bluuebunny/crossref_metadata_2025 huggingface dataset:
The Hausdorff moments in statistical mechanics
Authors: Scalas E. , Viano G. A.
Published: July 2002

A new method for solving the Hausdorff moment problem is presented which makes use of Pollaczek polynomials. This problem is severely ill posed; a regularized solution is obtained without any use of prior knowledge. When the problem is treated in the L2 space and the moments are finite in number and affected by noise or round-off errors, the approximation converges asymptotically in the L2 norm. The method is applied to various questions of statistical mechanics and in particular to the determination of the density of states. Concerning this latter problem the method is extended to include distribution valued densities. Computing the Laplace transform of the expansion a new series representation of the partition function Z(β) (β=1/kBT) is obtained which coincides with a Watson resummation of the high-temperature series for Z(β).
Anosov actions on noncommutative algebras
Authors: Emch G. G. , Narnhofer H. , Thirring W. , Sewell G. L.
Published: July 2002

An axiomatic framework for a quantum mechanical extension to the theory of Anosov systems is constructed, and it is shown that this retains some of the characteristic features of its classical counterpart, e.g., nonvanishing Lyapunov exponents, a vectorial K-property, and exponential clustering. The effects of quantization are investigated on two prototype examples of Anosov systems, namely, the iterations of an automorphism of the torus (the ‘‘Arnold Cat’’ model) and the free dynamics of a particle on a surface of negative curvature. It emerges that the Anosov property survives quantization in the case of the former model, but not of the latter one. Finally, we show that the modular dynamics of a relativistic quantum field on the Rindler wedge of Minkowski space is that of an Anosov system.
Dyon-Skyrmion lumps
Authors: Brihaye Y. , Kleihaus B. , Tchrakian D. H.
Published: July 2002

We make a numerical study of the classical solutions of the combined system consisting of the Georgi–Glashow model and the SO(3) gauged Skyrme model. Both monopole-Skyrmion and dyon-Skyrmion solutions are found. A new bifurcation is shown to occur in the gauged Skyrmion solution sector.
Weak coupling limit and removing an ultraviolet cutoff for a Hamiltonian of particles interacting with a quantized scalar field
Authors: Hiroshima Fumio
Published: July 2002

An interaction system consisting of particles and a quantized scalar field is considered. The Hamiltonian of the system is defined as a self-adjoint operator in a Hilbert space. An ultraviolet cutoff is imposed on the Hamiltonian. A renormalized Hamiltonian is defined by subtracting a renormalization term from the Hamiltonian. Our aim in this paper is to remove the ultraviolet cutoff and take the weak coupling limit simultaneously for the renormalized Hamiltonian. By using a functional integral that contains a vector-valued stochastic integral, a Schrödinger Hamiltonian with a many-body Coulomb potential (resp., Yukawa potential) is derived, if the mass of the quantized scalar field is zero (resp., positive).
Hidden supersymmetry and Berezin quantization of N=2, D=3 spinning superparticles
Authors: Gorbunov I. V. , Lyakhovich S. L.
Published: July 2002

The first quantized theory of N=2, D=3 massive superparticles with arbitrary fixed central charge and (half) integer or fractional superspin is constructed. The quantum states are realized on the fields carrying a finite-dimensional, or a unitary infinite-dimensional, representation of the supergroups OSp (2|2) or SU (1,1|2). The construction originates from quantization of a classical model of the superparticle we suggest. The physical phase space of the classical superparticle is embedded in a symplectic superspace T*(R1,2)×L1|2, where the inner Kähler supermanifold L1|2≅OSp(2|2)/[U(1)×U(1)]≅SU(1,1|2)/[U(2|2)×U(1)] provides the particle with superspin degrees of freedom. We find the relationship between Hamiltonian generators of the global Poincaré supersymmetry and the “internal” SU(1,1|2) one. Quantization of the superparticle combines the Berezin quantization on L1|2 and the conventional Dirac quantization with respect to space–time degrees of freedom. Surprisingly, to retain the supersymmetry, quantum corrections are required for the classical N=2 supercharges as compared to the conventional Berezin method. These corrections are derived and the Berezin correspondence principle for L1|2 underlying their origin is verified.
State vector reduction as a shadow of a noncommutative dynamics
Authors: Heller Michael , Sasin Wiesław , Odrzygóźdź Zdzisław
Published: July 2002

A model, based on a noncommutative geometry, unifying general relativity and quantum mechanics, is developed. It is shown that the dynamics in this model can be described in terms of one-parameter groups of random operators, and that the noncommutative counterparts of the concept of state and that of probability measure coincide. We also demonstrate that the equation describing noncommutative dynamics in the quantum mechanical approximation gives the standard unitary evolution of observables, and in the “space–time limit” it leads to the state vector reduction. The cases of the spin and position operators are discussed.
Time-optimal control of finite quantum systems
Authors: Weaver Nik
Published: July 2002

We investigate time-optimal control of finite quantum systems in the Born approximation. A bang–bang principle is found to follow from a result in [C. A. Akemann and J. Anderson, Mem. Amer. Math. Soc. 458 (1991)]. We also prove existence of time-optimal controls, characterize when they are unique, and assuming uniqueness, explicitly describe them.
Lagrangian submanifolds in product symplectic spaces
Authors: Janeczko S.
Published: July 2002

