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Dec 1982

Volume 25, Issue 12, pp. 2135-2415

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Transition from single to multiple double layers

Chung Chan and Noah Hershkowitz

Phys. Fluids 25, 2135 (1982); http://dx.doi.org/10.1063/1.863702 (3 pages) | Cited 18 times

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It is shown that laboratory double layers become multiple double layers when the ratio of Debye length to system length is decreased. This result exhibits characteristics described by boundary layer theory.
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52.40.Kh Plasma sheaths
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)

Exhaust rate measurements in a divertor with large mirror ratio

E. J. Strait

Phys. Fluids 25, 2137 (1982); http://dx.doi.org/10.1063/1.863703 (3 pages)

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The parallel ion fluid velocity in the scrape‐off layer of a poloidal divertor is observed to vary inversely with the mirror ratio in the divertor’s throat for ratios ranging from 1 to 5, in good agreement with models developed for bundle divertors. The density variation on a diverted field line also agrees qualitatively with the models, but the observed electric field does not.
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52.30.-q Plasma dynamics and flow
52.70.Ds Electric and magnetic measurements
52.55.Pi Fusion products effects (e.g., alpha-particles, etc.), fast particle effects

Destabilization of drift waves by a nonuniform radial electric field

Adel El‐Nadi and Hatem Hassan

Phys. Fluids 25, 2140 (1982); http://dx.doi.org/10.1063/1.863704 (2 pages) | Cited 6 times

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It is shown that drift waves can be destabilized in the presence of a nonuniform electrostatic field. This may explain the anomalous diffusion observed in tokamaks.
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52.35.Kt Drift waves
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)

A two‐grating method for combined beam splitting and frequency shifting in a two‐component laser‐Doppler velocimeter

Ari Glezer and Donald Coles

Phys. Fluids 25, 2142 (1982); http://dx.doi.org/10.1063/1.863705 (5 pages) | Cited 1 time

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The use of a rotating radial phase grating to carry out beam splitting and frequency shifting in a laser‐Doppler velocimeter is briefly reviewed. This technique is not new. However, the present design adds a substantial new element by using two overlapping radial gratings to produce a two‐channel system in which channel separation can be accomplished by electronic filtering of the signal from a single detector.
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47.80.-v Instrumentation and measurement methods in fluid dynamics
42.60.-v Laser optical systems: design and operation
42.79.Dj Gratings

Conical vortices: A class of exact solutions of the Navier–Stokes equations

C.‐S. Yih, F. Wu, A. K. Garg, and S. Leibovich

Phys. Fluids 25, 2147 (1982); http://dx.doi.org/10.1063/1.863706 (12 pages) | Cited 13 times

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A two‐parameter family of exact axially symmetric solutions of the Navier–Stokes equations for vortices contained within conical boundaries is found. The solutions depend upon the same similarity variable, equivalent to the polar angle ϕ measured from the symmetry axis, as flows previously discussed by Long and by Serrin, but are distinct from the cases they treated. The conical bounding stream surfaces of the present solution can be located at any angle ϕ=ϕ0, where 0<ϕ0<π. The flows in all of these cases, when solutions exist, are finite everywhere except at the cone vertex which is a source of axial momentum, but not of volume. Solutions are of three types, flow may be (a) towards the vertex on the axis and away from the vertex at the conical boundary, (b) towards the vertex both on the axis and at the cone, or (c) away from the vertex on the axis and towards it at the bounding cone. In the first and second case, strong shear layers form on the cone walls for high Reynolds numbers. In case (c), a region of strong axial shear and strong axial vorticity forms near the axis, even for low Reynolds numbers. The qualitative nature of the possible solutions is deduced, using methods of argument due to Serrin, and examples of flows are numerically computed for cone half‐angles of π/4, π/2 (flows above the plane z=0), and 3π/4. Regions of the parameter space where solutions are proven not to exist are given for the cone half‐angles given above, as well as regions where solutions are proven to exist.
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47.32.Ef Rotating and swirling flows

Instability and confined chaos in a nonlinear dispersive wave system

Enrique A. Caponi, Philip G. Saffman, and Henry C. Yuen

Phys. Fluids 25, 2159 (1982); http://dx.doi.org/10.1063/1.863707 (8 pages) | Cited 18 times

