bluuebunny/crossref_metadata_2025 huggingface dataset:
Flute instability in a plasma confined by perfectly reflecting end walls
Authors: Farina D. , Pozzoli R. , Ryutov D.
Published: July 2002

The magnetohydrodynamic stability of a low-pressure plasma confined along the magnetic field by the end walls that are perfectly reflecting the impinging particles is considered. It is shown that, if the magnetic field lines do not intersect the walls along the normal, a fast instability can develop. An explicit expression for the growth rate has been derived, and an analogy with the usual flute instability has been traced. The instability can play some role in the scrape-off layers of tokamaks with poloidal limiter.
Dynamics of a 19 MeV, 700 kA, 25 nsec electron beam in a long collisional gas cell
Authors: Sanford T. W. L. , Welch D. R. , Mock R. C.
Published: July 2002

The 13 TW pulsed electron beam generated by Hermes III [J. J. Ramirez et al., Digest of Technical Papers, 6th IEEE Pulsed Power Conference (IEEE, New York, 1987), pp. 294] is transported 10.8 m in a low-pressure gas with 79±1.5±[5]% energy transport efficiency. The uncertainties refer to the rms shot-to-shot variation and estimated systematic error, respectively. The high efficiency obtained is accomplished by removing the inward momentum of the beam at injection via an active magnetic lens. The reduced transverse momentum permits self-magnetic field confinement at low pressures with low inductive and collisional loss. The region of efficient transport lies between regions of instability. Consistent with experiment, the analytic and numerical models developed here predict that the m=1 resistive hose instability degrades transport above 100 Torr and plasma return-current instabilities disrupt the beam below 1 Torr. Within this pressure ‘‘window’’ of stable propagation, the models explain the mechanisms responsible for maximum transport.
Ion Bernstein wave propagation and absorption in general magnetic field configuration
Authors: Cardinali Alessandro
Published: July 2002

A linear analysis of ion Bernstein wave (IBW) propagation and absorption is considered in a general tokamak plasma magnetic equilibrium. The effects of elongation, triangularity, and Shafranov shift on radio-frequency (rf) absorption are discussed with respect to the simple case of circular and concentric magnetic surfaces. The ray-tracing equations are analytically and numerically solved in the flux surface coordinate system, and the power deposited in the plasma is calculated along the trajectory for the International Thermonuclear Experimental Reactor (ITER) [Nucl. Fusion 31, 1135 (1991)] plasma parameters.
Microturbulence damping mechanisms in the DIII-D tokamak*
Authors: Rettig C. L. , Peebles W. A. , Burrell K. H. , La Haye R. J. , Doyle E. J. , Groebner R. J. , Luhmann N. C.
Published: July 2002

Although it has long been suggested that microturbulence is responsible for anomalous transport, relatively little is known about turbulence drive and suppression mechanisms which determine the observed fluctuation levels. In the DIII-D (DIII-D) tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] during H-mode discharges, microturbulence has been observed to change in two stages. Collective far-infrared scattering has confirmed and quantified a rapid (≂100 μsec) suppression of edge microturbulence at the L→H transition, as well as locally increased edge electric field shear, consistent with theoretical models which predict microturbulence suppression due to E×B sheared flow. Additionally, during the subsequent H-mode phase, a slower (10–100 msec) reduction of interior microturbulence is observed, coincident with increased electric field shear and reduced R∇ne in the same region. This reduction is much larger in boronized discharges which also generally have larger rotation velocity. Experiments have been performed whereby the interior radial electric field is reduced while maintaining similar pressure profiles through the use of ‘‘magnetic braking’’ of toroidal rotation. As expected, the E×B Doppler frequency shift of the scattered fluctuation spectrum decreased as the electric field was reduced. The microturbulence levels were observed to increase when the interior electric field and the associated shear were reduced. Therefore, radial electric field control of microturbulence appears to be a possible route to transport control
Hamiltonian description and stability of magnetic electron vortices
Authors: Pavlenko Vladimir P. , Uby Lars
Published: July 2002

A Hamiltonian description and integral invariants of two-dimensional magnetic electron modes are derived. Vortex street solutions are given. Using the integrals, linear stability for long wavelength perturbations is established. It is shown that nonlinear stability cannot be proven using Arnol’d’s method.
Coherent structures in rotating non-neutral plasma
Authors: Lund Steven M. , Ramos Jesus J. , Davidson Ronald C.
Published: July 2002

Nonaxisymmetric (∂/∂θ≠0) rotating equilibria are investigated theoretically for strongly magnetized, low-density (ωpe2/ωce2≪1) pure electron plasmas confined in cylindrical geometry. These two-dimensional equilibria are also called rotating coherent structures, and are stationary (time independent) in a frame of reference rotating with angular velocity ωr=const about the cylinder axis (r=0). Radial confinement of the pure electron plasma is provided by a uniform axial magnetic field B0ez, and a grounded, perfectly conducting, cylindrical wall is located at radius r=rw. The analysis is based on a nonrelativistic, guiding-center model in the cold-fluid limit (the continuity and Poisson equations) that treats the electrons as a massless fluid (me→0) with E×B flow velocity Ve=−(c/B0)∇φ×ez. Within this model, general rotating equilibria with electron density ne≡nR(r,θ−ωrt) and electrostatic potential φ≡φR(r,θ−ωrt) have the property that the electron density is functionally related to the streamfunction ψR=−eφR+ωr(eB0/2c)r2 by nR=nR(ψR).

