bluuebunny/crossref_metadata_2025 huggingface dataset:
Gravitational energy of conical defects
Authors: Maluf José W. , Kneip Andreas
Published: July 2002

The energy density εg of asymptotically flat gravitational fields can be calculated from a simple expression involving the trace of the torsion tensor. The integral of this energy density over the whole space yields the Arnowitt–Deser–Misner (ADM) energy. Such energy expression can be justified within the framework of the teleparallel equivalent of general relativity, which is an alternative geometrical formulation of Einstein’s general relativity. In this paper we apply εg to the evaluation of the energy per unit length of a class of conical defects of topological nature, which include disclinations and dislocations (in the terminology of crystallography). Disclinations correspond to cosmic strings, and for a space–time endowed with only such a defect the well known expression of energy per unit length is obtained precisely. However for a pure space–time dislocation the total gravitational energy is zero.
Exotic coherent structures in the (2+1) dimensional long dispersive wave equation
Authors: Radha R. , Lakshmanan M.
Published: July 2002

In this paper, we investigate the integrability aspects of the (2+1) dimensional coupled long dispersive wave (2LDW) equation introduced recently by Chakravarty, Kent, and Newman and establish its Painlevé (P-) property. We then deduce its bilinear form from the P analysis and use it to construct wave type solutions for the field variables. We then identify line solitons for the composite field variable “qr” which eventually helps to bring out the peculiar localization behavior of the system by generating localized structures (dromions) for the composite field from out of only one ghost soliton driving the boundary. We have then extended this analysis to multidromion solutions.
On topology and quantum mechanics
Authors: Schlesinger Karl-Georg
Published: July 2002

The relationship between topology and quantum mechanics is considered in two different ways. We suggest regarding quantum mechanics as a first-order approximation to topology theory on a fixed set. In this spirit, the approach of quantizing the lattice τ(X) of topologies on a set X [C. J. Isham, “Quantum topology and quantization on the lattice of topologies,” Class. Quantum. Grav. 6, 1509–1534 (1989)] is shown to be easily applicable to a quantum mechanical lattice. In the main part of the paper we deal with the question of the quantization of the whole category of topological spaces and continuous injective maps. Ideas of the modern categorical approach to quantization, as known from topological quantum field theory, are invoked in this part. The final paragraphs are devoted to the problem of extending quantization, even to the level of the underlying set theory.
Weighted trace formula near a hyperbolic trajectory and complex orbits
Authors: Paul T. , Uribe A.
Published: July 2002

In this paper we consider a weighted trace formula for Schrödinger operators. More precisely, let ψjℏ and Ejℏ denote the eigenfunctions and eigenvalues of a Schrödinger-type operator Hℏ with a discrete spectrum. Let ψ(x,ξ) be a coherent state centered at a point (x,ξ) of a hyperbolic closed orbit γ. We show that, as ℏ→0, the leading term of ∑jφ{[Ej(ℏ)−E]/ℏ}|(ψ(x,ξ),ψjℏ)|2 can be expressed in terms of the analytic continuation on the upper and lower half-planes of the positive and negative frequencies part of φ. The result is also related to complex trajectories surrounding γ.
Orthonormal sets of localized functions for a Landau level
Authors: Zak J.
Published: July 2002

Maximal sets of commuting magnetic translations are used for constructing a set of eigenfunctions for a Landau level on a von Neumann–Gabor lattice. Localization and orthogonality turn out to be two conflicting features of this set. It is shown how to construct complete orthonormal sets of optimally localized eigenfunctions on a von Neumann–Gabor lattice for each Landau level. By using the Balian–Low theorem it is pointed out that the uncertainties of the orbit center coordinates cannot both be made finite.
Time-dependent scattering on fractal measures
Authors: Guerin Charles-Antoine , Holschneider Matthias
Published: July 2002

In this paper we study the time evolution for the Schrödinger equation and the wave equation on the line when the interaction term is a fractal measure. First, we extend the usual one-dimensional potential scattering formalism to interactions defined as measures. Then we show how to retrieve information on the fractality of the interaction term from time-dependent scattering data. In the case of the Schrödinger equation we shall obtain the wavelet correlation dimension of the scatterer. For the wave equation the whole set of generalized multifractal dimensions can be recovered, provided the scatterer actually is fractal (nonsmooth). In this latter case, we also show how the reflected wave packets can be interpreted in terms of wavelet transform of the interaction.
The effect of configuration mixing on the first-order moments of polarized hydrogen lines
Authors: Casini Roberto
Published: July 2002

We extend previous work on the algebraic first-order moments of polarization profiles of hydrogen lines in the presence of external fields, to include the effect of configuration mixing induced by the applied fields. An algebraic formula for hydrogen line shifts due to the quadratic Stark effect is derived, under the assumption that the applied electric field is weak enough that line quenching induced by field ionization can be neglected. The derivation of such a formula is made possible by an aimed use of standard techniques of projection-operator algebra and of the fundamental implications of the spectral theorem. The results of this paper should help in decreasing the amount of numerical work needed in the calculation of line shifts of hydrogen lines induced by the presence of electric fields, as the preliminary numerical calculation of the Hamiltonian eigenvalues and eigenvectors is avoided, thus making calculations tractable for lines of higher hydrogen series than considered so far, e.g., in applications of pressure-broadening theory.
Propagation of waves through non-Gaussian longitudinally correlated random media
Authors: Gozani Joseph
Published: July 2002

