bluuebunny/crossref_metadata_2025 huggingface dataset:
Perturbations of solutions of the Einstein–Maxwell equations with a null background electromagnetic field
Authors: Torres del Castillo G. F.
Published: July 2002

Expressions for the complete metric and vector potential perturbations of solutions of the Einstein–Maxwell equations with a null background electromagnetic field in terms of two complex scalar potentials are derived using Wald’s method of adjoint operators. The perturbations of the Bell–Szekeres solution, in the regions prior to the collision of the plane-fronted waves, are obtained by this approach. We find that there exist nontrivial u-independent perturbations (where ∂u defines the direction of propagation of the colliding wave) which, when the electromagnetic perturbation vanishes, are exact solutions of the Einstein–Maxwell equations.
Exact solution of the Ising model on group lattices of genus g>1
Authors: Regge Tullio , Zecchina Riccardo
Published: July 2002

We discuss how to apply the dimer method to Ising models on group lattices having nontrivial topological genus g. We find that the use of group extension and the existence of both external and internal group isomorphisms greatly reduces the number of distinct Pfaffians and leads to explicit topological formulas for their sign and weight in the expansion of the partition function. The complete solution for the Ising model on the Klein lattice group L(2,7) with g=3 is given.
Character states and generator matrix elements for Sp(4)⊃SU(2)×U(1)
Authors: Hambli N. , Michelson J. , Sharp R. T.
Published: July 2002

A new set of polynomial states (to be called character states) are derived for Sp(4) reduced to its SU(2)×U(1) subgroup, and the relevant generator matrix elements are evaluated for generic representations (a,b) of Sp(4). [The degenerate representations (a,0) and (0,b) were treated in our previous work and are also given in this paper]. The group–subgroup in question is that of the seniority model of nuclear physics.
Relativistic point interaction with Coulomb potential in one dimension
Authors: Benvegnù Stefan
Published: July 2002

The Dirac Hamiltonian in one space dimension is investigated under the influence of a potential of the form −γ/|x|. The corresponding (four-parameter) family of all self-adjoint extensions is given and described via the boundary form. The resolvent is calculated and the spectrum is studied. Furthermore, we examine the zero mass case. In the nonrelativistic limit we obtain the four-parameter family of Schrödinger operators with the Coulomb potential.
Taming of the wild group of magnetic translations
Authors: Varga Peter
Published: July 2002

We use a theorem of Auslander and Kostant on the representation theory of solvable Lie-groups for the study of some groups necessary for the description of certain quasi-periodic systems of solid-state physics. We show that the magnetic translation group is tame (Type I) if the magnetic field is not constant but fluctuating.
Geometric approach to inverse scattering for hydrogen-like systems in a homogeneous magnetic field
Authors: Arians Silke
Published: July 2002

We consider the Hamiltonian of one quantum particle in a homogeneous magnetic field and a scalar potential in three space dimensions. For a given magnetic field the high velocity limit of the scattering operator uniquely determines the scalar potential if it is of short range. If, in addition, long-range potentials are present, some knowledge of (the far out tail of) the long-range part is needed to define a modified Dollard wave operator and a scattering operator. Again its high velocity limit uniquely determines the total scalar potential for a given magnetic field. We generalize our results to a system of two interacting quantum particles with opposite electric charges.
Free boson representation of DYℏ(glN)k and DYℏ(slN)k
Authors: Ding X. M. , Hou B. Y. , Yuan Hou B. , Zhao L.
Published: July 2002

We construct a realization of the Yangian double DYℏ(glN)k and DYℏ(slN)k for an arbitrary level k in terms of free boson fields with a continuous parameter. In the ℏ→0 limit this realization becomes the Wakimoto realization of affine Lie algebras glN and slN, respectively. The vertex operators and the screening currents are also constructed with the same spirits; the screening currents commute with DYℏ(slN) modulo total difference.
Ordered products, W∞-algebra, and two-variable, definite-parity, orthogonal polynomials
Authors: Verçin A.
Published: July 2002

It has been shown that the Cartan subalgebra of W∞-algebra is the space of the two-variable, definite-parity polynomials. Explicit expressions of these polynomials, and their basic properties are presented. It also has been shown that they carry the infinite dimensional irreducible representation of the su(1,1) algebra having the spectrum bounded from below. A realization of this algebra in terms of difference operators is also obtained. For particular values of the ordering parameter s they are identified with the classical orthogonal polynomials of a discrete variable, such as the Meixner, Meixner–Pollaczek, and Askey–Wilson polynomials. With respect to variable s they satisfy a second order eigenvalue equation of hypergeometric type. Exact scattering states with zero energy for a family of potentials are expressed in terms of these polynomials. It has been put forward that it is the İnönü–Wigner contraction and its inverse that form a bridge between the difference and differential calculus.
On the second law of thermodynamics and contact geometry
Authors: Chen M. , Tseng H. C.
Published: July 2002