The streamfunction ψR satisfies the nonlinear equilibrium equation ∇2ψR=−4πe2nR(ψR)+2ωreB0/c with ψR=ωr(eB0/2c)rw2≡ψw=const on the cylindrical wall at r=rw. Following a general discussion of rotating equilibria, an integral equation formulation of the nonlinear equilibrium equation is developed to investigate equilibria with ‘‘waterbag’’ (step-function) density profiles. In this investigation, a numerical method is formulated that can be used to construct diverse classes of highly nonlinear waterbag equilibria. This method is employed to investigate two classes of nonaxisymmetric equilibria that are nonlinear extrapolations of well-known small-amplitude equilibria. These two classes of rotating equilibria bear strong similarities to coherent structures observed experimentally by Driscoll and Fine [Phys. Fluids B 2, 1359 (1990)].
On nonlocal electron heat conduction
Authors: Krasheninnikov S. I.
Published: July 2002

An improvement of the Albritton nonlocal electron heat transport model is proposed for high-Z plasmas. The thermal decay of the temperature perturbation in a uniform plasma as calculated by this model is compared with that obtained by Fokker–Planck simulations. Complete agreement is found up to values kλe≂0.1, where k is the wave number of the perturbation and λe is the thermal electron mean-free path.
Nonlinear magnetic field transport in opening switch plasmas
Authors: Mason R. J. , Auer P. L. , Sudan R. N. , Oliver B. V. , Seyler C. E. , Greenly J. B.
Published: July 2002

The nonlinear transport of magnetic field in collisionless plasmas, as present in the plasma opening switch (POS), using the implicit multifluid simulation code anthem [J. Comput. Phys. 71, 429 (1987)] is studied. The focus is on early time behavior in the electron–magnetohydrodynamic (EMHD) limit, with the ions fixed, and the electrons streaming as a fluid under the influence of ve×B Hall forces. Through simulation, magnetic penetration and magnetic exclusion waves are characterized, due to the Hall effect in the presence of transverse density gradients, and the interaction of these Hall waves with nonlinear diffusive disturbances from electron velocity advection, (ve⋅∇)ve, is studied. It is shown how these mechanisms give rise to the anode magnetic insulation layer, central diffusion, and cathode potential hill structures seen in earlier opening switch plasmas studies.
Stability of magnetically insulated ion diodes
Authors: Ott Edward , Antonsen T. M. , Chang C. L. , Drobot A. T.
Published: July 2002

Magnetically insulated ion diodes are examined for instability using analytical and numerical techniques. Two basic sources which drive instability are found: one due to a two-stream-type interaction between electrons and ions and the other due to ion transit time effects.
Nonideal magnetohydrodynamic instabilities and toroidal magnetic confinement
Authors: Furth Harold P.
Published: July 2002

The marked divergence of experimentally observed plasma instability phenomena from the predictions of ideal magnetohydrodynamics led in the early 1960’s to the formulation of finite-resistivity stability theory. Beginning in the 1970’s, advanced plasma diagnostics have served to establish a detailed correspondence between the predictions of the finite-resistivity theory and experimental plasma behavior—particularly in the case of the resistive kink mode and the tokamak plasma. Nonlinear resistive-kink phenomena have been found to govern the transport of magnetic flux and plasma energy in the reversed-field pinch. The other predicted finite-resistivity instability modes have been more difficult to identify directly, and their implications for toroidal confinement are still unresolved.
A route to turbulence in nonlinear development of an ion beam–plasma instability
Authors: Kono Mitsuo
Published: July 2002

Nonlinear evolution of the ion beam–plasma instability has been investigated by means of numerical simulations based on a hybrid code. A scenario on a path to the onset of turbulence has been found as follows. The initial exponential growth of the linear instability is saturated by beam trapping, which causes, in turn, amplitude oscillation. The more highly driven harmonics initiate the stochastic instability of the trapped particles. The trapped beam particles begin to wander from one potential wave trough to another and spread in phase space. A transition to turbulence is found to occur through subharmonic excitations because of a parametric decay instability.
On the mode equations for the electrostatic ballooning instability in tokamaks
Authors: Hirose A.
Published: July 2002

Some discrepancies are pointed out for kinetic and fluid dispersion relations of low-frequency electrostatic modes in tokamaks. It is shown that both electrons and ions contribute to the ballooning term, which is subject to finite ion Larmor radius correction.
The Alfvén wave spectrum as measured on a tokamak
Authors: Collins G. A. , Hofmann F. , Joye B. , Keller R. , Lietti A. , Lister J. B. , Pochelon A.
Published: July 2002

The detailed experimental data obtained on the TCA tokamak [Proceedings of the 11th Symposium on Fusion Technology (CEC, Luxembourg, 1981), Vol. I, p. 601] concerning the antenna loading and wave fields as a function of the Alfvén wave spectrum are presented. The plasma density, plasma current, working gas, toroidal magnetic field, and frequency were varied systematically and the detailed results are compiled and discussed. In addition the phasing of the antenna currents was varied systematically, thereby exciting different combinations of modes, including pure traveling waves. The conclusions relevant to the design of an antenna system have been stressed.
Measurement of the temporal, spatial, and saturation behavior of stimulated Brillouin scattering
Authors: Bernard J. E. , Meyer J.
Published: July 2002

