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Notes: It is known that streaming can be generated in a liquid bridge by vibrating an end wall. This phenomenon has been used in an attempt to minimize thermocapillary flow during crystal growth in a floating zone, by inducing such a streaming running in the opposite direction to it [Grugel et al., J. Cryst. Growth 142, 209 (1994)]. In the present theoretical study, the nature of this streaming and its effects on the average flow and temperature fields in a floating zone are investigated. It is noticed that in the experiment, the applied frequencies were high enough such that the corresponding wavelengths of the capillary ripples were much smaller than the dimensions of the zone. It is believed that the ripples were a traveling wave that generated the streaming in the direction of the wave propagation as a result of Stokes drift. For such a wave to be traveling, it must be dissipated sufficiently by viscosity upon reaching the other wall to guarantee negligible reflection there. Accordingly, a model is formulated to study the reduction of thermocapillary flow in a floating zone by means of streaming. It is found that for a half zone, streaming can minimize the thermocapillary flow near the vibrating wall and make the temperature uniform across the zone there. For a full zone, streaming can minimize the flow but cannot make the temperature uniform near the wall. For a long full zone, streaming can similarly minimize the flow. But in addition, the temperature near each wall is uniform with or without streaming. © 1998 American Institute of Physics.

Notes: The problem of the rotatory oscillation of an axi-symmetric body in an axi-symmetric, viscous, incompressible flow at low Reynolds number has been studied. In contrast to the steady rotation of a body, which involves solving the Laplace equation, the study of an oscillating body requires solution of the Helmholtz equation which results from the simplification of the unsteady Stokes equations. In the present work, we have numerically evaluated the local stresses and torques on a selection of free, oscillating, axi-symmetric bodies in the continuum regime in an axi-symmetric viscous incompressible flow. The Helmholtz equation was solved by a Green's function technique. The accuracy of the technique is tested against known solutions for a sphere, a prolate spheroid, a thin disk, and an infinitely long cylinder. Good agreements have been obtained. Finite cylinders have been studied and the edge correction factors for the circular disk geometry, that are basic to oscillating disk viscometers, have been calculated. It has been found that the calculated edge correction factors, based on the ratios of the real parts of the actual torques (calculated from this work) to the ideal torques, agree to within 1% to 10% with the reported values obtained by Clark et al. [Physica A 89, 539 (1977)] using the theory of Kestin and Wang [J. Appl. Mech. 24, 197 (1957)]. However, since the ratios of the real parts and the ratios of the imaginary parts of the torques do not coincide, the edge correction factors depend upon which ratio is used. © 1998 American Institute of Physics.

Notes: The advection of a passive scalar field by a rapidly decorrelating random velocity field with power-law scaling is computed by simulations in a cyclic square at resolutions of 40962 and 81922 grid points. Structure functions of the scalar field are measured and inertial-range scaling exponents are determined. The conditional mean of the scalar-field dissipation term and its moments are found. The results are compared with theoretical predictions and with other recent simulations. © 1998 American Institute of Physics.

Notes: Direct numerical simulations at 2563 resolution have been carried out to study the response of isotropic turbulence to the concurrent effects of solid-body rotation and stochastic, isotropic forcing at the large scales. Because spectral transfer to the smaller scales is weakened by rotation, energy input from forcing gradually builds up at the large scales, causing the overall kinetic energy to increase. At intermediate wave numbers the energy spectrum undergoes a transition from a limited k−5/3 inertial range to k−2 scaling recently predicted in the literature. Although the Reynolds stress tensor remains approximately isotropic and three-component, evidence for anisotropy and quasi-two-dimensionality in length scales and spectra in different velocity components and directions is strong. The small scales are found to deviate from local isotropy, primarily as a result of anisotropic transfer from the large scales. To understand the spectral dynamics of this flow, we study the detailed behavior of nonlinear triadic interactions in wave number space. Spectral transfer in the velocity component parallel to the axis of rotation is qualitatively similar to that in nonrotating turbulence; however, the perpendicular component is characterized by a much weakened energy cascade at high wave numbers and a local reverse transfer at the largest scales. The broader implications of this work are briefly addressed. © 1998 American Institute of Physics.

Notes: This work numerically investigates laminar plane twin-jet flows with side-wall confinement. Time-dependent computations on the full physical domain are performed in light of the possible emergence of flow unsteadiness and an asymmetric pattern. Of particular concern is how wall-confinement and jet momentum influence the transition of flow patterns. Results presented herein provide further insight into the complexities involving issues such as the variety of flow structure and the related bifurcations, jet–jet and jet–wall interactions, and flow instability involved in the confined twin-jet flow field. © 1998 American Institute of Physics.

Notes: In the present study we use two- and three-dimensional large-eddy simulations to examine the role of small-scale turbulence within a transitional separation bubble studied experimentally by Gaster (AGARD Conference Proceedings No. 4, 1966, pp. 813–854). In addition, several large-eddy simulation parameters and models are studied to show their effect on the computations. The inclusion of a small-scale turbulence model in the two-dimensional computations leads to an increase in the time-averaged separation bubble length and a slight reduction in the peak of the pressure coefficient distribution near reattachment. Increasing the filter width or increasing the Smagorinsky coefficient reduces the peak in the pressure coefficient distribution but also decreases the pressure coefficient within the pressure plateau. The two-dimensional LES accurately predicts the time-averaged bubble length of Gaster but does not accurately describe the experimental wall pressure distribution within the bubble. Three-dimensional LES computations allow the generation of vortex shedding and Görtler vortices within the separated region. A computation without a subgrid scale model allows the Görtler vortices to grow in strength and eliminate the boundary layer separation. The application of a subgrid scale model reduces the strength of Görtler vortices and spanwise vortex shedding. This produces a bubble size and time-averaged wall pressure distribution which compare favorably with experiment. Little difference is seen between the results using the constant coefficient and dynamic coefficient models. © 1998 American Institute of Physics.

Notes: Numerical modeling of the nonreactive mixing processes associated with a lobed fuel injector in a coflowing air stream is presented. The lobed fuel injector is a device which generates strong streamwise vorticity, producing locally high strain rates which can enhance the molecular mixing of reactants while delaying ignition in a controlled manner. Vortex element modeling is used to simulate flow field evolution and fuel element mixing characteristics for this lobed fuel injector. Quantitative predictions for vorticity generation and qualitative results for streamwise rollup compare well qualitatively with recent experimental investigations of this flow field [Smith et al., Phys. Fluids 9, 667 (1997)]. Parametric studies of the effects of lobe amplitude-to-wavelength ratio, lobe angle, and lobe shape for given flow conditions suggest that geometrical features may be optimized to enhance mixing and control reaction processes. © 1998 American Institute of Physics.

Notes: Direct Monte Carlo simulation is used to investigate the stability of a dilute freely evolving granular gas of hard disks. The boundary between stability and instability in the plane (α,L), where α is the restitution coefficient and L the size of the system, has been delineated. Instability is associated with the buildup of spatial correlations, which describes the formation of velocity vortices in the system. The simulation results are compared with theoretical predictions presented recently, and a good agreement is found. © 1998 American Institute of Physics.

Notes: We address direct simulation Monte Carlo (DSMC) implementation of phenomenological models of the rotational relaxation process suitable for an arbitrary gas mixture composed of atomic and quantized diatomic species. The macroscopic relaxation process is parametrized by a constant or temperature-dependent collision number Zr such as that of Parker [Phys. Fluids 2, 449 (1959)]. The energy redistribution properties predicted by such a model at the collision level are compared with a recent quasiclassical state-to-state model. Modified forms of the constant collision number, and thus constant relaxation probability, serial quantized Borgnakke–Larsen algorithm [Phys. Fluids A 5, 2278 (1993)] and the null collision SICS-D algorithm [Phys. Fluids A 4, 1782 (1992)] are shown to be equivalent. The generalization to an energy-dependent relaxation probability [Phys. Fluids 6, 4042 (1994)] leads to a systematic bias toward delayed relaxation, due to approximations inherent in the analytical formulation. The error induced in the predicted relaxation behavior as a function of temperature is approximately equivalent in magnitude to a previously proposed, but unrelated, correction factor [Phys. Fluids 6, 2191 (1994)], and also to the variation in the temperature-dependent Parker collision number over a wide range of conditions. Comparisons between DSMC and state-to-state calculations of the rotational distribution function in a relaxing bath quantify the microscopic limitations of the phenomenological model. Finally, a direct comparison of DSMC results with experimental shock layer measurements demonstrates that the energy-dependent relaxation model has a negligible advantage over the constant probability model when the collision number is chosen judiciously. © 1998 American Institute of Physics.

