bluuebunny/crossref_metadata_2025 huggingface dataset:
Algebraic treatment of the Kaluza–Klein monopole system
Authors: Chetouani L. , Guechi L. , Hammann T. F. , Lecheheb A.
Published: July 2002

In analogy to the Kepler problem, the Green’s function for a particle in the background of the Kaluza–Klein monopole is constructed through the algebraic approach, with the help of the Kustaanheimo–Stiefel variables and the generators of the SO(2,1) group in the exponential representation of Schwinger. The bound and continuum states are also obtained.
Tests of integrability of the supersymmetric nonlinear Schrödinger equation
Authors: Brunelli J. C. , Das Ashok
Published: July 2002

In this paper various conventional tests of integrability are applied to the supersymmetric nonlinear Schrödinger equation. It is found that a matrix Lax pair exists and that the system has the Painlevé property only for a particular choice of the free parameters of the theory. It is also shown that the second Hamiltonian structure generalizes to superspace only for these values of the parameters. It has not been possible to construct a zero curvature formulation of the equations based on OSp(2‖1). However, this attempt yields a nonsupersymmetric fermionic generalization of the nonlinear Schrödinger equation which appears to possess the Painlevé property.
Cosmological models expressible as gradient vector fields
Authors: Rebouças M. J. , Skea J. E. F. , Tavakol R. K.
Published: July 2002

Classes of cosmological models, for which Einstein’s equations reduce to two-dimensional dynamical systems, are studied in the presence of stochastic perturbations using the steady state of the associated Fokker–Planck equations and Zeeman’s notion of ε-stability. In all cases, a set of variables is found for which the dynamical systems are expressible as gradient vector flows, showing that the associated cosmologies are stochastically stable. Such models are also important in connection with application of catastrophy theory to cosmology.
Variational formulation of a moment problem quantization method
Authors: Handy Carlos R. , Maweu John , Atterberry Leticia Soto
Published: July 2002

The eigenvalue moment method (EMM) has proven to be an effective technique for generating converging lower and upper bounds to the bosonic ground state energy of singular, strongly coupled, quantum systems. Application of EMM theory requires an appropriate linearization of the highly nonlinear Hankel–Hadamard (HH) moment determinant constraints for the (n+1)×(n+1) Hankel matrices ℳn[u]≡M̂n0+∑i=1msM̂niu i), dependent on the missing moment variables {u(i)}≡u. We propose an alternate variational formulation utilizing the functions Det(ℳn+1[u])/Det(ℳn[u]), which we prove to be locally convex over the missing moment subset satisfying the HH positivity conditions Det(ℳν[u])≳0, for ν≤n. Additional features of this variational formulation facilitate its application to important problems such as the octic, sextic, and quartic anharmonic oscillators.
Geometrical interpretation of BRST symmetry in topological Yang–Mills–Higgs theory
Authors: Lee Chang-Yeong
Published: July 2002

We study the topological Yang–Mills–Higgs theories in two and three dimensions and the topological Yang–Mills theory in four dimensions in a unified framework of superconnections. In this framework, we first show that a classical action of topological Yang–Mills type can provide all three classical actions of these theories via appropriate projections. Then we obtain the Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST transformation rules encompassing these three topological theories from an extended definition of curvature and a geometrical requirement of the Bianchi identity. This is an extension of Perry and Teo’s work in the topological Yang–Mills case. Finally, comparing this result with our previous treatment in which we used the ‘‘modified horizontality condition,’’ we provide a meaning of the Bianchi identity from the BRST symmetry viewpoint and thus interpret the BRST symmetry in a geometrical setting.
Euler and Navier–Stokes limits of the Uehling–Uhlenbeck quantum kinetic equations
Authors: Arlotti Luisa , Lachowicz Miroslaw
Published: July 2002

The Uehling–Uhlenbeck evolution equations for gases of identical quantum particles either fermions or bosons, in the case in which the collision kernel does not depend on the distribution function, are considered. The existence of solutions and their asymptotic relations with solutions of the hydrodynamic equations both at the level of the Euler system and at the level of the Navier–Stokes system are proved.
Non-Abelian topological mass generation in four dimensions
Authors: Hwang Dae Sung , Lee Chang-Yeong
Published: July 2002

We study the topological mass generation in the 4 dimensional non-Abelian gauge theory, which is the extension of Allen et al.’s work in the Abelian theory. It is crucial to introduce a one form auxiliary field in constructing the gauge invariant non-Abelian action which contains both the one form vector gauge field A and the two form antisymmetric tensor field B. As in the Abelian case, the topological coupling mB∧F, where F is the field strength of A, makes the transmutation among A and B possible, and consequently we see that the gauge field becomes massive. We find the BRST/anti-BRST transformation rule using the horizontality condition, and construct a BRST/anti-BRST invariant quantum action.
The Dirac–Maxwell equations with cylindrical symmetry
Authors: Booth H. S. , Radford C. J.
Published: July 2002

A reduction of the Dirac–Maxwell equations in the case of static cylindrical symmetry is performed. The behavior of the resulting system of o.d.e.s. is examined analytically and numerical solutions presented. There are two classes of solutions. The first type of solution is a Dirac field surrounding a charged “wire.’’ The Dirac field is highly localized, being concentrated in cylindrical shells about the wire. A comparison with the usual linearized theory demonstrates that this localization is entirely due to the nonlinearities in the equations which result from the inclusion of the “self-field.’’ The second class of solutions have the electrostatic potential finite along the axis of symmetry but unbounded at large distances from the axis.
Higher-dimensional dromion structures: Jimbo–Miwa–Kadomtsev–Petviashvili system
Authors: Ruan Hang-yu , Lou Sen-yue
Published: July 2002

