bluuebunny/crossref_metadata_2025 huggingface dataset:
Side-wall gas ‘‘creep’’ and ‘‘thermal stress convection’’ in microgravity experiments on film growth by vapor transport
Authors: Rosner Daniel E.
Published: July 2002

While ‘‘no-slip’’ boundary conditions and the Navier–Stokes equations of continuum fluid mechanics have served the (moderate-to-‘‘high’’ pressure) vapor transport community well until now, it is pointed out that transport conditions within highly nonisothermal ampoules (e.g., those used to grow organic solid thin films in microgravity experiments) are such that the nonisothermal side walls ‘‘drive’’ (rather than damp) the dominant convective flow, and the familiar Stokes–Fourier–Fick laws governing the molecular fluxes of momentum, energy, and (species) mass in the ‘‘continuum’’ field equations will often prove to be inadequate, even at Knudsen numbers as small as 10−3. The implications of these interesting gas kinetic phenomena under microgravity conditions, and even under ‘‘Earth-bound’’ experimental conditions, are outlined here, along with a tractable approach to their systematic treatment.
Weakly nonlinear behavior of periodic disturbances in two-layer Couette–Poiseuille flow
Authors: Renardy Yuriko
Published: July 2002

The stability of a plane Couette–Poiseuille flow consisting of two layers of different fluids is analyzed using methods of bifurcation theory. The fluids have different viscosities and densities, and there is surface tension at the interface. The center manifold theorem is used to justify the derivation of the final amplitude evolution equation. The nonlinear calculations are carried out with two alternative approaches. One approach is to keep the combined volume flux fixed, and the other is to keep the pressure gradient in the horizontal direction fixed. Numerical results are presented for some Couette flow profiles and a Poiseuille flow profile at low speeds, showing that traveling waves are supported at the interface. A computation at a high speed is also presented. The derivation and numerical results are compared with those of a formal approach, employing multiple scales, which has been used on related problems.
‘‘Breakthrough’’ via dipolar-vortex/jet formation in shock-accelerated density-stratified layers
Authors: Yang Xiaolong , Zabusky Norman J. , Chern I-Liang
Published: July 2002

Convective ‘‘breakthrough’’ after an inclined planar light fluid layer is struck by a shock wave is observed and quantified. The results of direct numerical simulations are interpreted and a convective breakthrough time tb is quantified. Initially, vorticity of opposite sign is deposited on each interface of the layer. Breakthrough occurs when these vortex regions approach and ‘‘bind’’ into a dipolar vortex (or jet head) that moves away from the wall. Variations of tb with Mach number of the incoming shock waves are given.
On one property of Lamb vector in isotropic turbulent flow
Authors: Tsinober A.
Published: July 2002

It is shown that the potential part of Lamb vector λ=ω×u, ω=∇×u, where u is an isotropic Gaussian solenoidal random field, is much larger than its solenoidal part. This result shows that purely kinematic properties of turbulent flow can lead to essential reduction of its nonlinearity and thereby to impose considerable constraints on flow dynamics and topology.
An analytical solution for the scalar probability density function in homogeneous turbulence
Authors: Gao Feng
Published: July 2002

The probability density function (pdf) of a passive scalar in homogeneous turbulence is studied using the mapping closure model recently developed by Kraichnan and co-workers. An analytical solution for the mapping equation is derived. This solution preserves the boundedness of the scalar fields and yields the pdf’s that relax to Gaussian distributions, in agreement with experiments and numerical simulations.
The effects of rotation on initially anisotropic homogeneous flows
Authors: Mansour Nagi N. , Shih Tsan-Hsing , Reynolds William C.
Published: July 2002

Rotation of initially anisotropic homogeneous flows is studied using a model spectral tensor. It is shown that the anisotropy changes because of the influence of rotation through phase scrambling. Phase scrambling causes the Reynolds stresses to develop with damped oscillations. The final Reynolds stress anisotropy is found to be proportional to the initial structural tensor anisotropy. Closure models for the rapid pressure strain terms should reflect this change in anisotropy, and should drive the anisotropy to reach its final predicted state. Finally, it is shown that long-time integration using direct numerical simulations should be treated with care because phase scrambling effects on a discrete wave space can cause loss of resolution when time becomes large.
Shock-to-detonation transition: A model problem
Authors: Bdzil J. B. , Kapila A. K.
Published: July 2002

The process by which a trigger ignited shockless weak detonation is transformed into a classical Zeldovich–von Neumann–Doering (ZND) detonation as the trigger wave decelerates is considered in detail. This occurs as the trigger speed passes through the Chapman–Jouguet velocity DCJ. The model that is developed describes the birth and subsequent growth of a shock in the weak detonation reaction zone. This shock ultimately sustains the shock-ignited ZND detonation. The time-dependent solution presented here fills one of the many gaps in the understanding of detonation flows; an understanding based almost entirely on steady wave structures.
Coherence and chaos in a model of turbulent boundary layer
Authors: Zhou Xiang , Sirovich L.
Published: July 2002

