzer J. , Suttrop W. , Salzmann H. ,   ASDEX Upgrade Team,   NBI Group
Published: July 2002

Experimental evidence is presented from the ASDEX Upgrade (Axially Symmetric Divertor Experiment) tokamak [Plasma Physics and Controlled Nuclear Fusion Research 1993 (International Atomic Energy Agency, Vienna, 1994), Vol. I, p. 127] of a robust relation between the edge radial pressure gradient and the global confinement of the plasma. This relation transcends the power flowing across flux surfaces near the edge and thus suggests that the usual model of cross-field heat transport, where local gradients increase with increasing local power flow, is not appropriate.
Observation of magnetohydrodynamic stability limit in a cusp-anchored gas-dynamic trap
Authors: Anikeev A. V. , Bagryansky P. A. , Deichuli P. P. , Ivanov A. A. , Karpushov A. N. , Maximov V. V. , Pod’minogin A. A. , Stupishin N. V. , Tsidulko Yu. A.
Published: July 2002

In this paper, the observation of magnetohydrodynamic (MHD) stability limit in a fully axisymmetric gas-dynamic trap is reported. Transition through the stability boundary was studied by varying the plasma pressure in the stabilizing cusp end cell and simultaneously measuring the particle and energy lifetimes in the central cell. Energy and particle balance of the neutral beam heated plasma was measured and compared in unstable and stable regimes of operation. It was observed that if the calculations based on the energy principle predicted the plasma to be stable, experimentally measured transverse losses appeared to be smaller than the longitudinal ones. In the opposite case, the transverse losses were dominant thus indicating transition through the MHD stability boundary in the cusp-anchored gas-dynamic trap.
Formation of wave-front pattern accompanied by current-driven electrostatic ion-cyclotron instabilities
Authors: Ishiguro Seiji , Sato Tetsuya , Takamaru Hisanori , Watanabe Kunihiko ,   Complexity Simulation Group
Published: July 2002

Formation of a wave-front pattern accompanied by an electrostatic ion-cyclotron instability driven by electrons drifting along a magnetic field is investigated by two-and-half dimensional particle simulations. A clear spatial wave-front pattern appears as the ion cyclotron wave grows due to the instability. When the electron stream is uniform in the system, an obliquely intersected stripe wave-front pattern is formed. When the stream has a bell-shaped pattern across the magnetic field, a V-shaped stripe wave-front pattern appears. The wave fronts have small angles with the magnetic field lines and propagate from the high-stream region to the low-stream region.
High-performance discharges in the Small Tight Aspect Ratio Tokamak (START)
Authors: Gates D. A. , Akers R. , Appel L. , Carolan P. G. , Conway N. , Dowling J. , Gryaznevich M. , Hender T. , Kwon O. J. , Martin R. , Nightingale M. , Price M. , Roach C. , Sykes A. , Tournianski M. R. , Walsh M. , Warrick C. D. ,   START team,   NBI team
Published: July 2002

The Small Tight Aspect Ratio Tokamak (START) [A. Sykes et al., Nucl. Fusion 32, 769 (1994)] spherical tokamak has recently achieved the record value of toroidal β∼30% in a tokamak-like configuration. The improvements that have made these results possible are presented along with a description of the global equilibrium parameters of the discharges. The ideal magnetohydrodynamic (MHD) stability of these discharges is analyzed, and they are found to be in close proximity to both the ballooning limit and the external current driven kink limit, but they are found to be far from the pressure driven external kink limit. Disruptivity for a range of shots is not correlated with the normalized β limit, but does correlate well with the empirical high-li disruption limit. The transport properties of these high-β equilibria are analyzed and compared to conventional tokamak scaling laws and transport models. The global transport is at least as good as that predicted by the ITER97-ELMy (edge-localized) scaling law. The local ion transport is in good agreement with that predicted by neoclassical models. The electron transport is anomalous, showing rough agreement with the Lackner–Gottardi transport model.
Precise control of the global rotation of strongly coupled ion plasmas in a Penning trap
Authors: Huang X.-P. , Bollinger J. J. , Mitchell T. B. , Itano W. M. , Dubin D. H. E.
Published: July 2002