We analyze the global structure of Lagrangian Grassmannian in the product symplectic space and investigate the local properties of generic symplectic relations. The cohomological symplectic invariant of discrete dynamical systems is generalized to the class of generalized canonical mappings. Lower bounds for the number of two-point and three-point symplectic invariants for billiard-type dynamical systems are found and several examples of symplectic correspondences encountered from physics are presented.
Analogies between finite-dimensional irreducible representations of SO(2n) and infinite-dimensional irreducible representations of Sp(2n,R). II. Plethysms
Authors: King R. C. , Wybourne B. G.
Published: July 2002

The basic spin difference character Δ″ of SO(2n) is a useful device in dealing with characters of irreducible spinor representations of SO(2n). It is shown here that its kth-fold symmetrized powers, or plethysms, associated with partitions κ of k factorize in such a way that Δ″⊗{κ}=(Δ″)r(κ)Πκ, where r(κ) is the Frobenius rank of κ. The analogy between SO(2n) and Sp(2n,R) is shown to be such that the plethysms of the basic harmonic or metaplectic character Δ̃ of Sp(2n,R) factorize in the same way to give Δ̃⊗{κ}=(Δ̃)r(κ)Π̃κ. Moreover, the analogy is shown to extend to the explicit decompositions into characters of irreducible representations of SO(2n) and Sp(2n,R) not only for the plethysms themselves, but also for their factors Πκ and Π̃κ. Explicit formulas are derived for each of these decompositions, expressed in terms of various group–subgroup branching rule multiplicities, particularly those defined by the restriction from O(k) to the symmetric group Sk. Illustrative examples are included, as well as an extension to the symmetrized powers of certain basic tensor difference characters of both SO(2n) and Sp(2n,R).
Topology and perturbation theory
Authors: Manjavidze J.
Published: July 2002

This paper contains description of the fields nonlinear modes successive quantization scheme. It is shown that the path integrals for absorption part of amplitudes are defined on the Dirac (δ-like) functional measure. This permits arbitrary transformation of the functional integral variables. New form of the perturbation theory achieved by mapping the quantum dynamics in the space WG of the (action, angle)-type collective variables. It is shown that the transformed perturbation theory contributions are accumulated exactly on the boundary ∂WG. Abilities of the developed formalism are illustrated by the Coulomb problem. This model is solved in the WC=(angle, angular momentum, Runge–Lentz vector) space and the reason of its exact integrability is emptiness of ∂WC.
Local optimization of the summation of divergent power series
Authors: Walkup J. R. , Dunn M. , Watson D. K.
Published: July 2002

A method of optimizing a sequence of economized rational approximants (ERAs) to produce a sequence of approximants with enhanced convergence properties is described. It is shown that such a technique improves upon the error of the Padé approximants at a chosen value of the independent variable, and in some cases leads to dramatic improvement, even in cases where Padé approximants behave erratically. The procedure is tested on six known functions, with improved convergence and accuracy in each case. The procedure is then applied to the problem of evaluating a perturbation series of an atomic system, diamagnetic hydrogen, with significant improvement in both convergence and accuracy as well.
On sign reversal of the linear thermal expansion coefficient of fullerite C60 at helium temperatures
Authors: Loktev V. M.
Published: July 2002

An attempt is made to interpret the low-temperature negative thermal expansion of solid C60 on the basis of an assumption concerning the freezing of all (thermally activated) rotations and the formation of anisotropic intermolecular potential ensuring libron vibrations of fullerene molecules in the equilibrium position displaced relative to the isotropic potential minimum.
Evolution of resonant wave triads in three-dimensional boundary layers
Authors: El-Hady Nabil M.
Published: July 2002

An analysis is presented that examines the modulation of different instability modes that satisfy the triad resonance conditions in time and space in a three-dimensional, boundary-layer flow. Detuning parameters are used for the wavenumbers and frequencies. The nonparallelism of the mean flow is taken into account in the analysis. At the leading-edge region of an infinite swept wing, different resonant triads comprised of traveling cross-flow, stationary cross-flow, vertical vorticity, and Tollmien–Schlichting modes are investigated. The spatial evolution of the resonating triad components are studied.
Simultaneous measurements of instantaneous concentrations of two reacting species in a turbulent flow with a rapid reaction
Authors: Komori Satoru , Kanzaki Takao , Murakami Yasuhiro
Published: July 2002

An original technique is developed to measure simultaneously the instantaneous concentrations of two reacting species being mixed and reacted in a turbulent flow with a second-order rapid reaction between acetic acid and ammonium hydroxide. The technique combines laser fluorescence and electrode-conductivity methods and it enables simultaneous measurements of concentrations of two reacting species with a spatial resolution much less than the concentration–dissipation scale in grid-generated tubulence.
Two nonlinear control schemes contrasted on a hydrodynamiclike model
Authors: Keefe Laurence R.
Published: July 2002

