bluuebunny/crossref_metadata_2025 huggingface dataset:
Hydrodynamic modes of a uniform granular medium
Authors: McNamara Sean
Published: July 2002

This paper uses a fluid-mechanical model of a granular medium to calculate the hydrodynamic modes of a spatially uniform basic state. These modes are the granular analogs of the heat, sound, and shear modes of the standard fluid. Attention is focused on the possibility of an unstable mode that might result in the spontaneous development of inhomogeneities in density. Two cases are considered: the cooling medium which loses energy without replenishment, and the heated medium which reaches a steady state when an energy source balances the loss of energy through particle collisions. The spatially uniform state of the cooling granular medium is unstable. Two modes, analogous to the shear and heat conduction modes of a standard fluid, are unstable at long wavelengths. The growth of these modes is algebraic, rather than exponential, in time. The shear mode does not involve the formation of density inhomogeneities, but the heat mode does. At long wavelengths the heat mode can be visualized by imagining a converging velocity increasing the density of particles in a certain region. The increased collisional dissipation of granular thermal energy reduces the pressure, and prevents it from reversing the convergent velocities, so the condensation is not checked. The stability of the heated granular medium depends on the energy source. If the energy source selectively deposits energy in hot regions of a disturbance, the diffusion and collisional damping can be overwhelmed, and the disturbance grows exponentially. The standard fluid (completely elastic particles) can be recovered as a special case of the heated granular medium. In all cases, waves analogous to the sound and heat conduction modes are present. In some cases, a second type of sound wave is present at long wavelengths with the peculiar property of being damped more quickly for more elastic particles.
On statistical correlations between velocity increments and locally averaged dissipation in homogeneous turbulence
Authors: Chen Shiyi , Doolen Gary D. , Kraichnan Robert H. , She Zhen-Su
Published: July 2002

Kolmogorov postulated in 1962 [J. Fluid Mech. 13, 82 (1962)] that the magnitude of velocity increments δur across an inertial range distance r in high Reynolds number flows is typically (rεr)1/3, where εr is the locally averaged dissipation rate. This refined similarity hypothesis has been widely used in discussions of anomalous exponents of velocity structure functions in connection with the scaling exponents of εr. Recently Hosokawa and Yamamoto [Phys. Fluids A 4, 457 (1992)] have presented numerical evidence from turbulence simulations that δur is uncorrelated with εr in moderate Reynolds number flows. In the present paper, results of similar measurements are offered for flow fields with a wide range of Reynolds numbers obtained from high-resolution numerical simulations of both forced and decaying isotropic turbulence. The present results show clear evidence of correlations between δur and εr, irrespective of the Reynolds number. Kolmogorov’s hypothesis is verified for r somewhat larger than the viscous dissipation scale, but at much larger distances the correlation seems to be weaker.
Theoretical modeling of drift cyclotron loss-cone instability mode structures
Authors: Burkhart G. R. , Guzdar P. N. , Koepke M. E.
Published: July 2002

Measurements of the drift cyclotron loss-cone instability mode structure have recently been performed on MIX [Phys. Fluids 29, 3439 (1986)], an axisymmetric mirror machine characterized by a small width Maxwellian cold stream and a larger width loss-cone plasma. To model these measurements the Fourier-space integral equation was solved, derived from the linearized Vlasov equation for electrostatic perturbations, with both a matrix version technique and a WKB approximation. It is found that the mode is prohibited from the cold stream region by the process of mode conversion, which explains experimental results quite well.
Fluctuations and anomalous transport in tokamaks
Authors: Wootton A. J. , Carreras B. A. , Matsumoto H. , McGuire K. , Peebles W. A. , Ritz Ch. P. , Terry P. W. , Zweben S. J.
Published: July 2002

This is a review of what is known about fluctuations and anomalous transport processes in tokamaks. It mostly considers experimental results obtained after, and not included in, the reviews of Liewer [Nucl. Fusion 25, 543 (1985)], Robinson [in Turbulence and Anomalous Transport in Magnetized Plasmas (Ecole Polytechnique, Palaiseau, France, 1986), p. 21], and Surko [in Turbulence and Anomalous Transport in Magnetized Plasmas (Ecole Polytechnique, Palaiseau, France, 1986), p. 93]. Therefore much of the pioneering work in the field is not covered. Emphasis is placed on results where comparisons between fluctuations and transport properties have been attempted, particularly from the tokamak TEXT [Nucl. Technol./Fusion 1, 479 (1981)]. A brief comparison of experimentally measured total fluxes with the predictions of neoclassical theory demonstrates that transport is often anomalous; fluctuations are thought to be the cause.

