bluuebunny/crossref_metadata_2025 huggingface dataset:
Painlevé property, auto-Bäcklund transformation, Lax pairs, and reduction to the standard form for the Korteweg–De Vries equation with nonuniformities
Authors: Brugarino T.
Published: July 2002

It is demonstrated that the KdV equation with nonuniformities, ut+a(t)u+(b(x,t)u)x +c(t)uux+d(t)uxxx +e(x,t)=0, has the Painlevé property if the compatibility condition among the coefficients of it holds: bt+(a−Lc)b+bbx +dbxxx =2ah+hL(d/c2)+(dh/dt)+ce +x[2a2+aL(d3/c4)+(da/dt) +L(d/c)L(d/c2)+(d/dt)L(d/c)], where L=(d/dt)lg and h(t) is an arbitrary function of t. The auto-Bäcklund transformation and Lax pairs for this equation are obtained by truncating the Laurent expansion. Furthermore, assuming the compatibility condition, then the KdV equation with nonuniformities is transformable, via suitable variable transformations, to the standard KdV.
Quantum equations for simple interacting strings: Their exact solutions and physical implications
Authors: Hsu J. P.
Published: July 2002

A string can have a simple potential interaction only when it has a constant radius. The Hamiltonian for such a string is characterized by a cyclic radial momentum pr. Physical properties of this interacting string (or ‘‘ring’’) are illustrated by exact solutions of quantum ring equations (with a ‘‘flavor potential’’) in the four-dimensional space-time and in a particular reference frame. The energy eigenstates of the ring are ultrastable because flavor transitions between different states are forbidden. Furthermore, the ring can be permanently confined by a potential ∝r−1 ln(λr), and the size of the ring can be detected by scattering processes. In the absence of the electroweak interaction, a simple composite quark model based on a particle–ring interaction is discussed. It is found that the relation ms/mc≊mb/mt≊mb′/mb′ holds independently of the parameters in the potential. Differences and similarities between quantum rings and Nambu strings are discussed.
WKB theory of wave tunneling for Hermitian and nearly Hermitian vector systems of integral equations
Authors: Kull H. J. , Kashuba R. J. , Berk H. L.
Published: July 2002

A general theory of wave tunneling in one dimension for Hermitian and nearly Hermitian vector systems of integral equations is presented. It describes mode conversion in terms of the general dielectric tensor of the medium and properly accounts for the forward and backward nature of the waves without regard to specific models. Energy conservation in the WKB approximation can be obtained for general Hermitian systems by the use of modified Furry rules that are similar to those used by Heading for second-order differential equations. Wave energy absorption can then be calculated perturbatively using the conservation properties of the dominant Hermitian operator. Operational graphical rules are developed to construct global wave solutions and to determine the direction of energy flow for spatially disconnected roots. In principle, these rules could be applied to systems with arbitrary mode complexity. Coupling coefficients for wave tunneling problems with up to four interacting modes are calculated explicitly.
Approximation of Schrödinger eigenvalues and eigenfunctions by canonical perturbation theory: The periodically driven quantum rotator
Authors: Nardini Franco
Published: July 2002

A first-order approximate formula for eigenvalues and eigenfunctions of the Schrödinger operator of the periodically driven quantum rotator is given by means of the classical perturbation theory and an estimate for the remainder is provided; in the nonresonant case the remainder is of order 2 while in the resonant case the remainder turns out to be of order 3/2. In the first case, to what extent the procedure can be interated to higher orders is also discussed.
Treatment of higher-order Lagrangians via the construction of dynamically equivalent first-order Lagrangians
Authors: Hebda Piotr W.
Published: July 2002

For a given, in general, singular Lagrangian containing higher-order time derivatives, a dynamically equivalent Lagrangian with only first-order time derivatives is constructed. A Hamiltonian structure for this first-order Lagrangian is then found with the use of the Dirac theory of constraints. It is shown that in the case of a nonsingular higher-order Lagrangian, the Ostrogradsky dynamics is derived in this way. Further, it is shown that ambiguities characteristic of higher-order Lagrangian systems do not appear when using this construction. In particular, it is shown that the addition of a total time derivative term to the higher-order Lagrangian can only induce a time-independent canonical transformation, even in the case of a singular Lagrangian.
Phase-spaces and dynamical descriptions of infinite mean-field quantum systems
Authors: Unnerstall T.
Published: July 2002

Following the work of P. Bona [J. Math. Phys. 29, 2223 (1988)], a class of infinite mean-field quantum lattice systems is considered within the framework of algebraic quantum mechanics, and the following question is discussed: Which are the possible dynamical descriptions of the system, i.e., in which representations π of the system’s quasilocal C*-algebra 𝒜 do the local time evolutions converge in the thermodynamic limit to an automorphism group of a certain enlarged C*-algebra 𝒞π containing π(𝒜) and (some of) the classical observables of the system in π. To this end we associate a ‘‘classical state space’’ Eπ to any representation π (which is a subset of the phase-space E⊇RL defined by Bona for the largest possible representation), and show how it is characterized by the π-normal states, thereby obtaining a way to determine Eπ explicitly in many cases. The answer to the question posed then reads: The limiting (Heisenberg) dynamics exists in π on 𝒞π if and only if the set Eπ is invariant under the flow φQt on E which describes the time evolution of classical observables. Conversely, to any invariant, closed subset B of E, there exists a dynamical description of the quantum system with classical state space B.
An asymptotic analysis of quantum evolution with electromagnetic fields
Authors: Saksena A. , Osborn T. A. , Molzahn F. H.
Published: July 2002