Using successive approximations, we derive a hierarchical set of integro-differential equations for the evolution of the statistical moments of a wave propagating through non-Gaussian longitudinally correlated media. A closure procedure in the spirit of the Ornstein–Uhlenbeck process produces the most general set of equations currently available. The procedure can be applied to a large class of Cauchy problems in mathematical physics.
Analytical study of fractionally charged solitons in a one-dimensional trimerized electron–phonon system
Authors: Shirasaki Ryōen , Iwano Kaoru
Published: July 2002

The fractionally charged solitons in a trimerized electron–phonon system are studied by both analytical and numerical methods. To make those methods possible, an effective Lagrangian is derived by diagrammatic calculations. It is found that this Lagrangian is similar to that derived by the so-called derivative expansion. Both the phase and amplitude parts of the complex order parameter are included in the Lagrangian, and here we particularly focus on the nonlinear coupling between them. When the electron–phonon coupling is very weak, the aforementioned coupling is also weak, and so the soliton is almost considered to be a pure phase soliton with a constant amplitude. While, in the intermediate electron–phonon coupling case, the two parts of the order parameter are nonlinearly coupled. As a result, the soliton changes its pattern from that of a phase soliton to a strongly amplitude-deformed one. Our both methods, i.e., the analytical and numerical ones, succeed in giving such changes as gradual ones. Moreover, the coincidence of the two results is also good at a quantitative level.
Diffusion in solid helium (A review)
Authors: Grigor’ev V. N.
Published: July 2002

The results of experimental investigations of diffusion processes in solid helium are reviewed. It is shown that 3He impurities in hcp 4He are narrow-band quasiparticles whose motion can be adequately described in the existing theory of quantum diffusion. The observed peculiarities of 3He diffusion in the bcc phase of concentrated 3He–4He solutions, i.e., a noticeable diffusive transport at concentrations higher than critical, the independence of the diffusion coefficient D on the concentration for x<20%3He, an abrupt increase in D for x≃20%, and a dependence of D on the diffusion length in the latter case, have not received a quantitative interpretation. The relation between diffusion phenomena in concentrated solutions and the percolation problem is emphasized. The results of experiments on vacancy diffusion are analyzed, and it is proved that vacancies in 3He–4He are wide-band quasiparticles.
On the large-scale structure of the turbulent wake of a flat plate
Authors: Jovic S. , Ramaprian B. R.
Published: July 2002

A simple heat-tagging technique was used to isolate and analyze the large-scale coherent structures present in the two-dimensional wake of a flat plate. The results indicate the presence of these coherent structures even at 250 momentum thicknesses downstream of the trailing edge. These structures have a vortexlike topology and carry a significant amount of the total shear stress. The present results for the flat-plate wake seem to be in general agreement with those that have been obtained in cylinder wakes by other contemporary investigators using more complex techniques of eduction and signal enhancement.
Hydrodynamic modes of a granular shear flow
Authors: Mello T. M. , Diamond P. H. , Levine H.
Published: July 2002

Linear hydrodynamic modes for a monodisperse granular medium of slightly inelastic spheres in the collisional regime are considered. The dispersion relation is found for a flow in which the grains are fluidized by external shearing, such as occurs in a planar shear cell. One important consequence of this analysis is that flows used in typical shear cells may be supersonic, i.e., that the propagation speed of compressional density waves can be lower than the granular flow speed. Also, even at low frequencies and long wavelengths, there is nontrivial damping of density waves due to the dissipation of fluctuation energy into true thermal energy. This implies that it is important to consider both the strong compressibility and the dissipative processes when considering collective modes of these systems. The implications of this for linear stability are examined for the example of a Couette flow.
Nonlinear interaction of a detonation/vorticity wave
Authors: Lasseigne D. G. , Jackson T. L. , Hussaini M. Y.
Published: July 2002

The interaction of an oblique, overdriven detonation wave with a vorticity disturbance is investigated by a direct two-dimensional numerical simulation using a multidomain, finite-difference solution of the compressible Euler equations. The results are compared to those of linear theory, which predict that the effect of exothermicity on the interaction is relatively small except possibly near a critical angle where linear theory no longer holds. It is found that the steady-state computational results whenever obtained in this study agree with the results of linear theory. However, for cases with incident angle near the critical angle, moderate disturbance amplitudes, and/or sudden transient encounter with a disturbance, the effects of exothermicity are more pronounced than predicted by linear theory. Finally, it is found that linear theory correctly determines the critical angle.
Wave number space dynamics of enstrophy cascade in a forced two-dimensional turbulence
Authors: Ohkitani Koji
Published: July 2002

Enstrophy cascade in two-dimensional turbulence is studied numerically together with dynamics of a passive scalar and the first Lyapunov vector. (i) the vorticity field is decomposed into elliptic (e) and hyperbolic (h) regions by using Weiss’ conditional sampling method. The k−1 law of the enstrophy spectrum associated with the h region extends with the dissipation wave number, while the jumplike spectrum associated with the e region does not. Asymptotic recovery of the k−1 law is thereby suggested in the inviscid limit. Weiss’ decomposition is also applied to the enstrophy spectral flux to elucidate the interaction between e and h regions. (ii) Temporally intermittent nature of the enstrophy cascade is revealed on the (k-t) plane by tracing the wave number with active transfer. Active(inactive) periods are related with a higher(lower) enstrophy dissipation rate. (iii) the wave number characteristic to the enstrophy spectrum of the first Lyapunov vector is also traced on the (k-t) plane. When the peak wave number lies in the inertial subrange, enstrophy dissipation is likely to be large.
Infinite stream of Hele–Shaw bubbles
Authors: Burgess D. , Tanveer S.
Published: July 2002