Starting from an n “plane” soliton solution of a conditionally integrable (n+1)-dimensional system, one can find a dromion solution which is localized in all directions for a suitable potential. The dromion structures for a (3+1)-dimensional conditionally integrable system, Jimbo–Miwa–Kadomtsev–Petviashvili (JMKP) equation system, are studied in detail. Though a special type of multi-dromion solution is allowed for the JMKP system, all the dromions can only be located on a moving line. The interactions among dromions are not elastic. In addition to a phase shift, the “shape” of two dromions may also be changed after interaction.
Nonlinear operators. II
Authors: Schwartz Charles
Published: July 2002

This work extends the previous development of new mathematical machinery for nonlinear operators acting on a vector space. Starting from the usual concept of inner product, we find that Hermitian, anti-Hermitian, and unitary nonlinear operators can be defined without bringing in the ideas of a dual vector space or adjoint operators. After looking briefly at how these general ideas might be used in classical mechanics and to extend the linear Schrödinger equation of quantum theory, the topic of Lie groups and Lie algebras is studied. Many, but not all, of the familiar features of that topic are extended to nonlinear operators. New representations are found for a few simple cases of interest to physics, and some provocative implications for elementary particle theory are discussed.
Algebraic approach to scattering theory of the Fokker–Planck equation
Authors: Miyazawa Toru
Published: July 2002

The one-variable Fokker–Planck equation is studied in a scattering formalism. Scattering processes are represented by paths in one-dimensional space, and the paths are treated as algebraic objects that constitute infinite-dimensional representations of SL(2, C). Various expressions for the scattering coefficients are derived in a systematic way by means of algebraic methods with considerations on symmetries.
Some new results on the Blaszak–Marciniak lattice: Bäcklund transformation and nonlinear superposition formula
Authors: Hu Xing-Biao , Zhu Zuo-Nong
Published: July 2002

The so-called Blaszak–Marciniak lattice is considered. By the dependent variable transformation, the Blaszak–Marciniak lattice is transformed into a quart-linear form. By introducing an auxiliary variable, we further transform it into the bilinear form. A corresponding Bäcklund transformation is obtained. Furthermore, a nonlinear superposition formula is proved rigorously. As an application of the obtained results, soliton solutions are derived.
Relativistic eccentric anomalies
Authors: Teleman Kostake
Published: July 2002

We use Kepler’s eccentric anomaly in order to get explicit equations for the planetary orbits in a solar system. By successively modifying the corresponding Lagrangian, we build a Lagrangian for a relativistic two-body problem, the trajectories of which are conics in Minkowski space. The equations of these trajectories, projected on a three-space, exhibit new anomalies.
Conserved operators of the generalized elliptic Ruijsenaars models
Authors: Komori Yasushi , Hikami Kazuhiro
Published: July 2002

We construct the integrable families of the generalized elliptic Ruijsenaars models by use of the Yang–Baxter equation and the reflection equation. The higher order conserved operators of these models are explicitly presented.
New direct linearizations for KdV and solutions of the other Cauchy problem
Authors: Sabatier Pierre C.
Published: July 2002

The author showed previously that there are several equations that “directly linearize” the Korteweg de Vries equation. They may give different classes of solutions and they correspond either to generalized Gelfand Levitan or generalized Marchenko inversion equations. The idea is developed here with a precise goal: solving by linear methods the “other Cauchy problem” for KdV, i.e., the boundary value problem where the solution is known at fixed x, together with its two first derivatives. After several new direct linearization equations are given and analyzed, the one that solves the problem is eventually obtained. It also corresponds to a new inverse spectral problem, whose scalar equations are fourth order, and that is first studied in the Gelfand Levitan form, and then studied and completely solved in the Marchenko form. The methods given here can be extended probably to most nonlinear integrable equations, and suggest several new problems.
Construction of relativistic quantum fields in the framework of white noise analysis
Authors: Grothaus Martin , Streit Ludwig
Published: July 2002

We construct a class of Euclidean invariant distributions ΦH indexed by a function H holomorphic at zero. These generalized functions can be considered as generalized densities w.r.t. the white noise measure, and their moments fulfill all Osterwalder–Schrader axioms, except for reflection positivity. The case where F(s)=−(H(is)+12s2), s∈R, is a Lévy characteristic is considered in Rev. Math. Phys. 8, 763 (1996). Under this assumption the moments of the Euclidean invariant distributions ΦH can be represented as moments of a generalized white noise measure PH. Here we enlarge this class by convolution with kernels G coming from Euclidean invariant operators 𝒢. The moments of the resulting Euclidean invariant distributions ΦHG also fulfill all Osterwalder–Schrader axioms except for reflection positivity. For no nontrivial case we succeeded in proving reflection positivity. Nevertheless, an analytic extension to Wightman functions can be performed. These functions fulfill all Wightman axioms except for the positivity condition. Moreover, we can show that they fulfill the Hilbert space structure condition and therefore the modified Wightman axioms of indefinite metric quantum field theory [Dynamics of Complex and Irregular Systems (World Scientific, Singapore, 1993)].
Adiabatic evolution for systems with infinitely many eigenvalue crossings
Authors: Joye A. , Monti F. , Guérin S. , Jauslin H. R.
Published: July 2002