The measurements necessary to determine any such fluctuation-driven fluxes are described. The diagnostics used to measure these quantities, together with some of the statistical techniques employed to analyze the data, are outlined. In the plasma edge detailed measurements of the quantities required to directly determine the fluctuation-driven fluxes are available. The total and fluctuation-driven fluxes are compared: the result emphasizes the importance of edge turbulence. No model adequately describes all the measured properties. In the confinement region experimental observations are presently restricted to measurements of density and potential fluctuations and their correlations. Various distinct turbulence features that have been observed are described, and their characteristics compared with the predictions of various models. Correlations observed between these fluctuations and plasma transport properties are summarized. A separate section on magnetic fluctuations shows there is very little information available inside the plasma, generally prohibiting quantified comparisons between fluctuation levels and transport. Both coherent and turbulent magnetic fluctuations are addressed, and the differences between low and high plasma pressure (low and high beta) are noted. The contributions of alternate confinement devices, such as stellarators and reversed field pinches, to understanding tokamak anomalous transport are discussed. Finally, future directions are proposed.
Global Alfvén eigenmode studies
Authors: Booth W. D. , Oakes M. E. , Valanju P. M.
Published: July 2002

Impedance measurements and magnetic probes are used to study driven global Alfvén eigenmodes in a small tokamak. The probes measure the field amplitudes in the outer region of the plasma, complementing earlier laser measurements in the plasma interior. An approximate analytic model is used to help determine mode numbers. The measured field profiles and impedance values are found to compare favorably with the predictions of a cylindrical, kinetic theory calculation. Measured widths of resonances are consistently found to be larger than theoretical predictions.
Influence of sheared poloidal rotation on edge turbulence
Authors: Biglari H. , Diamond P. H. , Terry P. W.
Published: July 2002

The impact of radially sheared poloidal flows on ambient edge turbulence in tokamaks is investigated analytically. In the regime where poloidal shearing exceeds turbulent radial scattering, a hybrid time scale weighted toward the former is found to govern the decorrelation process. The coupling between radial and poloidal decorrelation results in a suppression of the turbulence below its ambient value. The turbulence quench mechanism is found to be insensitive to the sign of either the radial electric field or its shear.
Multiple-frequency electron-cyclotron heating of hot-electron rings in a bumpy torus
Authors: Rasmussen D. A. , Bigelow T. S. , Batchelor D. B. , Hillis D. L. , Haste G. R. , Quon B. H. , Hankins O. E.
Published: July 2002

The use of multiple-frequency microwave power for electron-cyclotron heating significantly increased the ring stored energy in the SM-1 simple mirror device. Multiple-frequency electron-cyclotron heating (MFECH) was used on the ELMO Bumpy torus (EBT) in an effort to increase its hot-electron beta. No substantial improvement in the ring parameters was observed in a series of two-frequency ECH experiments, with frequency separations up to 90 MHz, in contrast to the dramatic improvement found in the axisymmetric SM-1 experiment. The toroidal canting of the EBT mirror sectors introduces asymmetries that destroy the superadiabatic behavior of the energetic electrons, reduce microwave heating efficiency, and produce additional ring losses. These effects qualitatively explain the different multiple-frequency heating results obtained in EBT and SM-1.
Trapped particle instability induced by axial shear in E×B velocity
Authors: Byers J. A. , Cohen R. H.
Published: July 2002

A new nonflute form of the E×B shear-driven trapped particle mode is obtained for a simplified square well equilibrium model of a tandem mirror. The mode is more unstable for a larger passing density in contrast to the curvature-driven trapped particle mode. Under some circumstances this mode can avoid the stabilizing effect of strong anchor curvature by isolating to the center cell and can do so without paying the magnetohydrodynamic (MHD) penalty for bending the field lines, thus requiring a large center cell ion gyroradius for stabilization.
Kinetic and fluid approaches to low-frequency magnetohydrodynamics: A comparison
Authors: Hassam A. B.
Published: July 2002

Kinetic and fluid approaches to the problem of low-frequency magnetohydrodynamic flute stability of plasmas where the equilibrium electron gradient-B drift is larger than the curvature drift are compared. It is shown that the two approaches are practically identical for frequencies below the curvature drift frequency. The identical nature of the approaches has to do with the fact that the large gradient-B drift has the primary effect of maintaining the electron temperature constant along its path; since this fact is independent of the collision frequency, the same equation of state applies to both approaches.
Pitot pressure indications of condensation in a nozzle flow
Authors: Bailey A. B. , Price L. L.
Published: July 2002

Some recent experimental studies of the expansion of gases from a diverging nozzle into hard vacuum have shown that for some nozzle flow conditions there are large off-centerline spikes in the exit plane pitot pressure profiles. Based on the results of the present study it has been suggested that pressure spikes of this type result from the presence of condensation in the expanding flow.
Ponderomotive and sideband coupling effects of ion-cyclotron heating on interchange stability
Authors: Cohen Bruce I. , Rognlien Thomas D.
Published: July 2002

Two-fluid theory is used to calculate the nonlinear effect of a finite-amplitude ion-cyclotron wave on the simple interchange stability of a magnetically confined plasma. The ion-cyclotron wave nonlinearly modifies interchange stability through ponderomotive effects and coupling to sidebands of the ion-cyclotron wave. Nonlinear stability criteria for flute modes are derived. The nonuniformity and polarization of the ion-cyclotron wave significantly influence the results. A theoretical explanation for recent experimental observations in axisymmetric mirror and tandem mirror plasmas of reduced levels of magnetohydrodynamic activity in the presence of ion-cyclotron resonant heating remains elusive.
Coherent nonlinear destabilization of tearing modes: The effect of the mass flow
Authors: Kleva Robert G. , Drake J. F. , Bondeson Anders
Published: July 2002

