bluuebunny/crossref_metadata_2025 huggingface dataset:
Laser-produced plasma with large amplitude density modulation of controllable wavelength
Authors: Laberge M. , Meyer J.
Published: July 2002

A 6 nsec 1010 W/cm2 ruby laser pulse irradiates a grating with spacing in the 6–35 μm range. The expansion of the plasma above the surface is observed using interferometry and shadowgraphy. The plasma is found to be modulated with ñ/n up to 8%. Such a plasma can be used to accelerate charged particles.
Accelerator and target studies for heavy ion fusion at the Gesellschaft für Schwerionenforschung
Authors: Meyer-ter-Vehn J. , Witkowski S. , Bock R. , Hoffmann D. H. H. , Hofmann I. , Müller R. W. , Arnold R. , Mulser P.
Published: July 2002

The new Schwerionen-Synchrotron (SIS)/Experimenteller Speicher-Ring (ESR) heavy ion accelerator facility [Nucl. Instrum. Methods A 278, 7, 19 (1989)], built for basic atomic and nuclear physics at Darmstadt (Federal Republic of Germany), also provides unique possibilities to study rf accelerator and beam/target interaction physics for inertial confinement fusion driven with heavy ion beams. It is the first machine that offers this opportunity. Beam parameters and experiments planned over the next five years are discussed.
MeV ion confinement in the TFTR tokamak
Authors: Zweben S. J. , Boivin R. L. , Duvall R. E. , Fredrickson E. D. , Goldston R. J. , Mynick H. E. , Strachan J. D. , White R. B.
Published: July 2002

In this paper the confinement of the MeV ions that are created by D–D reactions in the TFTR tokamak [in Plasma Physics and Controlled Nuclear Fusion Research 1988 (IAEA, Vienna, 1989), Vol. 1, p. 27] is described. The ions that escape from the plasma are measured by a new type of detector located just outside the plasma edge. Most measurements made with this detector are consistent with the first-orbit loss of these ions. Exceptions are correlated with strong magnetohydrodynamic activity, and a preliminary explanation is presented.
Neoclassical quasilinear transport theory of fluctuations in toroidal plasmas: Further considerations
Authors: Shaing K. C.
Published: July 2002

The effects of the radial electric field Er on fluctuation-induced transport fluxes and the fluctuation spectrum in toroidal plasmas are further studied to clarify the ideas originally developed in an earlier paper [Phys. Fluids 31, 2249 (1988)]. A specific tokamak example is employed in the discussion. It is found that even in the presence of fluctuations, the parallel flow in tokamaks is damped by the neoclassical viscosity on a time scale of the order of ν−1ii, with νii the collision frequency. The toroidal flow is damped by the anomalous ion viscosity on a time scale of the order of the confinement time. The radial electric field always has an effect on the fluctuation spectrum and fluctuation-induced transport fluxes in tokamaks except when d(Erq/r)/dr=0 (where q is the safety factor and r is the minor radius) if the radial dependence of the toroidal magnetic field is neglected by considering the invariant property of the drift kinetic equation when there is a change in Er. The condition implies the rigid-body toroidal rotation associated with E×B drift, with E (B) the electric (magnetic) field. The fact that the fluctuation-induced transport fluxes can depend on Er through the fluctuation spectrum and the thermodynamic force does not contradict their intrinsic ambipolarity property. The results are shown to be invariant under Galilean transformation.
Nonlinear dynamics of the gyrotron traveling wave amplifier
Authors: Chu K. R. , Barnett L. R. , Lau W. K. , Chang L. H. , Lin A. T. , Lin C. C.
Published: July 2002

Mode interactions in the gyrotron traveling wave tube amplifier (gyro-TWT) are examined with particle simulations and compared with experimental observations. Studies focus on the competition between the absolute and convective instabilities. Detailed diagnostics on mode structures, field growth profiles, and evolution of electron distribution in momentum and energy spaces allow an in depth look at the basic physical processes, such as the mechanism of mode competition and suppression. Mutual verifications between the theory and experiment have strengthened understanding of the multimode behavior and added to the predictability of high-power gyro-TWT’s.
Collisionless plasma transport across loop magnetic fields
Authors: Horton W. , Liu C. , Burns B. , Tajima T.
Published: July 2002

Collisionless transport properties of a plasma across loop magnetic fields devoid of a toroidal component are considered. In particular, chaotic single particle orbits in the geomagnetic tail are used to calculate the collisionless electrical conductivity. It is shown that the stochasticity from inhomogeneous magnetic fields leads to a power law decay of the single particle correlation function similar to an elastic collisional process. The height integrated dissipative part of the collisionless conductivity governs the irreversible stochastic heating of the plasma sheet. Formulas for the electrical conductivity as a function of the finite gyroradius parameter and the aspect ratio of the magnetic field loops are derived and tested numerically.
Toroidal ion temperature gradient-driven weak turbulence
Authors: Mattor Nathan
Published: July 2002