In this paper we consider the second law of thermodynamics for a dissipative system and its symmetry property in terms of contact geometry. We first show that the inaccessibility condition of Caratheodory and the assumption of semipositive definite property of the dissipative energy are equivalent to Clausius’ inequality. The inaccessibility condition then gives rise to a generalized Gibbs relation (GGR). By means of the GGR a 1-form ω can be defined such that the zero of ω reproduces the GGR. Such 1-form ω has the property ω∧(dω)n≠0 and ω∧(dω)n+1=0. The integral surface of the GGR is an n-dimensional 1-graph space G (Legendre submanifold) of a 1-jet space J1(En,R), where En is the base space of J1(En,R) with thermodynamic variables as its coordinates. The (2n+1)-dimensional J1(En,R) equipped with the 1-form ω is also called a contact bundle K, where the intensive thermodynamic variables are considered as the contact elements to K at every x. Next we construct an isovector field Xf such that the inaccessibility condition is invariant under the contact transformations generated by Xf. Finally, suppose under some specific assumptions the dynamical equations of the thermodynamic variables x can be approximated by the flow equations of a vector field XG on G. We can lift XG to Xf such that the 1-graph space G as well as the inaccessibility condition are preserved under the contact transformations generated by Xf.
Algebraic solutions for point groups: The tetrahedral group for the group chain T⊃C3
Authors: Chen Jin-Quan , Fan Peng-Dong
Published: July 2002

A new technique, the double-induced technique, is introduced for constructing irreducible symmetry operators (ISO’s) adapted to the group chain G⊃G(s). Simple algebraic expressions of irreducible matrices, the ISO’s and symmetry adapted functions (SAF’s) are derived for the group chain T⊃C3 for both single-valued and double-valued representations in a unified way. The simplicity of the results lies in the fact that the ISO’s and SAF’s are functions of only the quatum numbers of the group chain [the analogy of (j,m) for the group chain SO3⊃SO2], without involving any irreducible matrix elements. The symmetries of the SAF’s are disclosed for the first time.
Unified treatment of the Coulomb and harmonic oscillator potentials inDdimensions
Authors: Lévai G. , Kónya B. , Papp Z.
Published: July 2002

Quantum mechanical models and practical calculations often rely on some exactly solvable models like the Coulomb and the harmonic oscillator potentials. The D dimensional generalized Coulomb potential contains these potentials as limiting cases, thus it establishes a continuous link between the Coulomb and harmonic oscillator potentials in various dimensions. We present results which are necessary for the utilization of this potential as a model and practical reference problem for quantum mechanical calculations. We define a Hilbert space basis, the generalized Coulomb–Sturmian basis, and calculate the Green’s operator on this basis and also present an SU(1,1) algebra associated with it. We formulate the problem for the one-dimensional case, too, and point out that the complications arising due to the singularity of the one-dimensional Coulomb problem can be avoided with the use of the generalized Coulomb potential.
Weyl-type fields with geodesic lines of force
Authors: Guilfoyle Brendan S.
Published: July 2002

The static electrogravitational equations are studied and it is shown that an aligned type D metric that has a Weyl-type relationship between the gravitational and electric potential has shear-free geodesic lines of force. All such fields are then found and turn out to be the fields of a charged sphere, charged infinite rod and charged infinite plate. A further solution is also found with shearing geodesic lines of force. This new solution can have m>|e| or m<|e|, but cannot be in the Majumdar–Papapetrou class (in which m=|e|). It is algebraically general and has flat equipotential surfaces.
Alternative sets of hyperspherical harmonics: Satisfying cusp conditions through frame transformations
Authors: Heim Thomas A. , Green Dmitry
Published: July 2002

By extending the concept of Euler-angle rotations to more than three dimensions, we develop the systematics under rotations in higher-dimensional space for a novel set of hyperspherical harmonics. Applying this formalism, we determine all pairwise Coulomb interactions in a few-body system without recourse to multipole expansions. Our approach combines the advantages of relative coordinates with those of the hyperspherical description. In the present method, each Coulomb matrix element reduces to the “1/r” form familiar from the two-body problem. Consequently, our calculation accounts for all the cusps in the wave function whenever an interparticle separation vanishes. Unlike a truncated multipole expansion, the calculation presented here is exact. Following the systematic development of the procedure for an arbitrary number of particles, we demonstrate it explicitly with the simplest nontrivial example, the three-body system.
The generalized Moyal–Nahm and continuous Moyal–Toda equations
Authors: Castro Carlos , Plebański Jerzy
Published: July 2002

We present in detail a class of solutions to the 4D SU(∞) Moyal–anti-self-dual Yang–Mills (ASDYM) equations (an effective 6D theory) that are related to reductions of the generalized Moyal–Nahm equations using the Ivanova–Popov ansatz. The former yields solutions to the ASDYM/SDYM equations for arbitrary gauge groups in four dimensions. A further dimensional reduction of the above effective 6D equations yields solutions to the Moyal–anti-self-dual gravitational equations in four dimensions. The self-dual Yang–Mills/self-dual gravity case requires a separate study. The SU(2) Toda lattice and SU(∞) (continuous) Moyal–Toda lattice equations are derived from the Moyal–Nahm equations. An explicit map taking the Moyal heavenly form (after a rotational Killing symmetry reduction of the Moyal heavenly equations) into the SU(2) Toda lattice field is found. Finally, the generalized Moyal–Nahm equations are conjectured that contain the (continuous) SU(∞) Moyal–Toda lattice equations, after a suitable reduction process. Embeddings of the different types of Moyal–Toda lattice equations into the Moyal–Nahm equations are described.
Central charge and the Andrews–Bailey construction
Authors: Chim Leung
Published: July 2002