The dynamics of coherent structures in the wall region of a turbulent channel flow is considered. The Karhunen–Loève eigenfunctions and Galerkin procedure are used to derive the dynamical description. In a previous treatment of this problem by Aubry et al. [J. Fluid Mech. 192, 115 (1988)] the analysis required an inhomogeneous pressure term to be supplied from outside the theory. In the first part of this paper this theory is reconsidered on the basis of the construction of wall eigenfunctions that have a full channel validity. As a result of the methods developed here, a well-posed Hermitian theory is developed and convergence questions do not arise. Among a number of important consequences is the fact that no exterior pressure is required by the present theory. In the second part of this paper it is shown that the behavior of the resulting model equations include intermittency, quasiperiodic, and chaotic solutions. In the final part of this paper three-dimensional effects are introduced into the dynamics in order to produce a physically more realistic dynamical theory. It is felt that the bursting and ejection events in turbulent boundary layers is given a more satisfactory explanation within this framework.
Vorticity form of turbulence transport equations
Authors: Lele Sanjiva K.
Published: July 2002

The exact transport equations describing the turbulent kinetic energy, Reynolds stresses, and the dissipation rate of the turbulent kinetic energy are written in their vorticity form. The limiting behavior of the transport equations describing the irrotational fluctuations at the free-stream edges of shear flows is directly deduced from the exact transport equations. Additional relations of pure kinematic origin are also indicated. It is suggested that the formulation developed may be useful in improving the turbulence transport models.
Numerical simulation of Richtmyer–Meshkov instabilities
Authors: Cloutman L. D. , Wehner M. F.
Published: July 2002

The results of detailed numerical simulations of the Richtmyer–Meshkov instability of the interface between layers of air and either helium or SF6 in a shock tube are reported. Two- and three-dimensional simulations based on both the Euler and Navier–Stokes equations were obtained by a finite difference method that employs a front-tracking technique to keep the interface sharp. The nature of the flow patterns induced by the instability is discussed. The results of a numerical resolution study and a demonstration of the influence of boundary layers are presented also. Agreement with experimental data is found to be satisfactory, with the exception of the initial instability growth rate.
Vortex breakdown in the polar region between rotating spheres
Authors: Bar-Yoseph P. , Roesner K. G. , Solan A.
Published: July 2002

The flow field in the polar region between a rotating and stationary, co- or counter-rotating sphere was studied numerically by a steady-state axisymmetric finite-element code and experimentally by flow visualization using a photochromic dye excited by a UV laser. The experimental results show that at a critical Reynolds number a steady axisymmetric vortex breakdown bubble forms at the polar axis, as predicted by the computation. At higher values of the Reynolds number, and depending on the gap, the eccentricity of the spheres along the axis of rotation, and their rotation ratio, further unsteady structures are observed experimentally, viz., an axially oscillating bubble, or a three-dimensional irregular structure.
On the interpretation of phase measurements of oscillatory thermocapillary convection in liquid bridges
Authors: Kuhlmann Hendrik C. , Rath Hans J.
Published: July 2002

In their study of time-dependent thermocapillary convection in cylindrical liquid bridges Velten et al. [Phys. Fluids A 3, 267 (1991)] determined the azimuthal flow structure by measuring the phase of the temperature oscillations at three different azimuthal angles. Their explanation of the data in terms of modes with wave number m=0 is not always compatible with the normal-mode decomposition of the disturbances at the threshold. A new interpretation is given that explains the peculiar phase measurements in terms of pairs of m≠0 counterpropagating waves.
Navier–Stokes relaxation to sinh–Poisson states at finite Reynolds numbers
Authors: Montgomery David , Shan Xiaowen , Matthaeus William H.
Published: July 2002

A mathematical framework is proposed in which it seems possible to justify the computationally-observed relaxation of a two-dimensional Navier–Stokes fluid to a ‘‘most probable,’’ or maximum entropy, state. The relaxation occurs at large but finite Reynolds numbers, and involves substantial decay of higher-order ideal invariants such as enstrophy. A two-fluid formulation, involving interpenetrating positive and negative vorticity fluxes (continuous and square integrable) is developed, and is shown to be intimately related to the passive scalar decay problem. Increasing interpenetration of the two fluids corresponds to the decay of vorticity flux due to viscosity. It is demonstrated numerically that, in two dimensions, passive scalars decay rapidly, relative to mean-square vorticity (enstrophy). This observation provides a basis for assigning initial data to the two-fluid field variables.
Measurements on transition to turbulence in a Taylor–Couette cell with oscillatory inner cylinder
Authors: Målo/y Knut Jo/rgen , Goldburg Walter
Published: July 2002

The transition line at onset of instability and the distance between the vortex rolls in a Taylor–Couette with an oscillatory inner cylinder having zero mean velocity are measured. When the amplitude of the velocity oscillations increases slightly above the critical value, a transition to a turbulent ‘‘mixing regime’’ takes place. In this regime, homodyne correlation spectroscopy have been used to measure the characteristic velocity fluctuations 〈δvq(l)〉 between points separated by a distance l. Scaling of the correlation function G(τ,q,l) was found, i.e., G(τ,q,l)=G(x), where x=qτ〈δvq(l)〉, with 〈δvq(l)〉∼l0.76.
Singularities of the Euler equation and hydrodynamic stability
Authors: Tanveer S. , Speziale Charles G.
Published: July 2002

Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived. Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular point in the unphysical domain. These results are used to relate the motion of complex singularities to the stability of steady solutions of the Euler equation. A sufficient condition for instability is conjectured. Several examples are presented to demonstrate the efficacy of this sufficient condition which include the class of elliptical flows and the Kelvin–Stuart cat’s eye.
Lagrangian velocity correlations in homogeneous isotropic turbulence
Authors: Gotoh Toshiyuki , Rogallo Robert S. , Herring Jackson R. , Kraichnan Robert H.
Published: July 2002

The Lagrangian velocity autocorrelation and the time correlations for individual wave-number bands are computed by direct numerical simulation (DNS) using the passive vector method (PVM), and the accuracy of the method is studied. It is found that the PVM is accurate when Kmax/kd≥2 where Kmax is the maximum wave number carried in the simulation and kd is the Kolmogorov wave number. The Eulerian and Lagrangian time correlations for various wave-number bands are compared. At moderate to high wave number the Eulerian time correlation decays faster than the Lagrangian, and the effect of sweep on the former is observed. The time scale of the Eulerian correlation is found to be (kU0)−1 while that of the Lagrangian is [∫0k p2E(p)dp]−1/2. The Lagrangian velocity autocorrelation in a frozen turbulent field is computed using the DIA, ALHDIA, and LRA theories and is compared with DNS measurements. The Markovianized Lagrangian renormalized approximation (MLRA) is compared with the DNS, and good agreement is found for one-time quantities in decaying turbulence at low Reynolds numbers and for the Lagrangian velocity autocorrelation in stationary turbulence at moderate Reynolds number. The effect of non-Gaussianity on the Lagrangian correlation predicted by the theories is also discussed.
Slip effects in a confined rarefied gas. I: Temperature slip
Authors: Wadsworth Dean C.
Published: July 2002

The model problem of a gas confined between stationary heated plates is analyzed numerically to quantify slip effects for gas densities ranging from near-continuum to highly rarefied conditions. Calculations are performed with the direct simulation Monte Carlo technique using two gas–surface interaction models and with a finite-difference Navier–Stokes method using slip boundary conditions. Comparisons are made with experimental density profiles and with previous discrete ordinate calculations using a model form of the Boltzmann equation. To the resolution of the experimental data, both direct simulation Monte Carlo and the Navier–Stokes equations with slip provide very good agreement for essentially all cases considered, while the discrete ordinate results are less accurate. The calculated pressure and temperature profiles show slightly larger differences. The details of the gas–surface interaction model have a relatively small effect on calculated density profiles. The direct simulation Monte Carlo and no-slip Navier–Stokes results are found to agree quantitatively for all properties at very small Knudsen number [O(10−3)]. Detailed direct simulation Monte Carlo quantities near the plates are used to quantify discrepancies in the continuum slip models and suggest possible improvements.
On streamwise vortices in turbulent wakes of cylinders
Authors: Bays-Muchmore B. , Ahmed A.
Published: July 2002

Flow-visualization methods were used to explore the structure of streamwise vortices and their interactions with the von Kármán vortices in the immediate wakes of cylinders. The experiments were conducted in a water tunnel at Reynolds numbers from 330–21 000 based on cylinder diameter. Over this entire range of Reynolds number, pairs of counter-rotating streamwise vortices were observed immediately behind the cylinders, with a mean spanwise spacing of approximately one pair per diameter. The streamwise vortices significantly distorted the von Kármán vortices, but only on their upstream-facing sides. The cylinder near-surface-flow topology was found to include a secondary separation line containing ‘‘dominant-foci structures’’ whose spanwise locations correlated with those of the streamwise vortices.
Exact nonlinear helically symmetric solutions of hydromagnetic equations
Authors: Namikawa Tomikazu
Published: July 2002

Exact solutions of nonlinear helically symmetric hydromagnetic equations for a highly conducting fluid in a cylindrical geometry are obtained. These solutions may be useful because they can be expressed in terms of arbitrary scalar functions, and are applicable to astrophysics and laboratory plasmas.
Numerical simulations of ion temperature gradient-driven turbulence
Authors: Ottaviani M. , Romanelli F. , Benzi R. , Briscolini M. , Santangelo P. , Succi S.
Published: July 2002

High resolution numerical simulations of plasma turbulence driven by ion temperature gradients in the presence of magnetic field inhomogeneities have been performed with special attention to the behavior of the anomalous ion energy flux. The pressure gradient evolution is treated consistently with energy transport, allowing for the study of the saturated state in situations of relevance to tokamak plasmas. It is found that the presence of large-scale coherent structures significantly affects the turbulent losses, leading to a reduction of the flux with respect to mixing length estimates.
Experimental results on hydrodynamic instabilities in laser-accelerated planar packages
Authors: Kilkenny J. D.
Published: July 2002

The growth, saturation, and generation of higher harmonics by the Rayleigh–Taylor instability is reviewed. Further experiments measuring the growth of Rayleigh–Taylor instabilities in laser-accelerated planar packages of Nova [Rev. Sci. Instrum. 57, 2101 (1986)] are described. The measured growth rate of the fundamental and harmonics is in good agreement with two-dimensional computer modeling with the stabilizing effect of ablation included.
The meandering orbit effect on stabilization of the tilting instability in a field-reversed configuration
Authors: Horiuchi Ritoku , Sato Tetsuya
Published: July 2002

