bluuebunny/crossref_metadata_2025 huggingface dataset:
Modular invariance on the torus and Abelian Chern–Simons theory
Authors: Guerrero J. , Calixto M. , Aldaya V.
Published: July 2002

The implementation of modular invariance on the torus as a phase space at the quantum level is discussed in a group-theoretical framework. Unlike the classical case, at the quantum level some restrictions on the parameters of the theory should be imposed to ensure modular invariance. Two cases must be considered, depending on the cohomology class of the symplectic form on the torus. If it is of integer cohomology class n, then full modular invariance is achieved at the quantum level only for those wave functions on the torus which are periodic if n is even, or antiperiodic if n is odd. If the symplectic form is of rational cohomology class n/r, a similar result holds—the wave functions must be either periodic or antiperiodic on a torus r times larger in both directions, depending on the parity of nr. Application of these results to the Abelian Chern–Simons theory is discussed.
Exact solutions of the Dirac equation in a nonfactorizable metric
Authors: Hounkonnou M. N. , Mendy J. E. B.
Published: July 2002

We present the covariant generalization of the Dirac equation in a nonfactorizable metric and give the corresponding exact solutions in terms of special functions as well as the explicit form of the spinor solution. Then we treat the particular case of the Weyl equation for the neutrinos.
Quasi-Lagrangian systems of Newton equations
Authors: Rauch-Wojciechowski Stefan , Marciniak Krzysztof , Lundmark Hans
Published: July 2002

Systems of Newton equations of the form q̈=−12A−1(q)∇k with an integral of motion quadratic in velocities are studied. These equations generalize the potential case (when A=I, the identity matrix) and they admit a curious quasi-Lagrangian formulation which differs from the standard Lagrange equations by the plus sign between terms. A theory of such quasi-Lagrangian Newton (qLN) systems having two functionally independent integrals of motion is developed with focus on two-dimensional systems. Such systems admit a bi-Hamiltonian formulation and are proved to be completely integrable by embedding into five-dimensional integrable systems. They are characterized by a linear, second-order partial differential equation PDE which we call the fundamental equation. Fundamental equations are classified through linear pencils of matrices associated with qLN systems. The theory is illustrated by two classes of systems: separable potential systems and driven systems. New separation variables for driven systems are found. These variables are based on sets of nonconfocal conics. An effective criterion for existence of a qLN formulation of a given system is formulated and applied to dynamical systems of the Hénon–Heiles type.
Time ordering, energy ordering, and factorization
Authors: Lam C. S.
Published: July 2002

Relations between integrals of time-ordered product of operators, and their representation in terms of energy-ordered products are studied. Both can be decomposed into irreducible factors and these relations are discussed as well. The energy-ordered representation was invented to separate various infrared contributions in gauge theories. It is shown that the irreducible time-ordered expressions can be used to accomplish the same purpose. Besides, it has the added advantage of being factorizable.
Quantum grammars
Authors: Malyshev V. A.
Published: July 2002

We consider quantum (unitary) continuous time evolution of spins on a lattice together with quantum evolution of the lattice itself. In physics such evolution was discussed in connection with quantum gravity. It is also related to what is called quantum circuits, one of the incarnations of a quantum computer. We consider simpler models for which one can obtain exact mathematical results. We prove existence of the dynamics in both Schrödinger and Heisenberg pictures, construct KMS states on appropriate C*-algebras. We show (for high temperatures) that for each system where the lattice undergoes quantum evolution, there is a natural scaling leading to a quantum spin system on a fixed lattice Z, defined by a renormalized Hamiltonian.
Thermodynamics of toroidal black holes
Authors: Peça Claudia S. , Lemos José P. S.
Published: July 2002

The thermodynamical properties of toroidal black holes in the grand canonical ensemble are investigated using York’s formalism. The black hole is enclosed in a cavity with finite radius where the temperature and electrostatic potential are fixed. The boundary conditions allow one to compute the relevant thermodynamical quantities, e.g., thermal energy, entropy, and specific heat. This black hole is thermodynamically stable and dominates the grand partition function. This means that there is no phase transition, such as the one encountered for spherical black holes.
On the dimension of the global attractor for a damped semilinear wave equation with critical exponent
Authors: Huang Yu , Yi Zhao , Yin Zhaoyang
Published: July 2002

We obtain in this paper a precise estimate of upper bound of the Hausdorff dimension of the global attractor for a damped semilinear wave equation with critical exponent. The obtained Hausdorff dimension decreases as the damping grows and is uniformly bounded for large damping, which conforms to physical intuition. The obtained results generalize and correct the corresponding results obtained by Zhou recently.
The planar singular solutions of Stokes and Laplace equations and their application to transport processes near porous surfaces
Authors: Sangani A. S. , Behl S.
Published: July 2002