From the equivalence of the bosonic and fermionic representations of finitized characters in conformal field theory, one can extract mathematical objects known as Bailey pairs. Recently Berkovich, McCoy, and Schilling have constructed a “generalized” character formula depending on two parameters ρ1 and ρ2, using the Bailey pairs of the unitary model M(p−1,p). By taking appropriate limits of these parameters, they were able to obtain the characters of model M(p,p+1), N=1 model SM(p,p+2), and the unitary N=2 model with central charge c=3(1−2/p). In this letter we computed the effective central charge associated with this “generalized” character formula using a saddle point method. The result is a simple expression in dilogarithms which interpolates between the central charges of these unitary models.
Spin-mass content of the Bhabha particle and the group chain SU(4)⊃Sp(4)⊃SU(2)×U(1)
Authors: Smirnov Yu. F. , Sharma Anju
Published: July 2002

The relativistic particles described by the Bhabha equation (Bhabha particles) can possess several values of masses (Mτ=n/2τ) and spins s⩽n/2. In order to find the spin-mass content of such particles corresponding to the general irrep 〈n1n2〉 of the group Sp(4)∼O(5) which is the symmetry group of the Bhabha equation, the noncanonical chain of groups Sp(4)⊃SUs(2)×Uτ(1) is considered. In this paper, we construct the basis of the irrep 〈n1n2〉 in a boson realization form using the method of elementary permissible diagrams. This is achieved by the introduction of special “symplectic” bosons. The maximum and minimum values of spin s are established for each value of τ. The multiplicity of degenerate pairs (s,t) can be easily calculated with the help of the generating function obtained in this paper.
Dynamical symmetry approach to periodic Hamiltonians
Authors: Li Hui , Kusnezov Dimitri
Published: July 2002

We show that dynamical symmetry methods can be applied to Hamiltonians with periodic potentials. We construct dynamical symmetry Hamiltonians for the Scarf potential and its extensions using representations of su(1,1) and so(2,2). Energy bands and gaps are readily understood in terms of representation theory. We compute the transfer matrices and dispersion relations for these systems, and find that the complementary series plays a central role as well as nonunitary representations.
(Super)conformal many-body quantum mechanics with extended supersymmetry
Authors: Wyllard Niclas
Published: July 2002

We study N=4 supersymmetric quantum-mechanical many-body systems with M bosonic and 4M fermionic degrees of freedom. We also investigate the further restrictions of conformal and superconformal invariance. In particular, we construct conformal N=4 extensions of the AM−1 Calogero models, which for generic values of the coupling constant are not SU(1,1|2) superconformal. This class of models is also extended to arbitrary (even) N. We give both Hamiltonian and (classical) Lagrangian formulations. In the latter case, we use both component and N=4 superfield formulations.
Functional integration
Authors: Cartier Pierre , DeWitt-Morette Cécile
Published: July 2002

Three approaches to functional integration are compared: Feynman’s definition and the Feynman–Kac formula, Bryce DeWitt’s formalism, and the authors’ axiomatic scheme. They serve to highlight the evolution of functional integration in the second half of the twentieth century.
Factorization and small-energy asymptotics for the radial Schrödinger equation
Authors: Aktosun Tuncay
Published: July 2002

The radial Schrödinger equation is considered when the potential is real valued, is integrable, and has a finite first moment. The Jost function, the scattering matrix, the number of bound states for the potential are expressed in terms of the corresponding quantities associated with the fragments of the potential. An improved expansion on the small-energy asymptotics of the Jost solution is presented.
Asymptotic dynamics in quantum field theory
Authors: Horan Robin , Lavelle Martin , McMullan David
Published: July 2002

A crucial element of scattering theory and the LSZ reduction formula is the assumption that the coupling vanishes at large times. This is known not to hold for the theories of the Standard Model and in general such asymptotic dynamics is not well understood. We give a description of asymptotic dynamics in field theories which incorporates the important features of weak convergence and physical boundary conditions. Applications to theories with three and four point interactions are presented and the results are shown to be completely consistent with the results of perturbation theory.
Wave operators for the surface Maryland model
Authors: Jakšić Vojkan , Molchanov Stanislav
Published: July 2002

We study scattering properties of the discrete Laplacian H on the half-space Z+d+1=Zd×Z+ with the boundary condition ψ(n,−1)=λ tan(πα⋅n+θ)ψ(n,0), where α∈[0,1]d. We denote by H0 the Dirichlet Laplacian on Z+d+1. Khoruzenko and Pastur [Phys. Rep. 288, 109–126 (1997)] have shown that if α has typical Diophantine properties then the spectrum of H on R\σ(H0) is pure point and that corresponding eigenfunctions decay exponentially. We demonstrated in an earlier paper [Lett. Math. Phys. 45, 185 (1998)] that for every α independent over the rationals the spectrum of H on σ(H0) is purely absolutely continuous. In this paper, we continue the analysis of H on σ(H0) and prove that whenever α is independent over the rationals, the wave operators Ω±(H,H0) exist and are complete on σ(H0). Moreover, we show that under the same conditions H has no surface states on σ(H0).
Direct derivation of scaling relation of prepotential in N=2 supersymmetric G2 Yang–Mills theory
Authors: Ohta Yűji
Published: July 2002

