bluuebunny/crossref_metadata_2025 huggingface dataset:
Closed formula for the matrix elements of the volume operator in canonical quantum gravity
Authors: Thiemann T.
Published: July 2002

We derive a closed formula for the matrix elements of the volume operator for canonical Lorentzian quantum gravity in four space–time dimensions in the continuum in a spin-network basis. We also display a new technique of regularization which is state dependent but we are forced to it in order to maintain diffeomorphism covariance and in that sense it is natural. We arrive naturally at the expression for the volume operator as defined by Ashtekar and Lewandowski up to a state-independent factor.
Time-frequency transfer function calculus (symbolic calculus) of linear time-varying systems (linear operators) based on a generalized underspread theory
Authors: Matz Gerald , Hlawatsch Franz
Published: July 2002

We introduce a generalized concept of underspread linear time-varying systems (linear operators) which contains a previous definition as a special case. We show that an existing approximate transfer function calculus (symbolic calculus) can be extended to this wider and practically more relevant class of underspread operators. As a mathematical underpinning of this calculus, we establish explicit bounds on various error quantities associated with it. The transfer function calculus provides a theoretical basis for various methods recently proposed for nonstationary signal processing, and it has important implications in the theory of time-varying power spectra.
Solving Poisson’s equation with interior conditions
Authors: McCarthy J. E. , Yu. Backhaus E. , Fajans J.
Published: July 2002

We consider the problem of extending the solution of a particular two-dimensional Poisson equation to a larger domain. This problem is related to the problem of putting a non-neutral plasma into equilibrium by applying a suitable wall potential, and to similar problems in two-dimensional fluid dynamics. While one cannot always find an exact solution, one can always find an approximate solution if the plasma has no holes.
Classification and conformal symmetry in three-dimensional space–times
Authors: Hall G. S. , Capocci M. S.
Published: July 2002

Three-dimensional manifolds admitting Lorentz metrics are studied. The first part of the paper gives a classification of the Ricci and curvature tensors and also of the conformal (Schouten–Cotton–York) tensor. The second part of the paper investigates Killing and conformal symmetry and also the nature of the zeros of the associated vector fields. The maximum dimension of the Killing and conformal algebras is calculated. A theorem regarding the reduction of the conformal algebra to a Killing algebra of a conformally related metric is given.
On the theory of dynamic properties of semiquantum helium
Authors: Ignatyuk V. V. , Mryglod I. M. , Tokarchuk M. V.
Published: July 2002

A general theoretical approach is developed for describing the dynamic properties of semiquantum fluids on the basis of the nonequilibrium statistical operator technique. A set of equations of generalized hydrodynamics is derived and the particular case of thermo-viscoelastic model of a fluid is analyzed in details in the hydrodynamic limit. The case of intermediate and large values of the wave vector is also discussed. The Markov approximation for transport kernels is used to obtain a closed set of equations for dynamic correlation functions. The problem is considered in the context of relation with the experimental data on neutron scattering and the theoretical results known previously in the literature.
Convection rolls in a shallow cavity heated from a side
Authors: Wang Tzyy-Ming , Korpela Seppo A.
Published: July 2002

Longitudinal roll structure of convection in a shallow cavity heated from a side has been calculated by using pseudospectral approximations. A transient calculation of the oscillatory flow, which appears as a result of an instability of the base flow for low Prandtl number fluids, is seen to be caused by the interaction of two oppositely traveling waves. Finite-amplitude motions break the even symmetry of the streamlines and isotherms, but retain their shift-reflect symmetry. The energy transfer mechanisms are discussed.
Elevation solitary waves with surface tension
Authors: Vanden-Broeck Jean-Marc
Published: July 2002

Elevation solitary waves propagating at the surface of a fluid of finite depth are computed numerically by a boundary integral equation method. Both gravity and surface tension are included in the dynamic boundary condition. The solitary waves are approximated by long periodic waves whose wavelengths are about 100 times the depth of the fluid. Previous numerical and analytical results are confirmed and extended. For a given value of the Bond number 0<τ<1/3, there is a two-parameter family of waves with a train of ripples in the far field. It is shown that, for sufficiently small solitary waves, there are solutions for which the amplitude of the ripples vanish. These particular solutions form, for each value of 0<τ<1/3, a one-parameter family of solutions. Moreover they are accurately described by the classical solution of the Korteweg–de Vries equation.
On the solenoidality of the Lamb vector
Authors: Shtilman Leonid
Published: July 2002

The correlation between reduction of the nonlinearity and other characteristic quantities of turbulent flow is investigated numerically. It is shown in physical space that in the regions exhibiting strong depletion of nonlinearity, the enstrophy and the enstrophy production are large. In the same regions vorticity has a tendency to be perpendicular to the eigenvector of rate of strain corresponding to the smallest eigenvalue. No correlation has been found between reduction of nonlinearity and dissipation.
Measurement and prediction of the conditional variance in a turbulent reactive-scalar mixing layer
Authors: Li J. D. , Bilger R. W.
Published: July 2002