We formulate an adiabatic theorem adapted to models that present an instantaneous eigenvalue experiencing an infinite number of crossings with the rest of the spectrum. We give an upper bound on the leading correction terms with respect to the adiabatic limit. The result requires only differentiability of the considered projector, and some geometric hypothesis on the local behavior of the eigenvalues at the crossings.
Random Schrödinger operators arising from lattice gauge fields. I. Existence and examples
Authors: Knill Oliver
Published: July 2002

We consider new models of ergodic Schrödinger operators whose existence relies on a cohomological theorem of Feldman and Moore in ergodic theory. These operators generalize the Harper operator which describes the case of a constant magnetic field. An example is the case when the magnetic field is given by independent random variables attached to the lattice plaquettes. A generalization of the Feldman–Moore theorem by Lind to non-Abelian groups also allows us to consider Schrödinger operators obtained from non-Abelian lattice gauge fields. The existence result extends to more general graphs like to operators on tilings and to higher dimensions. We compute some moment expansions for the density of states. For example, for independent, identically and uniformly distributed magnetic fields, a model which has been studied at least since 1970, and whose existence can also be seen without involving the above-mentioned existence theorem, we show that the nth moment is the number of closed paths in the two-dimensional lattice starting at the origin for which the winding number vanishes at each plaquette point. This goes beyond the Brinkman–Rice self-retracing path approximation. Other examples are a higher dimensional example, a one-dimensional Anderson model which can be treated in this framework, as well as the Hofstadter model with constant magnetic field, where one averages over all possible magnetic fields. We also reprove a result of Jitomirskaya–Mandelshtam stating that the deterministic Aharonov–Bohm model is a compact perturbation of the free Laplacian.
Nonstandard Feynman path integral for the harmonic oscillator
Authors: Loo Ken
Published: July 2002

Using Nonstandard Analysis, we will provide a rigorous computation for the harmonic oscillator Feynman path integral. The computation will be done without having prior knowledge of the classical path. We will see that properties of classical physics falls out naturally from a purely quantum mechanical point of view. We will assume that the reader is familiar with Nonstandard Analysis.
World-line Green functions with momentum and source conservations
Authors: Sato Haru-Tada
Published: July 2002

Based on the generating functional method with an external source function, a useful constraint on the source function is proposed for analyzing the one- and two-loop world-line Green functions. The constraint plays the same role as the momentum conservation law of a certain nontrivial form, and transforms ambiguous Green functions into the uniquely defined Green functions. We also argue reparametrizations of the Green functions defined on differently parameterized world-line diagrams.
K slicing the Schwarzschild and the Reissner–Nordstrom spacetimes
Authors: Qadir Asghar , Siddiqui Azad A.
Published: July 2002

A K slicing of the Reissner–Nordstrom (RN) spacetime is shown to provide a complete foliation of the region up to the inner horizon, and the horizon to correspond to the limit as K→±∞. The implications of this foliation in the context of York time are discussed.
Exact solutions in Einstein–Yang–Mills–Dirac systems
Authors: Rudolph Gerd , Tok Torsten , Volobuev Igor
Published: July 2002

For the first time, exact solutions for the full self-consistent Einstein–Yang–Mills–Dirac systems with gauge groups SU(2) and SU(4) in Robertson–Walker space–time R×S3 are presented, which are symmetric under the action of the group SO(4) of spatial rotations. The approach is based on the dimensional reduction method for gauge, spinor, and gravitational fields and relates symmetric solutions in EYMD theory to certain solutions of an effective dynamic system. The solutions are interpreted as solutions of the cosmological type with an oscillating Yang–Mills field, which exchanges energy with a spinor field. The explicit form of the solution for the spinor field shows that its energy changes the sign in the process of the evolution of the Yang–Mills field from one vacuum to another.
Bäcklund transformation and its superposition principle of a Blaszak–Marciniak four-field lattice
Authors: Ma Wen-Xiu , Hu Xing-Biao , Zhu Si-Ming , Wu Yong-Tang
Published: July 2002

A four-field lattice furnished by Blaszak and Marciniak is transformed into bilinear form upon introducing two auxiliary independent variables. A Bäcklund transformation in bilinear form is found for the lattice and the corresponding nonlinear superposition formula is rigorously established. As a consequence, soliton solutions to the lattice are derived.
Symplecton for Uh(sl(2)) and representations of SLh(2)
Authors: Aizawa N.
Published: July 2002

Polynomials of boson creation and annihilation operators which form irreducible tensor operators for Jordanian quantum algebra Uh(sl(2)), called h-symplecton, are introduced and their properties are investigated. It is shown that many properties of symplecton for Lie algebra sl(2) are extended to h-symplecton. The h-symplecton is also a basis of irreducible representation of SLh(2) dual to Uh(sl(2)). As an application of the procedure used to construct h-symplecton, we construct the representation bases of SLh(2) on the quantum h-plane.
The intermittency factor of scalars in turbulence
Authors: Chatwin P. C. , Sullivan Paul J.
Published: July 2002

