bluuebunny/crossref_metadata_2025 huggingface dataset:
On local inverse transforms
Authors: Sabatier Pierre C.
Published: July 2002

The direct linearization of a nonlinear partial differential equation, when it is possible, is a purely algebraic process, which should not imply strong conditions on the solutions at infinity. Thus, it should be possible to manage it in such a way that the relevant inversion equation is not of the Marchenko form, but others, e.g., the true Gelfand–Levitan form, which preserves the local character of the approach. This is demonstrated on the Korteweg–de Vries case.
The q-harmonic oscillator in a lattice model
Authors: van Leeuwen Hans , Maassen Hans
Published: July 2002

We give an explicit proof of the pair partitions formula for the moments of the q-harmonic oscillator, and of the claim made by Parisi that the q-deformed lattice Laplacian on the d-dimensional lattice tends to the q-harmonic oscillator in distribution for d→∞.
Resolution of some mathematical problems arising in the relativistic treatment of the S states of three-electron systems
Authors: Feldmann D. Matthew , Pelzl Paul J. , King Frederick W.
Published: July 2002

Some of the mathematical difficulties that arise in the evaluation of the Breit–Pauli relativistic energy corrections for the S states of three-electron systems are resolved. Evaluation of the expectation value of the Breit–Pauli Hamiltonian using explicitly correlated wave functions leads to sets of integrals that diverge individually. By appropriately combining these integrals, and using some judicious series expansions, all the integration problems are resolved in terms of well-known auxiliary functions.
Gibbs states for AF algebras
Authors: Golodets Valentin Ya. , Neshveyev Sergey V.
Published: July 2002

We consider a special class of C*-systems containing asymptotically Abelian binary shifts and shifts of Temperley–Lieb algebras. We study Gibbs states for these systems corresponding to potentials with finite range interaction, and obtain the same results as the well-known Araki’s results for a one-dimensional quantum lattice. In particular, it is proved that a Gibbs state in the infinite volume is a translation invariant KMS state having the exponential uniform clustering property. Entropic properties of the Gibbs states are also discussed. This allows us, in particular, to construct new examples of quantum K-systems.
Deformations of massless Gupta–Bleuler triplets in 3+2 De Sitter space
Authors: Lesimple Marc
Published: July 2002

We study deformations of massless indecomposable representations (Gupta–Bleuler triplets) for the De Sitter group SO(3,2), showing that there is no deformation of such representations toward a kind of massive Gupta–Bleuler triplets which would have corresponded to an analog of a Higgs–Kibble mechanism in anti De Sitter space.
The topological structure of the space–time disclination
Authors: Duan Yishi , Li Sheng
Published: July 2002

The space–time disclination is studied by making use of the decomposition theory of gauge potential in terms of the antisymmetric tensor field and φ-mapping method. It is shown that the self-dual and anti-self-dual parts of the curvature compose the space–time disclinations which are classified in terms of topological invariants—winding number. The projection of space–time disclination density along an antisymmetric tensor field is quantized topologically and characterized by Brouwer degree and Hopf index.
On the use of a new integral theorem for the quantum mechanical treatment of electric circuits
Authors: Magnus W. , Schoenmaker W.
Published: July 2002

We present a new integral theorem based on the well-known Gauss and Stokes theorems which provides a straightforward physical interpretation of the quantum mechanical energy balance equation governing the steady-state propagation of charge carriers through closed electric circuits.
Simplicial quantum gravity in the elongated phase
Authors: Gionti Gabriele
Published: July 2002

We discuss the elongated phase of four-dimensional simplicial quantum gravity by exploiting recent analytical results. In particular using Walkup’s theorem we prove that the dominating configurations in the elongated phase are treelike structures called “stacked spheres.” Such configurations can be mapped into branched polymers and baby universes arguments are used in order to analyze the critical behavior of theory in the weak coupling regime.
A rigorous path integral for quantum spin using flat-space Wiener regularization
Authors: Bodmann Bernhard , Leschke Hajo , Warzel Simone
Published: July 2002

Adapting ideas of Daubechies and Klauder [J. Math. Phys. 26, 2239 (1985)] we derive a rigorous continuum path-integral formula for the semigroup generated by a spin Hamiltonian. More precisely, we use spin coherent vectors parametrized by complex numbers to relate the coherent representation of this semigroup to a suitable Schrödinger semigroup on the Hilbert space L2(R2) of Lebesgue square-integrable functions on the Euclidean plane R2. The path-integral formula emerges from the standard Feynman–Kac–Itô formula for the Schrödinger semigroup in the ultradiffusive limit of the underlying Brownian bridge on R2. In a similar vein, a path-integral formula can be constructed for the coherent representation of the unitary time evolution generated by the spin Hamiltonian.
Classical and quantum mechanics of jointed rigid bodies with vanishing total angular momentum
Authors: Iwai Toshihiro
Published: July 2002

