bluuebunny/crossref_metadata_2025 huggingface dataset:
Role of vibronic interactions in the electronic properties of a silicon cluster, (SiH)8
Authors: Kato Takashi , Yoshizawa Kazunari , Yamabe Tokio
Published: July 2002

The role of vibronic interactions in the optical properties of octasilacubane (SiH)8 with Oh symmetry is studied. The lowest optically allowed transition occurs when an electron in the t2u highest occupied molecular orbital (HOMO) is promoted to the t2g lowest unoccupied molecular orbital (LUMO)+2 or an electron in the t2g HOMO−1 is promoted to the t1u LUMO, from the point of view of a one-electron approximation. How the frontier orbitals can couple to the molecular vibrations of (SiH)8 is discussed in detail from density-functional-theory calculations. The vibronic coupling constants of some vibrational modes to the T1u1 electronic excited state that stems from the possible two lowest optically allowed transitions in (SiH)8 are calculated. The low-frequency threefold degenerate T2g mode of 197 cm−1 and the twofold degenerate Eg mode of 403 cm−1 have large vibronic coupling constants, and the vibronic coupling would provide the absorption band at 3.5 eV with approximate energy separations of 25 and 50 meV, respectively, if the optical absorption spectrum is measured in the gas phase or dilute matrix.
Phase behavior of end-functionalized polymers confined between two surfaces
Authors: Kuznetsov Dmitri V. , Balazs Anna C.
Published: July 2002

Using scaling theory, we determine the equilibrium behavior of a melt of functionalized and nonfunctionalized polymers confined between two infinite, planar surfaces, which model clay sheets. The functionalized chains contain two end groups (one at each chain end) that are highly attracted to the surfaces. Through these calculations, we delineate the conditions for the formation of thermodynamically stable polymer/clay mixtures in terms of the end-group adsorption energy, volume fraction of the end-functionalized chains, and polymer chain lengths.
Photodissociation of formic acid
Authors: Su Hongmei , He Yong , Kong Fanao , Fang Weihai , Liu Ruozhuang
Published: July 2002

The photodissociation of formic acid has been studied experimentally and theoretically. Ab initio calculations were performed to study the dissociative profiles of five reaction channels on the S0, S1, and T1 potential energy surfaces. The vibrationally excited nascent products were detected using a time-resolved Fourier transform infrared spectrometer after laser photolysis at 248 or 193 nm. In the 248 nm photolysis, the HCOOH molecule was first excited to the S1 state, but it was found that the dissociation takes place on the S0 surface after internal conversion. The products of the vibrationally excited CO, CO2(v3) and H2O(v1) were detected. During the dissociation process the vibrationally energized molecule is geometrically memorized and dynamically controlled, with the yield preference of CO and H2O over that of CO2 and H2. The ratio of CO(v⩾1)/CO2(v⩾1) is estimated as <7.5. Vibrationally excited CO (v) and CO2(v3) are also found in the 193 nm photolysis but the CO/CO2 ratio increases to 11. Most of the dissociation is thought to occur on the S0 state. At this wavelength another dissociation channel which produces OH and HCO radicals on S1 surface has been identified. The dissociation is unlikely to occur on the T1 surface, as the energy barriers are fairly high.
On the hyperbolic complex linear symmetry groups and their local gauge transformation actions
Authors: Zhong Zai-Zhe
Published: July 2002

The hyperbolic complex linear groups and the isomorphic relation between these groups and real linear groups are discussed. A local hyperbolic complex gauge symmetry of the hyperbolic complex sesquilinear field is equivalent to some local real gauge symmetry of the real bilinear field.
Lie symmetries of some equations of the Fokker–Planck type
Authors: Sastri C. C. A. , Dunn K. A.
Published: July 2002

The structure of the local Lie groups of symmetries of some partial differential equations of the Fokker–Planck type in one space dimension is investigated. A connection between these groups and the group SL2(R) is established in the sense that they are all shown to be locally isomorphic to SL2(R)A, where A is the radical. It is conjectured that the groups of Lie symmetries of all Fokker–Planck equations in one space dimension have this structure. The notion of partial invariance, due to Ovsiannikov, is applied to the equations studied. It appears plausible that the class of partially invariant solutions of these equations is larger than the class of invariant solutions although no explicit demonstration of this claim is available at present.
Dynamical group chains and integrity bases
Authors: Gilmore R. , Draayer J. P.
Published: July 2002

An algorithm for constructing a Hamiltonian from the generators of a dynamical group G, which is invariant under the operations of a symmetry group H ⊆ G, is presented. In practice, this algorithm is subject to a large number of simplifications. It is sufficient to construct an integrity basis of H scalars in terms of which all H scalars can be expressed as polynomial functions. In many instances the integrity basis exists in 1–1 correspondence with the Casimir operators for a group–subgroup lattice based on the pair H ⊆ G. When this is so the theory embodies natural symmetry limits and analytic results for observables can be given. Examples of the application of the algorithm are given for the dynamical group SU(2) with symmetry subgroups C3 and U(1) and for SU(N) ⊇ SO(3), N=3, 4, and 6.
Practical pretheories of QED. I. Properties of the interaction picture
Authors: Yoakam M. C.
Published: July 2002