The shortcomings of the standard definition of the intermittency factor of a dispersing scalar in turbulence are summarized. In particular, this definition is not suitable for use in theoretical work. A new definition of the intermittency factor in terms of the mean concentration is given, and this is practically convenient and has a clear physical interpretation. Furthermore, the proposed new intermittency factor has an illuminating role in the structure of the probability density function of the scalar.
Equilibrium shapes and stability of charged and conducting drops
Authors: Pelekasis N. A. , Tsamopoulos J. A. , Manolis G. D.
Published: July 2002

It was shown by Rayleigh [Philos. Mag. 14, 184 (1882)] that a conducting spherical drop becomes unstable when the net dimensionless charge on its surface, Qc, exceeds the value of 4(π)1/2 . More recently, Tsamopoulos et al. [Proc. R. Soc. London Ser. A 401, 67 (1985)] have shown, both analytically and numerically, that at this point a transcritical bifurcation occurs. The finite element methodology that they employed is limited to cases where the drop shapes are not very deformed because of truncation problems with mesh representing the infinitely extending surrounding medium. This situation has now been rectified by employing the integral form of Laplace’s equation, which only requires discretization and solution on the surface of the drop. Thus a hybrid method results with the integral equations solved via boundary element techniques, while finite elements are still used for the remaining governing equations. Using this hybrid method, previous results have been reproduced much more accurately and efficiently. In addition, new solution families have been discovered. In particular, several shape families that are not symmetric about the equatorial plane were found to bifurcate from the families of two- and four-lobed shapes. A disjoint family with saddle point shapes was found to extend to small values of charge. It corresponds to the Frankel–Metropolis family that is well known in nuclear physics (Cohen et al. [Ann. Phys. 82, 557 (1974)]). All newly discovered solution families are linearly unstable.
Analysis of vibrational-translational energy transfer using the direct simulation Monte Carlo method
Authors: Boyd Iain D.
Published: July 2002

A new model is proposed for energy transfer between the vibrational and translational modes for use in the direct simulation Monte Carlo method (DSMC). The model modifies the Landau–Teller theory for a harmonic oscillator and the rate of transition is related to an experimental correlation for the vibrational relaxation time. Assessment of the model is made with respect to three different computations: relaxation in a heat bath, a one-dimensional shock wave, and hypersonic flow over a two-dimensional wedge. These studies verify that the model achieves detailed balance, and excellent agreement with experimental data is obtained in the shock wave calculation. The wedge flow computation reveals that the usual phenomenological method for simulating vibrational nonequilibrium in the DSMC technique predicts much higher vibrational temperatures in the wake region. Additionally, the numerical performance of the new model is equal to that of the phenomenological scheme.
Random sweeping effect in isotropic numerical turbulence
Authors: Sanada T. , Shanmugasundaram V.
Published: July 2002

Results from full numerical simulations of the Navier–Stokes equations for three-dimensional, stationary, and isotropic turbulence are used (1) to study the scaling properties of two-time modal velocity correlations and (2) to determine the dominant process in the decorrelation of the small-scale velocities. The main results obtained are (1) that the convective sweeping of the small scales by the energy-containing large scales determines the scaling property of the inertial- and near-dissipation ranges and (2) that the sweeping effect is dominant in the decorrelation of the small scales. Reynolds-number dependence of the decorrelation is also considered.
Binary and trinary scalar mixing by Fickian diffusion—Some mapping closure results
Authors: Jiang Tai-Lun , Givi Peyman , Gao Feng
Published: July 2002

The amplitude mapping closure of Kraichnan [Bull. Am. Phys. Soc. 34, 2298 (1989); Phys. Rev. Lett. 63, 2657 (1989)] is used for statistical description of the mixing process by Fickian diffusion of a stochastically distributed scalar variable. This closure is invoked in the context of an evolution equation for the single-point probability density function (pdf) of the scalar from initially symmetric binary and trinary states. In the binary case, a simple recipe is provided for the time scaling relation which is very useful in model implementation. In the trinary case, it is shown that after a fixed elapsed time, the pdf relaxes to a distribution similar to that of the binary mixing. The magnitude of this time is independent of the initial extent of departure from a binary state; however, the rate of evolution toward an asymptotic Gaussian state depends on the level of the departure. In both cases, the closure predictions for the scalar flatness factor and the correlation of the mean square scalar–scalar gradients agree well with those obtained by direct numerical simulations (DNS). However, some features of the results are different from those of earlier DNS of mixing in stationary turbulence. These differences are likely attributed to inadequacy of the amplitude mapping closure at the single-point level in accounting for the effects of turbulence stretching.
Variable soft sphere molecular model for air species
Authors: Koura Katsuhisa , Matsumoto Hiroaki
Published: July 2002

A reliable set of cross-section parameters of the variable soft sphere (VSS) molecular model is determined for the Monte Carlo simulation of air species from the transport collision integrals or potential parameters provided by Cubley and Mason [Phys. Fluids 18, 1109 (1975)] over the high-temperature range 300–15 000 K. The VSS cross-section parameters for the inverse-power-law potential are also determined from the viscosity coefficients recommended by Maitland and Smith [J. Chem. Eng. Data 17, 150 (1972)] for common species in the low (20–300 K) and high (300–2000 K) temperature ranges.
Enhancement of spanwise coherence in laminar vortex streets
Authors: Lefrançois Marcel , Ahlborn Boye
Published: July 2002