Equations for the second-order conditional moments of reactive scalars are derived. For one-step reaction with equal diffusivity these can be reduced to a single equation for the conditional variance, which is the same for all reactive species. The various terms in the equation have been modeled in light of the experimental data for a turbulent reactive-scalar mixing layer. In comparison with conventional second-order moment closure the conditional means do not vary with the cross-stream position, the turbulent flux in the cross-stream direction is negligible while the source term needs special attention. Experimental results of the conditional variance at different points across the mixing layer and at various streamwise locations are presented. At each streamwise location the data in general collapse onto each other although the scatter is large. The modeled equations have been solved numerically and are compared with the experimental data. The prediction generally agrees with the data. Two models have been used for the conditional conserved scalar dissipation. One model assumes that the conditional scalar dissipation equals the unconditional one and the other is derived from a mapping closure. Both models give almost identical results for the conditional means and only a small difference for the conditional variance.
Multisolitary plasma surface waves in the presence of an external pump field
Authors: Gradov O. M. , Stenflo L.
Published: July 2002

It is shown that an external electromagnetic pump wave, which interacts with the electrostatic surface oscillations in a semi-infinite plasma with a sharp boundary, can excite a sequence of solitary waves on the plasma surface.
Dissipative trapped electron modes in l=2 torsatrons
Authors: Dominguez N. , Carreras B. A. , Lynch V. E. , Diamond P. H.
Published: July 2002

Trapped electron modes could play an important role in enhancing losses in a toroidal confinement device. However, no direct evidence of these instabilities has been found in such devices. The dissipative trapped electron modes [Sov. Phys. Dokl. 14, 470 (1969)] in l=2 torsatrons using the high-n ballooning formalism and considering the full three-dimensional geometry are studied. Using a perturbative analysis, it is found that there are toroidally localized as well as helically localized eigenfunctions in the ballooning space for these nonaxisymmetric devices. The helically localized eigenfunctions give the largest growth rates. It is shown that the helical symmetric limit gives a very good description of the helically induced modes for stellarators such as the Advanced Toroidal Facility [Fusion Technol. 10, 179 (1986)]. In this limit, the criteria for the density gradient and the temperature gradient for the existence of the dissipative trapped electron modes in l=2 stellarators are found. Also, it is found that the radial width of the unstable modes can be very broad, and therefore their effects could possibly be detected in future experimental studies with density control.
Impurity and neutral effects on the dissipative drift wave in tokamak edge plasmas
Authors: Zhang Y. Z. , Mahajan S. M.
Published: July 2002

Possible destabilizing mechanisms for the linear electrostatic dissipative drift waves (in tokamak edge plasmas) are investigated in slab geometry. The effects of processes such as ionization, charge exchange, radiation, and rippling are examined. In particular, the impurity condensation associated with radiation cooling is evaluated appropriately for the drift wave ordering, which is found to be an important driving mechanism in contrast to the results of earlier studies [R. J. Thayer and P. H. Diamond, Phys. Rev. Lett. 65, 2784 (1990)]. It is also shown that the role of ionization is quite complicated, and depends strongly on the manner in which the equilibrium is achieved. The linear eigenmode equation is studied both analytically and numerically. For the range of parameters relevant to TEXT tokamak [K. W. Gentle, Nucl. Fusion Technol. 1, 479 (1981)], both the charge exchange and the rippling effect are found to be unimportant for instability.
Nonsingular linear theory for stimulated microwave emission in crossed-field devices
Authors: Riyopoulos Spilios
Published: July 2002

The small signal stability of crossed-field devices fed by a thin electron beam is analyzed. The situation differs from diocotron modes in that the interaction cavity supports slow wave eigenmodes in vacuum. The rippling of the beam causes a modification of the vacuum dispersion relation and mode profiles. The growth rate is found by equating the rate of change of the power flux with the fast scale averaged wave–particle energy exchange rate. The radio frequency (rf) power flow including the energy circulating in the anode structure is related to the wave amplitude via the interaction impedance. The singularities at resonance, the trademark of any linear theory, are avoided by following the particle guiding center (GC) orbits in reference frame with the wave synchronous. The small signal gain is found by expansion in powers of the rf amplitude. A finite linear growth results, even for symmetric particle excursions, due to the self-field of the rippled beam. Near resonance the growth rate is independent of the detuning between the phase and drift velocities. Higher-order contributions to the instability are caused by the nonlinear bunching of the GC distribution in space and are symmetric relative to resonance. Symmetric frequency response is a unique feature of crossed-field devices (CFD’s) opposed to the antisymmetric growth characterizing other ‘‘unbound electron’’ devices [gyrotrons, free-electron lasers (FEL’s), traveling-wave tubes (TWT’s)]. The growth rate goes over to the diocotron growth when all the impedance comes from the rippled beam (i.e., smooth anode at infinite distance). The perturbed mode profiles are nonsingular; the profile singularities of standard linear theories reflect the singularities of the particle orbits at resonance.
Coupled tearing modes in plasmas with differential rotation
Authors: Dewar R. L. , Persson M.
Published: July 2002

The global asymptotic matching equations for multiple coupled resistive modes of arbitrary parity in a cylindrical plasma are derived. Three different variational principles are given for the outer region matching data, while the inner region analysis features a careful treatment of the symmetry-breaking effect of a gradient in the equilibrium current for a zero-β slab model. It is concluded that the usual constant-ψ result remains valid and constrains the matrix matching formalism. The dispersion relation is compared with initial value calculations of a double tearing mode when there are small relative rotation velocities between the rational surfaces. In treating differential rotation within the asymptotic matching formalism, flow is ignored in the outer region and is assumed to affect the inner response solely through a Doppler shift. It is shown that the relative rotation can have a strong stabilizing effect by making all but one rational surface effectively ideal.
Ion-streaming instabilities in a thermal barrier
Authors: Tsang Kang T.
Published: July 2002