Three-dimensional tearing modes are shown to be linearly unstable in a helical equilibrium containing large-amplitude q=2 magnetic islands and their associated plasma flow. The source of the instability is a steep current gradient which is formed at the inner separatrix of the q=2 islands as they evolve. The coherent flow associated with the q=2 islands has a strong influence on the growth of the three-dimensional modes. In particular, this flow can dominate the resistivity in the linear stability analysis of these modes.
3ω/2 harmonic emission from thin foils
Authors: Aboites V. , Hughes T. P. , McGoldrick E. , Sim S. M. L. , Karttunen S. J. , Evans R. G.
Published: July 2002

Temporally and spectrally resolved 3ω0/2 harmonic emission has been recorded from 1.05 μm laser-irradiated thin foil targets which become underdense during the laser pulse of 600–900 psec. Changes in the spectra of both the backscattered and forward scattered harmonic light are observed coincident with the disappearance of the nc surface. The results are analyzed by considering the matching conditions for the generation of the 3ω0/2 light, including the effects of plasma wave refraction in the inhomogeneous plasma.
Stability of a hot-electron-stabilized symmetric tandem mirror with thermal barrier
Authors: Tsang Kang T.
Published: July 2002

It is shown that in general the stability of a hot-electron-stabilized symmetric tandem mirror is the same as the stability of its barrier-plug cell alone, plus an additional limitation on the center-cell length such that the center-cell Alfvén frequency is higher than the average barrier-plug E×B drift and the hot-electron precession frequency. The stability of the hot-electron barrier-plug cell is studied extensively.
Stabilization of interchange modes in mirror plasmas by resonant coupling to ion-cyclotron sidebands
Authors: Stefan V. , McBride J. B.
Published: July 2002

Based on a nonlinear, local mode–mode coupling relation, the resonant interaction of flute-interchange modes with radio frequency (rf ) wave fields in the ion-cyclotron range of frequencies (ICRF) is studied. It is shown that interchange modes can be stabilized because of resonant coupling to electrostatic ion-cyclotron sidebands. Stabilization takes place if the frequency of the rf field is somewhat higher than the local ion-cyclotron frequency, as observed in contemporary experiments on mirror devices.
Observations of the dissipative trapped electron instability in a mirror plasma produced by electron-cyclotron resonance
Authors: Suetsugu Y. , Kawai Y.
Published: July 2002

The dissipative trapped electron instability driven by the finite Larmor radius effects is observed in a mirror plasma produced by electron-cyclotron resonance using the Lisitano coil. The effect of the radial electron temperature gradient on the excitation of this mode is studied theoretically and experimentally. It is found that the electron temperature gradient opposite to the density gradient tends to stabilize this mode.
The anisotropic plasma fluid stress tensor and its dispersion relation
Authors: Evangelidis E. A. , Neethling J. D.
Published: July 2002

Using the concept of an anisotropic plasma as a working hypothesis, a stress tensor has been constructed that is determined by five independent coefficients. As an application the general expression for the dispersion relation is derived. Under certain limiting conditions it was found that the plasma mode ω2ε =(4πηεe2)/mε decays exponentially because of the c33 coefficient, with a decay time τ33=2ρ0/c33k2.
Kinetic description of betatron oscillation instability for nonrelativistic nonneutral electron flow
Authors: Davidson Ronald C. , Uhm Han S.
Published: July 2002

The linearized Vlasov–Poisson equations are used to investigate the electrostatic stability properties of nonrelativistic nonneutral electron flow in a planar diode with cathode located at x=0 and anode at x=d. The electron layer is immersed in a uniform applied magnetic field B0êz, and the equilibrium flow velocity V0yb(x) is in the y direction. Stability properties are calculated for perturbations about the choice of self-consistent Vlasov equilibrium f0b (H,Py) =(n̂b/2πm) δ(H) δ(Py), which gives an equilibrium with uniform electron density (n̂b =const) extending from the cathode (x=0) to the outer edge of the electron layer (x=xb). Assuming flute perturbations, the eigenvalue equation is simplified and solved analytically for long-wavelength, moderately high-frequency perturbations satisfying k2x2b ≪1 and (ω−kVd)2 ≊ω2v =ω2c −ω̂2pb. The present analysis is restricted to electron densities below the Brillouin flow (ω̂2pb <ω2c) and the nonzero electric field at the cathode. The eigenvalue equation leads to a fourth-order algebraic dispersion relation for the complex eigenfrequency. The dispersion relation is solved numerically, and detailed stability properties are investigated as a function of system parameters for both the upshifted branch (ω−kVd ≊+ωv) and the downshifted branch (ω−kVd≊−ωv). For a sufficiently thin electron layer, it is found that only the upshifted branch exhibits instability. Typically, instability exists for a range of ω̂2pb/ω2c.
Long waves in a canal with a porous plate located at a step
Authors: Tyvand Peder A.
Published: July 2002

A linear shallow water theory of waves in a canal is considered. The energy dissipated by a porous plate located at a step where both the depth and width of the canal changes abruptly is calculated. It is found that a broadening of the canal, combined with a plate with optimal properties, is an efficient way of dissipating wave energy. It is also possible to have a strong wave damping without any reflection.
Helical axis stellarator equilibrium and resistive ballooning
Authors: Depassier M. C. , Cooper W. A.
Published: July 2002