Exact solutions are presented for a steady stream of bubbles in a Hele–Shaw cell when the effect of surface tension is neglected. These solutions form a three-parameter family. For specified area and distance between bubbles, the speed of the bubble remains arbitrary when surface tension is neglected. However, numerical and analytical evidence indicates that this arbitrariness is removed by the effect of surface tension. The branch of solutions that corresponds to the McLean–Saffman finger solution were primarily studied. A dramatic increase was observed in bubble speeds when the distance between bubbles is on the order of a bubble diameter, which may have relevance to experiments done by Maxworthy [J. Fluid Mech. 173, 95 (1986)].
Rapid compression of grid-generated turbulence by a moving shock wave
Authors: Honkan A. , Andreopoulos J.
Published: July 2002

Most of the previous work on turbulence amplification by shock wave interaction is limited to shock wave/boundary layer types of interactions where additional effects due to shock wave oscillation, streamline curvature, and flow separation complicate the understanding of the physics involved in this phenomenon. The present experimental study has focused on interactions of a normal shock with grid-generated turbulence in a shock tube. The decaying turbulence behind the grid is characterized by a variation of length scales with downstream distance and is subjected to an interaction with the reflected shock traveling in the opposite direction. Considerable amplification of turbulence has been found after the interaction which depends on the length scale of the incoming flow. Spectral analysis has also indicated that large eddies are amplified more than small eddies during interactions with shock waves of the same strength.
Maxwell’s second- and third-order equations of transfer for non-Maxwellian gases
Authors: Baganoff D.
Published: July 2002

Condensed algebraic forms for Maxwell’s second- and third-order equations of transfer are developed for the case of molecules described by either elastic hard spheres, inverse-power potentials, or by Bird’s variable hard-sphere model. These highly reduced, yet exact, equations provide a new point of origin, when using the moment method, in seeking approximate solutions in the kinetic theory of gases for molecular models that are physically more realistic than that provided by the Maxwell model. An important by-product of the analysis, when using these second- and third-order relations is that a clear mathematical connection develops between Bird’s variable hard-sphere model and that for the inverse-power potential.
Unsteady separation for Stokes flows in two dimensions
Authors: Smith S. H.
Published: July 2002

Some simple solutions are presented to the unsteady Stokes flow equations which describe the development of the slow viscous flow due to a line rotlet. Four different geometries are considered, with the rotlet (a) in front of a plane wall, (b) inside a circular cylinder, (c) outside a circular cylinder, (d) between two parallel walls; also, the development is considered (i) after the impulsive introduction of a potential vortex, and (ii) after the impulsive introduction of a line source of angular momentum. Separation occurs in all these situations, and one is able to trace the movement of the separation points, and the formation of eddies, for different times. A number of distinctive physical phenomena are detected.
On the linear stability of cellular spiral Couette flow
Authors: Ali Mohamed E. , Weidman P. D.
Published: July 2002

The stability of flow in an annulus capped at both ends and bounded by a fixed outer cylinder and a spiraling inner rod is determined in the context of linear theory. For infinite aspect ratio and constant fluid properties the problem is governed by a Taylor number Ta, an axial Reynolds number Re, and the radius ratio η. Linear stability is tested with respect to both axisymmetric (n=0) and nonaxisymmetric (n≠0) disturbances for η=0.2, 0.4, 0.6, 0.8 over the range 0≤Re≤2000. The evolution of axial wave number, axial phase speed, and spiral inclination angle with increasing Re at each η through all mode transitions to an asymptotic state n=N is reported. It is found that N=2, 4, 7, 19 for η=0.2, 0.4, 0.6, 0.8, respectively, and that the asymptotic state is reached at Re≂2000 for all radius ratios. The asymptotic state is characterized by critical Taylor numbers and frequencies that approach constant values while critical wave numbers fall off as Re−1. In this same limit the counter-rotating vortex pairs align themselves axially within the annulus. A conjecture is made on the influence of η on stability in the high Reynolds number limit.
On the nonlinear internal waves excited in the flow of a linearly stratified Boussinesq fluid
Authors: Hanazaki Hideshi
Published: July 2002

A numerical study of the internal gravity waves excited by an obstacle in the flow of a linearly stratified Boussinesq fluid is described. Solutions of the Navier–Stokes equations agree quantitatively well with the solutions of Grimshaw and Yi’s equation [J. Fluid Mech. 229, 603 (1991)] near resonance. The equation of Grimshaw and Yi can describe well the upstream waves even when the Froude number F is fairly small (F=0.5). Therefore it is a good model of the nonlinear internal waves excited in a linearly stratified Boussinesq fluid. When the wave amplitude is large, the first disappearance of the horizontal velocity is also well predicted by the solution of the equation of Grimshaw and Yi, although the equation cannot predict the subsequent time development.
Prandtl–Batchelor flow in a channel
Authors: Giannakidis G.
Published: July 2002