A gauge theoretical treatment proves to have been successful in the study of systems of point particles; the center-of-mass system is made into a principal fiber bundle, on which is defined a natural connection. The gauge theoretical approach may be generalized to be applicable to a system of rigid bodies. The present article deals with a system of two identical axially symmetric cylinders jointed together by a special type of joint. This system is the model made by Kane and Scher and reformulated later by Montgomery, in order to study the falling cats who can land on their legs when released upside down. With the no-twist condition, the system turns out to have the configuration space diffeomorphic with SO(3), which is made into a principal O(2) bundle over RP2, the real projective space of dimension two, and endowed with a natural connection. An optimal control problem for this system with the vanishing total angular momentum is satisfactorily treated in this bundle picture. Along with a certain performance index, the Maximum Principle gives rise to a Hamiltonian system on the cotangent bundle T*(SO(3)) of SO(3). This Hamiltonian system is shown to admit a symmetry group O(2), which is not the structure group, but comes from the material symmetry of the respective cylinders. Moreover, quantization of this “classical” system is carried out, giving rise to a quantum system with the constraints of the vanishing total angular momentum. Through the symmetry by the structure group O(2), the reduction procedure is performed for both the classical and the quantum systems. It then turns out that the respective reduced systems, classical and quantum, admit the material symmetry group O(2), in general.
Solitary waves in slender magnetic flux tubes as solutions of the Leibovich–Pritchard–Roberts equation
Authors: Weisshaar Eckhard
Published: July 2002

The Leibovich–Pritchard–Roberts evolution equation is solved numerically. Time-independent solitary wave solutions, as well as time-dependent solutions, are obtained. It is shown that the profiles of the solitary wave solutions are not self-similar and their existence is restricted to amplitudes below some critical value. On the other hand, the solitary waves interact like solitons.
The measurement and interpretation of fractal dimensions of the scalar interface in turbulent flows
Authors: Prasad R. R. , Sreenivasan K. R.
Published: July 2002

One of the recently established results concerns the fractal-like properties of surfaces such as the turbulent/nonturbulent interface. Although several confirmations have been reported in recent literature, enough discussion does not exist on how various flow features as well as measurement techniques affect the fractal dimension obtained; nor, in one place, is there a full discussion of the physical interpretation of such measurements. This paper serves these two purposes by examining in detail the specific case of the interface of scalar-marked regions (scalar interface) in turbulent shear flows. Dimension measurements have been made in two separate scaling regimes, one of which spans roughly between the integral and Kolmogorov scales (the K range), and the other between the Kolmogorov and Batchelor scales (the B range). In the K range, the fractal dimension is 2.36±0.05 to high degree of reliability. This is also the dimension of the vorticity interface. The dimension in the B range approaches (logarithmically) the value 3 in the limit of infinite Schmidt number, and is 2.7±0.03 when the diffusing scalar in water is sodium fluorescein (Schmidt number of the order 1000). Among the effects considered are those of (a) the flow Reynolds number, (b) developing regions such as the vicinity of a jet nozzle or a wake generator, (c) the free-stream and other noise effects, (d) the validity of the method of intersections usually invoked to relate the dimension of a fractal object to that of its intersections, (e) the effect of intersections by ‘‘slabs’’ of finite thickness and ‘‘lines’’ of finite width, and (f) the computational algorithm used for fractal dimension measurement, etc. The authors’ previous arguments concerning the physical meaning of the fractal dimension of surfaces in turbulent flows are recapitulated and amplified. In so doing, turbulent mixing is examined, and by invoking Reynolds and Schmidt numbers similarities, the fractal dimensions of scalar interfaces are deduced when the Schmidt number is small, unity, and large.
The effect of walls on a spatially growing supersonic shear layer
Authors: Zhuang Mei , Dimotakis Paul E. , Kubota Toshi
Published: July 2002

The inviscid instability, with respect to supersonic disturbances of a spatially growing plane mixing layer inside parallel flow guide walls, is investigated using linear stability analysis. For supersonic convective Mach numbers, it is found that the maximum amplification rates of the shear layers approach an asymptotic value and that this maximum amplification rate increases to its maximum value and decreases again as the distance between the walls decreases continuously. Contour plots of the pressure perturbation fields indicate that there are waves propagating outward from the shear layer along the Mach angle, and that the walls provide a feedback mechanism between the growing shear layer and this compression/expansion wave system. The streak lines of the flow confirm that the spreading rate of the shear layer is unusually small for supersonic disturbances.
An explanation for anomalous vortex merger in rotating-tank experiments
Authors: Carnevale G. F. , Cavazza P. , Orlandi P. , Purini R.
Published: July 2002

Theory and simulations based on the two-dimensional Euler equation predict a critical distance of separation for the merger of two like-signed vortices. By the symmetry of the equation, this separation must be the same for both cyclone and anticyclone pairs. In rotating-tank experiments, the observed critical separation distance for anticyclone merger is in accord with predictions; however, pairs of cyclones have been found to merge in all cases examined, even with separations substantially greater than the predicted critical separation. The hypothesis that this discrepancy is due to the presence of Ekman volume fluxes, which are not incorporated in the two-dimensional theory, is examined and found not quantitatively supportable. A second hypothesis is that the parabolic curvature of the free upper surface of the fluid in the rotating tank induces motion of the cyclones toward the center of the tank and hence promotes the cyclone pair merger. Quasigeostrophic simulations which capture this ‘‘topography effect’’ show good agreement with the rotating-tank experiments.
Influence of pore roughness and pore-size dispersion in estimating the permeability of a porous medium from electrical measurements
Authors: Achdou Y. , Avellaneda M.
Published: July 2002