In this paper, a theory of toroidal ion temperature gradient-driven weak turbulence near the threshold is presented. The model considers gyrokinetic ions and adiabatic electrons in toroidal geometry. The linear theory considers modes with kθρi∼O(1) (generally not considered in toroidal theories), giving a toroidal threshold regime dominated by transit resonances (as opposed to the more usually considered drift resonances), and with a stability threshold of ηtorthresh≂1+2εn[2/τ+1/(1+ŝ)]. It is shown that when 0<ηi−ηtorthresh<2(1+1/τ)1/2 ×Ln/(RLT)1/2 then 0<γ<ωr, and a weak turbulence expansion can be used to treat the nonlinearity. The instability is saturated via nonlinear ion resonance, and it is shown that this nonlinear process transfers energy directly from the waves to the ion distribution function, and does not conserve wave energy. The saturated spectrum is calculated, and the resulting ion thermal conductivity is found to be χi=(1+1/τ)1/2[(ηi−ηtorth/ηi] ((LT)1/2/R3/2)ρ3iΩi, which is smaller than typical mixing length estimates by a factor of about LT/R, but in the range of tokamak observations. The diffusive nature of the transport (requiring a short radial step size) is reconciled with the broad radial extent of the toroidally coupled linear modes by postulating that it is the nonlinear beat wave between linear modes (not the radial width of a single linear mode) that determines the step length appropriate for transport.
Destabilized ion acoustic mode in toroidal plasmas
Authors: Hirose A.
Published: July 2002

An unstable long-wavelength electrostatic mode well described by ω≂ωs (the ion acoustic transit frequency) has been identified in an isothermal (Ti≂Te) tokamak. The ion Landau damping is prohibited by the ion magnetic drift provided ω≳0. For realistic discharge parameters, the mode frequency exceeds the diamagnetic frequency by a factor 2 to 3 at the stability boundary.
Numerical simulation of ion-temperature-gradient-driven modes
Authors: Xu X. Q. , Rosenbluth M. N.
Published: July 2002

Ion-temperature-gradient-driven modes in the presence of ion–ion collisions in a toroidal geometry with trapped ions have been studied by using a one-and-one-half-dimensional (11/2-D) linearized gyrokinetic particle simulation code in the electrostatic limit. The purpose of the investigation is to try to understand the physics of flat density discharges, in order to test the marginal stability hypothesis. Results giving threshold conditions of LTi/R0, and linear growth rates and mode frequencies over all wavelengths for the collisionless ion-temperature-gradient-driven modes are obtained. The behavior of ion-temperature-gradient-driven instabilities in the transition from slab to toroidal geometry, with trapped ions, is shown. A Monte-Carlo scheme for the inclusion of ion–ion collisions, in which ions can undergo Coulomb collisional dynamical friction, velocity space diffusion, and random walk of guiding centers, has been constructed. The effects of ion–ion collisions on the long wavelength limit of the ion modes is discussed.
Double plasma and grid excitation of sinusoidal ion acoustic waves
Authors: Schott Ludwig
Published: July 2002

Sinusoidal ion acoustic waves are excited in a double plasma device by applying a signal either between the driver and the target plasma (DP mode) or directly to the grid that separates the two plasmas (grid mode). The amplitude of the waves close to the grid is not a smooth function of frequency but it has distinct extrema. The experimental results are in qualitative agreement with a simple model, which assumes that the waves are excited by modulated ion beams that pass symmetrically in both directions through the grid.
Plasma corners. II: Arbitrary profiles
Authors: Spies G. O.
Published: July 2002

Ordinary plasma corners are studied in two-dimensional magnetohydrostatic equilibria with arbitrary axial current density profiles. The corner structure depends only on the nearby current density profile and the multiplicity of the magnetic stagnation point. A simple corner, for instance, is right-angled if the current density is bounded at the separatrix or diverges more slowly than any power of the poloidal magnetic flux, but is acute-angled or even cusped otherwise. As an application, the magnetohydrodynamic interchange stability criterion is shown to be violated near simple corners in Z-pinch equilibria.
The coalescence instability in collisionless plasmas
Authors: Pritchett P. L.
Published: July 2002

The process whereby magnetic island structures tend to merge into larger units is known as magnetic island coalescence. This coalescence process is investigated for the case of a collisionless plasma by means of two-dimensional particle simulations. The pairwise merging of a preformed island chain leads to a gentle redistribution of the density and current density profiles. The linear growth rates substantially exceed the magnetohydrodynamic (MHD) values for ρ/λ≥0.1, where ρ is the asymptotic ion gyroradius and λ is the current sheet half-thickness. The nonlinear evolution of the collisionless tearing instability in a long system is found to lead to a much more violent coalescence process resulting in the formation of a vacuum X region. This stage is characterized by enhanced growth rates for the long-wavelength modes that exceed the maximum linear tearing growth rate, super-Alfvénic flows away from the reconnection X line, substantial bulk heating in the parallel direction, and the formation of energetic particle tails in the direction of the inductive electric field.
Theory of energetic alpha-particle-driven Alfvén wave turbulence
Authors: Gang Fongyan
Published: July 2002

A theory of energetic alpha-particle-driven Alfvén wave turbulence is presented. Attention is focused on the nonlinear saturation of turbulence through bulk ion Compton scattering. It is found that the ion Compton scattering, while conserving total fluctuation energy, induces a nonlinear spectral shift away from linear alpha particle growth rate toward higher poloidal wave number kθ, thus reducing the power transfer between the energetic alpha particles and the Alfvén wave turbulence. Saturation is obtained when this reduced alpha-Alfvén wave power transfer is balanced by the linear electron Landau damping. The saturation level of turbulence and turbulent particle transports for both energetic alphas and bulk plasmas are calculated. The implications of these results on the alpha particle and bulk plasma confinement are discussed.
Three-dimensional non-neutral plasma shapes
Authors: Peurrung A. J. , Fajans J.
Published: July 2002

