bluuebunny/crossref_metadata_2025 huggingface dataset:
Hierarchies of Korteweg–de Vries type equations
Authors: Svinin Andrei K.
Published: July 2002

An eigenvalue problem is considered. New hierarchies of bi-Hamiltonian systems are constructed. Some examples of these systems and their reductions are presented.
The q deformation of super high-order Virasoro algebra
Authors: Zha Chao-Zheng , Zhao Wei-Zhong
Published: July 2002

The high-order Virasoro algebra (HOVA) is extended to supersymmetric HOVA (SHOVA) and deformed on the quantum supersymmetric hyperplane C1‖1. Then the q-deformed Jacobi identities and central extension are formulated. Finally, the Hopf algebra structure of q-deformed SHOVA is defined.
Classification of finite dimensional unitary irreps for U
q[gl(m‖n)]
Authors: Gould M. D. , Scheunert M.
Published: July 2002

All finite dimensional irreducible unitary representations of the quantum supergroup Uq[gl(m‖n)] are classified in terms of their highest weights, for generic q≳0.
Type-I quantum superalgebras, q-supertrace, and two-variable link polynomials
Authors: Gould Mark D. , Links Jon R. , Zhang Yao-Zhong
Published: July 2002

A new general eigenvalue formula for the eigenvalues of Casimir invariants, for the type-I quantum superalgebras, is applied to the construction of link polynomials associated with any finite dimensional unitary irrep for these algebras. This affords a systematic construction of new two-variable link polynomials associated with any finite dimensional irrep (with a real highest weight) for the type-I quantum superalgebras. In particular infinite families of nonequivalent two-variable link polynomials are determined in fully explicit form.
Comment on Ricci collineations of static spherically symmetric spacetimes [J. Math. Phys. 35, 3005–3012 (1994)]
Authors: Bertolotti R. , Contreras G. , Núñez L. A. , Percoco U. , Carot J.
Published: July 2002

We present a counter example to a theorem given by Amir et al. [J. Math. Phys. 35, 3005–3012 (1994)]. We also comment on a misleading statement of the same reference.
Path integrals for spinning particles, stationary phase and the Duistermaat–Heckmann theorem
Authors: Ercolessi E. , Morandi G. , Napoli F. , Pieri P.
Published: July 2002

We examine the problem of the evaluation of both the propagator and of the partition function of a spinning particle in an external field at the classical as well as the quantum level, in connection with the asserted exactness of the stationary phase approximation. At the classical level we argue that exactness of this approximation stems from the fact that the dynamics (on the two-sphere S2) of a spinning particle in a magnetic field is the reduction from R4 to S2 of a linear dynamical system on R4. At the quantum level, however, and within the path integral approach, the restriction, inherent to the use of the stationary phase approximation, to regular paths clashes with the fact that no regulators are present in the action that enters the path integral. This is shown to lead to a prefactor for the path integral that is strictly divergent, except in the classical limit. A critical comparison is made with the various approaches that have been presented in the literature. The validity of a formula given in literature for the spin propagator is extended to the case of motion in an arbitrary magnetic field.
Quantization of the multifold Kepler system
Authors: Iwai Toshihiro , Uwano Yoshio , Katayama Noriaki
Published: July 2002

For over a century, the Kepler problem and the harmonic oscillator have been known as the only central force dynamical systems, all of whose bounded motions are periodic. Two of the authors (T. I. and N. K.) have found an infinite number of dynamical systems possessing such a periodicity property, which have been called multi-fold Kepler systems or ν-fold Kepler systems, with ν a positive rational number. If ν is allowed to take the real positive numbers, say ν=α, then for the α-fold Kepler system, all the bounded motions become periodic or not, according to whether the parameter α is a rational number or not. A purpose of this paper is to quantize the α-fold Kepler system and thereby to figure out a quantum analog of the closed orbit property of the α-fold Kepler system. It will turn out that the quantized α-fold Kepler system admits accidental degeneracy in energy levels or not, according to whether α is a rational number or not.
Dynamic conductance and quantum noise in mesoscopic conductors
Authors: Büttiker M.
Published: July 2002

We present results for the dc conductance, the ac conductance, and the current–current fluctuation spectra of mesoscopic, phase-coherent conductors based on a second quantization approach to scattering and a self-consistent potential approach. A second quantization approach permits an investigation of statistical effects due to the symmetry of the wave functions under exchange of particles. A self-consistent approach is needed to enforce overall charge conservation and to obtain current conserving expressions for frequency-dependent conductances and fluctuation spectra. For the particular example of a mesoscopic capacitor we present microscopic expressions for the electrochemical capacitance and the charge relaxation resistance.
Multiplicity, invariants, and tensor product decompositions of compact groups
Authors: Klink W. H. , Ton-That T.
Published: July 2002