The influence of pore-size dispersion and pore roughness on the dynamic and the dc permeability of porous media is analyzed through simple models and computer simulations. In particular, attention is focused on the systematic errors that arise from these geometric features when using the empirical fit for the dynamic permeability k(ω)≊(Λ2/F)f1(Λ2ω/ν) [Johnson et al., J. Fluid Mech. 176, 379 (1986); Zhou and Sheng, Phys. Rev. B 39, 12027 (1989)] and the estimate for the dc permeability kdc≊Λ2/8F [Johnson et al., Phys. Rev. Lett. 57 2565 (1986)]. Here, Λ and F are, respectively, the electrically weighted volume-to-surface ratio and the formation factor. It is found that, for in-parallel models, Λ underestimates the effective hydrodynamic radius L, while for in-series models, Λ overestimates L. Departures from the aforementioned fits are substantial even if moderate-sized disperson exists for the in-parallel geometry. For the in-series model, the agreement with the empirical fits is very good, unless a broadband pore-radius distribution f(R), R≪1, exists. The quality of the empirical estimates in pores with rough surfaces is investigated in microgeometries consisting of ‘‘corrugated’’ tubes. It is shown that the electric field can produce large Joule heating on the pore surface, and lead, in some cases, to an underestimate of the effective hydrodynamic radius by Λ, which is inversely proportional to the surface dissipation. The accuracy of the estimates based on the Λ parameter depends on whether an ‘‘effective tube’’ containing the electric field and the velocity field at all frequencies can be identified. Careful numerical calculations of Stokes flows on various ‘‘corrugated’’ capillaries are made over a wide frequency range, and the ac and dc permeabilities are compared with the aforementioned empirical theories.
Absolute–convective instabilities and their associated wave packets in a compressible reacting mixing layer
Authors: Hu F. Q. , Jackson T. L. , Lasseigne D. G. , Grosch C. E.
Published: July 2002

In this paper the transition from convective to absolute instability in a reacting compressible mixing layer with finite rate chemistry is examined. The reaction is assumed to be one step, irreversible, and of Arrhenius type. It is shown that absolute instability can exist for moderate heat release without backflow. The effects of the temperature ratio, heat release parameter, Zeldovich number, equivalence ratio, direction of propagation of the disturbances, and the Mach number on the transition value of the velocity ratio are given. The present results are compared to those obtained from the flame sheet model for the temperature using the Lock similarity solution for the velocity profile. Finally, the structure of the wave packets produced by an impulse in the absolutely unstable flow is examined.
The m=1 helicity source spheromak experiment
Authors: Fernández J. C. , Wright B. L. , Marklin G. J. , Platts D. A. , Jarboe T. R.
Published: July 2002

In this paper extensive measurements of magnetic equilibrium and source parameters in the m=1 helicity source spheromak experiment are described (previously called the kinked z-pinch source [Comments Plasma Phys. Control Fusion 9, 161 (1985)]). In the cylindrical entrance region connecting the stabilized z-pinch helicity source to the spheromak flux conserver, the observed equilibrium configuration is the helical azimuthal m=1 state with no net axial flux. In the flux conserver, the equilibrium is a spheromak (m=0) state with an m=1 distortion. The magnetic equilibria observed are compared to theory. The performance of the source relative to coaxial helicity sources is also examined.
Computer simulation of Alfvén wave heating
Authors: Geary J. L. , Leboeuf J.-N. , Tajima T.
Published: July 2002

A particle simulation study of shear Alfvén wave resonance heating is presented. A particle simulation model has been developed for this application that incorporates Darwin’s formulation of the electromagnetic fields with a guiding center approximation for electron motion perpendicular to the ambient magnetic field. With this model, several cases of Alfvén wave heating are examined in both uniform and nonuniform simulation systems in a two-dimensional slab. When the antenna parameters match the shear Alfvén resonance condition, the simulation plasmas in the homogeneous cases react strongly with the driven wave. For the inhomogeneous case studies, the kinetic Alfvén wave develops in the vicinity of the shear Alfvén resonance region. The electrons kinetically react with the wave through a collisionless process. The electron velocity distribution function flattens about the parallel phase velocity of the wave with accompanying changes in the spatial structure of the wave. The electron heating rate is in good agreement with the Landau damping model. A substantial electron current is also generated parallel to the applied magnetic field. The ions gain energy by oscillating in the wave electric fields.
Canonical coordinates for guiding center particles
Authors: Meiss J. D. , Hazeltine R. D.
Published: July 2002

Canonical coordinates are obtained for the guiding center Hamiltonian up to a quadrature. The configuration variables are two angles, and the canonical momenta are angular momenta. These coordinates are valid for arbitrary magnetic fields including nonaxisymmetric ones whose field lines may be chaotic. Examples of application of canonical coordinates to tokamak geometry are given.
Application of escape probability to line transfer in laser-produced plasmas
Authors: Lee Yim T. , London Richard A. , Zimmerman George B. , Hagelstein Peter L.
Published: July 2002

