bluuebunny/crossref_metadata_2025 huggingface dataset:
Canonical general relativity: The diffeomorphism constraints and spatial frame transformations
Authors: Clayton M. A.
Published: July 2002

Einstein’s general relativity with both metric and vielbein treated as independent fields is considered, demonstrating the existence of a consistent variational principle and deriving a Hamiltonian formalism that treats the spatial metric and spatial vielbein as canonical coordinates. This results in a Hamiltonian in standard form that consists of Hamiltonian and momentum constraints as well as constraints that generate spatial frame transformations—all appearing as primary, first class constraints on phase space. The formalism encompasses the standard coordinate frame and vielbein approaches to general relativity, and the constraint algebra derived herein reproduces known results in either limit.
Towards a classification of Euler–Kirchhoff filaments
Authors: Nizette Michel , Goriely Alain
Published: July 2002

Euler–Kirchhoff filaments are solutions of the static Kirchhoff equations for elastic rods with circular cross sections. These equations are known to be formally equivalent to the Euler equations for spinning tops. This equivalence is used to provide a classification of the different shapes a filament can assume. Explicit formulas for the different possible configurations and specific results for interesting particular cases are given. In particular, conditions for which the filament has points of self-intersection, self-tangency, vanishing curvature or when it is closed or localized in space are provided. The average properties of generic filaments are also studied. They are shown to be equivalent to helical filaments on long length scales.
Finite-band solutions of the classical Boussinesq–Burgers equations
Authors: Geng Xianguo , Wu Yongtang
Published: July 2002

The classical Boussinesq–Burgers hierarchy is decomposed into two systems of solvable ordinary differential equations with the help of the Lax representations of stationary evolution equations, from which the finite-band solutions of the higher-order classical Boussinesq–Burgers equations are obtained.
Radial conformal motions in Minkowski space–time
Authors: Herrero Alicia , Morales Juan Antonio
Published: July 2002

A study of radial conformal Killing fields (RCKF) in Minkowski space–time is carried out, which leads to their classification into three disjointed classes. Their integral curves are straight or hyperbolic lines admitting orthogonal surfaces of constant curvature, whose sign is related to the causal character of the field. Otherwise, the kinematic properties of the timelike RCKF are given and their applications in kinematic cosmology is discussed.
Gravitational waves in vacuum spacetimes with cosmological constant. I. Classification and geometrical properties of nontwisting type N solutions
Authors: Bičák Jiřı́ , Podolský Jiřı́
Published: July 2002

All nontwisting Petrov-type N solutions of vacuum Einstein field equations with cosmological constant Λ are summarized. They are shown to belong either to the nonexpanding Kundt class or to the expanding Robinson–Trautman class. Invariant subclasses of each class are defined and the corresponding metrics are given explicitly in suitable canonical coordinates. Relations between the subclasses and their geometrical properties are analyzed. In the subsequent paper these solutions are interpreted as exact gravitational waves propagating in de Sitter or anti-de Sitter spacetimes.
A path space formula for Gauss vectors in Chern–Simons quantum electrodynamics
Authors: Challifour John L. , Clancy John P.
Published: July 2002

Canonical quantization of a Chern–Simons gauge field minimally coupled to a spinor field is studied as an indefinite metric quantum field theory in the usual covariant gauges, by using a lattice cutoff. For this model, we show that positivity for the indefinite metric, Gauss’ Law, gauge invariance and Osterwalder–Schrader positivity for a self-adjoint Hamiltonian are equivalent. In addition, the path-space formula for the Osterwalder–Schrader semigroup is constructed in terms of a Euclidean scalar, massive, Gaussian random field.
New solvable and quasiexactly solvable periodic potentials
Authors: Khare Avinash , Sukhatme Uday
Published: July 2002

Using the formalism of supersymmetric quantum mechanics, we obtain a large number of new analytically solvable one-dimensional periodic potentials and study their properties. More specifically, the supersymmetric partners of the Lamé potentials ma(a+1)sn2(x,m) are computed for integer values a=1,2,3,… . For all cases (except a=1), we show that the partner potential is distinctly different from the original Lamé potential, even though they both have the same energy band structure. We also derive and discuss the energy band edges of the associated Lamé potentials pm sn2(x,m)+qm cn2(x,m)/dn2(x,m), which constitute a much richer class of periodic problems. Computation of their supersymmetric partners yields many additional new solvable and quasiexactly solvable periodic potentials.
Two new potentials for the free particle model
Authors: Morales J. , Peña J. J.
Published: July 2002

In this work, is proposed a very simple method for obtaining the generalized potential associated with a known standard potential. The procedure is straightforward because it only uses two Ricatti-type relationships as enough condition to find a generalized potential; one particular equation is needed to identify the specific potential under study and one general Ricatti relationship is used to find the corresponding generalized potential. Moreover, the method is completely general due to the fact that an arbitrary potential has been considered in its development for which the procedure can also be used to find new potentials which could be needed in the modeling of important quantum interactions. The usefulness of the proposed approach, is shown with the treatment of the three- and one-dimensional potential for the free particle model. This work example leads to two new potentials whose Hamiltonians are isospectral when they are compared with the former Hamiltonian.
Two-parameter differential calculus on the h-superplane
Authors: Çelik Salih , Çelik Sultan A.
Published: July 2002