The temporal growth rates, spatial behavior, and saturation characteristics of stimulated Brillouin scattering (SBS) occurring in a CO2 laser–gas jet experiment are investigated experimentally by picosecond Thomson scattering of ruby laser light as well as by intensity and spectral measurements of the backscattered light. Exponential temporal growth of the ion acoustic waves was observed and found to have a growth rate in good agreement with theory. Spatial modulations in the ion-acoustic-wave amplitude resulting from plasma inhomogeneities were found to limit the backscattered reflectivity to less than 10%. The ion acoustic waves saturate at a fluctuation amplitude of <20%. Ion trapping is shown to account for the observed saturation as well as temporal modulations in the ion-acoustic-wave amplitude and sibebands in the backscattered spectra.
Nonlinear critical layers eliminate the upper branch of spatially growing Tollmien–Schlichting waves
Authors: Goldstein M. E. , Durbin P. A.
Published: July 2002

This Letter is concerned with the effect of nonlinear critical layers on spatially growing Tollmien–Schlichting waves in a Blasius boundary layer. It is shown that they effectively eliminate the upper branch of the neutral stability curve predicted by strictly linear theory.
Effects of magnetic separatrix and pressure pedestal on finite beta external kink–tearing modes
Authors: Lee Jae Koo
Published: July 2002

The roles of a magnetic separatrix and of a steep-edge pressure gradient on finite beta external kink and tearing modes in tokamaks are examined by using a newly developed initial value code. For fixed profiles of current density and pressure, the separatrix is found to have a weak effect on the linear characteristics of the global mode. The presence of a steep pressure gradient at the plasma edge reduces the overall growth rate in a similar fashion for both cases with and without the separatrix.
Direct numerical simulations of chemically reacting turbulent mixing layers
Authors: Riley James J. , Metcalfe Ralph W. , Orszag Steven A.
Published: July 2002

The results of direct numerical simulations of chemically reacting, turbulent mixing layers are presented. The reaction considered is a binary, irreversible reaction with no heat release, so that only the effect of the turbulence on the chemical reaction is investigated. The simulation results are shown to be consistent with similarity theory, and are found to be in approximate agreement with laboratory data, even though there are no adjustable parameters in the method.
Axisymmetric problem of vortex sound with solid surfaces
Authors: Miyazaki T. , Kambe T.
Published: July 2002

A general formulation of the axisymmetric vortex sound is given, and three typical problems are considered in detail, in which the acoustic wave is generated by a vortex ring interacting with either a sphere, a circular disk, or a circular aperture of a plane wall in an axisymmetric manner. The velocity potentials induced by the vortex in the presence of the body are determined by the method of dual integral equations or the image vortex. From the vortex trajectories, the acoustic wave fields are determined. The method of matched asymptotic expansions yields the result that the force exerted on the body is related to the profile of the dipole component. It is also found that the wave amplitude is expressed in terms of the value of a streamfunction at the vortex position, which represents a hypothetical potential flow around the body and is defined appropriately in each problem.
Analytic mirror equilibria with new long-thin terms
Authors: Goodman Daniel L. , Freidberg Jeffrey P. , Lane Barton
Published: July 2002

An analytic equilibrium for a tandem mirror with quadrupole symmetry is derived. By expanding simultaneously in β (plasma pressure/magnetic pressure) and λ (long-thin parameter), and using a maximal ordering, both effects enter competitively. These new long-thin corrections extend the results of Pearlstein et al. [Phys. Fluids 24, 1326 (1981); Phys. Fluids 27, 2781 (1984)] and can be shown to be the dominant terms in some cases. The new terms make the flux surfaces more diamond shaped than previously thought and change the scaling of the flux surface distortions with β. Using model pressure and field profiles, simple analytic expressions for the new corrections and flux surface are found and compared with the results of the vepec 3-D equilibrium code [J. Comput. Phys. 46, 189 (1982)]. For the Constance mirror (submitted to Phys. Rev. Lett.), good agreement with the code is found for flux surface shapes and β scaling.
Linear mode conversion and singularities of geometric optics approximation in plasmas
Authors: Friedland L.
Published: July 2002

