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Nov 1980

Volume 23, Issue 11, pp. 2151-2335

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A random flight model of inhomogeneous turbulent dispersion

P. A. Durbin

Phys. Fluids 23, 2151 (1980); http://dx.doi.org/10.1063/1.862908 (3 pages) | Cited 19 times

Online Publication Date: 21 July 2008

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The effect of finite memory time cannot be ignored in many dispersion problems: It is proposed that a random flight model will be more satisfactory than the diffusion approximation in such situations. A calculation of dispersion in open channel flow is presented.
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47.27.T- Turbulent transport processes
02.50.-r Probability theory, stochastic processes, and statistics
47.60.-i Flow phenomena in quasi-one-dimensional systems

Memory effects in the motion of a suspended particle in a turbulent fluid

M. Gitterman and V. Steinberg

Phys. Fluids 23, 2154 (1980); http://dx.doi.org/10.1063/1.862909 (7 pages) | Cited 8 times

Online Publication Date: 21 July 2008

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The noninstantaneous behavior of the velocity correlation function for a turbulent fluid leads to memory effects in the equation of motion of a particle suspended in such a fluid. This effect is a direct consequence of the fluctuation‐dissipation theorem, which connects the correlation properties of the random force with a memory function. As a result, the equation of motion of a suspended particle in a turbulent flow is an integro‐differential rather than a differential equation, and the diffusion coefficient of a suspended particle and that of a fluid do not coincide even in the simplest model. The velocity correlation function of a particle and its diffusion coefficient are found for a simple model.
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47.27.T- Turbulent transport processes
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

A variational principle for turbulent flow

Melvin E. Stern

Phys. Fluids 23, 2161 (1980); http://dx.doi.org/10.1063/1.862910 (10 pages) | Cited 4 times

Online Publication Date: 21 July 2008

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A general control theory is proposed to select the realized stationary state whenever the equations of motion are densely nonunique (degenerate). For the turbulent flow in a pipe with given pressure gradient, the theory implies that the discharge is an extremum. Quantitative results, such as von Kárman’s constant, emerge when this variational principle is combined with inequalities pertaining to the mean field. The control theory is also applied to fully turbulent thermal convection, and a variational principle for this problem is obtained which is also consistent with measurements.
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47.27.-i Turbulent flows
02.30.Xx Calculus of variations
02.30.Yy Control theory

Stability of rotation‐modified plane Poiseuille flow

Anatolij Gusev and Fritz H. Bark

Phys. Fluids 23, 2171 (1980); http://dx.doi.org/10.1063/1.862911 (7 pages) | Cited 4 times

Online Publication Date: 21 July 2008

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The linear stability problem for the steady shear flow between two parallel planes, which rotate with the same angular velocity around a common axis, is considered. The critical Reynolds number Rc depends on the Taylor number T, which is a measure of the ratio between the Coriolis force and the viscous forces. The parameter range 1⩽t≃100 is studied. It is shown that the critical Reynolds number has a minimum value Rc?31 for T?9.5. It is also shown that, for large values of T, the most unstable mode approaches the most unstable mode associated with the Ekman layer. For 1.75≲T≲3, the theoretical results agree qualitatively with experimental results obtained by other investigators. The disagreement between experiment and theory for smaller values of T is presumably due to inlet effects in the experimental apparatus.
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47.20.-k Flow instabilities
47.15.Fe Stability of laminar flows

Linear centrifugal instability of a thick Stokes’ layer

P. W. Duck

Phys. Fluids 23, 2178 (1980); http://dx.doi.org/10.1063/1.862912 (4 pages)

Online Publication Date: 21 July 2008

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The linear centrifugal instability of a Stokes’ layer, produced by a circular cylinder torsionally oscillating in an infinite viscous fluid is investigated. The problem is studied over a range of ratios of Stokes’ layer thickness to cylinder radius, and the results are seen to agree reasonably well with previously reported experimental measurements.
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47.15.Fe Stability of laminar flows
47.20.-k Flow instabilities

Radiation damping of long, finite‐amplitude internal waves

N. R. Pereira and L. G. Redekopp

Phys. Fluids 23, 2182 (1980); http://dx.doi.org/10.1063/1.862913 (2 pages) | Cited 4 times

Online Publication Date: 21 July 2008

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Numerical solutions of a damped, nonlinear wave equation are presented. The equation describes the propagation of waves in a narrow thermocline or inversion which lose energy by exciting internal waves in the weakly stratified ambient environment. The results provide estimates for the persistence of finite‐amplitude internal waves propagating in a thermoclinic waveguide.
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41.20.Jb Electromagnetic wave propagation; radiowave propagation
47.35.-i Hydrodynamic waves
47.55.Hd Stratified flows
92.60.hh Acoustic gravity waves, tides, and compressional waves

Inertial and equilibrium shear retardation of electrohydrodynamic instability growth

James F. Hoburg

Phys. Fluids 23, 2184 (1980); http://dx.doi.org/10.1063/1.862914 (5 pages) | Cited 1 time