We introduce a noncommutative differential calculus on the two-parameter h-superplane via a contraction of the (p,q)-superplane. We manifestly show that the differential calculus is covariant under GLh1,h2(1|1) transformations. We also give a two-parameter deformation of the (1+1)-dimensional phase space algebra.
Wavelets and orthogonal polynomials based on harmonic oscillator eigenstates
Authors: Dai Dao-Qing
Published: July 2002

We present a new method for the construction of wavelets. The main tool is the harmonic oscillator eigenstates. With the help of their properties we are able to construct wavelets which have explicit expressions and have exponential decay in both time domain and frequency domain. Moreover we get a new family of polynomials which are orthogonal in a weighted squarely integrable function space.
Temperature-induced change in the ESR spectrum of the Fe3+ ion in polyaniline
Authors: Vasyukov V. N. , D’yakonov V. P. , Shapovalov V. A. , Aksimentyeva E. I. , Szymczak H. , Piechota S.
Published: July 2002

Research on polyaniline doped with K3[Fe(CN)6] has revealed an effect which is manifested in an unusual temperature-induced change in the ESR spectrum of the Fe3+ ion. At low temperature (T=4.2 K) one observes the first resonance line (g1=4.22±0.03), and at high temperature (T=295 K) the second line (g2=2.13±0.05). The transition from the low-to the high-temperature spectrum occurs gradually and is accompanied by a redistribution of the absorption intensity. The observed properties of the temperature dependence of the ESR spectrum are typical of systems with a multiple-minimum potential.
Nonlinear interaction between the sinuous and varicose instability modes in a plane wake
Authors: Leib S. J. , Goldstein M. E.
Published: July 2002

The nonlinear interaction between sinuous and varicose instability modes in a plane wake is examined in the nonlinear–nonequilibrium critical layer regime. Equations governing the evolution of the instability wave amplitudes and critical layer vorticity distributions are derived. Numerical solutions for these equations are obtained for a number of wake defects and initial amplitude ratios. The results show that the primary effects of the nonlinear interaction are the suppression of the varicose mode and the downstream shift of the peak of the sinuous mode.
Filamentation of unstable vortex structures via separatrix crossing: A quantitative estimate of onset time
Authors: Polvani L. M. , Flierl G. R. , Zabusky N. J.
Published: July 2002

The onset of filamentation for compact vortex structures in two-dimensional incompressible flows is elucidated. An estimate is presented for the filamentation time of an unstably perturbed Kirchhoff ellipse, obtained from a linear analysis of the geometry of the instantaneous corotating streamfunction.
Effect of rigid boundaries on the onset of convective instability in a triply diffusive fluid layer
Authors: Lopez Amalia R. , Romero Louis A. , Pearlstein Arne J.
Published: July 2002

The onset of convection in a triply diffusive, incompressible motionless Newtonian fluid layer of infinite horizontal extent bounded by rigid parallel walls is studied by means of a linear stability analysis. The qualitative features of most of the results carry over from the case of stress-free boundaries studied earlier by Pearlstein, Harris, and Terrones [J. Fluid Mech. 202, 443 (1989)]. One striking feature that does not carry over from the stress-free case, however, is the possibility of quasiperiodic bifurcation from the steady motionless state via two pairs of complex conjugate temporal eigenvalues with incommensurable imaginary parts crossing into the right half-plane at the same combination of Rayleigh numbers. The impossibility of this type of quasiperiodic bifurcation from the rest state in the rigid case is discussed in terms of the topology of the disconnected neutral curves. The numerical method employed is suitable for the computation of disconnected oscillatory neutral curves in other stability problems for which a low-order exact dispersion relation does not exist.
Near wakes of a circular cylinder in stratified flows
Authors: Ohya Y. , Nakamura Y.
Published: July 2002

Near wakes of a circular cylinder in linearly stratified flows are experimentally investigated by means of flow visualization and measurements of vortex shedding frequencies, at Reynolds numbers 5×103–104 and stratification parameters K smaller than 1.0. The study demonstrates that as K increases from zero, the vortex shedding from a circular cylinder is progressively strengthened, while the Strouhal number becomes gradually lower than that for a homogeneous flow. At a certain critical value of K, the enhanced vortex shedding is suddenly weakened and the Strouhal number increases sharply to a high value.
Asymptotic behavior of curvature of surface elements in isotropic turbulence
Authors: Girimaji S. S.
Published: July 2002

The asymptotic behavior of the curvature of material elements in turbulence is investigated using Lagrangian velocity-gradient time series obtained from direct numerical simulations of isotropic turbulence. Several material-element ensembles of different initial curvatures and shapes are studied. It is found that, at long times, the (first five) moments of the logarithm of characteristic curvature (C) and shape factor (S) asymptote to values that are independent of the initial curvature or shape. This evidence strongly suggests that the asymptotic pdf’s of the curvature and shape of material elements are stationary and independent of initial conditions. Irrespective of initial curvature or shape, the asymptotic shape of a material surface is cylindrical with a high probability.
On the modeling of scalar diffusion in isotropic turbulence
Authors: Girimaji Sharath S.
Published: July 2002