Discussions and generalizations of the usage of variational methodology for second-quantized quantum field theories are presented, including extensions to situations [which mimic quantum electrodynamics (QED)] in which the new canonical variables obtained for different pictures are not the simple images of the interaction picture canonical variables. Methods helpful for segregating the new canonical variables and for insuring Poincaré invariance of the resultant theories are included; the latter being necessary because most of the state-evolution equations are not explicitly invariant (covariant). A parametrization of the boson commutators is introduced which includes the Proca and Coester fields as special cases and which, in the zero-mass limit, includes the Yennie, Landau, and Feynman gauge fields. If the Coester fields satisfy the Lorentz condition in the weak-convergence limit, then it is shown that all fields parametrized in this fashion satisfy the Lorentz condition in the weak-convergence limit, and that invariance under field interchange of such heavy-meson field operators reduces to special gauge invariance in the zero-mass limit. Superfield formalism for the spinor fields is introduced in which none of the spinor fields are segregated as ‘‘physical’’ fields.
The ℋℋ equation in arbitrary canonical coordinates
Authors: Torres del Castillo G. F.
Published: July 2002

Extending previous results, the equation which determines the algebraically special solutions to the Einstein vacuum field equations is given in an arbitrary system of coordinates adapted to the congruence of totally null two-dimensional surfaces that these space-times possess. The action of the transformations which relate any pair of these coordinate systems is also given.
A twistor approach to Nahm’s equations
Authors: Wainwright P. R.
Published: July 2002

It has been shown that Nahm’s equations T′=TΛT may be regarded as dimensionally reduced self-duality conditions. Ward’s twistor method is applied to construct a holomorphic vector bundle corresponding to each solution of these equations, and a simple expression for the transition matrix is derived. Some elementary examples are given for which this procedure may be explicitly reversed to generate solutions of Nahm’s equations from given transition matrices.
Electrodynamics in eight-dimensional space
Authors: Chandola H. C. , Rajput B. S.
Published: July 2002

Generalized electromagnetic fields and the corresponding generalized electromagnetic field tensor in a real eight-dimensional space-time manifold have been constructed, in terms of which the generalized Maxwell’s field equations have been derived. The Lorentz force acting on a charged particle moving in generalized electromagnetic fields has been derived by constructing an eight-velocity vector in this space.
Resolving the discrete ambiguities in amplitude determinations
Authors: Moravcsik Michael J.
Published: July 2002

Necessary and sufficient criteria are presented for eliminating discrete ambiguities in the determination of reaction amplitudes from the bilinear products of amplitudes that are measured in experiments. In terms of a geometrical analog, the criteria require closed loop diagrams with an odd number of broken lines and an odd number of solid lines. The results are applicable to the general mathematical problems of solving a set of simultaneous bilinear algebraic equations for several unknowns.
Mass eigenfunction expansions for the relativistic Kepler problem and arbitrary static magnetic field in relativistic quantum theory
Authors: Hostler Levere C.
Published: July 2002

We investigate the existence of orthogonality and completeness relations for the eigenvalue problem associated with the differential operator Λ=−ΠμΠμ −ieσ ⋅ (E+iB), Πμ=−i ∂μ−eAμ. The operator Λ acts on 2×1 Pauli-type spinor fields defined over all Minkowski space, and may be interpreted as the square of the mass of a charged Dirac particle moving in an external c-number electromagnetic field. We show that Λ is self-adjoint with respect to the not positive-definite inner product (φb; φa)=∫ d4x φ̄bφa, where φ̄b is defined as φ̄b=φ†b(−iΠ↙4−σ⋅Π↙). A proof is provided for the Coulomb case that the mass eigenfunctions form a complete set in spite of the indefinite metric in Hilbert space. The mass eigenfunction expansion of the propagator is worked out explicitly for the Kepler case. This mass eigenfunction expansion is expected to be quite useful for bound state calculations in quantum electrodynamics, since it involves the covariant denominators (m′)2−(m)2.
Exact solutions of an algebraically extended Kaluza–Klein theory
Authors: Mann R. B.
Published: July 2002

The four-dimensional field equations in an algebraically extended Kaluza–Klein theory are solved in the static spherically symmetric case. Eight distinct classes of solutions are found, some of which are free of singularities in both the metric and the electromagnetic field.
Boson approximants for lattice Fermi systems
Authors: Garbaczewski Piotr
Published: July 2002

We demonstrate that Bose systems can be used to simulate properties of their Fermi partners in thermal bath, provided the spectral property HB =PHBP +(1−P)HB(1−P), HF =PHBP can be proved in the state space of the Bose system. The approximation accuracy can be made arbitrarily good by varying the (free) coupling parameter λ∈(0,∞), and permits studying of fermionic partition or correlation functions in a finite volume by means of the standard techniques (Bose:path integral, Monte Carlo, etc).
The Wigner transformation is of finite order
Authors: Várilly Joseph C. , Gracia-Bondía José M.
Published: July 2002

The Wigner integral transformation, which intertwines the twisted product and the composition of kernels, is of order 24. Indeed, it commutes with, and its sixth power equals, the Fourier cotransformation.
Homogeneous space-times of Gödel-type in higher-derivative gravity
Authors: Accioly A. J. , Gonçalves A. T.
Published: July 2002