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Calculations of a discrete nonlinear dispersive wave system show that as the degree of nonlinearity increases, the system experiences in turn, periodic, recurring, chaotic, transitional, and periodic motions. A relationship between the instability of the initial configuration and the long‐time behavior is identified. The calculations further suggest that the corresponding continuous system will exhibit chaotic motions and energy‐sharing among a narrow band of unstable modes, a phenomenon which we call ‘‘confined chaos.’’
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47.35.-i Hydrodynamic waves
47.20.-k Flow instabilities
41.20.Jb Electromagnetic wave propagation; radiowave propagation
02.60.Nm Integral and integrodifferential equations

Evolution of groups of gravity waves with moderate to high steepness

Ming‐Yang Su

Phys. Fluids 25, 2167 (1982); http://dx.doi.org/10.1063/1.863708 (8 pages) | Cited 16 times

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Experimental measurements of evolution of a deep‐water wave group are described. Wave groups are found to change rapidly over a few tens of wavelengths when the initial steepness 0.09≤a0k0≤0.28. The transition creates envelope solitons composed of waves with smaller steepness and lower carrier frequency than the initial state. The carrier frequencies of the envelope solitons can be downshifted as much as 25%. The transition process is irreversible, but does not lead to total randomness.
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47.35.-i Hydrodynamic waves
92.10.Lq Turbulence, diffusion, and mixing processes in oceanography

A modulated point‐vortex model for geostrophic, β‐plane dynamics

Norman J. Zabusky and James C. McWilliams

Phys. Fluids 25, 2175 (1982); http://dx.doi.org/10.1063/1.863709 (8 pages) | Cited 47 times

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A new modulated point‐vortex model is presented for the equivalent barotropic equations of potential vorticity: qt−ψyqx +ψxqy=0, (q=κ+βy, κ=∇2ψ−γψ). The discrete model conserves ∑m(qm0 −β∗ym)2 in analogy with the conserved ∫ ∫κ2 dx dy. An analytical study is made for the general two point‐vortex system. For equal vortices, the solution has a monotonic drift ∝(−β). A comparison is made of numerical solutions of the point‐vortex model and corresponding solutions of a finite‐difference model on a periodic domain. For an initially monopolar distribution of ∇2ψ−γ2ψ, an x drift in the direction of sign (−β) and a y drift in the direction of the sign of the extremum of κ is obtained in both cases that are in agreement at short times. The y drift is associated with the development of a spreading Rossby wave wake, as a consequence of the conservation law. For a ‘‘tilted’’ dipolar region of vorticity we observe near‐periodic oscillations. The modulated point‐vortex model is also applicable to drift waves in a plasma.
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47.32.Ef Rotating and swirling flows
92.10.Fj Upper ocean and mixed layer processes
92.60.hk Convection, turbulence, and diffusion
52.35.Kt Drift waves

Point vortex motions with a center of symmetry

Hassan Aref

Phys. Fluids 25, 2183 (1982); http://dx.doi.org/10.1063/1.863710 (5 pages) | Cited 12 times

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The equations of motion for point vortices are well known to preserve certain discrete symmetries of the initial state. The case of a center of symmetry is considered in detail here, since this particular instance seems to have been overlooked in the classical literature. This symmetry provides a generalization of the early studies by Gröbli and Greenhill wherein several axes of symmetry are present, a case which leads to an effective one‐body problem. The center of symmetry yields an effective two‐body problem which is Hamiltonian and integrable. As an example the ‘‘double alternate ring’’ configurations, circular analogs of the vortex street introduced by Havelock, are considered. A fully nonlinear mode wherein these double rings asymptotically dissolve into freely moving vortex pairs is found analytically. The paper concludes with a discussion of the relevance of such modes to our understanding of the disintegration of vortex streets in two‐dimensional flow.
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47.32.Ef Rotating and swirling flows
47.10.-g General theory in fluid dynamics

Small‐amplitude waves produced by a submerged vorticity distribution on the surface of a viscous liquid

A. Prosperetti and L. Cortelezzi

Phys. Fluids 25, 2188 (1982); http://dx.doi.org/10.1063/1.863711 (5 pages) | Cited 2 times