The objectives of this paper are (i) to establish analytically some important features of the scalar diffusion process in turbulence and (ii) to derive a closure model for this process in terms of the scalar probability density function (pdf). The present analysis shows that in isotropic turbulence the conditional scalar dissipation [χ(ψ)=D<∂φ/∂xi∂φ/∂xi‖φ=ψ≳], its derivative (∂χ/∂ψ), and the conditional scalar diffusion [Θ(ψ)=D<∂2φ/∂xi ∂xi‖φ=ψ≳] are zero at the extreme values of scalar concentration. Models for conditional-dissipation ratio (χ/εs) and conditional-diffusion ratio (Θ/εs) are derived from the observation [Girimaji, Combust. Sci. Technol. 78, 177 (1991); NASA Contract. Rep. CR 4446 (1992)] that the scalar pdf can be characterized by the β pdf at all stages of non-premixed mixing. The conditional-dissipation model is compared with the DNS data of Eswaran and Pope [Phys. Fluids 31, 506 (1988)] and the mapping-closure-based model [O’Brien and Jiang, Phys. Fluids A 3, 3121 (1991)]. The application of the model to multiscalar mixing is also briefly discussed.
Wall reflections of solitary waves in Marangoni–Bénard convection
Authors: Linde H. , Chu X.-L. , Velarde M. G. , Waldhelm W.
Published: July 2002

In Marangoni–Bénard convection with mass transfer from the air to the liquid, an experimental exploration of reflections of solitary waves at walls has been carried out. Mach stems are observed for small enough incident angles. Upon increasing the incident angle the stem disappears thus leading to regular reflections with, however, the angle of reflection being generally larger than the incident angle.
A dynamic mixed subgrid-scale model and its application to turbulent recirculating flows
Authors: Zang Yan , Street Robert L. , Koseff Jeffrey R.
Published: July 2002

The dynamic subgrid-scale eddy viscosity model of Germano et al. [Phys. Fluids A 3, 1760 (1991)] (DSM) is modified by employing the mixed model of Bardina et al. [Ph.D dissertation, Stanford University (1983)] as the base model. The new dynamic mixed model explicitly calculates the modified Leonard term and only models the cross term and the SGS Reynolds stress. It retains the favorable features of DSM and, at the same time, does not require that the principal axes of the stress tensor be aligned with those of the strain rate tensor. The model coefficient is computed using local flow variables. The new model is incorporated in a finite-volume solution method and large-eddy simulations of flows in a lid-driven cavity at Reynolds numbers of 3200, 7500, and 10 000 show excellent agreement with the experimental data. Better agreement is achieved by using the new model compared to the DSM. The magnitude of the dynamically computed model coefficient of the new model is significantly smaller than that from DSM.
Modeling of the deformation of a liquid droplet impinging upon a flat surface
Authors: Fukai J. , Zhao Z. , Poulikakos D. , Megaridis C. M. , Miyatake O.
Published: July 2002

This article presents a theoretical study of the deformation of a spherical liquid droplet impinging upon a flat surface. The study accounts for the presence of surface tension during the spreading process. The theoretical model is solved numerically utilizing deforming finite elements and grid generation to simulate accurately the large deformations, as well as the domain nonuniformities characteristic of the spreading process. The results document the effects of impact velocity, droplet diameter, surface tension, and material properties on the fluid dynamics of the deforming droplet. Two liquids with markedly different thermophysical properties, water and liquid tin, are utilized in the numerical simulations because of their relevance in the industrial processes of spray cooling and spray deposition, respectively. The occurrence of droplet recoiling and mass accumulation around the splat periphery are standout features of the numerical simulations and yield a nonmonotonic dependence of the maximum splat radius on time.
Geometry of isothermal and isoconcentration surfaces in thermal turbulence
Authors: Gluckman B. J. , Willaime H. , Gollub J. P.
Published: July 2002

The geometry of isothermal surfaces for Rayleigh–Bénard convection at Rayleigh numbers R in the range 107 to 3×108 (close to the soft to hard turbulence transition) are measured. The measurements were made by imaging the color of light scattered from chiral nematic particles suspended in the fluid. Although the isotherms are multiply connected and convoluted, they do not display fractal scaling. The minimum scale for convolutions can be understood as resulting from the competition between folding and thermal diffusion. The isotherms are characterized statistically by the probability distribution of the local curvature, which may be described approximately as a stretched exponential. The distribution is essentially independent of the position and orientation of the plane of observation, and of R over the range explored. The geometry of the isotherms is compared to that of isoconcentration surfaces for dye injected into the flow; the latter do show a limited range of approximate fractal scaling because of the smaller diffusivity of the dye. The thermal measurements are supplemented by simultaneous measurements of the velocity field obtained by particle image velocimetry. Unstable waves often form on the thermal boundary layers in regions of high horizontal velocity gradient.
Development of flute modes on expanding plasma clouds
Authors: Winske D.
Published: July 2002