The planar singular solutions of Stokes and Laplace equations are derived and applied to a number of transport problems associated with porous surfaces. The velocity, pressure, concentration, and temperature slip coefficients are determined exactly for the semi-infinite periodic arrays of spheres and these are compared with the predictions of two approximate continuum theories formulated by Brinkman [Appl. Sci. Res. A1, 27 (1947)] and Chang and Acrivos [J. Appl. Phys. 59, 375 (1986)] to assess the utility of such theories in accurately predicting various overall properties related to the porous surfaces. It is found that in general these theories provide fairly accurate estimates of these properties even when the length scales based on the relevant macroscopic properties such as the permeability are much smaller than the length scales characterizing the microstructure of the porous media.
A spectrum model for weakly anisotropic turbulence
Authors: Shih Tsan-Hsing , Reynolds William C. , Mansour Nagi N.
Published: July 2002

A simple model, parametrized by the Reynolds stress anisotropy, is proposed for the spectrum of weakly anisotropic turbulence. It contains a model constant that affects its region of realizability. This spectrum model is used to derive a one point closure to the rapid pressure-strain term. The derived pressure-strain model is linear in the Reynolds stress anisotropy and is of the same form as the closure model of Launder, Reece, and Rodi (LRR) [J. Fluid Mech. 68, 537 (1975)]. The spectrum model becomes unrealizable in some regions of wave space for sufficiently large anisotropy of the Reynolds stress, and this is used to infer the region of validity of the linear closure model. It is found that the extent of the valid region is very small when the model constant is set to match rapid distortion theory, and largest for a model constant set close to the value suggested by LRR. However, even the largest valid domain does not extend very far from isotropy, suggesting inherent weakness in the linear pressure-strain models.
Mixing enhancement by expansion waves in supersonic flows of different densities
Authors: Li C. , Kailasanath K. , Book D. L.
Published: July 2002

When expansion waves pass through an interface between compressible fluids of different densities, the interface is Rayleigh–Taylor unstable if the low-density fluid is accelerated into the high-density fluid by the pressure gradient associated with the expansion waves. Numerical simulations of the evolution of interface structures interacting with expansion waves launched by a piston receding from the interface show rapid growth of mushroomlike structures from small disturbances. This is an indication of a strong Rayleigh–Taylor instability on the interface. In order to study the application of this concept to mixing enhancement in supersonic flows, simulations of a shear layer formed by supersonic flows of different densities passing through expansion waves have been performed. It is found that this instability enhances mixing by creating vorticity when the expansion waves generate a negative scalar product of the density and pressure gradients in the interface region.
Direct, high resolution, four-dimensional measurements of the fine scale structure of Sc≫1 molecular mixing in turbulent flows
Authors: Dahm Werner J. A. , Southerland Kenneth B. , Buch Kenneth A.
Published: July 2002

Results from highly resolved, four-dimensional measurements of the fine structure of the fully space- and time-varying Sc≫1 conserved scalar field and the associated scalar energy dissipation rate field in a turbulent flow are presented. The resolution achieved in all three spatial dimensions and in time reaches down to the local strain-limited molecular diffusion scale in the flow, allowing all three components of the instantaneous scalar gradient vector field ∇ζ(x,t) and their time evolution at every point in the data space to be directly evaluated. Results are presented in the form of fine structure maps of the instantaneous dissipation field loge ∇ζ⋅∇ζ(x,t) in several spatially adjacent data planes within an individual three-dimensional spatial data volume, as well as in several temporally successive data planes from a sequence of such three-dimensional data volumes. The degree of anisotopy in the underlying scalar gradient field is characterized in terms of the joint distribution β(ϑ,φ) of spherical orientation angles. The probability density of true scalar energy dissipation rates is presented and compared with the distributions that would result from lower-dimensional measurements of the scalar gradient vector. From this the ‘‘spottiness’’ of the scalar dissipation field is directly quantified by determining the true fraction of the total dissipation that occurs in any given volume fraction of the flow.
Mixing transition and the cascade to small scales in a plane mixing layer
Authors: Moser R. D. , Rogers M. M.
Published: July 2002

Direct numerical simulations of time-developing plane mixing layers have been performed using a variety of initial conditions. Up to two pairings of the dominant spanwise rollers have been simulated. When the flow is sufficiently three dimensional, a pairing can cause the mixing layer to undergo a transition to small-scale turbulence. This small-scale transition is accompanied by increased mixing of a passive scalar, similar to observations of the mixing transition in experiments. As part of the transition process, thin vortex sheets are generated by vortex stretching and roll up as in a two-dimensional mixing layer. This higher-order rollup is part of the cascade to small-scale turbulence. Estimates are obtained for the degree of three-dimensionality required for the pairing to initiate the transition.
Asymptotic solution of transonic nozzle flows with homogeneous condensation. II. Supercritical flows
Authors: Delale Can F. , Schnerr Günter H. , Zierep Jürgen
Published: July 2002

A detailed analysis of supercritical transonic nozzle flows with stationary normal shock waves is presented. A classification scheme based on the normal shock location is obtained using asymptotic methods, and four distinct supercritical flow regimes are distinguished. A simple shock fitting technique that determines the shock location within any desired precision is introduced. Consequently, an algorithm that exhibits the asymptotic solution in each supercritical flow regime is developed for the expansion of moist air in nozzles with atmospheric supply conditions by utilizing the classical nucleation theory and the Hertz–Knudsen droplet growth law. Good agreement with the recent static pressure measurements and visualized shock locations is achieved in relatively slender nozzles when the condensed phase is assumed to consist purely of water drops.
Monte Carlo direct simulation of the Taylor instability in rarefied gas
Authors: Riechelmann Dirk , Nanbu Kenichi
Published: July 2002

