bluuebunny/crossref_metadata_2025 huggingface dataset:
A semiclassical study of the photodissociation dynamics of a coupled two-surface model of HCl+ by an intense laser field in the long-wavelength limit
Authors: Gill R. , Yanagawa R. , Thachuk M.
Published: July 2002

The photodissociation of HCl+ on two coupled potential surfaces is studied in the long wavelength regime with a semiclassical method employing classical trajectories and a hopping algorithm. Dissociation probabilities, product kinetic energy distributions, and branching ratios are presented. In addition, two mechanisms are introduced to explain trends in these properties. One mechanism produces large product kinetic energies and is an extension to two-coupled surfaces of the “wagging tail” mechanism seen in a previous one-surface study [M. Thachuk and D. M. Wardlaw, J. Chem. Phys. 102, 7462 (1995)]. The other mechanism is an extended barrier-suppression mechanism and accounts for the bulk of the product kinetic energy distribution, and in particular rationalizes the low energy part of these distributions as well as the branching ratios. It is shown that most of the trajectories undergo at most one nontrivial hop before dissociating so that the dynamics is dominated by the motion near the barrier to dissociation. This provides a simple, intuitive model for understanding the overall dynamics.
Solitary wave solutions to the Einstein equations
Authors: Letelier P. S.
Published: July 2002

The soliton solutions to the vacuum Einstein equations generated by the special class of Einstein–Rosen metrics described by linear combinations of homogeneous solutions to the usual cylindrically symmetric wave equation are studied.
Propagation coefficients for fixed-isospin (T,T
z) average and related spectroscopic sum rules
Authors: Nomura Masao
Published: July 2002

The reduction relation for the fixed-isospin (T,Tz) average of a general operator in the model space of many fermions is described in two forms with and without recourse to factorization of isospin z components. Algebraic treatment is developed to deduce various types of expressions for each propagation coefficient that plays the role of the Green’s function in each form of the reduction relation. Propagation coefficients are described also in relation to sum rules as to fixed-isospin spectroscopic factors. These results lead to novel identities among n-j symbols and factorials.
Confining optical potentials
Authors: Gomez F. J. , Rañada M. F. , Sesma J.
Published: July 2002

The possibility of confining a quantum particle in an optical potential, the imaginary part of which would be related to the existence of inelastic reaction channels coupled to the elastic one, is considered. Pure imaginary potentials of various (constant, linear, and parabolic) radial shapes are studied. The numerical dependence of the energies and mean-lives of the confined states is explicitly shown. Analytical expressions for such dependence are also given in some cases.
Wavelike solutions to the Einstein equations coupled to neutrino and gauge fields
Authors: Torres del Castillo G. F.
Published: July 2002

Starting from the plane-wave metric, solutions to the Einstein field equations coupled to a Weyl neutrino field and to a Yang–Mills field are found. These solutions can be superposed to yield a solution with both sources if the direct interaction between them is neglected. A solution to the coupled Einstein–Yang–Mills–Weyl equations that represents a multiplet of neutrino fields interacting with the gauge field and the gravitational field is also found. All these solutions contain arbitrary functions.
Imperfect fluids and repulsive gravitation
Authors: Ponce de León J.
Published: July 2002

Imperfect fluid sources to the Schwarzschild exterior solution are studied under the assumption that the metric coefficients g00 and g11 of the interior solution satisfy the relation g00 g11=−1. It was found that the core of such a distribution is gravitationally repulsive provided the energy density is positive.
Finite-dimensional representations of the special linear Lie superalgebra sl(1,n). I. Typical representations
Authors: Palev Tchavdar D.
Published: July 2002

In a series of two papers all finite-dimensional irreducible representations of the special linear Lie superalgebra sl(1,n) are written down in a matrix form. This paper develops a background for constructing the representations. Expressions for the transformation of the basis under the action of the generators are given for all induced and, hence, for all typical sl(1,n) modules.
Sufficient conditions for zero not to be an eigenvalue of the Schrödinger operator
Authors: Ramm A. G.
Published: July 2002

It is proved that if H=−∇2+q(x)≥0, Im q=0, ‖q(x)‖≤c(1+‖x‖)−a, c=const>0, a>2, then zero is not an eigenvalue of H. An example is given of H≥0, with zero a resonance (half-bound state) and q=q(‖x‖) compactly supported and integrable. An example of a potential q=O(r−2) is known, for which H≥0 and zero is an eigenvalue. This shows that a>2 is the optimal condition for zero not to be an eigenvalue of H≥0. If the condition H≥0 does not hold and H is an operator in L2(R3), then zero can be an eigenvalue even if q∈C∞0. If H is an operator in L2(R1) or in L2(R1+), R1+ =[0,∞), then zero cannot be an eigenvalue of H provided that a>2; here conditions H≥0 and Im q=0 can be dropped. Global estimates of the Green’s function of H from below and above are given.
Addition theorems for B functions and other exponentially declining functions
Authors: Weniger E. Joachim , Steinborn E. Otto
Published: July 2002