Rotating asymmetric electric fields have been applied to control the rotation frequency (and hence the density) of non-neutral plasmas, which are confined in Penning-type traps and have relaxed close to thermal equilibrium characterized by a global rigid-body rotation. “Infinite” confinement times and density compression were first reported for uncorrelated plasmas of ∼108 Mg+ ions with temperatures ranging from 1 K to 5×104 K (4 eV) [Huang et al., Phys. Rev. Lett. 78, 875 (1997)]. In this paper, the rotating field technique has been applied to control strongly coupled plasmas of ∼105 Be+9 ions which are laser-cooled to millikelvin temperatures so that the plasma freezes into a solid with a crystalline lattice. Here, Bragg diffraction peaks from crystals provide an accurate way of measuring the rotation frequency, and it is observed that the plasma rotation can be phase locked to the applied rotating field without any slip. In essence, these corotating plasmas have reached thermal equilibrium with the rotating field, and the azimuthally asymmetric boundaries of the equilibrium states have been measured experimentally. Both rotating dipole and quadrupole fields have been used to provide this precise control of the plasma rotation. However, the effectiveness of the dipole field depends on the presence of multiple ion species. With the rotating dipole field, density compression to near the Brillouin limit and increase of the rotation frequency to near the cyclotron frequency have been achieved.
Deuterium–tritium plasmas in the Joint European Torus (JET): Behavior and implications
Authors: Gibson A. ,   JET Team
Published: July 2002

This paper reports the first deuterium–tritium (D-T) fusion experiments in the geometry of the International Thermonuclear Experimental Reactor (ITER) [R. Aymar, V. Chuyanov, M. Huguet, R. Parker, Y. Shimamura, and the ITER Joint Central Team and Home Teams, Proceedings of the 16th International Conference on Fusion Energy (International Atomic Energy Agency, Vienna), Fusion Energy 1, 3 (1996)], with long pulse length and an ITER-like divertor. Physics aspects, such as the isotope dependence of confinement, the H-mode (high confinement) threshold, shear optimisation, heating methods, high fusion performance and alpha particle heating, are discussed together with their implications. The technology aspects of tritium wall loading and clean-up, the close coupled tritium plant and the future remote handling divertor target exchange are also mentioned.
Periodic equilibria of the Vlasov–Maxwell system
Authors: Attico N. , Pegoraro F.
Published: July 2002

A general method is presented for deriving one-dimensional equilibrium solutions of the Vlasov-Maxwell system that extend the well-known Harris solution. In particular, spatially periodic solutions are constructed. These are needed in kinetic simulations of collisionless nonlinear reconnection processes when periodic boundary conditions are used.
Distributions of alpha particles escaping to the wall during sawtooth oscillations in the Tokamak Fusion Test Reactor
Authors: Kolesnichenko Ya. I. , Lutsenko V. V. , White R. B. , Yakovenko Yu. V. , Zweben S. J.
Published: July 2002

It has been observed experimentally in deuterium–tritium shots of the Tokamak Fusion Test Reactor (TFTR) [D. J. Grove and D. M. Meade, Nucl. Fusion 25, 1167 (1985)] that crashes of sawtooth oscillations may result in very inhomogeneous flux of alpha particles to the wall. To explain this phenomenon, both theoretical analysis and numerical simulation have been carried out. It is concluded that the “crash-induced prompt loss,” i.e., the orbital loss of marginally trapped particles arising because of the crash-induced orbit transformation of circulating particles, is responsible for the flux near the bottom of the vessel, whereas the crash-induced stochastic diffusion of moderately trapped particles explains the large signal near the equatorial plane of the torus. The calculated poloidal distributions of the integral alpha flux are in reasonable agreement with experimental data. The energy spectrum of the escaping particles has also been calculated, which can be used for diagnostics of the crash type.
The role of particle sinks and sources in Alcator C-Mod detached divertor discharges
Authors: Lipschultz B. , Terry J. L. , Boswell C. , Goetz J. A. , Hubbard A. E. , Krasheninnikov S. I. , LaBombard B. , Pappas D. A. , Pitcher C. S. , Wising F. , Wukitch S.
Published: July 2002