The ion distribution function in a thermal barrier is modeled by counter-streaming Maxwellian distribution. Its stability with respect to parallel propagating electrostatic and electromagnetic modes is investigated both analytically and numerically. It is found that the electrostatic mode is stable if Te/Ti ≲3.5, and the electromagnetic mode is stable if the streaming velocity is less than the Alfvén speed. The latter condition implies the barrier potential must be less than the average magnetic energy per particle.
Thermal barrier potential of a tandem mirror
Authors: Katanuma I. , Kiwamoto Y. , Ishii K. , Miyoshi S.
Published: July 2002

The relation between the electrostatic potential and the low energy electron density under electron cyclotron resonance heating (ECRH) in the thermal barrier of a tandem mirror is investigated analytically and numerically. The distribution function of mirror trapped electrons at low energy is found to stretch out in the perpendicular direction to the magnetic field and to be well approximated by a bi-Maxwellian (T⊥≥T∥) rather than by a Maxwellian. Under this approximation it is found analytically that the conventionally used Boltzmann formula derived from the full Maxwellian plasma for the barrier depth is modified to another expression including the ratio between T⊥ and Te (central cell electron temperature). The bounce-averaged Fokker–Planck simulations show that T⊥/Te itself is a function of the potential depth and that the conventional formula is modified to q(φb−φe)=Te ln(αnc/nb) with α=1.5–1.8 depending on ECRH power. This expression agrees well with experimental results on GAMMA 10 [Phys. Rev. Lett. 55, 939 (1985)].
Magnetic pumping by magnetosonic waves in the presence of noncompressive electromagnetic fluctuations
Authors: Borovsky Joseph E.
Published: July 2002

In a quiescent collisionless plasma the motion of charged particles within a magnetosonic wave is reversible, but in the presence of electromagnetic plasma waves that pitch-angle scatter the particles, this is no longer true, and the plasma may be magnetically pumped by the magnetosonic wave, extracting energy from the wave. The particles that are energized are in resonance with the catalyst electromagnetic waves but gain their energy from the magnetosonic wave. To study this mechanism, three types of numerical simulations are used. In the first type, the magnetic pumping of an element of plasma is numerically simulated in detail by following the magnetosonic-wave-driven convection of the particle distribution through pitch-angle/momentum space and by computationally solving a pitch-angle diffusion equation for the distribution-function evolution under the action of the electromagnetic fluctuations. It is found that the magnetosonic-wave energy is transferred predominantly to high-energy particles. In the second type of simulation, the absorption of magnetosonic waves by a semi-infinite plasma and the resulting plasma heating and expansion are followed. It is found that magnetosonic waves produce a hot surface layer on the plasma that is ablated by the wave energy. In the third type of simulation, a Fokker–Planck equation for the magnetic-pumping process is numerically solved. It is found that this momentum-diffusion description is a satisfactory representation of magnetic pumping by small-amplitude magnetosonic waves.
Linear stability of force-free equilibria
Authors: Jensen Torkil H. , Chu Ming-Sheng , Greene John M.
Published: July 2002

A sufficient stability criterion, applicable to all force-free equilibria of magnetized plasmas surrounded by a rigid conducting shell, is found. Magnetic field lines may penetrate the shell, vacuum regions may exist inside the shell, and no assumptions on topology—or symmetry—are required. Stability is determined from the sign of the minimum of a functional. This minimum value depends on certain constraints that are adjustable. In one extreme of the range of adjustment, the known stability criterion of ideal magnetohydrodynamics (MHD) is recovered; in the other extreme the criterion approaches that of Taylor equilibria. In this range the constraints relevant for tearing modes are identified. A procedure for evaluating the minimum of the functional, believed suitable for numerical implementation, is given.
Fokker–Planck calculation of hot electron buildup in the thermal barrier region of a tandem mirror
Authors: Katanuma I. , Kiwamoto Y. , Sawada K. , Miyoshi S.
Published: July 2002

The hot electron buildup by second harmonic electron cyclotron resonance heating in the thermal barrier region of a tandem mirror has been studied by using a Fokker–Planck code with a self-consistent potential profile taken into account. It has been found that the evolution of the hot electron population and the potential profile consists of two phases. In the first phase the rf diffusion is dominant and a quick increase in both the hot electron density and the mean energy is observed. No further increase in the mean energy is observed thereafter. The potential is deepest during the first phase. The second phase starts in the mean free time of the pitch angle scattering of hot electrons on cold electrons and ions. In this phase the hot electron population increases at the rate of the pitch angle scattering. The potential dip becomes shallow because of the accumulation of pitch-angle-scattered passing ions.
On the existence of uniform momentum zones in a turbulent boundary layer
Authors: Meinhart Carl D. , Adrian Ronald J.
Published: July 2002