In this paper addition theorems are derived for a special class of exponentially declining functions, the so-called B functions Bmn,l (α,r) [E. Filter and E. O. Steinborn, Phys. Rev. A 18, 1 (1978)]. Although these B functions have a relatively complicated analytical structure they nevertheless have some mathematical properties that are particularly advantageous in connection with multicenter problems. Also, all the commonly occurring exponentially declining functions like, for instance, bound-state hydrogen eigenfunctions and Slater-type functions, can be expressed by simple finite sums of B functions. Consequently, addition theorems for these functions can also be written down immediately. The various addition theorems for B functions are derived by applying suitable generating differential operators to the well-known addition theorem of the special B function Bm−l,l, which is that solution of the modified Helmholtz equation that is irregular at the origin and regular at infinity [E. J. Weniger and E. O. Steinborn, J. Math. Phys. 26, 664 (1985)]. All differentiations, which have to be done in this approach, can be expressed in closed form leading to comparatively compact addition theorems.
Curvatures, Gauss–Bonnet and Chern–Simons multiplets in old-minimal N=1 supergravity
Authors: Ferrara S. , Villasante M.
Published: July 2002

The complete form of the three curvature multiplets of old-minimal supergravity are given. The full super-Gauss–Bonnet theorem is derived and the Chern–Simons multiplets constructed. The latter construction allows a coupling to antisymmetric tensor fields that is the supersymmetric generalization of the Green–Schwarz mechanism occurring in superstring theories.
Quantum mechanics of the damped pulsating oscillator
Authors: Abdalla M. Sebawe , Ramjit Ursula A. T.
Published: July 2002

A harmonic oscillator subject to the combined effects of damping and pulsating is represented by a Kanai–Caldirola Hamiltonian. The equations of motion are solved in the Heisenberg picture in the case of weak pulsation. The rotating-wave approximation (RWA) is used to obtain the motion in the neighborhood of the principal resonance. The RWA Schrödinger equation is solved exactly and pseudostationary and quasicoherent states are described. The transition probability between quasicoherent and coherent states is obtained and the gain in energy is discussed.
The three-dimensional Euclidean quantum group E(3)q and its R-matrix
Authors: Celeghini Enrico , Giachetti Riccardo , Sorace Emanuele , Tarlini Marco
Published: July 2002

A contraction procedure starting from SO(4)q is used to determine the quantum analog E(3)q of the three-dimensional Euclidean group and the structure of its representations. A detailed analysis of the contraction of the R-matrix is then performed and its explicit expression has been found. The classical limit of R is shown to produce an integrable dynamical system. By means of the R-matrix the pseudogroup of the noncommutative representative functions is considered. It will finally be shown that a further contraction made on E(3)q produces the two-dimensional Galilei quantum group and this, in turn, can be used to give a new realization of E(3)q and E(2,1)q.
Some exact results for N-point massive Feynman integrals
Authors: Davydychev A. I.
Published: July 2002

By using the Mellin–Barnes representation for massive denominators, some exact results for classes of one-loop N-point massive Feynman integrals are obtained for arbitrary values of the line indices (the powers of denominators) and of the space-time dimension. A representation for corresponding massless integral is also derived.
On coadjoint orbits of rotational perfect fluids
Authors: Penna Vittorio , Spera Mauro
Published: July 2002

In this paper the structure of vortex coadjoint orbits pertaining to perfect fluids having smooth vorticities in R3, within the framework set up by J. Marsden and A. Weinstein [Physica D 7, 305–323 (1983)], in terms of an associated Hamiltonian Kähler manifold (the Clebsch manifold, described in terms of the so-called Clebsch variables) is investigated. The topological quantization of Mikhailov and Kuznetsov is related to geometric quantization. Natural candidates for the coherent states on the Clebsch manifold are also exhibited.
Positive discrete series of osp(2‖2,R) and (para)supersymmetric quantum mechanics
Authors: Debergh N.
Published: July 2002

The energy spectra of the systems corresponding to the superposition of (para) bosons and (para)fermions are analyzed. Such a study is subtended by the exploitation of the positive discrete series of the superalgebra osp(2‖2,R) associated with the two relative parabose and parafermi sets of trilinear structure relations. In particular, the spectra corresponding to exact or broken supersymmetry are recovered for specific values of the orders of paraquantization but new ones are also present with their own typical properties.
Symmetries of the KdV equation and four hierarchies of the integrodifferential KdV equations
Authors: Lou Sen-yue
Published: July 2002

Using the inverse strong symmetry of the Korteweg–de Vries (KdV) equation on the trivial symmetry and τ0 symmetry, one gets four new sets of symmetries of the KdV equation. These symmetries are expressed explicitly by the multi-integrations of the Jost function of the KdV equation and constitute an infinite dimensional Lie algebra together with two hierarchies of the known symmetries. Contrary to the general belief, the time-independent symmetry groups of the KdV and mKdV equations are non-Abelian and the infinite dimensional Lie algebras of the KdV and mKdV equations are nonisomorphic though two equations are related by the Miura transformation. Starting from these sets of symmetries, four hierarchies of the integrodifferential KdV equations, which can be solved by the Schrödinger inverse scattering transformation method, are obtained. Some of these hierarchies enjoy a common strong symmetry and/or same local conserved densities.
Global smooth solution for the Klein–Gordon–Zakharov equations
Authors: Boling Guo , Guangwei Yuan
Published: July 2002