Notes: The convective flow field in a vessel is investigated by laser Doppler Anemometry (LDA) and Particle Image Velocimetry (PIV, namely Particle Tracking Velocimetry—PTV). The vessel is heated from below along a linear element at a temperature higher than that of the fluid. Hot fluid raises up and generates two counterrotating vortices. For a given aspect ratio, the two vortices become unstable and start to oscillate on a vertical plane (orthogonal to the heating element). This regime is investigated for increasing Rayleigh numbers to analyze the transition from regular to irregular conditions. The main transition mechanism is observed to be mostly connected to type II intermittency, a mechanism not frequently observed in experiments. However, at some Rayleigh numbers the present data does not definitely rule out type III intermittency. The phenomenon is analyzed by looking at the main frequencies in the spectrum of the horizontal velocity component and their changes with the Rayleigh number at a point above the heating element. Modifications in the local energy spectrum are analyzed by using the Wavelet Transform (WT) tool. Data obtained by PTV measurements make it possible to point out the spatial configuration of the flow and to determine the two velocity components on the measurement plane. These data are used to clarify the fundamental mechanisms of the transition. Instabilities are observed as sudden changes between two regimes of oscillations of the two counterrotating vortices: the first is characterized by oscillations centered on the vertical axis and the second by nonsymmetrical oscillations. © 1998 American Institute of Physics.

Notes: Forced advection of passive scalar by a smooth d-dimensional incompressible velocity in the presence of linear damping is studied. Acting separately advection and damping do not lead to an essential intermittency of the steady scalar statistics, while being mixed together produce a very strong non-Gaussianity in the convective range: 2n-th moment of scalar difference, 〈[θ(t;r)−θ(t;0)]2n〉 is proportional to rξ2n, ξ2n=min{2n,d2/4+2αdn/[(d−1)D]−d/2}, where α/D measures the rate of the damping in the units of the stretching rate. The probability density function (PDF) of the scalar difference is also found. © 1998 American Institute of Physics.

Notes: This Brief Communication presents a simple second-order differential equation extracted from experimental data, which can mimic the velocity fluctuations that are typical of bursting. The starting time series concerns the longitudinal component of turbulent velocity measured near the wall in a hydraulically smooth pipe flow. By means of standard conditional sampling techniques, we found the typical behavior of velocity fluctuations during the bursting events, to which we then applied the trajectory method in order to extract the equation of motion. The resulting equation, containing quadratic and cubic nonlinearities, follows the original time series very well, and may represent a useful starting point for the construction of more complex models of this phenomenon.© 1998 American Institute of Physics.

Notes: An analytical model for predicting the universal time scale for formation of vortex rings generated through impulsively started jets is considered. The model is based on two assumptions, namely the validity of the slug model in simulating the discharge process of the fluid out of the cylinder and the approximation of the vortex at the pinch off moment by a vortex in the Norbury family. The nondimensional stroke length L/D (referred to as "formation number," following Gharib et al. [J. Fluid Mech. 360, 121 (1998)]) predicted by the model satisfactorily matches the experimental observation of Gharib et al. The model introduces two nondimensional parameters that govern the limiting formation number: nondimensional energy End and circulation Γnd. The predicted value of End matches very well with the experimental data. It is also predicted that there is a limiting value for the nondimensional circulation in the range 1.77(approximately-less-than)Γnd(approximately-less-than)2.07. © 1998 American Institute of Physics.

Notes: Experiments on flow stability and pattern formation in Couette flow between two cylinders with highly elastic polymer solutions are reported. It is found that the flow instabilities are determined by the elastic Deborah number, De, and the polymer concentration only, while the Reynolds number becomes completely irrelevant. A mechanism of such "purely elastic" instability was suggested a few years ago by Larson, Shaqfeh, and Muller [J. Fluid Mech. 218, 573 (1990)], referred to as LMS. It is based on the Oldroyd-B rheological model and implies a certain functional relation between De at the instability threshold and the polymer contribution to the solution viscosity, ηp/η, that depends on the polymer concentration. The elastic force driving the instability arises when perturbative elongational flow in radial direction is coupled to the strong primary azimuthal shear. This force is provided by the "hoop stress" that develops due to stretching of the polymer molecules along the curved streamlines. It is found experimentally that the elastic instability leads to a strongly nonlinear flow transition. Therefore, the linear consideration by LMS is expanded to include finite amplitude velocity perturbations. It is shown that the nature of the elastic force implies major asymmetry between inflow and outflow in finite amplitude secondary flows. This special feature is indeed exhibited by the experimentally observed flow patterns. For one of the flow patterns it is also shown that the suggested elastic force should be quite efficient in driving it, which is important evidence for the validity of the mechanism proposed by LMS. Further, the predicted relation between De and ηp/η is tested. At fixed ηp/η the elastic instability is found to occur at constant Deborah number in a broad range of the solution relaxation times in full agreement with the theoretical prediction. The experimentally found dependence of the Deborah number on ηp/η also agrees with the theoretical prediction rather well if a proper correction for the shear thinning is made. This provides further support to the proposed instability mechanism. © 1998 American Institute of Physics.

Notes: In this paper numerical simulations of the irrotational fluid flow associated with the entry of circular disks of a given mass into a semi-infinite fluid domain in the limits of very low to moderate Froude numbers are reported. This work is motivated by an experimental study performed by Glasheen and McMahon who investigated the low-Froude-number water entry of circular disks and found a linear relationship between the cavity seal depth and the Froude number and also showed that a single value of a modified drag coefficient is sufficient to predict the drag force on the disk. The numerical calculations performed in this paper confirm these experimental findings for steady cavity regimes and identify the ranges of Froude number and dimensionless mass values for which these results hold. Excellent agreement between the numerical computations and analytical velocity predictions, as well as the experimental cavity seal depth measurements, are obtained although the agreement between the measured and the computed drag coefficient values is not as good. The cavity seal depth and the drag coefficient are also found to depend on the disk mass and the numerical results in this paper show that for any disk of dimensionless mass M there exists a value of the Froude number for which the cavity dynamics are steady. Also, a very low-Froude-number regime in which gravitational forces are dominant and for which the cavity dynamics are qualitatively different than for low-to-moderate-Froude-number cases is also numerically explored in this paper. Finally, a bifurcation in the cavity seal mechanism from deep seal to surface seal was found at a Froude number F=105. © 1998 American Institute of Physics.

Notes: The stability of an axisymmetric liquid bridge between unequal circular disks in an axial gravity field is examined for all possible values of the liquid volume and disk separation. The parameter defining the disk inequality is K, the ratio between the radii of the smaller and larger disks. Both axisymmetric and nonaxisymmetric perturbations are considered. The parameter space chosen to delimit the stability regions is the Λ-V plane. Here, Λ is the slenderness (ratio of the disk separation to the mean diameter, 2r0, of the two support disks), and V is the relative volume (ratio of the actual liquid volume to the volume of a cylinder with a radius equal to r0). Wide ranges of the Bond number and the ratio K are considered. Emphasis is given to previously unexplored parts of the stability boundaries. In particular, we examine the maximum volume stability limit for bridges of arbitrary Λ and the minimum volume stability limit for small Λ bridges. The maximum volume stability limit was found to have two distinct properties: large values of the critical relative volume at small Λ, and the possibility that stability is lost to axisymmetric perturbations at small values of K. For a set of K, the maximum Bond number beyond which stability of the bridge is no longer possible for any combination of V and Λ is determined. In addition, the maximum value of the actual liquid volume of a stable bridge that can be held between given disks for all possible disk separations was examined for fixed Bond number. It is found that this volume decreases as K decreases and (depending on the sign of the Bond number) tends to the critical volume of a sessile or pendant drop attached to the larger disk. © 1998 American Institute of Physics.

Notes: This paper presents a method for calculating the external inductance and mutual inductance coefficients of tokamak plasma configurations in a consistent way. The method actually solves the external equilibrium problem, linking the poloidal equilibrium fields with the value of the total plasma current and the geometric parameters that describe the plasma cross section. This link imposes constraints upon the values of the inductance for superconducting tori obtained by a previous method described by S. P. Hirshman and G. H. Neilson [Phys. Fluids 29, 790 (1986)]. Only if these constraints are properly taken into account do their results correspond to real tokamak equilibrium configurations. The present method is illustrated by calculating the external equilibrium parameters for a wide range of values of the tokamak aspect ratio. Of particular interest are the results for the external inductance, the elongation, and the vertical equilibrium field in the low aspect-ratio range A〈1.5. © 1998 American Institute of Physics.

Notes: Alfvén resonances, where the local flow speed relative to the boundary is equal to the local Alfvén speed, introduce novel dynamical features in a differentially rotating plasma. The spatial structure and dynamics of current sheets in such plasmas is investigated analytically as well as numerically. The current sheets at Alfvén resonances tend to power-law singularities. The growth of current sheets is algebraic in time in the linear regime and saturates in the presence of dissipation without the intervention of nonlinear effects. These results have significant implications for forced reconnection and Alfvén wave dissipation in laboratory and space plasmas. © 1998 American Institute of Physics.

Notes: In this paper a time evolution equation for internal kink oscillations is derived. It is valid for both stable and unstable plasma regimes, and incorporates the response of an energetic particle population. A linear analysis reveals a parallel between (i) the time evolution of the spatial derivative of the internal kink radial displacement and (ii) the time evolution of the perturbed particle distribution function in the field of an electrostatic wave (Landau problem). It is shown that diamagnetic drift effects make the asymptotic decay of internal kink perturbations in a stable plasma algebraic rather than exponential. However, under certain conditions the stable root of the dispersion relation can dominate the response of the on-axis displacement for a significant period of time. The form of the evolution equation naturally allows one to include a nonlinear, fully toroidal treatment of energetic particles into the theory of internal kink oscillations. © 1998 American Institute of Physics.