A steady, inviscid, incompressible, two-dimensional flow in a channel containing a vortex patch bounded by a vortex sheet is calculated numerically. The results cover a wide range of the channel width and the value of the jump in Bernoulli’s constant across the vortex sheet. An asymptotic theory is used to check the results for very narrow channels. A comparison with the solutions of the Navier–Stokes equations around an infinite array of circular cylinders [Fornberg, J. Fluid Mech. 225, 655 (1991)] is performed to check if the present flow can be used as a model for the wake.
On the initial formation of a defect structure in a two-dimensional mixing layer
Authors: Nassef Hany , Browand F. K.
Published: July 2002

Dislocations in the wave fronts downstream of the splitter plate in a two-dimensional (2-D) mixing layer are produced by oscillating two semi-span-flaps at different frequencies. Two frequency ratios are studied, 11:10 and 5:4. The vortices which grow from the two initially unstable wave trains form in the ratio of the frequencies: There are nh vortices per beat cycle on the high-frequency side, and nl vortices per beat on the low-frequency side. The vortices interact in a central, interconnection zone. Dye injected from the splitter plate is swept into the vortices and recorded with a video camera. Two injection methods are used, sheet injection for full viewing of the interconnection zone, and point injection for estimates of spanwise velocity. For a given frequency ratio the spanwise velocity scales with the parameter, d/λh, where λn is the wavelength corresponding to the higher frequency, and d is the phase separation between wave crests. Furthermore, addition of the parameter, ζ2=(nh/nl)2, scales the results for the two separate frequency ratios.
Thermocapillary migration of a small chain of bubbles
Authors: Wei Huailiang , Subramanian R. Shankar
Published: July 2002

The quasistatic thermocapillary migration of a chain of two or three spherical bubbles in an unbounded fluid possessing a uniform temperature gradient is investigated in the limit of vanishing Reynolds and Péclet numbers. The line of bubble centers is permitted to be either parallel or perpendicular to the direction of the undisturbed temperature gradient. The governing equations are solved by a truncated-series, boundary-collocation technique. Results are presented which demonstrate the impact of the presence of other bubbles on a test bubble. In the three-bubble case, a simple pairwise-additive approximation is constructed from the reflections solution, and found to perform well except when the bubbles are close to each other. Also, features of the flow topology in the fluid are explored. Separated reverse flow wakes are found in the axisymmetric problem, and other interesting structures are noted for the case in which the line of centers is perpendicular to the applied temperature gradient. The observed flow structure is shown to be the result of superposition of simpler basic flows.
The Kelvin–Helmholtz instability for surface waves in currents of uniform vorticity
Authors: Brevik I. , Sund H.
Published: July 2002

The Kelvin–Helmholtz (KH) instability is investigated for the case when linear monochromatic water waves of wave number k are propagating in a current whose undisturbed horizontal velocity profile is linear down to some depth h, and zero beneath. The present paper generalizes the work of Esch [J. Fluid Mech. 12, 192 (1962)] to the case of finite water depth D. Surface tension is neglected. The result of the analysis is a quartic equation for the phase velocity. The presence of a finite water depth tends to stabilize the flow field: The interval in kh, for which complex roots of the dispersion equation occur, becomes narrower as the depth decreases. Also, the growth rate of the flow decreases. The main results are illustrated graphically, and supplemented by analytic approximations in the limiting case when D/h lies close to unity.
Evolution of bounded beam–plasma interactions in a one-dimensional particle simulation
Authors: Morey I. J. , Boswell R. W.
Published: July 2002

A particle-in-cell code has been used to study the electron beam–plasma interaction, with nb<np, in a bounded one-dimensional system. Sheaths form on the boundaries because electrons leave the system as a result of the beam–plasma interaction heating the plasma electrons. The ions are chosen to be immobile since most time scales are too short for ion motion. The sheaths reflect waves and beam electrons, so that the interaction rapidly reaches a nonlinear stage. Standing waves have been observed. Despite this, the rate at which the beam–plasma interaction heats the plasma is found to agree with linear and quasilinear theory for weak beams in long systems, except when nb≳np/4 or the interaction length, L≳3vb/fpe.
New electron-temperature-gradient drift wave instabilities and anomalous thermal transport in magnetized electron plasmas
Authors: Shukla P. K. , Murtaza G.
Published: July 2002

New electron-temperature-gradient-driven electrostatic drift wave instabilities are shown to arise in magnetized electron plasmas. The quasilinear electron energy transport caused by such nonthermal drift waves is also obtained.
Optimization of elongated plasma shapes and their current profiles with respect to pressure-driven modes
Authors: Helton F. J. , Greene J. M.
Published: July 2002

Optimized equilibria were obtained in three different moderately elongated devices. The plasma cross-sectional shape and current profile were optimized to Mercier and ballooning modes for plasma equilibria in a racetrack device, a V-shaped bean device, and a spherical shell device. The resulting q profiles were nonmonotone. In general, triangulating the plasma increased the Mercier and ballooning stability limits. The spherical shell-shaped equilibrium has inherently favorable Mercier and ballooning stability properties.
Power deposition and current drive by intense microwave beams in tokamaks
Authors: Kritz Arnold H. , Smith Gary R. , Nevins William McCay , Cohen R. H.
Published: July 2002