Decomposing tensor products of irreducible representations of compact groups almost always involves multiplicity, wherein some irreducible representations occur more than once in the direct sum decomposition. We show that the multiplicity can always be specified by polynomial group invariants. The setting is a Bargmann–Segal–Fock space in n×N complex variables, where n is the number of labels needed to specify the tensor product and N is the dimension of the fundamental representation of the compact group. Both the tensor product and direct sum bases are realized as polynomials in this space, and it is shown how Clebsch–Gordan and Racah coefficients can be computed by suitably differentiating these polynomials. The example of SU(N) is discussed in detail, and it is shown that the multiplicity can be computed as the solution of certain diophantine equations arising from powers of group invariants, namely minors of determinants.
On the second law of thermodynamics for a dissipative system
Authors: Chen M.
Published: July 2002

In this paper we consider dissipative fluxes as well as the conserved variables as a set of independent variables characterizing the thermodynamic state of a nonequilibrium system. We then generalize the traditional internal energy balance equation so that contributions due to the dissipative fluxes are taken into consideration. On the other hand, the second law is formulated in terms of Caratheodory’s inaccessibility condition in conjunction with the assumption that dissipative energy associated with internal work arising from irreversible processes be semipositive definite. We show that the second law formulated in this manner is equivalent to Kelvin’s principle and Clausius’s principle, as well as Clausius’s inequality.
Nonlinear spinor field in Bianchi type-I Universe filled with perfect fluid: Exact self-consistent solutions
Authors: Saha B. , Shikin G. N.
Published: July 2002

Self-consistent solutions to nonlinear spinor field equations in general relativity have been studied for the case of Bianchi type-I space–time filled with perfect fluid. The initial and the asymptotic behaviors of the field functions and the metric one have been thoroughly studied. The absence of initial singularity for some types of solutions and also the isotropic mode of space–time expansion in some special cases should be emphasized.
Orthogonality relations and supercharacter formulas of U(m|n) representations
Authors: Alfaro Jorge , Medina Ricardo , Urrutia Luis F.
Published: July 2002

In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of complex conjugated and mixed representations. Our results are expressed in terms of the Young tableaux notation for irreducible representations. We use the supersymmetric Harish–Chandra–Itzykson–Zuber integral and the character expansion technique as mathematical tools for deriving these relations. As a byproduct we also obtain closed expressions for the supercharacters and dimensions of some particular irreducible U(m|n) representations. A new way of labeling the U(m|n) irreducible representations in terms of m+n numbers is proposed. Finally, as a corollary of our results, new identities among the dimensions of the irreducible representations of the unitary group U(N) are presented.
Coherent states in quaternionic quantum mechanics
Authors: Adler Stephen L. , Millard Andrew C.
Published: July 2002

We develop Perelomov’s coherent states formalism to include the case of a quaternionic Hilbert space. We find that, because of the closure requirement, an attempted quaternionic generalization of the special nilpotent or Weyl group reduces to the normal complex case. For the case of the compact group SU(2), however, coherent states can be formulated using the quaternionic half-integer spin matrices of Finkelstein, Jauch, and Speiser, giving a nontrivial quaternionic analog of coherent states.
Schouten–Nijenhuis brackets
Authors: Norris L. K.
Published: July 2002

The Poisson and graded Poisson Schouten–Nijenhuis algebras of symmetric and antisymmetric contravariant tensor fields, respectively, on an n-dimensional manifold M are shown to be n-symplectic. This is accomplished by showing that both brackets may be defined in a unified way using the n-symplectic structure on the bundle of linear frames LM of M. New results in n-symplectic geometry are presented and then used to give globally defined representations of the Hamiltonian operators defined by the Schouten–Nijenhuis brackets.
Partially solvable quantum many-body problems in D-dimensional space (D=1,2,3,…)
Authors: Calogero F.
Published: July 2002

A simple technique employed almost three decades ago to manufacture partially solvable quantum many-body problems is revisited. [A quantum problem is “partially solvable” if (only) some of its eigenvalues and eigenfunctions can be exhibited]. The models thereby generated are characterized by Hamiltonians of normal form, i.e., standard kinetic plus momentum-independent potential energy; in most cases the latter features three-body, in addition to two-body and one-body, interactions. The setting refers to D-dimensional space; the examples focus on D=1, D=2, and D⩾2, and include generalizations of, and additional results on, cases recently discussed in the literature, as well as new models.
Commuting difference operators arising from the elliptic C2(1)-face model
Authors: Hasegawa Koji , Ikeda Takeshi , Kikuchi Tetsuya
Published: July 2002

We study a pair of commuting difference operators arising from the elliptic C2(1)-face model. The operators, whose coefficients are expressed in terms of the Jacobi’s elliptic theta function, act on the space of meromorphic functions on the weight space of the C2-type simple Lie algebra. We show that the space of functions spanned by the level one characters of the affine Lie algebra sp∧(4,C) is invariant under the action of the difference operators.
On the electromagnetic scattering problem for an infinite dielectric cylinder of an arbitrary cross section located in the wedge
Authors: Podlipenko Yu. K. , Shestopalov Yu. V.
Published: July 2002