The feasibility of shear flow control using strategies originated by Hübler (H), and by Ott, Grebogi, and Yorke (OGY), has been examined numerically employing fully developed and transitional solutions of the Ginzburg–Landau equation as models for such flows. The general message of this study is that control of nonlinear systems is best obtained by making maximum use possible of the underlying natural dynamics. The effectiveness of both methods in obtaining control of fully developed flows depends strongly upon the ‘‘distance’’ in state space between the uncontrolled flow and goal dynamics. If the goal dynamics is an unstable nonlinear solution of the equation, or a close approximation, and the flow is nearby at the instant control is applied, both methods perform reliably and at low-energy cost in reaching and maintaining this goal. For example, under conditions when the spatially complex and temporally chaotic uncontrolled flow exists on a strange attractor of Lyapunov dimension Dλ≂120, several different spatially periodic limit cycle motions (Dλ=1) were successfully maintained by both methods using less than 1% of the energy of the chaotic motion.

However, when the goal dynamics is not nearby the uncontrolled flow state at the instant control is attempted, both methods can fail in their own unique way. In the H method the failure occurs because multiple solutions of the forced equation result from the same forcing. This could be a generic problem in all nonlinear systems, the Navier–Stokes equations included. In some cases this failure may be avoided by defining and controlling to a sequence of intermediate goals that lead to the ultimate dynamics. This staged approach to a goal shows potential of helping the OGY method when it also fails. Here the ‘‘targeting’’ methods useful in low-dimensional systems for moving from uncontrolled states to a goal region fail because of the underlying complexity of the attractor, or because the goal dynamics are not embedded within the chaotic attractor of the uncontrolled system. There are conceptual difficulties in applying the OGY method to transitional, convectively unstable flows, but within certain limitations the H method works well, though at a large cost in energy terms. It works best when the goal dynamics rearranges the energy of the uncontrolled flow into new nonlinear forms, rather than simply trying to suppress it. The performance of both methods degrades due to noise and the spatially discrete nature of realistic forcing, but these effects are not difficult to predict. It is suggested that channel flows may be particularly amenable to control by either the H or OGY methods, while the H method seems more appropriate for boundary layers.
Calculation of Hamada coordinates for a large-aspect-ratio tokamak
Authors: Coronado M. , Trejo J. Galindo
Published: July 2002

The application of the well-known moment equation approach to neoclassical transport requires the use of Hamada coordinates in three-dimensional toroidal plasmas. The lack of analytical expressions and the difficulty associated with the numerical calculation of these coordinates has strongly limited the use of this approach. In this paper analytical calculations of Hamada coordinates for a large-aspect-ratio tokamak are presented. Knowledge of these coordinates for this relatively simple two-dimensional case will allow, for the first time, a general analytical application of the moment equation approach, and also a check of this approach against well-known results. In particular, it is shown here that the approach correctly reproduces the Pfirsch–Schlüter diffusion rate.
Broadening of the lower hybrid k∥ spectrum by toroidal effects
Authors: Barbato E. , Romanelli F.
Published: July 2002

Toroidal geometry affects the evolution of k∥ (the component of the wave vector parallel to the magnetic field) along the lower hybrid, (LH) wave trajectories. In this paper such variations are investigated both analytically and numerically. The main parameters governing this phenomenon are found and how k∥ upshift can occur within this scheme is elucidated. As a figure of merit a k∥- upshift factor is defined and discussed in a dimensionless parameter space in which all the LH experiments can be represented. Finally, a discussion of whether and when toroidal effects can fill the gap between the high phase velocity of the injected LH waves and the electron thermal velocity is presented by analyzing different experimental situations.
Inversion of the ballooning transformation
Authors: Hazeltine R. D. , Newcomb W. A.
Published: July 2002

The ballooning formalism can be viewed, not just as an eikonal representation, but as an integral transform, analogous to the Fourier or Laplace transforms, with a uniquely defined inverse. Here, the inversion theorem is proved, and an error in the previous literature is corrected.
Experimental and theoretical studies of a 35 GHz cyclotron autoresonance maser amplifier
Authors: DiRienzo A. C. , Bekefi G. , Chen C. , Wurtele J. S.
Published: July 2002

Experimental and theoretical studies of a cyclotron autoresonance maser (CARM) amplifier are reported. The measurements are carried out at a frequency of 35 GHz using a mildly relativistic electron beam (1.5 MeV, 130 A, 30 nsec) generated by a field emission electron gun followed by an emittance selector that removes the outer, hot electrons. Perpendicular energy is imparted to the electrons by means of a short bifilar helical wiggler. The entire system is immersed in a uniform axial magnetic field of 6–8 kG. With an input power of 17 kW at 35 GHz from a magnetron driver, the saturated power output is 12 MW in the lowest TE11 mode of a circular waveguide, corresponding to an electronic efficiency of 6.3%. The accompanying linear growth rate is 50 dB/m. When the system operates in the superradiant mode (in the absence of the magnetron driver) excitation of multiple waveguide modes is observed. A three-dimensional simulation code that has been developed to investigate the self-consistent interaction of the copropagating electromagnetic waveguide mode and the relativistic electron beam is in good agreement with the experimental observations.
The evolution of resistive ballooning modes in the banana-plateau collisionality regime
Authors: Sundaram A. K. , Callen J. D.
Published: July 2002