The three-dimensional shapes of azimuthally asymmetric non-neutral plasmas are investigated numerically, and a simple theory is developed that predicts these shapes in many circumstances.
Modification of short scale-length tearing modes by the Hall field
Authors: Fruchtman A. , Strauss H. R.
Published: July 2002

The calculation of the growth rate of tearing modes is extended to short scale lengths by including the Hall field. A unified dispersion relation is found that describes usual tearing modes at one limit and the Hall tearing modes with the enhanced growth rate at the opposite limit. The dispersion relation is valid for both collisional and collisionless plasmas.
Adjustable levels of strong turbulence in a positive/negative ion plasma
Authors: Sheehan D. P. , McWilliams R. , Rynn N.
Published: July 2002

Positive/negative ion plasmas, composed of Ba+, SF6−, and residual electrons, were observed to display characteristics of strong turbulence. Experiments on the UCI Q machine linked the presence of negative ions (and the depletion of electrons) with large density fluctuations (δn/n≂1), large-amplitude, low-frequency electrostatic noise (f≤20 kHz), and rapid transport of ions across magnetic field lines (D⊥≂104 cm2/sec). Ion velocity distributions were heated parallel to and cooled perpendicular to the confining magnetic field. The partial pressure of gaseous SF6 was shown to serve as a regulator of plasma turbulence. Turbulence levels could be smoothly varied from quiescent states (δn/n≂0.01) to strongly turbulent states (δn/n≂1).
Edge turbulence and total radiation in the TJ-I tokamak
Authors: Ochando M. A. , Pedrosa M. A. , Balbín R. , García-Cortés I. , Hidalgo C.
Published: July 2002

The correlation between edge radiation, electron temperature, and density fluctuations has been studied in the vicinity of the upper poloidal limiter of the TJ-I tokamak [Phys. Fluids B 4, 4007 (1992)]. When edge impurity radiation is strongly peaked in the proximity of the limiter radius, electron temperature fluctuations are notably higher than density fluctuations. Results suggest that edge turbulence may be driven by radiative instabilities.
Viscous flow through a rotating square channel
Authors: Kheshgi Haroon S. , Scriven L. E.
Published: July 2002

Fully developed flow of an incompressible Newtonian fluid driven by a pressure gradient through a square channel that rotates about an axis perpendicular to the channel roof is analyzed here with the aid of the penalty/Galerkin/finite element method. Coriolis force throws fast-moving fluid in the channel core in the direction of the cross product of the mean fluid velocity with the channel’s angular velocity. Two vortex cells form when convective inertial force is weak. Asymptotic limits of rectilinear flow and geostrophic plug flow are approached when viscous force or Coriolis force dominates, respectively. A flow structure with an ageostrophic, virtually inviscid core is uncovered when Coriolis and convective inertial forces are both strong. This ageostrophic two-vortex structure becomes unstable when the strength of convective inertial force increases past a critical value. The two-vortex family of solutions metamorphoses into a family of four-vortex solutions at an imperfect bifurcation composed of a pair of turning points.
Electron-cyclotron maser instability caused by hot electrons
Authors: Wong H. K. , Wu C. S. , Gaffey J. D.
Published: July 2002

The electron-cyclotron maser instability is studied for energetic electrons with a loss-cone distribution. The instability can occur at all angles of propagation for a wide range of parameters. The growth rate is significantly reduced by the presence of a population of cold electrons, and the instability can be supressed if the density of the cold electrons is sufficiently large and the temperature of the energetic electrons is not too high.
Operation of a plasma focus device as a compact electron accelerator
Authors: Smith John R. , Luo C. M. , Rhee M. J. , Schneider R. F.
Published: July 2002

The electron beam produced by a compact plasma focus device has been investigated. The Mather geometry plasma focus electrodes were modified to permit extraction of accelerated electrons. Performance of the plasma focus as an electron accelerator using different gas species and pressures is investigated. Also, results from measurements of the beam parameters are given.
Magnetic surface wave instabilities in plasmas
Authors: Yu M. Y. , Stenflo L.
Published: July 2002

Techniques of plasma surface wave theory are introduced to obtain new results for magnetic electron waves at the interface of two plasma regions with distinct properties. The procedure generalizes and simplifies problems involving sharp density jumps often encountered in laser– or beam–plasma interaction. As an example, a new magnetic instability is discussed.
Filamentation instability of a self-pinched hollow electron beam
Authors: Uhm Han S. , Hughes Thomas P.
Published: July 2002

Filamentation stability properties of a self-pinched hollow electron beam propagating through a collisional plasma channel are investigated within the framework of linearized Vlasov–Maxwell equations, assuming that the beam is thin and that the equilibrium and perturbed space-charge fields are neutralized by background plasma. It is further assumed that the perturbations are well tuned with kβbc+lωb and satisfy la≪R0, where l and k are the azimuthal and axial wavenumbers, βbc and ωb are the axial velocity and the rotational frequency of the beam, and 2a and R0 are the thickness and mean radius of the beam. From the stability analysis, two distinctive unstable mechanisms are identified: the return-current driven instability and the resistively driven instability. It is also found that high-l-mode perturbations are easily stabilized by a spread in the canonical angular momentum. Making use of a linearized particle-in-cell code, numerical simulations are performed. The agreement between the analytical results and those of simulations is excellent.
Comparison of collision operators for drift and magnetohydrodynamic-interchange modes in unsheared slab geometry
Authors: Rewoldt G. , Tang W. M. , Hastie R. J.
Published: July 2002