A singular perturbation expansion of solutions to the Schrödinger initial value problem is constructed using an approximate propagator. For a nonrelativistic quantum system interacting with time-dependent external electromagnetic fields, this approximate propagator defines a gauge invariant semiclassical expansion that is realized by large mass scaling. The asymptotic nature of this approximation is established by constructing error estimates that bound the Hilbert space norm difference between the exact and approximate evolved states. The maximum order of the approximation is determined explicitly as a function of the number of derivatives supported by the scalar and vector potentials. The asymptotic expansion is obtained when the configuration space Ω=Rd, and also for problems where Ω is a proper subset of Rd and the self-adjoint Hamiltonian is defined using a supplementary boundary condition—typically Dirichlet or periodic.
Deformations of Lie group and Lie algebra representations
Authors: Lesimple Marc , Pinczon Georges
Published: July 2002

A complete study of deformations of Lie group and Lie algebra representations, including differentiability and integrability results, is given. Adapted results are given in the semisimple case. A notion of induced deformations is introduced. Various examples are given, including deformations of indecomposable representations.
A perturbative approach to the Thomas–Fermi equation in terms of the density
Authors: Cedillo Andrés
Published: July 2002

A fast and absolute converging sequence, for the Thomas–Fermi (TF) initial slope, was obtained by applying a perturbative approach [C. M. Bender et al., J. Math. Phys. 30, 1447 (1989)] to the TF equation written in terms of the electronic density. By this procedure the truncated series does not alternate, in contrast to a previous work [B. J. Laurenzi, J. Math Phys. 31, 2535 (1990)] based in the traditional TF equation.
Quantum mechanics inversion for symmetry scattering
Authors: Wehrhahn R. F. , Melnikov Yu. B.
Published: July 2002

Symmetry scattering is related to the scattering by an effective local potential in the Schrödinger frame using the quantum mechanics inversion techniques of Marchenko, Gel’fand, and Levitan. Exact solutions or exponentially convergent approximations are found.
On the Kadomtsev–Petviashvili hierarchy, Ŵ∞ algebra, and conformal SL(2,R)/U(1) model. II. The quantum case
Authors: Yu Feng , Wu Yong-Shi
Published: July 2002

This article is devoted to constructing a quantum version of the famous Kadomtsev–Petviashvili (KP) hierarchy by deforming its second Hamiltonian structure, namely, the nonlinear Ŵ∞ algebra. This is achieved by quantizing the conformal noncompact SL(2,R)k/U(1) coset model, in which Ŵ∞ appears as a hidden current algebra. For the quantum Ŵ∞ algebra at level k=1, an infinite set of commuting quantum charges in explicit and closed form was successfully constructed. Using them, a completely integrable quantum KP hierarchy is constructed in the Hamiltonian form. A two-boson realization of the quantum Ŵ∞ currents has played a crucial role in this exploration.
Applications of singularity theory to gravitational lensing. I. Multiple lens planes
Authors: Levine H. I. , Petters A. O. , Wambsganss J.
Published: July 2002

The basic local and global features of stable multiple plane gravitational lens systems are investigated using tools from singularity theory. All stable multiple plane time-delay and lensing maps are classified, and the following global facts are proven under the weaker assumption of local stability. First, every locally stable multiple plane lensing map has an even number of cusps whether the associated deflector is singular or not. Second, for nonsingular deflectors the sum of the projectivized rotation numbers of its caustics is zero, while for singular ones it is negative and even. Third, if the deflector has g point masses on a single plane, then g is given by the formula g=−1/2∑c r(c), where r(c) is the projectivized rotation number of the critical curve c and the sum runs through all critical curves. Fourth, explicit counting formulas and bounds are found for the number of cusps for certain caustic networks. Finally, the latter yields that two point masses on a single lens plane will generate at least six cusps. However, if the masses are put generically on separate lens planes, then there are at least eight cusps.
Algebraic solution for the Natanzon hypergeometric potentials
Authors: Cordero Patricio , Salamó Sebastián
Published: July 2002

An algebraic method—based on a strategy that makes use of a realization of the algebra SO(2,1)—in terms of differential operators is used to solve the bound state problem for the most general Natanzon potentials for which the Schrödinger equation can be reduced to hypergeometric form (hence, hypergeometric potentials).
Distributed Gaussian polynomials and associated Gaussian quadratures
Authors: Karabulut Hasan , Sibert Edwin L.
Published: July 2002

An orthogonal function set called distributed Gaussian orthogonal polynomials is constructed from equally spaced Gaussians and the corresponding quadrature is studied. The infinite chain limit of both polynomials and the quadrature is studied and analytical expressions are found for polynomials, quadrature points, weights, and Lagrange functions. The connections to Wannier functions are explored, and a way of constructing Wannier functions from Gaussians is proposed.
The Dirac operator and gamma matrices for quantum Minkowski spaces
Authors: Podleś P.
Published: July 2002

Gamma matrices for quantum Minkowski spaces are found. The invariance of the corresponding Dirac operator is proven. We introduce momenta for spin 1/2 particles and get (in certain cases) formal solutions of the Dirac equation.
The one-particle energy spectrum of weakly coupled quantum rotators
Authors: Angelescu Nicolae , Minlos Robert A. , Zagrebnov Valentin A.
Published: July 2002