Flow visualization experiments with stripped dye markings show that the vortices in the wake of an impulsively started circular cylinder initially form with random phase along the span. In successive vortex generations, small perturbations disappear within a few cycles, and the eddies align parallel to the cylinder. The spanwise coherence is enhanced if vortex shedding is initiated by trigger plates.
A hydrodynamic model of the oscillating screen viscometer
Authors: Davis A. M. J.
Published: July 2002

The viscometer consists of an oscillating screen immersed in a fluid and free to rotate about an axis in its plane. The viscosity can be determined from the measured ratio of the periodic driving force to the screen motion when an adequate hydrodynamical model of the immersed oscillator is available. The screen is formed by a square mesh of thin wire whose dimensions invite comparison with asymptotic results for narrow hollow bodies translating in Stokes flow. These indicate that the closed hole structure of the grid plays an important role in determining its motion. It is shown that this role diminishes as the frequency increases. The computed results, obtained from a system of linear equations, are consistent with experimental values over the appropriate range of frequency.
Linear eddy simulations of mixing in a homogeneous turbulent flow
Authors: McMurtry Patrick A. , Gansauge Todd C. , Kerstein Alan R. , Krueger Steven K.
Published: July 2002

The linear eddy mixing model is used to predict the evolution of a decaying scalar field in statistically steady homogeneous turbulent flow over a wide range of Reynolds and Schmidt numbers. Model results at low Reynolds number and order unity Schmidt number are shown to be in good overall agreement with direct numerical simulations. Results at higher Schmidt and Reynolds numbers reproduce conventional scaling properties of the scalar statistics. Predictions of Schmidt number and Reynolds number sensitivity of the evolution of the scalar concentration probability density function are presented and interpreted.
Phase-inflection parametric instability behavior near threshold with application to laser–plasma stimulated Raman scattering (SRS) instabilities in exploding foils
Authors: Williams E. A. , Johnston T. W.
Published: July 2002

Previous absolute instability results for significant growth from a parametric instability involving oppositely directed modes coupled by a uniform pump with phase inflection coupling (Δk=k″x2/2) are extended to higher modes and to thresholds. The results are applied to stimulated Raman scattering experiments done with exploding foils.
Sawtooth oscillations about helical current channels
Authors: Theobald M. L. , Montgomery David , Doolen G. D. , Dahlburg J. P.
Published: July 2002

An existing pseudospectral code for solving the three-dimensional equations of ‘‘reduced’’ magnetohydrodynamics is extended by adding a temperature equation. Resistivities and thermal conductivities are given their (isotropic) Braginskii temperature dependences, and are advanced self-consistently. Realistic-looking sawtooth oscillations are observed at modest Lundquist and Reynolds numbers. However, the oscillations are excited upon, and relax back to, a helical (rather than an axisymmetric) current channel.
Comments on ‘‘Plasma current drive by injection of photons with helicity’’ [Comm. Plasma Phys. Controlled Fusion 1
2, 165 (1989)]
Authors: Schalit M. A. , Bellan P. M.
Published: July 2002

Ohkawa has proposed a tokamak current-drive scheme [Comm. Plasma Phys. Controlled Fusion 12, 165 (1989)], which relies on the injection of circularly polarized magnetohydrodynamic waves. It is shown here that the favorable current-drive efficiency predicted by Ohkawa is not attained because excessive power is dissipated by the fluctuating fields. The ratio of power absorbed by the plasma to the dc Ohmic power required to drive the same current is Pabsorbed/POhmic≊4(Ba/b)2, where Ba is the static toroidal field strength and b is the strength of the fluctuating field.
Two-dimensional Vlasov treatment of free-electron laser sidebands
Authors: Sharp W. M. , Yu S. S.
Published: July 2002

The Kroll–Morton–Rosenbluth equations [IEEE J. Quantum Electron. QE-17, 1436 (1981)] for a helical-wiggler free-electron laser are generalized to treat an electron beam with a prescribed radial density profile and an equilibrium distribution function that is an arbitrary function of the longitudinal action J. The principal approximation is the assumption that betatron frequencies of beam particles are low compared with typical synchrotron frequencies. Vlasov equilibria for finite-amplitude primary waves with time-varying phase are calculated for several distribution functions. Using these equilibria, radial eigenvalue equations for the frequency and growth rate of small-amplitude sidebands are derived and solved numerically. The radial mode structure is found to have no appreciable effect on sideband growth when the beam radius is large compared with [2ks  min(Ω0, dφ0/dz)]−1/2, where ks and φ0 are the wavenumber and phase of the primary wave and Ω0 is the maximum synchrotron ‘‘frequency’’ in z of trapped electrons. In these effectively one-dimensional cases, the dispersion relation depends only on the distribution function and on a dimensionless density parameter η̄=kwa2wω2b/(c2γ3rΩ30i), where kw is the wiggler wavenumber, aw=eAw/(mc2) is the dimensionless wiggler vector potential, ωb is the maximum plasma frequency of the beam, and γr is the Lorentz factor for resonant particles. Both the upper and lower sidebands for a deeply trapped distribution (J≊0) have a maximum growth rate of (31/2/2)(η̄2/2)1/3 for η̄≪1 and (31/2/2)(η̄/2)1/3 for η̄≫1, and distributions with a spread in J invariably show slower sideband growth. For beams with a smaller radius, the radial density variation causes a further reduction in the peak sideband growth rate and narrows the spectrum of unstable modes.
Nonlinear hydromagnetic waves in a cylindrical current-carrying plasma. II. Exact helically symmetric solutions
Authors: Hamabata Hiromitsu
Published: July 2002