The ion kinetic effect in the tilt disruption of a field-reversed configuration is investigated by means of a three-dimensional particle simulation. It is found that the tilt disruption is completely suppressed when s̄≊1, where s̄ measures the number of ion gyroradii over the radial distance between the magnetic separatrix line and the field-null line. A prolate magnetic well is formed around the field-null line, in which ions do not execute gyration but meander along the field-null line. For the case of s̄≊1 a large number of ions exist in the magnetic well and move on stable orbits around the major axis with an average rotation velocity nearly equal to half the thermal velocity. As s̄ becomes larger than 1, the number of ions in the magnetic well decreases and the stabilization effect is reduced. It is also found that an anisotropy is created in the ion thermal pressure profile owing to the anisotropy of the meandering orbits and that the electric field fluctuation always remains at a low level, and thus the electric field plays no essential role in the tilt stabilization.
Short-pulse, laser–plasma interaction including collisions and ionization
Authors: Wallace J. M. , Forslund D. W. , Kindel J. M. , Olson G. L. , Comly J. C.
Published: July 2002

A computational approach for simulations in the emerging field of short-pulse (τ<1 psec), high-intensity (I=1017–1019 W/cm2 ) laser–plasma interactions is introduced. The approach is a particle-in-cell method (PIC) which, as unique features, incorporates electron–ion collisions at relativistic energies and the time variation of the ionization state of the plasma. This has been incorporated into the wave two-dimensional plasma simulation code [Phys. Fluids 18, 1017 (1975)] for the purpose of simulating experiments at the Los Alamos Bright Source facilities [Phys. Rev. A 39, 454 (1989)]. However, the computational methods should be useful for work in laser fusion and other areas where rapid ionization occurs.
Coherent structures in two-dimensional plasma turbulence
Authors: Huld T. , Nielsen A. H. , Pecseli H. L. , Juul Rasmussen J.
Published: July 2002

Low-frequency, flute-type electrostatic fluctuations propagating across a strong, homogeneous magnetic field are studied experimentally. The fluctuations are generated by the Kelvin–Helmholtz instability. The presence of relatively long-lived vortexlike structures in a background of wide-band turbulent fluctuations is demonstrated by a conditional sampling technique. Depending on plasma parameters, the dominant structures can appear as monopole or multipole vortices, dipole vortices in particular. The importance of large structures for the turbulent plasma diffusion is discussed. A statistical analysis of the randomly varying plasma flux is presented.
Stability of high-beta large-aspect-ratio tokamaks
Authors: Cowley S. C.
Published: July 2002

High-beta (β≫ε/q2) large-aspect-ratio (ε≪1) tokamak equilibria are shown to be always stable to ideal magnetohydrodynamics (MHD) modes that are localized about a flux surface. Both the ballooning and interchange modes are shown to be stable. This work uses the analytic high-beta large-aspect-ratio tokamak equilibria developed by Cowley et al. [Phys. Fluids B 3, 2069 (1991)], which are valid for arbitrary pressure and safety factor profiles. The stability results make no assumption about these profiles nor the shape of the boundary.
Loss cone region in toroidal helical systems
Authors: Itoh K. , Sanuki H. , Todoroki J. , Kamimura T. , Itoh S.-I. , Fukuyama A. , Hanatani K.
Published: July 2002

An analytic formula is derived for the loss cone in toroidal helical systems. Particular emphasis is put on the loss region for the particles that are barely trapped in the helical ripples. Effects of the radial electric field and shifts of the magnetic axis are discussed. Comparison with the numerical calculation confirms that the simple analytic formula gives good approximations.
Upper bounds on fluctuational power absorption in a turbulent pinch
Authors: Wang Cai Yi , Bhattacharjee A. , Hameiri Eliezer
Published: July 2002

An upper bound is given for the fluctuational power absorption in a steady, driven reversed-field pinch. The functional χ, which is the ratio of the power dissipated by fluctuations to the mean Ohmic power, is expressed in terms of the mean magnetic field B0 by using energy conservation. Maxima of χ are obtained from a variational principle which includes the helicity and toroidal flux constraints. The largest upper bound is found with the natural boundary condition derived from the variational principle itself. It is shown that the theoretical bound is not inconsistent with observations from the Los Alamos ZT-40M experiment [Phys. Fluids 27, 1671 (1984)].
The role of edge current density on kink mode stability and its implication for magnetohydrodynamic activity associated with edge localized modes
Authors: Manickam Janardhan
Published: July 2002

The stability of a plasma equilibrium to the external kink mode is shown to be dependent on the details of the current density near the plasma edge and the value of the safety factor, q, at the edge. The buildup of the current density near the plasma edge is shown to decrease the shear in the safety-factor profile and lead to destabilization of the kink mode. Tokamak plasmas in the high confinement mode of operation have high current density near the edge and are known to exhibit activity referred to as edge localized modes. An important feature of this activity is intermittent bursts of magnetohydrodynamic (MHD) activity near the plasma edge. A model is proposed for the MHD activity in terms of the external kink mode. The role of the plasma geometry and equilibrium profiles is discussed.
On the Hall effect on vertical Alfvén waves in an isothermal atmosphere
Authors: Campos L. M. B. C.
Published: July 2002