In this paper the initial value problem to the Klein–Gordon–Zakharov equations in two dimensions is discussed. Without assuming that the Cauchy data are small, we prove the existence and uniqueness of the global smooth solution for the problem via the so-called continuous method and delicate a priori estimates. Also the asymptotic behaviour of the solution to the K–G–Z equations with a small parameter approaching zero is studied.
Liouville vortex and φ4 kink solutions of the Seiberg–Witten equations
Authors: Nergiz Serdar , Saçlıog̃lu Cihan
Published: July 2002

The Seiberg–Witten equations, when dimensionally reduced to R2, naturally yield the Liouville equation, whose solutions are parametrized by an arbitrary analytic function g(z). The magnetic flux Φ is the integral of a singular Kaehler form involving g(z); for an appropriate choice of g(z), N coaxial or separated vortex configurations with Φ=2πN/e are obtained when the integral is regularized. The regularized connection in the R1 case coincides with the kink solution of φ4 theory.
Extension of Giacomini’s results concerning invariants for one-dimensional time-dependent potentials
Authors: Bouquet Serge , Lewis H. Ralph
Published: July 2002

One-dimensional time-dependent potentials are considered for which an invariant can be expressed in terms of the potential and the momentum according to the formulation of Giacomini. New solutions of Giacomini’s equations are derived. In addition, possibilities are discussed for extending Giacomini’s approach to more general systems.
Becchi–Rouet–Stora cohomology of zero curvature systems. II. The noncomplete ladder case
Authors: Carvalho M. , Vilar L. C. Q. , Sasaki C. A. G. , Sorella S. P.
Published: July 2002

The Yang–Mills-type theories and their BRS cohomologies are analyzed within the zero curvature formalism.
Kinks and geodesic incompleteness
Authors: Dunn K. A. , Harriott Tina A. , Williams J. G.
Published: July 2002

The problem of geodesic incompleteness is examined for space–times with Finkelstein–Misner kinks. A discussion of spherically symmetric kink space–times is followed by specific examples in which geodesics, initially incomplete in the original space–time, are shown to be extendible by the Kruskal technique. The structure of the two Kruskal patches and their matching at the patch boundaries are worked out in detail for one such example. Comments are made concerning a possible link between extendibility and energy conditions. It is shown that the kinds of spherically symmetric kink space–times examined in the present paper do not satisfy the strong energy condition.
Topological properties of single gravisolitons
Authors: Gleiser Reinaldo J. , Garate Alexander , Nicasio Carlos O.
Published: July 2002

The possibility of assigning topological properties to gravisolitons has been recently discussed by Belinsky, who considered perturbations of certain diagonal metrics with two commuting Killing vectors. The discussion given by Belinsky relies on the properties of the solitonic part of the projection of the four-dimensional space–time metric onto the two-dimensional space spanned by the Killing vectors. In that context, for single soliton perturbations, he finds two types of, in principle, disjoint solutions, characterized respectively by the functions μin and μout, such that one can assign a ‘‘topological charge’’ to the corresponding space–time. In this article we analyze this problem, studying in detail the single soliton perturbation of a Bianchi-type VI0 background, and prove that when we consider the full four-dimensional metric, it is possible to construct locally smooth extensions that connect sectors associated to μin to sectors associated to μout. Therefore, the concept of ‘‘topological charge’’ for this type of gravisolitons needs to be revised. Some ideas in this direction are discussed in this paper. We also show that this behavior is not restricted to the particular case of a Bianchi-type VI0 background, but holds in general for the whole set of diagonal background metrics considered by Belinsky. An interesting side result is that the soliton perturbation ‘‘erases’’ the ‘‘cosmological’’ singularity that appears naturally in the background metrics, and that they can be extended to regions not covered in the original charts. In the particular case of a Bianchi-type VI0 background, the resulting extended metric is regular everywhere. Finally we present an extension of the soliton metric to the background by matching these metrics through a null hypersurface. This extension requires the presence of a ‘‘null dust’’ on the matching hypersurface, and therefore the resulting space–time is not a vacuum everywhere.
Quantum Clifford algebras from spinor representations
Authors: Bautista R. , Criscuolo A. , Durdević M. , Rosenbaum M. , Vergara J. D.
Published: July 2002

A general theory of quantum Clifford algebras is presented, based on a quantum generalization of the Cartan theory of spinors. We concentrate on the case when it is possible to apply the quantum-group formalism of bicovariant bimodules. The general theory is then singularized to the quantum SL(n,C) group case, to generate explicit forms for the whole class of braidings required. The corresponding spinor representations are introduced and investigated. Starting from our Clifford algebras we introduce the quantum-Euclidean underlying spaces compatible with different choices of *-structures from where the analogues of Dirac and Laplace operators are built. Using the formalism developed, quantum Spin(n) groups are defined.
Split structures in general relativity and the Kaluza–Klein theories
Authors: Gladush V. D. , Konoplya R. A.
Published: July 2002