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The small‐amplitude waves generated by a submerged vorticity distribution on the surface of a viscous fluid are studied. The linearized initial‐value problem is considered, and a closed‐form solution for each monochromatic component is obtained. The results of the theory are illustrated by a numerical synthesis of these components for the case of a vortex filament in water.
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47.35.-i Hydrodynamic waves
47.10.-g General theory in fluid dynamics

Strained spiral vortex model for turbulent fine structure

T. S. Lundgren

Phys. Fluids 25, 2193 (1982); http://dx.doi.org/10.1063/1.863957 (11 pages) | Cited 181 times

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A model for the intermittent fine structure of high Reynolds number turbulence is proposed. The model consists of slender axially strained spiral vortex solutions of the Navier–Stokes equation. The tightening of the spiral turns by the differential rotation of the induced swirling velocity produces a cascade of velocity fluctuations to smaller scale. The Kolmogorov energy spectrum is a result of this model.
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47.27.-i Turbulent flows
47.32.Ef Rotating and swirling flows
47.10.-g General theory in fluid dynamics

Unsteady natural convection about a sphere at small Grashof number

Takao Sano

Phys. Fluids 25, 2204 (1982); http://dx.doi.org/10.1063/1.863958 (3 pages) | Cited 3 times

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Unsteady low‐Grashof‐number natural convection about a sphere is studied when the surface temperature of the sphere is suddenly increased. It is shown that the solutions for the velocity and temperature are, respectively, expressed in terms of three expansions reflecting the existence of three distinct regions in the (r, t) plane, r and t being a nondimensional radial coordinate and nondimensional time, respectively.
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47.27.T- Turbulent transport processes
47.15.-x Laminar flows
02.30.Mv Approximations and expansions

Exchange of energy and momentum between gases at different temperatures

F. Bampi and A. Morro

Phys. Fluids 25, 2207 (1982); http://dx.doi.org/10.1063/1.863959 (4 pages) | Cited 4 times

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The interaction mechanisms between gases at different temperatures are investigated within the thermodynamic theory of mixtures. Conditions a priori on the phenomenological coefficients are derived by having recourse to the Galilean invariance and the entropy principle for mixtures. The results so obtained, which, owing to their thermodynamic origin, must hold for any kinetic derivation, turn out to be satisfied by known kinetic expressions.
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51.30.+i Thermodynamic properties, equations of state
51.10.+y Kinetic and transport theory of gases
05.70.-a Thermodynamics

Determination of the density perturbation at the wall for the Rayleigh problem

Barry D. Ganapol

Phys. Fluids 25, 2211 (1982); http://dx.doi.org/10.1063/1.863960 (7 pages) | Cited 2 times

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The Rayleigh problem, a fundamental time‐dependent problem of gas kinetics, is studied in the context of the constant collision frequency BGK model. An analytical result, expressed in terms of the stationary solution, is obtained and numerically evaluated. Asymptotic solutions in both the small and large time limit are also presented and compared to results of other theories.
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51.10.+y Kinetic and transport theory of gases

Stellarator equilibria with weak helical curvature

Guthrie Miller

Phys. Fluids 25, 2218 (1982); http://dx.doi.org/10.1063/1.863961 (5 pages)

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General low‐β stellarator equilibria having weak helical curvature are calculated analytically. Important properties of these equilibria are also calculated; separatrix location, stability toward transverse shifts, and flute interchange stability.
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52.55.Fa Tokamaks, spherical tokamaks
52.55.Hc Stellarators, torsatrons, heliacs, bumpy tori, and other toroidal confinement devices
52.30.-q Plasma dynamics and flow
52.55.Dy General theory and basic studies of plasma lifetime, particle and heat loss, energy balance, field structure, etc.
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)

Ideal magnetohydrodynamic stability of axisymmetric mirrors

D. A. D’Ippolito, B. Hafizi, and J. R. Myra

Phys. Fluids 25, 2223 (1982); http://dx.doi.org/10.1063/1.863962 (8 pages) | Cited 6 times

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The governing partial differential equation for general mode‐number pressure‐driven ballooning modes in a long‐thin, axisymmetric plasma is derived within the context of ideal magnetohydrodynamics. It is shown that the equation reduces in special limits to the Hain–Lüst equation, the high‐m diffuse p(ψ) ballooning equation, and the low‐m sharp‐boundary equation. A low‐β analytic solution of the full partial differential equation is presented for quasiflute modes in an idealized tandem mirror model to elucidate the relationship of the various limiting cases.
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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.)
52.30.-q Plasma dynamics and flow
52.55.Dy General theory and basic studies of plasma lifetime, particle and heat loss, energy balance, field structure, etc.