The general, unreduced, one-dimensional, linear wave propagation problem in weakly inhomogeneous plasmas is considered. Conventional geometric optics perturbation expansion reduces this high-order, multimode problem to the solution of a first-order ordinary differential equation for the wave amplitude along the rays given by εi=0, where εi is one of the eigenvalues of the generalized tensor E characterizing the problem. In some plasma regions, however, this perturbation expansion, based on following only one mode at a time, fails, predicting fast variation of the zero-order amplitude and local wave vector k of the wave, or leading to large first-order corrections to the amplitude. Typically, in this region either (a) an additional eigenvalue of E becomes small and couples a new mode into the problem, or (b) all the eigenvalues except εi remain large; however, ∂εi/∂kx→0, x being the direction of the inhomogeneity. Following an earlier work on case (a), a renormalization technique is employed in formulating a consistent, nonsingular, eikonal type perturbation expansion in case (b). The method yields a single, second-order, ordinary differential equation for amplitude of the wave, in contrast to case (a), more naturally described by a system of two first-order equations for the amplitudes of the coupled modes. Both theories thus comprise a complete general description of pairwise, linear mode conversion in the aforementioned singular regions. The approach is illustrated by the example of wave interaction in a cold magnetized plasma with plane parallel stratification. The importance of studying the unreduced problem is demonstrated by showing that in case (a) the information on the type of singularity can be lost by formulating the problem in terms of the conventional, reduced dielectric tensor.
Degenerate toroidal magnetohydrodynamic equilibria and minimum B
Authors: Bishop C. M. , Taylor J. B.
Published: July 2002

It is shown that there is a unique configuration of toroidal magnetic surfaces. This configuration corresponds to more than one plasma equilibrium. It is the configuration of isodynamic equilibria. These equilibria include toroidal minimum-B equilibria and the distinction between these unstable systems and the stable minimum-B mirror systems is discussed.
Alfvén continuum with toroidicity
Authors: Riyopoulos S. , Mahajan S.
Published: July 2002

The symmetry property of the magnetohydrodynamic (MHD) wave propagation operator is utilized to express the toroidal eigenmodes as a superposition of the mutually orthogonal cylindrical modes. Because of the degeneracy among cylindrical modes with the same frequency but resonant surfaces of different helicity, the toroidal perturbation produces a zeroth-order mixing of the above modes. The toroidal eigenmodes of frequency ω20 have multiple resonant surfaces, with each surface shifted relative to its cylindrical position and carrying a multispectral content. Thus a single helicity toroidal antenna of frequency ω0 couples strongly to all different helicity resonant surfaces with matching local Alfvén frequency. Zeroth-order coupling between modes in the continuum and global Alfvén modes also results from toroidicity and degeneracy. The perturbation technique used in this study is the MHD counterpart of the quantum-mechanical methods and is applicable through the entire range of the MHD spectrum.
Nonlinear collective processes and the confinement of a pure-electron plasma
Authors: Crawford John David , O’Neil T. M.
Published: July 2002

For an electron plasma that is magnetically confined in a cylindrical field geometry, radial expansion occurs only if the angular momentum of the plasma changes. In the absence of external torques, the plasma can be confined forever. Confinement experiments have suggested that the small asymmetries in the confining fields are an important external source of angular momentum. Recent transport experiments show that such field errors may excite waves and thereby enhance radial transport. A detailed theory of the nonlinear couplings between the electrostatic collective modes and perturbing asymmetric fields is presented, with emphasis on three-wave and induced scattering-type interactions. Via these interactions, field errors may trigger instabilities. Thresholds for such instabilities are derived and the resulting transfer of angular momentum is analyzed. The theory is applied to a simple model of a long column in order to estimate the field error levels required by the thresholds. The theoretical formalism is based on a variational formulation of the Vlasov–Poisson equations that is well suited to discussing the nonlinear interactions of global modes in bounded equilibria.
Maximum instabilities of compressible jets
Authors: Zaninetti L.
Published: July 2002

The stability of a jet in a compressible fluid is examined for the case of a rectangular velocity profile, where the jet is a cylindrical region of uniform velocity separated from the external uniform medium by a vortex sheet. Numerical results are presented for the maximum instability of the ordinary mode that arises when the flow is supersonic. These instabilities have an e-folding length and a typical wavelength greater than the jet radius.
Time resolved Thomson scattering measurements of the electron and ion temperatures in a high intensity laser–plasma interaction
Authors: Bernard J. E. , Baldis H. A. , Villeneuve D. M. , Estabrook Kent
Published: July 2002

Time resolved Thomson scattering from thermal plasma fluctuations is used to measure the electron and ion temperatures in the interaction of a short pulse (1 nsec FWHM), high intensity (∼2×1014 W/cm2) CO2 laser beam with a preformed carbon plasma. Time histories of the plasma temperatures with a temporal resolution of ∼150 psec were obtained in a single irradiation/discharge event by streaking the Thomson scattering spectrum. The experimentally measured electron temperature was found to be lower than that predicted by computer simulations. The discrepancy is attributed mainly to a decrease in the inverse bremsstrahlung absorption coefficient at high laser intensities (vosc/ve>1) .
False collisions in the direct simulation Monte Carlo method
Authors: Nanbu K. , Igarashi S. , Watanabe Y.
Published: July 2002

In the direct simulation Monte Carlo method the molecular collision in a cell is calculated regardless of molecule positions. It is indicated that disregard of the positions causes false collisions, which never occur in the molecular dynamics method. By calculating a radial flow in cones with various apex angles, it is shown that the distortion of the flow by the false collisions increases with the apex angle.
Saturation of Kelvin–Helmholtz fluctuations in a sheared magnetic field
Authors: Scott Bruce D. , Terry P. W. , Diamond P. H.
Published: July 2002