The ground state of a lattice model of weakly interacting quantum rigid rotators is analyzed by the cluster expansion method applied to its Feynman–Kac representation. The Hamiltonian of the infinite crystal in the ground state is shown to have a branch of absolutely continuous spectrum separated by gaps from the rest of the spectrum, describing the one-particle excitations.
Prandtl number dependence of turbulent temperature structure function: A unified theory
Authors: Effinger Hans , Grossmann Siegfried
Published: July 2002

The structure function Dθ(r) of a passive scalar, e.g., the temperature, in fully developed turbulence is calculated directly from the Navier–Stokes and diffusion equations. A variable range decomposition of the turbulent flow field is used to derive a parameter-free equation for Dθ(r), valid for all values of r and all (molecular) Prandtl numbers Pr, thus representing a unified description of passive scalar diffusion. Here Dθ(r) shows three distinct ranges of r behavior; we give the Pr dependence of the borders between them. In the inertial range the turbulent Prandtl number is Prturb =0.40.
Convective stability in the Rayleigh–Bénard and directional solidification problems: High-frequency gravity modulation
Authors: Wheeler A. A. , McFadden G. B. , Murray B. T. , Coriell S. R.
Published: July 2002

The effect of vertical, sinusoidal, time-dependent gravitational acceleration on the onset of solutal convection during directional solidification is analyzed in the limit of large modulation frequency Ω. When the unmodulated state is unstable, the modulation amplitude required to stabilize the system is determined by the method of averaging, and is 𝒪(Ω). Comparison of the results from the averaged equations with numerical solutions of the full linear stability equations (based on Floquet theory) show that the difference is 𝒪(Ω1/2). When the unmodulated state is stable, resonant modes of instability occur at large modulation amplitude. These are analyzed using matched asymptotic expansions to elucidate the boundary-layer structure for both the Rayleigh–Bénard and directional solidification configurations. The leading-order term for the modulation amplitude is of 𝒪(Ω2); the first-order correction of 𝒪(Ω3/2) is calculated, and the results are compared with numerical solutions of the full linear stability equations. Based on these analyses, a thorough examination of the dependence of the stability criteria on the unmodulated Rayleigh number, Schmidt number, and distribution coefficient, is carried out.
The equations of nearly incompressible fluids. I. Hydrodynamics, turbulence, and waves
Authors: Zank G. P. , Matthaeus W. H.
Published: July 2002

A unified analysis delineating the conditions under which the equations of classical incompressible and compressible hydrodynamics are related in the absence of large-scale thermal, gravitational, and field gradients is presented. By means of singular expansion techniques, a method is developed to derive modified systems of fluid equations in which the effects of compressibility are admitted only weakly in terms of the incompressible hydrodynamic solutions (hence ‘‘nearly incompressible hydrodynamics’’). Besides including molecular viscosity self-consistently, the role of thermal conduction in an ideal fluid is also considered. With the inclusion of heat conduction, it is found that two distinct routes to incompressibility are possible, distinguished according to the relative magnitudes of the temperature, density, and pressure fluctuations. This leads to two distinct models for thermally conducting, nearly incompressible hydrodynamics—heat-fluctuation-dominated hydrodynamics (HFDH’s) and heat-fluctuation-modified hydrodynamics (HFMD’s). For the HFD case, the well-known classical passive scalar equation for temperature is derived as one of the nearly incompressible fluid equations and temperature and density fluctuations are predicted to be anticorrelated. For HFM fluids, a new thermal transport equation, in which compressible acoustic effects are present, is obtained together with a more-complicated ‘‘correlation’’ between temperature, density, and pressure fluctuations. Although the equations of nearly incompressible hydrodynamics are envisaged principally as being applicable to homogeneous turbulence and wave propagation in low Mach number flow, it is anticipated that their applicability is likely to be far greater.
Liquid-metal flows in sliding electrical contacts with arbitrary magnetic-field orientations
Authors: Talmage G. , Walker J. S. , Brown S. H. , Sondergaard N. A. , Branover H. , Sukoriansky S.
Published: July 2002

In certain situations, liquid-metal sliding electrical contacts for high-current and low-voltage electrical machines may prove a viable alternative to solid metal brushes. Before it can be ascertained whether such an option is feasible, the problems inherent in a liquid-metal flow through a narrow gap between a fixed and a moving surface with free surfaces beyond each gap end must be explored. The flow occurs in the presence of an arbitrarily oriented magnetic field. By assuming that the secondary flow is negligible, the problem reduces to a fully developed magnetohydrodynamic (MHD) duct flow problem. In the parameter range presented here, the liquid-metal flow can be laminar or turbulent, requiring that both regimes be analyzed. The numerical results from the mathematical model presented herein for laminar flow with arbitrary Hartmann number M and with arbitrary magnetic-field orientation indicate that, even with an O(1) Hartmann number, the flow is already beginning to evolve into the distinct regions predicted by the asymptotic solution for M≫1 derived from singular perturbation theory. However, the actual velocity and electric potential distributions only agree approximately with those predicted by the large M asymptotic solutions. The numerical results presented in this work for the turbulent MHD flow are profoundly different from their corresponding laminar counterparts. Velocity magnitudes are significantly reduced in the turbulent MHD flows, and as a consequence, the magnitude of the current density increases. Thus, according to the mathematical model presented in this paper, liquid-metal sliding electrical contacts in external magnetic fields appear to transport current more efficiently in the turbulent regime than the laminar regime under the conditions of the calculations.
Invariant two-dimensional structures of vorticity field in nonviscous fluid
Authors: Chen Hudong
Published: July 2002

