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Mar 1988

Volume 31, Issue 3, pp. 423-707

Page 1 of 2 Pages Next Page | Jump to Page

Effect of a strong‐current ion ring on spheromak stability

C. Litwin and R. N. Sudan

Phys. Fluids 31, 423 (1988); http://dx.doi.org/10.1063/1.866823 (4 pages) | Cited 3 times

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The stability of a spheromak with an energetic ion ring, carrying a current comparable to the plasma current, to the tilt mode is considered. For small departures from sphericity a perturbative approach is applied to an appropriate energy principle in order to calculate the lowest nontrivial kinetic contribution of the ion ring. An analytic stability criterion is obtained. It is seen that the prolate configuration becomes more stable while the oblate one is less stable than in the absence of the ring. The prolomak becomes stable when the ring kinetic energy exceeds the magnetic energy within the separatrix.
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52.55.Jd Magnetic mirrors, gas dynamic traps
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)

Electron diamagnetism and toroidal coupling of tearing modes

S. C. Cowley and R. J. Hastie

Phys. Fluids 31, 426 (1988); http://dx.doi.org/10.1063/1.867019 (3 pages) | Cited 15 times

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Using a simple model for the layer of the tearing mode, it is demonstrated that toroidally coupled tearing modes with two rational surfaces are most unstable when the ω∗’s of the electrons at the rational surfaces are equal. The onset of instability may then occur because of the tuning of ω∗ rather than the passage of Δ′‐like quantities through zero. This mechanism for the onset of instability is sharp since the resonance is narrow. The effect of toroidal rotation is also discussed.
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52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.35.Tc Shock waves and discontinuities
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)

Nonlinear unstable viscous fingers in Hele–Shaw flows. II. Numerical simulation

E. Meiburg and G. M. Homsy

Phys. Fluids 31, 429 (1988); http://dx.doi.org/10.1063/1.866824 (11 pages) | Cited 34 times

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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.
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47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.55.Kf Particle-laden flows
47.56.+r Flows through porous media

Bubble competition in Rayleigh–Taylor instability

Juan A. Zufiria

Phys. Fluids 31, 440 (1988); http://dx.doi.org/10.1063/1.866825 (7 pages) | Cited 46 times

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The penetration of a front of light fluid into a heavy fluid in a Rayleigh–Taylor unstable flow is studied by using a model that simulates the competition among the bubbles formed in the interface when the density ratio of the two fluids is very large. Several different initial conditions have been considered, and it is found that the front moves with constant acceleration. The values obtained for the acceleration of the front are in very good agreement with experimental results obtained by Read [Physica D 12, 45 (1984)].
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47.20.-k Flow instabilities
47.55.Hd Stratified flows
47.55.Kf Particle-laden flows
47.10.-g General theory in fluid dynamics

The dynamics of bubble growth for Rayleigh–Taylor unstable interfaces

C. L. Gardner, J. Glimm, O. McBryan, R. Menikoff, D. H. Sharp, and Q. Zhang

Phys. Fluids 31, 447 (1988); http://dx.doi.org/10.1063/1.866826 (19 pages) | Cited 70 times

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A statistical model is analyzed for the growth of bubbles in a Rayleigh–Taylor unstable interface. The model is compared to solutions of the full Euler equations for compressible two phase flow, using numerical solutions based on the method of front tracking. The front tracking method has the distinguishing feature of being a predominantly Eulerian method in which sharp interfaces are preserved with zero numerical diffusion. Various regimes in the statistical model exhibiting qualitatively distinct behavior are explored.
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47.40.-x Compressible flows; shock waves
68.03.Kn Dynamics (capillary waves)
68.05.-n Liquid-liquid interfaces

Fluid flow due to a stretching cylinder

C. Y. Wang

Phys. Fluids 31, 466 (1988); http://dx.doi.org/10.1063/1.866827 (3 pages) | Cited 37 times

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The fluid flow outside of a stretching cylinder is studied. The problem is governed by a third‐order nonlinear ordinary differential equation that leads to exact similarity solutions of the Navier–Stokes equations. Because of algebraic decay, an exponential transform is used to facilitate numerical integration. Asymptotic solutions for large Reynolds numbers compare well with numerical results. The heat transfer is determined.
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47.15.-x Laminar flows
02.30.Hq Ordinary differential equations

Chaotic advection in pulsed source–sink systems

Scott W. Jones and Hassan Aref

Phys. Fluids 31, 469 (1988); http://dx.doi.org/10.1063/1.866828 (17 pages) | Cited 47 times