The rarefied flow of monatomic gas between an inner rotating cylinder and an outer stationary cylinder is simulated by the Monte Carlo direct simulation method. The flow is assumed to be axisymmetrical. A new idea to calculate the axisymmetrical flow is proposed. Simulations are performed for Knudsen numbers in the range 0.004<Kn<0.04 at a fixed rotation speed. The calculated torque coefficients show a very good agreement with experimental data not only for vortex free but also for vortical flow regimes. Once the Taylor vortices have developed, they cause a change of the circumferential velocity profile up to 35%. This is the first numerical simulation of Taylor vortices via solutions of the Boltzmann equation using the molecular approach.
Ion temperature effects on ion charge-state distributions of an electron cyclotron resonant ion source
Authors: Whaley D. R. , Getty W. D.
Published: July 2002

A method is described for determining ion cyclotron resonance (ICR) heating effects on multiply charged-ion energy distributions using a Monte Carlo fit to experimental time-of-flight spectrometer data. The method is general but is used here specifically to separate the effects of plasma ambipolar potential spread and ion temperature in an electron cyclotron resonance (ECR) heated magnetic mirror ion source (MIMI) [Phys. Fluids 28, 3116 (1985)]. A steady-state equilibrium model is also developed that models the relevant atomic processes occurring in MIMI plasmas. This model and the Monte Carlo analysis are used to relate the effect of midplane ICR heating on end loss ion charge state distributions to its effect on the confined ion distributions. The model allows for collisional, moderately collisional, and collisionless confinement, specific to each charge state in the distribution. Both experiment and modeling show that increased ion temperature causes a shift to lower-Z ion populations in both the confined and end loss charge-state distributions.
Relativistic transport theory for a two-temperature magnetized plasma
Authors: Metens T. , Balescu R.
Published: July 2002

The relativistic kinetic theory of linear transport is worked out within the framework of a new moment method. A complete analytical study of the transport in a two-temperature inhomogeneous magnetized fusion plasma is given. The transport relations and coefficients are derived from the kinetic equation with the full relativistic Beliaev–Budker collision operator and the impact of relativistic effects on the confinement are investigated.
m=1 kink mode for layer widths comparable to the ion Larmor radius
Authors: Berk H. L. , Mahajan S. M. , Zhang Y. Z.
Published: July 2002

A kink-tearing eigenmode equation is derived for a slab layer geometry in the limit me/mi≪βi≪L2n/L2s (me/mi ≡mass ratio, βi≡ ion beta value, Ln ≡gradient scale length, Ls ≡shear length) and when the electron collision frequency is comparable to the eigenfrequency. It is essential for consistency to retain arbitrary ion Larmor radius effects, which are described with the use of the Padé approximation. The asymptotic solution of the inhomogeneous eigenvalue problem is obtained using simple approximations to the eigenfunction. A dispersion relation duplicates previously derived results when a Lorentzian conductivity model is used for electrons, while a new dispersion relation is obtained if electrons are described by kinetic dynamics. The dispersion relation is analytically and numerically investigated. The numerical results are compared to a more complicated and presumably more ‘‘rigorous’’ asymptotic expression. It is shown that this asymptotic expression requires quite a small value for (me/mi)βi for accuracy. A fitting formula is found that is more accurate than the asymptotic formula for moderate values of (me/mi)βi. The dissipationless dispersion relation is discussed and it is shown that local shear at the q=1 surface can have a stronger effect than the value of δŴc [the magnetohydrodynamics (MHD) energy] on the system’s stability properties. When stability is predicted, electron dissipation due to collisions or electron Landau damping destabilizes a low frequency negative energy mode that is present. Electron temperature gradients are shown to reduce Landau damping and thus decrease the destabilizing drive on the negative energy mode.
The effect of a tilted magnetic field on the equilibrium of a pure electron plasma
Authors: Hart Grant W.
Published: July 2002

If the magnetic field in a pure electron plasma containment device is not aligned with the axis of the conducting walls, the electrons in the device will accumulate at the ends of the plasma where the magnetic field lines come closest to the walls and the electrons bound to the field lines can be closest to their image charges. If the plasma is also offset radially from the center (as with an l=1 diocotron mode), then more density will accumulate at one end than the other. As the plasma revolves around the center, the electrons will slosh from one end to the other, creating a measurable signal. This signal has been experimentally measured and its origin verified using a three-dimensional equilibrium code. This signal can be used experimentally to align the magnetic field with the conducting walls.
Formation of a flux core spheromak
Authors: Finn John M. , Guzdar Parvez N.
Published: July 2002