A general theorem concerning any Gödel-type solution of higher-derivative gravity field equations, which may be produced by any reasonable physical source with a constant energy-momentum tensor, is analyzed. The resulting class of metrics depends on two parameters, one of which is related to the vorticity. A general class of solutions of Gödel-type space-time-homogeneous universes in the context of the higher-derivative theory is exhibited. This is the most general higher-derivative solution of such type of metric and includes all known solutions of Einstein’s equations related to these geometries as a special case. A number of completely causal rotating models is also obtained. Some of them present the interesting feature of having no analogs in the framework of general relativity.
Nonlinearly coupled oscillators in quantum mechanics: A normal form approach
Authors: Kummer Martin , Gompa Raghuramaiah
Published: July 2002

Quantum mechanical Hamiltonians of the form of n harmonic oscillators coupled via an interaction of the form ε times a polynomial in the position and momenta variables are studied in a rigorous Hilbert space setting. In particular, normal form theory is used to define the mth approximation to the associated Schrödinger initial value problem and it is shown that it deviates in norm from the exact solution by a term of order εm+1 ‖t‖ (t=time) provided only that the initial vector is confined to an appropriate dense subspace. The main concentration is on the case in which there exist no resonances of order ≤m between the frequencies of the n oscillators, but the case of two oscillators in 1:1 resonance is also taken up.
On self-similar Tolman models
Authors: Maharaj S. D.
Published: July 2002

The self-similar spherically symmetric solutions of the Einstein field equation for the case of dust are identified. These form a subclass of the Tolman models. These self-similar models contain the solution recently presented by Chi [J. Math. Phys. 28, 1539 (1987)], thereby refuting the claim of having found a new solution to the Einstein field equations.
On the structure of spatial infinity. II. Geodesically regular Ashtekar–Hansen structures
Authors: Chruściel Piotr T.
Published: July 2002

The ambiguities in the differentiable structure of Ashtekar–Hansen completions satisfying a geodesic condition are analyzed. The results obtained imply, in particular, uniqueness up to a four-parameter family of ‘‘logarithmic transformations’’ of completions of asymptotically flat space-times stationary ‘‘in a neighborhood of i0.’’
Branching rules for the hyperoctahedral group
Authors: Doeraene J. P. , Amunategui G. Iommi
Published: July 2002

Reduction theorems for the decomposition of induced and irreducible characters of W(Bn) in terms of induced and irreducible characters of W(Bn−1), respectively, are given.
Decomposition of the scalar superfield in ten dimensions
Authors: Kwon P. , Villasante M.
Published: July 2002

Explicit expressions for the irreducible superfields included in the ten-dimensional scalar superfield are derived by using a method based in a Cartan subalgebra.
An alternate characterization of integrability
Authors: Das Ashok , Huang Wen-Jui
Published: July 2002

This paper will show that the existence of at least three independent symplectic forms (related in a simple way) on the phase space of a dynamical system is a sufficient condition for the integrability of the system.
Electron transport in quasi-one-dimensional random structure
Authors: Pavlov B. S. , Pankratov M. A.
Published: July 2002

A model of the Markovian chain of N atoms is constructed with the help of extension theory. Behavior of averaged wave functions of random Dirac operator is studied for finite and large N with respect to parameters of the model and Markovian process. Study of a random Dirac operator is connected with the study of nonrandom double-dimensional non-self-adjoint Dirac operator. Dynamics of bands of effective periodic operator with respect to the Markovian parameter is presented.
Grassmannian Legendre functions
Authors: Chan Fuk-Lok , Lau Kim-Ming , Finkelstein Robert J.
Published: July 2002

The Grassmannian analogues of the Legendre polonomials are obtained from the corresponding Grassmannian Hermite multinomials. The generating function, recurrence relations, and differential equation are given. In contrast to the Hermitian case there is no Berezin weight function that orthogonalizes these functions. Generalizations to the Tchebyscheff and Gegenbauer cases are also possible.
The Berry connection and Born–Oppenheimer method
Authors: Bohm A. , Kendrick B. , Loewe Mark E. , Boya L. J.
Published: July 2002

By performing the most general Born–Oppenheimer procedure, the (non-Abelian) Berry connection for quantum systems in a quantum environment is derived. This method is then applied to the rapid rotation of a particle about a slowly changing axis, as exemplified by the electronic motion of a diatomic molecule. The angular part of the resulting dynamics for the quantum environment is equivalent to that of a monopole.
q deformations of the oscillator
Authors: Finkelstein R. J.
Published: July 2002

Generating functions that interpolate between the generating functions for Hermitian multilinears and the corresponding Grassmann multilinears are considered. The new functions that arise in this way may be related to state functions of q-deformed harmonic oscillators.
Schrödinger equation for convex plane polygons. II. A no-go theorem for plane waves representation of solutions
Authors: Amar V. , Pauri M. , Scotti A.
Published: July 2002