Diffraction of time-harmonic E-polarized electromagnetic waves by an infinite dielectric cylinder of arbitrary cross section located inside a wedge parallel to its axis is considered. By the methods of potential theory, the transmission problem is reduced to a system of two one-dimensional Fredholm integral equations with the kernels having logarithmic singularities; integration is performed over the boundary of the cylinder cross section. Existence and uniqueness of solutions are proved both for the system of integral equations and the transmission problem. The kernels of integral equations are represented as rapidly convergent series.
Algebraic exact solvability of trigonometric-type Hamiltonians associated to root systems
Authors: Kamran Niky , Milson Robert
Published: July 2002

In this article, we study and settle several structural questions concerning the exact solvability of the Olshanetsky–Perelomov quantum Hamiltonians corresponding to an arbitrary root system. We show that these operators can be written as linear combinations of certain basic operators admitting infinite flags of invariant subspaces, namely the Laplacian and the logarithmic gradient of invariant factors of the Weyl denominator. The coefficients of the constituent linear combination become the coupling constants of the final model. We also demonstrate the L2 completeness of the eigenfunctions obtained by this procedure, and describe a straightforward recursive procedure based on the Freudenthal multiplicity formula for constructing the eigenfunctions explicitly.
Quantum scalar field in D-dimensional static black hole space–times
Authors: Binosi Daniele , Zerbini Sergio
Published: July 2002

An Euclidean approach for investigating quantum aspects of a scalar field living on a class of D-dimensional static black hole space–times, including the extremal ones, is reviewed. The approach makes use of a near-horizon approximation of the metric and ζ-function formalism for evaluating the partition function and the expectation value of the field 〈φ2(x)〉. After a review of the nonextreme black hole case, the extreme one is considered in some detail. In this case, there is no conical singularity, but the finite imaginary time compactification introduces a cusp singularity. It is found that the ζ-function regularized partition function can be defined, and the vacuum expectation value of the field, is finite on the horizon, as soon as the cusp singularity is absent, namely, the manifold is smooth and the corresponding temperature is T=0. It is suggested that the requirement of having a smooth near-horizon geometry always selects the correct black hole equilibrium temperature.
Linearization stability of the Einstein equation for Robertson–Walker models. I
Authors: Bruna Lluı́s , Girbau Joan
Published: July 2002

This is the first part of a series of two papers. In this article we study the linearization stability of the Einstein equation in the presence of matter. We have slightly changed the classic definition of this concept for the vacuum spacetime and a more general one adapted to our case is given. We consider a Robertson–Walker model (V,g,T) where V stands for the spacetime, g for a Robertson–Walker metric, and T for a stress-energy tensor of a perfect fluid. We write V=S×I where S is a spacelike hypersurface of V and I an ↛-interval. We show that in the case S has a constant curvature K equal to 0, the Einstein equation G(g)=χT is linearization stable at g. In a subsequent paper we shall prove that in the case K=1 the opposite occurs. The case K=−1 remains as an open question.
General solution of string inspired nonlinear equations
Authors: Bandos I. , Ivanov E. , Kapustnikov A. A. , Ulanov S. A.
Published: July 2002

We present the general solution of the system of coupled nonlinear equations describing dynamics of D-dimensional bosonic string in the geometric (or embedding) approach. The solution is parametrized in terms of the left- and right-moving Lorentz harmonic variables providing a special coset space realization of the product of two (D−2)-dimensional spheres SD−2=[SO(1,D−1)/SO(1,1)×SO(D−2)⨷KD−2].
Convergence of PN approximation for the neutron transport equation with reflective boundary condition
Authors: Yuan Guang-wei
Published: July 2002

In this paper the spherical harmonic function method for the plane geometry neutron transport equation with reflective boundary condition is discussed. The existence and uniqueness for the solution of the spherical harmonic approximation (PN) equation are studied, and then the convergence of the solution of the PN equation as N→∞ to the solution of the neutron transport equation is proved.
On Killing vector fields and Newman–Penrose constants
Authors: Kroon Juan Antonio Valiente
Published: July 2002

Asymptotically flat space–times with one Killing vector field are studied. The Killing equations are solved asymptotically using polyhomogeneous expansions (i.e., series in powers of 1/r and ln r), and solved order by order. The solution to the leading terms of these expansions yields the asymptotic form of the Killing vector field. The possible classes of Killing fields are discussed by analyzing their orbits on null infinity. The integrability conditions of the Killing equations are used to obtain constraints on the components of the Weyl tensor (Ψ0,Ψ1,Ψ2) and on the shear (σ). The behavior of the solutions to the constraint equations is studied. It is shown that for Killing fields that are non-supertranslational the characteristics of the constraint equations are the orbits of the restriction of the Killing field to null infinity. As an application, the particular case of boost-rotation symmetric space–times is considered. The constraints on Ψ0 are used to study the behavior of the coefficients that give rise to the Newman–Penrose constants, if the space–time is non-polyhomogeneous, or the logarithmic Newman–Penrose constants, if the space–time is polyhomogeneous.
Energy spectrum of a finite chain of cylindrical potential wells
Authors: Glushko E. Ya.
Published: July 2002