It is generally shown that the dynamics of three-dimensional nonviscous flows possesses invariant two-dimensional structures if these flows are invariant under translations along their vorticity field directions. In such a two-dimensional fluid, the vorticity field direction is fixed in time everywhere, while its intensity obeys a scalar equation similar to that in the two-dimensional line-vortex case. The most general flow having such a two-dimensional structure is perhaps the helically invariant flow. Expressed in terms of some generalized coordinates according to its spatial symmetry, the dynamics of such a flow admits a Hamiltonian description. A general steady-state condition for such a flow is also derived. Furthermore, using Boltzmann statistics, the equilibrium distribution of the intensity of the vorticity field is shown to satisfy a nonlinear partial differential equation, similar to the sinh-Poisson equation for the line-vortex case.
On the variational method of closure in the theory of turbulence
Authors: Bazdenkov S. V. , Kukharkin N. N.
Published: July 2002

The variational approach to the closure problem of turbulence theory with particular attention to the perturbation–variation method of Qian [Phys. Fluids 26, 2098 (1983)] is studied. It is shown that although the method is based on a clear physical idea, it is not self-consistent. The procedure to obtain the equation for the dynamic damping coefficient does contain arbitrariness, which leads to the dependence of this equation on the choice of variables. This ambiguity is illustrated by numerical evaluations of the Kolmogorov constant in two-dimensional and three-dimensional cases. The equation for the dynamic damping coefficient, which is invariant, with respect to the change of variables, is obtained and analyzed. The principal inevitability of arbitrariness in closure methods is discussed.
Structure of normal shock waves: Direct numerical analysis of the Boltzmann equation for hard-sphere molecules
Authors: Ohwada Taku
Published: July 2002

The structure of normal shock waves is investigated on the basis of the standard Boltzmann equation for hard-sphere molecules. This fundamental nonlinear problem in rarefied gas dynamics is analyzed numerically by a newly developed finite-difference method, where the Boltzmann collision integral is computed directly without using the Monte Carlo method. The velocity distribution function, as well as the macroscopic quantities, is accurately obtained. The numerical results are compared with the Mott-Smith and the direct simulation Monte Carlo results in detail. The analytical solution for a weak shock wave based on the standard Boltzmann equation is also presented up to the second order of the shock strength together with its explicit numerical data for hard-sphere molecules.
Inertial ranges and resistive instabilities in two-dimensional magnetohydrodynamic turbulence
Authors: Politano H. , Pouquet A. , Sulem P. L.
Published: July 2002

Direct numerical simulations of decaying two-dimensional magnetohydrodynamic flows at Reynolds numbers of several thousand are performed, using resolutions of 10242 collocation points. An inertial range extending to about one decade is observed, with spectral properties depending on the velocity–magnetic field correlation. At very small scales, resistive tearing destabilizes current sheets generated by the inertial dynamics and leads to the formation of small-scale magnetic islands, which may then grow and reach the size of inertial scales.
Self-modulation of low-frequency oscillations in a plasma
Authors: Honzawa Tadao
Published: July 2002

Experimental results are reported on the self-modulation of low-frequency oscillations in a plasma. The phenomenon is observed to occur at large amplitudes above a threshold. This is clearly shown by violent changes in the envelope form of externally modulated oscillations. Resultant spiky forms of the oscillation envelopes are observed to change strongly depending on parameters such as the rf frequency, the rf amplitude, and so on. Furthermore, spectral observations give additional information on the properties of the spiky oscillations. Finally, the observed phenomenon is qualitatively interpreted using a theory on the parametric process.
Almost two-dimensional treatment of drift wave turbulence
Authors: Albert J. M. , Similon P. L. , Sudan R. N.
Published: July 2002

The approximation of two-dimensionality is studied and extended for electrostatic drift wave turbulence in a three-dimensional, magnetized plasma. It is argued on the basis of the direct interaction approximation that in the absence of parallel viscosity, purely 2-D solutions exist for which only modes with k∥=0 are excited, but that the 2-D spectrum is unstable to perturbations at nonzero k∥. A 1-D equation for the parallel profile gk⊥(k∥) of the saturated spectrum at steady state is derived and solved, allowing for parallel viscosity; the spectrum has finite width in k∥, and hence finite parallel correlation length, as a result of nonlinear coupling. The enhanced energy dissipation rate, a 3-D effect, may be incorporated in the 2-D approximation by a suitable renormalization of the linear dissipation term. An algorithm is presented that reduces the 3-D problem to coupled 1- and 2-D problems. Numerical results from a 2-D spectral direct simulation, thus modified, are compared with the results from the corresponding 3-D (unmodified) simulation for a specific model of drift wave excitation. Damping at high k∥ is included. It is verified that the 1-D solution for gk⊥(k∥) accurately describes the shape and width of the 3-D spectrum, and that the modified 2-D simulation gives a good estimate of the 3-D energy saturation level and distribution E(k⊥).
Experimental measurements of lower-hybrid wave propagation in the Versator II tokamak using microwave scattering
Authors: Rohatgi R. , Chen K.-I. , Bekefi G. , Bonoli P. , Luckhardt S. C. , Mayberry M. , Porkolab M. , Villasenor J.
Published: July 2002