The application of an escape probability method to treat transfer of optically thick lines in laser-produced plasmas in plane-parallel geometry is described. The escape probability calculated is valid in a plasma with any locally linear velocity profile. It reduces to the standard result for a static plasma and to the result of Sobolev [Sov. Astron. Astrophys. J. 1, 678 (1957)] for large ion velocity gradients. As examples, escape probability is applied to model the effect of optically thick line trapping in both exploding foil and ablating massive slab targets. Compared to detailed numerical calculations for the line transfer in these targets, the escape probability gives quite accurate estimates. This can be understood in terms of the large Doppler shifts in the line profiles that are generated by the ion velocity in the plasmas.
Megavolt, multikiloamp K
a band gyrotron oscillator experiment
Authors: Black W. M. , Gold S. H. , Fliflet A. W. , Kirkpatrick D. A. , Manheimer W. M. , Lee R. C. , Granatstein V. L. , Hardesty D. L. , Kinkead A. K. , Sucy M.
Published: July 2002

A Ka-band gyrotron oscillator experiment using a 1–1.35 MeV, multikiloampere beam from a pulse line accelerator has produced approximately 250 MW at 35 GHz in a circular TE62 mode with a peak efficiency exceeding 10%. Time-dependent simulation studies have been used to predict the behavior of a high-peak-power, short-pulse gyrotron in this parameter range. The simulations demonstrate the occurrence of such phenomena as hard excitation of the gyrotron as a result of the time dependence of the voltage pulse. The experimental results are in reasonable agreement with the predictions of theory.
Weibel instability with constant driving source
Authors: Wallace J. M. , Epperlein E. M.
Published: July 2002

A method has been developed for performing numerical particle-in-cell simulations of the Weibel instability in which the driving anisotropy is held constant. With the method, the instability is computed to grow to saturation in a well-behaved manner. Initially, growth is in close agreement with the predictions of linear theory. Subsequently, the growth rate falls below linear-theory predictions as magnetic fields grow to substantial levels. And finally, the instability reaches saturation, after which a steady state is established. A single mode comes to dominate the magnetic field at late times in the simulations. This is the mode identified in linear theory as the most rapidly growing. The method has been employed to investigate the importance of the Weibel instability in laser-produced plasmas. It is found that, because of saturation, the fields do not grow sufficiently to affect heat flow (ωcτ<1) in the overdense plasma. In the near-critical underdense plasma, the fields would have, at most, marginal influence for shorter wavelength irradiation (λL≤0.25 μm) but possibly substantial influence at longer wavelengths (λL≥1 μm).
Guiding center theory and simulations of the crossed-field amplifier
Authors: Riyopoulos Spilios
Published: July 2002

Electrons in crossed-field devices execute complicated orbits in crossed static electric and magnetic fields, driven at the same time by slow rf waves. The dynamics is considerably simplified by averaging the fast-time-scale, periodic gyromotion. The reduced equations derived here follow the slow guiding center drift in the synchronous frame of reference moving at the phase velocity of the wave. In that frame, the streamlines follow the equipotential surfaces of the transformed fields. In steady-state, the flow is incompressible. A closed, nonlinear set of equations, based on the guiding center flow, is developed to model the crossed-field amplifier behavior. The effects of the electron hub surrounding the cathode are included. The secondary production at the cathode is computed self-consistently through the secondary emission coefficient and the average impact energy. The equations are implemented in a numerical algorithm that is much faster and more efficient than existing particle codes and shows excellent agreement with experimental results for characteristic curves, tube gain, and efficiency, over a wide parameter regime.
Parametric decay of an electron-Bernstein wave excited by the optical mixing of two microwave beams
Authors: Asthana Meenu
Published: July 2002

Nonlinear theory of an electron-Bernstein wave at lower-hybrid frequency is developed. Fluid theory is applied for the excitation of a lower-hybrid wave whereas a kinetic model is used for the electron-Bernstein mode as fluid theory breaks down for short-wavelength perturbations, and the propagation of these waves depends upon the cyclotron motion of the electrons about the field lines. The nonlinearity arises because of electrons motion, introduced through ponderomotive force. The electron-Bernstein wave is assumed to be excited by optical mixing of two microwave beams. The nonlinear dispersion relation and growth rates are calculated for three-wave and four-wave parametric interaction processes. Since the electron-Bernstein wave is nonlinearly excited by two intense beams, there is no power threshold and the excited power increases proportionally to the product of the incident powers. The investigation appears to be of great potential because of recent significant developments in gyrotron technology.
Equilibrium of non-neutral plasma in toroidal geometry with applied electric field
Authors: Bhattacharyya S. N. , Avinash K.
Published: July 2002

The equilibrium and stability of non-neutral plasma in toroidal geometry with applied electric field is studied. The calculations are done in a large aspect ratio, thin ring approximation, using a circuit model. Toroidal corrections to the l=1 (l is the poloidal mode number) mode are obtained. These corrections reduce the l=1 cylindrical diocotron frequency. It is shown that under certain conditions, the external electric field can stabilize dissipative l=1 diocotron oscillations.
Geometric phase, rotational transforms, and adiabatic invariants in toroidal magnetic fields
Authors: Bhattacharjee A. , Schreiber G. M. , Taylor J. B.
Published: July 2002