In the present article we discuss whether or not ansatzes more general than those considered hitherto, for the representation in terms of plane waves of eigensolutions of the Schrödinger equation for a free particle in a plane convex polygonal domain, lead to the construction of a complete set for a class of domains larger than the well-known one, containing the polygons for which such a complete set can be obtained in terms of a superposition of a finite number of plane waves. Our conclusion is in the negative. Comments are also made on some features of a representation in terms of analytic functions of two complex variables.
On generalized Loewner systems: Novel integrable equations in 2+1 dimensions
Authors: Konopelchenko B. G. , Rogers C.
Published: July 2002

A reinterpretation and generalization of a class of infinitesimal Bäcklund transformations originally introduced in a gas-dynamics context by Loewner in 1952 leads to a linear representation for a novel class of 2+1-dimensional nonlinear equations. The latter may be parametrized in terms of a triad of eigenfunctions. Moreover, like the well-known integrable Davey–Stewartson and Nizhnik–Novikov–Veselov equations, the nonlinear systems typically contain the two spatial variables on an equal footing. The ∂̄-dressing method is outlined for these generalized Loewner systems. It is noted that basic reductions lead to 2+1-dimensional versions of the principal chiral-fields model, Toda lattice system, and notably the classical sine–Gordon equation. Loewner systems on Grassmannian, the projective CPn and RPn manifolds, are considered. In particular, the 2+1-dimensional integrable sine–Gordon system in which x and y occur in a symmetric manner arises naturally in this context. A gauge-equivalent system likewise emerges out of a special reduction of a 2+1-dimensional Toda lattice scheme constructed here via the Loewner formalism.
The antipode of and star operations in a Hopf algebra
Authors: Scheunert M.
Published: July 2002

It is pointed out that a star operation in a Hopf algebra, i.e., an involutive semilinear mapping of the Hopf algebra into itself which is (anti)multiplicative and (anti)comultiplicative, automatically satisfies a certain compatibility relation with the antipode.
Hilbert spaces of analytic functions for the SL(2,R) coherent states and a class of associated integral transforms
Authors: Basu Debabrata
Published: July 2002

It is shown that the Bargmann–Segal Hilbert spaces of entire analytic functions and Bargmann’s canonical Hilbert spaces of functions analytic within the open unit disc are connected by simple integral transform pairs. A further consequence of this analysis is the analog of the Bargmann transform for the SL(2,R) [or SU(1,1)] group.
The superalgebra embedding of OSP(1‖2) in SL(1‖2) and the grade star representations of SL(1‖2)
Authors: Daumens Michel
Published: July 2002

First, it is shown that the superalgebra embedding of osp(1‖2) in sl(1‖2) allows to characterize the irreducible representation states of sl(1‖2) without any missing label. Through this embedding the general nonpositive definite scalar product in the osp(1‖2) representation space can be generalized to the sl(1‖2) representation space. Then grade star representations of sl(1‖2) are derived by considering this nonpositive scalar product.
On the construction of quasi-exactly solvable Schrödinger operators on homogeneous spaces
Authors: Milson Robert
Published: July 2002

The closure conditions for a quasi-exactly solvable operator is the requirement that a second-order Lie algebraic differential operator be equivalent, up to scale-change, to a Schrödinger operator on curved space. The present work begins with an invariant characterization of the closure conditions, and after a series of steps gives a reformulation of the closure conditions in terms of finite-dimensional representations of the underlying Lie algebra. These techniques are used to give a complete solution to the closure condition for two different planar realizations of 𝔰𝔩(2). Along the way two theorems about homogeneous solutions to the closure conditions are introduced and proved. Also introduced is the class of ‘‘Abelian’’ solutions to the closure conditions. Such solutions appear on flat spaces and give rise to a Schrödinger operator with zero potential. The concluding remarks highlight remaining questions and give references to research that address said questions.
Semiclassical approximation for Schrödinger operators on a two-sphere at high energy
Authors: Thomas Lawrence E. , Wassell Stephen R.
Published: July 2002

Let H=−ΔS+V be a Schrödinger operator acting in L2(S), with S the two-dimensional unit sphere, ΔS the spherical Laplacian, and V a smooth potential. Approximate eigenfunctions and eigenvalues for H are obtained involving expansions in inverse powers of the classical angular momentum variables, provided that these variables are in a region of phase space where the corresponding classical Hamiltonian is nearly integrable. The analysis is carried out in a Bargmann representation, where ΔS becomes a quadratic expression in the sum of two quantum harmonic oscillator Hamiltonians, and V becomes a pseudodifferential operator.
Angular momentum and space–time hyperboloids
Authors: Lozada Abraham
Published: July 2002

For a classical field theory, in Minkowski space–time, the field momentum and angular momentum are defined as an integral of the appropriate density over an asymptotically null hyperboloid. We prove that for the electromagnetic field these quantities are well defined even for charged sources where infrared divergences are a problem for defining the angular momentum. Moreover, it is also shown that if the angular momentum density is integrated over a null plane, the angular momentum is not well defined for charged sources.
On the geometry of non-holonomic Lagrangian systems
Authors: de León Manuel , de Diego David M.
Published: July 2002

We present a geometric framework for non-holonomic Lagrangian systems in terms of distributions on the configuration manifold. If the constrained system is regular, an almost product structure on the phase space of velocities is constructed such that the constrained dynamics is obtained by projecting the free dynamics. If the constrained system is singular, we develop a constraint algorithm which is very similar to that developed by Dirac and Bergmann, and later globalized by Gotay and Nester. Special attention to the case of constrained systems given by connections is paid. In particular, we extend the results of Koiller for Čaplygin systems. An application to the so-called non-holonomic geometry is given.
On separability of bi-Hamiltonian chain with degenerated Poisson structures
Authors: Błaszak Maciej
Published: July 2002