A series of 139 GHz microwave scattering experiments has been performed on the Versator II tokamak (B. Richards, Ph.D. thesis, Massachusetts Institute of Technology, 1981) to study the propagation of externally launched 0.8 GHz lower-hybrid waves. During lower-hybrid current drive, the launched waves are found to follow a highly directional resonance cone in the outer portion of the plasma. Wave power is also detected near the center of the plasma, and evidence of wave absorption is seen. Scattering of lower-hybrid waves in k space by density fluctuations appears to be a weak effect, although measurable frequency broadening by density fluctuations is found, Δω/ω=3×10−4. In the detectable range (2.5<N∥<5.5) the N∥ spectra inferred from the scattering measurements are quite similar above and below the current drive density limit. Numerical modeling of these experiments using ray tracing is also presented.
Stationary propagating magnetic electron vortices
Authors: Nycander Jonas , Pavlenko Vladimir P.
Published: July 2002

The nonlinear theory of the magnetic electron mode is developed. It is shown that the model equations describing this mode has stationary localized solutions of the monopole vortex type. The vortices travel in the direction perpendicular to the inhomogeneities of the plasma with a velocity determined by the ratio between the temperature perturbation and the magnetic field of the vortex. For the vortex to be stationary and localized, this velocity must be larger than the phase velocity of the linear waves.
Ion acoustic solitary waves in relativistic plasmas
Authors: Ghosh Kamal Kumar , Ray Dipankar
Published: July 2002

In a recent paper, Roychoudhury and Bhattacharyya [Phys. Fluids 30, 2582 (1987)] found solitary wave solutions in a relativistic plasma using an approximate pseudopotential. Since the integral of an approximation to a differential equation does not always approximate the integration of the differential equation, in the present paper a rigorous analytical study has been made to find the conditions for existence of soliton solutions in a relativistic plasma.
Stretched three-dimensional plasma equilibria with field-aligned flow
Authors: Birn J.
Published: July 2002

A three-dimensional equilibrium theory [J. Geophys. Res. 92, 11 101 (1987)] for stretched plasma configurations, such as the Earth’s magnetotail, is extended to include the effects of field-aligned flow. The magnetohydrodynamic (MHD) equations for this case can be solved in a general way by reduction to a set of ordinary differential equations and an ordinary integral. The solutions represent lowest-order solutions of an asymptotic expansion of the MHD equations for small electric field and weak time dependence. Simplified equations are presented for two-dimensional equilibria and for incompressible flow. Possible magnetospheric applications include the configuration of the geotail near and beyond the termination of the closed field line region, the steady motion of a plasmoid (a plasma bubble severed from the Earth) through the distant geotail, and configurations at the magnetopause, the interface between the magnetosphere and the shocked solar wind plasma. For illustration, solutions for the steady motion of a two-dimensional plasmoid through the distant magnetotail are presented.
Theory of hydrodynamic trapped-ion-temperature-gradient-driven turbulence
Authors: Biglari H. , Diamond P. H.
Published: July 2002

A novel, nonlinearly coupled, two-dimensional (2-D), two-field set of equations is derived to model the turbulent dynamics of trapped-ion-temperature-gradient-driven convective cells. Statistical mechanical arguments are employed to show that, in spite of the two-dimensional character of the system, the direction of spectral energy flow is from large to small scales. Steady-state fluctuation levels are derived from the evolution equation for temperature spectra, and the ensuing particle and heat transport coefficients are shown to be comparable to conventional estimates associated with electron drift wave turbulence.
Fully kinetic plasma-sheath theory for a cold-electron emitting surface
Authors: Ordonez C. A.
Published: July 2002

The fully kinetic, one-dimensional, plasma-sheath theory by Schwager and Birdsall [Phys. Fluids B 2, 1057 (1990)] is further developed. A cold-electron emitting surface is included and a three-dimensional plasma is considered. The sheath potential is not assumed to equal the floating potential so that the theory applies to a current-carrying sheath. Appropriate values are found for higher-order moments of the velocity distribution which depend on the three-dimensional velocity distribution width. Distribution functions in terms of energy and angle are derived. The (effective) temperature, the total energy flux, and the heat flux are evaluated in terms of exact analytic functions. The normalized magnitude of the floating potential for a deuterium plasma with equal ion and electron temperatures is calculated to be ψf=3.2 for δ=0 and ψf=1.8 for δ=0.75 where δ is the electron emission coefficient. The normalized magnitude of the sheath potential for the same plasma (with δ=0) is calculated to be ψs=3.9 for γ=0.02 and ψs=2.8 for γ=−0.02 where γ is the normalized current density. A self-consistent integral solution for the electrostatic potential profile within the sheath is derived.
Collision integrals for the interaction of the ions of nitrogen and oxygen in a plasma at high temperatures and pressures
Authors: Stallcop James R. , Partridge Harry , Levin E.
Published: July 2002