In contrast to the classical gauge group cases, any method to exactly prove the scaling relation which relates moduli and prepotential is not known in the case of exceptional gauge groups. This paper provides a direct method to establish this relation by using Picard–Fuchs equations. In particular, it is shown that the scaling relation found by Ito in N=2 supersymmetric G2 Yang–Mills theory actually holds exactly.
Symmetries, exact solutions, and nonlinear superposition formulas for two integrable partial differential equations
Authors: Gordoa Pilar R.
Published: July 2002

We recently introduced two new sixth-order partial differential equations (PDEs) associated with third-order scattering problems. Here we extend our study of these PDEs by considering the construction of exact solutions both by using the method of symmetry reduction due to Lie, and by using their Darboux transformations (DTs). Amongst the ordinary differential equations (ODEs) obtained by symmetry reduction is an ODE due to Cosgrove that is believed to define a new Painlevé transcendent. This ODE provides soliton solutions for our integrable PDEs that include arbitrary functions of time. The DTs for our PDEs allow the recovery of these solutions and in addition provide other solutions which are not associated with Lie symmetries (either classical or nonclassical). We also consider the iteration of the corresponding Bäcklund transformations (BTs) for these PDEs. The theorem of permutability allows us to reduce this process of iterating the DT from one of solving a third-order linear equation (the spatial part of the Lax pair) to that of solving either a second-order linear equation (for one PDE), or quite remarkably to that of solving a first-order linear equation (for the other PDE). These linear differential equations have coefficients involving three previous solutions of the PDE, and are a natural extension of the linear algebraic equation found by applying the theorem of permutability to the Korteweg–de Vries equation.
A kinematic method to obtain conformal factors
Authors: Herrero Alicia , Morales Juan Antonio
Published: July 2002

Radial conformal motions are considered in conformally flat space–times and their properties are used to obtain conformal factors. The geodesic case leads directly to the conformal factor of Robertson–Walker universes. General cases admitting homogeneous expansion or orthogonal hypersurfaces of constant curvature are analyzed separately. When the two conditions above are considered together a subfamily of the Stephani perfect fluid solutions, with acceleration Fermi–Walker propagated along the flow of the fluid, follows. The corresponding conformal factors are calculated and contrasted with those associated with Robertson–Walker space–times.
Exact constructions of square-root Helmholtz operator symbols: The focusing quadratic profile
Authors: Fishman Louis , de Hoop Maarten V. , van Stralen Mattheus J. N.
Published: July 2002

Operator symbols play a pivotal role in both the exact, well-posed, one-way reformulation of solving the (elliptic) Helmholtz equation and the construction of the generalized Bremmer coupling series. The inverse square-root and square-root Helmholtz operator symbols are the initial quantities of interest in both formulations, in addition to providing the theoretical framework for the development and implementation of the “parabolic equation” (PE) method in wave propagation modeling. Exact, standard (left) and Weyl symbol constructions are presented for both the inverse square-root and square-root Helmholtz operators in the case of the focusing quadratic profile in one transverse spatial dimension, extending (and, ultimately, unifying) the previously published corresponding results for the defocusing quadratic case [J. Math. Phys. 33, 1887–1914 (1992)]. Both (i) spectral (modal) summation representations and (ii) contour-integral representations, exploiting the underlying periodicity of the associated, quantum mechanical, harmonic oscillator problem, are derived, and, ultimately, related through the propagating and nonpropagating contributions to the operator symbol. High- and low-frequency, asymptotic operator symbol expansions are given along with the exact symbol representations for the corresponding operator rational approximations which provide the basis for the practical computational realization of the PE method. Moreover, while the focusing quadratic profile is, in some respects, nonphysical, the corresponding Helmholtz operator symbols, nevertheless, establish canonical symbol features for more general profiles containing locally-quadratic wells.
Giant magnetoresistance of La0.5Pb0.2Ca0.2Y0.1MnO3−δ films obtained by magnetron sputtering
Authors: Khartsev S. I. , Krivoruchko V. N. , Pashchenko V. P.
Published: July 2002

Magnetoresistive properties of thin La0.5Pb0.2Ca0.2Y0.1MnO3−δ films obtained by magnetron sputtering technique are studied. A giant decrease in resistance (up to 98%) in magnetic fields H=10 T is observed at a temperature of 175 K. The physical factors responsible for the effect of composition and preparation technique on their magnetotransport properties are discussed. The mechanisms and empirical relations describing the temperature and field dependences of the resistive properties of films are also discussed.
Evolution and breaking of liquid film flowing on a vertical cylinder
Authors: Rosenau Philip , Oron Alexander
Published: July 2002

An amplitude equation is derived, which describes the evolution of a disturbed film interface H(τ,Z,Y) flowing down an infinite vertical cylindrical column. Using a new approach, which accounts for fast spatial changes, the nonlinear evolution of the interface is shown to be governed by Hτ+βHHZ+αHZZ +γ∇2{N[(1/ω2)H+∇2H]}=0, where ω is the normalized cylinder radius and α, β, and γ are constants, ∇≡(∂Z, ∂Y), and N=[1+ε4(∇H)2]−3/2. It is shown numerically that for some linearly unstable equilibria the evolving waves break in a finite time.
Evolution of coherent structures in a plane shear layer
Authors: Yang Zhongmin , Karlsson Sture K. F.
Published: July 2002