The theory of resistive ballooning modes relevant to the banana-plateau collisionality regime is studied using the recently developed neoclassical magnetohydrodynamics equations. Employing the ballooning mode formulation and a multiple length scale analysis, a generalized set of poloidal flux surface-averaged equations coupling the parallel ion flow velocity V∥i, the vector potential A∥, and the electrostatic potential φ are derived. A particularly simple case in which the parallel sound wave coupling reduces the order of the differential equation in the frequency range ‖ω‖≫ωs, where ωs=scs/qR0, s is the shear parameter, cs is the sound speed, and qR0 is the connection length, is dealt with. The calculations show that a new class of localized pressure-gradient-driven ballooning modes with growth rates varying as (νe+μe)1/2 is possible, where νe is the electron collision frequency and μe is the electron neoclassical poloidal flow viscous damping frequency. It is shown that the resistive ballooning modes are sensitive to variations of a parameter η (=‖d ln P0/d ln q‖) within the tokamak plasma. The enhanced ion polarization and pinch type currents are found to cause stabilization of resistive modes. Further, our model highlights a smooth transition from the Pfirsch–Schlüter to the (neoclassical) banana-plateau collisionality regimes. The relevance of these results to ISX-B experiments [Phys. Rev. Lett. 50, 503 (1983)] is briefly pointed out.
Particle dynamics and current-free double layers in an expanding, collisionless, two-electron-population plasma
Authors: Hairapetian G. , Stenzel R. L.
Published: July 2002

The expansion of a two-electron-population, collisionless plasma into vacuum is investigated experimentally. Detailed in situ measurements of plasma density, plasma potential, electric field, and particle distribution functions are performed. At the source, the electron population consists of a high-density, cold (kTe≂4 eV) Maxwellian, and a sparse, energetic ( (1)/(2) mv2e≂80 eV) tail. During the expansion of plasma, space-charge effects self-consistently produce an ambipolar electric field whose amplitude is controlled by the energy of tail electrons. The ambipolar electric field accelerates a small number (∼1%) of ions to streaming energies which exceed and scale linearly with the energy of tail electrons. As the expansion proceeds, the energetic tail electrons electrostatically trap the colder Maxwellian electrons and prevent them from reaching the expansion front. A potential double layer develops at the position of the cold electron front. Upstream of the double layer both electron populations exist; but downstream, only the tail electrons do. Hence, the expansion front is dominated by retarded tail electrons. Initially, the double layer propagates away from the source with a speed approximately equal to the ion sound speed in the cold electron population. The propagation speed is independent of the tail electron energy. At later times, the propagating double layer slows down and eventually stagnates. The final position and amplitude of the double layer are controlled by the relative densities of the two electron populations in the source. The steady-state double layer persists till the end of the discharge (Δt≂1 msec), much longer than the ion transit time through the device (t≂150 μsec). On the low-potential side, the double layer generates a monoenergetic, neutralized ion beam with no stationary background plasma. The field-aligned double layer contains no trapped or counter-streaming ions, and is current free; i.e., the relative electron–ion drift is zero.
Axial dynamics in field-reversed theta pinches. I: Formation
Authors: Tuszewski M. , Armstrong W. T. , Chrien R. E. , Hugrass W. N. , McKenna K. F. , Rej D. J. , Siemon R. E. , Taggart D. P. , Wright B. L.
Published: July 2002

Bias field scans are performed at various fill pressures in the FRX-C [Fusion Technol. 9, 13 (1986)] and FRX-C/LSM [Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1989), Vol. II, p. 517] field-reversed theta pinches. These data show a systematic degradation of the confinement properties of field-reversed configurations whenever strong axial implosions occur during plasma formation. This limitation prevents access to the desired regime of large-size and long-lived field-reversed configurations. The cause of the confinement degradation must be due to some formation or gross stability problem. Here many studies are reported that attempt to correlate confinement degradation with some formation characteristic. These investigations remain inconclusive and suggest further stability studies presented in a companion paper.
The effect of collisions in maintaining a non-Maxwellian plasma distribution in a spherically convergent ion focus
Authors: Rosenberg M. , Krall Nicholas A.
Published: July 2002

It is shown that, for a moderately long time scale, two-body collisions can actually help in maintaining a non-Maxwellian ion velocity distribution in a plasma. This effect occurs when the ions have orbits large enough to transit spatial regions with different physical parameters in a single collision time. The effect is applied to ions confined in a spherically convergent ion focus (SCIF), where collisions at the edge of a spherical potential well help maintain convergent non-Maxwellian flow in the rest of the device.
Collective parametric instabilities of many overlapping laser beams with finite bandwidth
Authors: DuBois D. F. , Bezzerides Bandel , Rose Harvey A.
Published: July 2002