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The onset of chaos in passive advection of particles by flow caused by a pulsed source–sink system is documented. This type of model is of interest in various applications. It is of fundamental interest as the first example of a flow without circulation about any contour at any instant displaying chaotic particle paths. Standard chaos diagnostics such as Poincaré sections and Lyapunov exponents are studied as are more conventional flow visualization measures such as streaklines. Numerical stirring experiments for various collections of particles are performed and the properties of a certain one‐dimensional map induced by the two‐dimensional flow are examined.
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47.10.-g General theory in fluid dynamics
47.15.km Potential flows
05.45.-a Nonlinear dynamics and chaos

The three‐dimensional boundary layer in the entry region of curved pipes with finite curvature ratio

L. S. Yao and S. A. Berger

Phys. Fluids 31, 486 (1988); http://dx.doi.org/10.1063/1.866829 (9 pages) | Cited 6 times

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The major flow development in the region within a distance O((aR)1/2) from the entrance of a curved pipe occurs near the pipe wall, where a is the radius of the pipe cross section, assumed circular, and R is the radius of curvature of the central axis of the pipe. A three‐dimensional boundary‐layer solution is obtained for elucidating the physics of this developing flow; in particular, the effect of nonzero curvature ratio α=a/R on the geometric similarity of the flow. The numerical results show that the series solution in terms of α is valid only when α≤0.1 and s≤0.1 (aR)1/2, where s is the distance from the inlet along the pipe axis. The crossover of the axial wall shear is purely a geometric property and its location is a strong function of α. It is also demonstrated that (aR)1/2 is the proper length scale by showing that the solution of the first region, s∼O(a), is included in that of the second, s∼O(aR)1/2.
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47.60.-i Flow phenomena in quasi-one-dimensional systems
87.19.U- Hemodynamics
87.19.Wx Pneumodyamics, respiration

Bifurcation in axisymmetric Czochralski natural convection

Alessandro Bottaro and Abdelfattah Zebib

Phys. Fluids 31, 495 (1988); http://dx.doi.org/10.1063/1.866830 (7 pages) | Cited 9 times

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Numerical simulations using a finite volume method with primitive variables formulation are presented for a natural convection flow in the Czochralski melt. In the limit of very small Prandtl numbers it is shown that unsteadiness appears in the form of regular oscillations for sufficiently high values of the Rayleigh number. Such regular oscillations are preceded by a multicell motion structure in the melt, with flow separation at the wall. The critical value of the Rayleigh number for the onset of the oscillations is determined by carrying out a series of time dependent calculations.
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47.27.T- Turbulent transport processes
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking

Nonlinear particle diffusion in a time‐dependent host medium

D. H. Zanette and R. O. Barrachina

Phys. Fluids 31, 502 (1988); http://dx.doi.org/10.1063/1.866831 (4 pages) | Cited 2 times

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The dynamics of a gas in a time‐dependent host medium is studied by means of a generalized Boltzmann equation. Removal and regeneration events, as well as linear external sources, are taken into account. The corresponding continuity equation is solved, and the time evolution of the system is investigated, with particular attention paid to its asymptotic regime.
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51.10.+y Kinetic and transport theory of gases
05.20.Dd Kinetic theory

Direct numerical simulations of the turbulent mixing of a passive scalar

V. Eswaran and S. B. Pope

Phys. Fluids 31, 506 (1988); http://dx.doi.org/10.1063/1.866832 (15 pages) | Cited 223 times

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The evolution of scalar fields, of different initial integral length scales, in statistically stationary, homogeneous, isotropic turbulence is studied. The initial scalar fields conform, approximately, to ‘‘double‐delta function’’ probability density functions (pdf ’s). The initial scalar‐to‐velocity integral length‐scale ratio is found to influence the rate of the subsequent evolution of the scalar fields, in accord with experimental observations of Warhaft and Lumley [J. Fluid Mech. 88, 659 (1978)]. On the other hand, the pdf of the scalar is found to evolve in a similar fashion for all the scalar fields studied; and, as expected, it tends to a Gaussian. The pdf of the logarithm of the scalar‐dissipation rate reaches an approximately Gaussian self‐similar state. The scalar‐dissipation spectrum function also becomes self‐similar. The evolution of the conditional scalar‐dissipation rate is also studied. The consequences of these results for closure models for the scalar pdf equation are discussed.
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47.27.Gs Isotropic turbulence; homogeneous turbulence

Couette flow of a binary gas mixture

Dimitris Valougeorgis

Phys. Fluids 31, 521 (1988); http://dx.doi.org/10.1063/1.866833 (4 pages) | Cited 14 times