The Alfvén wave equation in an atmosphere in the presence of Ohmic and Hall currents is obtained. It is shown that, for vertical propagation and vertical external magnetic field, there is no coupling to gravity or compressibility, because the magnetic field and velocity perturbation are transverse, and hence horizontal. The wave equation is valid for Alfvén speed, external magnetic field, gyrofrequency, and Ohmic diffusivity arbitrary functions of altitude; under these conditions the transverse wave perturbation is shown to decouple into right- and left-polarized waves. The wave field in an isothermal atmosphere, under a uniform magnetic field, is affected by the Hall current only through a change of propagation speed. The neglect of Ohmic compared to Hall current is justified for low-density plasma, e.g., in the solar wind. It is shown that the Hall effect changes the eigenfrequencies and eigenfunctions of standing atmospheric waves. It does not change the scaling of asymptotic wave fields at high altitude, but it breaks equipartition of energy at low altitude, e.g., for propagating waves, even when the ray approximation holds. Possible extensions of this problem are discussed in connection with Alfvén waves in the solar wind.
Atomic physics effects on dissipative toroidal drift wave stability
Authors: Beer M. A. , Hahm T. S.
Published: July 2002

The effects of atomic physics processes such as ionization, charge exchange, and radiation on the linear stability of dissipative drift waves are investigated in toroidal geometry, both numerically and analytically. For typical Tokamak Fusion Test Reactor (TFTR) [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (IAEA, Vienna, 1987), Vol. 1, p. 51] and Texas Experimental Tokamak (TEXT) [Nucl. Technol. Fusion 1, 479 (1981)] edge parameters, overall linear stability is determined by the competition between the destabilizing influence of ionization and the stabilizing effect due to the electron temperature gradient. An analytical expression for the linear marginal stability condition, ηcrite, is derived. The instability is most likely to occur at the extreme edge of tokamaks with a significant ionization source and a steep electron density gradient.
Can Landau-fluid models describe nonlinear Landau damping?
Authors: Mattor Nathan
Published: July 2002

The question of whether the ‘‘Landau-fluid’’ description of wave-particle resonances [e.g., Hammett and Perkins, Phys. Rev. Lett. 64, 3019 (1990)] can describe nonlinear Landau damping is addressed. It is found that this model can provide an adequate description of the Compton scattering of electron drift waves, but fails in the case of ion-temperature-gradient-driven modes near the threshold. The general conclusion is that Landau-fluid models have difficulty describing the dynamics associated with the product of two or more deeply resonant propagators.
Improved confinement and edge plasma fluctuations in the STOR-M tokamak
Authors: Zhang W. , Xiao C. , Conway G. D. , Mitarai O. , Sarkissian A. , Skarsgard H. M. , Zhang L. , Hirose A.
Published: July 2002

An improved Ohmic confinement phase has been observed in the STOR-M tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1988 (International Atomic Energy Agency, Vienna, 1989), Vol. 1, p. 323] after application of a turbulent heating (TH) pulse. This improved Ohmic confinement phase is characterized by (a) increased n̄e, (b) reduced Hα radiation from the edge, (c) reduced density and magnetic fluctuations at the edge, (d) a steeper density profile at the edge, and (e) a more negative radial electric field. Almost complete suppression of sawtooth oscillations during the improved confinement phase has also been observed. A linear dispersion relation describes the density and magnetic fluctuations in the frequency range up to 350 kHz. In the region r<a (r≳a) the propagation direction of the density fluctuations is in the electron (ion) diamagnetic direction. The reduction of rms density and magnetic fluctuations after the TH pulse is largely due to suppression of relatively high frequency (≤500 kHz) components. The density fluctuations (ñ/ne) in the scrape-off layer remain intact after the pulse.
Nonlinear plasma evolution and sustainment in the reversed field pinch
Authors: Cappello S. , Paccagnella R.
Published: July 2002

In this paper numerical results of three-dimensional (3-D) resistive magnetohydrodynamic (MHD) plasma simulations are presented. A system of coupled nonlinear differential equations is evolved in time over a significant fraction of the macroscopic resistive diffusion time scale. The dynamical evolution resembles the main features of the famous Lorenz system. In fact, sensitivity of MHD equations on initial distribution of spectral energy and stochastic oscillations in phase space have been found. At least two dynamic attractors of the motion have been identified. Moreover, in analogy with Lorenz’s system, the stochastic motion can be damped by an enhanced dissipation and the fixed point can be recovered. In this paper more specific topics are also considered, which are relevant to the reversed field pinch (RFP), such as the role of different modes in the ‘‘dynamo’’ mechanism for plasma sustainment and the associated transport due to stochastic diffusion.
‘‘Reduced’’ magnetohydrodynamics and minimum dissipation rates
Authors: Montgomery David
Published: July 2002

It is demonstrated that all solutions of the equations of ‘‘reduced’’ magnetohydrodynamics approach a uniform-current, zero-flow state for long times, given a constant wall electric field, uniform scalar viscosity and resistivity, and uniform mass density. This state is the state of minimum energy dissipation rate for these boundary conditions. No steady-state turbulence is possible. The result contrasts sharply with results for full three-dimensional magnetohydrodynamics before the reduction occurs.
Anomalous particle and electron energy pinches
Authors: Dominguez R. R.
Published: July 2002