Structuring that results from plasma streaming at sub-Alfvénic speeds across an external magnetic field is considered. Previously, it has been proposed the lower hybrid drift instability enhanced by the deceleration of the plasma by the field produces the flute modes observed on the surface of expanding laser produced plasmas and the AMPTE magnetotail releases [Eos (Trans) 63, 843 (1982)]. An appropriate dispersion equation to describe the properties of the unstable waves has been derived and particle simulations carried out to show the growth and evolution of the instability. The salient features of this earlier work are reviewed here, and then additions and refinements to the theory and simulations are described. In particular, the scaling of the wave properties with the ratio of the ion gyroradius to the magnetic confinement radius is discussed and the nonlinear evolution of the instability is investigated more thoroughly. The consequences of these results, both for the laser experiments and for AMPTE, are also considered. To this end, a comparison of the linear and nonlinear properties of the waves observed in the simulations with those seen in the experiments is carried out. While there is considerable discrepancy between the observed and predicted wavelengths of the modes, the effects considered here are in the direction of reducing the disagreement.
Time evolution from linear to nonlinear stages in magnetohydrodynamic parametric instabilities
Authors: Hoshino M. , Goldstein M. L.
Published: July 2002

The nonlinear evolution of the magnetohydrodynamic (MHD) parametric instability of wave fluctuations propagating along an unperturbed magnetic field is investigated. Both a magnetohydrodynamic perturbation-theoretical approach and a nonlinear MHD simulation are used. It is shown that high harmonic waves are rapidly excited by wave–wave coupling, and that the wave spectrum evolves from a state containing a small number of degrees of freedom in k space to one which contains a large number of degrees of freedom. It is found that the spectral evolution prior to nonlinear saturation is well described by the perturbation theory. During this stage, the ratio of the growth rate of the nth harmonic wave to the linear growth rate of the fundamental wave is n. The nonlinear saturation stage is characterized by a frequency shift of the fundamental wave that destroys the wave–wave resonance condition which, in turn, causes the wave amplitude to cease its growth.
Self-similar spherical expansion of a laser plasma or of detonation products into a low-density ambient gas
Authors: Liberman M. A. , Velikovich A. L.
Published: July 2002

Self-similar solutions are given which represent an analytic theory of a spherical explosion at the stage when the action of the mass source (a detonation wave in the explosive or an ablation front in an irradiated target) driving a shock wave in the ambient gas is relevant. It is shown that during this stage, which precedes that described by the conventional blast-wave theory, the velocity of the shock wave in the ambient gas is constant.
Nonlinear evolution of Alfvén waves in a finite beta plasma
Authors: Som B. K. , Dasgupta Brahmananda , Patel V. L. , Gupta M. R.
Published: July 2002

A general form of the derivative nonlinear Schrödinger (DNLS) equation, describing the nonlinear evolution of Alfvén waves propagating parallel to the magnetic field, is derived by using two-fluid equations with electron and ion pressure tensors obtained from Braginskii [in Reviews of Plasma Physics (Consultants Bureau, New York, 1965), Vol. 1, p. 218]. This equation is a mixed version of the nonlinear Schrödinger (NLS) equation and the DNLS, as it contains an additional cubic nonlinear term that is of the same order as the derivative of the nonlinear terms, a term containing the product of a quadratic term, and a first-order derivative. It incorporates the effects of finite beta, which is an important characteristic of space and laboratory plasmas.
Analytic solutions and particle simulations of cross-field plasma sheaths
Authors: Gerver M. J. , Parker S. E. , Theilhaber K.
Published: July 2002

Particle simulations have been made of an infinite plasma slab, bounded by absorbing conducting walls, with a magnetic field parallel to the walls. The simulations have been either one dimensional or two dimensional, with the magnetic field normal to the simulation plane. Initially, the plasma has a uniform density between the walls and there is a uniform source of ions and electrons to replace particles lost to the walls. In the one-dimensional (1-D) case, there is no diffusion of the particle guiding centers and the plasma remains uniform in density and potential over most of the slab, with sheaths about a Debye length wide where the potential rises to the wall potential. In the two-dimensional (2-D) case, the density profile becomes parabolic, going almost to zero at the walls, and there is a quasineutral presheath in the bulk of the plasma, in addition to sheaths near the walls. Analytic expressions are found for the density and potential profiles in both cases, including, in the 2-D case, the magnetic presheath resulting from a finite ion Larmor radius, and the effects of the guiding center diffusion rate being either much less than or much greater than the energy diffusion rate. These analytic expressions are shown to agree with the simulations. A 1-D simulation with Monte Carlo guiding center diffusion included gives results that are in good agreement with the much more expensive 2-D simulation.
Low-n stability calculations for three-dimensional stellarator configurations
Authors: Garcia L. , Carreras B. A. , Dominguez N. , Leboeuf J. N. , Lynch V. E.
Published: July 2002

A set of reduced magnetohydrodynamic (MHD) equations to study linear stability in general toroidal configurations is presented. The equations are derived by applying the averaging method to an equilibrium represented in a straight-field-line coordinate system. They permit the calculation of the low-n stability of fully three-dimensional (3-D) equilibria for stellerator configurations with either a planar or a helical magnetic axis. Numerical solutions are shown to agree well with marginal stability boundaries given by the classical stellerator expansion when average stellarator equilibria with a planar magnetic axis are used as input.
Saturation of drift instabilities by E×B advection of resonant electrons
Authors: Dimits A. M.
Published: July 2002