A two-dimensional plane shear layer perturbed by small-amplitude plane acoustic waves was studied experimentally. The perturbation consists of two different modes with equal amplitude, a fundamental mode and its first subharmonic. The evolution of the shear layer is influenced substantially by the phase difference between the two perturbation modes, resulting in two distinct vortex merging processes. For the pairing process, two neighboring vortices rotate around one another and gradually amalgamate. In a certain range of the phase difference, every other vortex weakens and vanishes within a few wavelengths while all the vortices remain aligned. In this tearing process of amalgamation, the subharmonic mode does not develop as large amplitude as during the pairing process. The energy distributions as well as the growth of the shear layer are different for these two kinds of vortex amalgamation.
Particle rotation in a Couette flow
Authors: Ye J. , Roco M. C.
Published: July 2002

The rotational velocity of neutrally buoyant particles was measured in a planar Couette flow. The flow cross section is rectangular with a 4-to-1 (200 mm/50 mm) aspect ratio. The mixtures consist of uniform polystyrene spheres and a glycerol–water solution of specific density 1.052. Four sphere sizes have been tested: 3, 4.76, 6.35, and 7.94 mm. Particle motion in turbulent flow was recorded with a high-speed SP-2000 motion analysis system. The characteristics of particle motion, including particle spin, were measured as a function of the distance from the wall, at three shear rates corresponding to Re=4.6, 6.8, and 9.2×104. It was found that the particle angular velocity normalized by shear rate is a function of the normalized distance to the moving and stationary walls. The flow conditions are defined with measurements on mean velocities, particle velocity fluctuations, kinetic energy, inertial stresses, and diffusion coefficients.
A numerical study of nonlinear waves in a transcritical flow of stratified fluid past an obstacle
Authors: Hanazaki Hideshi
Published: July 2002

A numerical study of the flow of stratified fluid past an obstacle in a horizontal channel is described. Upstream advancing of waves near criticality (resonance) appears in the case of ordinary two-layer flow, in which case the flow is described well by the solution of the forced extended Korteweg–de Vries (fEKdV) equation which has a cubic nonlinear term. It is shown theoretically that the upstream waves in the general two-layer flow cannot be well described by the forced KdV equation except when the wave amplitude is very small. The critical-level flow is also governed by the fEKdV equation. However, because of the smallness of the coefficient of the quadratic nonlinear term, the bore cannot propagate upstream at exact resonance. The results for the linearly stratified Boussinesq flow show good agreement with the solution of the Grimshaw and Yi [J. Fluid Mech. 229, 603 (1991)] equation at least for exact resonance. The cases of various strengths of forcing and the negative forcing are investigated to see the effect of the amplitude on the nonlinear-wave-propagation mechanism.
Sound speeds in suspensions in thermodynamic equilibrium
Authors: Temkin S.
Published: July 2002

This work considers sound propagation in suspensions of particles of constant mass in fluids, in both relaxed and frozen thermodynamic equilibrium. Treating suspensions as relaxing media, thermodynamic arguments are used to obtain their sound speeds in equilibrium conditions. The results for relaxed equilibrium, which is applicable in the limit of low frequencies, agree with existing theories for aerosols, but disagree with Wood’s equation. It is shown that the latter is thermodynamically correct only in the exceptional case when the specific heat ratios of the fluid and of the particles are equal to unity. In all other cases discrepancies occur. These may be significant when one of the two phases in the suspension is a gas, as is the case in aerosols and in bubbly liquids. The paper also includes a brief discussion of the sound speed in frozen equilibrium.
Finite amplitude steady waves in the Blasius boundary layer
Authors: Rotenberry James M.
Published: July 2002

The stability of the flow over a flat plate to finite amplitude disturbances is studied using a model by Milinazzo and Saffman [J. Fluid Mech. 160, 281 (1985)]. The traveling wave solutions which bifurcate from the Orr–Sommerfeld neutral stability curve of the Blasius profile are calculated numerically. This curve is the intersection of the zero energy plane with a neutral stability surface in energy, Reynolds number, and wave-number space. Although the bifurcation is supercritical at the ‘‘nose’’ of this curve, it is shown that it is subcritical elsewhere and that the minimum Reynolds number for the existence of traveling waves is less than the critical Reynolds number of the Orr–Sommerfeld neutral stability curve. This result suggests that finite amplitude disturbances can initiate transition.
Theory of first-order plasma heating by collisional magnetic pumping
Authors: Laroussi M. , Roth J. Reece
Published: July 2002

Plasma heating by collisional magnetic pumping is investigated theoretically. This treatment yields solutions to the energy transfer equations in the form of an energy increase rate, which gives quantitatively the amount of energy increase per rf driving cycle. The energy increase rates (or heating rates) proportional to the first and second powers of the field modulation factor δ (defined as the ratio of the change in the magnitude of the magnetic field to its background dc value) are derived for an arbitrary rf waveform of the pumping magnetic field. Special cases are examined, including the sinusoidal and sawtooth pumping waveforms. The energy increase rate in the case of a sawtooth waveform was found to be proportional to the first power of δ (first-order heating). This heating rate is many orders of magnitude larger than heating for the sinusoidal case: The latter is proportional to the square of δ and is strongly dependent on the collisionality of the plasma. The use of a sawtooth pumping waveform improves the efficiency of collisional magnetic pumping and heating rates comparable to those possible with ion or electron cyclotron resonance heating methods may be achieved.
Self-field-induced chaoticity in the electron orbits in a helical-wiggler free-electron laser with axial guide field
Authors: Chen Chiping , Davidson Ronald C.
Published: July 2002