The rotational transform associated with the magnetic surfaces of a toroidal magnetic field with a nonplanar axis is an example of the angle anholonomy which recently has been much discussed in quantum and classical dynamics (the Berry phase and Hannay angle). The same anholonomic angle appears in the phase of a charged particle spiraling around its guiding center in a strong magnetic field. This accounts for a contribution to the longitudinal invariant, associated with the guiding-center motion, which is different for guiding-center orbits that circulate in opposite directions and is absent for orbits that are reflected between mirrors.
One-dimensional simulations of current-driven plasma sheaths
Authors: Swanekamp S. B. , Grossmann J. M. , Ottinger P. F. , Geary J. L.
Published: July 2002

A one-dimensional model that treats both electron and ion dynamics with the particle-in-cell method is used to study nonequilibrium electron effects in current-driven plasma sheaths. These simulations show two distinct phases of operation: a low impedance phase, where the diode voltage is small, followed by a phase of rapidly increasing diode voltage and impedance. Early in the low impedance phase, the initial plasma electrons are accelerated toward the anode to conduct the discharge current. Emitted electrons are drawn into the anode–cathode gap by the uncovered positive space charge, leading to the formation of virtual cathodes in the diode. Trapping and heating of the emitted electrons occur as a result of nonequilibrium dynamics in the time-varying virtual cathode potential structure associated with the rising circuit current. The virtual cathode potential structure is characterized by a large potential hill with a large potential drop occurring in the anode sheath. The potential drop in the anode sheath is comparable to the potential rise in the cathode sheath and is responsible for keeping the net diode voltage low during the low impedance phase. The virtual cathode electric field structure accelerates ions toward both electrodes, resulting in a significant depletion of ion charge by the end of the low impedance phase. During the transition to high impedance rapid growth of the cathode sheath is observed. This growth occurs to provide the ions necessary to shield the electric field of the cathode sheath from the bulk plasma. The substantial loss of ions at the anode during the low impedance phase causes the cathode sheath and voltage to grow faster than predicted by quasistatic models. This effect is more pronounced in the higher density simulation, where the loss of ions during the low impedance phase is more significant.
Klein–Gordon equation and reflection of Alfvén waves in nonuniform media
Authors: Musielak Z. E. , Fontenla J. M. , Moore R. L.
Published: July 2002

A new analytical approach is presented for assessing the reflection of linear Alfvén waves in smoothly nonuniform media. The general one-dimensional case in Cartesian coordinates is treated. It is shown that the wave equations, upon transformation into the form of the Klein–Gordon equation, display a local critical frequency (Ωc) for reflection: At any location in the medium, reflection becomes strong as the wave frequency descends past this characteristic frequency set by the local nonuniformity of the medium. This critical frequency is given by the transformation as an explicit function of the Alfvén velocity (VA), and its first (V′A) and second (V■A) derivatives, and hence as an explicit spatial function. The transformation thus directly yields, without solution of the wave equations, the location in the medium at which an Alfvén wave of any given frequency becomes strongly reflected and has its propagation practically cut off. The local critical frequency is the square root of the larger coefficient of the zeroth-order term in the two transformed wave equations; which equation has the larger coefficient is determined by the local nonuniformity. Hence, the critical frequency can switch from one equation to the other as the nonuniformity changes. Consequently, it is necessary to transform both wave equations to deduce that the critical frequency is Ωc=((V′A)2+‖2VAV■A‖)1/2/2.
Study of the diffusion across a magnetic field in a beam–plasma interaction using a drift-kinetic Vlasov code
Authors: Ghizzo A. , Bertrand P. , Shoucri M. , Fijalkow E. , Feix M.
Published: July 2002

A drift-kinetic Eulerian Vlasov code, with fluid equations for the ions, is developed to study the problem of the injection of an electron beam into a two-dimensional magnetized plasma, often referred to as direct current (dc) helicity injection. The diffusion of electrons across a magnetic field in the presence of a beam–plasma instability is studied. The case of a magnetic field tilted with respect to the beam direction is considered. The competition between the velocity shear Kelvin–Helmholtz (KH) and the beam–plasma (BP) instabilities is investigated in order to analyze the plasma heating and current drive mechanism induced by the beam injection. The KH instability generates low-frequency plasma convection motion associated with cE×B/B2 drift. In particular, the diffusion coefficients Dy and Dv ∥ describing, respectively, the anomalous diffusion process induced in space across the magnetic field by the KH instability, and the velocity diffusion process due to the kinetic effects induced in velocity space along the magnetic field by the BP instability, are computed using test-particle diagnostics. In the present Cartesian model, it is found that Dy = Dv∥ tan2 θ/ωce2 where θ is the angle between the magnetic field and the x axis. This relation which links the electron dynamics in the x-y real space and in the x-v∥ phase space is verified by the numerical code. The Vlasov code provides a powerful tool to study particle diffusion in space and in phase space, especially in the low-density regions of the distribution function.
The electrostatic wake of a superthermal test electron in a magnetized plasma
Authors: Ware A. A. , Wiley J. C.
Published: July 2002

The electrostatic potential is determined for a test electron with v∥ ≫ vTe in a uniform magnetized plasma (ωce ≫ ωpe). In the frame of the test electron, part of the spatially oscillatory potential has spherical symmetry over the hemisphere to the rear of the electron and is zero ahead of the electron. A second part of different character, which makes the potential continuous at the plane containing the electron, is oscillatory in the radial direction but decreases almost monotonically in the axial direction.
Quasioptical treatment of electromagnetic Gaussian beams in inhomogeneous and anisotropic plasmas
Authors: Nowak S. , Orefice A.
Published: July 2002