We construct a general approach to the decomposition of the tangent bundle of pseudo-Riemannian manifolds into direct sums of subbundles, and the associated decomposition of geometric objects. An invariant structure Hr defined as a set of r projection operators is used to induce decomposition of the geometric objects into those of the corresponding subbundles. We define the main geometric objects characterizing decomposition. Invariant nonholonomic generalizations of the Gauss–Codazzi–Ricci’s relations have been obtained. All the known types of decomposition (used in the theory of frames of reference, in the Hamiltonian formulation for gravity, in the Cauchy problem, in the theory of stationary spaces, and so on) follow from the present work as special cases when fixing a basis and dimensions of subbundles, and parametrization of a basis of decomposition. Various methods of decomposition have been applied here for the unified multidimensional Kaluza–Klein theory and for relativistic configurations of a perfect fluid. Discussing an invariant form of the equations of motion we have found the invariant equilibrium conditions and their 3+1 decomposed form. The formulation of the conservation law for the curl has been obtained in the invariant form.
A differential-geometric interpretation of Kirchhoff’s elastic rods
Authors: Hu Kai
Published: July 2002

In this article, Kirchhoff’s elasticity theory of rods is revisited but from a viewpoint of Riemannian geometry. By means of the Cayley–Klein parameter, the theory under clamped-end conditions can be regarded as a geometry of paths on some geometrically distorted three-sphere produced by a constrained elastic energy functional. Using this geometric formulation, the uniqueness of elasticae with prescribed initial values of the strains can be easily shown. On the other hand, a family of elasticae with prescribed values of orthonormal frames at two endpoints is demonstrated to be parametrized by an open set in R3. In particular, a criterion of the nonuniqueness of elasticae satisfying clamped-end conditions is given in terms of a geometric concept—conjugate points.
The super-separability of the three-body inverse-square Calogero system
Authors: Benenti S. , Chanu C. , Rastelli G.
Published: July 2002

The geometrical theory of the variable separation for the Hamilton–Jacobi equation is applied to the classical three-body inverse-square Calogero system. It is proved that this system is separable in infinitely many inequivalent ways, related to five different kinds of separable webs in the Euclidean three-space, and the corresponding systems of independent first integrals in involution are computed.
Effect of a crystal–melt interface on Taylor-vortex flow
Authors: McFadden G. B. , Coriell S. R. , Murray B. T. , Glicksman M. E. , Selleck M. E.
Published: July 2002

The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case that the stationary outer cylinder is a crystal–melt interface rather than a rigid surface. A radial temperature difference is maintained across the liquid gap, and equations for heat transport in the crystal and melt phases are included to extend the ordinary formulation of this problem. The stability of this two-phase system depends on the Prandtl number. For small Prandtl number the linear stability of the two-phase system is given by the classical results for a rigid-walled system. For increasing values of the Prandtl number, convective heat transport becomes significant and the system becomes increasingly less stable. Previous results in a narrow-gap approximation are extended to the case of a finite gap, and both axisymmetric and nonaxisymmetric disturbance modes are considered. The two-phase system becomes less stable as the finite gap tends to the narrow-gap limit. The two-phase system is more stable to nonaxisymmetric modes with azimuthal wavenumber n=1; the stability of these n=1 modes is sensitive to the latent heat of fusion.
Effect of wall cooling on the stability of compressible subsonic flows over smooth humps and backward-facing steps
Authors: Al-Maaitah Ayman A. , Nayfeh Ali H. , Ragab Saad A.
Published: July 2002

The effect of wall cooling on the two-dimensional linear stability of subsonic flows over two-dimensional surface imperfections is investigated. Results are presented for flows over smooth humps and backward-facing steps with Mach numbers up to 0.8. The results show that, whereas cooling reduces the viscous instability, it increases the shear-layer instability and hence it increases the growth rates in the separation region. The coexistence of more than one instability mechanism makes a certain degree of wall cooling most effective. For the Mach numbers 0.5 and 0.8, the optimum wall temperature is about 80% of the adiabatic wall temperature.
Spatial simulation of instability control by periodic suction blowing
Authors: Danabasoglu G. , Biringen S. , Streett C. L.
Published: July 2002

The applicability of active control by periodic suction blowing in spatially evolving plane Poiseuille flow is investigated by the direct simulation of the three-dimensional, incompressible Navier–Stokes equations. The results reveal that significant reductions in perturbation amplitudes can be obtained by a proper choice of the control wave amplitude and phase. The upstream influence of the control wave is shown to be confined to a region in the vicinity of the control slot with no apparent effect on the flow development.
Bounded and unbounded patterns of the Benney equation
Authors: Rosenau P. , Oron A. , Hyman J. M.
Published: July 2002

The boundedness of 2-D liquid film flows on an inclined plane in the context of the regularized Benney, uτ+λu2ux+[(μu6−νu3)ux]x +σ{u3[uxx/(1+ε2ux2)3/2]x}x=0, and the Benney (ε=0) equation are studied. Here u, x, τ are the rescaled film thickness, the longitudinal coordinate, and time, respectively; λ, μ, and ν are non-negative constants determined at equilibrium; and ε is the parameter related to the film aspect ratio. For a vertical plane (ν=0) a critical curve λ=λc(μ) has been found bifurcating from the point (λ,μ)=(0,1) which divides the λ-μ space into two domains. When λ≳λc(μ) the initial data evolves into modulating traveling waves similar to the solutions of the Kuramoto–Sivashinsky equation. However, when λ<λc(μ), either an infinite spike forms in the solution in finite time and the original Benney model breaks down or the solution of the regularized Benney equation forms an infinite slope when the wavelike solution attempts to become multivalued. In a tilted plane (ν≳0) the boundedness of the emerging pattern is sensitive to the choice of initial data. It is also found that the Benney equation does not describe wave breaking where the solution develops an infinite slope.
Compressibility effects on large structures in free shear flows
Authors: Samimy M. , Reeder M. F. , Elliott G. S.
Published: July 2002