An approximate analytic solution of the Schrödinger equation is obtained for a finite quasi-one-dimensional system of cylindrical potential wells. The system is considered as a model of an atomic chain or a quantum filament. It is shown that a smooth variation of the transverse size of a cylindrical quasi-one-dimensional system may modify the spectrum due to the creation (annihilation) of transverse quanta. The threshold nature of the states of a wide chain associated with the quantization of longitudinal motion is considered.
The rise and distortion of a two-dimensional gas bubble in an inviscid liquid
Authors: Baker G. R. , Moore D. W.
Published: July 2002

A two-dimensional gas bubble moves under gravity in an inviscid incompressible liquid. Boundary-integral methods are used to calculate the shape and position of the bubble surface. Two independent codes, based on the point-vortex method and the surface-dipole method, give results in good agreement with each other, up to the time of incipient self-intersection of the bubble surface. The results agree with previous theoretical work, valid over a smaller time interval of Baumel et al. [Can. J. Phys. 60, 999 (1982)] but there are quantitative differences with the experimental work of Walters and Davidson [J. Fluid Mech. 12, 408 (1962)]. The jet that forms at the rear of the bubble is taller and thinner in the calculations than in the experiments. Surface tension effects reduce the discrepancy only slightly. The evolution of the bubble surface is shown to be very sensitive to initial perturbations of bubble shape. If these have high enough wavenumber, Rayleigh–Taylor jets form on the upper surface.
Scalar mixing in isotropic turbulence
Authors: Kosály George
Published: July 2002

Eswaran and Pope [Phys. Fluids 31, 506 (1988)] performed direct numerical simulations to study the influence of the initial scalar integral length scale on mixing in stationary, isotropic turbulence. Their data demonstrate that both the decay rate and the shape of the rms versus time curve depend on the initial value of the scalar-to-velocity integral length-scale ratio. The present paper discusses modifications of the high Reynolds number theory of Corrsin [AIChE J. 10, 870 (1964)]. The predictions mirror the behavior found in the moderate Reynolds number simulations.
Scaling of the ‘‘bursting’’ period in turbulent boundary layer and duct flows
Authors: Shah D. A. , Antonia R. A.
Published: July 2002

Measurements have been made in fully developed turbulent duct and boundary layer flows of the average bursting period over a one decade variation in Reynolds number. The bursting period was determined by two methods: the variable interval time averaging scheme in the form used by Blackwelder and Haritonidis [J. Fluid Mech. 132, 87 (1983)] and the modified u-level scheme of Luchik and Tiederman [J. Fluid Mech. 174, 529 (1987)] in which ejections from the same burst are grouped. All these authors concluded that the bursting period scaled on inner variables. The present results indicate that this conclusion is valid only over a relatively small Reynolds number range, in which low Reynolds number effects are known to be important. At higher Reynolds numbers, scaling on mixed variables provides the best agreement with the data although scaling on outer variables cannot be ruled out.
The role of the Bardina model in large eddy simulation of turbulent channel flow
Authors: Horiuti Kiyosi
Published: July 2002

A direct test of the turbulence models employed in large eddy simulation is made for plane channel flow. As in previous studies, it is confirmed that inclusion of the models for the subgrid-scale (SGS) cross-stress terms is necessary. An important finding in the present study is that the Bardina model for the SGS cross-stress term has a strong negative correlation with the Leonard term, and that the major role of the Bardina model is to cause the backscattering of SGS energy.
The influence of particles on the spatial stability of two-phase mixing layers
Authors: Yang Yongqi , Chung J. N. , Troutt T. R. , Crowe C. T.
Published: July 2002

A modified Rayleigh equation has been derived for the study of spatial instability of gas–particle two-phase mixing layers. The particles are assumed to have a material density much greater than the carrier fluid. The mathematical model is based on the assumptions that the mean flow profile can be approximated as that of the particle-free single-phase mixing layer and that the two phases are in dynamic equilibrium at the start of the perturbation. The resulting eigenvalue problem was solved numerically. The major finding from the analysis is that the presence of the particles enhances the stability of the two-phase flow and decreases the amplification rate of perturbations in the flow. The results show that the stability of the flow is enhanced with increased particle loading and decreased free-stream velocity ratio. For a given free-stream velocity ratio, the most amplified growth rates decrease almost linearly with the particle loading. The most amplified growth rate, however, occurs near the same angular frequency as that of the particle-free flow. The effect of particle on the perturbation phase velocity is most significant for smaller values of the angular frequency. However, the presence of particles does not change the phase velocity at the angular frequency corresponding to the most amplified rate for the single-phase flow. The phase velocity of the perturbations is slower compared to particle-free flows for modes with frequencies below the maximum amplified frequency, while it is the opposite for modes at frequencies above the maximum amplified frequency. The profiles of streamwise and cross-stream velocity fluctuations are also modified by the existence of particles. The magnitude of effects is related closely to the particle loading. For temporal instability of a two-phase mixing layer, the growth rate in time decreases linearly with increasing particle loading, which is consistent with the spatial instability results.
A bifurcation study of convective heat transfer in porous media
Authors: Weinitschke H. J. , Nandakumar K. , Ravi Sankar S.
Published: July 2002