The main effect of the Gaussian behavior of an electromagnetic beam consists in a waist formation in focal regions, where the ordinary geometric optics would collapse. The characteristic features of Gaussian beams, both when they interact with the components of transmission lines and when they propagate through inhomogeneous and anisotropic media (as happens, for instance, in the case of diagnostic or heating experiments in magnetoactive plasmas of fusion interest), are of crucial relevance for many technical and scientific purposes. The present paper is devoted to the analysis of the propagation of Gaussian beams, showing in particular that a properly formulated eikonal equation contains all the elements required by a correct ray tracing procedure, basically amounting to a first-order description of the beam diffraction. Simple methods are proposed, apt to follow numerically the beam evolution for a quite general choice of refractive media and of wave launching conditions. Numerical results are presented for Gaussian beam propagation in vacuum, in isotropic and anisotropic media, and compared (evidencing significant deviations) to the corresponding ones in the optical case.
Nonlinear interaction of photons and phonons in a relativistically hot electron–positron gas
Authors: Shukla P. K. , Tsintsadze N. L. , Tsintsadze L. N.
Published: July 2002

Nonlinear interaction between intense photons and sound waves in a relativistically hot electron–positron plasma is considered. The modulational instability of a constant amplitude photon is investigated and the formation of polarons (localized photon envelopes trapped in a self-created density cavity) is discussed. The relevance of this investigation to astrophysical plasmas is pointed out.
Turbulent flow structure in the near field of a swirling round free jet
Authors: Komori Satoru , Ueda Hiromasa
Published: July 2002

Turbulent flow structure in the near field of a swirling round free jet is experimentally and theoretically investigated in a low-speed wind tunnel. The experiments are conducted in a slightly heated swirling jet with an irrotational, low-speed, coflowing stream. Velocity and temperature are simultaneously measured using a laser Doppler anemometer and a resistance thermometer, respectively. The results show that in a strongly swirling jet, the ambient fluid is rapidly entrained into the jet in the region near the convergent nozzle exit. The entrainment rate shows a value about twice as large as that in a nonswirling jet, even in the immediate vicinity of the nozzle exit. This rapid entrainment is attributed to the recirculating flow which is formed by the adverse pressure induced to balance the strong centrifugal force. The flow structure is compared with the numerical predictions based on a two-equation model of the type k-ε. The predictions and experimental results both agree well.
Decay instability of an extraordinary electromagnetic wave into whistler and magnetized electron plasma waves in fusion plasmas
Authors: Sharma R. P. , Kumar A.
Published: July 2002

Parametric decay instability of an extraordinary electromagnetic wave into a magnetized electron plasma wave and a whistler wave propagating at an angle with respect to the static magnetic field has been considered. Application of the present investigation to tandem mirrors and tokamaks has been pointed out. For example (i) for the tandem-mirror parameters at the second harmonic cyclotron resonance in the thermal barrier minimum, the convective threshold ∼100 W/cm2, (ii) for tokamak parameters when the extraordinary mode is launched from outside the torus, the convective threshold ∼1 kW/cm2 for this decay process.
The anomalous Doppler instability during lower-hybrid current drive
Authors: Luckhardt S. C. , Bers A. , Fuchs V. , Shoucri M.
Published: July 2002

The anomalous Doppler instability is investigated for two-dimensional velocity distributions f(v∥,v⊥) appropriate for lower-hybrid current drive. In this case, in contrast to the runaway electron problem, this mode becomes unstable at high density when the ratio ω2pe/ ω2ce is sufficiently large. Increasing the maximum velocity v2 of the rf (radio-frequency) plateau, v1≤v∥ ≤v2, is also a destabilizing influence. In this paper expressions are given for the growth rate of the electrostatic waves obeying the dispersion relation ω=ωpe (1+ω2pe/ ω2ce)−1/2 k∥/k, employing both analytic expressions for f(v∥,v⊥) and numerical solutions for f from the two-dimensional Fokker–Planck equation. The analytical and numerical results are in close agreement.
Stimulated Raman scattering of nonlinear space-charge and transverse magnetic waves with a longitudinal wiggler
Authors: Fenstermacher D. L. , Seyler C. E.
Published: July 2002

A formulation is given for the parametric coupling of nonlinear space-charge waves with transverse magnetic (TM) waveguide modes through a longitudinal wiggler field. The model is based upon the simplifying assumption of thin electron beam geometry, which requires only one-dimensional dynamics of the space-charge waves, and is an exact formulation in the limit of infinitesimally thin beams. A reduced model, obtained through the application of standard time-averaging techniques, leads to an analytic expression for the parametric growth rate as a function of beam parameters, pump strength, and wave mismatch. A numerical code is developed and used to solve the unapproximated model equations, and comparisons are made with the analytic theory. Agreement is good in the domain of applicability of the theory. It is also found numerically that nonlinear steepening and associated slowing of the space-charge waves—aspects usually neglected in ponderomotive theories—have important consequences on the evolution of the instability in the strongly nonlinear regime.
Neoclassical transport coefficients for finite-aspect-ratio and bean-shaped tokamak plasmas
Authors: Crume E. C. , Beasley C. O. , Hirshman S. P. , van Rij W. I.
Published: July 2002