The general procedure for the kinetic analysis of low-frequency electrostatic and electromagnetic modes in toroidal geometry is now well known. In the collisionless limit the relevant dynamics (e.g., trapped particles, resonances, etc.) can be treated appropriately. However, with the introduction of collisional effects, it is customary for tractability to employ model collision operators that do not rigorously satisfy all conservation properties of more exact collision operators. Insight into the essential required features of such operators can be gained by studying models with increasing levels of completeness for a simpler, unsheared slab geometry. The results presented here for this simpler geometry can provide guidance in choosing model collision operators for toroidal-geometry kinetic calculations.
A thermal distribution function for relativistic magnetically insulated electron flows
Authors: Desjarlais M. P. , Sudan R. N.
Published: July 2002

A distribution function is presented that may be used to study the effects of finite temperature on the equilibrium and stability properties of magnetically insulated electron flows. This distribution function has the useful property that it generates the thoroughly studied class of constant Q=ω2p/Ω2 equilibria in its zero-temperature limit. Analytic solutions are given for the general, constant Q, zero-temperature equilibria.
A full wave description of the accessibility of the lower-hybrid resonance to the slow wave in tokamaks
Authors: Woods A. M. , Cairns R. A. , Lashmore-Davies C. N.
Published: July 2002

Mode conversion between the fast and slow electromagnetic waves in the lower-hybrid frequency range is considered. This phenomenon determines the accessibility of the lower-hybrid resonance to the slow wave, and is also of theoretical interest because the mode coupling differs in certain aspects from cases previously investigated by the authors and others. A second-order approximation is used in the mode conversion region leading to Weber’s equation from which transmission coefficients are then obtained in various cases. Ray-tracing results are recovered for a plasma with a linear density profile in a uniform magnetic field. The effect of including a magnetic field gradient is to move the mode conversion region to the plasma edge. The second part of the paper provides justification for the use of Weber’s equation. The exact fourth-order system of ordinary differential equations for the problem is set down and a linear transformation, which is an extension of that given by Heading, reveals the second-order nature of the coupling process. Numerical solutions of the fourth-order system yield transmission coefficients in excellent agreement with the second-order theory, and also demonstrate that the electric field variation across the mode conversion region is well approximated, via the above transformation, by the second-order theory.
Kinetic description of harmonic instabilities in a planar wiggler free-electron laser
Authors: Davidson Ronald C.
Published: July 2002

The linearized Vlasov–Maxwell equations are used to investigate harmonic stability properties for a planar wiggler free-electron laser (FEL). The analysis is carried out in the Compton regime for a tenuous electron beam propagating in the z direction through the constant-amplitude planar wiggler magnetic field B0=−Bw  cos k0zêx. Transverse spatial variations are neglected (∂/∂x =0=∂/∂y), and the case of an FEL oscillator (temporal growth) is considered. Assuming ultrarelativistic electrons and κ2=a2w/(γ20−1) ≪1, where a2w =e2B2w /m2c4k20 and γ0mc2 is the electron energy, the kinetic dispersion relation is derived in the diagonal approximation for perturbations about general beam equilibrium distribution function G+0(γ0). Because of the wiggler modulation of the axial electron orbits, strong wave–particle interaction can occur for ω≊[k+k0(1+2l)] βFc, where βFc is the axial velocity, ω and k are the wave oscillation frequency and wavenumber, respectively, and l=0, 1, 2, . . . are harmonic numbers corresponding to an upshift in frequency. The strength of the lth harmonic wave–particle coupling is proportional to Kl(b1) =[Jl (b1)−Jl+1 (b1)]2, where b1=(k/8k0)κ2. Assuming that G+0(γ0) is strongly peaked around γ0=γ̂≫1, detailed lth harmonic stability properties are investigated for (a) strong FEL instability corresponding to monoenergetic electrons (Δγ=0), and (b) weak resonant FEL instability corresponding to a sufficiently large energy spread that ‖Im ω/[k+k0(1+2l)] Δvz ‖≪1.

For monoenergetic electrons the characteristic maximum growth rate scales as [Kl (b̂1)(1+2l)]1/3, which exhibits a relatively weak dependence on harmonic number l. Here, b̂1= 1/2 [a2w/(2+a2w)] (1+2l). On the other hand, for weak resonant FEL instability, the growth rate scales as Kl (b̂1)/(1+2l), which decreases rapidly for harmonic numbers l≥1.
Electrostatic end plugging accompanied by a central-cell density increase in an axisymmetric tandem mirror
Authors: Ferron J. R. , Goulding R. , Nelson B. A. , Intrator T. , Wang En Yao , Severn G. , Hershkowitz N. , Brouchous D. , Pew J. , Breun R. A. , Majeski R.
Published: July 2002