An alternate design for compact tori, specifically of the spheromak type, is studied. In this design, the ‘‘flux core spheromak’’ [Nucl. Fusion 29, 219 (1989)], the externally imposed bias field links the confinement region of closed flux surfaces. The advantages of this configuration are: (i) it enjoys greater stability to magnetohydrodynamic (MHD) modes, particularly the tilt and shift; (ii) it has a poloidal divertor, and an amount of poloidal flux separating the closed flux surface region from the walls; and (iii) it might be sustained by helicity injection. Results are presented showing the dependence of the geometry on the distribution of bias flux on the conducting walls and showing the optimization of the 2-D formation scheme to minimize the contact of the plasma with coils, electrodes, and walls. This last topic involves taking advantage of current sheet formation and subsequent tearing, as in formation of the MS spheromak [Phys. Fluids 28, 3154 (1985)]. The parameters which can be varied to produce this favorable formation scheme via tearing, rather than a formation that proceeds off the reversal coils, are explored. In addition, it is found that there is strong viscous heating of the ions in this early reconnection phase.
Three-dimensional filamentation of light in laser plasmas
Authors: Schmitt Andrew J.
Published: July 2002

The first calculations of time-dependent laser–plasma filamentation in three dimensions are reported. These calculations are done with a three-dimensional laser propagation code based on a previous two-dimensional code [Phys. Fluids 31, 3079 (1988)]. The effect of incident beam structure, and in particular optical smoothing techniques, on the behavior of filamentation is studied. Both ponderomotive and thermal conduction dominated nonlinearities are considered, and calculations are done simulating both homogeneous nonabsorbing plasmas and inhomogeneous laboratory plasmas. Random phase screen (RPS) and induced spatial incoherence (ISI) optical smoothing techniques are investigated and compared to generic unsmoothed laser beams. Qualitative examples are presented and scaling studies are done and compared to a simple theoretical analysis. In typical laser–plasma interactions without optical smoothing, three-dimensional effects lead to greatly increased filament intensities, as expected. Peak filament intensities of order 100–500 times the average intensity are routinely observed (without optical smoothing), as compared to earlier two-dimensional calculations where peak intensities were of order 10–50 times average. In spite of this tendency to create stronger filaments, three-dimensional filamentation (when measured on a time-averaged basis) can be suppressed by using ISI smoothing. Under the same conditions, instantaneous ISI intensities can show considerable enhancement, although much less than the unsmoothed beams. RPS smoothing exhibits less filamentation suppression. Under laser-fusion reactor conditions, calculations indicate that ISI suppression can completely eliminate filamentation.
High-power magnetic-compression heating of field-reversed configurations
Authors: Rej D. J. , Taggart D. P. , Baron M. H. , Chrien R. E. , Gribble R. J. , Tuszewski M. , Waganaar W. J. , Wright B. L.
Published: July 2002

Magnetic compression heating experiments at the 1 GW level on field-reversed configuration (FRC) compact toroid plasmas are reported. FRC’s formed in a tapered theta-pinch coil have been translated into a single-turn compression coil, where the external magnetic field is slowly raised up to seven times its initial value. Significant electron and ion heating consistent with the expected B4/5 adiabatic scaling is observed, despite significant particle diffusion, which is enhanced during compression. The n=2 rotational instability is enhanced during compression, but has been controlled to an extent by the application of an external quadrupole field. The particle and flux confinement times, τN and τφ, remain approximately equal and decrease roughly with the square of the plasma radius R during compression, implying a constant nonclassical field-null resistivity. The observed τN and τφ magnitudes and scalings are compared with classical and anomalous transport theories, and existing empirical models. Particle diffusion dominates the energy confinement, accounting for three-fourths of the total losses. Upper bounds on the electron thermal diffusivities are estimated.
High-n helicity-induced shear Alfvén eigenmodes
Authors: Nakajima N. , Cheng C. Z. , Okamoto M.
Published: July 2002

The high-n helicity-induced shear Alfvén eigenmodes (HAE) are considered both analytically and numerically for the straight helical magnetic system, where n is the toroidal mode number. The eigenmode equation for the high-n HAE modes is derived along the field line and, with the aid of the averaging method, is shown to reduce to the Mathieu equation asymptotically. The discrete HAE modes are shown to exist inside the continuum spectrum gaps. The continuous spectrum gaps appear around ω2=ω2A[N(lι■−m)/2]2 for N=1,2,..., where ωA is the toroidal Alfvén transit frequency, and l, m, and ι■ are the polarity of helical coils, the toroidal pitch number of helical coils, and the rotational transform, respectively. For the same ωA and ι■, the frequency of the helical continuum gap is larger than that of the continuum gap in tokamak plasmas by ‖l−ι■−1m‖. The polarity of helical coils l plays a crucial role in determining the spectrum gaps and the properties of the high-n HAE modes. The spectrum gaps near the magnetic axis are created by the helical ripple with circular flux surfaces for l=1, and ≥3 helicals. For l=2 helical systems, the spectrum gaps are created by the ellipticity of the flux surfaces. These analytical results for the continuum gaps and the existence of the high-n HAE modes in the continuum gaps are confirmed numerically for the l=2 case, and it is found that the HAE modes exist for mode structures with the even and the odd parities.
Spatial autoresonance: Enhancement of mode conversion due to nonlinear phase locking
Authors: Friedland L.
Published: July 2002