An approximate analytic solution of the magnetohydrodynamic (MHD) equilibrium equation for large-aspect-ratio, helically symmetric systems is obtained. The resistive ballooning stability of these equilibria is studied numerically and analytically. We find that the ballooning modes scale as the resistivity to the third power. They are driven by the helical nature of the magnetic axis and by the elliptic distortion of the flux surfaces away from a circle.
Use of the two-ion hybrid as an impurity diagnostic
Authors: Chen Francis F. , Dimonte G. , Christensen T. , Neil G. R. , Romesser T. E.
Published: July 2002

In a plasma containing more than one ion species, the frequencies of the ion–ion hybrid resonances can be a sensitive measure of the densities of the minor species, but only if the frequency shifts caused by electron motions are small, as experimental observations suggest. By calculating the eigenfrequencies for ion–ion hybrid waves taking into account collisions, Landau damping, electron inertia, electromagnetic effects, and density gradients, it is found that the frequency shifts are not negligible unless k∥ is extremely small. Treatment of the sheath boundary conditions at the ends of a plasma column shows that the effective value of k∥ can indeed be sufficiently small, and that the uncorrected resonance frequency is surprisingly accurate over a wide parameter range. Data from an Ar–Xe discharge demonstrate the usefulness of this technique for measuring impurity concentrations.
Gain enhancement in a longitudinal magnetic wiggler by use of a coherently gyrophased electron beam
Authors: Fruchtman Amnon
Published: July 2002

The growth rate of the instability in the lowbitron [Appl. Phys. Lett. 39, 845 (1981)]—the longitudinal wiggler beam interaction device—is shown to be enhanced significantly by the use of a coherently gyrophased electron beam.
Comment on ‘‘Simulations of the single-mode, bump-on-tail instability’’ [Phys. Fluids 2
8, 2773 (1985)]
Authors: Dewar R. L.
Published: July 2002

Careful analytical estimation of the saturation condition for a monochromatic wave growing on a weak warm beam, using a theory based on particle orbits in the sudden and adiabatic switching approximations, gives satisfactory agreement with numerical simulations.
Supercritical shocks in nozzle flows with nonequilibrium condensation
Authors: Clarke Joseph H. , Delale Can F.
Published: July 2002

Supercritical normal shock waves in fully choked nozzle flows with nonequilibrium condensation are considered. The continuous subcritical nozzle flow solution is supplemented by the normal shock jump conditions to account for the frozen, gas dynamic, normal shock wave embedded in the droplet growth zone caused by supercritical heat addition from condensation. The location of the normal shock wave is then determined by employing Barschdorff’s [Forsch. Ingenieurwes. 37, 146 (1971)] shock fitting technique, which in this work is converted into a noniterative analytical framework.
Taylor–Maccoll problem in relativistic gasdynamics
Authors: Granik A.
Published: July 2002

The supersonic flow of the ultrarelativistic fluid around a circular cone is considered. This flow is described by the equation identical to the Taylor–Maccoll [Proc. R. Soc. London Ser. A 139, 278 I (1933)] equation in nonrelativistic gasdynamics. The characteristics of the post-shock gas are found. The maximum cone angles at which the shock is attached to the cone are less than the respective values in nonrelativistic gasdynamics.
Tandem mirror trapped particle instability driven by axial shear in E×B rotation
Authors: Byers J. A.
Published: July 2002

A complete solution is obtained for the growth rate and real frequency of electrostatic trapped particle modes driven by the axial shear in the equilibrium E×B rotational frequency ωE in the eikonal limit for a simplified square well equilibrium model of a tandem mirror. The instability takes on a flute character for some region of parameter space, principally at low mode number and large passing fraction, with a growth rate γ2=m2∼((ΔωE)2), in agreement with prior calculations, but is nonflute elsewhere, even with zero curvature. The mode is more unstable for larger passing density in contrast to the curvature-driven trapped particle mode which is stable for larger passing density. This feature makes the mode probably more dangerous for more strongly collisional devices. In the flute regime this mode appears identical to the magnetohydrodynamic (MHD) flute version of the shear mode. Depending on the sign of the charge of the passing species and the sign of the change in ωE, this trapped particle mode can isolate itself to the center cell and thus avoid the stabilizing effect of strong anchor curvature and can do so without paying the MHD penalty for bending the field lines, thus requiring large center cell ion gyroradius for stabilization. For some typical tandem equilibria, this worst form of the mode is not possible since the mode tends to isolate to the anchor rather than to the center cell. In this case the shear in the rotation can also help to stabilize the curvature-driven mode.
New analytical solution for an ion-acoustic soliton in a two-ion plasma
Authors: Sharma S. R. , Yashvir  , Bhatnagar T. N.
Published: July 2002

A new analytical solution is obtained for an ion-acoustic soliton, which is much closer to the exact solution than the Korteweg–de Vries (KdV) solution. The case of a two-ion plasma is considered in detail, and the results are compared with those of the dressed soliton solution. The effect of multiple ionization of the ion species is also discussed.
The stimulated Raman threshold. I. Experiment
Authors: Amini Behrouz , Chen Francis F.
Published: July 2002

The threshold intensity for excitation of the stimulated Raman backscatter instability has been measured at 9.58 μm in a well-diagnosed plasma free of Brillouin scattering. The initial level of density fluctuations was independently measured by ruby laser scattering. The observed threshold of 1×1011 W/cm2 is somewhat below the calculated ‘‘absolute’’ threshold for underdense plasmas, and the apparent noise level is higher than that measured directly.
Theory of Raman sidescattering for a laser-produced plasma with an exponential density profile
Authors: Kutty A. P. G. , Sinha B. K.
Published: July 2002