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The linearized binary model described by Hamel [Phys. Fluids 8, 418 (1964)] is used to obtain a set of kinetic equations and boundary conditions for the Couette flow problem. The derived set of two coupled integrodifferential equations is solved by iteration implementing standard discretization techniques. Highly accurate numerical results are presented for the mass velocity distribution and the total shear stress of the binary gas system.
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47.45.-n Rarefied gas dynamics
51.10.+y Kinetic and transport theory of gases

Conditions for the validity of unmagnetized‐plasma theory in describing weakly magnetized plasmas

P. A. Robinson

Phys. Fluids 31, 525 (1988); http://dx.doi.org/10.1063/1.866834 (10 pages) | Cited 12 times

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An investigation is made of the conditions under which the expression for the dielectric tensor from magnetized‐plasma theory may be approximated by that from unmagnetized‐plasma theory. Surprisingly, the conditions usually quoted are shown to be inaccurate chiefly because they make no reference to the form of the plasma distribution function. Corrected conditions depend strongly on the distribution function and their application is thus highly problem‐dependent. For completely arbitrary distributions these conditions are generally stronger than the commonly quoted ones for weakly damped waves. By contrast, the conditions applicable to axisymmetric distributions can be weaker than some of those commonly quoted. A geometric interpretation of the revised conditions for axisymmetric distributions is given in terms of the resonance ellipses of cyclotron maser theory and is illustrated with reference to dispersion and instability of Langmuir and Bernstein waves in weakly magnetized plasmas. These results apply to all weakly magnetized plasmas that can be described by the linearized Vlasov equations and imply that some investigations which have used the commonly quoted conditions to justify use of unmagnetized‐plasma theory may be in error on this point.
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52.25.Mq Dielectric properties

Kinetic theory of electron drift vortex modes

Roger D. Jones

Phys. Fluids 31, 535 (1988); http://dx.doi.org/10.1063/1.866835 (3 pages) | Cited 9 times

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Magnetic electron drift vortex modes are examined using a kinetic theory. The dispersion is found to be much different than that obtained from the fluid theory. For frequencies much smaller than the electron plasma frequency, the waves are heavily Landau damped. The modes are weakly damped at frequencies just below the plasma frequency and hence have an electromagnetic rather than magnetic character.
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52.25.Mq Dielectric properties
52.35.Kt Drift waves

Electromagnetic effects on parametric instabilities of Langmuir waves

K. Akimoto

Phys. Fluids 31, 538 (1988); http://dx.doi.org/10.1063/1.866836 (9 pages) | Cited 9 times

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Electromagnetic effects on parametric instabilities of Langmuir waves in unmagnetized plasmas are investigated. A fully electromagnetic treatment of these instabilities removes discontinuities of frequencies that are found to be present in the wave vector space of the electrostatic dispersion equation. Furthermore, it was found that a pair of novel parametric instabilities of Langmuir pump waves emerge owing to the electromagnetic effects. Both of them excite electromagnetic plasma waves near the plasma frequency. One of them is the hybrid modulational instability, which is a four‐wave up‐conversion process. As the wave vector of the pump wave increases the hybrid parametric decay instability becomes dominant. This is a three‐wave down‐conversion instability, which has been investigated previously [Space Sci. Rev. 26, 3 (1980); Phys. Rev. A 27, 552 (1983); Astrophys. J. 308, 954 (1986)].
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52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)

Linear spectrum of magnetostatic and thermally conducting planar plasmas

D. Hermans, M. Goossens, W. Kerner, and K. Lerbinger

Phys. Fluids 31, 547 (1988); http://dx.doi.org/10.1063/1.866837 (15 pages) | Cited 4 times

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The linear spectrum of 1‐D magnetostatic and thermally conducting equilibrium plasmas is analyzed. It is found that the influence of thermal conduction is fundamentally different on the various parts of the linear spectrum of ideal magnetohydrodynamics and that it is by far the most profound for the slow magnetoacoustic part. The ideal Alfvén continuous spectrum is unaffected by thermal conduction. However, the ideal slow continuous spectrum is replaced by the isothermal slow continuous spectrum. This new continuous spectrum owes its existence to thermal conduction but is independent of κ and involves a different range of continuum frequencies. In addition to these two continuous parts, the spectrum consists of discrete slow and fast magnetoacoustic modes and thermal modes. The point eigenvalues of the fast magnetoacoustic modes are slightly distorted in proportion to κ. However, the point eigenvalues of the slow magnetoacoustic modes lie on well‐defined curves in the complex plane that are independent of κ and controlled by the ideal slow and isothermal slow continua. The discrete slow magnetoacoustic spectrum hangs, as it were, on the ideal slow and isothermal slow continua and is determined by the nonuniformity of the equilibrium. The thermal modes are the result of the inclusion of the nonideal effect of thermal conduction in the energy equation.
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52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
95.30.Qd Magnetohydrodynamics and plasmas
96.60.Ly Helioseismology, pulsations, and shock waves