Interest in plasma pinches has recently increased due to the observation in electron cyclotron heated (ECH) plasmas in the Doublet III-D (DIII-D) tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] of an electron energy pinch. Previous work on drift wave-induced particle and electron energy pinches concluded that they were only possible in strictly collisionless plasmas, ν*=0, an assumption not applicable to electron-cyclotron heating experiments. In the present work it is shown that a more detailed quasilinear analysis predicts a particle pinch at moderate collisionality, ν*=0.2 to 1.0, when the electron temperature gradient parameter ηe is in the range ηe=2 to 3. Further, the quasilinear analysis is expanded to include the effects of turbulent resonance broadening on the circulating electrons. It is then found that, in addition to a particle pinch (qualitatively the same as the quasilinear prediction), a simultaneous particle and electron energy pinch at moderate collisionality can occur at ηe≂1, which is lower than in ECH experiments where ηe=2 to 3.
A model for magnetic energy storage and Taylor’s relaxation in the solar corona. I: Helicity-constrained minimum energy state in a half-cylinder
Authors: Aly J. J.
Published: July 2002

The problem of the existence of a minimum energy state is studied in the set ℋ of all the magnetic fields B: (i) occupying the half-cylinder D={r<R,z≳0}; (ii) having a normal component vanishing on the vertical part {r=R} of the boundary of D and taking given values Q(r) on its horizontal part {z=0}; (iii) having a relative helicity equal to a prescribed value H. It is first shown that the only field that may possibly be an energy minimizer in ℋ is the unique (and therefore axisymmetric) constant-α force-free field Bα contained in that set. Thus it is proved that Bα minimizes the energy indeed if and only if 0≤‖H‖≤Hc≤∞, where Hc is an estimated critical value. For Hc≤‖H‖≤∞, on the contrary, it is possible to construct in ℋ nonaxisymmetric fields with an energy smaller than that of Bα and no minimum energy state does exist. However, Bα still minimizes the energy for Hc ≤‖ H‖ ≤ Haxc (with possibly Haxc = ∞) if attention is restricted to the axisymmetric fields of ℋ. These results are used to put a limit on the validity of a popular model of the heating of the solar corona, in which the field of a coronal structure is supposed to release sporadically, by Taylor’s relaxation, a part of the energy it continuously extracts from the kinetic energy of the photospheric motions. It is argued that, as a consequence of the results above, one of the basic assumptions of the model breaks down when the field becomes highly sheared. It is speculated that, in such a situation, a completely new regime should set up, in which helicity and energy are continuously ejected at large distances by the system.
On ray stochasticity during lower-hybrid current drive in tokamaks
Authors: Bizarro João P. , Moreau Didier
Published: July 2002

Using a combined ray-tracing and Fokker–Planck code, a comprehensive and detailed analysis is presented on the importance of toroidally induced ray stochasticity for the modeling of lower-hybrid (LH) current drive in tokamaks and for the dynamics of the launched power spectrum. The injected LH power distribution in poloidal angle and in parallel wave index is accurately represented by taking into account the poloidal extent of the antenna and by efficiently covering the full range of its radiated spectrum. The influence of the balance between the wave damping and the exponential divergence of nearby ray trajectories in determining the shape and robustness of the predicted LH power deposition profiles is emphasized. When stochastic effects are important, code predictions are shown to be stable with respect to small changes in plasma parameters and initial conditions, and to be consistent with experimental data, provided a sufficiently large number of rays is used. Sensitivity studies indicate that the component of the launched power spectrum that is not affected by stochastic effects is well described by a grid in parallel wave index whose spacing may be as large as 10−1, whereas the component that is affected by such effects suffers strong randomization and needs a grid whose spacing must not exceed 10−3. Ray stochasticity tends to broaden the launched power spectrum, to increase the LH power deposition in the inner half of the plasma, and to favor power deposition profiles that are spread over most of the plasma cross section and whose dependence on the injected LH power distribution in poloidal angle and in parallel wave index is weak. It is found that stochastic effects may be effectively reduced by using bottom launch schemes. The fact that it is, in general, misleading to divide a priori the launched power spectrum into ‘‘accessible’’ and ‘‘inaccessible’’ parts is stressed.
Observation of a quasicoherent mode in the Texas Experimental Tokamak
Authors: Tsui H. Y. W. , Schoch P. M. , Wootton A. J.
Published: July 2002

A quasicoherent feature localized near the magnetic flux surface having a safety factor q=3 has been detected by Langmuir probe and heavy ion beam probe (HIBP) measurements in the edge plasma of the Texas Experimental Tokamak (TEXT) [Nucl. Technol. Fusion 1, 479 (1981)]. A mode is identified with relatively low poloidal wave number (m=12) compared to the usual broadband turbulence with m in the range of 50 to 100. In contrast to the turbulent activity, this mode is collisional and does not produce a fluctuation-driven radial particle flux via the coupling between density and potential fluctuation. A comparison with the expectation of the drift-tearing activity indicates that the mode can be collisional drift-tearing unstable.
Investigations of diffusional effects in applied-B ion diodes
Authors: Westermann T. , Schuldt R.
Published: July 2002