Instantaneous velocity fields in the x-y plane of a zero pressure gradient turbulent boundary layer are measured using particle image velocimetry. It is found that there exist random, time-varying zones in the u-ν fields in which the streamwise momentum is remarkably uniform. The largest dimension of a typical zone is proportional to the boundary layer thickness. The zone closest to the wall contains viscous-inertial inclined structures similar to those found in low Reynolds number wall turbulence. A second zone is located above the wall zone in a region that coincides roughly with the logarithmic layer. The wake region of the boundary layer contains a complicated, time-varying pattern of several nearly-constant-momentum zones. The zones are separated from each other and from the free stream by thin viscous shear layers that contain concentrations of spanwise vorticity.
Characteristics of a young turbulent spot
Authors: Singer Bart A.
Published: July 2002

A young turbulent spot develops in a spatially developing direct numerical simulation of an incompressible constant-pressure boundary layer exposed to a strong localized disturbance. The data are analyzed to determine both the gross characteristics of the spot and the substructures that develop inside the spot. The calculations confirm that hairpinlike vortices are added near the trailing edge of the spot. However, the computations also suggest that the importance of large spanwise vorticity structures may have been overestimated by previous experiments. The current simulation data reveal that streamwise vortices are more intense and more numerous. In addition, the streamwise vortices provide at least one route for the entrainment of near-wall fluid into the turbulent spot near the leading edge.
On the stability of an axisymmetric rotating flow in a pipe
Authors: Wang S. , Rusak Z.
Published: July 2002

The linear stability of an inviscid, axisymmetric and rotating columnar flow in a finite length pipe is studied. A well posed model of the unsteady motion of swirling flows with compatible boundary conditions that may reflect the physical situation is formulated. A linearized set of equations for the development of infinitesimal axially-symmetric disturbances imposed on a base rotating columnar flow is derived. Then, a general mode of axisymmetric disturbances, that is not limited to the axial-Fourier mode, is introduced and an eigenvalue problem is obtained. Benjamin’s critical state concept is extended to the case of a rotating flow in a finite length pipe. It is found that a neutral mode of disturbance exists at the critical state. In the case of a solid body rotating flow with a uniform axial velocity component, analytical solution of the eigenvalue problem is found. It is demonstrated that the flow changes its stability characteristics as the swirl changes around the critical level. When the flow is supercritical an asymptotically stable mode is found, and when the flow is subcritical, an unstable mode of disturbance may develop. This result cannot be predicted by Rayleigh’s classical stability criterion. In the case of a general columnar swirling flow in a pipe, the asymptotic solution of the eigenvalue problem around the critical state is also studied. It is shown that the critical swirl ratio is a point of exchange of stability for any swirling flow in a finite length pipe. This result reveals an unknown instability mechanism of swirling flows that cannot be detected by previous stability analyses and sheds new light on the relation between stability of vortex flows and the vortex breakdown phenomenon.
The Karhunen–Loéve decomposition of minimal channel flow
Authors: Webber G. A. , Handler R. A. , Sirovich L.
Published: July 2002

Minimal channel flow is analyzed by means of the Karhunen–Loéve (KL) decomposition. It is shown that the most energetic modes are streamwise rollers followed by outward tilted quasi-streamwise vortices. Both of these mode types have a strong similarity to structures seen in physical experiments. Temporal plots of roll energy, propagating energy, bulk velocity, and representational entropy have been obtained. Study of the evolution of these variables shows a consistent pattern of growth and decay in which entropy plays a key role in describing the events in the turbulent process. The roll and propagating modes are also shown to make independent contributions to the Reynolds stress with the roll modes dominating the profile near the walls and the propagating modes having larger values towards the channel center. A comparison of the KL dimension of this flow and a full channel flow shows that the dimension scales with box size, i.e., it confirms the assertion that dimension is an extensive variable.
Hamilton’s principle for quasigeostrophic motion
Authors: Holm Darryl D. , Zeitlin Vladimir
Published: July 2002

We show that the equation of quasigeostrophic (QG) potential vorticity conservation in geophysical fluid dynamics follows from Hamilton’s principle for stationary variations of an action for geodesic motion in the f-plane case or its prolongation in the β-plane case. This implies a new momentum equation and an associated Kelvin circulation theorem for QG motion. We treat the barotropic and two-layer baroclinic cases, as well as the continuously stratified case.
Stabilization of the hydrodynamic flame instability by a weak shock
Authors: Bychkov Vitaliy V.
Published: July 2002

The problem of stabilization of the hydrodynamic flame instability due to collision of a flame with a weak shock is revised. It is shown that correct treatment of this problem leads to results different from the Markstein solution [G. H. Markstein, Nonsteady Flame Propagation (Pergamon, Oxford, 1964)]. It is obtained that depending on the shock intensity a flame-shock collision may lead to temporary reduction of the perturbation amplitude at the flame front, to complete suppression of initial perturbations, or to inversion of the flame shape. Scalings for the shock intensity leading to stabilization or destabilization of a flame front are obtained.
Steep nonlinear global modes in spatially developing media
Authors: Pier Benoı̂t , Huerre Patrick , Chomaz Jean-Marc , Couairon Arnaud
Published: July 2002