Electron trapping by intense wave electric fields can alter the power deposition of electron-cyclotron waves in a tokamak when high-power sources are employed. The effect of wave trapping is examined in a ray-tracing study that utilizes plasma and wave parameters appropriate for the Microwave Tokamak Experiment (MTX) [National Technical Information Service Document No. DE-88016919 (1986)]. It is found that while wave trapping does result in some degradation in the rate of power deposition, single-pass power deposition is expected to remain significant in MTX. In examining current drive for MTX, the influence of electron trapping in the magnetic wells of the tokamak equilibrium field is included. Relativistic and magnetic trapping effects reduce the driven current by 25% to 50%. This initial study does not include the effects of gradients in the magnetic field and wave vector and therefore provides lower bounds for the power deposition and driven current.
Role of the Bernstein modes in the electron cyclotron second-harmonic wave absorption
Authors: Petrillo V. , Maroli C. , Lampis G.
Published: July 2002

The propagation and absorption of perpendicular second-harmonic electron cyclotron waves in a plasma slab are studied by means of propagation equations directly deduced from the Vlasov–Maxwell system. An electromagnetic wave injected from the vacuum into the plasma can be transformed into a quasielectrostatic forward mode, which, in turn, is converted into a Bernstein backward wave. The occurrence of this double-conversion process and the global absorption and reflection are analyzed and the dependence of the phenomena on the plasma parameters and wave characteristics is investigated.
Approximate formulas for cyclotron radiation at intermediate temperatures (5–50 keV)
Authors: Bornatici M. , Ruffina U.
Published: July 2002

The validity of various approximate formulas that have been proposed for the electron cyclotron emission and absorption at temperatures for which finite-Larmor-radius effects need to be retained to orders higher than the lowest significant one is analyzed in terms of the error of a given approximation with respect to the exact value. An exponential approximation constructed from the two-term series representation of the Bessel functions turns out to be the best one for the relevant (low harmonics) part of the spectrum and for a fairly wide range of temperatures.
A tearing mode energy principle for an axisymmetric force-free plasma
Authors: Chu M. S. , Chance M. S. , Greene J. M. , Jensen T. H.
Published: July 2002

A self-adjoint, gauge invariant stability functional δWTG for determination of a sufficient condition of tearing mode stability is obtained for a plasma with a uniform pressure. The plasma is stable if there is no free energy available to support energy flux into the singular layer. The Δ′ concept, valid in simple geometries, is generalized to reflect variation of equilibrium quantities on the flux surface. The relationship of δWTG to the ideal stability functional and other possible forms of tearing mode stability functionals is clarified through gauge transformations.
The convective growth of the beam–plasma instability
Authors: Rowland H. L.
Published: July 2002

Using a newly modified version of a low noise Vlasov code, a series of simulations studying the convective growth of the cold-beam, warm-plasma instability is performed. The scalings of spatial growth on beam density and velocity are in good agreement with earlier theoretical predictions. In agreement with Bers [Basic Plasma Physics (North Holland, Amsterdam, 1983), p. 451], the spatial growth rate ki λD =γ/(v1v2v3 )1/3, where γ is the temporal growth rate and vα is the linear group velocity of the three modes coupled by the instability. For the cold-beam, warm-plasma instability, this reduces to the standard formula ki λD =(3)1/2/2 (nb ve /6npvb)1/3.
Maximum beta for a small-aspect-ratio tokamak
Authors: Holmes J. A. , Charlton L. A. , Hogan J. T. , Carreras B. A. , Lazarus E. A.
Published: July 2002

Ideal linear magnetohydrodynamic (MHD) stability calculations demonstrate reasonable adherence at low aspect ratio (AR<2) to the Troyon scaling relationship for maximum beta, resulting in a broad regime of stable high-beta equilibria. For a specific low-aspect-ratio case (AR=5/3), a wide range of stable equilibria having volume-averaged beta, 〈β〉, in excess of 20% is found. A systematic approach for estimating the maximum beta is used. First, the aspect ratio is reduced, for fixed shape and profiles, starting from the Troyon optimized case at AR=2.5; the plasma cross-section shape is then varied for fixed profiles at fixed AR=5/3; and finally, pressure and safety factor profiles are varied for fixed shape and aspect ratio. The calculations are carried out for low n (n=1–3), usually with a conducting wall at a radius of 1.5 times the plasma minor radius, for n=∞ ballooning modes, and for Mercier stability. Several additional ‘‘spot checks’’ on the effects of moving the conducting wall to infinity and of the stability of n=0 and n=4 and 5 modes indicate good stability properties for these, also. The calculations presented here demonstrate a straightforward extrapolation of the Troyon scaling formula to low aspect ratio, in spite of qualitative differences previously noted in low-aspect-ratio equilibria.
Plasma kinetic theory without the Markovian approximation: Numerical results
Authors: Pocobelli G.
Published: July 2002

A numerical computation is carried out for the evolution of the amplitude and the frequency shift of a monochromatic electron wave in an unmagnetized plasma by using a recently generalized quasilinear theory. The numerical results show that the theory gives a good representation of trapping phenomena. It is found that trapping originates from retaining fast scale terms, both in the orbits and in the propagation of the perturbed distribution f′. Such terms in the latter represent space and time correlations of the orbits, or, equivalently, the ‘‘memory’’ of the average distribution f̄. Both theory and computation were done in the regime f′≪ f̄, or eΦ/T<1. Mode-coupling terms are not needed in such a regime.
Line tying of interchange modes in a nearly collisionless mirror-trapped plasma
Authors: Vandegrift Guy
Published: July 2002