Notes: A formalism is developed for optimizing the design of feedback coils placed around a tokamak plasma in order to control the resistive shell mode. It is found that feedback schemes for controlling the resistive shell mode fail whenever the distortion of the mode structure by the currents circulating in the feedback coils becomes too strong, in which case the mode escapes through the gaps between the coils, or through the centers of the coils. The main aim of the optimization process is to reduce this distortion by minimizing the coupling of different Fourier harmonics due to the feedback currents. It is possible to define a quantity α0 which parametrizes the strength of the coupling. Feedback fails for α0≥1. The optimization procedure consists of minimizing α0 subject to practical constraints. If there are very many evenly spaced feedback coils surrounding the plasma in the poloidal direction then the optimization can be performed analytically. Otherwise, the optimization must be performed numerically. The optimal configuration is to have many, large, overlapping coils in the poloidal direction. © 1998 American Institute of Physics.

Notes: The dynamics of relativistic runaway electrons in tokamak plasmas is analyzed using a test particle description that includes acceleration in the toroidal electric field, collisions with the plasma particles, and deceleration due to synchrotron radiation losses. The region of momentum space in which electron runaway takes place is determined. It is found that relativistic and synchrotron radiation effects lead to a critical electric field ER〉(kTe/mec2)ED, below which no runaways are generated. In addition, the trajectories of the test electrons in momentum space show a stable equilibrium point that sets a limit on the energy that the runaway electrons can reach. Analytical expressions are given for this energy limit as a function of the toroidal electric field and plasma parameters. The dominant radiative mechanisms limiting the runaway electron energy are identified in the whole range of electric field values. © 1998 American Institute of Physics.

Notes: A simple equation for Stringer spin up due to anomalous transport valid in arbitrary toroidal symmetric geometry is derived. Additional terms are found compared with previous work that can be traced to a different ordering of the parallel velocity. The influence of elongation and Shafranov shift is shown to be small. Neoclassical viscosity is included and the case of both small and large viscosity are discussed.© 1998 American Institute of Physics.

Notes: A study on preheating effects in laser-driven shock waves is presented. Two different diagnostics were used: the color temperature measurement deduced by recording the target rear side emissivity in two spectral bands, and the rear surface reflectivity measurement by using a probe beam. In order to test the response of the two diagnostics to the preheating, three types of targets characterized by different radiative properties were used. The greater sensitivity of the second diagnostic compared with the first was demonstrated. A model which calculates the reflectivity using a one-dimensional hydrodynamic code data was developed. In this model, the wave propagation equations in the expanding plasma using an appropriate model for the electron–ion collision frequency applicable to the cold solid-hot plasma transition were solved. The comparison between the calculated and measured reflectivities allows us to estimate the preheating process. © 1998 American Institute of Physics.

Notes: The effect of plasma on backward wave oscillator (BWO) emission in a 12–18 GHz frequency range is given. It is shown that the Ku band emission corresponds to the cylindrically symmetric transverse magnetic TM01 and not the higher mode. Due to the slowing down of waves with the increase in plasma density there occurs a BWO mode switching, i.e., BWO switches from a bounded mode to an unbounded one. Here the analysis for the switched BWO in the unbounded mode is given. The expressions for the temporal and spatial growth rates in the presence of plasma are obtained. The efficiency calculations are also given. Comparison of the results with that of a previous experiment [IEEE Trans. Plasma Sci. 18, 497 (1990)] has been carried out. © 1998 American Institute of Physics.

Notes: The steady state of the driven oscillations of the system consisting of N oscillators coupled by friction is considered. It is shown that for large values of N this state is asymptotically described by the F-function previously introduced in the theory of resonant magnetohydrodynamic (MHD) waves in plasmas. © 1998 American Institute of Physics.

Notes: A new expression of Δ′ and instability criterion for m≥2 tearing modes is derived for arbitrary magnetic shear configuration in the low beta and large aspect ratio limit. Local solutions of an ideal external kink equation are solved analytically by means of proper expansion and transformation. An analytic expression of the criterion parameter Δ′ results from the analytic solutions. The instability criterion obtained depends on the location of the resistive layer, and on a dimensionless parameter λ related to the ratio of the gradients of the equilibrium current density and of the rotational transform. Strauss's Δ′ formula and the previous instability criterion are recovered as a special case in the large-m limit without a conducting wall. Considering both the boundary conditions at the plasma core and the conducting wall, the expression of Δ′ is extended to include the stabilizing effect of the conducting wall. The properties of tearing instability are analyzed based on the expression of Δ′. © 1998 American Institute of Physics.

Notes: The spectrum of unstable perturbations of a simple magnetized atmosphere is studied. Magnetic field lines are straight, horizontal, and line tied to conducting walls at both ends. The temperature has horizontal variation across the field lines as well as vertical variation. The unstable spectrum close to marginal stability is found to be continuous from zero to a maximum growth rate. The structure of the unstable continuum modes is calculated in the dissipationless limit. The presence of singularities in the eigenfunction does not affect the growth rate significantly, nor does it lead to plasma heating. © 1998 American Institute of Physics.

Notes: A self-consistent set of equations for the fast space–time evolution of fluctuations and the slow space–time evolution of density and flows in a toroidal plasma, relevant for simulations using field-aligned coordinates in thin flux tubes, has been derived. The methodology for the derivation of these equations is outlined for a model set of equations for the plasma edge, specific to resistive ballooning modes but readily adaptable to other instabilities. The derivation proceeds by first writing the axisymmetric and fluctuating equations in the usual toroidal coordinate system. These are then transformed to the twisted coordinate flux-tube system. Most simulations which use twisted flux-tube computational grids transform to the field-aligned coordinate system first and then take averages to obtain the slow evolution. They however miss some terms since the two operations, namely, multiscale separation and coordinate transformation, do not necessarily commute, because of subsidiary assumptions on the box size. In the present formulation, all the relevant neoclassical effects such as the Pfirsch–Schlüter current and the Stringer spin-up as well as the toroidal Reynolds stress are properly included. This set of multiscale equations is appropriate for the study of the formation and evolution of transport barriers. © 1998 American Institute of Physics.

Notes: In this paper we describe a new theory of like particle collisional transport for a non-neutral plasma confined in a Penning trap. The theory is valid in the regime ωb〉ωE, ωb〉νc, and rc〈λD where ωb is the axial bounce frequency, ωE is the E×B rotation frequency, νc is the collision frequency, rc is the cyclotron radius, and λD is the Debye length. In this regime each particle can be bounce averaged into a long rod and the transport understood as arising from the E×B drift motion of the rods due to long-range mutual interactions. This is a very different mechanism than is considered in the classical theory of transport, where a particle guiding center undergoes a step of order rc as a result of a velocity scattering collision. For the parameter range considered, the new theory predicts transport rates that are orders of magnitude larger than those predicted by classical theory and that scale with magnetic field strength like 1/B rather than 1/B4. The new theory differs from a previous analysis of transport due to E×B drift interactions of charged rods, in that the finite length of the rods is taken into account. This enables transport to occur even for the case of an E×B drift rotation frequency that is a monotonic decreasing function of radius (as was the case in recent experiments). © 1998 American Institute of Physics.

Notes: On the China Tokamak (CT-6B) [Nucl. Fusion 36, 1669 (1996)], application of negative limiter bias resulted in enhanced Er shear in the naturally occurring Er shear layer near the fixed limiter radius with negligible change of plasma density, electron temperature, the parallel plasma flow, and the impurity ion radiation power. In the layer, decreased turbulent fluctuation, reduced poloidal correlation and increased nonlinear coupling of the turbulence were observed to be very possibly correlated with enhanced Er shear. The results suggest that there exists interaction of Er shear with turbulence, and an Er shear-induced shift in the phase angle between density and poloidal electric field fluctuations and nonlinear three-wave coupling may play an important role in suppressing edge turbulence. © 1998 American Institute of Physics.

Notes: The eigenfunctions of the equation ∇×bn=λnbn are the solutions of a Sturm-Liouville operator and form an orthonormal basis for the expansion of magnetic fields on any closed domain. Equilibria can be formed by summing individual eigenfunctions bn. The so-called Taylor state is a member of the general class of equilibria consisting entirely of a single mode with the lowest eigenvalue. It is interesting to note that the more general configurations formed by sums of these eigenfunctions are not necessarily zero pressure, nor are they necessarily stable. Physical insight can be gained from decomposition in this way. Stability calculations are greatly simplified in this choice of basis functions, especially for incompressible modes with ∇⋅ξ=0. The magnetohydrodynamic (MHD) δW equation can be written as a bilinear form δW=an*Wnmam, where the Wnm matrix can be composed from the integrated scalar triple products of the m=0 equilibrium basis curl-eigenfunction states and the forward and adjoint curl-eigenfunction magnetic perturbations. The problem of ideal MHD stability in simple geometries (but general equilibria) becomes tractable for PC solutions. The general procedure for stability analysis in arbitrary geometries is given, and detailed calculations for spherical equilibria are given. © 1998 American Institute of Physics.