A class of collective three-wave parametric instabilities resulting from the overlap of N, phase-independent, converging laser beams, each with finite frequency bandwidth and modest spatial incoherence is considered. A statistical analysis is employed based on the random phase approximation (RPA) to derive the thresholds, growth rates, and spatial gain coefficients for these instabilities. When the laser beams are symmetrically distributed in a converging conical array it is argued that collective parametric instabilities can be excited in which one of the daughter waves propagates along the symmetry axis of the cone and is coupled equally to all the pump beams and to the other daughter waves that lie in another cone determined by the matching conditions. For a sufficiently large number of beams the collective modes have lower thresholds than the single-beam instabilities. The collective thresholds are greater than or equal to the incoherent thresholds for a single beam containing N times the single-beam power. To be effective the spatial extent of the beam overlap region must be long enough to allow significant convective amplification or absolute instability. A potentially dangerous collective instability, resulting from stimulated Raman scattering (SRS), has a common electron plasma wave along the axis of symmetry and has a low threshold for coherent beams. This common plasma wave may be detrimental to laser fusion as a potential source of hot electrons. Sufficient bandwidth and angular divergence of the beams can suppress this instability relative to a more benign collective mode where the scattered light is the common mode along the symmetry axis.
Mode conversion at electron cyclotron harmonics with finite k∥
Authors: Hu J. L. , Swanson D. G.
Published: July 2002

Relativistic plasma mode conversion-tunneling equations at the second and third electron cyclotron harmonics are derived. A finite k∥ is introduced which keeps the coupling between the O-mode, the X-mode and the Bernstein wave in the mode conversion problem for the first time. The solutions for these mode conversion problems without absorption are obtained, and the connection formulas between different wave branches are established. The corresponding transmission, reflection and conversion coefficients are also given. A comparison between the coupled equation and the uncoupled equations is also made.
Resonance absorption in high-intensity contrast, picosecond laser–plasma interactions*
Authors: Meyerhofer D. D. , Chen H. , Delettrez J. A. , Soom B. , Uchida S. , Yaakobi B.
Published: July 2002

The interaction of high-intensity contrast, picosecond, 1-μm laser pulses with solid metal targets is studied with Kα emission from multilayer targets, fast ion blowoff, and other diagnostics. It is found that the characteristics of the interaction are determined by the intensity of the p-polarized component of the incoming laser field, rather than the total intensity. Consistent with resonance absorption, 20%–30% of the laser energy is deposited into suprathermal electrons that have temperatures from 2–10 keV.
Cyclotron resonance in an inhomogeneous magnetic field
Authors: Albert Jay M.
Published: July 2002

Relativistic test particles interacting with a small monochromatic electromagnetic wave are studied in the presence of an inhomogeneous background magnetic field. A resonance-averaged Hamiltonian is derived which retains the effects of passage through resonance. Two distinct regimes are found. In the strongly inhomogeneous case, the resonant phase angle at successive resonances is random, and multiple resonant interactions lead to a random walk in phase space. In the other, adiabatic limit, the phase angle is determined by the phase portrait of the Hamiltonian and leads to a systematic change in the appropriate canonical action (and therefore in the energy and pitch angle), so that the cumulative effect increases directly with the number of resonances.
Generation of extraordinary mode radiation by an electrostatic pump
Authors: Saleem H. , Chaudhry M. B. , Murtaza G. , Shukla P. K.
Published: July 2002

It is shown that an electrostatic wave near the upper-hybrid resonance frequency can parametrically excite extraordinary (X-) mode radiation accompanied by a great variety of low-frequency oscillations. The latter may include the lower-hybrid, the electron-acoustic, the ion-cyclotron, and the shear Alfvén waves. Nonlinear dispersion relations and the growth rates are obtained for each case. Comparison of our investigation to an earlier work and its possible application to space plasmas are pointed out.
Single-mode saturation of a linearly unstable plasma
Authors: Burnap C. , Miklavčič M. , Willis B. L. , Zweifel P. F.
Published: July 2002

The nonlinear oscillations of an electron plasma described by the collisionless Vlasov equation are studied using a perturbation technique previously applied by Simon and Rosenbluth [Phys. Fluids 19, 1567 (1976)]. It is proved by a characteristic argument that the plasma is globally stable, so that Bogoliuboff’s method of ‘‘secular regularization’’ is applicable. Assuming the plasma is confined in a box, and that only the lowest mode is unstable, it is shown that the ‘‘eigenmode dominance’’ approximation of Simon and Rosenbluth fails to conserve energy, but that energy and momentum conservation can be regained by considering interaction between the discrete and continuum modes. A formula is derived for the amplitude and phase of the saturated nonlinear oscillations. In a subsidiary result, it is shown that nonlinear effects damp the steady-state oscillations predicted by linearized theory for some stable plasmas.
Stokes flow past three spheres: An analytic solution
Authors: Kim Sangtae
Published: July 2002

Stokes flow past three spheres is solved analytically by use of (new) addition theorems that transform vector harmonics between different coordinate centers. The extension to other special configurations of N spheres is indicated. The method is illustrated for uniform flow past three spheres in a triangular cluster, with good agreement with experimental sedimentation velocities.
The velocity skewness measured in grid turbulence
Authors: Maxey M. R.
Published: July 2002

The slow decay of turbulent kinetic energy downstream of the grid is shown to contribute to the skewness of the velocity fluctuations. Estimates are given that show that energy decay has much stronger influence on the odd-order moments than the even-order moments.
Disturbed film flow on a vertical plate
Authors: Kheshgi Haroon S. , Scriven L. E.
Published: July 2002