The convective heat transfer in a homogeneous porous duct of rectangular cross section in a horizontal orientation is examined. The flow is modeled by the Darcy equation and an averaged, single-equation model is used for the heat transfer. The aspect ratio of the duct (γ=a/b) appears as the natural geometrical parameter and the Rayleigh number Ra, which is the product of the Grashof number and the Prandtl number, appears as the natural dynamical parameter. Uniqueness of the solution at low values of Ra is demonstrated. The complete structure of the symmetric and asymmetric stationary solutions is traced numerically up to values of Ra of about 10 000, using arclength continuation. The limit points and the symmetry breaking bifurcation points are calculated numerically by using the appropriate extended system formulations. The manner in which these singular points unfold is examined as the aspect ratio is varied over 0.6≤γ≤1.4. Determination of linear stability shows that branches of stationary solutions above a Ra of about 4100 are unstable to arbitrary perturbations. The origin of a curve of Hopf points on one of the fold curves is detected around Ra=6560, γ=1.365.
Flow through rotating rectangular ducts
Authors: Nandakumar K. , Raszillier H. , Durst F.
Published: July 2002

The bifurcation structure of two-dimensional, pressure-driven flows through a rectangular duct that is rotating about an axis perpendicular to its own is examined at a fixed Ekman number (Ek=ν/b2Ω) of 0.01. The solution structure for flow through a square duct (aspect ratio γ=1) is determined for Rossby numbers (Ro=U/bΩ) in the range of 0–5 using a computational scheme based on the arclength continuation method. The structure is much more complicated than reported earlier by Kheshgi and Scriven [Phys. Fluids 28, 2968 (1985)]. The primary branch with two limit points in Rossby number and a hysteresis behavior between the two- and four-cell flow structure that was computed by Kheshgi and Scriven is confirmed. An additional symmetric solution branch, which is disconnected from the primary branch (or rather connected via an asymmetric solution branch), is found. This has a two-cell flow structure at one end, a four-cell flow structure at the other and three limit points are located on the path. Two asymmetric solution branches emanating from symmetry breaking bifurcation points are also found for a square duct. Thus even within a Rossby number range of 0–5 a much richer solutions structure is found with up to five solutions at Ro=5. An eigenvalue calculation indicates that all two-dimensional solutions develop some form of unstable mode by the time Ro is increased to 5.0. In particular, the four-cell solution becomes unstable to asymmetric perturbations as found in a related problem of flow through a curved duct. The paths of the singular points are tracked with respect to variation in the aspect ratio using the fold following algorithm. A transcritical point is found at an aspect ratio of 0.815 and below which the four-cell solution is no longer on the primary branch. When the channel cross section is tilted even slightly (1°) with respect to the axis of rotation, the bifurcation points unfold and the two-cell solution evolves smoothly as Rossby number is increased. The four-cell solutions then become genuinely disconnected from the primary branch. The uniqueness range in Rossby number increases with increasing tilt.
The enhancement of mixing by chaotic advection
Authors: Jones Scott W.
Published: July 2002

The stirring and mixing of passive scalars by laminar flows that generate chaotic particle trajectories is studied by numerical experiment and scale analysis. There are two principal results. The first result is that the time scale of the maximum mixing rate of diffusive particles across a material contour diverges like the logarithm of the Péclet number as Pe→∞ (Pe=UL/D where U, L, and D are a typical velocity scale, length scale, and the molecular diffusivity, respectively). This logarithmic divergence is explained on the basis of a simple scaling argument that equates the striation thickness of the advected tracer with a characteristic diffusion length. A similar analysis, performed for a linear shear flow, suggests that in this limit the divergence is more rapid for integrable advection, for the shear flow it is like Pe1/3. The second result is that the time scale for the homogenization of tracer within a bounded domain is also proportional to the logarithm of Pe. This result can also be explained by equating length scales, in this case the separation distance between adjacent filaments of the tracer distribution and a diffusion length. In contrast, the time scale of homogenization when particle trajectories are regular is linear in Pe.
High-Reynolds-number thermocapillary flows in shallow enclosures
Authors: Rivas Damián
Published: July 2002

Steady thermocapillary flows of low-Prandtl-number fluids in shallow rectangular enclosures under an imposed-heat-flux configuration are studied in the absence of gravitational forces. The Navier–Stokes equations are solved numerically for Reynolds numbers up to 104. The pressure correction method is used to treat the pressure-velocity coupling, in particular, the SIMPLEC approximation is considered. In the numerical simulation, the free surface is assumed flat. This hypothesis is justified a posteriori; free surface deformations are computed by domain perturbation for small capillary numbers. The numerical results show the existence of a boundary layer along the free surface and the existence of a strong vortex close to the vertical wall. The characteristic velocity in the boundary layer responds to Ostrach’s scaling of thermocapillary boundary layers, and the wall vortex responds to Batchelor’s model for steady laminar flows with closed streamlines at large Reynolds numbers. The calculated surface deformations have the following feature: When inertia effects are important, the wall vortex induces a depression of the free surface in the region above it, which results in an elevation in the region below the heater; this behavior is opposite to that for the case of small Reynolds numbers.
Advection of a vortex pair atmosphere in a velocity field of point vortices*
Authors: Meleshko V. V. , Konstantinov M. Yu. , Gurzhi A. A. , Konovaljuk T. P.
Published: July 2002