Kelvin–Helmholtz unstable flows are numerically investigated in the context of a sheared E×B flow profile and a sheared magnetic field in the collisional, electrostatic limit. In the extreme form of this limit, density fluctuations are small and the system is described by the nonlinear E×B vorticity dynamics. In order to focus on the role of magnetic shear localization, the computations are confined to two dimensions. For weak magnetic shear the fluctuations become turbulent and saturate by nonlinear cascade to small (dissipative) scales. In a strong magnetic shear regime near the linear stability boundary, nonlinear spatial broadening allows direct access to resistive shear dissipation, leading to saturation at small amplitude with nearly all the fluctuation energy in the longest-wavelength mode. This is in accordance with previous investigation using a statistical closure analysis [Phys. Fluids 29, 231 (1986)]. The amount of broadening is proportional to the linear growth rate. The fluctuation amplitude scaling with magnetic shear is found to agree closely with the theory.
Nonlinear saturation of collisionless trapped particle instability in tandem mirrors
Authors: Kim S. Y. , Sen A. K.
Published: July 2002

A collisionless trapped particle instability with magnetohydrodynamiclike growth rate is expected in tandem mirrors. To study its nonlinear state, a two-dimensional polarization drift nonlinearity in a cylindrical geometry is considered. Using three-wave nonresonant mode coupling of radially nonlocal eigenfunctions, two-mode coupling equations for the unstable fundamental and stable first-order radial harmonics are derived. The solution of mode-coupled equations yields the nonlinear saturation level. Mode coupling to the damped higher-order radial harmonics is the principal saturation mechanism of the unstable fundamental radial harmonic.
Self-organization in three-dimensional compressible magnetohydrodynamic flow
Authors: Horiuchi Ritoku , Sato Tetsuya
Published: July 2002

A three-dimensional self-organization process of a compressible dissipative plasma with a velocity-magnetic field correlation is investigated in detail by means of a variational method and a magnetohydrodynamic simulation. There are two types of relaxation, i.e., fast relaxation in which the cross helicity is not conserved and slow relaxation in which the cross helicity is conserved approximately. In the slow relaxation case the cross helicity consists of two components with opposite sign that have almost the same amplitude in the large wavenumber region. In both cases the system approaches a high correlation state, dependent on the initial condition. These results are consistent with observational data of the solar wind. Selective dissipation of magnetic energy, normal cascade of magnetic energy spectrum, and inverse cascade of magnetic helicity spectrum are observed for the sub-Alfvénic flow case, as was observed previously for the zero-flow case. When the flow velocity is super-Alfvénic, the relaxation process is altered significantly from the zero-flow case.
Current drive with whistler waves
Authors: de Assis Altair S. , Busnardo-Neto J.
Published: July 2002

A self-consistent, one-dimensional, quasilinear formulation is used to calculate the efficiency of current generation by whistler waves (ωci≪ω≪ωce ) in the weak-source regime. Estimates of the efficiency compare well with recent measurements in the ACT-1 device [Phys. Rev. Lett. 55, 1669 (1985)] and also in the Irvine Torus [Phys. Rev. Lett. 56, 835 (1986)].
Radiative instabilities in a sheared magnetic field
Authors: Drake J. F. , Sparks L. , Van Hoven G.
Published: July 2002

The structure and growth rate of the radiative instability in a sheared magnetic field B have been calculated analytically using the Braginskii fluid equations. In a shear layer, temperature and density perturbations are linked by the propagation of sound waves parallel to the local magnetic field. As a consequence, density clumping or condensation plays an important role in driving the instability. Parallel thermal conduction localizes the mode to a narrow layer where k∥ =k⋅B/‖B‖ is small and stabilizes short wavelengths k>kc, where kc depends on the local radiation and conduction rates. Thermal coupling to ions also limits the width of the unstable spectrum. It is shown that a broad spectrum of modes is typically unstable in tokamak edge plasmas and it is argued that this instability is sufficiently robust to drive the large-amplitude density fluctuations often measured there.
Detailed measurements of anisotropic mirror plasma ion energy distributions during drift cyclotron loss-cone instability
Authors: Booske J. H. , McCarrick M. J. , Ellis R. F. , Paquette J. A.
Published: July 2002

Using improved computer filtering and a reconstruction analysis we have been able to extract additional details on a mirror plasma’s midplane ion energy distribution from the current–voltage (I–V) curve of a voltage-swept electrostatic end loss analyzer (ELA). For the University of Maryland’s MIX-1 plasma [Phys. Fluids 23, 3439 (1976)], the diagnostic technique has provided us with important information on the ‘‘loss-cone region’’ of an anisotropic ion distribution during drift cyclotron loss-cone (DCLC) instability experiments. Observations include convincing verification of ion distribution modification during DCLC evolution and an enhancement of the loss-region boundary over that predicted by simplified trapping theory. The reconstruction analysis involves matching the differentiated I–V curves (i.e., dI/dV vs V) to theoretically predicted curves based on model midplane ion distribution functions. The theoretical curves are obtained from the model midplane distributions by a mapping transformation based on conservation of magnetic moment and total energy of each ion along lines of magnetic flux.
One-dimensional detonation stability: The spectrum for infinite activation energy
Authors: Buckmaster J. , Neves J.
Published: July 2002