Exact wave solutions of the nonlinear magnetohydrodynamic equations for a highly conducting incompressible fluid within an axisymmetric container are obtained for the case when the physical quantities are helically symmetric in cylindrical coordinates. The solutions represent the waves propagating helically on the cylindrical surfaces, under the influence of helical magnetic and velocity fields whose strength varies with radius. The solutions are applicable to astrophysical and laboratory plasmas as well as the Earth’s core.
Experimental studies of linear high-beta heliac plasma configurations
Authors: Greenfield C. M. , Koepke M. E. , Ribe F. L.
Published: July 2002

The formation and quasi-equilibrium of a high-beta heliac plasma are investigated in the High-Beta Q Machine [Phys. Fluids 30, 2885 (1987)], a linear high-beta l=1 stellarator with an internal current carrying conductor (hardcore). The hardcore current rise time is varied from 9 μsec to smaller values comparable with that of the main compression field (450 nsec). Flux contours and plasma pressure calculated from internal magnetic-probe measurements are used to distinguish between nearly axisymmetric plasma confined near the hardcore and the heliac plasma confined near the magnetic axis. For the shorter hardcore rise times, the axisymmetric plasma pressure becomes small compared to that of the heliac. Further analysis of the data allows calculation of the currents flowing in the plasma, the rotational transform, and the magnetic well depth. Appreciable axial current is observed, consistent with induction by the changing magnetic fields during the heliac formation. The observed relationship between the axial current and rotational transform is confirmed by computer modeling using the hase magnetohydrodynamic equilibrium code [Nucl. Fusion 23, 1061 (1983)].
Renormalization group analysis of reduced magnetohydrodynamics with application to subgrid modeling
Authors: Longcope D. W. , Sudan R. N.
Published: July 2002

The technique for obtaining a subgrid model for Navier–Stokes turbulence introduced by Yakhot and Orszag [J. Sci. Comput. 1, 3 (1986); Phys. Rev. Lett. 57, 1772 (1986)], based on renormalization group analysis (RNG), is extended to the reduced magnetohydrodynamic (RMHD) equations. A RNG treatment of the Alfvén turbulence (perpendicular scale k−1⊥≪k−1∥ parallel scale) supported by the RMHD equations leads to effective values of the viscosity and resistivity at large scales, k→0, dependent on the amplitude of turbulence. When the RNG analysis is augmented by the Kolmogorov argument for energy cascade the effective viscosity and resistivity become independent of the molecular quantities. This leads to a ‘‘universal’’ subgrid model, which all models approach at the largest scales. A self-contained system of equations is derived for the range of scales, 0<k<K, where K=π/Δ, is the maximum wave number for a grid size Δ. In this system the resistive and viscous dissipation is represented by differential operators, whose coefficients depend upon the amplitudes of the large-scale quantities being computed.
Variational form for a viscous plasma
Authors: Ishida A. , Steinhauer L. C. , Berk H. L.
Published: July 2002

The variational formulation for a fluid plasma including the parallel and gyroviscosities is developed using the basic approach of Berk et al. [Phys. Fluids 24, 2245 (1981)]. The equivalence of the variational problem to the original viscous fluid equations of motion is shown. The theory is developed for an axisymmetric plasma with no magnetic field in the azimuthal direction and therefore applies to field-reversed configurations and axisymmetric mirrors. This theory offers the advantage of describing both parallel and transverse ion kinetic effects within the simplicity afforded by a variational fluid model.
Turbulent transport processes in a tokamak’s high-mode confinement
Authors: Yoshizawa Akira
Published: July 2002

Turbulent transport processes in a tokamak’s high (H-)mode confinement are investigated using the concept of a turbulent magnetohydrodynamic (MHD) dynamo. Under this concept, the effect of the poloidal rotation is linked with the turbulent cross helicity to reduce the level of MHD fluctuations. The poloidal rotation is also shown to be sustained under the combined effects of the shear of a toroidal plasma current and the turbulent cross helicity.
Plasma heating and current drive by an obliquely propagating upper-hybrid cyclotron beat wave
Authors: Amin M. R. , Cairns R. A.
Published: July 2002

Excitation of an obliquely propagating upper-hybrid cyclotron beat wave is considered for plasma heating and current drive in tokamaks. The beat wave is excited by the interaction of two intense free-electron laser (FEL) pulses at their difference frequency. The three-wave nonlinear interaction equations in a magnetized plasma are solved numerically in a steady-state two-dimensional (2-D) geometry for this purpose. The 2-D toroidal inhomogeneity effect and the effect of finite spatial width of the pump microwave pulses are taken into account for the beat wave excitation. To illustrate the principle, the microwave tokamak experiment (MTX) [Plasma Phys. Controlled Fusion 30, 57 (1988)] is considered. It has been found that the fraction of total input power of the pump microwaves deposited in the cyclotron beat wave is lower than the case of a Langmuir type beat wave considered by Amin and Cairns [Nucl. Fusion 30, 327 (1990)]. However, increasing the input powers of the pump microwaves, a substantial amount of input power can be deposited in the excited beat wave. The beat wave eventually transfers this power to the electrons by cyclotron damping. It has also been found that for the same input parameters, right-hand polarized pumps are more efficient than left-hand polarized pump microwaves for beat wave excitation.
The stochastic nature of ion-cyclotron-resonance wave–particle interaction in tokamaks
Authors: Helander P. , Lisak M.
Published: July 2002