The motion of a relativistic electron is analyzed in the field configuration consisting of a constant-amplitude helical wiggler magnetic field, a uniform axial magnetic field, and the equilibrium self-electric and self-magnetic fields produced by the non-neutral electron beam. By generating Poincaré surface-of-section maps, it is shown that the equilibrium self-fields destroy the integrability of the motion, and consequently part of phase space becomes chaotic. In particular, the Group I and Group II orbits can be fully chaotic if the self-fields are sufficiently strong. The threshold value of the self-field parameter ε=ω2pb/4Ω2c for the onset of beam chaoticity is determined numerically for parameter regimes corresponding to moderately high beam current (and density). It is found that the characteristic time scale for self-field-induced changes in the electron orbit is of the order of the time required for the beam to transit one wiggler period. An analysis of the first-order, self-field-induced resonances is carried out, and the resonance conditions and scaling relations for the resonance width are derived. The analytical estimates are in good qualitative agreement with the numerical simulations.
Bootstrap current and Ware pinch in drift-wave turbulent transport
Authors: Hegna C. C. , Bhattacharjee A. , Efthimion P. C.
Published: July 2002

Quasilinear theory is used to calculate contributions to the bootstrap current, Ware pinch, and parallel resistivity due to drift-wave fluctuations. It is shown that drift-wave oscillations can produce large anomalous cross-field fluxes, but have little effect on parallel transport. Specifically, the anomaly in the bootstrap current and Ware pinch is proportional to the spectral average of k⊥k∥, which vanishes because of the parity properties of the drift-wave eigenfunction. Implications for recent perturbative experiments on tokamak fusion test reactor (TFTR) [Phys. Rev. Lett. 66, 421 (1990)] are discussed.
The angular dependence of the absorption of 0.35 μm laser light by high-Z, laser-produced plasmas
Authors: Drake R. P. , Kauffman R. L. , Lasinski B. F. , Cable M. D. , Suter L. J. , Ze F.
Published: July 2002

Experiments to study the angular dependence of laser-light absorption in long-scale-length, planar plasmas are reported. Flat-topped, 1 nsec pulses of 0.35 μm laser light, with up to 2.5 kJ at average laser intensities of 3×1013 to 6×1015 W/cm2, were used to irradiate thick, gold targets at angles of incidence of 0° to >50°. The scattered light was measured using a number of diagnostics, and the absorption was inferred from these measurements. The absorption decreased somewhat with increasing laser intensity, typically remaining above 90% for laser intensities below 1015 W/cm2, and was very weakly dependent upon the angle of incidence. Modeling of the reflected light was used to constrain the properties of the plasma and of the reflecting mechanism. No simple model of a single mechanism is consistent with all aspects of the data.
dc space-charge-induced frequency up-shift in a quasioptical gyrotron
Authors: Alberti S. , Tran M. Q. , Tran T. M.
Published: July 2002

Recent experiments on a 100 GHz quasioptical gyrotron have shown that for a large resonator setup [Phys. Fluids B 2, 1654 (1990)] the observed frequency up-shift between the starting current and a current of 10 A corresponds to a shift of 4–5 longitudinal modes. In this Letter it is shown that the interpretation of this frequency up-shift should involve the current-dependent electron beam voltage depression in the beam tunnel and the interaction region for both the single-mode and multimode time evolution codes.
Observation of a steady-state field-reversed equilibrium
Authors: Zwi H. R. , Kuthi A. , Wong A. Y. , Wells B.
Published: July 2002

Steady-state quiescent field-reversed configurations are produced in the toroidal UCLA RACETRACK [Rev. Sci. Instrum. 57, 2720 (1986)] by rotating magnetic fields. Observed pressure and magnetic field profiles agree with high β, rigid electron rotor theory. Full penetration of the right-hand component of the rotating field and slight ion drag by the electrons were observed for the first time.
Stimulated Raman scattering from density cavities in laser-produced plasmas
Authors: Barr H. C. , Boyd T. J. M. , Mackwood A. P.
Published: July 2002

The occurrence of stimulated Raman scattering from within localized density cavities that may be present in many laser-produced plasmas is studied. Then scattering in both the backward and forward directions from a single cavity becomes absolutely unstable, with a common growth rate and zero inhomogeneous plasma thresholds whenever electron plasma waves are totally trapped within the cavity. Both back- and forward scattering mechanisms contribute to this common growth rate. A cavity therefore equalizes the growth of emission in backward and forward directions. Forward scattering in its own right gives rise to absolute growth. The threshold for absolute growth is then set by damping, and by Landau damping of the plasma wave in particular. Only very modest density depressions are needed to trap the long-wavelength weakly damped plasma waves. Absolutely unstable back- and forward scattering from within shallow cavities in the underdense coronal plasmas of laser fusion targets may prove to be commonplace rather than the exception, although growth rates are generally slow and sensitive to the cavity density and scale.
Time-dependent quasi-one-dimensional flow models for linear magnetohydrodynamic generator channels
Authors: Massarini A. , Borghi C. A.
Published: July 2002