Notes: A drift wave transport model, recently developed by Ottaviani, Horton and Erba (OHE) [Ottaviani et al., Plasma Phys. Controlled Fusion 39, 1461 (1997)], has been implemented and tested in a time-dependent predictive transport code. This OHE model assumes that anomalous transport is due to turbulence driven by ion temperature gradients and that the fully developed turbulence will extend into linearly stable regions, as described in the reference cited above. A multiplicative elongation factor is introduced in the OHE model and simulations are carried out for 12 discharges from major tokamak experiments, including both L- and H-modes (low- and high-confinement modes) and both circular and elongated discharges. Good agreement is found between the OHE model predictions and experiment. This OHE model is also used to describe the performance of the International Thermonuclear Experimental Reactor (ITER) [Putvinski et al., in Proceedings of the 16th IAEA Fusion Energy Conference, Montréal, Canada, 1996 (International Atomic Energy Agency, Vienna, 1997), Vol. 2, p. 737.] A second version of the OHE model, in which the turbulent transport is not allowed to penetrate into linearly stable regions, has also been implemented and tested. In simulations utilizing this version of the model, the linear stability of the plasma core eliminates the anomalous thermal transport near the magnetic axis, resulting in an increase in the core temperatures to well above the experimental values. © 1998 American Institute of Physics.

Notes: General equations proving useful in the context of strong electron photon interactions are derived. Such interactions are driven by launching short and powerful laser pulses on a material medium. Relativistic nonlinear equations are obtained from the system of fluid and Maxwell equations through a suitable perturbative approach into three main parameters: q (energy parameter), δ (time parameter), and α (spatial parameter). Numerous phenomena are recovered—such as relativistic self-focusing, low-frequency electric and magnetic wake fields generation, the creation of pulse frequency harmonics, nonlinear Compton scattering—while their generating sources are specified. But also new processes are identified, arising from possible couplings among the above quoted effects. Particular emphasis is put on the coupling of self-induced magnetic field with its generating pump, leading itself to the possible magnetic relativistic guiding of light. © 1998 American Institute of Physics.

Notes: Numerical simulation results of stimulated Brillouin scattering (SBS) using HERCULES [H. X. Vu, J. Comput. Phys. 124, 417 (1996)], an adiabatic fluid-electron particle-in-cell (PIC) code, are presented. The results of these PIC simulations are compared against fluid simulations, and good agreement is obtained for sufficiently weak laser intensities. When the laser intensity is sufficiently strong for ion trapping to be significant, PIC and fluid simulations differ substantially. The trapping time and nonlinear frequency shift obtained in the PIC simulations are in good agreement with analytical predictions. The SBS reflectivity is shown to be very sensitive to frequency mismatch between the light wave used to seed the instability and the incident laser.

Notes: The threshold conditions for the confinement bifurcations in the H-1 heliac [S. M. Hamberger et al., Fusion Technol. 17, 123 (1990)] are studied experimentally. The thresholds include the magnetic field, the rf power, and the neutral gas filling pressure. It is shown that in any combination of these parameters it is the radial electric field Er that is driven to a critical value before the bifurcation. A mechanism of the electric field formation is suggested, which is based on the balance of the electron and ion losses. The ion loss, at low magnetic field and high ion temperature observed in H-1, is dominated by the direct orbit loss mechanism. This is shown by modeling of the exact ion orbits and by comparing a qualitative picture of the Er formation with the experimental data. Relative efficiency of the electron and ion heating in the inner regions of plasma define the conditions for either low-to-high (L–H) or high-to low (H–L) confinement bifurcations in H-1. © 1998 American Institute of Physics.

Notes: Electron beam instabilities occurring in a gyrotron electron beam can induce an energy spread which might significantly deteriorate the gyrotron efficiency. Three types of instabilities are considered to explain the important discrepancy found between the theoretical and experimental efficiency in the case of quasi-optical gyrotrons (QOG): the electron cyclotron maser instability (ECMI), the electrostatic Bernstein instability (BI) and the Langmuir instability (LI). When the magnetic field gradient in drift tubes of QOG is low, the ECMI can develop in the drift tube at very low electron beam currents. Experimental measurements show that with a proper choice of absorbing structures in the beam tunnel, this instability can be suppressed. At high beam currents, the BI can induce a significant energy spread at the entrance of the interaction region. The induced energy spread scales approximately linearly with the electron beam density and for QOG one observes that the beam density is significantly higher than the beam density of an equivalent cylindrical cavity gyrotron. © 1998 American Institute of Physics.

Notes: A linear theory model is developed to analyze gyrotron traveling wave tubes (gyro-TWT) employing nonuniform interaction structures, which can be tapered wall waveguide, severed tubes, or distributed lossy wall waveguides. Effects of the wall loss, reflections caused by the nonuniformity of the waveguide, and beam–wave interactions inside the sever region are incorporated in this theory. In addition, self-excited oscillations in the gyro-TWT induced by absolute instabilities or reflections can also be studied by the same theory. Good agreements with the self-consistent particle-tracing code have been achieved. This theory can be used to provide a first-cut design of a stable gyro-TWT. © 1998 American Institute of Physics.

Notes: Helicon waves in a plasma confined by a cylinder are treated. The undamped normal modes of the helicon (H) and Trivelpiece–Gould (TG) waves have distinctly different wave patterns at high magnetic fields but at low fields have similar patterns and therefore interact strongly. Damping of these modes, their excitation by antennas, and the rf plasma absorption efficiency are considered. Nonuniform plasmas are treated by solving a fourth-order ordinary differential equation numerically. A significant difference between this and earlier codes which divide the plasma into uniform shells is made clear. Excitation of the weakly damped H wave, followed by conversion to the strongly damped TG wave which leads to high helicon discharge efficiency, is examined for realistic density profiles. A reason for the greater heating efficiency of the m=+1 vs the m=−1 mode for axially peaked profiles is provided. © 1998 American Institute of Physics.

Notes: The scalings of heat transport with safety factor (q), normalized collisionality (ν), plasma beta (β), and relative gyroradius (ρ*) have been measured on the DIII-D tokamak [Fusion Technol. 8, 441 (1985)]. The measured ρ*, β and ν scalings of heat transport indicate that E×B transport from drift wave turbulence is a plausible basis for anomalous transport. For high confinement (H) mode plasmas where the safety factor was varied at fixed magnetic shear, the effective (or one-fluid) thermal diffusivity was found to scale like χeff∝q2.3±0.64 , with the ion and electron fluids having the same q scaling to within the experimental errors except near the plasma edge. The scaling of the thermal confinement time with safety factor was in good agreement with this local transport dependence, τth∝q−2.42±0.31 ; however, when the magnetic shear was allowed to vary to keep q0 fixed during the (edge) safety factor scan, a weaker global dependence was observed, τth∝q95−1.43±0.23. This weaker dependence was mainly due to the change in the local value of q between the two types of scans. The combined ρ*, β , ν and q scalings of heat transport for H-mode plasmas on DIII-D reproduce the empirical confinement scaling using physical (dimensional) parameters with the exception of weaker power degradation. © 1998 American Institute of Physics.

Notes: The quadratic response tensor provides a complete description of second-order wave processes in a nonlinear medium. The first exact expression is derived for the quadratic response tensor of a warm collisionless plasma, whose particles have a nonrelativistic Maxwellian velocity distribution. The exact expression is written in terms of a set of generalized plasma dispersion functions which satisfy simple symmetry properties and recursion relations and which can be expressed in terms of the standard nonrelativistic plasma dispersion function. © 1998 American Institute of Physics.

Notes: A new class of low aspect ratio toroidal hybrid stellarators is found using a more general plasma confinement optimization criterion than quasisymmetrization. The plasma current profile and shape of the outer magnetic flux surface are used as control variables to achieve near constancy of the longitudinal invariant J* on internal flux surfaces (quasiomnigeneity), in addition to a number of other desirable physics target properties. A range of compact (small aspect ratio A), low plasma current devices have been found with significantly improved confinement, both for thermal as well as energetic (collisionless) particle components. With reasonable increases in magnetic field and geometric size, such devices can also be scaled to confine 3.5 MeV alpha particle orbits.

Notes: Numerical simulations of ion temperature gradient (ITG) mode transport with gyrofluid flux tube codes first lead to the rule that the turbulence is quenched when the critical E×B rotational shear rate γE−crit exceeds the maximum of ballooning mode growth rates γ0 without E×B shear [Waltz, Kerbel, and Milovich, Phys. Plasmas 1, 2229 (1994)]. The present work revisits the flux tube simulations reformulated in terms of Floquet ballooning modes which convect in the ballooning mode angle. This new formulation avoids linearly unstable "box modes" from discretizing in the ballooning angle and illustrates the true nonlinear nature of the stabilization in toroidal geometry. The linear eigenmodes can be linearly stable at small E×B shear rates, yet Floquet mode convective amplification allows turbulence to persist unless the critical shear rate is exceeded. The flux tube simulations and the γE−crit(approximate)γ0 quench rule are valid only at vanishing relative gyroradius. Modifications and limits of validity on the quench rule are suggested from analyzing the finite relative gyroradius "ballooning-Schrödinger equation" [R. L. Dewar, Plasma Phys. Controlled Fusion 39, 437 (1997)], which treats general "profile shear" (x variation in γ0) and "profile curvature" (x2 profile variation). © 1998 American Institute of Physics.