Saturation of the collisionless and weakly collisional drift instabilities by nonlinear E×B advection of resonant electrons is considered. The nonlinear E×B advection of the resonant electrons around the O points and X points of the potential shuts off the linear phase shift between the electron density and the potential, and hence the linear growth, and produces residual oscillations at the E×B-trapping frequency. Two analytical solutions of a three-mode model of Lee et al. [Phys. Fluids 27, 2652 (1984)], which describes the saturation of drift waves by this mechanism, are found. The first is an exact solution in the form of a steadily propagating wave of constant amplitude, and is relevant when electron pitch-angle scattering is present. The second is an approximate time-dependent analytical solution, obtained using the method of O’Neil [Phys. Fluids 8, 2255 (1965)], and is relevant to the collisionless case. The predictions that follow from this solution for the saturation level and for the amplitude oscillation frequency are in excellent agreement with the direct numerical solutions of the three-mode system.
Gyroharmonic maser instability for weakly relativistic electrons with a loss-cone distribution
Authors: Yoon Peter H. , Krauss-Varban D.
Published: July 2002

The weakly relativistic dielectric tensor for a system of electrons comprised of cold and energetic populations, embedded in a neutralizing background, is reformulated in terms of an infinite series representation in powers of λ=αck⊥/ωc, where α2 is a parameter proportional to the average thermal energy of the energetic electrons, k⊥ is the perpendicular component of the wave vector k, and ωc is the electron gyrofrequency. The energetic electrons are assumed to have a loss-cone feature in the perpendicular momentum space. The present formalism can be used in the problem of cyclotron maser (i.e., emissions near the fundamental ω≊ωc) as well as more general gyroharmonic maser (i.e., multiharmonics) emissions resulting from weakly relativistic loss-cone electrons. This is because, unlike the previous theories in which certain approximations such as the single-harmonic approximations are made, the present formalism retains contributions from the entire harmonics. As a result, the present formalism is valid for arbitrary ωp/ωc, where ωp is the total electron plasma frequency. As an application, growth rates for the X-mode and Z-mode gyroharmonic maser instabilities are calculated for a propagation angle θ=90° at various energies, and for ωp/ωc ranging from 0.1 to 1.
Numerical simulation of ablative Rayleigh–Taylor instability
Authors: Gardner John H. , Bodner Stephen E. , Dahlburg Jill P.
Published: July 2002

Numerical simulations over a wide range of parameters of the linear stability of an ablating laser-produced plasma show a linear decrease in the growth rate with increasing ablation velocity. Simulations in planar and spherical geometries, with red and blue laser light, at high and low intensities, and at high and low accelerations, all seem to nearly follow a consistent law γ=0.9√kg − 3kva, when va is defined as the mass ablation rate divided by the peak density, in agreement with the eigenvalue analysis of Takabe and co-workers [Phys. Fluids 26, 2299 (1983); 28, 3676 (1985)].
Transport processes in magnetically confined plasmas
Authors: Callen J. D.
Published: July 2002

Intensified studies of plasma transport in toroidal plasmas over the past three to five years have progressed through increased understanding in some areas and changed perceptions about the most important issues in other areas. Recent developments are reviewed for six selected topics: edge fluctuations and transport; L–H mode transition; core fluctuations; modern plasma turbulence theory; transient transport; and global scaling. Some of the developments that are highlighted include: the role of a strongly sheared poloidal flow in edge plasma turbulence, transport and the L–H transition; change of focus from k⊥ ρs ∼ 1 to k⊥ ρs ≪ 1 fluctuations in tokamak plasmas; modern direct-interaction-approximation plasma turbulence and hybrid fluid/kinetic theoretical models; and transient transport experiments that are raising fundamental questions about our conceptions of local transport processes in tokamaks.
Measurements of ion velocity and density in the plasma sheath
Authors: Goeckner M. J. , Goree J. , Sheridan T. E.
Published: July 2002

Using laser-induced fluorescence, the ion velocity and density inside a dc plasma sheath have been measured. A polished planar electrode, biased at −100 V, was aligned so that a laser beam struck it at normal incidence. Using this arrangement, the ion velocity component perpendicular to the electrode surface was measured. By detecting the fluorescence while scanning the laser frequency, a line shape was recorded that had two peaks, due to the Doppler shift from the incident and reflected beams. The separation of the peaks yielded an absolutely calibrated measure of the ion drift velocity, while the height of the peaks gave the ion density. As expected, in the sheath the measured ion density was lower and the velocity was higher than in this plasma. Using these measurements, it was confirmed that the ion flux is conserved in a sheath. The spatial profiles of ion velocity and density in the sheath were used to test a time-independent two-fluid theory, and good agreement was found. The data were also compared to Child’s law, which showed good agreement near the electrode but predicted the density poorly, as expected, near the plasma–sheath boundary.
Nonlinear resonant heating at electron cyclotron subharmonic frequency
Authors: Sita Janaki M. , Dasgupta Brahmananda
Published: July 2002