It is shown that the inclusion of weak nonlinearities may have a profound effect on the conservative linear mode conversion in inhomogeneous media. The phenomenon is demonstrated by adding a quadratic nonlinearity to the conventional system of integral equations describing spatial evolution of linear multicomponent waves. The nonlinear generalization of the reduced coupled mode equations then shows the possibility of a persistent interaction between the modes via the ‘‘spatial autoresonance,’’ i.e., the spatial self-adjustment of the nonlinear resonance condition. For a sufficiently strong nonlinearity this adjustment either (a) discontinues at some point when both interacting modes have the same action density sign and the initially excited mode transfers its action flux to the second mode, or (b) prevails indefinitely, in the case of positive–negative action density mode couplings, as the magnitudes of both modes grow continuously in space. The conditions for the spatial autoresonance are found and the effect is illustrated by numerical examples.
Long pulse x-ray emission from laser-irradiated exploding cylinders
Authors: Magelssen G. R. , Bach D. R. , Evans S. , Forslund D. W. , Hockaday R. G. , Studebaker J. K.
Published: July 2002

A CO2 laser was used to irradiate hollow polystyrene cylinders along their axis. The laser-generated high-energy electrons appear to uniformly heat the cylinder throughout its volume and the cylinder explodes. The imploding and stagnation character of the exploding cylinder gives rise to a long x-ray pulse, much longer than the laser pulse, and to a peak emission that occurs after the laser pulse. The fast ions that are generated appear not to interact with the thermal plasma. Two-dimensional calculations that reproduce much of the experimental x-ray signature and observed hydrodynamic flow are presented.
The coalescence instability and the development of current sheets in two-dimensional magnetohydrodynamics
Authors: Longcope D. W. , Strauss H. R.
Published: July 2002

A class of two-dimensional force-free equilibria are shown to be subject to an ideal linear instability. This instability is similar to the coalescence instability for chains of magnetic islands. Semianalytic methods are used to find second magnetic equilibrium which is accessible from the first and has lower magnetic energy. This equilibrium has a discontinuous magnetic field and current sheets at these discontinuities. Numerical simulations indicate that the nonlinear evolution of the instability allows the plasma to relax to this discontinuous equilibrium.
The interaction of ultrashort, powerful laser pulses with a solid target: Ion expansion and acceleration with time-dependent ambipolar field
Authors: Gamaly E. G.
Published: July 2002

The problem of ion expansion when a powerful subpicosecond laser pulse is incident upon a solid target is considered in conditions when the mean electron energy in the plasma is the function of time. It is shown that the problem can be solved for the simple case in which the electron has a power-law dependence with time during the laser pulse. The solutions which are obtained are significantly different from the well-known case of isothermal expansion. The ion density profile is much steeper and consequently the ion energy distribution has a very steep gradient in the high-energy tail. For the case when vte/vos<1 (vte and vos are the thermal and oscillation velocities of electrons, respectively) profile steepening due to the dynamics of the expansion dominates over that caused by the ponderomotive force. The problem considered is relevant to laser–matter interaction experiments where the electron energy has a strong dependence on time during the laser pulse. Some comparisons with recent experiments are presented.
Cavity mode analysis of plasma frequency waves in inhomogeneous cylindrical plasmas
Authors: Hutchinson I. H. , Gandy R. F.
Published: July 2002

A linear, electromagnetic analysis is presented of the cavity mode structure and dispersion relations for waves with frequency near the electron-plasma frequency in cylindrical plasmas with monotonically decreasing electron density and finite magnetic field. Analytic solutions are obtained which are exact in the limits when either the ratio of electron cyclotron to plasma frequency or the ratio of plasma size to parallel wavelength tends to infinity. Comparison with numerical solutions confirms that the analytic results are highly accurate even for fairly modest values of these ratios. Thermal effects are incorporated, including Landau (damping or) gain, which show the lowest-order transverse modes to have greatest gain. These modes are highly localized near the cylinder axis so that the plasma itself acts as a cavity, regardless of edge boundary conditions. The theory thus enables an interpretation to be made of maser action in quasicylindrical plasmas such as tokamaks.
Current enhancement for hose-unstable electron beams
Authors: Fernsler R. F. , Hubbard R. F. , Hui B. , Joyce G. , Lampe M. , Lau Y. Y.
Published: July 2002

An electron beam injected into a conducting medium produces inductive electric fields. These fields drive conduction currents that, for stable beams, oppose the beam current and thereby reduce the total (net) current. For unstable beams that undergo large transverse displacements, the inductive fields can reverse direction and drive conduction current parallel to the beam current. An analytic and numerical treatment of the latter effect is presented to explain current enhancement as observed for electron beams propagating in gases at pressures above 10 Torr.
Stabilization of magnetohydrodynamic modes by applied radio-frequency waves
Authors: D’Ippolito D. A. , Myra J. R.
Published: July 2002