If the confining potential of electrostatically trapped electrons fluctuates, then the number of trapped electrons also fluctuates. The linear relationship between potential fluctuations and the number of trapped electrons is investigated, considering two loss mechanisms for a nearly collisionless plasma: (1) small-angle collisions (diffusion), and (2) large-angle collisions. This nearly collisionless model predicts the line tying of interchange modes in a mirror-trapped plasma is orders of magnitude larger than previously thought for a fusion plasma, yet still not strong enough to completely line tie an axisymmetric mirror. Also, a nonlinearity in the response can occur at low amplitude.
Analysis of free-electron lasing stimulated by a counterpropagating plasma wave
Authors: Akimoto K. , Yan Y. T.
Published: July 2002

A relativistic fluid theory is constructed to analyze the inverse Compton scattering of an unmagnetized counterpropagating plasma wave by a cold relativistic electron beam. A Langmuir wave and electromagnetic plasma wave wigglers are considered, and the properties of the two types of wigglers are comparatively discussed. The growth rates are comparable to those of the ac free-electron laser and the free-electron lasers with magnetostatic wigglers in the Raman regime.
Nonlinear behavior of magnetohydrodynamic modes near marginally stable states. II. Application to the resistive fast interchange mode
Authors: Nakajima Noriyoshi , Hamaguchi Satoshi
Published: July 2002

With the use of the general formulation developed in an earlier paper, the nonlinear evolution of the resistive fast interchange mode near the marginally stable state is obtained analytically. The nonlinear amplitude equation of the mode is shown to be of the Landau type. It is also shown that there is a stable equilibrium bifurcating from the initial equilibrium. Comparing this analytical result to numerical simulations, it is confirmed that the saturation level and the saturation time are well estimated by this Landau type of nonlinear amplitude equation.
Numerical drift orbit calculations for force-free spheromak configurations
Authors: Sahlin P. A. , Pierce W. , Biglari H. , Fleischmann H. H. , Jardin S. C.
Published: July 2002

A numerical analysis was performed of guiding-center (gc) orbits in a variety of spheromak-type force-free, numerically determined equilibria including the normal spherical configurations as well as configurations that are more prolate and oblate, and others having hollow or peaked current profiles. The calculated drift orbits differ significantly from the well-known drift orbits in tokamaks. In particular, the results indicate (i) the existence of particles trapped in separate hemispheres, (ii) the orbit widths d are about proportional to the Larmor radius ρ of the particle (calculated for the field maximum) up to ρ≊0.01–0.02 of the major separatrix dimension, (iii) many orbits, in particular on the outer flux lines, have their maximum normalized width dmax/ρL(ρL= local Larmor radius) away from the midplane of the configuration, and (iv) these maximum normalized widths are about 2–4 over most of the volume for all configurations except for prolate ones with a peaked current profile; in the latter configurations, orbits on outer field surfaces show dmax≤ρL.
Three-dimensional studies of helical equilibria and magnetic surface breaking due to the finite beta effect
Authors: Hayashi Takaya , Sato Tetsuya , Takei Akira
Published: July 2002

Three-dimensional equilibrium and breaking of magnetic surfaces due to the finite beta effect in a l=2 heliotron/torsatron configuration are studied by using a newly developed three-dimensional equilibrium code. The breaking is significantly suppressed as γc (pitch parameter) becomes smaller. An inward shift of the plasma by using the vertical field and elliptic (vertical) shaping using the quadrupole field can also suppress the breaking.
A kinetic theory for electron cyclotron maser interaction in a waveguide: Coupling between a transverse electric mode and a transverse magnetic mode
Authors: Schill Robert A. , Seshadri S. R.
Published: July 2002

A kinetic treatment valid at all harmonic cyclotron frequencies is presented for the electron cyclotron maser interaction between a tenuous annular relativistic electron beam and the transverse electric, TE0n, mode in a cylindrical waveguide. Including all equilibrium guiding center trajectory function effects, an improved dispersion relation valid near and far from resonance is obtained. Adding the transverse magnetic, TM0s, mode, the derived dispersion relation reveals that coupling between the two waveguide modes may be significant. Parameter regimes indicating when coupling may be significant are identified. For weakly relativistic and relativistic beams, a wide range of parameters exists when the operating frequency is near the cutoff of either mode. When far from cutoff, similar conclusions are made. A new, direct transfer mechanism between two empty waveguide modes in the presence of the beam is established. Under appropriate conditions, it is explicitly shown that the inclusion of the TM0n mode can enhance or inhibit the growth rate.
The rapid inward diffusion of cold ions in tokamaks and their effect on ion transport
Authors: Ware A. A.
Published: July 2002

The observed increase with density of the density asymmetry caused by the centrifugal force of toroidal motion in the PDX tokamak [Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1981), Vol. 1, p. 665], which is contrary to conventional theory, is explained by the presence of an excess of low-energy ions with 10%–15% concentration. The prime source being recycling, it is shown that low-energy ions undergo rapid inward diffusion (too rapid to thermalize with the outward diffusing energetic ions) because of the combined effects of large νPA, electrostatic diffusion, and negative Er and ∂Ti/∂r. The presence of the low-energy ions alters dramatically the predictions of neoclassical theory and many hydrogen and impurity ion transport phenomena now have simple explanations.
Beam dynamics in high-current cyclic electron accelerators
Authors: Chernin D.
Published: July 2002