Equations for the stimulated Raman sidescattering from a laser-produced plasma with an exponential density profile have been derived. They have been solved by using the WKB method, and the resulting Bohr–Sommerfeld condition has been solved numerically for the growth rates of the absolute instability and the frequency shifts as a function of the laser intensity, the density gradient scale length, and the plasma frequency. The results have been discussed and compared with the previously reported work on the plasma with linear density profile. Instability growth rates are found to be nearly the same for both cases, except for very steep density profiles, for which the difference can become appreciable. The two theories, one of which considers a hot plasma, lead to significantly different frequency shifts. It is found that, for high laser powers, the instability persists even for very steep profiles. Furthermore, for such profiles the maximum of the growth rate occurs far away from the quarter critical layer, for moderately high power lasers.
Statistical estimation of a nonlinear diffusion system in a gravitational field
Authors: Etori Kanji
Published: July 2002

A nonlinear diffusion equation with a diffusion coefficient depending on the number density of diffusing particles affected by gravity is solved approximately for a stationary state. As a result, expectation values of both the number density and its position are estimated to explain the shifts from a linear diffusion system in conventional theories.
Supersonic interface instabilities of accelerated surfaces and jets
Authors: Gardner Carl L.
Published: July 2002

The compressible Rayleigh–Taylor instability of a supersonic accelerated contact discontinuity between two gases is studied by numerically solving the two-dimensional Euler equations. The computed solutions exhibit a complicated set of nonlinear waves comprised of spike and bubble bow shocks, terminal shocks within the spike and bubble, Kelvin–Helmholtz rollup of the spike tip, and contact surface waves. The spike appears to attain a finite growth of aspect ratio approximately equal to 2. The propagation of a supersonic slab jet is also studied numerically, in order to compare and contrast the jet wave structure with that of the supersonic accelerated surface.
Stationary states of dissipative modes in cylindrical geometry
Authors: Dagazian R. Y. , Paris R. B.
Published: July 2002

The theory of resistive instabilities (tearing and interchange) has been reworked including the full collisional viscous tensor and thermal conductivity in cylindrical geometry. The existence of stationary states made possible by the presence of viscous effects is established. These states are important as they form the basis for calculating anomalous heat transport in weakly nonlinear regimes.
A nonlinear stability theorem for baroclinic quasigeostrophic flow
Authors: Swaters Gordon E.
Published: July 2002

The baroclinic quasigeostrophic equations describe the essential dynamics of large-scale, low-frequency atmospheric ocean flow. A nonlinear stability theorem is given based on a convexity argument of Arnold [Am. Math. Soc. Transl. 19, 267 (1969)], complementing a linear analysis by Blumen [J. Atmos. Sci. 25, 929 (1968)]. An a priori estimate bounding the growth of perturbation is derived.
Calculation of the electrical conductivity of a partially ionized gas
Authors: Simpson S. W.
Published: July 2002

The theoretical calculation of electron transport properties in partially ionized gases using a Laguerre (or Sonine) polynomial expansion has met with convergence difficulties in certain cases, in particular, when there is a Ramsauer minimum in the electron-neutral momentum transfer cross section. In this work, which deals specifically with electrical conductivity, it is shown that the difficulties can be avoided by choosing a (nonorthogonal) expansion that includes a limiting-case analytical solution. With some simplifications, the approach leads to a practical formula for the conductivity involving generalized collision integrals. A formula based on a BGK-type approximation to the electron–electron collision operator is also given. Calculated conductivities are found to agree well with the more sophisticated expansion method.
Wavenumber selection in large-amplitude axisymmetric convection
Authors: Buell Jeffrey C. , Catton Ivan
Published: July 2002

Unique wavenumbers are calculated for axisymmetric Rayleigh–Bénard convection as a function of the Rayleigh number (R) up to the second critical value for several different Prandtl numbers. The analysis assumes slightly bent rolls (large radius of curvature) and that there exists a horizontal pressure gradient strong enough to force the net mean flow induced by curvature to be zero. The assumptions are satisfied for axisymmetric convection in a large aspect ratio cylinder (however, this may not be the only case). Manneville and Piquemal [Phys. Rev. A 28, 1774 (1983)] found the initial slope of the selected wavenumber with respect to Rayleigh number (using an analytic solution valid for small amplitude solutions) and our calculations agree with theirs. This initial slope is sensitive to the Prandtl number (P), but at moderate to large R the selected wavenumber is approximately independent of P when P>3. For smaller P larger wavenumbers are found, but this does not contradict any available experimental evidence.
Monte Carlo neutral density calculations for a bumpy torus
Authors: Davis W. A. , Colchin R. J.
Published: July 2002

The steady-state nature of the ELMO Bumpy Torus (EBT) [J. Vac. Sci. Technol. 18, 1088 (1982), and references therein] plasma implies that the neutral density at any point inside the plasma volume determines the local particle confinement time. This article describes a Monte Carlo calculation of three-dimensional atomic and molecular neutral density profiles in EBT. The calculation has been done using various models for neutral source points, for launching schemes, for plasma profiles, and for plasma densities and temperatures. Calculated results are compared with experimental observations—principally spectroscopic measurements—both for guidance in normalization and for overall consistency checks. Implications of the predicted neutral profiles for the fast-ion decay measurement of neutral densities are also addressed.
Dipole vortex solutions of magnetohydrodynamic equations describing microturbulence
Authors: Yu M. Y. , Lisak M.
Published: July 2002