In this article, a general study of diffusional effects is made numerically as well as theoretically with the aim to reproduce not only the current scaling of ion diodes but also the divergence of the ion beam and physical features such as virtual cathode movement due to the diamagnetic effect. It has been observed experimentally that the ion current exceeds that quantity which would be expected in the presence of a strong magnetic field. It is demonstrated that with the introduction of a diffusional field Eθ into the stationary 21/2-dimensional particle-in-cell code based on boundary-fitted coordinates [T. Westermann, Nucl. Instrum. Methods A 263, 271 (1988)] the simulation results agree well with experiment. This ad hoc model is supported theoretically by linear stability analysis of the stationary state.
A model for inferring transport rates from observed confinement times in field-reversed configurations
Authors: Steinhauer Loren C. , Milroy Richard D. , Slough John T.
Published: July 2002

A one-dimensional transport model is developed to simulate the confinement of plasma and magnetic flux in a field-reversed configuration. Given the resistivity, the confinement times can be calculated. Approximate expressions are found which yield the magnitude and gross profile of the resistivity if the confinement times are known. These results are applied to experimental data from experiments, primarily TRX-1, to uncover trends in the transport properties. Several important conclusions emerge. The transport depends profoundly, and inexplicably, on the plasma formation mode. The inferred transport differs in several ways from the predictions of local lower-hybrid-drift turbulence theory. Finally, the gross resistivity exhibits an unusual trend with xs (separatrix radius rs divided by the conducting wall radius rc ), and is peaked near the magnetic axis for certain predictable conditions.
Nonlinear saturation of single-mode trapped electron instability
Authors: Kim S. Y. , Sen A. K.
Published: July 2002

The trapped electron instability, like other types of drift waves, may appear as a single mode in many linear plasma devices. Recognizing the significant variation of density gradient over the mode localization region, a nonlocal linear analysis in slab model yields eigenfunctions for Weber-like equations. Using three-wave, nonresonant, two-dimensional mode coupling based on these Weber-like eigenfunctions, two mode-coupling equations for the fundamental and higher-order radial harmonics are derived. The solution of these coupled equations yields the nonlinear saturation level of the unstable mode. Mode coupling to the damped higher-order radial modes is the principal physical saturation mechanism of the unstable fundamental mode.
Production of hot electrons for axisymmetric thermal barrier formation in a tandem mirror
Authors: Kiwamoto Y. , Saito T. , Cho T. , Yamaguchi N. , Mase A. , Sakasai A. , Kariya T. , Kondoh T. , Gotoh H. , Katanuma I. , Miyoshi S.
Published: July 2002

Hot electrons have been produced by second harmonic electron-cyclotron resonance heating in axisymmetric end mirrors of the tandem mirror GAMMA10 [Phys. Rev. Lett. 55, 939 (1985)] with an on-axis density fraction reaching 80% and temperature of 25–50 keV, satisfying theoretically required conditions for the formation of thermal barriers. The successful control of the electron temperature may be attributed to the relativistic detuning of the second harmonic resonance for localized microwave power absorption. The time evolutions of relevant parameters are studied with extensive diagnostics.
Plasma wave equations of state
Authors: Amendt Peter
Published: July 2002

A systematic description of wave equations of state is presented for three categories of plasma waves distinguished by superthermal, subthermal, and superluminous phase velocities. Each class entails the formulation of a distinct Vlasov fluid model where only the first coincides with well-known covariant fluid modeling. An investigation of the linearized version of this standard model is first undertaken. A complete, lowest-order, warm fluid model is derived without the drawbacks that characterize previous models such as the generation of spurious modes and the absence of a Bernstein wave spectrum. The improved fluid model is obtained by avoiding a premature truncation of the hierarchy of linearized moment equations near cyclotron and acoustic resonance and is applied to representative types of waves in a warm, magnetized plasma. Relativistic corrections and anisotropic properties of the corresponding dispersion relations are used to illustrate the utility and rigor of the theory.

The conspicuous absence of a subthermal wave within this improved model motivates the subsequent derivation of a novel fluid model with associated moments that involve averages of derivatives of the electron distribution function. The first moment equation reproduces the Boltzmann relation while succeeding equations in the hierarchy provide constraints on the spatial dependence of the distribution function. A linearized analysis yields the ion-acoustic mode together with an isothermal equation of state in the long wavelength limit. The key distinction with previous work is the complete avoidance of a pressure and an appropriate (third) moment representation for temperature in the collisionless, subthermal regime. A relativistic analog to this unusual approach is developed for the case of ultrarelativistic electron plasma waves. This requires the formulation of a noncovariant near-thermal equilibrium fluid modeling with associated moments that are not relativistically dilatated. An isothermal equation of state is recovered in tandem with the adoption of a third fluid moment definition for relativistic temperature. This definition of effective temperature differs from the relativistic thermodynamic version which follows from an assumed form invariance of the defining equations of nonrelativistic thermodynamics in the relativistic regime. The introduction of these two latter models is intended to provide a more general notion of equation of state without recourse to an assumption on the form of the stress-energy tensor.
Numerical simulation of turbulent heat flows
Authors: Waltz R. E.
Published: July 2002