A kinetic theory describing the nonlinear interaction of radio-frequency waves with low-frequency magnetohydrodynamic modes is presented. The calculation of the nonlinear force density on a fluid element includes both ponderomotive and sideband mode coupling terms and allows arbitrary rf wave polarization. Electromagnetic effects and wave–particle interactions are retained in the analysis. The influence of the nonlinear force on magnetohydrodynamic plasma stability is calculated self-consistently, and a generalized low-mode-number ballooning equation is obtained for paraxial magnetic mirror geometry. The low-frequency stability problem is thereby shown to involve the coupling of four waves and the system of governing equations is presented. Specialized limits of the general equations are discussed, and a physical interpretation of rf stabilization is given. It is shown that stability is enhanced by placing the antenna and conducting cavity walls close to the plasma surface.
Line-tying of interchange modes in a hot electron plasma
Authors: Gerver M. J. , Lane B. G.
Published: July 2002

The dispersion relation of low-frequency (ω≪ωci) electrostatic flute-like interchange modes in a mirror cell with a fraction α of hot bi-Maxwellian electrons, with bulk line-tying to cold (nonemitting) end walls, has been solved using a slab model and the local approximation. In the absence of line-tying, hot-electron interchange modes are never completely stabilized (in contrast to the conventional theory [Phys. Fluids 9, 820 (1966); Phys. Fluids 19, 1255 (1976)], which assumes monoenergetic hot electrons and has little relevance to real plasmas). In the presence of line-tying, hot-electron interchange modes are more effectively stabilized than magnetohydrodynamic (MHD) interchange modes, because (1) the line-tying is enhanced by a factor of (ω/νe)1/2 when the wave frequency ω is greater than the cold-electron collision frequency νe; and (2) hot-electron interchange modes can be completely stabilized, rather than merely having their growth rates reduced, if there is a spread of hot-electron-curvature drift velocities. Predictions of the minimum α needed for instability and of the first azimuthal mode number m to go unstable, and of the scaling of these quantities with neutral gas pressure, are in good quantitative agreement with observations of hot-electron interchange instabilities in the Tara tendem mirror experiment [Bull. Am. Phys. Soc. 30, 1581 (1985)], provided a correction is made for the fact that the modes in Tara are not flute-like, but should have higher amplitudes in the plug than in the central cell. The theory may also explain observations in other experiments [Phys. Fluids 27, 1019 (1984); Phys. Fluids 19, 1203 (1976)]. Increasing the ion temperature Ti should have a modest stabilizing effect. In addition to the hot-electron interchange modes, there are also ion-driven interchange modes, which are unstable even in the absence of hot electrons, but generally have low growth rates, much less than MHD growth rates. Even these modes may be completely stabilized by finite Larmor radius and line-tying when Ti is sufficiently great.
Invariance properties of the root-mean-square emittance in a linear system
Authors: Rhee M. J.
Published: July 2002

It is shown that for a beam of arbitrary distribution function, the root-mean-square emittance is invariant under any linear transformation if the determinant of transfer matrix is unity. The invariance condition is generalized by defining a normalized root-mean-square emittance to include the case with a nonunity determinant which is associated with an axial acceleration.
Solitons and beam reflection in an ion-beam plasma system
Authors: Kono Mitsuo
Published: July 2002

Reflection and acceleration of resonant particles by solitons have been studied numerically in an ion-beam plasma system based on a hybrid code. A soliton whose velocity is less than the beam velocity is amplified first in a self-similar way because of the beam bunching up to the onset of reflection and then is supplied with energy lost by the reflected beam. The soliton is saturated by emission of a baby soliton, which in turn grows again until it emits another baby soliton. These processes repeat themselves. A soliton with a velocity larger than that of the beam initiates beam acceleration. The beam reflection associated with the collision processes of solitons is also observed.
Particle gyration in the presence of nonuniform static or oscillatory electric fields: Gyrofrequency shift and gyrophase locking
Authors: Auerbach Steven P.
Published: July 2002

Gyromotion is studied by applying averaging techniques to exact equations for the guiding-center position, magnetic moment, and gyrophase. A static nonuniform force F is shown to shift the gyrofrequency from Ω to ω=Ω−∇⊥⋅(F/2mΩ). The effects of this gyrofrequency shift on heating are discussed, as is the prospect of experimentally observing the phenomenon. It is also shown that an oscillatory force of sufficient amplitude, whose frequency ω* is close to Ω, can cause phase locking, i.e., can force the particle to gyrate at the driving frequency ω*. A rough criterion for an electrostatic wave with electric field E to cause phase locking is that vE/ρδω≥1, where vE =cE/B, ρ is the gyroradius, and δω=ω*−Ω. Thus a weak wave can cause phase locking if the frequency mismatch is small. Phase locking is enhanced if the magnetic field has a well, which provides a large volume over which ‖B‖ is nearly uniform. Comparison with experimental measurements on the 2XIIB magnetic mirror experiment [J. Phys., Coll. 6, Suppl. No. 12, 38, C6 (1977)] shows that phase locking may account for the puzzling observation of a highly monochromatic wave at the central cyclotron frequency.
Finite ion temperature effects on collisional and semicollisional tearing modes
Authors: Dong J. Q. , Guzdar P. N. , Lee Y. C.
Published: July 2002