The one-dimensional stability of detonation waves characterized by one-step irreversible Arrhenius kinetics is examined. The description of the steady structure in the limit of infinite activation energy is well known, and an examination is made of the linear unsteady perturbation equations in the same limit. The spectrum contains both a single real positive eigenvalue that vanishes in the limit and an infinite number of nonvanishing eigenvalues that define a growth rate which is an increasing function of frequency. Plausible qualitative extrapolation to finite activation energies provides an explanation of experimental results obtained by Alpert and Toong [Astronaut. Acta 17, 539 (1972)].
Empirical modeling and the dependence of reversed field pinch loop voltage on edge plasma conditions
Authors: Moses R. W. , Schoenberg K. F. , Baker D. A.
Published: July 2002

Empirical modeling of the dependence of loop voltage on edge plasma conditions in the reversed field pinch is discussed. Specific concerns are raised regarding magnetohydrodynamic-based models that assume a large local dissipation of magnetic helicity at the plasma edge. A kinetic model is presented in which loop voltage can be affected by fast electrons carrying momentum directly to the walls or limiters, without a large edge helicity dissipation.
Resistive electrostatic instabilities
Authors: Tang W. M. , Romanelli F. , Briguglio S.
Published: July 2002

The appropriate toroidal equations governing the stability properties of resistive electrostatic instabilities are derived and analyzed. These equations include the influence of impurity gradients and are valid for both strongly collisional and semicollisional regimes. Analytic and numerical solutions have been obtained in the sheared slab limit with toroidal curvature effects approximated with the familiar constant gravity model. The results indicate that for relevant experimental conditions, the resistivity-gradient-driven class of electrostatic modes is difficult to excite. Hence, with the possible exception of the very edge, these instabilities do not appear to be a likely candidate to account for the large thermal transport observed in the exterior region of most tokamak plasmas.
Nonaxisymmetric evanescent waves in a viscous liquid jet
Authors: Lin S. P. , Webb R.
Published: July 2002

The linear stability of a viscous liquid jet emanating into a gas with respect to spatially growing nonaxisymmetric disturbances is analyzed. The numerical solution of the characteristic equation and some analytical arguments are used to show that the nonaxisymmetric disturbances in the liquid jet are evanescent waves. Hence, a support is given to the commonly adopted assumption that nonaxisymmetric disturbances are more stable than the axisymmetric ones in a viscous liquid jet emanating into an ambient gas.
Inertial range statistics of Burgers turbulence
Authors: Gotoh Toshiyuki
Published: July 2002

Velocity structure function of Burgers turbulence in the inertial range is studied by mapping closure. It is shown that in the inertial range 〈‖u(x+l,t)−u(x,t)‖q〉= n(t)〈‖Δu(t)‖q〉‖l‖ and the spectrum E(k,t)=(1/2π)n(t)〈‖Δu(t)‖2〉k−2 for initially support broad spectrum, where n(t) is the average of the number density of shocks and 〈‖Δu(t)‖q〉 is qth moment of shock strength. Agreement with DNS is found to be good for initially Gaussian fields. Statistics at large time is also studied by the mapping closure using time dependent reference field. It is found that the length scale of the field and the decay law of the total kinetic energy are self-similar in time and various quantities are given as functions of the exponent n of the initial energy spectrum E(k,0) ∝ kn at low wave-number range. Extension to more general initial conditions with non-Gaussian statistics is also discussed.
Direct numerical simulation of two-particle relative diffusion in isotropic turbulence
Authors: Yeung P. K.
Published: July 2002

The relative diffusion of fluid particle pairs in statistically stationary isotropic turbulence is studied by direct numerical simulation, at a Taylor-scale Reynolds number of about 90. The growth of two-particle separation exhibits asymptotic stages at small and large diffusion times. Through the two-particle separation, particle–pair velocity correlations are closely related to the Eulerian spatial structure of the turbulence. At large times, the square of the separation distance has a chi-square probability distribution. At the moderate Reynolds number of the simulations, for this asymptotic distribution to be reached before the particles begin to move independently of each other, the initial separation must be small compared to the Kolmogorov scale. In an inertial frame moving with the initial particle velocities, the velocity increments of two fluid particles become uncorrelated only if their initial velocities are uncorrelated, which requires their initial separation be large compared to the integral length scale. For sufficiently large initial separations, the relative velocity increments and mean-square dispersion in this moving frame display a resemblance to inertial range scaling, but with a proportionality constant that is much smaller than classical estimates. At large times, the degree of preferential alignment between the separation and relative velocity vectors is weak, but the product of the separation distance and the velocity component projected along the separation vector is sustained on average.
Universality of probability density functions in turbulent channel flow
Authors: Dinavahi Surya P. G. , Breuer Kenneth S. , Sirovich Lawrence
Published: July 2002

Probability density functions (PDFs) of the fluctuating velocity components, as well as their first and second derivatives, are calculated using data from the direct numerical simulations (DNS) of fully developed turbulent channel flow. It is observed that, beyond the buffer region, the PDF of each of these quantities (except for u,y), is independent of the distance from the channel wall. It is further observed that, beyond the buffer region, the PDFs are also independent of Reynolds number. Similar behavior is observed for the PDFs of the second derivatives. The pseudodissipation rate of kinetic energy exhibits lognormal behavior.
The dynamical limit of one-dimensional detonations
Authors: He Longting , Lee John H. S.
Published: July 2002