Previous work on simulating turbulence in finite beta tokamak plasmas with isothermal models is extended to include temperature perturbations and temperature gradients in a collisional plasma. Turbulent heat as well as plasma flows are treated. The toroidal ion temperature gradient mode is the dominant source of turbulence in the model. Electron temperature gradients can stabilize the electron collisional drift mode and lead to reverse plasma flows (or thermal pinches). Magnetic electron heat conduction is found to be very small when correlations between temperature and magnetic field perturbations are considered. Quasilinear theory and mixing length rules are found to give a good representation of the results.
Electrostatic confinement in the edge layer of field-reversed configurations
Authors: Steinhauer Loren C.
Published: July 2002

Although a field-reversed configuration (FRC) has closed magnetic field lines, its particle confinement time is strongly influenced by the flow in the edge layer located outside the separatrix. Previous simple analyses of the edge layer have used fluid models with freely streaming end loss. However, a review of experimental results uncovers major inconsistencies between the fluid picture and actual measurements. In particular, the edge layer is unusually broad; the global particle confinement does not show the expected scaling with FRC length; the magnetic flux imbedded in the edge layer is inconsistent with that in the jet region; and the outflow speed in the jet is anomalously high. The most promising explanation for these anomalies is electrostatic confinement, which is well known in mirror and magnetic cusp plasmas. A tentative description of the electrostatic structure and plasma flow in the edge layer is presented.
Toroidal magnetic field generation during compact toroid formation in a field-reversed theta pinch and a conical theta pinch
Authors: Milroy Richard D. , Brackbill J. U.
Published: July 2002

The influence that the Hall and ∇Pe terms, in a generalized Ohm’s law, have on the formation of a compact toroid in a field-reversed theta pinch and a conical theta pinch has been examined. The inclusion of these terms leads to the spontaneous generation of toroidal magnetic fields and toroidal velocities. The toroidal fields in the end regions reach peak values of almost 50% of the external poloidal field during the early stages of formation. When the coil geometry is the same at each end of the theta pinch, equal and opposite toroidal fields are generated by the Hall effect, so that no net toroidal flux is generated. When the geometry is not the same at each end, the Hall effect can lead to a net toroidal flux. Calculations for both a conical theta pinch experiment and a field-reversed configuration translation experiment demonstrate the generation of net toroidal flux, as observed experimentally.
Numerical results on instabilities of ‘‘top hat’’ jets
Authors: Zaninetti Lorenzo
Published: July 2002

The Kelvin–Helhmoltz stability of the cylindrical interface between two compressible fluids is studied when the arguments of the Bessel and Hankel functions are large. The real and imaginary parts of the wave frequency, c, are derived through numerical computations.
Relaxation of toroidal plasmas
Authors: Bhattacharjee A. , Glasser A. H. , Avinash  , Sedlak J. E.
Published: July 2002

Equilibria with minimum energy are constructed from a variational principle in which the potential energy of a plasma is minimized, subject to a small set of global invariants. These invariants are preserved exactly, by ideal motions of the plasma, and approximately, by a tearing mode of the m=1, n=1 type. Estimates of decay rates for the energy and the invariants are given. A tokamak window with low q and zero current on the boundary is found and shown to be ideally and resistively stable. The reversed-field pinch (RFP) window and the transition region between the two windows is found to be unstable to high-n modes.
Reflection of an ion-acoustic soliton from a planar boundary
Authors: Imen K. , Kuehl H. H.
Published: July 2002

The reflection of a planar ion-acoustic soliton from an insulated or a biased metallic planar wall is studied. Numerical solutions of the cold-ion fluid equations, the Boltzmann distribution for electrons, and Poisson’s equation show that the incident soliton is partially reflected and partially absorbed by the wall. The reflection is larger for wider solitons and for a more negatively biased wall. The numerical results are in reasonable agreement with the recent experiment of Nishida [Phys. Fluids 27, 2176 (1984)].
Numerical simulations of turbulent spots in plane Poiseuille and boundary-layer flow
Authors: Henningson Dan , Spalart Philippe , Kim John
Published: July 2002

Direct numerical simulations of turbulent spots in plane Poiseuille and boundary-layer flows are performed. Mature, self-similar spots are obtained. The propagation velocities and spreading angles are found to compare well with corresponding experiments. The difference in shape of the two spots is also clearly discernible: the turbulent parts are contained within arrowhead regions that point in opposite directions for the two cases. The wing-tip region of the Poiseuille spot is also found to consist of a large-amplitude semiturbulent wave packet.
Experimental investigation of the helical magnetic instability of an arc discharge in an axial magnetic field and comparison with theory
Authors: Hülsmann H. G. , Mentel J.
Published: July 2002

The helical magnetic instability of arcs is investigated experimentally at a long low current H2 arc in a tube of 20 mm diam. The measurements are compared with theoretical results given in a preceding paper [Phys. Fluids 30, XXXX (1987)] in which a first order homogeneous differential equation for the helix amplitude was derived from the basic differential equations. Confirmation is achieved for the critical external axial magnetic field which just destabilizes the arc. It amounts to only a few gauss. Agreement is also found for the growth rate of the instability in both cases of destabilization by an external magnetic field and by the self-magnetic field. The measured growth rates have an order of magnitude of 1000 sec−1.