Space-time correlations were used to study compressibility effects on large structures in mixing layers. Two high Reynolds number mixing layers with Mc=0.51 (case 1) and 0.86 (case 2) were studied. The results indicate that the structures in case 1 are similar to those in the subsonic case, but less organized. The structures in case 2 are highly three dimensional, with a good spatial but a poor temporal organization. The streamwise correlations showed a decay rate 4 to 5 times greater for case 2 relative to case 1. While the spanwise correlations for case 1 showed trends similar to incompressible mixing layers, the behavior of case 2 was very different. The pressure fluctuations in the fully developed region of case 2 displayed significant rms variation in the spanwise direction with a well-defined pattern. Based on these measurements, the structures in case 2 seem to be of a horseshoe type, transversely spanning the mixing layer with the head in the low-speed side and the legs inclined in both the x-y and the x-z planes.
Subharmonic instabilities of finite-amplitude monochromatic waves
Authors: Cheng Minquan , Chang Hsueh-Chia
Published: July 2002

Finite-amplitude monochromatic waves in free-shear layers, planar jets, gravity–capillary waves, free-convection boundary layers, and falling films are often first destabilized by disturbances twice or two-thirds their wavelength or period. The transition to the 1/2 mode allows energy transfer to modes with lower wave numbers or lower frequencies and it precedes the onset of wide-spectrum turbulence in the above systems. A center-unstable manifold theory is used to derive the onset criteria for these subharmonic instabilities in terms of a critical amplitude of the fundamental or a critical value of a control parameter. It is shown that, in contrast to classical results, a finite-amplitude wave is always unstable to disturbances with 1/2 its wave number (frequency) if the subharmonic is linearly unstable. This instability is either oscillatory or static depending on the phase difference (frequency mismatch) between the fundamental and the subharmonic and on the amplitude of the fundamental. For a given phase difference, there exists a critical amplitude beyond which the static instability triggers a most efficient energy transfer to the 1/2 mode and causes it to grow monotonically. Inefficient oscillatory interaction occurs below this critical amplitude of the fundamental. In contrast, the fundamental −3/2 interaction is always oscillatory except when there is perfect resonance (no frequency mismatch). The theory presented here contains a rigorous and explicit derivation of amplitude equations for spatially evolving open-flow systems without recourse to Gaster transformation or multiscale expansions. This new formulation is partially demonstrated on the inviscid shear layer.
Tracer dispersion in rough channels: A two-dimensional numerical study
Authors: Koplik J. , Ippolito I. , Hulin J. P.
Published: July 2002

Numerical results are presented on the hydrodynamic dispersion of passive tracer in flow through a two-dimensional channel bounded by parallel plates, one having substantial rugosities perpendicular to the flow. The simulation is based on the numerical solution of the microscopic Stokes and convention-diffusion equations, over a range of Péclet numbers and of degrees of rugosity of the channel. One observes a tenfold increase of the effective dispersion between the smooth plate case (classical Taylor dispersion) and the maximum rugosity case, attributable to the trapping of tracer inside deep rugosities. The results are analyzed in terms of tracer exchange models, involving a characteristic exchange time between the low- and high-velocity zones and their relative volume fractions, as a function of the Péclet number and the relative depth of the rugosities. The simulations are compared to ‘‘echo’’ dispersion experiments in which the tracer is first injected into the model and then, upon reversal of the fluid flow, drawn back through the inlet.
Oblique and parallel wave interaction in the near wake of a circular cylinder
Authors: Yang Pan-Mei , Mansy Hussein , Williams David R.
Published: July 2002

Detailed velocity measurements have been made to investigate the structure of the low-frequency vortex dislocations that appear in the indigenous wake of a circular cylinder. It is shown that one mechanism for the production of vortex dislocations is the superposition of two waves with slightly different frequencies, where the higher frequency wave is parallel to the cylinder axis and the lower frequency is an oblique wave. In contrast to the discrete vortex concept that implies discontinuous shedding frequencies, the measured amplitude and phase distribution of the interacting waves are shown to be continuous along the span of the cylinder. Both waves (parent modes) exist simultaneously and overlap in the wake. The difference mode associated with the vortex dislocations is produced by the nonlinear interaction of the parent modes, and its maximum amplitude is at the location where the parent modes have comparable magnitude. The spanwise phase and amplitude distributions of the difference mode are ‘‘predicted’’ by taking the product of the complex wave amplitudes of the parent modes.
A generalized discrete mapping treatment of nonresonant ripple transport in a tokamak
Authors: Albert Jay M. , Boozer Allen H.
Published: July 2002

A discrete mapping is used to analyze nonresonant ripple transport in a tokamak. Pitch-angle scattering is manifested in two different terms, as in a previous treatment of resonant ripple transport. The mapping is a generalization of one which recovers the standard banana-drift regime. This is one limit of the more general mapping presented here; in the other, the quasilinear value for the diffusion coefficient emerges. When the quasilinear value applies, it can be either much greater or much less than the corresponding banana-drift value, depending on the parameter values of the mapping.
A Van der Waals-like theory of plasma double layers
Authors: Katz Ira , Davis V. A.
Published: July 2002