Notes: The structure and scaling of the H-mode (high mode) pedestal are examined for discharges in the DIII-D tokamak [Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1986), p. 159]. For typical conditions, the pedestal values of the ion and electron temperatures Ti and Te are comparable. Measurements of main ion and C6+ profiles indicate that the ion pressure gradient in the barrier is 50%–100% of the electron pressure gradient for deuterium plasmas. The magnitude of the pressure gradient in the barrier often exceeds the predictions of infinite-n ballooning mode theory by a factor of 2. Moreover, via the bootstrap current, the finite pressure gradient acts to entirely remove ballooning stability limits for typical discharges. For a large dataset, the width of the pressure barrier δ is best described by the dimensionless scaling δ/R∝(βpolped)0.4 where (βpolped) is the pedestal value of poloidal beta and R is the major radius. Scalings based on the poloidal ion gyroradius or the edge density gradient do not adequately describe overall trends in the data set and the propagation of the pressure barrier observed between edge-localized modes. The width of the Ti barrier is quite variable and is not a good measure of the width of the pressure barrier. © 1998 American Institute of Physics.

Notes: Fluid equations are derived that describe wave-particle resonances, which usually require kinetic theory. The phase velocity transform is introduced, which decomposes a function of space and time into a sum over components with constant phase velocity. This leads to a new technique to solve partial differential equations, similar but not identical to the Radon transform, and produces recursive solutions. This technique is applied to the collisionless drift kinetic equation, to give closure of the fluid moment hierarchy. The result is a new term in the highest moment equation that retains many nonlinear wave-particle effects not before described by fluid equations.

Notes: 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. © 1998 American Institute of Physics.

Notes: The Nova laser [E. M. Campbell, Laser Part. Beams 9, 209 (1991)] was used to shock-compress liquid deuterium and obtain new principal Hugoniot measurements of density and pressure between 0.3 and 2.1 Mbar. In this pressure-density region, deuterium is predicted to transform from a molecular insulating fluid to an atomic conducting fluid. Nova data show a rapid increase in density from 0.6 g/cc at 0.3 Mbar, to 1 g/cc at 0.6 Mbar, suggestive of such a transition. The observed sixfold compression near 1 Mbar is larger than predicted by many widely used equation of state models.

Notes: The effect of beam structure on propagation through underdense plasma is examined in two different examples. First, it is shown that the distribution of intensities within a laser beam affects how the beam deflects in the presence of transverse plasma flow. A detailed analysis of beam deflection shows that the rate scales linearly with intensity and plasma density, and inversely with plasma temperature. When the plasma flow is subsonic, the deflection rate is proportional to the ion damping decrement, and scales as M/(1−M2)3/2, where M is the transverse flow Mach number. When the plasma flow is supersonic, the deflection rate scales as 1/[M(M2−1))1/2]. Next, the effect of beam structure on channel formation by very intense laser beams is studied. A diffraction-limited beam with ∼3 TW of input power forms a channel through 400 μm of plasma, whereas when this beam is phase aberrated, channel formation does not occur.

Notes: Techniques have been developed to improve the uniformity of the laser focal profile, to reduce the ablative Rayleigh–Taylor instability, and to suppress the various laser–plasma instabilities. There are now three direct-drive ignition target designs that utilize these techniques. An evaluation of these designs is still ongoing. Some of them may achieve the gains above 100 that are necessary for a fusion reactor. Two laser systems have been proposed that may meet all of the requirements for a fusion reactor. © 1998 American Institute of Physics.

Notes: The population kinetics of dense hydrogen-like plasmas is investigated within a quantum kinetic approach. Recombining plasmas are considered for the isothermal, the isoenergetic and the adiabatic case. In the latter cases, additionally to the rate equations, balance equations for the temperatures of the plasma species are used. The influence of many-body effects on the relaxation is discussed. Comparisons are given with a recent experiment on laser-produced carbon plasmas. © 1998 American Institute of Physics.

Notes: This study details particle-in-cell simulations of the multipactor effect and discharges created using this effect. A detailed secondary emission model which accounts for the energy and impact angle dependence of yield is developed to simulate accurately the phenomenon. It is shown that a steady state multipactor can be built up from a very low density initial electron distribution and an oscillatory steady state can be achieved. Steady state is reached when the cavity detuning and space charge of the built-up beam balance the phase focusing. The results for a more accurate secondary electron distribution are compared with simpler analytic models and extended. It is shown that, while the energy spread of secondary electrons differs from the monoenergetic analytical model, the weighted average energy is the same. Resistive loading of the circuit due to multipacting electrons is presented. The behavior of the system with Q values of between 20 and 200 is discussed. © 1998 American Institute of Physics.

Notes: The nonlinear interaction between random phase photons and sound waves in ultra-relativistically hot electron-positron plasmas is considered. The modulational instability of a broad photon spectrum is investigated. Explicit expressions for the growth rates are obtained in limiting cases. © 1998 American Institute of Physics.

Notes: A soft x-ray microscope (E(approximately-less-than)3 keV) with high spatial resolution (∼3 μm) has been characterized at the University of Rochester's Laboratory for Laser Energetics and used for initial experiments on the Omega laser system [Boehly et al., Opt. Commun. 133, 495 (1997)] to study the hydrodynamic stability of directly driven planar foils. The microscope, which is an optimized Kirkpatrick–Baez-type design, is used to obtain four x-ray radiographs of laser-driven foils. Time-resolved images are obtained with either custom-built framing cameras (time resolution ∼80 ps) or by using short-pulse backlighter beams (Δt(approximately-less-than)200 ps). In the former case, a spatial resolution of ∼7 μm was obtained (limited by the framing camera), while in the latter case a resolution of ∼3 μm was obtained. This paper details the testing, calibration, and initial use of this microscope in the laboratory and on Omega. © 1998 American Institute of Physics.

Notes: Simulations have identified charge-density variations as driving the dominant emittance growth mechanism for high-current, low-emittance induction linacs using solenoidal focusing, once the beam enters the emittance-dominated regime. In this paper, we use the radial equation of motion, including the nonlinearities resulting from radial density variations, to understand this effect. Nonlinearities in the beam's radial motion while in a solenoid arise from the noncancellation of the effects from the diamagnetic axial magnetic field and the potential depression of the beam, if the beam density is nonuniform. Any initial density variation drives a logarithmic increase in additional higher-order density variations (through the differential betatron motion), and an emittance growth that scales logarithmically, or greater (even potentially faster than linear), with the axial distance along the accelerator. The growth rate depends on the beam current, the focusing force, and the accelerating gradient, and for typical machine parameters, the growth rate can be faster than linear with distance. The magnitude of the emittance growth depends critically on the matching of the beam from the injector to the beamline. This formalism leads to a criterion of how uniform the beam density has to be and how well the beam needs to be matched in order not to have an unacceptable emittance growth. © 1998 American Institute of Physics.

Notes: The existence of a critical gradient is an important feature of many transport models. [M. Kotschenreuther et al., Phys. Plasmas 2, 2381 (1995)]. However, fundamental differences exist in the dynamics near marginal stability, depending on whether the transport phenomena are controlled by strict (linear) marginal stability or by a self-organized criticality. One of the most striking differences is in the stiffness of the profiles. In this paper, a sand pile model is used to gain some basic understanding of the stiffness of the profile under different dynamics. © 1998 American Institute of Physics.

Notes: The one-dimensional (1-D) spatially periodic system of N classical particles, interacting via a Coulomb-like repulsive long-range force, is studied using classical mechanics. The usual Bohm–Gross dispersion relation for the collective modes is obtained in the absence of quasiresonant particles. In the presence of R quasiresonant particles, the evolution equations for M long-wavelength modes are coupled to the particles' motion through a self-consistent wave–particle Hamiltonian. The wave–particle Lagrangian is derived from the full N-body Lagrangian. The derivation relies on an explicit scale separation argument and avoids the use of kinetic theory and continuous medium formalism. © 1998 American Institute of Physics.

Notes: Detailed ray tracing, of wave propagation in a plasma near electron cyclotron resonances, suggests that refraction can lead to reduced absorption, in some cases. By studying the full wave equation for the ordinary wave near the fundamental, in a slab model, it is shown that such refraction does indeed reduce absorption, for this particular case, but that wave energy tunnelling can significantly modify the result. © 1998 American Institute of Physics.