A time-dependent quasi-one-dimensional approximation of a magnetohydrodynamic (MHD) compressible flow in a linear channel has been considered. For the numerical solution of the problem three different algorithms have been utilized (MacCormack’s [AIAA Hypervelocity Impact Conference (American Institute of Aeronautics and Astronautics, Washington, DC, 1969), AIAA Paper No. 69–354], Godunov’s [Numerical Methods in Fluid-Dynamics (Springer-Verlag, New York, 1977), pp. 28–38], and Casulli’s [Int. J. Numer. Methods Fluids 4, 1001 (1984)] algorithms). They are based on the finite-difference method. These models are utilized for the prediction of the behavior of electrical, thermal, and dynamic quantities during transients and during the occurrence of faults in MHD channels. A comparison of the methods when analyzing a load variation for a Faraday channel is considered.
New approach to the problem of the propagation of electrostatic perturbations in Vlasov plasmas
Authors: Colombo V. , Coppa G. G. M. , Ravetto P.
Published: July 2002

The present paper represents a revisitation of the classical problem of the propagation of longitudinal electrostatic waves in a plasma. Within the linearized Vlasov equation model, a new technique is proposed that does not utilize both Fourier and Laplace transformations as is customary, but rather leads to a time convolutive integral equation for the plasma density. This approach seems to present two main advantages: first, one can avoid some analytical difficulties found with the usual treatments; second, the integral equation obtained can be solved by means of direct numerical techniques that do not require the use of integral transformations. Some typical results obtained by means of the proposed method are presented and discussed. Finally, the possible use of the present methodology for the study of the spatial distribution induced in a plasma by an external harmonic electric field is shown and some of its interesting physical features are discussed.
Gyroaveraged equations for both the gyrokinetic and drift-kinetic regimes
Authors: Dimits A. M. , LoDestro L. L. , Dubin D. H. E.
Published: July 2002

The regime of validity of nonlinear gyrokinetic equations is extended to cover uniformly both the usual drift-kinetic and gyrokinetic regimes through the use of an expansion in the parameter ε∼(ρ/λ⊥)e(φ−v∥ Az/c)/T. Here, ρ is the gyroradius, λ⊥ is the scale length of the electrostatic and parallel magnetic potentials φ and Az, c is the speed of light, and T is the temperature. This is made possible by a preparatory split of the potentials into gyrophase-dependent and independent parts. For nonlinear fluctuations saturated at mixing-length levels (e.g., with eφ/T∼λ⊥ /L, where L is the equilibrium scale length), ε is of order ρ/L for all scales λ⊥ ranging from ρ to L, and is therefore small in plasmas of fusion interest.
On the nonlinear theory of the long-wavelength radiative condensation instability
Authors: Meerson B. , Steele C. D. C. , Milne A. M. , Priest E. R.
Published: July 2002

Nonlinear evolution of the radiative condensation instability (RCI) of an optically thin plasma is investigated in the framework of a one-dimensional model. The model is applicable for motions either along a sufficiently strong magnetic field, when the transverse heat conduction is suppressed, or perpendicular to a straight, shear-free magnetic field. The long-wavelength limit of the RCI is considered when the characteristic radiative cooling time is much shorter than the acoustic (or magnetoacoustic) time. The case when the isochoric thermal mode is damped, while one of the two ‘‘acoustic’’ (or ‘‘magnetoacoustic’’) modes is unstable, is studied. Two different problems of the instability are considered. In the first, the heat conduction is negligible and the instability is described by a reduced set of equations, which formally coincide with those of a gas whose effective compressibility as a function of the density is of alternating sign. The study starts with small perturbations and follows them numerically into the nonlinear regime. It is shown that, during the first stage of the instability, cool plasma condensations develop, these being surrounded by rarefied and hot plasma regions. Subsequently the condensations expand unless mass inflow into the system is disallowed. The condensation boundaries represent a new type of shock wave which develops in such a ‘‘normal-anomalous’’ gas dynamics. These shock waves have a monotonic density profile, but a nonmonotonic pressure profile. Properties of the shock waves are investigated analytically and numerically. If the mass inflow is disallowed, stable equilibrium condensations develop, the boundaries of which represent contact discontinuities. In the second problem, the heat conduction is relatively large, so that direct crossover between the long-wavelength limit and the heat conduction-dominated short-wavelength limit occurs. In this case also either static or expanding plasma condensations are shown to develop, depending on the boundary conditions. An analytical description of the static equilibria is presented.
Homogeneous dynamos: Theory and practice*
Authors: Roberts P. H. , Jensen T. H.
Published: July 2002