The general set of low-frequency nonlinear fluid equations describing microturbulence in an inhomogeneous warm plasma with a strong magnetic field is shown to possess two-dimensional solitary vortex solutions.
Effects of viscosity on plasma equilibria
Authors: Kim Y. B. , Callen J. D.
Published: July 2002

High-beta large ion-gyroradius plasmas in the University of Wisconsin Octupole [Phys. Rev. Lett. 46, 1394 (1981)] exhibited an anomalous diamagnetism that is smaller than the prediction from ideal magnetohydrodynamic (MHD) theory by a factor of up to 5. The effects of viscosity on the equilibrium diamagnetism are presented and shown to be qualitatively consistent with the experimental results.
Destabilization of Alfvén-resonant modes by resistivity and diamagnetic drifts
Authors: Aydemir A. Y. , Hazeltine R. D. , Meiss J. D. , Kotschenreuther M.
Published: July 2002

The existence of unstable resistive drift-Alfvén modes is shown in a cylindrical geometry. The modes, driven by nonuniformities in the diamagnetic drift frequency, are unstable even when the associated purely resistive mode is stable. The growth rate has a weak, η1/4, dependence on resistivity. Because of their large growth rates, they may play an important role in tokamak confinement.
Phase space density representation of inviscid fluid dynamics
Authors: Abarbanel Henry D. I. , Rouhi A.
Published: July 2002

A formulation of inviscid fluid dynamics based on the density F(x,v,t) in a single-particle phase space [x=(x1,x2,x3), v=(v1,v2,v3)] is presented. This density evolves in time according to a Poisson bracket of F with H(x,v,t)—a Hamiltonian in the same single-particle phase space. Compressible flows of barotropic fluid and homogeneous, incompressible flows are disscussed. The main advantage of the phase space density formulation over either Euler or Lagrange formulations is the algebraic and conceptual ease in making fully Hamiltonian approximations to the flow by altering H(x,v,t) and the Poisson brackets appropriately. The example of a shallow layer of rapidly rotating fluid where a Rossby number expansion is desired will be discussed in some detail. Changes of phase space coordinates that give an approximate H (expanded in Rossby number) and exact Poisson brackets will be exhibited. The resulting quasigeostrophic equations for F are two-dimensional partial differential equations to every order in Rossby number. The extension to multiple layers will be presented.
Infrared properties of an anisotropically stirred fluid
Authors: Rubinstein Robert , Barton J. Michael
Published: July 2002

A renormalization group is developed for the Navier–Stokes equations driven by an anisotropically correlated random stirring force. The stirring force generates homogeneous turbulence with a preferred direction. The force correlation is the sum of a small anisotropic perturbation and an isotropic correlation chosen so that the fixed point of the renormalization group has a k−5/3 energy spectrum. Fixed points for the anisotropic correlation are found near this isotropic fixed point. Two types of anisotropy are analyzed. When the additional stirring is in the plane perpendicular to the preferred direction, the renormalized viscosity is increased. When it is aligned with the preferred direction, the viscosity is decreased. A possible connection with the inverse energy cascade of 2-D turbulence is discussed.
Anomalous resistivity in an inhomogeneous plasma
Authors: Akama H. , Nambu M.
Published: July 2002

A general expression for the effective collision frequency associated with current-driven ion sound turbulence in an inhomogeneous plasma is given based on generalized ponderomotive forces. The order of magnitude is estimated for each of the terms for the generalized ponderomotive forces.
Landau constant of plane Poiseuille flow near the neutral state
Authors: Fujimura Kaoru
Published: July 2002

Two kinds of nonlinear stability theories are examined, Herbert’s method [J. Fluid Mech. 126, 167 (1983)] and that of Watson [J. Fluid Mech. 9, 371 (1960)]. They are compared by calculating the first Landau constant of plane Poiseuille flow numerically according to their definitions. It is found that ‖λ(H)1r−λ(W)1r‖/λ(H)1r ∝λ0 is satisfied near the neutral state, where λ(H)1r and λ(W)1r are the real parts of the first Landau constant defined by the methods of Herbert and Watson, respectively, and λ0 is the linear growth rate. This conclusion is consistent with the error estimation by Herbert, but is more accurate.
Discrete set selection of Saffman–Taylor fingers
Authors: Kessler David A. , Levine Herbert
Published: July 2002

A study of the linear stability of the discrete set of steady-state Saffman–Taylor finger solutions at finite surface tension is presented. It is shown by explicit computation that members of the set aside from the lowest width finger are linearly unstable. This completes the demonstration that finite surface tension effects determine uniquely the allowed interfacial pattern in the steady-state regime.
Monte Carlo estimates of particle and energy confinement times in a bumpy torus and a bumpy square with poloidal electric fields
Authors: Tolliver J. S. , Hedrick C. L.
Published: July 2002