Two-dimensional inviscid flows governed by a vortex pair in the presence of another point vortex or vortex pair on an unbounded plane are considered analytically and via numerical simulations. For some integrable cases of vortex motion, the stirring process of a fixed closed volume of surrounding fluid (‘‘atmosphere’’) initially trapped by vortex pair is investigated. Using the full classification of vortex movement types, it is shown that for all cases of vortex pair direct and exchange scattering the stirring process is regular. Some internal atmosphere regions conserve their existence and form after vortex interaction, resulting a ‘‘solitonlike’’ behavior. For general cases of vortex pair mutual trapping, the stirring process is chaotic. For limiting cases of vortex motions, the fluid particles reveal a regular behavior. A simple model for the qualitative description of recent experiments on vortex dipoles interaction is discussed. Although clearly an extreme idealization, the model appears to shed some light on what to expect in laboratory experiments.
Starting vortex and lift on an airfoil
Authors: Chang Chien-Cheng , Hsiau Ying-Chien , Chu Chin-Chou
Published: July 2002

Consider an airfoil which is impulsively started from rest to a constant speed relative to an otherwise quiescent fluid at an angle of attack. The paper attempts to propose a precise definition for the ‘‘starting vortex’’ in viscous flow and investigate how an airfoil gains its lift through the starting vortex. It is found adequate to view the vortex itself as a source of the lift through the vorticity contained within it. Actually, the total lift on the airfoil is contributed by all the regions of nonvanishing vorticity in the flow. For an impulsive flow, the initial lift is due to the vortex sheet distributed along the airfoil; the lift is then rapidly dominated by the starting vortex near the trailing edge. In the next stage, the regions of vorticity next to the airfoil on both sides gradually become the major contributor to the lift. Relative importance of the starting vortex is assessed based on the angle of attack and the Reynolds number.
Dynamical self-focusing of high-power free electron laser radiation in a magnetized plasma
Authors: Lontano M. , Sergeev A. M. , Cardinali A.
Published: July 2002

Under the action of very intense free electron laser (FEL) radiation, a homogeneous plasma can manifest nonlinear behavior and dramatically change the spatial distribution of the incident electromagnetic beam. The dominant mechanism is the constriction depletion of the plasma due to an averaged ponderomotive force. The unstable character of the FEL-beam plasma system and the consequent self-focusing are studied in the dynamical ‘‘supersonic limit.’’ The self-similar structure of the high-frequency field and density distributions is computed and the form of a ‘‘trace,’’ left by a moving ‘‘focus’’ in the plasma is determined.
Relativistic particle dynamics in a steepening magnetosonic wave
Authors: Lembege B. , Dawson J. M.
Published: July 2002

Acceleration of both electrons and ions to relativistic energy by large amplitude magnetosonic waves is investigated by use of numerical simulation. Nonlinear effects are shown to form the saturation mechanism and limit the amplitude below the level where a particle specie can undergo unlimited acceleration, which is expected theoretically. Spiky structures appear both in density and field waveforms that are characteristics of the relativistic regime. Both electrons and ions are strongly accelerated by Elx×Bz drift and Ety field, but their resonance features versus fields are strongly different. Around the trapping time, relativistic electron solitonlike wavelets are triggered from the main wave ramp; a few mechanisms are proposed for their interpretation. Both electrons and ions are strongly heated at the expense of the wave energy. This damping in association with the large space charge effects resulting from the spiky structures is the origin of some observed saturation level in the field energy.
The frictional force in counterstreaming plasmas
Authors: Bardsley J. N. , Boercker D. B. , Penetrante B. M.
Published: July 2002

The purpose of this Brief Communication is to calculate the frictional force between two fully ionized plasmas that are moving with respect to one another. Such a calculation is relevant to the expansion of explosion debris into a preionized gas, and to the heating or fueling of a fusion reactor by plasma injection. When the charge densities of the two plasmas are of smilar magnitude, the frictional force is significantly different from that appropriate to the stopping of test particles or to the calculation of electrical conductivity.
Observations of field profile modifications in a Raman free-electron laser amplifier
Authors: Xu K. , Bekefi G. , Leibovitch C.
Published: July 2002

Measurements of the spatial distribution of the rf electric field intensities and phases induced in a free-electron laser (FEL) amplifier operating in the collective (Raman) regime are reported. The studies are carried out at a microwave frequency of ∼10 GHz in a FEL using a mildly relativistic electron beam of ∼160 keV energy and 1– 4 A current. The probing of the ponderomotive (space-charge) and electromagnetic waves is accomplished by means of small movable electric dipole antennas inserted into the interaction region.
Magnetic fluctuations due to thermally excited Alfvén waves
Authors: Agim Y. Z. , Prager S. C.
Published: July 2002