Flow of incompressible Newtonian liquid films is governed by the Navier–Stokes system with shear-free, balanced-normal-stress, and kinematic boundary conditions at the free surface. This system is solved here for the evolution of finite-amplitude two-dimensional disturbances to otherwise steady flow down a vertical plate by means of a finite element method adapted for free boundary problems. When flow is specified to be spatially periodic, fully developed steady flows that ensue approach time-periodic states, i.e., waves, the finite amplitude of which depends upon their wavelength. The family of time-periodic states connects to the steady, fully developed flow at a Hopf bifurcation that lies at a critical disturbance length, in agreement with the Orr–Sommerfeld analysis. Initial disturbances to flow down a plate of finite length grow as they propagate downward. In all cases studied here, however, steady flow is eventually approached.
Ponderomotive force in a nonisothermal plasma
Authors: Lee Nam C. , Parks George K.
Published: July 2002

In this paper a formula is derived for the ponderomotive force of electromagnetic fields in collisionless and inhomogeneous plasma when the temperature varies slowly in space and time. This result, compared to the current formula for the isothermal case, has an additional term that involves the temperature gradient. The new result is valid in anisotropic medium and better suited for application to both laboratory and space plasma situations in which the plasma is anisotropic.
An experimental investigation of ‘‘vortex shocks’’
Authors: Krishnamoorthy S. , Marshall J. S.
Published: July 2002

An experimental study of the response of an intake vortex following cutting by a thin blade traveling normal to the vortex axis has been performed in order to examine the validity of predictions of ‘‘vortex shock’’ formation obtained from recent theories of vortex filaments with variable core radius. For the problem of cutting of an intake vortex with an ambient axial flow, the vortex filament theories predict formation of a ‘‘vortex shock’’ on the side of the vortex on which the ambient axial flow compresses the vortex axis and formation of a ‘‘vortex expansion wave’’ on the side which is stretched by the axial flow. Both the predicted vortex shock and vortex expansion wave propagate away from the blade in opposite directions. In the experiments, the formation of a sudden distortion of the vortex just following cutting by the blade is observed, which forms on the same side of the vortex on which the vortex shock is predicted to occur and propagates away from the blade at roughly the same speed as predicted for the vortex shock. The disturbance appears visually similar to a traveling vortex breakdown. The form of the disturbance varies with the ambient vortex state and the blade speed, although forms similar to bubble, spiral, and double-helix-type breakdowns have been observed. No vortex shock is observed on the opposite side of the vortex, on which the filament theory predicts formation of a vortex expansion wave. Several aspects of the experiments which are not included in the predictions of vortex filament theories are also noted, including the nonaxisymmetric form of the vortex shock and the rapid suction of blade boundary layer fluid into the vortex core following cutting of the vortex.
Thermophoresis of a spherical particle in a rarefied gas: Numerical analysis based on the model kinetic equations
Authors: Beresnev Sergey , Chernyak Vladimir
Published: July 2002

A kinetic theory for the thermophoretic force and velocity of a spherical particle in a rarefied gas is presented. The analysis is carried out on the basis of the linearized Bhatnagar–Gross–Krook (BGK) and S model [Fluid Dyn. 3, 95 (1968)] kinetic equations. The integral-moment method of solution for arbitrary values of Knudsen number is employed. The set of integral moment equations was solved by the Bubnov–Galerkin method. The possibility of arbitrary energy and tangential momentum accommodation of gas molecules on the particle surface is taken into account in the boundary condition. The particle–gas heat conductivity ratio Λ is assumed to be arbitrary. The results obtained are compared to the available theoretical and experimental data.
An O(N) algorithm for Stokes and Laplace interactions of particles
Authors: Sangani Ashok S. , Mo Guobiao
Published: July 2002

A method for computing Laplace and Stokes interactions among N spherical particles arbitrarily placed in a unit cell of a periodic array is described. The method is based on an algorithm by Greengard and Rokhlin [J. Comput. Phys. 73, 325 (1987)] for rapidly summing the Laplace interactions among particles by organizing the particles into a number of different groups of varying sizes. The far-field induced by each group of particles is expressed by a multipole expansion technique into an equivalent field with its singularities at the center of the group. The resulting computational effort increases only linearly with N. The method is applied to a number of problems in suspension mechanics with the goal of assessing the efficiency and the potential usefulness of the method in studying dynamics of large systems. It is shown that reasonably accurate results for the interaction forces are obtained in most cases even with relatively low-order multipole expansions.
Particle simulation study of driven magnetic reconnection in a collisionless plasma
Authors: Horiuchi Ritoku , Sato Tetsuya
Published: July 2002