The finite ion gyroradius effects on the stability of global tearing modes are studied using analytic and numerical techniques. It is found that in the collisional regime the modes are weakly stabilized compared to the zero ion temperature case. In the semicollisional regime, the stabilization is weaker than the polarization drift stabilization in the zero ion temperature case. There is overall a very minor finite ion temperature modification of the stability boundary in the plasma beta, collisionality space.
Enhancement of limiting current of charged particle beams by ponderomotive energy
Authors: Grebogi Celso , Uhm Han S.
Published: July 2002

A mechanism is proposed to greatly increase the space charge limiting current. It consists of making use of the negative ponderomotive energy of some appropriate cavity mode to thwart the buildup of the beam electrostatic energy. For present microwave technology, the calculations show, for instance, that a 70% increase in the limiting current of a 250 kV relativistic electron beam looks achievable.
Experimental test of the perturbation expansion for the Taylor instability at various wavenumbers
Authors: Heinrichs Richard M. , Cannell David S. , Ahlers Guenter , Jefferson Michael
Published: July 2002

Measurements of the Fourier components of the axial variation of the velocity component w in a Taylor–Couette apparatus containing ten pairs of vortices at various average wavenumbers q, as a function of ε≡R/Rc−1, are reported. For all values of q studied, excellent agreement with the perturbation expansion of Davey [J. Fluid Mech. 14, 336 (1962)] for the amplitudes of the Fourier components was obtained, provided the power law dependence on ε was taken as a function of ε̃≡ε−εm(q). Here εm(q) is the marginal stability curve, below which the laminar flow state is stable against perturbations of wavenumber q. The wavenumber dependence of the leading coefficients in the expansions for the fundamental and first harmonic was also measured, and it was found that while the coefficient for the fundamental was independent of q, the coefficient for the first harmonic monotonically decreased with increasing q, over the range studied.
The decay of a viscous vortex pair
Authors: Cantwell Brian , Rott Nicholas
Published: July 2002

The evolution of a viscous vortex pair is investigated through the use of a heuristic model. The model is based on the linear superposition of two Oseen vortices of opposite circulation spaced a distance 2b apart. The vortices are allowed to evolve through viscous diffusion and their mutual induction. The motion is unforced and as a consequence the total hydrodynamic impulse is exactly conserved for all time. In the model the total circulation in the upper half plane is assumed to remain initially constant. This constraint is applied up to a finite time when the model solution reaches its asymptotic form corresponding to a drifting Stokes dipole dominated by interdiffusion of vorticity across the plane of symmetry. The drift velocity of the vortex pair is determined by the condition that the integrated pressure force vanishes on the line of symmetry at all times. At large time this leads to an asymptotic value of the drift velocity which scales with the similarity properties of the Stokes solution. To provide a more rigorous foundation for the drift, the asymptotic behavior of the flow for large time is investigated through an expansion of the solution in inverse powers of the time. First the second-order pressure is determined as a solution of a Poisson equation with the source term generated by the first-order flow field. Surprisingly, the solution turns out to be independent of the drift. Nevertheless, an exact condition for the drift is found by considering the limiting form of the second-order pressure at infinity where the flow is irrotational and the pressure can be computed directly from the first-order velocity field using Bernoulli’s equation. In this latter approach the far field pressure is determined up to an unknown function of time which upon comparison with the Poisson solution is identified as the drift. The exact drift obtained in this fashion differs by only 10% from the value obtained using the pressure field of the heuristic model. Finally, it is shown that the existence of the complete second-order asymptotic solution of the Navier–Stokes equations requires the inclusion of the same drift in the first-order solution that was found from the examination of the pressure. The second-order vorticity and streamfunction are determined; the latter contains a

free constant to accommodate conditions at earlier times. Prospects for the existence of higher-order asymptotic terms are discussed.
Gravity flow of a viscous liquid down a slope with injection
Authors: Schwartz Leonard W. , Michaelides Efstathios E.
Published: July 2002

The free-surface lubrication equations are solved numerically for the time-dependent three-dimensional flow down an inclined plane produced by continuous injection through a circular orifice in the plane. The flow pattern ultimately becomes steady with stream depth and width scaling as the − (1)/(7) th power and (3)/(7) th power of the downslope distance from the orifice, in agreement with a known similarity solution. The predicted stream width gives partial agreement with a recent experimental result, even though significant thermal effects were present in the experiment. The physical prototype is flow of lava.
On the nonspherical collapse and rebound of a cavitation bubble
Authors: Zhang Sheguang , Duncan James H.
Published: July 2002