Power absorption in a plasma due to an ordinary wave propagating at right angles to the magnetic field at a cyclotron subharmonic frequency is investigated. The motion of the electron in an electromagnetic wave in the presence of a magnetic field has been described using a relativistic Hamiltonian with an adiabatic invariant characterizing the dynamical system. Second-order canonical perturbation theory is carried out to obtain the subharmonic response. The energy gain of an electron is obtained in terms of the change in the adiabatic invariant and is utilized to calculate power absorption at a cyclotron subharmonic (3/2ωc) frequency.
Pressure profiles, resonant Pfirsch–Schlüter currents, thermal instabilities, and magnetic island formation
Authors: Hegna C. C. , Callen J. D.
Published: July 2002

A prescription for constructing the plasma pressure profile in the vicinity of an equilibrium magnetic island is derived by solving a sourced pressure diffusion equation near the island region. For pressure sources and sinks that are relatively constant in space, it is found that the plasma pressure profile is insensitive to pressure sources; thus the pressure profile can be constructed by assuming that the net pressure flux across any topologically toroidal magnetic surface is constant. This construction of the pressure profile is also valid for magnetic islands that are slowly evolving in time. By coupling the pressure evolution equation with the magnetostatic equilibrium equations, the theory is applied to the case of self-consistent construction of pressure-gradient-driven magnetic islands. In particular, the question of resonant Pfirsch–Schlüter current induced magnetic islands and the role of thermal effects on nonlinear magnetic islands is addressed.
A review of the ac space-charge effect in electron–circuit interactions
Authors: Lau Y. Y. , Chernin D.
Published: July 2002

This paper provides a critical examination of traditional theoretical treatments of alternating current (ac) space-charge effects in vacuum electronic devices. By treating several simple examples, it is found that the commonly made decomposition of the first-order field into a ‘‘circuit part’’ and a ‘‘space-charge part’’ is ambiguous and misleading. In at least one case, this terminology has led to a formulation that double counts the effect of space charge in the beam–circuit interaction. In other cases, the ‘‘space-charge term’’ in the dispersion relation−equivalently Pierce’s space-charge parameter (QC)−has been improperly or incompletely evaluated. The implications for gyrotrons, peniotrons, free-electron lasers, Smith–Purcell-type generators, and crossed-field devices are addressed. The space-charge effects are briefly discussed in nonlinear theories and in particle simulations. For the models examined, it is found that the most useful and convenient representation for the ac fields is one based on an eigenfunction expansion of the ac magnetic field, even when that field is not itself important to the electron dynamics.
Higher-order solution of an ion-acoustic solitary wave in a plasma
Authors: Watanabe S. , Jiang B.
Published: July 2002

A simple method for obtaining higher-order solutions of a solitary wave is presented. The method is based on the higher-order approximation of the reductive perturbation method. As a model equation, the Korteweg–de Vries (KdV) equation with fifth-order dispersion term is employed and higher-order solutions are obtained. In the case of ion-acoustic solitary wave, the fourth-order solution is given explicitly and is compared with numerical solutions. The fourth-order solution is shown to be valid if a normalized wave amplitude is less than 0.5.
Experimental plasma wake-field acceleration project*
Authors: Militsyn B. L. , Bechtenev A. A. , Breizman B. N. , Chebotaev P. Z. , Koop I. A. , Kudryavtsev A. M. , Panasyuk V. M. , Shatunov Yu. M. , Skrinsky A. N.
Published: July 2002

A new experiment on plasma wake-field acceleration has been designed at the Budker Institute of Nuclear Physics in Novosibirsk. An intense modulated driving beam from the electron–positron booster (BEP), a storage ring, will be used to excite a nonlinear plasma wave in a dense plasma (n=1015 cm−3). Important advantages of this beam are its very low emittance (10−8 cm⋅rad in the vertical direction), high energy (850 MeV), and high intensity (1012 particles). A new technique for modulating this beam at a submillimeter wavelength is proposed. A simple numerical code has been developed to simulate the plasma wave excitation with plasma nonlinearity and with three-dimensional effects taken into account. The code allows the calculation of the radial structure of the nonlinear wake field including the focusing force which was mostly neglected in previous studies but which is especially important for experiment. The present numerical simulations show that, in the proposed experiment, a 1 GeV/m accelerating gradient over a macroscopic distance is attainable.
q-profile measurements in the Tokamak Fusion Test Reactor*
Authors: Levinton F. M. , Batha S. H. , Yamada M. , Zarnstorff M. C.
Published: July 2002

The q-profile plays a key role in determining plasma equilibrium and stability in tokamaks. With the development of the motional Stark effect (MSE) diagnostic, accurate q(R,t) profiles have been measured and utilized for equilibrium and stability analysis. A multichannel MSE polarimeter system on the Tokamak Fusion Test Reactor (TFTR) [Plasma Phys. Controlled Fusion 33, 1509 (1991)] has obtained data for several plasma conditions including L-mode, supershot, current ramps, and high βp. For sawtoothing discharges on TFTR, it is found that q(0)∼0.7, well below one, and remains below one throughout the entire evolution of the sawtooth cycle with an increase in q(0) of ≤0.1 after a sawtooth crash. During high βp operation or coinjection of neutral beams on TFTR a significant broadening of the current profile and an increase of q(0) is observed.
Kadomtsev–Petviashivili equation for an ion-acoustic soliton in a collisionless weakly relativistic plasma with finite ion temperature
Authors: Singh Sanjay , Honzawa Tadao
Published: July 2002