A new theory is presented that describes plasma double layers in terms of multiple roots of the charge density expression. Analogous to Van der Waals’ equation for simple fluids, the system is described using simple analytical expressions that contain the essential nonlinearity of the physics. Both theories predict multiple states and transitions between the states. Van der Waals’ theory is for the liquid–gas phase transition; the theory presented here is for double layers between two plasmas. Except within the double layer, the plasma is assumed to be quasineutral, that is, the charge density is almost zero. The expression used for charge density includes linear shielding at low potentials and current continuity at high potentials. The theory is independent of the details of the expression used for the charge density; it only requires that the charge density be a nonmonotonic function of potential. Multiple roots exist because of this nonlinearity; linear theories such as Debye shielding allow for only a single root. For two semi-infinite plasmas in planar geometry, the charge density has a single root when the separation of plasma potentials is less than a critical value. Above that, the root bifurcates into two symmetric branches that asymptotically approach the two boundary plasma potentials. The transition between the two roots is a double layer. For a plasma expanding spherically from a source into a uniform background plasma, the charge density equation roots have two branches that never cross. One branch corresponds to the source plasma and disappears abruptly at some radius away from the source. The other branch corresponds to the background plasma and disappears close to the source. The two branches coexist for a limited range of radii. A double layer provides the transition between the two branches. An ancillary condition, similar to the Maxwell construction, is used to locate this transition. The location of the double layers calculated using this theory is consistent with laboratory measurements.
Flux confinement measurements in large field-reversed configuration equilibria
Authors: Rej D. J. , Barnes G. A. , Baron M. H. , Chrien R. E. , Okada S. , Siemon R. E. , Taggart D. P. , Tuszewski M. , Webster R. B. , Wright B. L.
Published: July 2002

The poloidal magnetic flux φ in large field-reversed configuration plasmas is examined experimentally. A wide range of initial equilibrium conditions, with 1≤φ≤8 mWb, is produced by varying the reverse bias magnetic field strength. The flux confinement time τφ at first improves with bias, albeit with field-null resistivities an order of magnitude larger than classical. A further increase in bias results in a reduction of τφ, which is inconsistent with either classical or anomalous diffusion theory. The data suggest the importance of nondiffusive processes such as instabilities or formation dynamics.
Studies of hot dense plasmas produced by an intense subpicosecond laser
Authors: Milchberg H. M. , Freeman R. R.
Published: July 2002

The absorption of intense, subpicosecond ultraviolet laser pulses is used to infer transport properties of extremely heated, solid density material. The resistivity of solid aluminum has been determined in the temperature range 1–100 eV. Hot material expansion has been monitored using Doppler shifts induced in the spectrum of the specularly reflected heating pulses. This electron pressure-driven expansion of the material interface has been used to estimate plasma temperatures.
Wave propagation near a cyclotron resonance in a nonuniform equilibrium magnetic field
Authors: Cairns R. A. , Lashmore-Davies C. N. , Dendy R. O. , Harvey B. M. , Hastie R. J. , Holt H.
Published: July 2002

The inclusion of the variation of the equilibrium magnetic field across the Larmor orbits of the resonant particles is crucial for a self-consistent treatment of cyclotron resonance in plasmas. Two contrasting nonrelativistic self-consistent calculations [T. M. Antonsen and W. M. Manheimer, Phys. Fluids 21, 2295 (1978); C. N. Lashmore-Davies and R. O. Dendy, Phys. Fluids B 1, 1565 (1989)] which analyze perpendicular propagation in the same nonuniform magnetic field are compared. It is shown that the first of these, which is a full wave calculation, makes an approximation that eliminates the damping found in the second, which calculates optical depth via a Wentzel–Kramers–Brillouin (WKB) approximation. A new expansion of the exact integral equation describing the problem is given, producing full wave equations which incorporate the perpendicular damping. The equations are of the correct form to ensure energy conservation and can easily be obtained to any order in an expansion in terms of the ratio of Larmor radius to perpendicular wavelength.
Nonlinear stability theorem for rotating coherent structures in a non-neutral plasma column
Authors: Davidson Ronald C. , Lund Steven M.
Published: July 2002

A nonlinear stability theorem is developed for arbitrary-amplitude, two-dimensional coherent structures, nR(θ − ωr t) and φR(θ − ωr t), in a strongly magnetized, low-density (ω2pe/ω2ce ≪ 1) non-neutral plasma column confined radially by a uniform axial magnetic field B0êz. Here, a grounded, perfectly conducting, cylindrical wall is located at radius r = rw, and ωr = const is the angular rotation velocity of the coherent structures about the cylinder axis (r=0). A cold-fluid guiding-center model based on the continuity-Poisson equations is used to describe the nonlinear evolution of the electron density ne(r,θ,t) = nR + δne and electrostatic potential φ(r,θ,t) = φR + δφ. Making use of global (spatially averaged) nonlinear conservation constraints, it is shown that ∂nR(ψR)/∂ψR ≤ 0 is a sufficient condition for nonlinear stability of the rotating equilibrium state (φR,nR) to arbitrary-amplitude perturbations δne and δφ. Here, ψR(r,θ − ωr t) = −eφR(r,θ − ωr t) + ωr(eB0/2c)r 2 is an effective streamfunction, and the stability theorem is valid no matter how complex the radial and azimuthal structure of φR(r,θ − ωr t) and nR(r,θ − ωr t).
Anomalous impedance and anomalous ion heating due to gyrorelaxation through magnetohydrodynamic fluctuations
Authors: Yoshida Zensho
Published: July 2002