Effect of ion collisionality on ion‐acoustic waves

C. J. Randall

Phys. Fluids 25, 2231 (1982); http://dx.doi.org/10.1063/1.863963 (3 pages) | Cited 32 times

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The frequency and damping ratio of ion‐acoustic waves in plasmas with moderately collisional ions is obtained by numerical solution of the linearized Fokker–Planck equation for electron‐ion temperature ratios, ZTc/Ti=4, 8, 16, and 32.
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52.35.Dm Sound waves
52.20.Hv Atomic, molecular, ion, and heavy-particle collisions

Energy and momentum deposition in plasmas due to the lower hybrid wave by a finite source

Noriyoshi Nakajima, Hirotada Abe, and Ryohei Itatani

Phys. Fluids 25, 2234 (1982); http://dx.doi.org/10.1063/1.863729 (15 pages) | Cited 11 times

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Heating and current generation due to the lower hybrid wave are studied using particle simulation. In contrast with previous work, where only a single mode is treated, the main interest of this work is focused on the physical problems of a propagation cone consisting of many Fourier‐expanded modes. It is found that the trajectory of the propagation cone is well described up to the lower hybrid resonance layer using both the cold plasma approximation and the WKB method. An ion cross‐field drift due to the ponderomotive force is observed. A main discovery of this work is that the modes in the upper portion of the spectrum of the antenna play a key role in the creation of the ion high‐energy tail. This process cannot be explained by the linear theory and is called the cascade process judging from the time variation of the damping of each mode. The particle model is significantly improved using the elongated grid and the quadratic spatial interpolation. Applications of this model to simulations of other problems are expected to be fruitful in research on plasma physics and nuclear fusion.
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52.50.Gj Plasma heating by particle beams
52.40.-w Plasma interactions (nonlaser)
52.50.-b Plasma production and heating
52.65.-y Plasma simulation

Role of the relativistic mass variation in electron cyclotron resonance wave absorption for oblique propagation

I. Fidone, G. Granata, and R. L. Meyer

Phys. Fluids 25, 2249 (1982); http://dx.doi.org/10.1063/1.863730 (15 pages) | Cited 65 times

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The role of the relativistic mass variation on wave absorption in the electron cyclotron range of frequencies is investigated. It is first shown that the validity of the nonrelastivistic linear dispersion relation for a Maxwellian plasma is restricted by the conditions N2∥≫Te/mc2 and N2∥≫‖1−ω2c/ω2‖. A numerical investigation of wave damping in a plasma slab located in an inhomogeneous tokamak‐like magnetic field shows that for most angles of practical interest the latter condition is easily violated and, therefore, the nonrelativistic dispersion relation yields inaccurate results. The problem of the validity of the nonrelativistic quasilinear equation for oblique propagation is also discussed. Using a quasilinear model equation, it is shown that the inclusion of the relativistic mass variation in the diffusion coefficient results in a basic change of the wave–particle selective interaction compared to the nonrelativistic approximation for any value of Te or N∥.
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52.25.Os Emission, absorption, and scattering of electromagnetic radiation
52.40.-w Plasma interactions (nonlaser)

Electrostatic drift modes with stochastic particle diffusion

C. F. Zhang, R. Marchand, and Y. C. Lee

Phys. Fluids 25, 2264 (1982); http://dx.doi.org/10.1063/1.863731 (7 pages) | Cited 1 time

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The effect of stochastic particle diffusion on the collisionless universal mode in slab geometry is considered. Cross‐field particle diffusion is assumed to be caused by a model static magnetic field turbulence. The resultant eigenmode equation is an integral equation for the perturbed electrostatic potential, which is solved numerically. As stochastic particle diffusion is gradually turned on, its effect on the usual drift branch is found to be stabilizing. At the same time, however, there appears a new, stochasticity‐induced mode which, under certain circumstances, may become unstable.
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52.35.Kt Drift waves
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.55.Jd Magnetic mirrors, gas dynamic traps