Electrostatic end plugging is observed in a completely axisymmetric, three cell tandem mirror under conditions where the central-cell plasma density is always larger than the end-cell density. A factor of 4 increase in the central-cell density, to a maximum of 1.2×1013 cm−3 with simultaneous plasma beta of 13%, occurs upon application of the end plugging potential. Ion confining potentials of 25 V and 80 V at the two ends of the device, respectively, result in a factor of 2.5 increase in the axial confinement time for Tic =40 eV in agreement with the collisional flow model for ion confinement. The non-Boltzmann ion confining potential is caused by electron heating in the end cells by rf near the ion-cyclotron frequency. The initial central-cell density rise is caused by an increase in the ionization rate that occurs because of an increase in the electron temperature. The density remains high throughout the end-cell heating pulse as a result of increased particle confinement time. There is no nonambipolar radial ion loss in the core plasma (r≤16 cm) but inward radial transport of ions is observed at a rate consistent with ion–neutral collisions and a radial electric field in the negative radial direction. Steady-state thermal-barrier-like potential dips that are in agreement with the Boltzmann model for potentials are observed in the transitions between the central cell and the end cells.
Cool electron beam steady flows
Authors: Amendt Peter , Weitzner Harold
Published: July 2002

An improved warm fluid model [Phys. Fluids 28, 949 (1985)] constructed from moments of the relativistic Vlasov equation is used to examine classes of cool electron steady flows. A new family of cool steady flows is identified which is distinguished from the Bennett profile by a far less restrictive set of assumptions. In a sense the generality of these cool flows is more typical of the freedom found in strictly cold beam steady flows. Some examples are provided. The Bennett pinch is reexamined on the basis of an extension of this warm fluid model. It is found that the conditions necessary for neglecting heat flow also restrict the Bennett radius to be no larger than a beam skin depth when the beam temperature is isotropic and low. This maximum Bennett radius is shown to yield the Alfvén current limit exactly. For anisotropic beams the Bennett radius is reduced and is on the order of a Debye length. Through use of this fluid modeling, an essential connection between temperature, fractional charge neutralization, and the relativistic dilatation factor is found. The case of a rotating cool electron column is also analyzed through this fluid model. A rigid rotor solution is found only when the rest frame pressure is isotropic, which is in agreement with Newcomb’s [Phys. Fluids 29, 1854 (1986)] earlier result. When the rest frame pressure is anisotropic a particular sheared rotor solution is found. The use of this warm fluid modeling is intended to demonstrate a delicate interplay between the steady flow profiles possible and the thermodynamic properties of a relativistic beam.
Stability of ideal and resistive internal kink modes in toroidal geometry
Authors: Hastie R. J. , Hender T. C. , Carreras B. A. , Charlton L. A. , Holmes J. A.
Published: July 2002

The stability of the ideal and resistive m=1 internal modes is investigated for tokamak equilibria having a variety of different q(r) profiles, including nonmonotonic q(r) with multiple q=1 surfaces. Detailed comparisons between analytic theory and numerical results from a linear toroidal magnetohydrodynamic code are presented. Particular attention is paid to the study of equilibria that are near marginal stability.
Experimental studies of Raman scattering from foam targets using a 0.35 μm laser beam
Authors: Figueroa H. , Joshi C. , Clayton C. E.
Published: July 2002

Experimental studies of the forward scattered spectrum and stimulated Raman backscattering from foam targets are presented. An attempt has been made to isolate the effects of the presence of the quarter critical density on the Raman spectrum by creating plasmas with various peak plasma densities. The plasmas created had a length larger than 600 μm and a variable peak density between 0.11nc and slightly higher than 0.25nc. The total Raman reflectivity in the backward direction is of 0.3%, with 80% of its energy being scattered in a range of frequencies between 470 nm and 500 nm for all the targets used. The scattered intensity near the half-harmonic region shows a weak dependence on the presence of the nc/4 density layer. The forward scattered spectrum obtained from targets with average densities between 0.11nc and 0.22nc shows a broadband of frequencies similar to the backscattered spectrum indicating that the forward spectrum is probably being seeded by the beating of the plasma wave from stimulated Raman backscattering (SRS-B) with the ion acoustic wave from stimulated Brillouin scattering (SBS).
Strong shocks in an exponential atmosphere
Authors: Yousaf M.
Published: July 2002

An approximate method for estimating the strength of the overtaking wave developed by Chisnell and the present author [J. Fluid Mech. 120, 523 (1982)] is applied to the motion of a strong shock wave in a medium with exponentially varying density. The strength of the overtaking wave is calculated for various values of γ, the ratio of specific heats. There is a significant improvement in the accuracy of the propagation parameter for most values of γ.
Thermodynamic stability analysis of current-carrying plasmas
Authors: Brinkmann R. P.
Published: July 2002

A thermodynamic model is developed for plasma systems that are forced to carry an electrical current which prevents relaxation into global thermodynamic equilibrium. Complementary to earlier approaches in the framework of resistive magnetohydrodynamics, the role of nonresistive dissipation is analyzed by excluding momentum transfer between different particle species (electrons and ions). The general class of steady states compatible with the assumptions is found and their structures and symmetries are discussed. The second law of thermodynamics guarantees the existence of a generalized thermodynamic potential (including contributions of the electromagnetic field) which has a negative time derivate for all dynamical states subject to the equilibrium symmetry and boundary conditions. Applying Lyapunov’s theory, this functional provides a necessary and sufficient stability criterion. The linearized version of this criterion and the corresponding eigenvalue problem are also derived.
Boundary layer stability calculations
Authors: Bridges Thomas J. , Morris Philip J.
Published: July 2002