The corrections to the transport cross sections and collision integrals for Coulomb interactions arising from the application of realistic interaction energies of the ions of nitrogen and oxygen have been investigated. Accurate potential energy curves from an ab initio electronic structure calculation and a semiclassical description of the scattering are used to determine the difference between the cross sections for the real interaction forces and a Coulomb force for large values of the Debye shielding parameter. Graphs of the correction to the diffusion and viscosity collision integrals are presented for temperatures from about 10 000 K to 150 000 K. This correction can be combined with tabulations of the collision integrals for shielded Coulomb potentials to determine the contribution of N+–N+, N+–O+, and O+–O+ interactions to the transport properties of high-temperature air. Analytical forms have been fitted to the calculated results to assist this application.
Trapped particle dynamics in toroidally rotating plasmas
Authors: Hahm T. S.
Published: July 2002

A detailed single particle orbit analysis in toroidally rotating plasma yields new analytical formulas for the second adiabatic invariant, the bounce frequency, and the precession frequency up to the first-order correction in ρpi (poloidal ion gyroradius)/Lv (scale length of rotation velocity), for toroidal flow values of the order of ion thermal velocity. Toroidal plasma rotation effects on the trapped ion instabilities in tokamaks are investigated in the context of local theory. Toroidal plasma rotation increases both the fraction of trapped particles and their precession drift velocity. Consequently, the growth rate of trapped ion instability increases in both dissipative and collisionless regimes.
A theory of bifurcations and chaos observed in an ion sheath
Authors: Kono Mitsuo , Komori Akio
Published: July 2002

A theory of cascading bifurcations to chaos observed in a current-carrying ion sheath [Komori et al., Bull. Am. Phys. Soc. 36, 2408 (1991)] is developed. The ion sheath on both sides of a grid forms a potential well in which ions oscillate to give a primary motion, being subject to cascading bifurcations to chaos when an external oscillation field is applied to the grid. A model equation is derived to describe ion dynamics in the ion sheath which obeys the Child–Langmuir law for a large potential drop. The numerical solutions are shown to recover the observations.
Transport profiles induced by radially localized modes in a tokamak
Authors: Beklemishev A. D. , Horton W.
Published: July 2002

A new approach to the calculation of turbulent transport coefficients for radially localized modes is presented. The theory takes into account the nonuniformity of the distribution of rational (resonant) magnetic surfaces in minor radius. This distribution function is proportional to the density of available states of excitation. The resulting density of states correction qualitatively changes the radial profile of the transport coefficients, as compared to the usual local diffusivity formulas. The correction factor calculated for the ηi -mode turbulence increases toward the plasma edge and allows a better qualitative agreement of the radial χi profile with experimental data than the conventional approach.
Ultrasonically stimulated low-frequency oscillation and breakup of immiscible liquid drops: Photographs
Authors: Marston Philip L. , Goosby Stanley G.
Published: July 2002

Shape oscillation and fission of drops of an oil in water were studied photographically. Novel theoretical results are also presented concerning the resonance response of drops. The initial radii of the drops observed were typically between 1 and 2 mm. Two-lobed oscillations of moderate amplitude were driven by the temporally modulated radiation pressure of an ultrasonic wave. The tendencies for drops to elongate and break are discussed qualitatively. The oil is more compressible than water. Radiation stresses repel the oil from pressure nodes of the ultrasonic standing wave. The excitation of a transient deformation that appears to run around the drop’s surface is noted.
Influence of profile shape on the extraordinary-mode stability properties of relativistic non-neutral electron flow in a planar diode with applied magnetic field
Authors: Davidson Ronald C. , Tsang Kang T.
Published: July 2002

The cold-fluid extraordinary-mode eigenvalue equation is solved numerically to determine the influence of equilibrium profile shape on the detailed stability properties of relativistic non-neutral electron flow in a planar diode with cathode located at x=0 and anode at x=d. Stability properties are investigated for the class of equilibrium energy profiles γb(x) specified by γb(x)=λ cosh α1x+(1−λ) {[1−α22(b2−x2)]1/2/[1−α22b2]1/2} over the interval 0≤x≤b. Here α1 and α2 are constants (with α22b2<1), x=b is the outer edge of the electron layer, and λ is a constant parameter in the range of 0≤λ≤1. The corresponding equilibrium profiles for Bz(x), nb(x), and Ex(x) are determined self-consistently from the steady-state (∂/∂t=0) cold-fluid-Maxwell equations. As the parameter λ is varied from unity to zero there is a large change in the equilibrium profile for nb(x)/γb(x), ranging from nb(x)/γb(x)=const over the interval 0≤x<b when λ=1, to monotonic decreasing profiles for nb(x)/γb(x) when λ<1. The numerical analysis of the extraordinary-mode eigenvalue equation shows that the detailed stability properties are very sensitive to the shape of the equilibrium profiles. As λ is reduced from unity, and the profile for nb(x)/γb(x) becomes monotonic decreasing, it is found that the instability growth rate Im ω is reduced. Moreover, the more rapid the decrease in nb(x)/γb(x) (i.e., the smaller the value of λ), the more the growth rate is reduced. Indeed, in some parameter regimes, the instability growth rate can be reduced to zero over the range of wavenumber k examined numerically.
Richardson’s criterion for the stability of stratified shear flow
Authors: Miles John
Published: July 2002