The physical processes affecting the transport and acceleration of high-power, high-quality electron beams in cyclic accelerators are reviewed. A distinction is made between those effects that are unique to recirculating geometries and those that also occur in linacs. Among the former are included the phenomena of momentum compaction, orbital resonances, and the negative mass instability; among the latter are the beam break-up and other microwave instabilities, the effects of image forces, and the problem of matching an incoming beam envelope to a transport line. All have played prominent roles in the design and operation of existing and planned cyclic machines. These dynamical effects and some experimental approaches to controlling them are discussed.
Measurements of classical deceleration of beam ions in the DIII-D tokamak
Authors: Heidbrink W. W.
Published: July 2002

Studies of the slowing down of short pulses of deuterium beam ions in the DIII-D tokamak [Nucl. Fusion 28, 1897 (1988)] are extended to the regime where ion drag dominates electron drag. The deceleration of the beam ions is consistent with Sivukhin’s classical theory [Reviews of Plasma Physics (Consultants Bureau, New York, 1966), Vol. 4, p. 93] to within 25%.
Frontiers of particle beam physics
Authors: Sessler Andrew M.
Published: July 2002

First, a review is given of various highly developed techniques for particle handling that are, nevertheless, being vigorously advanced at the present time. These include soft superconductor radio-frequency cavities, hard superconductor magnets, cooling rings for ions and antiprotons, and damping rings for electrons. Second, attention is focused upon novel devices for particle generation, acceleration, and focusing. These include relativistic klystrons and free electron laser power sources, binary power multipliers, photocathodes, switched-power linacs, plasma beat-wave accelerators, plasma wake-field accelerators, plasma lenses, plasma adiabatic focusers, and plasma compensators.
Plasma physics at the final focus of high-energy colliders
Authors: Katsouleas T. , Su J. J. , Mori W. B. , Dawson J. M.
Published: July 2002

The plasma physics associated with intense electron and positron beams in high-energy colliders is discussed. The focusing and plasma oscillation of these beams are studied in the presence of an externally supplied plasma (a plasma lens) and in the self-consistent fields of the interpenetrating beams. A plasma lens can provide strong focusing of a beam by shielding the beam’s radial space-charge electric field and allowing it to self-pinch in its self-generated azimuthal magnetic field. The focusing force of a plasma lens can be equivalent to quadrupole magnet strengths of the order of hundreds of MG/cm. Theoretical and computational work characterizing the aberrations and final spot sizes possible with plasma lenses is presented. Furthermore, when the e+ and e− beams overlap at the interaction point (i.e., collide), they behave (temporarily) as a two-component plasma. The self-pinching or disruption of one beam by another in the e+e− plasma is modeled analytically and with two-dimensional particle-in-cell simulations.
Magnetohydrodynamic buoyancy-driven turbulence in thermally stratified conducting flow
Authors: Khait Vadim D.
Published: July 2002

Magnetohydrodynamic (MHD) buoyancy-driven instability has much in common with gravity-driven natural convection instability in thermally stratified fluids, in that account must be taken of the temperature dependence of conductivity in the former case and of density in the latter case. Employing the Monin–Obukhov theory of mixed convection in a stratified atmosphere, temperature and velocity profiles in MHD turbulent shear flow are obtained. The problem of the boundary-layer development is solved, and the heat and momentum fluxes are found. It is shown that the buoyancy force effects drastically change the fluxes when the Stuart number exceeds unity. Anode–cathode asymmetry observed experimentally on MHD devices is explained.
Recent results from the ATF torsatron
Authors: Murakami M. , Aceto S. C. , Anabitarte E. , Anderson D. T. , Anderson F. S. B. , Batchelor D. B. , Brañas B. , Baylor L. R. , Bell G. L. , Bell J. D. , Bigelow T. S. , Carreras B. A. , Colchin R. J. , Crocker N. A. , Crume E. C. , Dominguez N. , Dory R. A. , Dunlap J. L. , Dyer G. R. , England A. C. , Fowler R. H. , Gandy R. F. , Glowienka J. C. , Goldfinger R. C. , Goulding R. H. , Hanson G. R. , Harris J. H. , Hidalgo C. , Hillis D. L. , Hiroe S. , Hirshman S. P. , Horton L. D. , Howe H. C. , Hutchinson D. P. , Isler R. C. , Jernigan T. C. , Kaneko H. , Kwon M. , Langley R. A. , Leboeuf J. N. , Lee D. K. , Lo D. H. C. , Lynch V. E. , Lyon J. F. , Ma C. H. , Menon M. M. , Mioduszewski P. K. , Morita S. , Morris R. N. , Neilson G. H. , Ochando M. A. , Okamura S. , Paul S. , Qualls A. L. , Rasmussen D. A. , Richards R. K. , Ritz Ch. P. , Rome J. A. , Sanchez J. , Schwelberger J. G. , Shaing K. C. , Shepard T. D. , Simpkins J. E. , Thomas C. E. , Tolliver J. S. , Uckan T. , Vander Sluis K. L. , Wade M. R. , Wilgen J. B. , Wing W. R. , Yamada H. , Zielinski J. J.
Published: July 2002