In this paper numerical calculation of the spatial stability of disturbances in the parallel and nonparallel Blasius boundary layers is considered. Chebyshev polynomials are used for discretization. The problem with the boundary condition at infinity is overcome, and the resulting nonlinear matrix eigenvalue problem is attacked directly. The secondary eigenvalue problem for three-dimensional disturbances is shown to be uniformly stable, and particular solutions of this problem generated by the Orr–Sommerfeld equation are shown. A numerical solution of the nonparallel problem is considered using Chebyshev polynomials. The matrix equations are analyzed directly and the problem of uniqueness of the nonparallel correction is settled by careful application of the Fredholm alternative. Nonparallel corrections to the streamwise eigenfunction are shown.
Transport processes in random arrays of cylinders. I. Thermal conduction
Authors: Sangani A. S. , Yao C.
Published: July 2002

A numerical method is developed that takes into account the many-particle interactions in a rigorous manner to determine the effective thermal conductivity Km of a composite medium consisting of parallel circular cylinders of thermal conductivity αk suspended in a matrix of conductivity k. Numerical results for Km are presented for a wide range of α and φ, the area fraction of the cylinders, after averaging over several computer-generated random arrays of cylinders. The results obtained via this exact method are compared with those of various approximate analytical methods to assess their utility in predicting Km.
The plasma as a phase conjugate reflector
Authors: Nebenzahl I. , Ron Amiram , Tzach David , Rostoker Norman
Published: July 2002

Plasma is a nonlinear medium and two waves propagating in it interact electromagnetically with each other. If the plasma is pumped by two strong counterstreaming waves of equal frequency, and a third wave enters, the nonlinear interaction generates a fourth wave, phase conjugate to the third wave. This interaction becomes very significant if the frequency and wave vector differences between the third wave and one of the pump waves resonate with the frequency and wave vector of the ion acoustic mode of the plasma. This resonance can be predicted from a fluidlike description of the plasma, but it is shown that the Vlasov description can provide more details of behavior near the resonance. Possible applications of the emergent technology range from improved focusing of radiation in hyperthermia therapy of cancer to the formation of a microwave laser between a phase conjugate plasma reflector and a mirror, for improved radar imaging. Another application is cordless, self-guiding, power transmission.
Effect of counterstreaming ion flow on ion acoustic modes and stimulated Brillouin scattered light
Authors: Powers L. V. , Berger R. L.
Published: July 2002

The stimulated Brillouin scattering spectrum from a plasma is determined by the ion acoustic normal mode frequencies, which are dependent on the ion temperature and flow velocity. Thus these quantities are indirectly measured by the scattered light. The frequencies of ion acoustic normal modes and stimulated Brillouin scattered light are calculated for a model plasma formed by collisionlessly interpenetrating ion beams by assuming the ion–ion two-stream instability is marginally stable. The spectrum differs measurably from the spectrum expected from the hot, stationary plasma created by collisional stagnation. Comparison of the scattered light spectra for these two limiting cases suggests that careful observation of the scattered light near the laser frequency is a potentially useful diagnostic of the collisionality of interpenetrating ion beams.
Interactions between two bubbles under isothermal conditions and in a downward temperature gradient
Authors: Wei Huailiang , Subramanian R. Shankar
Published: July 2002

Results from experiments on the motion of a pair of air bubbles in a silicone oil under isothermal conditions as well as in a downward temperature gradient are reported. Three situations were investigated: motion driven by buoyancy, motion dominated by thermocapillarity, and motion when the gravitational force and the thermocapillary force on the larger bubble of the pair were comparable. The experimental results were found to be in good agreement with theoretical predictions from the method of reflections. When the gravitational force was slightly smaller than the thermocapillary force on the larger bubble in the pair, the larger bubble moved downward but the smaller bubble nearby was found to move upward. This counterintuitive behavior is actually consistent with expectation, and an explanation is given.
Nonlinear stability analysis of molten flow in laser cutting
Authors: Tasi Ming-Jye , Weng Cheng-I
Published: July 2002

The method of multiple scales is used to investigate the nonlinear stability behavior of a thin molten laser cutting. In this analysis, the balance of momentum and energy with the effects of phase change is considered. Under the assumption of long wavelength, a corresponding nonlinear generalized kinematic equation for the film thickness is thereby derived. The result shows that there exist supercritical stability in the linearly unstable region and subcritical instability in the linearly stable region. For higher cutting speeds, the surface roughness could be improved by decreasing the cutting speed or increasing the gas velocity due to the decreasing of the maximum equilibrium finite amplitude. On the other hand, for lower cutting speeds, the surface roughness could be improved by increasing the cutting speed or decreasing the gas velocity due to the increasing of the minimum threshold amplitude.
Toward a thermodynamic theory of hydrodynamics: The Lorenz equations
Authors: Velarde Manuel G. , Chu Xiao-lin , Ross John
Published: July 2002