A new frequency selection criterion valid in the fully nonlinear regime is presented for extended oscillating states in spatially developing media. The spatial structure and frequency of these modes are dominated by the existence of a sharp front connecting linear to nonlinear regions. A new type of fully nonlinear time harmonic solutions called steep global modes is identified in the context of the supercritical complex Ginzburg–Landau equation with slowly spatially varying coefficients. A similar formulation is likely to be applicable to fully nonlinear synchronized global oscillations in spatially developing free shear flows.
Effects of horizontal vibration on hopper flows of granular materials
Authors: Hunt M. L. , Weathers R. C. , Lee A. T. , Brennen C. E. , Wassgren C. R.
Published: July 2002

The current experiments investigate the discharge of glass spheres in a planar wedge-shaped hopper (45° sidewalls) that is vibrated horizontally. When the hopper is discharged without vibration, the discharge occurs as a funnel flow, with the material exiting the central region of the hopper and stagnant material along the sides. With horizontal vibration, the discharge rate increases with the velocity of vibration as compared with the discharge rate without vibration. For a certain range of acceleration parameters (20–35 Hz and accelerations greater than about 1 g), the discharge of the material occurs in an inverted-funnel pattern, with the material along the sides exiting first, followed by the material in the core; the free surface shows a peak at the center of the hopper with the free surface particles avalanching from the center toward the sides. During the deceleration phase of a vibration cycle, particles all along the trailing or low-pressure wall separate from the surface and fall under gravity for a short period before reconnecting the hopper. For lower frequencies (5 and 10 Hz), the free surface remains horizontal and the material appears to discharge uniformly from the hopper.
Characterization of laser-produced plasmas by ultraviolet Thomson scattering
Authors: La Fontaine B. , Baldis H. A. , Villeneuve D. M. , Dunn J. , Enright G. D. , Kieffer J. C. , Pépin H. , Rosen M. D. , Matthews D. L. , Maxon S.
Published: July 2002

Space–time-resolved Thomson scattering was used to characterize the electron and ion temperatures in laser produced plasmas of various atomic numbers (Z=6, 13, 32, 73, 92). A Nd:glass laser with intensity between 1013 and 5×1014 W/cm2 was used to produce plasmas of relevance to laser fusion and x-ray laser studies. A comparison of the electron temperature and density deduced from Thomson scattering, x-ray spectroscopy, and lasnex hydrocode simulations is presented.
Broken symmetry in ideal magnetohydrodynamic turbulence
Authors: Shebalin John V.
Published: July 2002

A numerical study of the long-time evolution of a number of cases of inviscid, isotropic, incompressible, three-dimensional fluid, and magnetofluid turbulence has been completed. The results confirm that ideal magnetohydrodynamic turbulence is nonergodic if there is no external magnetic field present. This is due essentially to a canonical symmetry being broken in an arbitrary dynamical representation. The broken symmetry manifests itself as a coherent structure, i.e., a nonzero time-averaged part of the turbulent magnetic field. The coherent structure is observed, in one case, to contain about 18% of the total energy.
Fast wave poloidal flow generation in a plasma
Authors: Wang C. Y. , Jaeger E. F. , Batchelor D. B. , Sidikman K. L.
Published: July 2002

Fast wave poloidal flow generation at the plasma edge of a tokamak is studied with a one-dimensional slab model. In the absence of mode conversion, the poloidal flow can be generated by a spatial change of plasma velocity and current density profiles due to strong minority ion power absorption at the minority ion cyclotron resonance. The electromagnetic force plays a more important role in the flow generation than does the plasma Reynolds stress. In the presence of mode conversion, the flow is mainly generated by interference between the long-wavelength transmitted fast wave and the short-wavelength ion Bernstein wave (IBW) from mode conversion. Flow shear generated in the presence of mode conversion varies spatially with a scale length similar to the IBW wavelength. With mode conversion, the plasma Reynolds stress becomes more important in the flow shear generation than the electromagnetic force. For both cases, the plasma Reynolds stress and the electromagnetic force are out of phase, so that the resultant flow shear is smaller than the larger of the two. The short scale length flow shear enhances the turbulence stabilization.
Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain
Authors: Lindl John
Published: July 2002

Inertial confinement fusion (ICF) is an approach to fusion that relies on the inertia of the fuel mass to provide confinement. To achieve conditions under which inertial confinement is sufficient for efficient thermonuclear burn, a capsule (generally a spherical shell) containing thermonuclear fuel is compressed in an implosion process to conditions of high density and temperature. ICF capsules rely on either electron conduction (direct drive) or x rays (indirect drive) for energy transport to drive an implosion. In direct drive, the laser beams (or charged particle beams) are aimed directly at a target. The laser energy is transferred to electrons by means of inverse bremsstrahlung or a variety of plasma collective processes. In indirect drive, the driver energy (from laser beams or ion beams) is first absorbed in a high-Z enclosure (a hohlraum), which surrounds the capsule. The material heated by the driver emits x rays, which drive the capsule implosion. For optimally designed targets, 70%–80% of the driver energy can be converted to x rays. The optimal hohlraum geometry depends on the driver. Because of relaxed requirements on laser beam uniformity, and reduced sensitivity to hydrodynamic instabilities, the U.S. ICF Program has concentrated most of its effort since 1976 on the x-ray or indirect-drive approach to ICF. As a result of years of experiments and modeling, we are building an increasingly strong case for achieving ignition by indirect drive on the proposed National Ignition Facility (NIF).