Nonlinear resonance of two‐dimensional ion layers

S. A. Prasad and G. J. Morales

Phys. Fluids 31, 562 (1988); http://dx.doi.org/10.1063/1.866838 (8 pages) | Cited 1 time

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A nonlinear theory of wave resonances in a two‐dimensional ion layer confined under the surface of liquid helium is presented. The ion layer is modeled as a two‐dimensional cold plasma fluid. In addition to the usual nonlinearities present in the continuity equation and the equation of motion, the theory considers a nonlinear dependence of the mass of a plasma particle on its velocity, as suggested by indirect experimental evidence. Secular perturbation theory is used to find the plasma response when the damped, nonlinear system is driven externally. For typical experimental parameters, the mass nonlinearity is found to be the dominant nonlinear effect, giving rise to a backbending of the resonance curve.
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52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.27.Jt Nonneutral plasmas
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
67.25.bh Films and restricted geometries

Structure of subcritical perpendicular shock waves

Harald J. Ziegler and Karl Schindler

Phys. Fluids 31, 570 (1988); http://dx.doi.org/10.1063/1.866839 (7 pages) | Cited 1 time

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The structure of quasineutral one‐dimensional stationary perpendicular shock waves is investigated within a two fluid model. Dissipation is considered to occur by resistivity. The influence of the entropy increase on the shock structure and especially the evolution of Sagdeev’s potential for shocks of finite strength is discussed quantitatively. The global structure of shocks with small resistivity is treated analytically.
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52.35.Tc Shock waves and discontinuities

Tearing modes in toroidal geometry

J. W. Connor, S. C. Cowley, R. J. Hastie, T. C. Hender, A. Hood, and T. J. Martin

Phys. Fluids 31, 577 (1988); http://dx.doi.org/10.1063/1.866840 (14 pages) | Cited 66 times

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The separation of the cylindrical tearing mode stability problem into a resistive resonant layer calculation and an external marginal ideal magnetohydrodynamic (MHD) calculation (Δ′ calculation) is generalized to axisymmetric toroidal geometry. The general structure of this separation is analyzed and the marginal ideal MHD information (the toroidal generalization of Δ′) required to discuss stability is isolated. This can then, in principle, be combined with relevant resonant layer calculations to determine tearing mode growth rates in realistic situations. Two examples are given: the first is an analytic treatment of toroidally coupled (m=1, n=1) and (m=2, n=1) tearing modes in a large aspect ratio torus; the second, a numerical treatment of the toroidal coupling of three tearing modes through finite pressure effects in a large aspect ratio torus. In addition, the use of a coupling integral approach for determining the stability of coupled tearing modes is discussed. Finally, the possibility of using initial value resistive MHD codes in realistic toroidal geometry to determine the necessary information from the ideal MHD marginal solution is discussed.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)

Power requirements for current drive

Allen H. Boozer

Phys. Fluids 31, 591 (1988); http://dx.doi.org/10.1063/1.866841 (5 pages) | Cited 23 times

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General formulas for the efficiency of current drive in toroidal plasmas are derived using entropy arguments. The highest possible efficiency for current drive in which a high‐energy electron tail is formed is shown to be p=Erj, with p and j the power and current densities and Er≊0.09n14 V/m with n14 the electron density in units of 1014/cm.3 The electric field required to maintain the current in a runaway discharge is also shown to equal Er. If the plasma current is carried by near‐Maxwellian electrons, waves that have a low phase velocity, compared to the energy of the electrons with which they interact, can drive a current with Ohmic efficiency, p=ηj2. Such waves were first discussed in the context of current drive by Fisch [Rev. Mod. Phys. 59, 175 (1987)].
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52.50.Gj Plasma heating by particle beams
52.55.Fa Tokamaks, spherical tokamaks

Ion distribution functions during ion cyclotron resonance heating at the fundamental frequency

Mohamed H. A. Hassan

Phys. Fluids 31, 596 (1988); http://dx.doi.org/10.1063/1.867020 (6 pages) | Cited 2 times