The ion viscosity associated with the gyrorelaxation dominates the dissipation of fluctuations in a fast reconnection process, where the magnetic compression becomes finite. The kink instability, which drives the fast reconnection, yields a spontaneous ν×B electric field that diminshes the toroidal current. The enhanced impedance of the discharge, which appears as an anomalous resistance of the discharge, is related to the ion gyrorelaxation dissipation. The viscosity contributes to the energy dissipation, while the helicity remains constant. This model of anomalous resistance applies to a turbulent discharge with an appreciable dynamo effect, and explains a part of the high resistance in an ultralow q discharge.
Mode coupling of the two-plasmon decay instability to ion-acoustic waves and the effect on (3/2)-harmonic emission
Authors: Meyer Jochen
Published: July 2002

The mechanism in which two-plasmon decay (TPD) waves have to propagate in the density gradient of a laser-irradiated plasma in order to scatter (3/2)-harmonic photons is shown not to be able to explain most features of observed (3/2)ω0 spectra. Instead, a process of mode coupling of TPD to ion waves, generated by stimulated Brillouin scattering, is proposed and analyzed. It is shown that all significant features of measured (3/2)ω0 spectra can be explained by this model. One important result indicates that these spectra can provide a good thermometer for laser-irradiated plasmas with a quarter-critical density.
Non-neutral plasma compression to ultrahigh density
Authors: Barnes D. C. , Turner Leaf
Published: July 2002

Oscillations of a cold, homogeneous, non-neutral plasma spheroid are considered. A new class of purely compressional, large-amplitude, nonlinear oscillations is found. With a periodically time-varying external electrostatic quadrupole and a static magnetic field, such oscillations periodically can produce arbitrarily large plasma densities with only a modest swing in the applied quadrupole. In limiting cases, one- to three-dimensional plasma oscillations are true normal modes, requiring no variation of the applied quadrupole. For appropriate parameters, peak density is associated with a very ‘‘soft core,’’ so that an extremely high density is associated with a very modest size at minimum density. Further, cold-plasma stability is examined for these cases. For three-dimensional oscillations, all modes are stable. For two-dimensional oscillations, modes with intermediate axial wavelengths are not examined in detail. Long-axial-wavelength modes are found to be unstable only for small oscillation amplitudes. These modes are stable at sufficiently large oscillation amplitude. Those modes with a very short axial wavelength are always stable. Thus, it is very likely that extremely high densities may be produced in a compact system.
Transit-time magnetic pumping induced by spontaneous fluctuations in a magnetohydrodynamic relaxation process
Authors: Yoshida Z. , Hasegawa A.
Published: July 2002

In the magnetohydrodynamic relaxation accompanying fast reconnections, magnetic fluctuations originating from kink-type instabilities yield a finite magnetic compression, and the corresponding transverse electric field is dissipated through transit-time damping. This dissipation mechanism does not change the helicity, while it dissipates the fluctuation energy to result in direct heating of ions. This is in contrast to a slow relaxation process based on the tearing mode turbulence, where the parallel electric field is predominantly dissipated, which accompanies preferential heating of electrons and dissipation of the helicity.
Slow-time-scale magnetic field driven by fast-time-scale electric fields
Authors: Zhu Shao-ping
Published: July 2002

Slow-time-scale magnetic fields driven by fast-time-scale electric fields are discussed from Vlasov–Maxwell equations in unmagnetized plasma. An equation for slow-time-scale magnetic fields is obtained for nonstationary plasma.
Theory of runaway collisional transport
Authors: Tessarotto Massimo , White Roscoe B.
Published: July 2002

The purpose of this paper is to formulate the transport problem for a multispecies rotating toroidal magnetoplasma in the so-called runaway regime, which is defined by an appropriate ordering of relevant characteristic frequencies, in particular, the Larmor frequency, the characteristic acceleration frequency due to the applied electric field and the effective collision frequency, all evaluated at some characteristic speed v0. A suitable form of the gyrokinetic equation is obtained to describe the time-dependent, multispecies plasma response to an applied electric field, in toroidal geometry and for a strongly rotating, quiescent, and collisional plasma. Its moment equations are proven to imply the reduction of the energy equation to Joule’s law, as well as consequences on the form of Ohm’s law and of the Grad–Shafranov equation. To construct an approximate solution of the gyrokinetic equation and to evaluate all relevant fluxes, appearing in the moment equations, a general variational solution method is developed.
Experimental exploration of profile control in the Princeton Beta Experiment-Modified (PBX-M) tokamak
Authors: Bernabei S. , Bell R. , Chance M. , Chu T. K. , Corneliussen M. , Davis W. , Gettlefinger G. , Gibney T. , Greenough N. , Hatcher R. , Hermann H. , Ignat D. , Jardin S. , Kaita R. , Kaye S. , Kessel C. , Kozub T. , Kugel H. , Lagin L. , LeBlanc B. , Manickam J. , Okabayashi M. , Oliver H. , Ono M. , Paul S. , Preische S. , Roney P. , Sauthoff N. , Schweitzer S. , Sesnic S. , Sun Y. , Takahashi H. , Tighe W. , Valeo E. , von Goeler S. , Voss K. , Mauel M. , Navratil G. , Cesario R. , Batha S. , Levinton F. , Rimini F. , Asakura N. , Jones S. , Kesner J. , Luckhardt S. , Paoletti F. , Woskow P. , Zolfaghari A. , Seki T. , Bell J. , Dunlap J. , England A. , Greenwood D. , Harris J. , Henkel G. , Hirschman S. , Isler R. , Lee D. , Blush L. , Conn R. , Doerner R. , Hirooka Y. , Lehmer R. , Schmitz L. , Tynan G.
Published: July 2002