The ignition target requirements for hohlraum energetics, radiation symmetry, hydrodynamic instabilities and mix, laser plasma interaction, pulse shaping, and ignition requirements are all consistent with experiments. The NIF laser design, at 1.8 MJ and 500 TW, has the margin to cover uncertainties in the baseline ignition targets. In addition, data from the NIF will provide a solid database for ion-beam-driven hohlraums being considered for future energy applications. In this paper we analyze the requirements for indirect drive ICF and review the theoretical and experimental basis for these requirements. Although significant parts of the discussion apply to both direct and indirect drive, the principal focus is on indirect drive.
Coherent structures and turbulent cascades in two-dimensional incompressible magnetohydrodynamic turbulence
Authors: Kinney R. , McWilliams J. C. , Tajima T.
Published: July 2002

Numerical solutions of decaying two-dimensional incompressible magnetohydrodynamic turbulence reach a long-lived self-similar state which is described in terms of a turbulent enstrophy cascade. The ratio of kinetic to magnetic enstrophy remains approximately constant, while the ratio of energies decreases steadily. Although the enstrophy is not an inviscid invariant, the rates of enstrophy production, dissipation, and conversion from magnetic to kinetic enstrophy are very evenly balanced, resulting in smooth power law decay. Energy spectra have a k−3/2 dependence at early times, but steepen to k−5/2. Local alignment of the intermediate and small-scale fields grows, but global correlation coefficients do not. The spatial kurtosis of current grows and is always greater than the vorticity kurtosis. Axisymmetric monopole patterns in the current (magnetic vortices) are dominant structures; they typically have a weaker concentric, nonmonotonic vorticity component. Fast reconnection or coalescence events occur on advective and Alfvén time scales between close vortices of like sign. Current sheets created during these coalescence events are local sites of enstrophy production, conversion, and dissipation. The number of vortices decreases until the fluid reaches a magnetic dipole as its nonlinear evolutionary end-state.
Dynamics and stability of a stagnating hot spot
Authors: Murakami M. , Shimoide M. , Nishihara K.
Published: July 2002

A simple model of a hot spot implosion is developed, where the key parameters are the areal density ρsRs, the central temperature Ts, and the implosion velocity v∞. The dynamics is dominated by the mechanical compressing work and the thermal conduction loss. A new type of self-similar solution is then found, describing the fluid motion in terms of ρsRs/T2s and v∞/√Ts. A scaling law for the minimum implosion velocity v∞* to reach the spark point (ρsRs,Ts) is derived: v∞*∝Ts5/2/ρsRs. The Rayleigh–Taylor (RT) instability in the stagnation phase is evaluated using the self-consistent spatial profile with density gradients, which is attributed to the thermal conduction. Substantial reduction of the RT growth is then found compared with the previous work without density gradients [Hattori et al., Phys. Fluids 29, 1719 (1986)].
Cryogenic deuterium target experiments with the GEKKO XII, green laser system
Authors: Tanaka Kazuo A. , Yamanaka Tatsuhiko , Nishihara Katsunobu , Norimatsu Takayoshi , Miyanaga Noriaki , Shiraga Hiroyuki , Nakai Mitsuo , Kitagawa Yoneyoshi , Kodama Ryosuke , Kanabe Tadashi , Azechi Hiroshi , Heya Manabu , Jitsuno Takahisa , Kado Masataka , Mima Kunioki , Nakatsuka Masahiro , Nishiguchi Akio , Takabe Hideaki , Takagi Masaru , Tsubakimoto Kouji , Tsukamoto Masahiro , Kato Yoshiaki , Izawa Yasukazu , Nakai Sadao
Published: July 2002

A series of experiments were conducted using cryogenic deuterium targets to study fundamental physics and implosion dynamics with the GEKKO XII glass laser system [IEEE J. Quantum Electron. QE-17, 1639 (1981)]. Preheat sources were found to be due to a shock wave and hot electrons. A new method to measure the fuel ρR using proton spectra was employed. Measured in detail were the implosion dynamics of cryogenic deuterium foam with a plastic ablator and a CH shell with a controlled pressure of deuterium gas targets. Under current experimental conditions sources of nonuniformity were discussed in terms of Rayleigh–Taylor instability.
A threshold for excitation of neoclassical tearing modes
Authors: Gorelenkov N. N. , Budny R. V. , Chang Z. , Gorelenkova M. V. , Zakharov L. E.
Published: July 2002

Stability criterion for neoclassical tearing modes is obtained from the drift kinetic equation. A finite amplitude of a magnetic island is required for mode excitation. The threshold is determined by the ratio of the transversal and the parallel transport near the island when the flattening of the pressure profile eliminates the bootstrap current. A number of supershots from the database of the Tokamak Fusion Test Reactor (TFTR) [D. J. Grove and D. M. Meade, Nucl. Fusion 25, 1167 (1985)] are compared with the theory. In cases where the modes were observed in experiment the stability criterion was violated.
Shear flow vortices in magnetospheric plasmas
Authors: Rankin R. , Frycz P. , Samson J. C. , Tikhonchuk V. T.
Published: July 2002