Earlier work on the thermodynamics of nonlinear systems is extended to the Lorenz model in a first attempt to apply the theory to hydrodynamics. An excess work, Φ, related to the work necessary for displacement of the system from stationary states is defined. The excess work Φ is shown to have the following properties: (1) The differential of Φ is expressed in terms of thermodynamic functions: the energy for viscous flow and the entropy for thermal conduction when taken separately; (2) Φ is an extremum at all stationary states, a minimum (maximum) at stable (unstable) stationary states, and thus yields necessary and sufficient criteria for stability; (3) Φ describes the bifurcation from homogeneous to inhomogeneous stationary states; (4) Φ is a Lyapunov function with physical significance parallel to that of the Gibbs free energy change (maximum work) on relaxation to an equilibrium state; (5) Φ is the thermodynamic ‘‘driving force’’ (potential) toward stable stationary states; (6) Φ̇ is a component of the total dissipation during the relaxation toward a stable stationary state; (7) for constraints leading to equilibrium Φ reduces to the known thermodynamic function, which is the work of displacing the system from the equilibrium for those given constraints; and (8) Φ qualitatively explains the positive energy release in both the destruction and formation of a convective structure in a Rayleigh–Bénard experiment.
Large-scale and periodic modes of rectangular cell flow
Authors: Gotoh Kanefusa , Murakami Youichi , Matsuda Norio
Published: July 2002

Linear stability of the rectangular cell flow: Ψ=cos kx cos y (0<k<1), is studied, both numerically and analytically. Owing to its spatial periodicity, the disturbances are characterized by the Floquet exponents (α,β). Based on numerical results, it is found that two types of the critical modes with vanishingly small exponents exist. One type (large-scale mode) has an almost uniform spatial structure. The other type (periodic mode) has a structure with the same periodicity as the main flow. The large-scale mode gives the critical Reynolds number in a more isotropic case (i.e., k≳0.6), while the periodic mode does so in the less isotropic case (i.e., k<0.6). Asymptotic expansions from (α,β)=(0,0) agree with the numerical results. Using the periodic mode, a possible explanation is given for the merging process of a pair of counter-rotating vortices observed in the experiments of a linear array of vortices by Tabeling et al. [J. Fluid Mech. 213, 511 (1990)].
Steadily translating vortices in a stratified fluid
Authors: Arendt Steve
Published: July 2002

The existence of steadily translating vortices in a semi-infinite barotropic fluid stratified by a constant gravitational field is considered. Assuming that the flow field of the vortex is subsonic and contains finite total kinetic energy, it is found that steadily translating vortices do not exist in three dimensions, but do exist in two dimensions. An analogy between a subsonic, barotropic, stratified fluid, and a uniform fluid with a free-slip planar boundary is exploited to show that the same result applies in a semi-infinite uniform fluid.
The long-wave interfacial instability of two liquid layers stratified by thermal conductivity in an inclined channel
Authors: Smith Marc K.
Published: July 2002

The flow of two liquid layers with different thermal conductivities confined in a rigid inclined channel cooled from below is susceptible to a long-wave interfacial instability. The results of Yih [Phys. Fluids 29, 1769 (1986)] on this problem are corrected and extended to layers of unequal thickness and to an arbitrary applied pressure gradient. The effects of direct liquid expansion and contraction as described in the conservation of mass equation are also included.
Starting and steady quadrupolar flow
Authors: Voropayev S. I. , Fernando H. J. S. , Wu P. C.
Published: July 2002

Planar flow induced in a viscous fluid by a small cylinder oscillating in the direction normal to its axis is modeled theoretically and reproduced experimentally. In the model, a line force dipole (force doublet) was used as the source of motion. In an initially quiescent unbounded fluid this source produces zero net momentum and generates symmetrical quadrupolar flow consisting of two dipolar vorticity fronts propagating in opposite directions from the source. For starting flow at low Reynolds numbers, a second-order unsteady solution is obtained in terms of a power series of the Reynolds number, Re=Q/4πν2, where Q is the forcing amplitude and ν is the kinematic viscosity. This solution demonstrates that, as time t→∞, the flow in the vicinity of the source becomes steady and radial. To describe this steady asymptote, the Jeffery–Hamel nonlinear solution for radial flow is used. A particular solution is derived using the nondimensional intensity Re of the force dipole as a governing parameter. It is shown that the problem permits a similarity solution for all values of Re when a mass sink of prescribed intensity q=q(Re) is added to the flow. This steady asymptote is reproduced experimentally, using a vertical porous cylinder that oscillates horizontally in the shallow upper layer of a two-layer fluid and sucks fluid through its porous walls.
A low-shear turbulent boundary layer
Authors: Hamelin Jennifer , Alving Amy E.
Published: July 2002