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The distribution function of ions during ion cyclotron resonance heating (ICRH) is studied analytically using a simplified one‐dimensional Fokker–Planck equation incorporating ion–ion and ion–electron collisions and rf quasilinear diffusion. By including source and loss terms in the equation, steady‐state and time‐dependent solutions, which are regular near the origin and vanish at high energies, are found. It is shown that an initially Maxwellian distribution function is transformed by the ICRH into a non‐Maxwellian distribution with a tail of energetic ions. The tail is more pronounced when quasilinear diffusion dominates over collisions and losses.
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52.50.Gj Plasma heating by particle beams
52.25.Fi Transport properties

Electric field profile in the presence of sawtooth activity in a tokamak

F. Alladio and G. Vlad

Phys. Fluids 31, 602 (1988); http://dx.doi.org/10.1063/1.866842 (4 pages) | Cited 11 times

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The two coupled diffusive equations for the perturbed electron temperature and poloidal magnetic field have been solved in the framework of the Kadomtsev model for the sawtooth activity. It is found that the time averaged toroidal electric field profile is radially nonuniform. A simple formula that describes the radial behavior of the toroidal electric field is proposed, and the effect on the power balance is presented.
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52.55.Fa Tokamaks, spherical tokamaks
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.25.Fi Transport properties

Relativistic electron beam heating of a hydrogen plasma in open confinement systems: Theoretical model

G. P. Gupta, T. Vijayan, and V. K. Rohatgi

Phys. Fluids 31, 606 (1988); http://dx.doi.org/10.1063/1.866843 (6 pages) | Cited 3 times

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A one‐dimensional theoretical model for predicting the heating of a hydrogen plasma in open confinement systems by a relativistic electron beam is presented. Direct energy transfer of beam electrons via interaction with large amplitude waves of the two‐stream instability and Ohmic dissipation of plasma return current caused by classical and anomalous resistivities are considered as power input terms. For loss terms, various atomic processes and heat conduction mechanisms are considered. In the light of observed changes in the average scattering angle of the beam inside the plasma, criteria deciding the character of beam–plasma interaction and the estimation of direct power transfer are discussed. The numerical results are presented with a reference to the results of the beam–plasma heating experiments reported in the literature. Better agreement is observed between the experiment and the present analysis.
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52.50.Gj Plasma heating by particle beams
52.40.Mj Particle beam interactions in plasmas
52.27.Ny Relativistic plasmas

Gyrokinetic particle simulation of ion temperature gradient drift instabilities

W. W. Lee and W. M. Tang

Phys. Fluids 31, 612 (1988); http://dx.doi.org/10.1063/1.866844 (13 pages) | Cited 77 times

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Ion temperature gradient drift instabilities have been investigated using gyrokinetic particle simulation techniques for the purpose of identifying the mechanisms responsible for their nonlinear saturation as well as the associated anomalous transport. For simplicity, the simulation has been carried out in a shear‐free slab geometry, where the background pressure gradient is held fixed in time to represent quasistatic profiles typical of tokamak discharges. It is found that the nonlinearly generated zero‐frequency responses for the ion parallel momentum and pressure are the dominant mechanisms giving rise to saturation. This is supported by the excellent agreement between the simulation results and those obtained from mode‐coupling calculations, which give the saturation amplitude as ‖eΦ/Te‖ ≂(‖ωl+iγl‖/Ωi)/(k⊥ ρs)2, and the quasilinear thermal diffusivity as χi ≂γl/k2⊥, where ωl and γl are the linear frequency and growth rate, respectively, for the most unstable mode of the system. In the simulation, the time evolution of χi after saturation is characterized by its slow relaxation to a much lower level of thermal conduction. On the other hand, a small amount of electron–ion collisions, which has a negligible effect on the linear stability, can cause significant enhancement of χi in the steady state.
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52.65.-y Plasma simulation
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Kt Drift waves

Numerical simulation of the reversed field pinch

P. Kirby

Phys. Fluids 31, 625 (1988); http://dx.doi.org/10.1063/1.866791 (5 pages) | Cited 13 times

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In this paper a series of numerical simulations of field reversal in the reversed field pinch is in the simulations described using an incompressible magnetohydrodynamic (MHD) model and a reference set of plasma conditions. Field reversal and maintenance are observed, but require values of the pinch parameter θ larger than in experiment. This discrepancy is shown to arise largely from the unrealistic resistivity profile in the reference conditions and may not be fundamental. Qualitative agreement with experiment is demonstrated in several areas. The view that field reversal occurs because of a simple MHD dynamo is therefore given support.
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52.65.-y Plasma simulation
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.55.Ez Theta pinch
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