Since significant poloidal structure in the electrostatic potential in Elmo Bumpy Torus (EBT) has been observed experimentally [Phys. Fluids 28, 2848 (1985)] and predicted theoretically (C. L. Hedrick, submitted to Phys. Fluids), a Monte Carlo calculation has been used to make estimates of the particle and energy confinement times in EBT with varying degrees of asymmetry in the electric field. The code is applicable to the bulk ion population and the ‘‘cool’’ electron population in EBT, but not to the intermediate-energy electrons believed to be responsible for the formation of the potential. A similar calculation is possible for an alternate magnetic field configuration known as a bumpy square, which is expected to have more symmetric potential profiles because of much better centering of the particle orbits. The calculations indicate that the confinement time in a bumpy square would be two to three orders of magnitude better than in EBT.
Analytical solutions for the growth of oblique waves in a plasma with a field-aligned beam
Authors: Summers Danny , Thorne Richard M.
Published: July 2002

The theory of kinetic instabilities in a plasma when the instabilities are driven by wave-particle resonance is addressed. Recent progress on the linear theory of resonant oblique wave growth in plasmas is extended to plasmas modeled by three standard forms of distribution, a bi-Maxwellian, a bi-Lorenzian, and a loss cone, each incorporating a field-aligned beam. The wave growth rates are shown to be functions of dimensionless integrals that can be expressed in terms of Bessel functions of argument equal to a normalized wave-normal variable. A marginal stability criterion is obtained, and accordingly we identify a threshold beam velocity for unstable growth of the waves. The simple analytical results derived can be readily applied to a wide variety of problems on oblique wave growth in space plasmas that hitherto were amenable only to extensive computer calculations.
Equipartition of energy in magnetohydrodynamics
Authors: Dassios George , Lucas R. J.
Published: July 2002

The time evolution of the energy for wave propagation in an infinite ideal magnetofluid is studied analytically. It is found that equipartition between the kinetic and potential energies is achieved. Equipartition occurs either in finite time or asymptotically as t→∞ depending upon whether the initial data are compactly supported or have finite energy, respectively.
Low-frequency azimuthally propagating (diocotron) waves in a non-neutral electron beam column
Authors: Chen K. W. , Kim S. H. , McKinley M. C.
Published: July 2002

Naturally occurring and externally driven stable low-frequency (6–500 kHz) oscillations have been observed for an electron beam column. Experimental data are presented for oscillations of 357 kHz (natural) and 181 kHz (driven). Phase shift measurements using six azimuthal probes spaced 60° apart show that the oscillations correspond to l=1 diocotron waves.
Confinement of a self-stabilized tokamak under average magnetic well conditions
Authors: Demchenko V. V. , Fu G. Y. , Van Dam J. W.
Published: July 2002

It is well known that the average favorable magnetic curvature of a tokamak is stabilizing with respect to pressure-driven magnetohydrodynamic instabilities at low beta and that self-stabilization occurs at finite beta in the so-called second stability regime. Here it is self-consistently investigated how these two effects, viz., the mean magnetic well and the self-stabilization, influence the energy confinement time in a tokamak, with the use of the ballooning mode transport model proposed by Connor, Taylor, and Turner [Nucl. Fusion 24, 642 (1984)].
Comments on ‘‘Motion of an electron bunch through a plasma’’ [Phys. Fluids 2
9, 262 (1986)]
Authors: Simon A. , Short R. W.
Published: July 2002

Shoucri and Storey [Phys. Fluids 29, 262 (1986)] have used a Vlasov code to follow the motion of a bunch of fast electrons through an isotropic plasma. The bunch sheds a train of oscillations. It is shown that the observed wavelength of this train follows from a calculation of the frequency of the fastest growing bump-on-tail instability mode in the bunch region.
Solutal convection in the melt during solidification of a binary alloy
Authors: Riahi D. N.
Published: July 2002

Nonlinear solutal convection in the melt under a planar solidifying surface is investigated in the limit of small segregation. Stationary solutions of the nonlinear problem are obtained and the preferred mode of convection is determined by a stability analysis. It is found that down-hexagons (where motion is downward at the cells’ centers) are stable for sufficiently small amplitude Ε, while both down-hexagons and squares are stable in a range of larger Ε. The dependence of various flow features on the segregation coefficient and the effective depth of the melt is discussed.
Radial oscillations and the ion hose instability of an electron beam propagating in a periodic ion channel
Authors: Bosch R. A. , Gilgenbach R. M.
Published: July 2002

Recently, the propagation of an electron beam through an ion channel with periodically varying ion density has been proposed as a method of transporting or modulating an electron beam. A theoretical treatment indicates that, in the absence of an external magnetic field, cylindrically symmetric radial oscillations of the beam electrons are excited by the channel, with resonant excitation occurring when the wavelength of the ion density variation equals the betatron wavelength. An analysis of the ion focusing regime (IFR) ion hose instability indicates that the e-folding length of this instability increases when the variations of the electron density are increased. In the absence of an external magnetic field and damping, moderate electron density variations (caused, for example, by a periodic ion channel or the nonrigidity of the beam and channel) result in a wavelength and e-folding length on the order of the beam-averaged betatron wavelength.
Studies of stimulated Raman scattering in a plasma filament
Authors: Barr H. C. , Boyd T. J. M. , Coutts G. A.
Published: July 2002