Magnetohydrodynamic fluctuations near thermal equilibrium

Eliezer Hameiri and Harvey A. Rose

Phys. Fluids 25, 2271 (1982); http://dx.doi.org/10.1063/1.863732 (7 pages) | Cited 1 time

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A statistical equilibrium ensemble for a class of nonlinear, ideal, compressible magnetohydrodynamics models is constructed. If the departure from thermal equilibrium is due to helical magnetic‐field configurations, then the magnetic‐field fluctuation spectrum differs profoundly from that predicted by Landau’s theory of fluid fluctuations which involves zero helicity. Some of the results of that theory however are recovered, as far as fluctuations of fluid‐dynamical (nonmagnetic) variables are concerned, in the linear limit of our nonlinear theory. Comparisons are also made with related models of incompressible plasma turbulence.
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52.30.-q Plasma dynamics and flow
52.25.Gj Fluctuation and chaos phenomena
52.55.-s Magnetic confinement and equilibrium

Nonlinear theory of a positive column in a magnetic field

F. Xu, F. L. Tang, and L. S. Chen

Phys. Fluids 25, 2278 (1982); http://dx.doi.org/10.1063/1.863700 (6 pages) | Cited 2 times

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A nonlinear theory of an intermediate pressure discharge column in a magnetic field is presented. Motion of the neutral gas is considered. The continuity and momentum transfer equations for charged particles and neutral particles are solved by numerical methods. The main result obtained is that the rotating velocities of ionic gas and neutral gas are approximately equal. Bohm’s criterion and potential inversion in the presence of neutral gas motion are also discussed.
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52.80.-s Electric discharges
51.50.+v Electrical properties (ionization, breakdown, electron and ion mobility, etc.)

Behavior of charged particles confined in a magnetic mirror

D. Bora, P. I. John, Y. C. Saxena, and R. K. Varma

Phys. Fluids 25, 2284 (1982); http://dx.doi.org/10.1063/1.863701 (5 pages) | Cited 6 times

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Experimental investigations of the nonadiabatic leakage of charged particles from a magnetic mirror have been conducted. The observations reveal the existence of multiple lifetimes for particles with similar energy and pitch angle. The variations of the time scales as a function of the particle density and radial position are investigated.
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52.55.Jd Magnetic mirrors, gas dynamic traps
52.20.-j Elementary processes in plasmas

Stability theory of drift‐type flute modes in finite‐β plasmas

Stefano Migliuolo

Phys. Fluids 25, 2289 (1982); http://dx.doi.org/10.1063/1.863728 (6 pages) | Cited 1 time

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The linear theory of flute modes in a finite‐β, inhomogeneous, magnetized plasma is developed. The collisionless Vlasov equation is used in a slab geometry, including the effects of a constant gravity field. The magnetic drift mode and the g×B mode are examined, and their stability properties are described. These two ‘‘modes’’ are shown to be different limits of the general finite‐β interchange mode. The wave‐particle resonances, between the flute modes and the particles that ∇B drift perpendicular to the unperturbed magnetic field, are included in a self‐consistent manner.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.35.Kt Drift waves

Density modification and energetic ion production at relativistic self‐focusing of laser beams in plasmas

D. A. Jones, E. L. Kane, P. Lalousis, P. Wiles, and H. Hora

Phys. Fluids 25, 2295 (1982); http://dx.doi.org/10.1063/1.863964 (7 pages) | Cited 37 times

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A two‐dimensional time‐dependent laser plasma interaction code is described and used to model the interaction between a 5 psec Nd glass laser pulse of peak power 1013 W and a 35 times ionized tin target. Parameters are chosen so that relativistic self‐focusing down to a diameter of the order of the wavelength of the laser light is observed in a distance comparable to the half intensity vacuum beam diameter. At later times strong modification of the plasma density by the nonlinear force is observed. The combination of relativistic self‐focusing and axial nonlinear force results in the acceleration of tin ions to a maximum energy of 5 GeV, in agreement with previous approximate calculations.
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52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma
52.50.Jm Plasma production and heating by laser beams (laser-foil, laser-cluster, etc.)
42.65.Jx Beam trapping, self-focusing and defocusing; self-phase modulation
52.25.Kn Thermodynamics of plasmas
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