Numerically calculated tokamak equilibria are used to compute banana-plateau transport coefficients for finite-aspect-ratio, finite-beta plasmas. Calculations are presented for the Spherical Torus Experiment (STX) (NTIS Document No. DE 86004663) and the Princeton Beta Experiment (PBX) (NTIS Document No. DE 86011173). In STX, the poloidal variation of B≡‖B‖ over a magnetic surface tends to be reduced in regions of large major radius R. The reduction of radial transport caused by this quasiomnigeneous condition is offset by increased drifts and trapping probabilities for smaller R. Thus the modulation Δ=(Bmax−Bmin)/(Bmax+Bmin) on a magnetic surface becomes the critical parameter determining neoclassical transport. In PBX, the bean-shaped topology of the magnetic surfaces leads to the presence of multiple magnetic wells. Numerical calculations confirm that analytic calculations of neoclassical transport based on the total fraction of circulating particles are valid even when geometrically distinct classes of trapped particles are present.
Nonlocal theory of beam-driven electron Bernstein waves
Authors: Jain V. K. , Tripathi V. K.
Published: July 2002

A nonlocal theory of electron Bernstein waves driven unstable by an axial beam (V=Vbẑ) of finite width has been developed. Assuming a parabolic density profile for the background plasma, an equation describing the mode structure of the wave is obtained in the slab geometry. The eigenfunctions are found to be Hermite polynomials. Expressions for the growth rates of the instabilities caused by Cerenkov and slow cyclotron interactions are derived. The results of the theory are applied to explain some of the experimental observations of Jain and Christiansen [Phys. Lett. A 82, 127 (1981)].
Stimulated Raman scattering in self-focused light filaments in laser-produced plasmas
Authors: Short R. W. , Seka W. , Bahr R.
Published: July 2002

The stimulated Raman scattering instability is treated for laser light propagating through a plasma in a self-focused filament. It is shown that self-focusing of hot spots in the incident laser beam can greatly enhance the growth rate of the instability. This result may help to explain experimental observations of Raman scattering at nominal incident intensities well below the theoretical threshold, and may also account for an anomalous spectral structure that has been observed at low intensities.
Theory of resistive pressure-gradient-driven turbulence
Authors: Carreras B. A. , Garcia L. , Diamond P. H.
Published: July 2002

Saturated resistive pressure-gradient-driven turbulence is studied analytically and with numerical calculations. Fluid viscosity and thermal diffusivity are retained in the analysis and calculations. Such dissipation guarantees the existence of a stable, high-m dissipation range, which serves as an energy sink. An accurate saturation criterion is proposed. The resulting predicted pressure diffusivity scales similarly to the mixing length estimate but is significantly larger in magnitude. The predictions of the analytic theory are in good quantitative agreement with the numerical results for fluctuation levels.
Runaway electron distributions and their stability with respect to the anomalous Doppler resonance
Authors: Fuchs V. , Shoucri M. , Teichmann J. , Bers A.
Published: July 2002

The stability of nonrelativistic runaway electron distributions with respect to the anomalous Doppler resonance is examined in a range of parameters of interest to tokamaks, i.e., for Y≡ωpe/Ωce≤2 and for Ohmic electric fields ε≡E/Ec≤0.1. Distribution functions are calculated numerically within a region up to 35ve (thermal velocities) using a finite-element 2-D Fokker–Planck code. Alternatively, an analytic approximation for the runaway distribution function is used, valid beyond the critical velocity vc≂ve(Ec/E)1/2. Stability thresholds in (ω,k∥) space are then determined. For example, for Y=1 and ε=0.1, and providing that the runaway tail extends at least to 30ve, unstable waves exist having ω≤0.6Ωce and k∥≤0.03Ωce/ve.
Monte Carlo computations of neoclassical transport
Authors: Lotz W. , Nührenberg J.
Published: July 2002

Neoclassical transport coefficients and confinement times in stellarators of general geometry and tokamaks with and without ripple are computed by Monte Carlo simulation over wide ranges of mean free paths, ratios of plasma to gyroradius, and radial electric fields. The results for monoenergetic particles can be represented by simple formulas using a transport coefficient normalized to the tokamak plateau value and a mean free path normalized to half the connection length. Transport coefficients obtained with monoenergetic particles subjected to pitch angle scattering and energy relaxation are convoluted with a Maxwellian energy distribution. The results are compared with theory and simulations using a particle distribution subjected to pitch angle as well as energy scattering. The overall agreement is good. Transport coefficients with Maxwellian energy distributions for l=2 stellarators and for various other stellarator configurations are shown. Particle transport coefficients, as well as energy transport coefficients, for these configurations are computed for ions (deuterons) as well as for electrons. Estimates of particle and energy confinement times are also obtained.
Hydrodynamic dispersion broadening of a sedimentation front
Authors: Martin J. , Rakotomalala N. , Salin D.
Published: July 2002