Notes: An ensemble of electrostatic waves propagating obliquely to the external uniform magnetic field accelerates the plasma electrons, giving rise to a mechanical energy in terms of finite magnetic moment (μ). In nonlinear analysis, this magnetic moment modifies the resonances among the harmonics (l) and the overlapping parameter (K) leading to stochasticity. It is shown that the threshold amplitude (φk) of electrostatic waves at the onset of chaos increases slowly for l=0 harmonics and sharply for higher harmonics (l≥1), owing to the effect of magnetic moment. A sharp decrease of threshold amplitude with wave vector (k) pertaining to the ensemble of waves for higher harmonics (l≥1) is also delineated. The findings may have astrophysical and cosmological signatures in the high energy particle regimes. © 1998 American Institute of Physics.

Notes: Conventional neoclassical transport theory does not pertain near the magnetic axis, where orbital variation of the minor radius and the poloidal field markedly change the nature of guiding-center trajectories. Instead of the conventional tokamak banana-shaped trajectories, near-axis orbits, called potato orbits, are radially wider and lead to distinctive kinetic considerations. Here it is shown that there is a plateau regime for the near-axis case; the corresponding potato-plateau ion thermal conductivity is computed. © 1998 American Institute of Physics.

Notes: A tokamak equilibrium model, local to a flux surface, is introduced which is completely described in terms of nine parameters including aspect ratio, elongation, triangularity, and safety factor. By allowing controlled variation of each of these nine parameters, the model is particularly suitable for localized stability studies such as those carried out using the ballooning mode representation of the gyrokinetic equations. © 1998 American Institute of Physics.

Notes: Experiments have been carried out on the 60-beam, 30 kJ OMEGA laser system [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] as part of an integrated program to diagnose all phases of direct-drive capsule implosions. Laser-imprint levels and Rayleigh–Taylor growth rates associated with the spherical implosions have been inferred from planar-foil radiography experiments. In spherical targets, measurements of the combined effects of imprint and unstable growth at the ablation surface have been carried out using the burnthrough technique [J. Delettrez et al., Phys. Plasmas 1, 2342 (1994)]. Target behavior during the deceleration phase has been investigated using a series of surrogate cryogenic capsules in which the main fuel layer is represented by a Ti-doped CH shell and the hot spot is represented by an Ar-doped deuterium fill gas. © 1998 American Institute of Physics.

Notes: The status of a distributed radiator heavy-ion target design is described. In integrated calculations this target ignited and produced 390–430 MJ of yield when driven with 5.8–6.5 MJ of 3–4 GeV Pb ions. The target has cylindrical symmetry with disk endplates. The ions uniformly illuminate these endplates in a 5 mm radius spot. Considerations which led to this design are discussed together with some previously unused design features: low-density hohlraum walls in approximate pressure balance with internal low-Z fill materials, radiation symmetry determined by the position of the radiator materials and particle ranges, and early time pressure symmetry possibly influenced by radiation shims. How this target scales to lower input energy or to lower beam power is discussed. Variant designs with more realistic beam focusing strategies are also discussed. Tradeoffs required for targets which accept higher particle energies are described.

Notes: Local thermodynamic equilibrium (LTE) breaks down in directly or indirectly driven laser plasmas because of sharp gradients, energy deposition, etc. For modeling non-LTE effects in hydrodynamical simulations, Busquet's model [Phys. Fluids B 5, 4191 (1993)] is very convenient and efficient. It uses off-line generated LTE opacities and equation of states via an effective, radiation-dependent ionization temperature Tz. An overview of the model is given. The results are compared with an elaborate collisional radiative model based on superconfigurations. The agreements for average charge Z* and opacities are surprisingly good, even more so when the plasma is immersed in a radiation field. Some remaining discrepancy at low density is attributed to dielectronic recombination. Improvement appears possible, especially for emissivities, because the concept of ionization temperature seems to be validated. © 1998 American Institute of Physics.

Notes: This paper summarizes extensive observational studies of the closest ultraluminous radio galaxy Cygnus A. These data are used to test jet theory for powering the double-lobed radio emitting structures. Issues addressed include: (i) jet stability, confinement, composition, and velocity, (ii) the double shock structure for the jet terminus and the origin of multiple radio hotspots, (iii) the nature of filamentary structure in the radio lobes, and (iv) the hydrodynamic evolution of the radio lobes within a hot cluster atmosphere. These data are also used to constrain models for relativistic particle acceleration and energy losses (Fermi acceleration and synchrotron aging), as well as to determine magnetic field strengths and morphologies in the radio source and in the surrounding intracluster medium. © 1998 American Institute of Physics.

Notes: A theoretical model for plasma instability in the equatorial F region of the nighttime ionosphere that takes into account the time-dependent aspect of the ambient plasma, where the density gradient increases with time, and that allows variation of mode amplitudes both along the geomagnetic field line and along the vertical direction is presented. The instability is excited due to the combined effects of the gravity and an eastward electric field in the presence of a density gradient, and the time-dependent density gradient arises because of the E0×B0 upward drift of the plasma and the decreasing (with altitude) recombination rate. The model is used to study the linear evolution of the instability and some results of the analysis are reported. The spatially localized plasma modes, predicted by the model, are consistent with the experimental observations. Due to the time-dependent density gradient, growth of the plasma modes is enhanced over what is obtained when the time dependence is ignored, and this enhancement increases with time.

Notes: Recent advances in novel technologies such as chirped pulse amplification and high gradient rf photoinjectors make it possible to study experimentally the interaction of relativistic electrons with ultrahigh intensity photon fields. Femtosecond laser systems operating in the TW–PW range are now available, as well as synchronized relativistic electron bunches with subpicosecond durations and THz bandwidths. Ponderomotive scattering can accelerate these electrons with extremely high gradients in a three-dimensional vacuum laser focus. The nonlinear Doppler shift induced by relativistic radiation pressure in Compton backscattering is shown to yield complex nonlinear spectra which can be modified by using temporal laser pulse shaping techniques. Colliding lasers pulses, where ponderomotive acceleration and Compton backscattering are combined, could also yield extremely short wavelength photons. Finally, strong radiative corrections are expected when the Doppler-upshifted laser wavelength approaches the Compton scale. These are discussed within the context of high field classical electrodynamics, a new discipline borne out of the aforementioned innovations. © 1998 American Institute of Physics.

Notes: Linear colliders, future electron acceleration concepts, and short pulse, ultrawideband millimeter-wave sources all require bright electron beams. Photoinjectors have demonstrated the ability to produce relativistic electron beams with low emittance and energy spread. The system described herein combines state-of-the-art capabilities in the laser and rf systems, advanced photocathode materials, and new concepts for synchronization. Phase jitter has been measured in detail, and schemes for alleviating this problem have undergone initial proof-of-principle testing. Direct mode locking of a multiple quantum well Al:GaAs solid-state laser oscillator by an rf signal sampled from within a high-power rf accelerator cavity was demonstrated for the first time. Characterization of the electron beam produced by the system is presented. The linear electron accelerator system is comprised of a 1.5 cell side-wall coupled standing wave accelerator structure, driven by a 20 MW Stanford Linear Accelerator Center (SLAC) Klystron operating at 8.548 GHz, a Ti:sapphire laser oscillator, and a chirped pulse Ti:sapphire laser amplifier. © 1998 American Institute of Physics.

Notes: The interaction of light (coherent and incoherent) with charged particle beams is explored in various configurations: incoherent scattering of coherent light (laser) from an incoherent particle beam (high temperature), coherent scattering of coherent light (laser) from a "cold" (bunched) beam, femtosecond generation of particle and light beams via "optical slicing" and Thomson/Compton scattering techniques, etc. The domains of ultrashort temporal duration (femtoseconds) as well as ultrashort wavelengths (x rays and shorter), with varying degrees of coherence, are explored. The relevance to a few critical areas of research in the natural sciences, e.g., ultrafast material, chemical and biological processes, protein folding, particle phase space cooling, etc. are touched upon. All the processes discussed involve proper interpretation and understanding of coherent states of matter and radiation, as well as the quality and quantity of information and energy embedded in them. © 1998 American Institute of Physics.

Notes: A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson [Phys. Fluids 18, 875 (1975)]. © 1998 American Institute of Physics.

Notes: Space plasma measurements, laboratory experiments, and simulations have shown that magnetohydrodynamic (MHD) turbulence exhibits a dynamical tendency towards spectral anisotropy given a sufficiently strong background magnetic field. Here the undriven decaying initial-value problem for homogeneous MHD turbulence is examined with the purpose of characterizing the variation of spectral anisotropy of the turbulent fluctuations with magnetic field strength. Numerical results for both incompressible and compressible MHD are presented. A simple model for the scaling of this spectral anisotropy as a function of the fluctuating magnetic field over total magnetic field is offered. The arguments are based on ideas from reduced MHD (RMHD) dynamics and resonant driving of certain non-RMHD modes. The results suggest physical bases for explaining variations of the anisotropy with compressibility, Reynolds numbers, and spectral width of the (isotropic) initial conditions. © 1998 American Institute of Physics.