The behavior of a cavitation bubble adjacent to a rigid wall is studied numerically with the boundary integral method described in Zhang, Duncan, and Chahine [J. Fluid Mech. 257, 147 (1993)]. In the previous work, the pressure inside the bubble was held constant (this is referred to herein as the empty bubble case). In the present calculations, an internal gas pressure, which is a function of the bubble volume, is included in the model. The present results are qualitatively similar to those in the empty bubble case in several ways: a wall-directed reentrant jet is formed in the later phase of the collapse; this jet impacts with the side of the bubble closest to the wall creating a toroidal-shaped bubble; and a shear layer develops along the impact interface. However, unlike the empty bubble, whose volume decreases monotonically to zero at the end of the collapse, the present gas-filled bubble reaches a minimum volume and then, due to its high internal gas pressure, begins to grow again (rebound). In the empty bubble case, the hydrodynamic pressure on the wall rises rapidly at the end of the calculation making it impossible to compute the maximum value of the pressure. In the present calculations, the pressure on the wall is found to reach a maximum value when the bubble starts to rebound. This timing of the pressure peak is in agreement with the experimental data of Tomita and Shima [J. Fluid Mech. 169, 535 (1986)] and Kimoto [International Symposium on Cavitation Research Facilities and Techniques (American Society of Mechanical Engineers, New York, 1987), Vol. 57, pp. 535–564], as are the orders of magnitude of the maximum pressures. Direct comparison with the numerical results of Best [J. Fluid Mech. 251, 79 (1993)] are also presented. Large differences in bubble shapes and flow fields are found.
The self-similar topology of passive interfaces advected by two-dimensional turbulent-like flows
Authors: Vassilicos J. C. , Fung J. C. H.
Published: July 2002

We study the topology, and in particular the self-similar and space-filling properties of the topology of line-interfaces passively advected by five different 2-D turbulent-like velocity fields. Special attention is given to three fundamental aspects of the flow: the time unsteadiness, the classification of local spatial flow structure in terms of hyperbolic and elliptic points borrowed from the study of phase spaces in dynamical systems and a classification of flow structure in wavenumber space derived from the studies of Weierstrass and related functions. The methods of analysis are based on a classification of interfacial scaling topologies in terms of K- and H- fractals, and on two interfacial scaling exponents, the Kolmogorov capacity DK and the dimension D introduced by Fung and Vassilicos [Phys. Fluids 11, 2725 (1991)] who conjectured that D≳1 implies that the interface is H-fractal. An argument is presented (in the Appendix) to show that D≳1 is a necessary condition for the evolving interface to be H-fractal through the action of the flow, and that D≳1 is also sufficient provided that no isolated regions exist where the flow velocity is either unbounded or undefined in finite time. D is interpreted to be a degree of H-fractality and is different from the Hausdorff dimension DH. In all our flows, steady and unsteady, interfaces in particular realisations of the flow reach a non-space-filling steady self-similar state where D and DK are both constant in time even though the interface continues to be advected and deformed by the flow.

It is found that D is equal to 1 in 2-D steady flows and always increases with unsteadiness, that DK generally decreases with unsteadiness where the interfacial topology is dominated by spirals, and that DK increases with unsteadiness where the interfacial topology is dominated by tendrils. In those flows with larger number of modes, DK is a non-increasing function of unsteadiness and a decreasing function of the exponent p of the flow’s self-similar energy spectrum E(k)∼k−p. DK’s decreasing dependences on unsteadiness and the exponent p can be explained by the presence of spirals in the eddy regions of the flow. The values of D and DK and their dependence on unsteadiness can change significantly only by changing the distribution of wavenumbers in wavenumber space while keeping the phases and energy spectrum constant.
On the modeling of homogeneous turbulence in a stably stratified flow
Authors: Sommer T. P. , So R. M. C.
Published: July 2002

The decay of incompressible, homogeneous turbulence in a stably stratified medium is investigated. A conventional high-Reynolds-number, two-equation model with suitable improvements for buoyancy effects is used to calculate the velocity field, while an explicit algebraic heat-flux model that depends on the velocity field and the transport of the temperature variance and its dissipation rate is invoked for the temperature field. The model thus derived could account for buoyancy flux and streamwise heat transport correctly and is used to investigate the decay of grid generated turbulence in a stably stratified medium. This class of flows displays countergradient transport of the vertical turbulent heat flux. Flows with buoyancy frequencies ranging from 0 to 2.42 are calculated. The results are compared with experimental data as well as with the calculations of a constant turbulent Prandtl number model, an algebraic-flux model and a second-order closure. The present model is found to be capable of correctly reproducing the countergradient heat transport phenomenon and the turbulence decay characteristics over the range of buoyancy frequency studied. However, the countergradient heat transport region is not captured by the algebraic flux and the constant turbulent Prandtl number model. Furthermore, the present results are in good agreement with data and with the predictions of a second-order closure.
Nonclassical effects in two-dimensional transonic flows
Authors: Schnerr G. H. , Molokov S.
Published: July 2002

The scientific interest and motivation for the investigation of Bethe–Zel’dovich–Thompson (BZT) fluids follows from the fact that all the nonclassical phenomena for these fluids occur for single phase standard fluids in equilibrium when the perfect gas law is replaced by a more realistic equation of state. Among others there are two most immediate and interesting engineering applications for these fluids, as working fluids in Rankine cycles of power systems and for proper design of fuel injectors in typical automotive or aircraft engines. Here we study transonic flows of BZT fluids and present exact solutions to the steady, two-dimensional transonic small disturbance equation in the physical and in the hodograph plane. The equations of the characteristics in the hodograph plane are obtained for the transonic small-disturbance equation of the second-, third-, and fourth-order nonlinearity. The solutions for inviscid, shock-free, transonic vortex flow, Ringleb flow, subsonic and sonic jets, and viscous radial flow are presented for BZT fluids.