A Kadomtsev–Petviashivili equation is derived for a two-dimensional ion-acoustic soliton propagating in a collisionless weakly relativistic plasma containing the finite temperature ions. This equation is solved in a stationary frame to obtain expressions for the phase velocity, amplitude, width, peak ion density, peak pressure, and energy of the soliton. It is shown that both the relativistic effect and the ion temperature greatly influence the phase velocity, amplitude, and the width. The soliton behavior is described in detail, and a comparison is made between the present results and the previous theories.
Sheath structure in a magnetized plasma
Authors: Holland D. L. , Fried B. D. , Morales G. J.
Published: July 2002

The sheath formed between a magnetized plasma and a particle absorbing wall is examined for the case in which the magnetic field intercepts the wall at a small angle 0°<ε≲9°, where sin ε=B⋅n̂/‖B‖, and n̂ is the unit normal to the wall. The model is time-independent and one-dimensional (1-D) with all functions varying only in the direction normal to the wall. The ions are modeled by a Maxwellian velocity distribution which is modified by the condition that ions, which would have hit the wall, are absent. For the electrons a fluid description is used, including the effects of electron–neutral collisions. The transport of particles due to turbulent electrostatic fluctuations is modeled by a constant electric field perpendicular to both B and n̂. It is found that in the range of angles under consideration, there are two distinct regimes of sheath formation. If ε≲ν̄=ν/Ωe (grazing incidence), where ν is the electron–neutral collision frequency and Ωe is the electron cyclotron frequency, then the properties of the sheath are determined by a parameter λ which is the ratio of the convective (E×B) and diffusive electron flows. If λ≲1, the wall potential is negative and the sheath scale length is on the order of an ion gyroradius. If λ≳1, the wall potential is positive and, for large λ, the sheath is characterized by two scales: a short length, which is a decreasing function of λ, adjacent to the wall, and the ion gyroradius farther from the wall. For ε≫ν̄, (oblique incidence) the potential at the wall is negative with a magnitude close to that of the unmagnetized plasma and is only weakly dependent on ε. In addition, for this case, the sheath scale length is on the order of an ion gyroradius and is weakly dependent on ε, larger values of ε resulting in a slightly shorter scale length.
Poloidal rotation, density asymmetries, and momentum confinement in tokamak experiments
Authors: Stacey W. M. , Jackson D. R.
Published: July 2002

Poloidal rotation speeds and density asymmetries are calculated for the deuterium and dominant carbon (oxygen) impurity ions in discharges in the Axially Symmetric Divertor Experiment (ASDEX) [Proceedings of the 13th Conference on Plasma Physics and Controlled Fusion Research, (International Atomic Energy Agency, Vienna, 1991), p. 325], Doublet III (DIII) [Nucl. Fusion 26, 543 (1986)], Impurity Studies Experiment (ISX-B) [Nucl. Fusion 23, 1017 (1983)], Joint European Torus (JET) [Nucl. Fusion 31, 31 (1991)] and Tokamak Fusion Test Reactor (TFTR) (National Technical Information Document No. PB92177187) for which vφ∼vth for the ions. These poloidal rotation speeds and density asymmetries are used to evaluate the neoclassical gyroviscous model for the momentum confinement time. The rather good agreement with experimental momentum confinement times obtained over this wide range of plasma parameters provides a measure of confidence in the calculated density asymmetries and poloidal rotation, as well as demonstrating that neoclassical calculations can predict momentum confinement in tokamaks.
Two-stage turbulence suppression and E×B velocity shear measured at the L–H transition
Authors: Philipona R. , Doyle E. J. , Luhmann N. C. , Peebles W. A. , Rettig C. L. , Groebner R. J. , Burrell K. H. , Gohil P. , Matsumoto H. , Stambaugh R. D.
Published: July 2002

At the onset of the L–H transition in the DIII-D tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p.159], a fast (≊100 μsec) suppression of microturbulence is observed as the edge transport barrier is formed. This fast edge suppression is followed by a much slower (tens of msec), but substantial (≥50%) reduction in the relative density fluctuation level. This second turbulence suppression phase, which is observed to correlate with growing E×B velocity shear, has been localized to the plasma interior, and may explain why the observed transport reduction in the H mode has been observed to extend deep into the plasma, well beyond the edge transport barrier.
Parabolic approximation method for fast magnetosonic wave propagation in tokamaks
Authors: Phillips C. K. , Perkins F. W. , Hwang D. Q.
Published: July 2002

Fast magnetosonic wave propagation in a cylindrical tokamak model is studied using a parabolic approximation method in which poloidal variations of the wave field are considered weak in comparison to the radial variations. Diffraction and wave interference effects, which are ignored by ray tracing methods, are included self-consistently using the parabolic method since continuous solutions for the wave electromagnetic fields are computed directly from an approximate form of the wave equation. Numerical results are presented which illustrate the cylindrical convergence of the launched waves into a diffraction-limited focal spot on the cyclotron absorption layer near the magnetic axis for a wide range of plasma confinement parameters.
Experimental studies of the equilibrium of a linear high-beta l=1 stellarator
Authors: Hedin E. R. , Koepke M. E. , Ribe F. L.
Published: July 2002