This paper describes experimental results measured in a low-shear turbulent boundary layer. The low-shear condition is exerted after the boundary layer reaches Reθ≂2000 and has the effect of removing the inner layer; thus, these are the first results to show the behavior of an outer-layer-only turbulent boundary layer. The removal of the inner layer causes the gradual decay of the turbulent stresses over eleven boundary-layer thicknesses (roughly 20 large-eddy length scales) of streamwise distance, with the decay beginning at the wall and propagating into the outer flow with increasing downstream distance. However, the structure of the outer layer is little affected by the perturbation, as demonstrated by stress (anisotropy) ratios, quadrant analysis, and spectral measurements. Although the lack of near-wall production implies this flow must eventually decay into isotropic turbulence, this decay occurs relatively slowly because the dissipation is also greatly reduced with the decrease in near-wall shear. In addition, the outer-layer production is significant in maintaining the turbulence level. These results show that, once formed, the outer-layer characteristics are not explicitly dependent on the presence of the inner layer. These results are compared with similar studies of isotropic turbulence near a shear-free wall. Very close to the wall the two flows both show that the normal-stress components respond differently to the presence of the wall. However, away from the wall the isotropic results underpredict the distance to which the tangential stresses are damped by the impermeability condition at the wall. Finally, the results show general similarities to those in a boundary layer just downstream of reattachment, after a similar low-shear condition over the separation bubble. This raises the possibility that many of the important features of the reattaching flow can be captured by the present, simpler experiment.
Numerical studies of real-gas effects on two-dimensional hypersonic shock-wave/boundary-layer interaction
Authors: Furumoto Gregory H. , Zhong Xiaolin , Skiba John C.
Published: July 2002

Nonequilibrium real-gas effects on surface heating rates, skin friction, and flow field unsteadiness of two-dimensional hypersonic shock-wave/boundary-layer interaction were studied by numerical simulations. The unsteady Navier–Stokes equations with nonequilibrium vibrational and chemical models for five-species air were solved by a finite-volume second-order TVD scheme together with a third-order semi-implicit Runge–Kutta scheme. Two cases of high-enthalpy shock/boundary layer interaction problems were studied in this paper. The freestream enthalpy was high enough to produce vibrational excitation and dissociation/recombination chemistry behind the shock. The first case was a steady two-dimensional shock/boundary layer interaction on a flat plate with a mixture of N2 and O2 in the freestream. It was found that the real gas effects reduce the size of the shock induced separation bubble and the magnitude of the surface heating rates. The second case was a self-sustained unsteady type IV shock–shock interference heating of a pure N2 flow over a cylinder. The results showed that type IV shock–shock interference heating flows with real-gas effects are inherently unsteady. Vortices are generated and shed off near the jet impingement point. This periodic shedding of the vortices contributes to the self-sustained oscillations of both the jet and other parts of the flow fields. In addition, the real-gas effects reduce the level of peak surface heating and peak surface pressure due to endothermic real-gas effects.
Sedimentation of homogeneous suspensions of non-Brownian spheres
Authors: Ladd Anthony J. C.
Published: July 2002

Dynamical simulations of bulk sedimentation have been carried out, using up to 32 000 solid particles. There is no evidence that the long-range hydrodynamic interactions are screened by changes in the pair correlation function at large distances. Instead the velocity fluctuations and diffusion coefficients diverge linearly with the width of the container, consistent with the random long-range microstructures observed in the simulations. Our data suggest that other mechanisms must be uncovered to account for experimental observations.
Asymptotic analysis of a vertical Bridgman furnace at large Rayleigh number
Authors: Foster M. R.
Published: July 2002

A vertical Bridgman furnace, through which an ampoule containing the melt of a certain dilute binary alloy is pulled at a fixed, and predetermined speed, provides a means of improving certain alloys. Radial segregation in the finished crystalline material can make it unusable. In this paper, we construct an asymptotic theory for the flow and solidification in the ampoule, for large Rayleigh numbers but at a small Biot number. We find large-Rayleigh-number solutions to be, to leading order, completely insensitive to the character of the side-wall boundary condition on vertical velocity. Two-dimensional equivalents of optimization conditions found by Tanveer are recovered for his two limiting cases—large thermal Rayleigh number, and large negative solutal Rayleigh number. Moderate surface tension at the crystal–melt interface is found to have no effect on the optimization conditions for the two limit cases, but it does somewhat reduce the magnitude of the segregation in both limits. In addition, we present new results for the case for which the two Rayleigh numbers are of comparable magnitude and show that there is an optimization possible for this case too. Conversion of the results of this paper to an axisymmetric geometry is shown to be trivial. Keeping careful track of the ordering, we indicate how to proceed to first effects of non-linearity at small Biot and/or Prandtl number.
The three-dimensional interaction of a vortex pair with a wall
Authors: Luton J. Alan , Ragab Saad A.
Published: July 2002

The interaction of vortices passing near a solid surface has been examined using direct numerical simulation. The configuration studied is a counter-rotating vortex pair approaching a wall in an otherwise quiescent fluid. The focus of these simulations is on the three-dimensional effects, of which little is known. To the authors’ knowledge, this is the first three-dimensional simulation that lends support to the short-wavelength instability of the secondary vortex. It has been shown how this Crow-type instability leads to three dimensionality after the rebound of a vortex pair. The growth of the instability of the secondary vortex in the presence of the stronger primary vortex leads to the turning and intense stretching of the secondary vortex. As the instability grows the secondary vortex is bent, stretched, and wrapped around the stronger primary. During this process reconnection was observed between the two secondary vortices. Reconnection also begins between the primary and secondary vortices but the weaker secondary vortex dissipates before the primary, leaving reconnection incomplete. Evidence is presented for a new type of energy cascade based on the short-wavelength instability and the formation of continual smaller vortices at the wall. Ultimately the secondary vortex is destroyed by stretching and dissipation leaving the primary vortex with a permanently distorted shape but relatively unaffected strength compared to an isolated vortex.