Separability of bi-Hamiltonian finite-dimensional chains with two degenerated Poisson tensors, which have Pfaffian quasi-bi-Hamiltonian representation, is proved.
A short survey of noncommutative geometry
Authors: Connes Alain
Published: July 2002

We give a survey of selected topics in noncommutative geometry, with some emphasis on those directly related to physics, including our recent work with Dirk Kreimer on renormalization and the Riemann–Hilbert problem. We discuss at length two issues. The first is the relevance of the paradigm of geometric space, based on spectral considerations, which is central in the theory. As a simple illustration of the spectral formulation of geometry in the ordinary commutative case, we give a polynomial equation for geometries on the four-sphere with fixed volume. The equation involves an idempotent e, playing the role of the instanton, and the Dirac operator D. It is of the form 〈(e−12)[D,e]4〉=γ5 and determines both the sphere and all its metrics with fixed volume form. The expectation 〈x〉 is the projection on the commutant of the algebra of 4 by 4 matrices. We also show, using the noncommutative analog of the Polyakov action, how to obtain the noncommutative metric (in spectral form) on the noncommutative tori from the formal naive metric. We conclude with some questions related to string theory.
The onset of convection in a multicomponent fluid layer
Authors: Terrones Guillermo , Pearlstein Arne J.
Published: July 2002

The onset of convective instability is investigated in a multicomponent fluid layer in which the density depends on N stratifying agencies with different diffusivities. The general equations required to determine the topology of the neutral curves and stability boundaries are given. We show that 1+2[(N−1)/2] (where [α] is the integer part of α) critical Rayleigh numbers are sometimes required to specify the linear stability criteria. This multivaluedness can be traced to the existence of disconnected neutral curves. The general theory is illustrated by a numerical example for the quintuply diffusive case (N=5).
High Reynolds number calculations using the dynamic subgrid-scale stress model
Authors: Piomelli Ugo
Published: July 2002

The dynamic subgrid-scale eddy viscosity model has been used in the large-eddy simulation of the turbulent flow in a plane channel for Reynolds numbers based on friction velocity and channel half-width ranging between 200 and 2000, a range including values significantly higher than in previous simulations. The computed wall stress, mean velocity, and Reynolds stress profiles compare very well with experimental and direct simulation data. Comparison of higher moments is also satisfactory. Although the grid in the near-wall region is fairly coarse, the results are quite accurate: the turbulent kinetic energy peaks at y+≂12, and the near-wall behavior of the resolved stresses is captured accurately. The model coefficient is o(10−3) in the buffer layer and beyond, where the cutoff wave numbers are in the decaying region of the spectra; in the near-wall region the cutoff wave numbers are nearer the energy-containing range, and the resolved turbulent stresses become a constant fraction of the resolved stresses. This feature is responsible for the correct near-wall behavior of the model coefficient. In the near-wall region the eddy viscosity is reduced to account for the energy transfer from small to large scales that may occur locally.
Full magnetohydrodynamic simulation of the tilting instability in a field-reversed configuration
Authors: Horiuchi Ritoku , Sato Tetsuya
Published: July 2002

Nonlinear evolution of the tilting instability in a field-reversed configuration (FRC) is investigated by means of a three-dimensional full magnetohydrodynamic simulation. Three types of plasma model are considered, i.e., case (a) where the plasma is confined by a uniform external field, case (b) where the plasma is confined by a mirror external field, and case (c) where the plasma rotates around the major axis. For the prolate FRC the internal tilt mode cannot stay at a low amplitude but keeps growing irrespective of whether the mirror field exists or not. When the initial configuration is substantially deformed, the instability triggers an external mode at the plasma–vacuum boundary because of the pressure imbalance. The outgoing flow driven by the external mode tears the plasma into two pieces, and the torn pieces move away toward the axial edges. The growth time is nearly equal to the transit time for the Alfvén wave to propagate over the plasma length. When the plasma is driven to spin with the Mach number of M=1.5, the growth rate is halved compared to the nonrotating case. The spin stabilization is expected to be complete for M>2.5. It is also found that the oblate FRC plasma is linearly unstable against the external tilt mode.
Weakly nonlinear steady-state oscillations in the Pierce diode
Authors: Hörhager M. , Kuhn S.
Published: July 2002