The threshold in wave amplitude for the onset of stochastic motion of ion-cyclotron-resonance-heated minority ions in tokamaks is calculated. As a separate result, the solutions to the guiding center equations of motion are presented. Full account is taken to the effects of the finite orbit width of high-energy particles and the ellipticity of the flux surfaces. The orbits of trapped particles are shown to become stochastic more easily than those of circulating particles, and near the trapped/passing boundary an arbitrarily weak wave field is needed for stochastization. Finite orbit width effects have significant impact on the results, decreasing the stochastization amplitude for highly energetic particles considerably, as compared with earlier theories. Nevertheless, for realistic JET parameters [Plasma Phys. Controlled Fusion 30, 1467 (1988)], only a small fraction of the minority ions move stochastically in a monochromatic ion-cyclotron range of frequencies (ICRF) wave field.
Kinetic treatment of nonlinear magnetized plasma motions: General geometry and parallel waves
Authors: Khabibrakhmanov I. Kh. , Galinsky V. L. , Verheest F.
Published: July 2002

The expansion of kinetic equations in the limit of a strong magnetic field is presented. This gives a natural description of the motions of magnetized plasmas, which are slow compared to the particle gyroperiods and gyroradii. Although the approach is three dimensional, this very general result is used in a present paper only to focus on the parallel propagation of nonlinear Alfvén waves. The derivative nonlinear Schrödinger-like equation is obtained. Two new terms occur compared to earlier treatments, a nonlinear term proportional to the heat flux along the magnetic field line and a higher-order dispersive term. It is shown that kinetic description avoids the singularities occurring in magnetohydrodynamic or multifluid approaches, which correspond to the degenerate case of sound speeds equal to the Alfvén speed, and shows that one cannot neglect parallel heat fluxes then, not even in the case of low parallel plasma beta. Finally, a truly stationary soliton solution is derived.
Magnetospheric substorms
Authors: Lui A. T. Y.
Published: July 2002

Magnetospheric substorms encompass a myriad of dynamical phenomena resulting from the coupling of the solar wind with the Earth’s magnetic field and the ionosphere. Although external solar wind conditions conducive to substorm development are generally regarded as identified, the precise cause for substorm onset remains an outstanding unresolved problem. The contending theories include externally driven magnetic reconnection, magnetosphere–ionosphere coupling, thermal catastrophe, macro- and microinstabilities (such as interchange/ballooning, Kelvin–Helmholtz, tearing, lower-hybrid drift, modified two-stream, and ion-Weibel instabilities). The conventional approach to substorm modeling is to describe the entire substorm episode on the basis of a single mechanism. After a brief review and critique of existing substorm models, a new paradigm is introduced in which compatible features among different models are synthesized into a single one which is superior to any individual model in consistency with observations. This new paradigm advocates that substorms may be triggered by more than one mechanism and also that the full set of substorm phenomena may only be accounted for by more than one physical process. Some unresolved substorm problems amenable to immediate future investigation are also identified.
Completely bootstrapped tokamak
Authors: Weening R. H. , Boozer A. H.
Published: July 2002

Numerical simulations of the evolution of large-scale magnetic fields have been developed using a mean-field Ohm’s law. The Ohm’s law is coupled to a Δ′ stabilty analysis and a magnetic island growth equation in order to simulate the behavior of tokamak plasmas that are subject to tearing modes. In one set of calculations, the magnetohydrodynamic (MHD)-stable regime of the tokamak is examined via the construction of an li -qa diagram. The results confirm previous calculations that show that tearing modes introduce a stability boundary into the li -qa space. In another series of simulations, the interaction between tearing modes and the bootstrap current is investigated. The results indicate that a completely bootstrapped tokamak may be possible, even in the absence of any externally applied loop voltage or current drive.
Ion-temperature-gradient instability driven transport and its parametric scaling
Authors: Song B. , Sen A. K. , Tham P.
Published: July 2002

Experiments are reported on the ion thermal transport due to the ion-temperature- gradient-driven instability (ITG mode) and its transport scaling properties with respect to instability parameters like fluctuation level ñ/ni and linear growth rate as well as the drive parameter ηi(=∂ ln[Ti]/∂ ln[ni]) in the Columbia Linear Machine [Phys. Fluids 26, 1044 (1983)]. The measured local ion thermal conductivity χ⊥(r) is highly anomalous and strongly correlated with the radial profile of the ITG mode. The linear scaling of the averaged thermal conductivity 〈χ⊥(r)〉 with the averaged mode fluctuation level 〈ñ/ni〉 and linear growth rate indicates strong turbulence-type scaling. The scaling of χ⊥ with the drive parameter ηi is offset linear.
Computer studies on the fast reconnection mechanism in a sheared field geometry
Authors: Ugai M.
Published: July 2002