Driven magnetic reconnection in a collisionless plasma, ‘‘collisionless driven reconnection,’’ is investigated by means of two-and-one-half-dimensional particle simulation. Magnetic reconnection develops in two steps, i.e., slow reconnection, which takes place in the early stage of the compression when the current layer is compressed as thin as the orbit amplitude of an ion meandering motion (ion current layer), and subsequent fast reconnection, which takes place in the late stage when the electron current is concentrated into the narrow region with a spatial scale comparable to the orbit amplitude of an electron meandering motion (electron current layer). The global dynamic evolution of magnetic reconnection is controlled by the physics of the ion current layer. The maximum reconnection rate is roughly in proportion to the driving electric field. It is also found that both ion heating and electron heating take place in accordance with the formation of two current layers and the ion temperature becomes two or more times as high as the electron temperature.
Nonlinear dynamics of standing shear Alfvén waves
Authors: Tikhonchuk V. T. , Rankin R. , Frycz P. , Samson J. C.
Published: July 2002

The nonlinear evolution of driven standing shear Alfvén waves is investigated by virtue of a model which includes the interaction of the waves with density perturbations excited by the ponderomotive force. It is shown that the plasma density perturbations take the form of a slow magnetosonic wave which nonlinearly shifts the frequency of the shear Alfvén wave and decouples it from the external source. This results in a complicated and sometimes chaotic temporal behavior of the amplitude of the excited waves which depends strongly on the plasma pressure, driver strength, and the frequency mismatch between the driver and shear Alfvén eigenmode. The results are discussed in the context of ultra low frequency (ULF) field line resonances in the Earth’s magnetosphere and the excitation of waves in the Alfvénic wave resonator near to the polar ionosphere.
Gyrokinetic simulation of internal kink modes
Authors: Naitou Hiroshi , Tsuda Kenji , Lee W. W. , Sydora R. D.
Published: July 2002

Internal disruption in a tokamak has been simulated using a three-dimensional magneto-inductive gyrokinetic particle code. The code operates in both the standard gyrokinetic mode (total-f code) and the fully nonlinear characteristic mode (δf code). The latter is a quiet low noise algorithm. The computational model represents a straight tokamak with periodic boundary conditions in the toroidal direction and a square cross section with perfectly conducting walls in the poloidal direction. The linear mode structure of an unstable m=1 (poloidal) and n=1 (toroidal) kinetic internal kink mode is clearly observed, especially in the δf code. The width of the current layer around the x-point, where magnetic reconnection occurs, is found to be close to the collisionless electron skin depth, indicating the importance of electron inertia. Both codes give very similar nonlinear results, in which full reconnection in the Alfvén time scale is observed along with the electrostatic potential structures created during this phase. The resulting E×B drift from the potential dominates the nonlinear phase after the full reconnection.
Self-consistent cutoff wave number of the ablative Rayleigh–Taylor instability
Authors: Betti R. , Goncharov V. N. , McCrory R. L. , Verdon C. P.
Published: July 2002

The cutoff wave number of the ablative Rayleigh–Taylor instability is calculated self-consistently by including the effects of finite thermal conduction. The derived cutoff wave number is quite different from the one obtained with the incompressible fluid (∇⋅ṽ=0) or sharp boundary models, and it is strongly dependent on thermal conductivity (K∼Tν) and the Froude number (Fr). The derivation is carried out for values of ν≳1, Fr≳1, and it is valid for some regimes of interest to direct and indirect-drive inertial confinement fusion (ICF). The analytic formula for the cutoff wave number is in excellent agreement with the numerical results of Kull [Phys. Fluids B 1, 170 (1989)].
Dynamics of current sheet formation and reconnection in two-dimensional coronal loops
Authors: Ma Z. W. , Ng C. S. , Wang Xiaogang , Bhattacharjee A.
Published: July 2002

Current sheet formation and magnetic reconnection in a two-dimensional coronal loop with an X-type neutral line are simulated numerically using compressible, resistive magnetohydrodynamic equations. Numerical results in the linear and nonlinear regimes are shown to be in good agreement with a recent analytical theory [X. Wang and A. Bhattacharjee, Astrophys. J. 420, 415 (1994)]. The topological constraint imposed by helicity-conserving reconnection is discussed. It is found numerically that helicity-conserving reconnection causes the initial X-point structure of the loop to change to Y points, with current sheets at the separatrices encompassing the Y points. Implications for observations are discussed.
Computer studies on dynamics of a large-scale magnetic loop by the spontaneous fast reconnection model
Authors: Ugai M.
Published: July 2002

The temporal dynamics of a large-scale magnetic loop is numerically studied on the basis of the two-dimensional spontaneous fast reconnection model. When a plasmoid, caused by the fast reconnection, propagates and collides with a wall boundary, across which plasma cannot flow, a large-scale magnetic loop is formed. The resulting magnetic loop is constructed by the reconnected field lines; inside the loop, the plasma, initially residing in the current sheet, is confined. As the reconnected field lines are piled up, the magnetic loop grows and swells outwards, so that a strong fast shock suddenly builds up at the interface between the growing loop and the strong reconnection jet. The fast shock, located ahead of the loop top, moves outwards with the growing loop, changing its strength with several peak and bottom Mach numbers. Accordingly, a localized spot-like region, where the plasma pressure is extremely enhanced, definitely comes out immediately ahead of the loop top. Along the loop side boundary, slow shocks stand, so that the resulting large-scale magnetic loop provides a very powerful energy converter in the sense that it is enclosed by slow and fast shocks.
Self-sustained magnetic islands
Authors: Chatenet J. H. , Luciani J. F. , Garbet X.
Published: July 2002