Recent experiments in the Advanced Toroidal Facility (ATF) torsatron [Plasma Physics and Controlled Nuclear Fusion Research 1990 (IAEA, Vienna, in press)] have emphasized the role of magnetic configuration control in transport studies. Long-pulse plasma operation up to 20 sec has been achieved with electron cyclotron heating (ECH). With neutral beam injection (NBI) power of ≥1 MW, global energy confinement times of 30 msec have been obtained with line-average densities up to 1.3×1020 m−3. The energy confinement and the operational space in ATF are roughly the same as those in tokamaks of similar size and field. The empirical scaling observed is similar to gyro-reduced Bohm scaling with favorable dependences on density and field offsetting an unfavorable power dependence. The toroidal current measured during ECH is identified as the bootstrap current. The observed currents agree well with predictions of neoclassical theory in magnitude and in parametric dependence. Variations of the magnetic configuration in discharges heated by ECH alone and by NBI change plasma transport and plasma profiles. Magnetic fluctuations respond to the concomitant pressure profile variations. Comparative studies of edge fluctuations in the Texas experimental tokamak (TEXT) [Plasma Physics and Controlled Nuclear Fusion Research 1990 (IAEA, Vienna, in press)] and the ATF stellarator showed remarkable similarity in the levels of fluctuations and the existence of a velocity shear layer.
Effects of limiters on reversed-field pinch confinement
Authors: Weber P. G. , Ingraham J. C. , Ellis R. F. , Wurden G. A. , Munson C. P. , Downing J. N.
Published: July 2002

This paper documents the effects on confinement of introducing discrete limiters into the edge plasma of the ZT-40M reversed-field pinch (RFP) [Fusion Technol. 8, 1571 (1985)]. RFP confinement is not significantly degraded by appropriately designed single limiters inserted to a sufficient depth for effective local vacuum vessel wall protection. Inserting limiters too deeply into the plasma results in excess limiter heating, and a consequent increase in the impurity content of the plasma. Under these conditions the plasma loop voltage increases. The heating of the limiters is observed to be asymmetric, with the majority of the heat flux in ZT-40M being attributable to suprathermal electrons [Tsupra∼2–3×Te(0)] reaching the edge moving almost unidirectionally along magnetic-field lines.
Observations of a Buneman double layer and associated electron heating in a high-voltage straight plasma discharge
Authors: Takeda Y. , Yamagiwa K.
Published: July 2002

The spatial evolution of a potential hump (electron hole) into a Buneman double layer was for the first time observed at the instant of current limitation in the initial phase of a high-voltage straight plasma discharge with a preexisting hydrogen plasma. Potential profiles along the axis numerically calculated from the real time E-field data demonstrate the formation of a strong double layer with an inverse potential jump (eφDL/kTe∼103) moving toward the center of the device with a mean velocity 1.2×108 cm/sec, nearly 0.3 times the electron thermal velocity. The strong HV double layer developed near the center then quickly grew up to an extremely strong dynamic double layer propagating toward the anode. The formation of a highly anisotropic velocity distribution of energetic electrons associated with the strong double layer was evidenced by intense hard x-ray emissions that were first detected in the direction almost parallel to the magnetic field with a delay time 250–350 nsec from the generation of the double layer.
Electromagnetic turbulent pressure in a plasma of inhomogeneous turbulence
Authors: Li Fang
Published: July 2002

A general expression of electromagnetic turbulent pressure in a plasma of inhomogeneous turbulence is derived from Vlasov’s equation using the properties of the spectrum of correlation of two fluctuating parameters. It is found that this pressure consists of two parts. One is the electromagnetic ponderomotive force produced by interaction between the nonresonant particles and the turbulent waves. The other is the direct transfer of momentum from the turbulent waves to the plasma through the interaction between the resonant particles and the waves. Corresponding representations of turbulent pressure for some turbulent oscillation modes (Alfvén waves, magnetohydrodynamic waves, whistlers, ion-acoustic oscillations, and Langmuir waves) are given for a plasma of Maxwellian distribution.
Ion cyclotron wave excitation by double resonance coupling
Authors: Fasoli A. , Good T. N. , Paris P. J. , Skiff F. , Tran M. Q.
Published: July 2002

A modulated high frequency wave is used to remotely excite low frequency oscillations in a linear, strongly magnetized plasma column. An electromagnetic wave is launched as an extraordinary mode across the plasma by an external waveguide in the upper-hybrid frequency regime f≊fUH≊fce≊8 GHz, with P≤2 W. By frequency modulating (at fFM≊1–60 kHz, with fci≂30 kHz) the pump wave, the resonant layer is swept radially across the profile and perpendicularly to the field lines at f=fFM. The resulting radial oscillation of the electron linear and nonlinear pressure can be considered to act as a source term for the ion wave. A localized virtual antenna is thereby created inside the plasma. Measurements of the ion dielectric response (interferograms and perturbed distribution functions) via laser-induced fluorescence identify the two branches (forward, or ion-acoustic-like, and backward, or Bernstein, modes) of the electrostatic dispersion relation in the ion cyclotron frequency range. By changing the modulation bandwidth, and thus the spatial excursion of the oscillating resonant layer, a control on the perpendicular wavelength of the excited mode can be exerted. In particular, the possibility of selective excitation of the ion Bernstein wave is demonstrated experimentally.