Detailed measurements of the magnitude and location of volumetric recombination occurring in the detached divertor of Alcator C-Mod tokamak [I. H. Hutchinson et al., Phys. Plasmas 1, 1511 (1994)] are presented. The drop in divertor plate ion current during detachment is due to two mechanisms: (1) volumetric recombination in the divertor plasma; and (2) reductions in the divertor ion source. Depending on plasma conditions, each of these can be the primary mechanism for the observed ion current reduction in detachment. The ion source during detachment is inferred and its magnitude is consistent with the measured divertor power flow. A scaling of the density in the divertor recombining region for L- (low confinement) mode plasmas is found, ne,r∝n̄e0.8⋅PSOL2/7. A model based on pressure variation along a flux surface during detachment is consistent with the main features of this scaling.
Recent progress in high performance and steady-state experiments on the Japan Atomic Energy Research Institute Tokamak-60 Upgrade with W-shaped divertor
Authors: Kusama Y. ,   the JT-60 Team
Published: July 2002

In the Japan Atomic Energy Research Institute (JAERI) Tokamak-60 Upgrade [H. Shirai and the JT-60 Team, Phys. Plasmas 5, 1712 (1998)], high performance and steady-state experiments have been conducted in the W-shaped divertor. The equivalent deuterium-tritium (D-T) fusion multiplication factor, QDTeq, was enhanced transiently up to 1.25 in the reversed shear plasma. The reduction in particle diffusivity in the internal transport barriers (ITB) region of the reversed shear plasma was confirmed as well as the thermal diffusivity. It was also confirmed that the correlation length of density fluctuations is reduced inside the ITB of density. The performance with a confinement-enhancement factor (H-factor, H89) of 2.2 and QDTeq of 0.16 was sustained in a quasi-steady-state in the high-poloidal-beta (βp) and high confinement mode (H-mode) regime. The reversed shear configuration with ITBs was sustained by injecting the lower-hybrid waves combined with neutral beam injection and fully noninductive current drive in the reversed shear plasmas was realized for the first time. The driven current by the negative-ion-based neutral beam (NNB) injection increased up to 0.6 MA. The H-mode transition was triggered with the NNB injection and the H-mode with H89∼1.6–1.8 was sustained. The toroidicity-induced Alfvén eigenmode was excited for a volume-averaged fast ion beta, 〈βh〉, as low as ∼0.1%.
“Profile consistency” features in strongly shaped Ohmic tokamak plasmas
Authors: Weisen H. , Behn R. , Furno I. , Moret J.-M. , Sauter O. ,   the TCV team
Published: July 2002

A large variety of shaped tokamak discharges have been created in the Tokamak à Configuration Variable (TCV) with main parameters BT<1.5 T, R0=0.88 m, a<0.25 m, Ip⩽1 MA [F. Hofmann, J. B. Lister, M. Anton et al., Plasma Phys. Controlled Fusion 36, B277 (1994)]. They include limited and diverted discharges with elongations up to 2.58 and triangularities between −0.7 and 1. Over the entire range of quasi-stationary sawtoothing Ohmic discharges investigated it is observed that the widths of plasma pressure profiles, 〈p〉/p(0) and the inversion radii scale as the widths of the current profiles, 〈j〉/j(0), where 〈 〉 refers to an average over the volume or, practically equivalently, the cross-sectional plasma area. These “profile consistency” features are in apparent agreement with theoretical considerations and can be viewed as an extension of previous studies in circular discharges. The observations identify the parameter 〈j〉/q0j(0) as the appropriate replacement for qa as a scaling parameter for arbitrary cross-sectional shapes. Using a simple current profile model with 0.8⩽q0⩽1 for the axial safety factor, it is shown that, for sawtoothing Ohmic discharges, such observations can be accounted for by the effects of sawtooth activity.
Neoclassical simulations of fusion alpha particles in pellet charge exchange experiments on the Tokamak Fusion Test Reactor
Authors: Redi M. H. , Batha S. H. , Budny R. V. , Darrow D. S. , Levinton F. M. , McCune D. C. , Medley S. S. , Petrov M. P. , von Goeler S. , White R. B. , Zarnstorff M. C. , Zweben S. J. ,   TFTR Team
Published: July 2002