The stability problem of one-dimensional piston supported gaseous detonations has been examined via both linear stability analysis and direct numerical simulation. It has been demonstrated that for other parameters being fixed, there are two critical values of the reduced activation energy, Ec1 and Ec2, according to which the propagation of planar detonation may be classified into three regimes: (i) when the reduced activation energy Ea is smaller than the first critical value, Ea<Ec1, the propagating detonation is stable: (ii) when Ec1<Ea<Ec2, the galloping oscillations appear in the propagation of detonations; (iii) when Ec2<Ea, the period of oscillations becomes infinitely large, the planar detonation cannot propagate via autoignition mechanism. Regime (iii) has never been pointed out in previous works. This regime occurs since the strong hydrodynamical instability effect makes the leading shock decay to a very low level which is too weak to cause a rapid autoignition.
Unsteady evolutions of vortex rings
Authors: Ye Qu-Yuan , Chu C. K.
Published: July 2002

Unsteady evolutions of vortex rings with linearly distributed vorticity and various core parameters are considered in an unbounded, inviscid fluid. The instability of a Norbury vortex with a moderate core thickness parameter α is also investigated. Contour integral expressions based on the Biot–Savart law for the velocity field induced by a vortex ring are derived. Numerical results show that all vortex rings except the Norbury vortices will undergo an unsteady evolution process to reach an asymptotic state. The process may be roughly divided into two major stages: initial large deformation stage and later asymptotic oscillating stage. Vortex filamentation is often observed during the first stage. In the second stage, the vortex oscillates periodically with nearly constant amplitude; its core closely resembles a Norbury vortex having the same circulation and impulse, but the dynamic properties and kinetic energies are different.
Critical dissipation rates in density stratified turbulence
Authors: Huq Pablo , Stretch D. D.
Published: July 2002

The estimation of a critical dissipation rate, εc, below which vertical transport ρw is completely suppressed, is examined in the context of laboratory experiments on shear-free, decaying, and stably stratified grid-generated turbulence. It is shown how the use of a criterion based on ρw=0 in these transient flows is not appropriate for obtaining a universal value for the critical dissipation rate expressed nondimensionally as εc/νN2. It remains unclear how any universal value of εc may be inferred from these laboratory experiments.
Instability in a spatially periodic open flow
Authors: Schatz Michael F. , Barkley Dwight , Swinney Harry L.
Published: July 2002

Laboratory experiments and numerical computations are conducted for plane channel flow with a streamwise-periodic array of cylinders. Well-ordered, globally stable flow states emerge from primary and secondary instabilities, in contrast with other wall-bounded shear flows, where instability generally leads directly to turbulence. A two-dimensional flow resembling Tollmien–Schlichting waves arises from a primary instability at a critical value of the Reynolds number, R1=130, more than 40 times smaller than for plane Poiseuille flow. The primary transition is shown to be a supercritical Hopf bifurcation arising from a convective instability. A numerical linear stability analysis is in quantitative agreement with the experimental observations, and a simple one-dimensional model captures essential features of the primary transition. The secondary flow loses stability at R2≊160 to a tertiary flow, with a standing wave structure along the streamwise direction and a preferred wave number in the spanwise direction. This three-dimensional flow remains stable for a range of R, even though the structures resemble the initial stages of the breakdown to turbulence typically displayed by wall-bounded shear flow. The results of a Floquet stability analysis for the onset of three-dimensional flow are in partial agreement with experiment.
Instantaneous flow field in an unstable vortex ring measured by holographic particle velocimetry
Authors: Meng Hui , Hussain Fazle
Published: July 2002

Instantaneous velocity field in the three-dimensional flow of an unstable vortex ring (Re=1360) in water has been measured by employing a newly developed holographic particle velocimeter, IROV. The vorticity distribution and circulation as a function of radius from the vortex core center are also presented.
A numerical study of three-dimensional bubble merger in the Rayleigh–Taylor instability
Authors: Li X. L.
Published: July 2002

The Rayleigh–Taylor instability arises when a heavy fluid adjacent to a light fluid is accelerated in a direction against the density gradient. Under this unstable configuration, a perturbation mode of small amplitude grows into bubbles of the light fluid and spikes of the heavy fluid. Taylor discovered the steady state motion with constant velocity for a single bubble or periodic bubbles in the Rayleigh–Taylor instability. Read and Youngs studied the motion of a randomly perturbed fluid interface in the Rayleigh–Taylor instability. They reported constant acceleration for the overall bubble envelope. Bubble merger is believed to cause the transition from constant velocity to constant acceleration. In this paper, we present a numerical study of this important physical phenomenon. It analyzes the physical process of bubble merger and the relationship between the horizontal bubble expansion and the vertical interface acceleration. A dynamic bubble velocity, beyond Taylor’s steady state value, is observed during the merger process. It is believed that this velocity is due to the superposition of the bubble velocity with a secondary subharmonic unstable mode. The numerical results are compared with experiments.
Boundary layer separation in a rotating container
Authors: Jahnke Craig C. , Valentine Daniel T.
Published: July 2002