An analytic theory of weakly nonlinear oscillations in the uniform Pierce diode [J. Appl. Phys. 15, 721 (1944)] with nontrivial external-circuit elements is presented. The theory is applicable to situations where linear stability analysis predicts just one unstable eigenmode which is oscillatory and whose growth rate is ‘‘sufficiently’’ small. All oscillating quantities are expanded in time Fourier series with fundamental frequency ω, and the n+1st harmonic is assumed to be one order smaller than the nth one. It is shown that determination of the nonlinear amplitudes and fundamental frequency requires calculation of all quantities up to at least the third order, and all spatial profiles and current amplitudes, as well as the nonlinear oscillation frequency, are calculated explicitly for period-one oscillations in the ‘‘three-harmonic approximation.’’ Representative numerical results are presented for the special cases when the external circuit is (a) short, (b) purely inductive, (c) purely resistive, and (d) purely capacitive. These are spot-checked against particle simulations run with PDW1 [J. Comput. Phys. 80, 253 (1989)] and, in the short-circuit case, are also compared with the genuinely numerical results of Godfrey [Phys. Fluids 30, 1553 (1987)]. In all cases considered, the fundamental frequency from the three-harmonic approximation is found to be in excellent agreement with the peak-to-peak frequency from the simulations. In the short-, resistive-, and capacitive-circuit cases, the three-harmonic amplitudes agree well with the simulation results only for ac current amplitudes well below 10% of the dc current. For large-amplitude oscillations found in the inductive-circuit case, however, the three-harmonic amplitudes are correct even for ac amplitudes many times larger than the dc current. To the authors’ knowledge, this is the first analytic theory describing self-consistent nonlinear steady-state oscillations in a bounded-plasma system.
Mode–particle resonances during near-tangential neutral beam injection in the Tokamak Fusion Test Reactor
Authors: Kaita R. , White R. B. , Morris A. W. , Fredrickson E. D. , McGuire K. M. , Medley S. S. , Murphy T. J. , Scott S. D.
Published: July 2002

Coherent magnetohydrodynamic modes have been observed previously during neutral beam injection in the PDX tokamak [Phys. Rev. Lett. 50, 891 (1983)] and they have now been seen in the TFTR tokamak [Phys. Fluids 26, 2958 (1983)]. Periodic bursts of oscillations were detected with several plasma diagnostics, and Fokker–Planck calculations show that the populations of trapped particles in both tokamaks are sufficient to account for fishbone destabilization if a resonant interaction, between the mode and the beam ions, is assumed. Estimates of mode parameters are in reasonable agreement with the experiments, and they indicate that the fishbone mode may continue to affect the performance of intensely heated tokamaks.
Comparison of drift wave models with fluctuation data from the interior of the TEXT tokamak
Authors: Ross David W. , Bravenec R. V. , Ritz Ch. P. , Sloan M. L. , Thompson J. R. , Wootton A. J. , Schoch P. M. , Heard J. W. , Crowley T. P. , Hickok R. L. , Simcic V. , Brower D. L. , Peebles W. A. , Luhmann N. C.
Published: July 2002

Experimental evidence for and against drift waves as the origin of the observed fluctuations and anomalous transport in the plasma interior is reviewed. Fluctuation spectra observed by far-infrared (FIR) scattering and a heavy ion beam probe (HIBP) are compared. The FIR system observes broad S(k,ω), which are spatially resolved at large k and readily identified with electron drift waves. At higher densities a clear ion feature, which may be associated with ion temperature gradient (ITG) modes, appears as well. A quasicoherent feature in the drift wave range of phase velocities is also found at the inner midplane. But interior HIBP measurements using a thallium beam have, by a two-point correlation method, measured wave numbers far too small (i.e., phase velocities far too high) to be those of drift waves of either variety. Some recent measurements with a cesium beam have produced phase velocities more closely in accord with drift waves at low frequencies. It is suggested that a new mode may be present, which is not drift wavelike. However, the phase velocity and coherence of the HIBP data exhibit qualitative features that suggest possible instrumental effects. Several of these are investigated, which individually do not appear to reconcile the data with a pure drift wave model. They are (1) sample volume size, (2) common mode effects such as cross-talk or path integrals of beam attenuation, and (3) two-stream instabilities. Reconciliation of these measurements is important to transport studies. That is, calculated particle and energy fluxes depend sensitively on the frequency and wave-number spectrum employed. The theoretical considerations about two-point correlations and possible instrumental effects are also relevant to other diagnostics using this technique.
Trapped-electron effects on time-independent negative-bias states of a collisionless single-emitter plasma device: Theory and simulation
Authors: Crystal T. L. , Gray P. C. , Lawson W. S. , Birdsall C. K. , Kuhn S.
Published: July 2002

Time-average values from particle simulations of a collisionless, single-emitter plasma device modeling single-ended Q machines or thermionic converters with a negatively biased collector are presented. These results quantitatively confirm the predictions of collisionless, kinetic plane-diode theory for spatial potential profiles that decrease monotonically. However, simulations of negative-bias potential profiles with a single internal maximum differ significantly from previous theoretical predictions which assumed electron phase space to have either (i) no trapped electrons or (ii) trapped electrons isothermal with the passing electrons. A more general class of trapped-electron model distributions is introduced from which new equilibrium potential values can be recovered that closely match the simulations. These simulations clearly demonstrate the sensitive role that trapped electrons play in shaping the potential profiles of the equilibrium (or slowly evolving) states of the simulated systems. The trapped-electron distributions in these simulations are themselves shown to be controlled critically by fluctuations whose levels are varied by the choice of particle injection scheme. These effects, although found and discussed here in the context of a particular model, are believed to be important in many bounded plasma systems where electrons can be trapped in potential wells.
Quantum-molecular-dynamics simulations of liquid metals and highly degenerate plasmas
Authors: Theilhaber Joachim
Published: July 2002