The development of the fast reconnection mechanism is systematically studied in a sheared (skewed) field geometry with no magnetic neutral (null) point. Initially, there are antiparallel fields (of component Bx0) with a current sheet in the middle, as well as a uniform sheared field component (Bz0). On the basis of the spontaneous fast reconnection model, a number of computations demonstrate that, initiated by a small disturbance, the fast reconnection mechanism can be fully established by releasing the energy associated with the antiparallel fields. Once the quasisteady fast reconnection mechanism is set up, the magnetic flux is drastically transferred, leading to an effective topological change of the skewed field configuration. The thin (shock) transition layer standing in the quasisteady fast reconnection region is divided into the intermediate wave region and the slow shock region. In the intermediate wave region, the magnetic field simply rotates without changing plasma quantities, whereas in the slow shock region a slow shock is combined with an intermediate wave. For the larger Bz0, the finite-amplitude intermediate wave becomes dominant so that the slow shock characteristics become obscure in the transition layer. The reconnection (flux transfer) rate is estimated to scale as E0/[1+tan2(Ω/2)], where Ω=2 tan−1(Bz0/Bx0), and E0 is the reconnection rate for the coplanar case (Bz0=0) and tends to decrease as the plasma beta becomes larger.
The Naval Research Laboratory Modified Betatron Accelerator and assessment of its results*
Authors: Kapetanakos C. A. , Len L. K. , Smith T. , Marsh S. J. , Loschialpo P. , Dialetis D. , Mathew J.
Published: July 2002

In this paper the experimental results of the Naval Research Laboratory (NRL) Modified Betatron Accelerator (MBA) [Phys. Rev. Lett. 64, 2374 (1990)] are briefly summarized and assessed. These results show that the addition of the strong focusing (SF) field made a substantial improvement in the confining properties of the device, at least in the intermediate time scale, and that the SF field together with the finite resistivity of the vacuum chamber wall is responsible for the trapping of the beam. There is extensive experimental evidence, suggesting that the slow beam loss during acceleration is caused by the cyclotron resonances. Reduction of several field errors together with operation at higher toroidal and SF field led to beam energies in excess of 20 MeV, while the trapped current was above 1 kA. Preliminary beam extraction experiments with 12 resonant coils have shown that a ∼80 G field disturbance is required to extract the beam from the MBA.
New fluid model for the turbulent transport due to the ion temperature gradient
Authors: Kim Chang-Bae , Horton Wendell , Hamaguchi Satoshi
Published: July 2002

A new set of equations appropriate for the study of the turbulence, due to the ion temperature gradient in the slab in the fluid description, is proposed. This model is similar to many existing models including the one used in the work of Hamaguchi and Horton (HH) [S. Hamaguchi and W. Horton, Phys. Fluids B 2, 1834 (1990)]. The main difference is that in this model the ion diamagnetic drift contributes to the kinetic energy in the energy balance relation. It is achieved through more complete analysis for the polarization drift due to the finite-Larmor-radius effects. The linear growth rate in the model is found to be smaller and the numerical results show that the heat transport is smaller by an order of magnitude when compared to HH.
Ion energy measurements on a reversed-field pinch experiment using Doppler broadening
Authors: Howell Robert B. , Nagayama Yoshio
Published: July 2002

Ion energies have been measured on the ZT-40M reversed-field pinch experiment using Doppler broadening of various impurity lines in the vacuum UV and ultraviolet range. The impurity ion temperatures are expected to relax quickly to the deuteron temperature according to the classical relaxation times. These ion temperatures as measured using O+6 (1623 Å) exceed the electron temperatures for plasma currents greater than 300 kA and fill pressures ≤2.0 mTorr. These investigations were carried out over a wide range of peak plasma currents 120 ≤Iφ<450 kA, with central electron densities 0.4≤ne≤1.2×1014 cm−3 yielding ion temperatures up to ∼500 eV. A zero-dimensional model using an approximation for the ion heating rate by the current driven electrostatic ion-cyclotron instability has been used to make comparison with the measured ion temperatures. This mechanism appears plausible but other mechanisms may be equally likely.
Low Reynolds number circular Couette flow past a wavy wall
Authors: Munson B. R. , Rangwalla A. A. , Mann J. A.
Published: July 2002

Theoretical and experimental results show that it is possible to obtain flow separation or reverse flow for low Reynolds number shear flow past a wavy wall. The region of reverse flow depends on the amplitude of the wall waves as well as the gap width. A comparison between the fourth-order perturbation results and experiment is given.
Computational study on excitation, propagation, and two-species-ion-plasma heating due to the ion-Bernstein wave
Authors: Okada H. , Abe H. , Itatani R. , Ono M.
Published: July 2002

External excitation, propagation, and ion heating for the ion-Bernstein wave (IBW) are studied for the single-ion and two-ion species plasmas, using particle simulation. It is found that the value of ω/Ωi near the antenna position influences the excitation characteristics of the IBW. The wavelength and group velocity of the propagating IBW agree well with those calculated from the linear dispersion relation. Corresponding to the experiment done with the JIPP T-II-U device [Phys. Rev. Lett. 54, 2339, (1985)], the 3ΩD heating process in the plasma composed of deuterium-like and hydrogen-like ions is investigated. The wave energy is deposited into the bulk and tail of the deuterium-like ions because of third harmonic cyclotron resonance and the bulk of the hydrogen-like ions because of 3/2 ΩH cyclotron subharmonic resonance.The possibility is also discussed that the heating efficiency may not depend on the concentration of the deuterium-like ion in the 3ΩD heating in the actual tokamak experiment.