Hydrodynamic dispersion is responsible for the spreading of the sedimentation front even in a noncolloidal monodisperse suspension. Measurements of the broadening of the top front observed during sedimentation have been used in determining the hydrodynamic dispersion coefficient. Hindered settling has an opposed effect and leads to the self-sharpening of the front. Both effects have to be taken into account simultaneously. This Letter provides a simple, but complete determination of the space and time concentration profile and shows that the final front should consist of a steady-shape profile propagating at constant velocity. With such a solution, the data of Davis et al. [AIChE J. 34, 123 (1988); J. Fluid Mech. 196, 107 (1988)] give hydrodynamic dispersion coefficient five times larger than their former analysis, in agreement with Lee et al. [Phys. Fluids A 4, 2601 (1992)].
Collisions of slightly deformable, high Reynolds number bubbles with short-range repulsive forces
Authors: Tsao Heng-Kwong , Koch Donald L.
Published: July 2002

A collision between two bubbles of radii a with an initial relative velocity 2U∞ is studied in the limit, Re≡ρU∞a/μ≫1 and We≡ρU2∞a/γ≪1. Here ρ and μ are the density and viscosity of the liquid and γ is the surface tension of the air–liquid interface. In the absence of colloidal forces, Chesters and Hoffman [Appl. Sci. Res. 38, 353 (1982)] showed that this situation leads to coalescence. The case where there is a nonhydrodynamic repulsive force between the gas–liquid interfaces of the two bubbles that is sufficient to prevent coalescence is considered. Such a force may arise due to ionic salts in aqueous solution or due to surfactants. The analysis shows the bubbles undergo a nearly elastic bounce on an O(a We1/2/U∞) time scale and the repulsive force per unit area must be at least 2γ/a for rebound. Also, experimental observations of bubble collisions in aqueous solutions using high-speed video photography are presented.
Reynolds stress description of opposed and impinging turbulent jets. II. Axisymmetric jets impinging on nearby walls
Authors: Champion Michel , Libby Paul A.
Published: July 2002

The flow arising from an axisymmetric turbulent jet with an exit plane in close proximity to the wall against which it impinges is analyzed. The reciprocal of a Reynolds number based on the kinematic viscosity adds here to the two parameters identified in Part I [Phys. Fluids A 5, 203 (1993)] as determining the flow characteristics of two opposed jets, namely the ratio of the turbulence scale to the separation of the jet exit from the wall and the ratio of the turbulence intensity to the mean exit velocity. With all three of these parameters suitably small there is indicated an asymptotic analysis which describes separately the flow in three distinct regions. The temperature of the impinging fluid is assumed to be slightly different from that of the wall so that the mean velocity components, the mean temperature, and the various Reynolds stresses and fluxes vary within a thin wall layer which consists of a viscous sublayer and a turbulent shear layer. When the Reynolds number is suitably high, the sublayer accounts for all of the change in the mean radial velocity and in the mean temperature. The analysis of the turbulence external to the wall layer is compared with experimental data on a turbulent jet impinging on a wall. Agreement with respect to the mean axial velocity and the intensities of the axial and radial velocity components is quite satisfactory. Comparison is made with experimental data on heat transfer to the wall; the predicted dependence of Nusselt number on Reynolds number is confirmed.
Solitary waves of permanent form in a deep fluid with weak shear
Authors: Derzho Oleg G. , Velarde Manuel G.
Published: July 2002

The Benjamin–Davis–Acrivos–Ono equation is generalized to account for finite, large amplitude solitary waves in a sheared deep fluid. It is shown how fine structure of stratification and weak noncritical shear in such geophysical flows do affect length (shape), wave (phase) velocity, and even stability of finite amplitude solitary waves.
Studying Burgers’ models to investigate the physical meaning of the alignments statistically observed in turbulence
Authors: Andreotti B.
Published: July 2002

The alignments between the vorticity, the vortex stretching vector, the pressure Hessian eigenvectors and the strain rate eigenvectors are computed and discussed in the case of the Burgers’ vortex and the Burgers’ layer. It is shown that the main physical properties of these models can be deduced from these alignments. Following this example, the alignments between these vectors in turbulent flows are interpreted as dominated by stretched, coherent and locally quasi-bidimensional regions. This induces a new and safer classification for the strain rate and the pressure Hessian eigenvalues.
Accounting for Reynolds stress and dissipation rate anisotropies in inertial and noninertial frames
Authors: Jongen T. , Mompean G. , Gatski T. B.
Published: July 2002

This paper presents a general procedure for including added effects, such as turbulent dissipation rate anisotropies, into algebraic stress formulations in both inertial and noninertial frames of reference. Explicit algebraic stress models, which assume an isotropic turbulent dissipation rate, have been developed previously and extended for application to noninertial frames. Independently, anisotropic dissipation rate models have also been developed. Recently, an algebraic, anisotropic dissipation rate model has been developed and used in conjunction with a full Reynolds stress closure. Unfortunately, in the theoretical formulations used previously for explicit algebraic models, the combination of the algebraic stress and algebraic dissipation rate models only appeared possible for inertial frames. The alternative procedure outlined here remedies this problem and allows for the construction of a composite model for both inertial and noninertial frames. This new composite model formulation is tested in homogeneous shear with and without rotation, and in strongly rotating channel and pipe flows using different types of anisotropic dissipation rate models.