A numerical scheme based on time-dependent density-functional theory, for the simulation of systems of classical ions and quantum mechanical electrons, has been developed with the aim of modeling simple metals or highly degenerate plasmas from first principles. The electrons are represented by a set of three-dimensional wave functions obeying one-particle Schrödinger equations, subject to an effective potential. A pseudospectral method is used for the solution of the Schrödinger equations, coupled to a classical molecular-dynamics simulation for the ions. The scheme yields accurate predictions for the radial distribution functions and the ionic diffusion coefficients in liquid sodium, and is shown to correctly account for shielding due to the fully responsive electron background. Preliminary simulation results for bulk hydrogen under astrophysical conditions are also presented, including the successful modeling of chemical bonding in the isolated hydrogen molecule.
Linear analysis of a finite length plasma-filled backward wave oscillator
Authors: Ali M. M. , Ogura K. , Minami K. , Watanabe T. , Destler W. W. , Granatstein V. L.
Published: July 2002

Absolute instability in a plasma-filled backward wave oscillator with sinusoidally corrugated slow wave structure driven by an intense relativistic electron beam has been analyzed numerically. The maximum spatial growth rate of the plasma-filled waveguide is found to be larger than that of an optimally designed vacuum structure. The excitation of a finite length structure is investigated. Although the spatial growth rates obtained in the linear theory increase with plasma density in the finite length plasma-filled structure for the fundamental TM01 mode of oscillation, negative global spatial growth rates prevent the coherent oscillation for intermediate ranges of plasma density, beam current, and even for structure length.
Feedback stabilization of plasma instabilities using a modulated ion beam
Authors: Tham P. , Sen A. K.
Published: July 2002

A new technique for feedback suppression using a modulated ion beam as a remote suppressor has been developed for the first time. A Langmuir probe was used as the sensor. The feedback loop was completed with a phase shifter and amplifiers. This technique was demonstrated by stabilizing the collisionless, curvature-driven trapped particle instability down to a baseline noise level with an appropriate feedback gain and phase. An important feature is that the injected ion beam is nonperturbing to the plasma, constituting only 1% of the plasma density. A simple theory to describe the experimental results is presented and its predictions show generally good agreement with the experiment. To indicate that this concept could also be extended to other plasma instabilities, the rotationally driven E×B mode was also stabilized. Since the basic mechanism of suppression is the cancellation of charge separation inherent in an instability, a modulated electron beam performed equally well. Such remote, nonperturbing particle beam suppressors have great potential for remote suppression of plasma instabilities in a variety of plasma devices.
Laser-induced fluorescence observations of a multipolar argon discharge
Authors: Bachet G. , Chérigier L. , Carrère M. , Doveil F.
Published: July 2002

Observations carried out with a laser-induced fluorescence diagnostic on several configurations of a multipolar discharge are presented. This diagnostic allows very accurate measurements of the ion velocity distribution function in the argon plasma and reveals the presence of double-hump velocity distribution functions due to ion acceleration in the static plasma potential and ion reflection on a multipolar magnetic field. These observations give a new insight to ion temperature and ion drifts inside the device.
Electron-hose instability of a relativistic electron beam in an ion-focusing channel
Authors: Lampe Martin , Joyce Glenn , Slinker Steven P. , Whittum David H.
Published: July 2002

A relativistic electron beam, propagating in an underdense ion-focusing channel that is embedded within a broad region of underdense plasma, is shown to be subject to a hose instability due to coupling with plasma electrons at the edge of the pure-ion region. The instability is studied by means of linearized analytic calculations of dispersion relations and asymptotic growth, numerical integrations of the linearized dynamical equations, and three-dimensional particle simulations of the full nonlinear evolution. Three cases are considered: (1) If the plasma density ni0(r), prior to the introduction of the beam, is uniform, the instability is absolute, grows very rapidly, and does not saturate nonlinearly until the thrashing of the beam carries it into the quasineutral plasma region. Thus the instability prevents orderly beam propagation. (2) If ni0(r) consists of a central channel with constant density, surrounded by lower density plasma, the instability is again absolute, but with a reduced growth rate. Over a limited range, propagation without significant disturbance is possible. If the propagation range is long, the instability is stabilized by phase mixing when the beam leaves the channel. The beam then is recentered, with consequent emittance growth. (3) If ni0(r) consists of a central channel with a rounded density profile, surrounded by lower density plasma, the instability is convective in the beam frame. If parameters are chosen correctly, the instability does not significantly inhibit long range propagation.
Correlation theory of a two-dimensional plasma turbulence with shear flow
Authors: Zhang Y. Z. , Mahajan S. M.
Published: July 2002