Theory and numerical simulations are used to investigate the nonlinear evolution of vortices generated by the Kelvin–Helmholtz (KH) instability of sheared plasma flows in the Earth’s magnetosphere. The extent of broadening of the shear flow, and the energy and enstrophy exchange between the shear flow and KH vortices, is characterized. A new stationary vortex street solution is found, and two distinct phases of the nonlinear dynamics are identified. The first involves a transient phase in which burst-like pulsations of the flow lead to a rapid dissipation of enstrophy. After the transient phase, an asymptotic state is reached that corresponds to a periodic chain of pairs of monopolar vortices. The consequences of the model results for the dynamics of field line resonances (FLRs) in the Earth’s magnetosphere are discussed, and it is shown, in particular, that broadening of the flow correlates well with observations of periodic reforming of FLR structures.
Motion of ions influenced by enhanced Alfvén waves
Authors: Wu C. S. , Yoon Peter H. , Chao J. K.
Published: July 2002

In this paper we discuss the dynamics of an ion interacting with large-amplitude Alfvén waves. The objective of the present analysis is to attain an in-depth understanding of the ion-pickup process which has been extensively studied in the literature by means of both quasilinear theory and numerical simulations. In general, results from self-consistent simulations provide a more complete picture of the ion pickup process, but details of the pickup process are not easily comprehended on the basis of these results. For this reason, the present study is carried out in which a test particle approach is used. It is found that for moderately large-amplitude Alfvén waves, an approximate analytical solution for the ion equation of motion can be obtained. This solution clarifies a number of basic issues such as (1) whether the cyclotron resonance is a necessary condition for the pickup to occur, (2) what is the role of initial ion phase space position on subsequent pitch angle scattering, and (3) how the wave amplitude affects the maximum velocity that an ion can gain along the direction of the ambient magnetic field during the pickup process.
Stability of global drift-kinetic Alfvén eigenmodes in DIII-D
Authors: Jaun A. , Vaclavik J. , Villard L.
Published: July 2002

Global Alfvén eigenmodes are studied using two different models for the plasma and the results compared with the instability threshold measured experimentally. Fluid-resistive models predict that continuum damped toroidicity induced Alfvén modes (TAE) are formed in the frequency range of the experimental instabilities, but using realistic values of the resistivity makes a stability analysis impossible for computational reasons. The kinetic plasma model solves this problem by taking into account the ion Larmor radius and the resonant Landau interactions between the particles and the wavefield. As a consequence drift-kinetic Alfvén eigenmodes (DKAE) are created by toroidal coupling between the global TAE wavefield, the mode converted kinetic Alfvén, ion-acoustic and drift waves. The power transfers between the wave and the particles show that the drift character of the wavefield in the core destabilizes DKAE modes through resonant interactions with the fast beam ions. The predicted beam pressure instability threshold is in agreement with the one measured experimentally.
Inertial confinement fusion ignition criteria, critical profiles, and burn wave propagation using self-similar solutions
Authors: Kishony Roy , Waxman Eli , Shvarts Dov
Published: July 2002

The ignition conditions, under which a thermonuclear burn wave propagates from an initial hot spot, and the characteristics of the propagating burn wave are investigated using a set of self-similar solutions. Although the self-similar solutions exist only for external density profile that decreases as ρout∝r−1, they are shown to provide natural ignition criteria and critical profiles for more general density profiles. The concept of working lines (WLs), attractors of trajectories in the ρR−T plane of propagating burn waves, is introduced for density profiles ρout∝r−ω. The WLs are found to be close and almost parallel to the ignition line (IL). The distance of the WLs from the IL is given analytically and shown to depend on all the physical processes involved. The spatial profiles of a burn wave propagating along the WLs are shown to be closely related to the self-similar critical profiles.
Aspect ratio scaling of toroidal plasma equilibria and the tokamak bootstrap effect
Authors: Weening R. H.
Published: July 2002

The aspect ratio scaling of toroidal plasma equilibria is examined using a parametrization of an exact Solov’ev solution to the Grad–Shafranov equation in Boozer coordinates. The equilibrium analysis suggests that simultaneous enhancements in magnetohydrodynamic (MHD) stability and the bootstrap effect are possible in tight aspect ratio (A→1) tokamaks. The fundamental physical mechanism causing the enhancements is shown to be the natural increase of the MHD safety factor q in tight aspect ratio toroidal geometries. The results of the scaling model suggest that the lowest bootstrap current fractions are obtained in tokamaks with aspect ratios A≈3. It is also shown that a tight aspect ratio bootstrapped tokamak can be a weakly paramagnetic device.
Two-dimensional effects in plasma radiation fronts and radiation front jumps in tokamak divertor plasmas
Authors: Krasheninnikov S. I.
Published: July 2002

The impact of two-dimensional (2-D) effects of energy transport on impurity radiation fronts in a tokamak divertor plasma is considered. It is shown that 2-D effects significantly alter both the physics of the fronts and the radiation loss from the divertor plasma, and may explain the experimental observations of impurity radiation region jumps from the target to the X point and easier access to a detached divertor regime in “vertical” target geometry in comparison with the “horizontal” case.
Large-scale gyrokinetic turbulence simulations: Effects of profile variation
Authors: Parker Scott E. , Kim Charlson , Chen Yang
Published: July 2002