Neoclassical simulations of alpha particle density profiles in high fusion power plasmas on the Tokamak Fusion Test Reactor [Phys. Plasmas 5, 1577 (1998)] are found to be in good agreement with measurements of the alpha distribution function made with a sensitive active neutral particle diagnostic. The calculations are carried out in Hamiltonian magnetic coordinates with a fast, particle-following Monte Carlo code which includes the neoclassical transport processes, a recent first-principles model for stochastic ripple loss and collisional effects. New calculations show that monotonic shear alpha particles are virtually unaffected by toroidal field ripple. The calculations show that in reversed shear the confinement domain is not empty for trapped alphas at birth and allow an estimate of the actual alpha particle densities measured with the pellet charge exchange diagnostic.
Bäcklund transformations, a simple transformation and exact solutions for dust-acoustic solitary waves in dusty plasma consisting of cold dust particles and two-temperature isothermal ions
Authors: Khater A. H. , Abdallah A. A. , El-Kalaawy O. H. , Callebaut D. K.
Published: July 2002

Dusty plasma with inertial dust fluid and two-temperature ions admits both compressive and rarefactive solitary waves. The Korteweg-de Vries equations (KdV-type equations) with cubic nonlinearity at the critical density of low-temperature isothermal ions are considered to discuss properties of dust-acoustic solitary waves. In the vicinity of the critical density of low-temperature ions, a KdV-type equation with mixed nonlinearity is discussed. The method of characteristics is used and the Bäcklund transformations (BTs) are employed to generate new solutions from the old ones. Another new solution of the KdV–mKdV equation is obtained using a simple transformation between the sine-Gordon equation and a linear equation combined with an extension of the tanh method of Malfliet.
Transitionless enhanced confinement and the role of radial electric field shear
Authors: Ernst D. R. , Bell R. E. , Bell M. G. , Budny R. V. , Coppi B. , Hammett G. W. , Hawryluk R. J. , Hill K. W. , Mansfield D. K. , Mikkelsen D. R. , Park H. K. , Porkolab M. , Scott S. D. , Schmidt G. L. , Synakowski E. J. , Zarnstorff M. C. ,   TFTR Group
Published: July 2002

Evidence is presented for the role of radial electric field shear in enhanced confinement regimes attained without sharp bifurcations or transitions. Temperature scans at constant density, created in the reheat phase following deuterium pellet injection into supershot plasmas in the Tokamak Fusion Test Reactor [J. D. Strachan, et al., Phys. Rev. Lett. 58, 1004 (1987)] are simulated using a physics-based transport model. The slow reheat of the ion temperature profile, during which the temperature nearly doubles, is not explained by relatively comprehensive models of transport due to Ion Temperature Gradient Driven Turbulence (ITGDT), which depends primarily on the (unchanging) electron density gradient. An extended model, including the suppression of toroidal ITGDT by self-consistent radial electric field shear, does reproduce the reheat phase. The extended reheat at constant density is observed in supershot but not L-Mode plasmas.
Magnetohydrodynamics stability of compact stellarators
Authors: Fu G. Y. , Ku L. P. , Cooper W. A. , Hirshman S. H. , Monticello D. A. , Redi M. H. , Reiman A. , Sanchez R. , Spong D. A.
Published: July 2002

Recent stability results of external kink modes and vertical modes in compact stellarators are presented. The vertical mode is found to be stabilized by externally generated poloidal flux. A simple stability criterion is derived in the limit of large aspect ratio and constant current density. For a wall at infinite distance from the plasma, the amount of external flux needed for stabilization is given by Fi=(κ2−κ)/(κ2+1), where κ is the axisymmetric elongation and Fi is the fraction of the external rotational transform. A systematic parameter study shows that the external kink mode in a quasiaxisymmetric stellarator (QAS) can be stabilized at high beta (∼5%) without a conducting wall by magnetic shear via three-dimensional (3D) shaping. It is found that external kinks are driven by both parallel current and pressure gradient. The pressure contributes significantly to the overall drive through the curvature term and the Pfirsch–Schluter current.