Notes: A two-dimensional (2-D), finite-difference computer code is developed to examine helicon antenna coupling, wave propagation, collisionless Landau, and collisional heating mechanisms. The code calculates the electromagnetic wave fields and power absorption in an inhomogeneous, cold, collisional plasma. The current distribution of the launching antenna, which provides the full antenna spectra, is included in the model. An iterative solution that incorporates warm plasma thermal effects has been added to the code to examine the contribution of collisionless (Landau) wave absorption by electrons. Detailed studies of the wave fields and electron heating profiles at low magnetic fields (B0〈100 G), where both Trivelpiece–Gould (TG) and helicon (H) modes are present, are discussed. The effects of the applied uniform magnetic field (B0=10–1000 G), 2-D (r,z) density profiles (ne0=1011–1013 cm−3), neutral gas pressures of 1–10 mTorr and the antenna spectrum on collisional and collisionless wave field solutions and power absorption are investigated. Cases in which the primarily electrostatic (TG) surface wave dominates the heating and the power is absorbed near the edge region and cases in which the propagating helicon wave transports and deposits its energy in the core plasma region are examined. © 1998 American Institute of Physics.

Notes: In the standard approach to the problem of shear stabilization of drift waves the diamagnetic drift velocity v* is regarded as a constant, which is usually not satisfied at the edge of a tokamak plasma. In configurations of this type, with a steep density gradient and radially sheared transverse velocity field, the magnetic shear stabilization criteria are severely restricted, and the velocity profile curvature v0″(x) is found to play a crucial role. In the strongly nonlinear regime, unstable drift waves may saturate into stationary coherent vortex-type structures. The latter include a tripolar vortex. © 1998 American Institute of Physics.

Notes: Electrostatic fluctuations are measured in the Extrap T2 reversed-field pinch [J. R. Drake et al., in Plasma Physics and Controlled Nuclear Fusion Research 1996 (International Atomic Energy Agency, Vienna, 1997), Vol. 2, pp. 193–199] using a Langmuir probe array. The electrostatic fluctuation, driven particle transport ΓnΦ is derived and found to constitute a large fraction of the total particle transport. The spectral density of all measured quantities exhibits a peak in the frequency range 100–250 kHz, which originates from fluctuations that are resonant close to the edge [n=−(40–80)]. This peak contains only about 10–20% of the total fluctuation power, but is shown to dominate ΓnΦ. The main reason for this is the high toroidal mode number as compared with internally resonant magnetohydrodynamic fluctuations. The edge resonant fluctuations also features a higher coherence (γ=0.5) and close to 90° phase shift between density and potential fluctuations. © 1998 American Institute of Physics.

Notes: In a number of experiments, stimulated Brillouin (SBS) or Raman backscattering (SRS) has been observed to be much more vigorous than the other although the expectations based on linear gain exponents are that they should both be reflecting large amounts of incident light. Multidimensional fluid simulations of the growth and saturation of these two instabilities driven by a nonuniform incident laser beam are presented. On the fast time scale, the nonlinear saturation occurs via an anomalous damping inspired by fundamental studies of Langmuir turbulence [D. F. DuBois et al., Bull. Am. Phys. Soc. 41, 1531 (1996)] and acoustic wave turbulence [B. I. Cohen et al., Phys. Plasmas 4, 956 (1997)]. Over a longer time scale, SRS and SBS are limited by quasilinear processes such as flows induced by the transfer of momentum from the light to the plasma and ion temperature increases caused by a loss of light energy in SBS. The simulations show a reduction of the SBS reflectivity under conditions of strong SRS reflectivity even if the laser energy is not depleted. The recent observations of decreasing SBS reflectivity with increasing plasma density [D. S. Montgomery, Phys. Plasmas 5, 1973 (1998)] are shown to be consistent with linear theory and nonlinear simulations of SBS provided the increasing levels of SRS are included. Because the reflectivity is produced by scattering in intense hotspots, where the local reflectivity can be very large, the SBS and SRS can be anticorrelated even when the total scattering is quite modest. © 1998 American Institute of Physics.

Notes: In a toroidally rotating tokamak plasma, heavy impurity ions accumulate on the outside of each flux surface under the action of the centrifugal force. The collision frequency therefore varies over the flux surface. This circumstance is shown to enhance the neoclassical transport processes, including the bootstrap current, by making collisions occur preferentially where the magnetic field is weak. © 1998 American Institute of Physics.

Notes: Dwivedi's claim [Phys. Plasmas 4, 3427 (1997)] that the dust-acoustic wave should not be viewed as a novel plasma wave is rebutted. The so-called acoustic-like mode introduced earlier by Dwivedi et al. [J. Plasma Phys. 41, 219 (1989)] rests physically on very dubious grounds, because it considers a plasma with two ion species in the presence of a fixed electron background. In addition, Dwivedi et al. have nowhere included heavy charged dust grains as potential applications of their (flawed) theoretical treatment. Hence Rao et al. (1990) were indisputably the first ones to point out the possibility of dust-acoustic modes, correctly so, as we argue, because a distinct name is fully justified by the enormous order-of-magnitude differences in the charge-to-mass ratios of the usual charged dust grains compared to "ordinary" ions and by the recent experimental verification. © 1998 American Institute of Physics.

Notes: Electron surface waves in a metal bound plasma slab have been detected and analyzed. In this work it is shown that the presence of a matrix sheath between the central quasineutral region and the metal walls allows for the propagation of surface waves analogous to those found in dielectric bound plasmas. Measurements of the dispersion relations and eigenfunctions of asymmetric and symmetric, electrostatic, surface, and body waves are made via particle-in-cell simulation of a plasma slab with sheaths. The plasma slab has finite temperature electrons and fixed ions of uniform density. The sheaths consist of electron free, fixed, uniform ion regions ("matrix sheath") of thickness ∼λDe. A linearized Vlasov theory is developed for comparison with the simulation. It is shown that the long wavelength approximation (kλDe(very-much-less-than)1) is not valid even for long wavelengths in the propagation direction. Collisionless damping of both surface and body waves is measured which compares well with theoretical estimates. © 1998 American Institute of Physics.

Notes: It is found that dust sheared flow in combination with the dust–neutral drag produce a dissipative instability of short-wavelength (in comparison with the ion gyroradius) electrostatic waves in nonuniform dusty magnetoplasmas. Furthermore, the nonlinear interactions between these finite amplitude short-wavelength waves give rise to a vortex chain which moves with a well defined constant velocity. The relevance of our investigation to laboratory and space plasmas has been pointed out. © 1998 American Institute of Physics.

Notes: The absorption of power is studied with fluid and gyrokinetic plasma models, when Alfvén resonances provide for a weak damping in a partially standing wave field. Examples chosen in slab and toroidal geometry show that the fluid predictions based on resonance absorption are generally very different from the Landau damping of mode-converted slow waves. They, in particular, suggest that the continuum damping of toroidal Alfvén eigenmodes (TAE) and the power deposition profiles obtained in the ion-cyclotron range of frequencies (ICRF) using fluid plasma models can be very misleading. © 1998 American Institute of Physics.

Notes: By using the Sagdeev pseudopotential method, solitary kinetic Alfvén waves (SKAW) are studied in a low-β plasma, taking into account the electron inertia and ion temperature. Solitary wave solutions, and the electric and magnetic fields, are obtained using the knowledge of the pseudopotential analysis in plasma dynamics. It is found that both hump and dip solitons exist for SKAWs, conforming to the results of Freja scientific satellite observations in space. © 1998 American Institute of Physics.

Notes: An equation describing the nonlinear development of an envelope of weakly dispersive transverse waves propagating along the ambient magnetic field in a warm two-fluid plasma is derived by using the Fourier transformation method. This equation contains three nonlinear terms, a cubic, a derivative of cubic, and a quadratic multiplied by a derivative term. For the case of small wave amplitude, the equation is of non-Schrödinger type that includes a linear term involved with mixed second-order derivatives (space and time), in addition to the usual two terms of the Schrödinger-type equation. This mixed derivative term arises from the inclusion of the displacement current in the formulation. The nonlinear terms in the derived equation explicitly contain a smallness parameter which vanishes in the limit of zero dispersion. The low frequency limit of the equation is compared with the standard derivative nonlinear Schrödinger equation (DNLS), and differences are discussed. The new equation predicts that the condition for the modulational instability for the low frequency circularly polarized waves does not depend on the sense of polarization, a result that differs from the usual DNLS equation. The high and intermediate frequency limits of the equation are also considered. © 1998 American Institute of Physics.

Notes: Drift wave maps, area preserving maps that describe the motion of charged particles in drift waves, are derived. The maps allow the integration of particle orbits on the long time scale needed to describe transport. Calculations using the drift wave maps show that dramatic improvement in the particle confinement, in the presence of a given level and spectrum of E×B turbulence, can occur for q(r) profiles with reversed shear. A similar reduction in the transport, i.e., one that is independent of the turbulence, is observed in the presence of an equilibrium radial electric field with shear. The transport reduction, caused by the combined effects of radial electric field shear and both monotonic and reversed shear magnetic q profiles, is also investigated. © 1998 American Institute of Physics.