Chandrasekhar’s derivation, from energy considerations, of the sufficient condition R>1/4 for stability of a stratified shear flow, in which R is the local Richardson number, is amended to obtain R>1, in agreement with the earlier arguments of Richardson, Taylor, and Prandtl(L. F. Richardson, Proc. R. Soc. London Ser. A 97, 354 (1920); G. I. Taylor, Rapp. P. V. Reun. Cons. Permanent Int. d’Exploration Mer 76, 35 (1931); Sci. Pap. 2, 240; L. Prandtl, Vorträge aus dem Gebiete der Aerodynamik und verwandten Gebieten (Springer, Berlin, 1930), pp. 1–7; L. Prandtl, Führer durch die Strömungslehre (Vieweg, Braunschweig, 1942), p. 337; Essentials of Fluid Dynamics [English translation of 1949 edition of Führer durch die Strömungslehre (Hafner, New York, 1952), pp. 381 and 382]).
Magnetic flux conversion and relaxation toward a minimum-energy state in spheromak plasmas
Authors: Janos A.
Published: July 2002

S-1 spheromak [Plasma Physics and Controlled Nuclear Fusion, 1984 (IAEA, Vienna, Austria, 1985), Vol. 2, p. 535] currents and magnetic fluxes have been measured with Rogowski coils and flux loops external to the plasma. Toroidal plasma currents up to 350 kA and spheromak configuration lifetimes over 1.0 msec have been achieved at moderate power levels. The plasma formation in the S-1 spheromak device is based on an inductive transfer of poloidal and toroidal magnetic flux from a toroidal ‘‘flux core’’ to the plasma. Formation is programmed to guide the configuration into a force-free, minimum-energy Taylor state. Properly detailed programming of the formation process is found not to be essential since plasmas adjust themselves during formation to a final equilibrium near the Taylor state. After formation, if the plasma evolves away from the stable state, then distinct relaxation oscillation events occur that restore the configuration to that stable state. The relaxation process involves reconnection of magnetic field lines, and conversion of poloidal to toroidal magnetic flux (and vice versa) has been observed and documented. The scaling of toroidal plasma current and toroidal magnetic flux in the plasma with externally applied currents is consistent with the establishment of a Taylor state after formation. In addition, the global magnetic helicity in the plasma is proportional to that injected from the flux core, independent of how that helicity is generated.
The effects of inertia on the stability of the convective flow in inclined particle settlers
Authors: Shaqfeh E. S. G. , Acrivos A.
Published: July 2002

A linear stability analysis of the base-state convective flows, which occur in inclined particle settlers and which were studied in a companion paper by Shaqfeh and Acrivos [Phys. Fluids 29, 3935 (1986)], is described. The analysis considers the spatial growth of small two-dimensional disturbances over the entire range of the parameters θ (the angle of inclination of the vessel), ω̂ (the wave frequency), R̂ (a stability Reynolds number), and ξ1/6 (the parameter governing inertial effects in the base flow). Numerical solutions to the relevant Orr–Sommerfeld equations for the wave growth rates and other important quantities are presented over this entire range. It is shown that, for very large values of R̂, these solutions approach asymptotically those of a certain set of Rayleigh equations which are also derived and solved. The results demonstrate that the base flows become most unstable when ξ1/6≊O(1), primarily owing to the development of an inviscid instability. This instability is shown to have a number of interesting characteristics including the fact that (a) it is insensitive to the inclination of the vessel, and (b) it tends to destabilize higher frequencies. In addition, it is demonstrated that, although it is very unstable for ξ1/6≊O(1), the flow restabilizes as ξ1/6→∞, as predicted by Prasad [J. Fluid. Mech. 150, 417 (1985)]. The analysis, therefore, bridges the gap between previous asymptotic results and, at the same time, resolves the existing paradox between the experimental observations of Schaflinger [Int. J. Multiphase Flow 11, 189 (1985)] and theoretical predictions. Moreover, it provides a theoretical basis for predicting the vigorous instabilities which are witnessed in practice.
Measurement of plasma wave frequency from absolute stimulated Raman scattering near the quarter-critical surface in a laser plasma
Authors: Villeneuve D. M. , Bernard J. E. , Baldis H. A.
Published: July 2002

Thomson scattering techniques were used to measure the frequency of plasma waves near the quarter-critical surface in a well-diagnosed plasma irradiated by a nanosecond CO2 laser with intensity ∼1014 W/cm2. The frequency ωp was shown to be less than ω0/2, in disagreement with the commonly used estimate ωp=ω0/2+ (9)/(8) (ve/c)2ω0. The theory of Afeyan and Williams [Phys. Fluids 28, 3397 (1985)] gives better agreement, and shows that the density scale length is more important than the temperature in determining the frequency shift.
The detuning of relativistic Langmuir waves in the beat-wave accelerator
Authors: McKinstrie C. J. , Forslund D. W.
Published: July 2002

In the beat-wave accelerator, a large-amplitude Langmuir wave is produced by the beating of two laser beams whose frequencies differ by approximately the plasma frequency. The growth of this Langmuir wave saturates because of a nonlinear shift in its natural frequency. At present, there are three different formulas for the nonlinear frequency shift in the literature. By taking all relevant nonlinearities into account, the original result of Akhiezer and Polovin [Dokl. Akad. Nauk SSSR 102, 919 (1955)] is shown to be correct. The maximum amplitude of the Langmuir wave depends on the incident laser intensity and the frequency mismatch, which is the difference between the beat frequency of the incident waves and the plasma frequency. Two different studies have produced contradictory conclusions on the ‘‘optimum’’ frequency mismatch. The reasons for this contradiction are discussed and the result of Tang, Sprangle, and Sudan [Phys. Fluids 28, 1974 (1985)] is shown to be essentially correct. However, the requirements for effective beam loading make practical use of the optimum configuration impossible.
Relation of wave energy and momentum with the plasma dispersion relation in an inhomogeneous plasma
Authors: Berk H. L. , Pfirsch D.
Published: July 2002