The effect of a plasma filament on the characteristics of stimulated Raman scattering is examined. The model representation of the filament allows an assessment of the way in which Raman growth rates are influenced not only by the density inhomogeneity transverse to the beam direction, but by the nonuniform intensities of the incident laser and scattered light, as well as by Landau damping in the plasma. The model determines global eigenvalues without recourse to local (WKB) approximations, or to phenomenological damping factors. In shallow filaments the concentration of the light gives rise to modest gains in growth, while for deeper filaments the effects of the inhomogeneity and of Landau damping are dominant and suppress the instability. In both cases the strongest growth occurs at the bottom of the filament. Waveguide effects in deep filaments can result in emission being constrained to wavelengths significantly shorter than twice that of the incident laser light.
Nonlinear unstable viscous fingers in Hele–Shaw flows. II. Numerical simulation
Authors: Meiburg E. , Homsy G. M.
Published: July 2002

The nonlinear stages of two-dimensional immiscible displacement processes in Hele–Shaw flows are investigated by means of large scale numerical simulations based on a purely Lagrangian vortex method. The vortex sheet at the interface between the two fluid phases is discretized into circular arcs with a continuous distribution of circulation, which renders our numerical technique highly accurate. A complicated unsteady growth mechanism is observed for the emerging viscous fingers, involving a combination of spreading, shielding, and tip splitting. As the surface tension is further reduced, smaller length scales arise and the fingertip exhibits a new splitting pattern in which three new lobes emerge instead of two. Monitoring the velocity as well as the radius of curvature at the fingertip demonstrates that the instability of the finger evolves in an oscillatory fashion. The two-lobe and the three-lobe splitting can thus be explained as different manifestations of the same instability mode. Comparison with experiment shows good qualitative but only fair quantitative agreement. By imposing a constraint on the curvature at the fingertip, experimental results, which show fingers of width considerably smaller than half the cell width and exhibit ‘‘dendritic’’ instability modes, are reproduced.
Quasilinear diffusion in a weakly inhomogeneous relativistic magnetized plasma
Authors: De Jagher P. C. , Sluijter F. W.
Published: July 2002

Quasilinear diffusion due to the presence of electromagnetic waves in a magnetized relativistic plasma is studied. It is shown that the diffusion equation contains a term (Ω/γ) ∂φ〈 f 0〉, thus taking into account finite gyroradii effects. Furthermore, it is shown that the diffusion coefficient is a tensor that has an antisymmetric part if the wave has a transverse component. Consequently, the quasilinear diffusion process due to transverse waves is described by an equation that contains a drag term.
The formation of vortex rings
Authors: Glezer Ari
Published: July 2002

Vortex rings are usually formed by a brief discharge of fluid from an orifice. In previous investigations, the geometry of the vortex generator has varied greatly from one experiment to another, with important consequences for the ensuing flow. The present work categorizes the generating conditions for vortex rings and classifies the conditions under which a given vortex generator produces either an initially laminar ring, which may or may not undergo instability and transition to turbulence, or an initially turbulent ring. A particularly simple vortex generator was devised and measurements were carried out to provide systematic data over a range of the important dimensionless parameters. The results of this survey are used to construct a transition map that reveals a reasonably well defined boundary separating vortex rings that are turbulent upon formation from those that are not. High-speed cinephotography of the formation and evolution of turbulent vortex rings suggests a possible connection between the generating conditions and the transition to turbulence.
Radial localization of drift cone and ion cyclotron loss cone modes
Authors: Burkhart G. R. , Guzdar P. N. , Littlejohn R. G.
Published: July 2002

The localization of drift and ion cyclotron modes as well as the drift cyclotron instability for both Maxwellian and loss cone ion energy distributions have been studied. The WKB method for integral equations is found to give insight into the mode structure as well as characteristics of the spectrum, and the method will be used to understand recent numerical results of other authors.
Linear theory of drift-tearing and -interchange modes
Authors: Copenhaver C.
Published: July 2002

A drift dispersion relation, as applied to a resistive incompressible plasma in cylindrical geometry, is derived. This dispersion relation incorporates both drift-tearing and drift-interchange modes and is valid throughout the collisional regime by including kinetic theory factors. The dispersion relation reduces to the drift-tearing dispersion relation in the zero pressure gradient limit, and to the classical resistive dispersion relation in the zero drift limit. The electron temperature-gradient instability is still present. Now, however, the introduction of the drift-interchange instability increases the growth rate further above the drift-tearing case.
Ion-Bernstein wave propagation in tokamak edge plasma during heating in the ion cyclotron range of frequencies
Authors: Antani S. N. , Scharer J. E.
Published: July 2002

The propagation of a directly launched ion-Bernstein wave is considered in the tokamak edge plasma region in the frequency range Ωi <ω< 2Ωi, and in the limit of small k⊥0ρi. Employing standard perturbation techniques, the wave scattering from a Gaussian spectrum of density fluctuations and the self-modulation resulting from the ponderomotive force nonlinearity are investigated. The results for the typical parameters of the PLT tokamak [Phys. Rev. Lett. 54, 2339 (1985)] and the ALCATOR-C tokamak [Phys. Rev. Lett. 59, 1201 (1987)] indicate that the scattering effect becomes important in the edge region as the fluctuation level is increased from 1% to 30%. Also, it is found that at the power levels currently being used in the experiments, large ponderomotive modifications in the plasma density are produced in the near zone of the launcher. In the weak nonlinearity limit, the ion-Bernstein wave is found to be modulationally unstable, thus implying the possibility of localized heating.