Notes: The formalism necessary to study the collective properties of a plasma system with inhomogeneous flows is nonlocal and generally in the form of an integrodifferential equation. Usually the eigenvalue condition is reduced to a second-order differential equation for simplicity. While the gross physical behavior of the system can be obtained from the second-order differential equation level of description, higher-order corrections are necessary for greater accuracy. The limit in which the scale-size of the velocity inhomogeneity is large compared to the ion gyroradius is considered and a transverse flow profile sharply localized in space ("top-hat" profile) is assumed. In this limit, a simple analytical method for the solution of the general eigenvalue condition to all orders is developed. A comparison of the properties of the solutions obtained from the second-order differential equation level of description with those obtained from higher orders is presented. Both the resonant (dissipative) and the nonresonant (reactive) effects of velocity shear are considered. It is found that while the overall features are well represented by the second-order level of description, the higher-order corrections moderate the destabilizing effects due to velocity shear, which can be quite significant in some cases. © 1998 American Institute of Physics.

Notes: Transitions to an enhanced confinement regime in tokamak plasmas with negative central magnetic shear have been observed in a number of devices. A simple model incorporating the nonlinear coupling between the turbulent fluctuations and the sheared radial electric field is added to a transport model in order to investigate the dynamics of the transition to this enhanced confinement mode. In this model, by incorporating both the instability growth rate profiles and particle and/or power deposition profiles, a rich variety of transition dynamics is uncovered. Transition dynamics and their concomitant thresholds are examined within the context of these models. In the course of investigating these transitions, potential methods for triggering and controlling these enhanced confinement regimes have been discovered and are discussed. © 1998 American Institute of Physics.

Notes: The sheared slab ηi instability is reconsidered in tokamak plasma with negative magnetic shear. A modified sheared slab model is presented to include both the magnetic shear and its variation with the magnetic surface. The results show that the slow variation of magnetic shear can aggravate the sheared slab ηi instability in the region near the minimum-q magnetic surface and that it has a weak stabilizing role in the plasma core near the axis. However, when the effect of the variation of magnetic shear increases, it can give rise to a stronger slab ηi instability. In addition, a linear mode coupling mechanism could be mediated by the variation of magnetic shear with a magnetic surface. © 1998 American Institute of Physics.

Notes: Circularly polarized Alfvén waves give rise to an α-dynamo effect that can be exploited to drive parallel current. In a "laminar" magnetic the effect is weak and does not give rise to significant currents for realistic parameters (e.g., in tokamaks). However, in reversed-field pinches (RFPs) in which magnetic field in the plasma core is stochastic, a significant enhancement of the α effect occurs. Estimates of this effect show that it may be a realistic method of current generation in the present-day RFP experiments and possibly also in future RFP-based fusion reactors. © 1998 American Institute of Physics.

Notes: A new technique for calculating a collisionless plasma along a field line is presented. The primary feature of this new ion-exospheric model is that it can handle an arbitrary (including nonmonotonic) potential energy distribution. This was one of the limiting constraints on the existing models in this class, and these constraints are generalized for an arbitrary potential energy composition. The formulation for relating current density to the field-aligned potential as well as formulas for density, temperature, and energy flux calculations are presented for several distribution functions, ranging from a bi-Lorentzian with a loss cone to an isotropic Maxwellian. A comparison of these results with previous models shows that the formulation reduces to the earlier models under similar assumptions. © 1998 American Institute of Physics.

Notes: The propagation of helicon waves and the plasma density has been measured in a cylindrical, magnetized plasma for a range of magnetic fields and input power levels. A transition in the coupling mechanism from electrostatic (E mode) to inductive (H mode) coupling is evidenced by a sharp change in the plasma density coinciding with a change in the wave fields from a linearly polarized standing wave, with highest amplitude close to the antenna to a right-hand elliptically polarized traveling wave with a phase velocity of about 6×106 m/s extending into the downstream region. An explanation of the transition to the H mode is put forward in terms of the conductivity across the magnetic field and an associated skin depth for power deposition. The polarization of the wave fields in the H mode is interpreted in terms of the interference between m=+1 and −1 modes (where m is the azimuthal mode number). © 1998 American Institute of Physics.

Notes: By using the hydrodynamic electron response with fixed (kinetic) ions along with Poisson's equation as well as Ampère's law, a system of nonlinear equations for low-frequency (in comparison with the electron gyrofrequency) long-(short-) wavelength electromagnetic waves in a nonuniform resistive magnetoplasma has been derived. The plasma contains equilibrium density gradient and sheared equilibrium plasma flows. In the linear limit, local dispersion relations are obtained and analyzed. It is found that sheared equilibrium flows can cause instability of Alfvén-like electromagnetic waves even in the absence of a density gradient. Furthermore, it is shown that possible stationary solutions of the nonlinear equations without dissipation can be represented in the form of various types of vortices. On the other hand, the temporal behavior of our nonlinear dissipative systems without the equilibrium density inhomogeneity can be described by the generalized Lorenz equations which admit chaotic trajectories. The density inhomogeneity may lead to even qualitative changes in the chaotic dynamics. The results of our investigation should be useful in understanding the linear and nonlinear properties of nonthermal electromagnetic waves in space and laboratory plasmas. © 1998 American Institute of Physics.

Notes: The contributions of untrapped and three groups of trapped particles to the longitudinal permittivity of a tokamak plasma with elliptic magnetic surfaces are derived for radio frequency waves in a wide range of frequencies, mode number, and plasma parameters. The analytical expressions of the longitudinal permittivity elements are obtained by using the kinetic theory of dielectric tensor elements, where the drift kinetic equation is solved as a boundary-value problem. Considered is a collisionless plasma model of an axisymmetric tokamak with small ellipticity and a large aspect ratio. The limit to the known results for toroidal plasmas with the circular cross-section of the magnetic surfaces is shown. © 1998 American Institute of Physics.

Notes: The results of two-dimensional calculations of eddy currents induced on external conducting walls surrounding a tokamak are reported. The computed eddy currents are generated by low-n (n=1,2,3) external ideal-magnetohydrodynamic (MHD) instabilities. For a given toroidal mode number n the eddy current patterns are found to be very similar in a variety of plasma configurations, e.g., different edge safety factors and different plasma–wall separation distances, in high beta plasmas. This result is promising for the design of active feedback coils for the stabilization of the resistive wall mode. Also, the effects of having a partial wall that has a poloidal gap on the outboard side are considered. Using the expected gap size in the proposed Korea Superconducting Tokamak Advanced Research (KSTAR) ["The KSTAR tokmak," in Proceedings of the 17th Symposium on Fusion Engineering, San Diego, 1997 (Institute of Electrical and Electronics Engineers, New York, in press), Paper No. O3.1], the calculation shows that active coils mounted behind the partial walls (the KSTAR passive plates) cover an adequate portion of the eddy current dominant region, enabling feedback stabilization. © 1998 American Institute of Physics.

Notes: The first measurements and numerical simulations of fusion neutrons from the gas–pusher interface of indirectly-driven inertial confinement fusion implosions have been performed using hydrogen-filled capsules made with a deuterated inner layer. Nonlinear saturation of the growth of hydrodynamic perturbations in high linear growth factor ((similar, equals)325) implosions was varied by adjusting the initial surface roughness of the capsule. The neutron yields are in quantitative agreement with the direct simulations of perturbation growth, and also with a linear mode superposition and saturation model including enhanced thermal loss in the mixed region. Neutron spectra from these capsules are broader than expected for the calculated ion temperatures, suggesting the presence of nonthermal broadening from mass motion during the fusion burn. © 1998 American Institute of Physics.

Notes: The effect of collisionality of ions on the formation of a positive sheath is investigated using a two-fluid model. It is the definition of the sheath edge that determines the sheath criterion. Bohm's sheath criterion is based on the collisionless sheath and a quasineutral presheath. When collisions of ions in the sheath or finite space charge of presheath are taken into account, a sheath criterion can also be obtained based on the boundary conditions chosen at the sheath edge. © 1998 American Institute of Physics.

Notes: Plasma confined in a magnetic dipole field is stabilized by the expansion of the magnetic flux. The stability of low beta electrostatic modes in a magnetic dipole field is examined when the distribution function is Maxwellian to lowest order. It is shown using a Nyquist analysis that for sufficiently gentle density and temperature gradients the configuration would be expected to be stable to both magnetohydrodynamic and collisionless interchange modes. Furthermore, it is shown that when it is stable to the interchange mode it is also stable to ion temperature gradient and collisionless trapped particle modes, as well as modes driven by parallel dynamics such as the "universal" instability. © 1998 American Institute of Physics.

Notes: In Heliotron E [K. Uo, Nucl. Fusion 25, 1243 (1985)] shifted-in vacuum magnetic field configuration, the q profile varies from just above 2 at the magnetic axis to 0.4 at the plasma edge. For low-β plasmas, resistive interchange modes are the dominant low-n instabilities at the plasma core. They saturate at low fluctuation levels. Above a threshold value, the ideal m/n=2/1 modes become unstable. They can be resonant or nonresonant modes depending on the value of q(0). In either case, their nonlinear evolution leads to a sudden crash of the pressure within the r/a=0.3 radius (sawtooth oscillation). When beta is increased further, the q=2 surface moves out of the plasma, and the ideal m/n=2/1 modes are effectively stabilized when q(0)〈1.85. As a result, the sawtooth oscillations are suppressed. © 1998 American Institute of Physics.