The expressions for wave energy and angular momentum commonly used in homogeneous and near-homogeneous media is generalized to inhomogeneous media governed by a nonlocal conductivity tensor. The expression for wave energy applies to linear excitations in an arbitrary three-dimensional equilibrium, while the expression for angular momentum applies to linear excitations of azimuthally symmetric equilibria. The wave energy ℰwave is interpreted as the energy transferred from linear external sources to the plasma if there is no dissipation. With dissipation, such a simple interpretation is lacking as energy is also thermally absorbed. However, for azimuthally symmetric equilibria, the expression for the wave energy in a frame rotating with a frequency ω can be unambiguously separated from thermal energy. This expression is given by ℰwave −ωLwave/ l, where Lwave is the wave angular momentum defined in the text and l the azimuthal wavenumber and it is closely related to the real part of a dispersion relation for marginal stability. The imaginary part of the dispersion is closely related to the energy input into a system. Another useful quantity discussed is the impedance form, which can be used for three-dimensional equilibrium without an ignorable coordinate and the expression is closely related to the wave impedance used in antenna theory. Applications to stability theory are also discussed.
Taylor–Goertler instability for thin-film flows
Authors: Eagles P. M.
Published: July 2002

A theory for steady-state thin-film flow on a curved bed is presented and disturbances of Taylor or Goertler type are calculated, with reasonable agreement with experimental work.
Raman backscattering and forward scattering thresholds in parabolic density profiles
Authors: Estabrook Kent , Kruer W. L. , Williams E. A.
Published: July 2002

The growth of stimulated Raman backscattering (RBS) and forward scattering (RFS), as a function of density and temperature in a parabolic density profile, is examined and simulation results are compared to analytic theory. This work is relevant to the burnthrough foil experiments, in which Raman scattering is explored in spatial scale lengths long enough to be relevant to high gain targets.
Dissipative mode coupling in ion-cyclotron resonance minority heating
Authors: Fuchs V. , Bers A.
Published: July 2002

Coupled wave equations and the corresponding wave-energy-flow conservation law describing the fast magnetosonic and ion-Bernstein waves are derived for minority heating in the ion-cyclotron range of frequencies. This fourth-order full-wave system is subsequently reduced in order through representation by means of two, completely decoupled, second-order systems. One is a second-order equation for the fast wave in which the Bernstein mode is treated as a driven response. The second is coupled-mode equations for amplitudes varying slowly under the influence of coupling, inhomogeneity, and dissipation. The coupled-mode equations are approximately solved for both high-field and low-field incidence to give the transmission and mode-conversion coefficients in closed form for arbitrary wavenumbers parallel to the magnetic field. Good agreement with fourth-order calculations is obtained.
Plasma production and heating in a tandem mirror central cell by radio-frequency waves in the ion cyclotron frequency range
Authors: Golovato S. N. , Brau K. , Casey J. , Coleman J. , Gerver M. J. , Guss W. , Hallock G. , Horne S. , Irby J. , Kumazawa R. , Kesner J. , Lane B. , Machuzak J. , Moran T. , Myer R. , Post R. S. , Sevillano E. , Smith D. K. , Sullivan J. D. , Torti R. , Wang L. , Yasaka Y. , Yao X. Z. , Zielinski J.
Published: July 2002

Plasma production and heating in the central cell of the Tara tandem mirror [Nucl. Fusion 22, 549 (1982); Plasma Physics and Controlled Nuclear Fusion Research, 1986, Proceedings of the 11th International Conference, Kyoto, Japan (IAEA, Vienna, 1987), Vol. 2, p. 251] have been studied. Using radio-frequency excitation by a slot antenna in the ion cyclotron frequency range (ICRF), plasmas with a peak β⊥ of 3%, density of 4×1012 cm−3, ion temperature of 800 eV, and electron temperature of 75–100 eV were routinely produced. The plasma radius decreased with increasing ICRF power, causing reduced ICRF coupling and saturation of the plasma beta. About 70% of the applied ICRF power can be accounted for in direct heating of both ions and electrons. Wave field measurements have identified the applied ICRF to be the slow, ion cyclotron wave. In operation without end plugging, the plasma parameters were limited by poor axial confinement and the requirements for maintenance of magnetohydrodynamic stability and microstability.
The viscous stability analysis of Long’s vortex
Authors: Khorrami Mehdi R. , Trivedi Prakash
Published: July 2002

The viscous stability analysis of Long’s vortex is performed. Some quantitative disagreements with the inviscid results of previous investigators are reported. The truncation of the infinite radial domain into a small computational domain utilized in past investigations is found to be the source of these discrepancies. More important, for small flow forces, a type-II Long’s vortex is shown to be destabilized by perturbations having positive azimuthal wave number. Based on previous numerical computations, it had been conjectured that these unstable eigenmodes may not exist. The stability characteristics of the unstable modes are fully mapped and are presented in detail.