Magnetic fluctuations resulting from the thermally excited magnetohydrodynamic waves are investigated using fluid and kinetic models to describe a stable, uniform, compressible plasma in the range above the drift wave frequency and below the ion cyclotron frequency. It is shown that the fluid model with resistivity yields spectral densities that are roughly Lorentzian and exhibit equipartition with no apparent cutoff in wavenumber space and a Bohm-type diffusion coefficient. Under certain conditions, the ensuing transport may be comparable to classical values. For a phenomenological cutoff imposed on the spectrum, the typical fluctuating-to-equilibrium magnetic field ratio is found to be of the order of 10−10. Physical mechanisms to obtain decay profiles of the spectra with increasing wavenumber as a result of dispersion and/or different forms of damping are investigated analytically in a cold fluid approximation and numerically, with a kinetic model. The mode dispersion resulting from the finite ion gyro-frequency is identified as the leading effect determining the spectral profile shapes. It is found that the amplitude of fluctuations may be within a factor of the value suggested by the cold plasma model. The results from both models are presented and compared in low- and high-beta regimes.
Importance of two-dimensional effects for the generation of ultra high pressures obtained in laser colliding foil experiments
Authors: Faral B. , Fabbro R. , Virmont J. , Cottet F. , Romain J. P. , Pépin H.
Published: July 2002

A 12 μm polyester foil is accelerated by a 0.26 μm wavelength laser and collides with a 15 μm thick molybdenum foil. The accelerating pressure is 45 Mbar (laser intensity≊3– 4×1014 W/cm2) and gives to the polyester foil a velocity of about 160 km/sec. The measurement of the shock pressure induced in the impacted foil is made with an improved step technique. When the initial spacing between the two foils is too large compared to the focal spot radius, i.e., larger than 20–30 μm, the different experimental results cannot be reproduced with one-dimensional simulations; this is only possible by using a two-dimensional Lagrangian code that has been developed and that takes into account the strong deformation of the accelerated foil. Finally, even with the low level of x-ray heating due to the ablation plasma, multihundred megabar pressures can be obtained within a very short time.
Prebunching in a collective Raman free-electron laser amplifier
Authors: Wurtele J. S. , Bekefi G. , Chu R. , Xu K.
Published: July 2002

Experiments, theory, and simulations are reported on the effects of electron prebunching in a mildly relativistic, low-current (200 kV, 1 A) free-electron laser amplifier operating in the collective (Raman) regime at a frequency of ∼10 GHz. Prebunching is established by injecting an electromagnetic wave into a bifilar helical wiggler and then transporting the bunched beam into a second magnetic wiggler region. The wave growth rate, Γ≡(1/P)(dP/dz), is deduced from measurements of the radiation intensity as a function of interaction length. Observations show that prebunching can increase the radiation growth rate Γ manyfold as compared with a system without prebunching.
Statistical properties of two-dimensional magnetohydrodynamic turbulence
Authors: Biskamp D. , Welter H. , Walter M.
Published: July 2002

The statistical properties of two-dimensional (2-D) magnetohydrodynamic (MHD) turbulence are studied by means of high-resolution numerical simulations. As a theoretical point of reference, the β model of intermittent turbulence is adapted to the MHD case. Comparison of simulation results for energy spectra with the β-model predictions shows intermittency corrections to be small, δ<0.2, while fourth-order correlation functions exhibit a stronger effect δ≂0.35, consistent with the numerically observed Reynolds-number dependence of the flatness factor F∝R1/2λ. An argument is given that this scaling valid for Rλ∼102 is, however, not characteristic of the asymptotic regime Rλ→∞, where a constant value of F is to be expected. The probability distributions of the field difference δv(x,t), δB(x,t) are Gaussian for large separation x or t, approaching an approximately exponential distribution for x, t→0. This behavior can be understood by a simple probabilistic argument. The probability distribution of the local energy dissipation rate ε is roughly consistent with a log-normal distribution at larger ε but shows a different behavior at small ε.
Spatial structure of particle-orbit loss regions in l=2 helical systems
Authors: Sanuki H. , Todoroki J. , Kamimura T.
Published: July 2002

Particle orbits and loss regions in both configuration and velocity spaces are studied on the basis of adiabatic invariants and guiding-center drift equations. The boundary of the loss region in the pitch angle major radius plane (χ0-ρ) is determined from the condition of whether the drift surfaces for helically trapped and transition particles hit the limiter or not. Two typical loss boundaries on the χ0-ρ plane are obtained. One determines the boundary of absolute confinement where no particles are lost. The other gives the boundary of the confined region of deeply trapped particles with v∥=0. An analytical form describing the latter boundary is also derived. Effects of ripple modulation and electrostatic potential on these loss boundaries are discussed for the improvement of particle confinement.
Gyroviscous stability theory with application to the internal tilt mode of a field-reversed configuration
Authors: Steinhauer L. C. , Ishida A.
Published: July 2002

The variational formulation for a gyroviscous fluid plasma is constructed. This theory offers a fluid-based description of perpendicular kinetic effects, generally called finite Larmor radius (FLR) effects. This approach avoids the complexity of a more complete kinetic treatment and avoids local singularities that can appear in the standard FLR expansion treatment. The method is applied to the internal tilt mode of a field-reversed configuration (FRC), an instance where standard FLR theory clearly breaks down. The relative simplicity of the variational gyroviscous fluid theory allows easy computation of stability properties, including the scaling of marginal stability conditions.
Experimental investigation of coherent drift waves in low magnetic fields
Authors: Kauschke U. , Oelerich-Hill G. , Piel A.
Published: July 2002