When the ion sound effect is neglected, a wide class of electrostatic plasma turbulence can be modeled by a two-dimensional equation for the generalized enstrophy Ψ, an inviscid constant of motion along the turbulent orbits. Under the assumption of a Gaussian stochastic electrostatic potential, an averaged Green’s function method is used to rigorously derive equations for the N-particle correlation functions for a dissipative and sheared flow. This approach is equivalent to the cumulant expansion method [T. H. Dupree, Phys. Fluids 15, 334 (1972); 21, 783 (1978)] used to study the Vlasov–Poisson system. For various cases of interest, appropriate equations are solved to obtain the absolute level as well as the detailed structure of the two-point correlation function C(r), and its Fourier transform, the enstrophy spectral function I(k). Uniformly valid analytical expressions are derived for the dissipative but shearless case resulting in a ‘‘fluctuation–dissipation’’ theorem relating the total spectral intensity to classical viscosity. These self-consistent results show a strong logarithmic modification of the mixing length estimates for the turbulence levels. For the extremely important and interesting problem of a sheared flow, the suppression of turbulence is demonstrated by using asymptotic analytical techniques in the inviscid range, and uniformly valid numerical methods for the dissipative system. The current asymptotic methods reproduce the results obtained in the orbit picture [Y. Z. Zhang and S. M. Mahajan, Phys. Fluids B 4, 1385 (1992)], but provide much clearer physical perspective and a better definition of crucial parameters like the decorrelation time. The uniformly valid numerical approach allows the determination of the change in spectral shape and intensity due to the presence of shear. It is found that the suppression is more effective for longer wavelengths as compared to the shorter wavelengths. This and other relevant issues, concerning the role of flows with shear (including its radial variation) in the understanding of the L–H transitions in tokamaks, are discussed.
Experimental and neoclassical electron heat transport in the LMFP regime for the stellarators W7-A, L-2, and W7-AS
Authors: Maassberg H. , Burhenn R. , Gasparino U. , Kühner G. , Ringler H. , Dyabilin K. S.
Published: July 2002

The electron energy balance is analyzed for equivalent low-density electron cyclotron resonance heated (ECRH) discharges with highly peaked central power deposition in the stellarators W7-A [Plasma Phys. Controlled Fusion 28, 43 (1986)], L-2 [Proceedings of the 6th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Berchtesgaden, 1976 (International Atomic Energy Agency, Vienna, 1977), Vol. 2, p. 115] and W7-AS [Proceedings of the 9th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Baltimore, 1982 (International Atomic Energy Agency, Vienna, 1983), Vol. 3, p. 141]. Within the long mean-free path (LMFP) collisionality regime in stellarators, the neoclassical electron heat diffusivity χe can overcome the ‘‘anomalous’’ one. The neoclassical transport coefficients are calculated by the dkes code (Drift Kinetic Equation Solver) [Phys. Fluids 29, 2951 (1986); Phys. Fluids B 1, 563 (1989)] for these configurations, and the particle and energy fluxes are estimated based on measured density and temperature profiles.

Neoclassical transport in the LMFP regime is minimum in W7-A and maximum in L-2, the standard configurations in W7-AS are in between. The radial electric field is estimated from the ambipolarity condition of only neoclassical particle fluxes. For these types of discharges in the quite different stellarator configurations, only the ‘‘electron root’’ exists in the innermost region, and, at the outer radii, only the ‘‘ion root.’’ In the region where both roots are found, a rather narrow shear layer in the poloidal plasma rotation is expected. Especially for W7-AS, a significant improvement of the neoclassical confinement is predicted in the ‘‘electron root’’ region. On the ‘‘ion root’’ side of the predicted ‘‘shear layer,’’ both the neoclassical energy and particle fluxes agree quite well with the experimental findings. At outer radii, the neoclassical fluxes are much lower. The predicted improvement for the ‘‘electron root’’ region is not found experimentally.
Two-dimensional self-focusing of short intense laser pulse in underdense plasma
Authors: Chen X. L. , Sudan R. N.
Published: July 2002

A simplified set of three-dimensional equations are derived for the propagation of an intense laser pulse of arbitrary strength a=eA/mc2 (where A is the magnetic vector potential of the laser pulse) in cold underdense plasma. In different limits, the equations can be easily reduced to those of previous one-dimensional models [Phys. Fluids 30, 526 (1987); Phys. Rev. A 40, 3230 (1989); 41, 4463 (1990)]. For ‖a‖≤1, an approximate set of equations from the averaged Lagrangian is obtained. The present study differs from previous work in that wave dispersion is also important for short laser pulse, and is included in the model equations. The axisymmetric two-dimensional model equations are solved numerically to show the effect of dispersion in the self-focusing process.
A theoretical model of bulk plasma generated by the electron-cyclotron-resonance mechanism
Authors: Uhm Han S. , Choi Eun H.
Published: July 2002

A theoretical model is developed to explain properties of the electron-cyclotron-resonance (ECR) plasma and an experiment is conducted to compare the theoretical predictions with experimental measurements. A theoretical expression of the electron temperature Te is obtained assuming that the plasma electrons are heated by the transverse electric field of the input microwave. The electron temperature is expressed as Te=a+bp−1/2, where p is the plasma-chamber pressure, and the coefficients a and b should be determined from system parameters. Making use of the ambipolar diffusion, the plasma potential φ is described in terms of the local plasma density np. That is eφ(r,z)=Te ln[np(r,z)/nw], where −e is the electron charge and nw is the plasma density at the surface of the chamber. For the case of low neutral density, the plasma density np is also expressed as np2=γ2p exp(−εi/Te)−γ∥, where εi is the ionization energy of neutrals by electrons and the constants γ2 and γ∥ should be determined from system parameters. These theoretical predictions agree reasonably well with experimental data.