A high-beta linear l=1 stellarator plasma is produced in a low-compression 3 m theta pinch whose compression coil (22 cm i.d.) is modified to have a helical offset of 2 cm and an axial helical period of 40 cm. Internal probes are used to determine the spatial structure and temporal behavior of the magnetic fields, plasma pressure, and current. The results are well described by ideal magnetodydrodynamic equilibrium theory.
A high magnetic Reynolds number dynamo
Authors: Perkins F. W. , Zweibel E. G.
Published: July 2002

A boundary-layer solution to a high magnetic Reynolds number R periodic dynamo model shows that: (1) flux expulsion forces the magnetic field into flux sheets; (2) the principal contribution to the α effect arises from regions of flow stagnation along a flux sheet; and (3) the α effect scales as R−1/2. Arguments for these effects persisting in turbulent dynamos are given.
Excitation of ion Bernstein waves from loop antennas
Authors: Skiff F. , Ono M. , Wong K. L.
Published: July 2002

Direct excitation and propagation of ion Bernstein waves from low-impedance current-carrying loop antennas in the ion cyclotron frequency range are studied over a range of plasma and antenna parameters. The dependence of wave coupling efficiency on plasma density and on wave frequency and parallel wavelength is obtained from measurements of wave amplitude and variations in antenna impedance. Comparisons are made to a simple nonuniform warm-plasma model of the coupling problem. Generally good agreement is found between theory and experiment. As a result, some guidelines are proposed concerning antenna design.
The general solution of Stokes flow in a half-space as an integral of the velocity on the boundary
Authors: Jansons Kalvis M. , Lister John R.
Published: July 2002

The motion in a half-space of a viscous fluid governed by the Stokes flow equations and driven by the instantaneous velocity on the boundary is considered. It is demonstrated that the flow field can be represented as an integral of the boundary velocity distribution, and the simple kernel function is derived. Previously it was thought necessary for the flow to be represented as an integral of the force distribution on the boundary; the velocity distribution was then related to the force distribution through an integral equation, which was solved numerically. Expressions for the stress field in terms of the velocity distribution on the boundary are also determined, and some technical difficulties involving the convergence of the integrals are discussed.
Influence of initial conditions on the flow patterns of a shock-accelerated thin fluid layer
Authors: Budzinski John M. , Benjamin Robert F. , Jacobs Jeffrey W.
Published: July 2002

Previous observations of three flow patterns generated by shock acceleration of a thin perturbed, fluid layer are now correlated with asymmetries in the initial conditions. Using a different diagnostic (planar laser Rayleigh scattering) than the previous experiments, upstream mushrooms, downstream mushrooms, and sinuous patterns are still observed. For each experiment the initial perturbation amplitude on one side of the layer can either be larger, smaller, or the same as the amplitude on the other side, as observed with two images per experiment, and these differences lead to the formation of the different patterns.
Transition in flow over heat-transfer strips
Authors: Masad Jamal A.
Published: July 2002

The effect of heat-transfer strips on transition in flow over a flat plate is investigated. The maximum value of the integrated growth rate (N factor) of the instability wave is used as a measure of single-frequency (controlled, forced) transition, and the most upstream location at which N reaches a value of 9 is used as the location of the onset of wideband (natural) transition. The effects of the heat-transfer-strip location, the heating level, the length of the heat-transfer strip, the flow free-stream Mach number, and an isolated roughness element on single-frequency and wideband transition locations in subsonic two-dimensional flow are evaluated. The effect of heating strips on transition in three-dimensional and supersonic flows is discussed.
Laser light scattering by shock waves
Authors: Panda J. , Adamovsky G.
Published: July 2002

Scattering of coherent light as it propagates parallel to a shock wave, formed in front of a bluff cylindrical body placed in a supersonic stream, is studied experimentally and numerically. Two incident optical fields are considered. First, a large diameter collimated beam is allowed to pass through the shock containing flow. The light intensity distribution in the resultant shadowgraph image, measured by a low light CCD camera, shows well-defined fringes upstream and downstream of the shadow cast by the shock. In the second situation, a narrow laser beam is brought to a grazing incidence on the shock and the scattered light, which appears as a diverging sheet from the point of interaction, is visualized and measured on a screen placed normal to the laser path. Experiments are conducted on shocks formed at various free-stream Mach numbers, M, and total pressures, P0. It is found that the widths of the shock shadows in a shadowgraph image become independent of M and P0 when plotted against the jump in the refractive index, Δn, created across the shock. The total scattered light measured from the narrow laser beam and shock interaction also follows the same trend. In the numerical part of the study, the shock is assumed to be a ‘‘phase object,’’ which introduces phase difference between the upstream and downstream propagating parts of the light disturbances. For a given shape and Δn of the bow shock the phase and amplitude modulations are first calculated by ray tracing. The wave front is then propagated to the screen using the Fresnel diffraction equation. The calculated intensity distribution, for both of the incident optical fields, shows good agreement with the experimental data.