Two common computational domains used in gyrokinetic turbulence simulations are a local flux-tube and a global whole plasma volume. The effect of a radially varying pressure gradient is found to explain some of the qualitative differences between these two models. It is shown that a coherent purely radial mode is the result of profile variation. In addition, as profile variation is increased, there is a fairly sudden transition to much lower levels of heat flux. This may explain lower values found in past global simulations. The self-generated purely radial electrostatic potential is found to be 180° out of phase with the flux-surface-averaged ion temperature. A theoretical relation between these two quantities is derived by relating the E×B nonlinearities for ion density and temperature for purely radial modes. This relation is used to explain the various radial mode shapes. Extending these results, a possible scheme is explored to reduce the heat flux by adding a ripple to the ion temperature profile. It may be possible to achieve similar results experimentally using ion cyclotron resonance heating. Finally, simulation results show the additional stabilizing effect of equilibrium Er shear from profile variation in the radial force balance equation.
Full-wave calculation of sheared poloidal flow driven by high-harmonic ion Bernstein waves in tokamak plasmas
Authors: Jaeger E. F. , Berry L. A. , Batchelor D. B.
Published: July 2002

A full-wave, one-dimensional spectral model is developed to study sheared poloidal flow driven by high-harmonic ion Bernstein waves (IBWs) in tokamak plasmas. The local plasma conductivity is corrected to lowest order in ρ/L where ρ is the ion Larmor radius and L is the equilibrium scale length. This correction takes into account gradients in equilibrium quantities and is necessary for conservation of energy. It is equivalent to the “odd-order derivative” terms in finite difference models. No assumption is made regarding the smallness of the ion Larmor radius relative to wavelength, and results are applicable to all orders in k⊥ρ where k⊥ is the perpendicular wave number. Previous numerical results for flow drive have relied on expansions in k⊥ρ, and are thus limited to cyclotron harmonics of two and below. In this article, we consider higher-harmonic cases corresponding to recent IBW flow drive experiments on the Tokamak Fusion Test Reactor [B. P. LeBlanc, R. E. Bell, S. Bernabei et al., Phys. Rev. Lett. 82, 331 (1999)] and the Frascati Tokamak Upgrade [R. Cesario, C. Castaldo, V. Pericoli-Ridolfini et al., “Recent Results of the Ion Bernstein Wave Heating Experiment on FTU,” in Proceedings of the 13th Topical Conference on Radio Frequency Power in Plasmas, 1999, Annapolis, MD, edited by S. Bernabei and F. Paoletti (American Institute of Physics, New York, 1999), p. 100]. In these cases, a directly launched high-harmonic IBW is used to drive poloidal flow near the fourth- and fifth-harmonic ion cyclotron layers. Other applications include high-harmonic fast wave heating in low aspect ratio tokamaks such as the National Spherical Torus Experiment [S. M. Kaye, M. Ono, Y.-K. M. Peng et al., Fusion Technol. 36, 16 (1999)].
Neutral bremsstrahlung measurement in an atmospheric-pressure radio frequency discharge
Authors: Park Jaeyoung , Henins Ivars , Herrmann Hans W. , Selwyn Gary S.
Published: July 2002

Neutral bremsstrahlung emission spectrum is measured in an atmospheric-pressure radio frequency (rf) capacitive discharge for a gas mixture of helium (99.5%) and oxygen (0.5%) using a high resolution triple monochromator between 450 and 1000 nm. Good agreement is obtained for spectral variation and absolute intensity between the observed neutral bremsstrahlung and theoretical emissivity calculated using electron–neutral momentum cross sections. Based on a theoretical fitting, the discharge is characterized by a time averaged electron density of 2.9×1011 cm−3 and an electron temperature of 1.9 eV for an input power density of 28 W/cm3.
Super-gain AlGaAs/GaAs heterojunction bipolar transistors using an emitter edge-thinning design
Authors: Lin Hao-Hsiung , Lee Si-Chen
Published: July 2002

A novel emitter edge-thinning structure was adopted for Npn Al0.5Ga0.5As/GaAs single heterojunction bipolar transistors grown by liquid phase epitaxy. In this structure, the emitter edge was etched down to approximately 0.1 μm thick such that the surface and emitter-base junction depletion regions could touch each other. As a result, the current is blocked from the emitter periphery and the surface leakage current is reduced which improves the current gain especially at low operating current. The best device thus obtained shows a common emitter current gain of 12 500 at a collector current of 50 mA which is the highest gain reported to date for the heterojunction bipolar transistors. The current gain characteristics were indeed improved especially at a collector current below 10 μA.
Optical and electrochemical properties of CuInSe2 and CuInS2-CuInSe2 alloys
Authors: Neff H. , Lange P. , Fearheiley M. L. , Bachmann K. J.
Published: July 2002

The fundamental optical transitions in single crystals of CuInS2xSe2−2x alloys have been studied by electrolyte electroreflectance (EER) spectroscopy. The band gap of the alloys increases nonlinearly with increasing sulphur content corresponding to a bowing parameter 0.14. The flatband potential derived from the EER spectra is in excellent agreement with differential capacitance measurements and determined as −0.350 V versus the saturated calomel electrode. CuInS2xSe2−2x liquid junction solar cells are reported that exhibit a long wavelength cutoff in the spectral response matching the EER data.