Density gradient-driven coherent drift waves are studied in straight-cylindrical geometry at low magnetic fields, where the finite Larmor corrections of the ions gain increasing influence. For the prominent peaks in multimode spectra the dispersion properties and radial distribution of the density fluctuations are found in reasonable agreement with the nonlocal model of Ellis et al. [Phys. Fluids 22, 2137 (1979)], whereas the local slab model turns out to be inadequate. The azimuthal wavenumbers are determined by digital cross-correlation techniques with fixed probe pairs. The phase velocity of minority peaks in the spectra is found to be close to that of the prominent peaks.
Maximum entropy principle for anisotropic plasma
Authors: Gedalin M.
Published: July 2002

Maximum entropy principle is applied to an anisotropic magnetized plasma where there is no free energy exchange among the longitudinal and transverse degrees of freedom.
Transition from resistive-G to ηi- driven turbulence in stellarator systems
Authors: Hong B.-G. , Horton W. , Hamaguchi S. , Wakatani M. , Yagi M. , Sugama H.
Published: July 2002

By an electromagnetic incompressible two-fluid model describing both ion temperature gradient drift modes (ηi modes) and resistive interchange modes (g modes), a new type of ηi mode is studied in cylindrical geometry including magnetic shear and an averaged curvature of Heliotron/Torsatron. This ηi mode is destabilized by the coupling to the unstable g mode. Finite plasma pressure beta increases the growth rate of this mode and the radial mode width also increases with plasma pressure beta indicating large anomalous transport in the Heliotron/Torsatron configuration. The transport from ηi mode exceeds that from resistive g when the mean-free-path exceeds the machine circumference. For plasma beta above two to three times the Suydam limit, the m=1/n=1 growth rate increases from the ηi mode value to the magnetohydrodynamic (MHD) value.
Resonant magnetohydrodynamic modes with toroidal coupling. Part I: Tearing modes
Authors: Connor J. W. , Hastie R. J. , Taylor J. B.
Published: July 2002

In a cylindrical plasma, tearing modes can be calculated by asymptotic matching of ideal magnetohydrodynamic (MHD) solutions across a critical layer. This requires a quantity Δ′ that represents the ‘‘discontinuity’’ in the ideal solution across the layer. In a torus, poloidal harmonics are coupled and there are many critical surfaces for each toroidal mode number, and correspondingly many discontinuities Δ′m. The ideal MHD solutions do not then determine the Δm but only a relation between them—described by an ‘‘E matrix.’’ The calculation of the E matrix for a large-aspect-ratio tokamak is discussed. In a weak-coupling approximation, it is tridiagonal and can be computed from integrals over the uncoupled eigenfunctions or from simple ‘‘basis functions’’ comprising triplets of coupled poloidal harmonics. This weak-coupling approximation fails if Δ′m is already small for an uncoupled harmonic. An alternative strong-coupling approximation is developed for this case.
Gradient effects on intense, pulsed electron-cyclotron-wave absorption and current drive
Authors: Cohen Ronald H. , Rognlien Thomas D.
Published: July 2002

Gradients along the magnetic field of the parallel index of refraction N∥ or the magnetic-field strength B can substantially alter the dynamics of electrons subjected to intense, pulsed electron-cyclotron waves. Electrons trapped in a phase-space island, or ‘‘bucket,’’ about a cyclotron resonance tend to remain trapped and be accelerated with the bucket as N∥ and B change. The process can result in a substantial increase in the opacity (with the optical thickness possibly exceeding the linear value) and an improvement in the efficiency with which current can be driven in a tokamak. In this paper, a semiquantitative theory for the absorption and current-drive efficiency is developed and compared with numerical calculations from a multiparticle orbit code. Applications to heating and current drive in present and future tokamaks are discussed.
Ballistic cross-field ion beam propagation in a magnetoplasma
Authors: Papadopoulos K. , Mankofsky A. , Davidson R. C. , Drobot A. T.
Published: July 2002

Long range cross-field ion beam propagation in a magnetoplasma has been studied in the high kinetic beta regime by using computer simulations and analytic techniques. A new regime of long range ballistic beam propagation has been discovered for narrow high-density beams. Ion beams with transverse size Δ≪Rb, where Rb is the ion beam gyroradius and mass density nbMb≫npMp, where nb(Mb),np(Mp) are the particle density (mass) of the beam and the ambient ions can propagate ballistically across the ambient magnetic field over distances varying from a minimum of (nb/np)Rb to over an order of magnitude longer depending on the extent of initial interpenetration of the beam and the background plasma. The propagation mode is characterized by the formation of a front at the head of the beam, which forces the plasma to move sideways and prevents beam-plasma interpenetration. The system momentum is locally balanced by a corresponding displacement of the head of the beam in the opposite direction to the plasma, which is equivalent to erosion of the beam front. The physics of the interaction is distinct from the conventional magnetohydrodynamic picture and requires kinetic treatment for beam ions. Scaling laws that can be tested by laboratory and space experiments are presented.