Numerical simulations of a single magnetic island evolution are presented in the regime where the island width is smaller than an ion Larmor radius. It is shown that the island rotation is controlled by particle diffusion due to collisions or a background of microturbulence. More precisely, for vanishing density gradient, the sign of rotation frequency is determined by the off-diagonal diffusion term, i.e., by the coefficient of the temperature gradient in the particle flux. As expected from the theory of a stationary island, there exist cases where linearly stable magnetic perturbations are nonlinearly self-sustained. This situation corresponds to large poloidal beta and temperature gradient. The drive is due to diamagnetic frequency effects. However, this situation is not generic, and islands can also decay. It is found that a magnetic island is self-sustained for a negative off-diagonal diffusion coefficient. This case occurs in a tokamak if the inward particle pinch is due to the temperature gradient.
Rapid reconnection in compressible plasma
Authors: Heyn Martin F. , Semenov Vladimir S.
Published: July 2002

A study of set-up, propagation, and interaction of non-linear and linear magnetohydrodynamic waves driven by magnetic reconnection is presented. The source term of the waves generated by magnetic reconnection is obtained explicitly in terms of the initial background conditions and the local reconnection electric field. The non-linear solution of the problem found earlier, serves as a basis for formulation and extensive investigation of the corresponding linear initial-boundary value problem of compressible magnetohydrodynamics. In plane geometry, the Green’s function of the problem is obtained and its properties are discussed. For the numerical evaluation it turns out that a specific choice of the integration contour in the complex plane of phase velocities is much more effective than the convolution with the real Green’s function. Many complex effects like intrinsic wave coupling, anisotropic propagation characteristics, generation of surface and side wave modes in a finite beta plasma are retained in this analysis.
Forced magnetic reconnection and the persistence of current sheets in static and rotating plasmas due to a sinusoidal boundary perturbation
Authors: Ma Z. W. , Wang Xiaogang , Bhattacharjee A.
Published: July 2002

The problem of forced reconnection in static and rotating plasmas due to a sinusoidal boundary perturbation is revisited. The primary focus of this paper is on inner region dynamics, including the effects of resistivity as well as viscosity. It is shown that for high-Lundquist-number plasmas, the use of the ‘‘constant-ψ’’ approximation in the linear and nonlinear regimes of forced reconnection is not justified. The linear and nonlinear dynamics in the inner region are characterized by the persistence of current sheets. Explicit analytical solutions for the time dependence of the reconnected flux and current sheet density are given, and tested by numerical simulations. These results differ qualitatively from earlier analytical results on forced reconnection in static plasmas [T. S. Hahm and R. M. Kulsrud, Phys. Fluids 28, 2412 (1985)] (except in a very restricted range of parameters) as well as rotating plasmas [R. Fitzpatrick and T. C. Hender, Phys. Fluids B 3, 644 (1991)]. Some qualitative implications for laboratory and space plasmas are discussed.
Dynamic current sheets with localized anomalous resistivity
Authors: Schumacher J. , Kliem B.
Published: July 2002

Two-dimensional compressible magnetohydrodynamic simulations of current sheet dynamics under the influence of localized anomalous resistivity are presented. The system is initially perturbed by several spots of anomalous resistivity distributed in the sheet. Following a phase of induced tearing resulting from the initial perturbation, magnetic island coalescence occurs until one island persists. Finally the evolution becomes eruptive, dominated by the acceleration and ejection of a plasmoid, as a consequence of the amplification of a small initial asymmetry after a few 102 Alfvén times. These processes are accompanied by strong enhancements of the current density. It exceeds the threshold of kinetic instability repeatedly and leads to recurrence of anomalous resistivity, which drives the evolution. Jets are formed, driven by field line reconnection and locally enhanced dissipation at dominant X-points. The conversion of magnetic energy into kinetic energy is most efficient during the acceleration phase of the plasmoid. The evolution becomes more impulsive and leads to stronger current density enhancements for higher Lundquist numbers.
Observation of bifurcation phenomena in an electron beam plasma system
Authors: Hayashi N. , Kawai Y.
Published: July 2002

Bifurcation phenomena are experimentally observed in an electron beam plasma system using a double plasma device. When an electron beam is injected into the target plasma, an unstable wave and the subharmonics of period 2, period 3, and period 4 are observed. The fundamental unstable wave is specified to be a beam mode wave excited by an electron beam plasma instability. It is confirmed that these bifurcation phenomena originate from nonlinearity of the unstable wave. The correlation dimensions and Lyapunov exponents indicate that the system becomes chaotic when the subharmonics of period 3 or period 4 appear.
Ion acoustic soliton excitation using a modulated high-frequency sinusoidal wave
Authors: Yi Seungjun , Bai Er-Wei , Lonngren Karl E.
Published: July 2002

Experiments on the excitation of ion acoustic solitons using a fine mesh grid in a normal two component plasma are described. The excitation is novel in that a modulated high-frequency sinusoidal wave voltage signal is applied to the grid. The carrier frequency of the high-frequency sinusoidal wave is above the ion plasma frequency. An interpretation of the velocity modulation and bunching of free streaming ions that pass through the grid to which the signal is applied is given.