The flow field induced in a cylindrical container by the rotation of the container and/or the end wall(s) about the axis of symmetry is highly vortical. If the container and the end walls are rotated at different angular velocities, a meridional flow develops due to the tilting and stretching of the axial vorticity created by the rotation of the bounding surfaces. In the present study, the flow field induced by the differential rotation of the container and one end wall while the other end wall remains fixed is numerically studied for a range of Reynolds numbers and ratios of the container to the end wall rotation rate. It is shown that the production of azimuthal vorticity by the tilting and stretching of axial vorticity causes the container side wall boundary layer to separate for a range of Reynolds numbers and ratios of the container to the end wall rotation rate.
Statistical stability criteria for turbulent flow
Authors: Malkus Willem V. R.
Published: July 2002

The average properties of many turbulent flows are remarkably reproducible, yet the detailed flows are never the same. Here necessary conditions are found for the stability of a statistically steady state with ideal reproducibility. The examples explored in this paper are the symmetry breaking large scale flows observed in high Rayleigh number Boussinesq convection. A necessary condition found is that an integral function of convective and advective local averages must be a maximum, selecting among the possible solutions. Although these many solutions may not be determined in this century, an estimate from above of this maximum can be sought among the class of vector fields compatible with derived integral constraints and the boundary conditions. The condition for statistical stability found here permits a first determination of a unique relation between the large scale mean flows and the heat flux without the introduction of empirical parameters. It is found that statistical stability at large Rayleigh number is achieved by that solution with maximum momentum transport, and not by the solution with maximum heat transport. The past limited data supports this deduction that the large scale flow approaches its maximum possible value. New experiments, with a stress free boundary condition, are proposed to explore these and other unanticipated theoretical results.
Fluctuations in passive scalar concentration convected by a helical flow in a conducting fluid
Authors: Zimmerman William B.
Published: July 2002

Recent statistical analyses of field trials and wind tunnel experiments show a new feature of fluctuations of tracer concentration dispersing in turbulent shear flow. For an ensemble of releases, the scatter-plot of the skewness S versus kurtosis K collapses to a quadratic curve lying above K=S2+1. Several explanations for this collapse have been put forth in the literature, including a model for cloud meander in instantaneous releases that does not treat the effects of turbulence on the internal structure of the cloud. In this paper, a model is proposed for the creation of internal striations within the cloud due to convection by the ABC-velocity field that is a paradigm for three-dimensional helical motions. The numerical simulations conducted here show that the collapse of the K-S scatter plot obtains under this more complicated situation where the smaller than cloud size structure is created by chaotic advection. Further, these simulations complement a recent multiscale analysis for eddy diffusivity of ABC flows.
Spatial and temporal filtering of experimental data for a priori studies of subgrid-scale stresses
Authors: Murray Joseph A. , Piomelli Ugo , Wallace James M.
Published: July 2002

The viability of utilizing experimental time series for the investigation of SGS physics is investigated by filtering temporal and spatial data from a DNS of fully developed turbulent channel flow. It is found that temporal filtering of single-point data corresponds to filtering in the streamwise direction, if an appropriate convection velocity is introduced. One-dimensional filtering, however, is not effective at separating the large and small scales in the near-wall region due to the strong flow anisotropy. Two-dimensional filtering in planes parallel to the wall is equivalent to three-dimensional filtering above y+≂10. Away from the wall, for y+≳50, where the turbulent eddies tend towards isotropy, streamwise (or temporal) filtering is adequate.
Spin-coating of a viscoplastic material
Authors: Burgess S. L. , Wilson S. D. R.
Published: July 2002

The flow of a thin film of a yield-stress material on a rotating disc is considered. For the constitutive relation we use the biviscosity model, of which the usual Bingham model is a limiting case. We show that this limiting process conflicts with the usual thin film approximation, so that care is needed to avoid contradictions. It is found that the flow consists of three regions: (1) an inner region centered on the axis of rotation which is unyielded, (2) a shear flow region adjacent to the disc which is bounded above by the yield surface and (3) a region near to the free surface which is unyielded and has the yield surface as lower boundary. It is in the third region that difficulties occur in the straightforward ‘‘Bingham limit.’’ For on the one hand the material is rigid, and on the other it is supposed to move outwards radially. This conflict can be removed by using the biviscosity model and a suitable limiting process.
Sideband instabilities of mixed barotropic/baroclinic waves growing on a midlatitude zonal jet
Authors: van der Vaart Paul C. F. , Dijkstra Henk A.
Published: July 2002

The instability of an arbitrarily shaped zonal jet on a midlatitude β-plane is considered within a two-layer quasi-geostrophic model with O(1) linear friction. Depending on the horizontal and vertical shear of the jet, it is susceptible to both barotropic and baroclinic instabilities. The linear stability boundaries are determined numerically for a parameter regime relevant to the Gulfstream. The weakly nonlinear (finite amplitude) evolution of the instabilities is shown to be governed by a Ginzburg-Landau equation and for arbitrary jet shapes the coefficients in this equation are computed numerically. The finite amplitude state is shown to become unstable to Benjamin-Feir sideband instabilities. The mixed baroclinic/barotropic character of the primary instability is crucial to this sideband instability which is shown to lead to complicated spatio-temporal behavior of the jet.