The experimental program of the Princeton Beta Experiment-Modified (PBX-M) tokamak [Phys. Fluids B2, 1271 (1990)] is directed toward tailoring plasma profiles to achieve greater stability and confinement and to gain access to the second stability region. Modification of the current density profile has been achieved with lower-hybrid current drive (LHCD), leading to a regime free of global magnetohydrodynamic modes, while raising the value of q(0) above unity. The diffusion of the fast electrons produced by LHCD has been examined using two-dimensional hard x-ray imaging. Ion Bernstein waves (IBW) have been used for ion heating: a preliminary analysis shows that ion heating was spatially localized and in agreement with theoretical calculations. Divertor biasing has modified the electric field inside the last closed surface, resulting in the formation of a transport barrier, which in turn has reduced the threshold power of neutral beam injection (NBI) for H-mode transition by 25%.
Suppression of Rayleigh–Taylor instability by the snowplow mechanism
Authors: Gol’berg S. M. , Velikovich A. L.
Published: July 2002

Rayleigh–Taylor instability developing in a layer of matter accelerated by the pressure of magnetic field or of a light fluid is shown to be suppressed if the accelerated layer scoops unperturbed matter, entraining it into motion. This stabilizing mechanism is effective for plasma focus devices, multicascade systems like magneto-cumulative (MC) generators of high-pulsed magnetic fields or multiple gas-puff Z pinches, for impact acceleration of thin foils by high-velocity plasma clouds. Linear stability analysis of one-dimensional solutions of the piston problem demonstrates that perturbation of the given wavelength λ does not grow appreciably until the thickness of the accelerated layer L(t) exceeds λ. Before that, if acceleration is increased rapidly enough, amplitudes of the long-wavelength perturbations remain almost constant. If acceleration is increased not too rapidly, stays constant, or is decreased, then the long-wavelength perturbations with λ≥2L(t) are damped.
Electron acceleration by electromagnetic waves in a weakly magnetized inhomogeneous plasma
Authors: Nishida Y. , Yoshizumi M. , Sugihara R.
Published: July 2002

Suprathermal electrons produced at the resonance absorption layer in a nonuniform plasma are accelerated more efficiently in the direction across both the density gradient and magnetic field in microwave–plasma interaction experiments. The experimental results are interpreted by a new Vp×B0 acceleration mechanism.
Nonlinear radial propagation of drift wave turbulence
Authors: Prakash M. , Chu C. K. , Hasegawa Akira
Published: July 2002

The linear and the nonlinear radial propagation of drift wave energy in an inhomogeneous plasma is studied numerically based on model equations of Hasegawa–Mima for the collisionless case and of Hasegawa–Wakatani–Taniuti–Kaw for the collisional case. In the linear regime the drift wave energy spreads out symmetrically along the direction of inhomogeneity with a finite group velocity. In the nonlinear regime for the collisionless case the radially located drift wave energy is found to propagate in the radial direction. However, the direction of propagation depends on the initial parameters of the pulse. In the collisional case the energy is found to propagate in the direction of decreasing resistivity. These results provide qualitative insights into the phenomenon of drift wave turbulence observed in tokamak plasmas.
Solutions of the Rankine–Hugoniot relations in relativistic magnetohydrodynamics
Authors: Carioli S. M.
Published: July 2002

By introducing a suitable fluid rest frame, it is possible to simplify considerably the form of the Rankine–Hugoniot relations for relativistic magnetohydrodynamics. General solutions can then be found that are independent of the problem geometry. In this article, solutions for fast magnetoacoustic shocks in a Synge gas are discussed.
Electrostatic Kelvin–Helmholtz instability produced by a localized electric field perpendicular to an external magnetic field
Authors: Pritchett P. L.
Published: July 2002

The evolution of a plasma with a localized electric field perpendicular to an external magnetic field is shown to be dominated by the Kelvin–Helmholtz instability. For small ion gyroradius, the instability is similar to the fluid mode. When the ion gyroradius is an appreciable fraction of the spatial extent of the electric field, the plasma is not in equilibrium, and the initial drift profile relaxes. Subsequent evolution still leads to vortex flows.
Ion heating by nonlinear Landau damping of ion Bernstein waves
Authors: Sugaya R.
Published: July 2002

It is shown theoretically that efficient ion heating occurs by nonlinear Landau damping because of the self-interaction of ion Bernstein waves, where heating efficiency, nonlinear damping of ion Bernstein waves, nonlinear wave–particle coupling coefficients, and virtual waves have sharp maxima at ω≂(m/2)ωci (m=3,5,7). Ion heating depends on k∥νti/ ωci and becomes significantly large for k∥νti/ ωci ≲0.1.