The magnetism of many naturally occurring bodies is attributed to the motion of conducting fluids in their interiors. Although the physical principles underlying such self-excited dynamos are identical to those governing an electric generator in a power station, they (unlike the commercial machine) operate in a simple homogeneous body of conductor, and are therefore less easily excited. The theory of such ‘‘homogeneous dynamos’’ is adumbrated here, and past attempts to construct working laboratory models are reviewed. Consideration is given to the possibility of conducting a turbulent homogeneous dynamo experiment in liquid sodium. The proposed configuration is a crude representation of the simplest of all theoretical dynamo models, that of Ponomarenko [J. Appl. Mech. Tech. Phys. 14, 755 (1972)]. In addition to demonstrating for the first time a homogeneous magnetohydrodynamic (MHD) dynamo in the laboratory, the experiment should enhance understanding of MHD turbulence, and provide insight into how the field generation process saturates.
Behavior of a continuous uranium plasma stream expanding across a weak magnetic field
Authors: Nishio Ryoji , Suzuki Kazumichi
Published: July 2002

When an electron beam generates a uranium vapor in the electron beam evaporator, a uranium plasma is formed on the evaporating surface and expands. It was confirmed experimentally that this plasma could expand with increasing its drift velocity and that the plasma possessed a Boltzmann electron distribution along the streamline, even when it propagated across a magnetic field of 40–50 G. This behavior can be understood by the cross-field plasma expansion theory at 1/ε→0 limit, where ε is the dielectric constant of plasma [Phys. Fluids 25, 730(1982)]. The ion drift energy calculated from the measured polarization electric field is in good agreement with that estimated from the potential distribution and vapor drift energy, which confirms the ion acceleration along the plasma stream.
Large amplitude ℓ=1 coherent structures in non-neutral plasmas confined in a cylindrical trap
Authors: Spencer Ross L. , Mason Grant W.
Published: July 2002

The computation of ℓ = 1 coherent structures in non-neutral plasmas with arbitrary density profiles and for large displacements of the plasma from the symmetry axis of a confining cylindrical trap is described. As the structures are displaced from the axis, they revolve about the symmetry axis with a frequency that typically increases with displacement. The plasma also is distorted into an approximately elliptical shape. The frequency shifts and the eccentricities as a function of displacement, plasma size, and the shape of the density profile are both computed numerically and calculated analytically. The results are shown to be consistent with data of Fine, Driscoll, and Malmberg [Phys. Rev. Lett. 63, 2232 (1989)] which are measured for relatively large, constant-density (waterbag) plasmas (R/a = 0.38–0.71) and modest off-axis displacements (D/a<0.3). Here R is the radius of the plasma at half of peak density when centered, D is the off-axis displacement, and a is the radius of the cylinder.
Self-generation of magnetic fields by sheared flows in weakly ionized plasmas
Authors: Huba J. D. , Fedder J. A.
Published: July 2002

A sheared, relative ion–neutral flow can generate a magnetic field in an unmagnetized, weakly ionized plasma. The field generation term is ∂B/∂t=(mec/e)∇×νen(Vi−Vn) where νen is the electron–neutral collision frequency, Vi is the ion fluid velocity, and Vn is the neutral fluid velocity. The time period over which the field grows is limited by diffusion, convection, or collisional relaxation of the relative drift. Since the field generation term scales as νen/Ωe relative to the other terms in the field induction equation, the maximum field generated is found from Ωe≂few νen so that Bmax≂few (mec/e)νen. Both analytical and numerical results are presented. The computational results are based upon a two-dimensional (2-D) magnetohydrodynamic (MHD) code which includes the following terms: ion–neutral drag, gravity, resistivity, recombination, the Hall term, and the shear-driven source term. The theory is applied to the generation of magnetic fields in an unmagnetized planetary ionosphere, such as Venus, and to cometary plasmas.
Axisymmetric parallel velocity shear instability in the tokamak edge
Authors: McCarthy D. R. , Drake J. F. , Guzdar P. N.
Published: July 2002

The parallel velocity shear instability in an axisymmetric toroidal edge plasma is studied numerically. In the presence of a large asymmetric particle transport and a limiter, sonic parallel flows develop that are peaked at the last closed flux surface. For α=ρsqR/aLv≳1, these flows are unstable to axisymmetric modes. The associated turbulence gives order unity fluctuation levels. It is located inside the last closed flux surface (LCFS) and on the inner half of the torus. There is an up–down asymmetry of the turbulence which is due to the diamagnetic drift and poloidal rotation. These results are compared to the experimental results from the Continuous Current Tokamak (CCT) (G. R. Tynan, Ph.D. thesis, 1991).
Parametric scaling of the stability of relativistic laminar flow magnetic insulation
Authors: Antonsen T. M. , Ott Edward , Chang C. L. , Drobot A. T.
Published: July 2002

The short wavelength limit of the magnetron instability of a relativistic sharp boundary electron sheath is examined. For short wavelengths the mode is localized to the sheath edge. This localization leads to a simple relationship (essentially a Lorentz transformation) between the relativistic and nonrelativistic growth rates. This relationship involves only equilibrium quantities evaluated at the sheath edge and explains previously noted trends that have been observed numerically.
Control of ion-velocity distributions in laser–target interaction experiments
Authors: Grun J. , Stellingwerf R. , Ripin B. H.
Published: July 2002

The width of ion-velocity distributions from laser-produced plasmas can be controlled experimentally by varying the size of the laser spot. This ion-velocity width is determined primarily by whether the ions are mostly in the rarefaction or steady-state regime. It is not dominated by the thermal distribution of the ions, as is sometimes assumed. A simple analytic theory shows that the distribution width is governed by the scaling parameter rs/cτ, where rs is the focal spot radius, c is the sound speed, and τ is the laser pulse length.