Online Publication Date: 21 July 2008

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The effects of fluid inertia and equilibrium shear rate on a normal field, surface‐coupled electrohydrodynamic instability in polar geometry are described. Instability growth is retarded and takes on a complex (propagating) part to degrees dependent upon the ratio of viscous diffusion time to electroviscous time and the product of rotation rate and viscous diffusion time. Implications relate directly to an electrically augmented mechanical shear mixing device and tradeoffs between mixing quality and material processing rate.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.15.Fe Stability of laminar flows

Transport equations for fast electrons in a moving Newtonian fluid

J. Robert Buchler

Phys. Fluids 23, 2189 (1980); http://dx.doi.org/10.1063/1.862915 (4 pages) | Cited 1 time

Online Publication Date: 21 July 2008

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The equations for the transport of relativistic electrons are derived inclusive of all terms of order (v/c). The equations are valid in all regimes, from diffusion to streaming. The moments of the electron distribution function, as well as the electron velocities, are measured in the fluid frame. No special geometry or symmetry is assumed.
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51.10.+y Kinetic and transport theory of gases
52.25.Dg Plasma kinetic equations
72.10.Bg General formulation of transport theory
95.30.Jx Radiative transfer; scattering

Simulations of the runaway electron distributions

J. C. Wiley, Duk‐In Choi, and Wendell Horton

Phys. Fluids 23, 2193 (1980); http://dx.doi.org/10.1063/1.862916 (11 pages) | Cited 22 times

Online Publication Date: 21 July 2008

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The time evolution of the electron distribution function is followed from an initial Maxwellian to the quasi‐steady‐state runaway distribution as a function of E/ED and Z using a new two‐dimensional Fokker–Planck code. The electron distributions are used to determine the runaway production rate, the current density along with the fraction of Ohmic power directed to the runaways, and the perpendicular and parallel temperatures of the high energy distributions. A simple parameterization of the high energy distribution is given and used to investigate the high frequency runaway instability for the infinite uniform plasma.
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52.25.Dg Plasma kinetic equations
52.20.Fs Electron collisions
52.65.-y Plasma simulation

Monte Carlo hybrid modeling of electron transport in laser produced plasmas

Rodney J. Mason

Phys. Fluids 23, 2204 (1980); http://dx.doi.org/10.1063/1.862903 (12 pages) | Cited 22 times

Online Publication Date: 21 July 2008

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A new Monte Carlo hybrid scheme for the transport of electrons in laser produced plamas is described in detail. Comparison is made with alternate schemes. The hot electrons are followed as collisional particles‐in‐cell. The cold electrons are a donor‐cell fluid. The self‐consistent E field is computed approximately by either a moment method which seeks to establish quasi‐neutrality, or by plasma‐period dilation that stretches the local plasma period up to the time step. Application is made to the transport of laser driven electrons in foil‐like geometries. Results from a large number of computer simulations are used to confirm the quasi‐neutrality of the scheme, to demonstrate important aspects of the hot electron collisionality, to explore the influence of return current E fields from classical and ion‐acoustic resistivity, and finally, to examine the efficiency of transport inhibition from thermal convection in the presence of density dips. Attention is drawn to the need for an even more fundamental particle description for the thermals.
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52.65.-y Plasma simulation
52.50.Jm Plasma production and heating by laser beams (laser-foil, laser-cluster, etc.)
52.25.Fi Transport properties

A confinement theorem for nonneutral plasmas

T. M. O’Neil

Phys. Fluids 23, 2216 (1980); http://dx.doi.org/10.1063/1.862904 (3 pages) | Cited 89 times

Online Publication Date: 21 July 2008

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A plasma consisting solely of particles of a single species is initially in the shape of a long column. It is confined by an axial magnetic field in a region of space bounded by a perfectly conducting and perfectly absorbing cylindrical wall. Conservation of angular momentum and conservation of energy are used to place an upper bound on the fraction of electrons that can ever reach the wall.
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52.55.Dy General theory and basic studies of plasma lifetime, particle and heat loss, energy balance, field structure, etc.

Particle and energy end loss from a collisionless plasma

Edward H. Klevans and S. Peter Gary

Phys. Fluids 23, 2219 (1980); http://dx.doi.org/10.1063/1.862905 (6 pages)

Online Publication Date: 21 July 2008

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A one‐dimensional free‐flow kinetic model is used to study the axial ion losses from a linear theta pinch under collisionless conditions. The effects of a simple mirror model are included. The loss due to ion thermal flux is shown to be much smaller than the total ion kinetic energy flux loss, thereby indicating that it is appropriate to neglect ion thermal conduction in numerical simulations of the Scylla IV‐P experiment.
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52.25.Fi Transport properties

Finite bandwidth induced stochasticity in a magnetic mirror

C. R. Menyuk and Y. C. Lee

Phys. Fluids 23, 2225 (1980); http://dx.doi.org/10.1063/1.862906 (17 pages) | Cited 9 times

Online Publication Date: 21 July 2008

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The electrostatic fluctuation spectrum in a magnetic mirror always has some finite bandwidth. The role of a finite bandwidth in destroying the superadiabatic motion of ions has been explored. It is found that virtually any bandwidth is sufficient to destroy the resonant island regions in velocity space; however, to destroy all of phase space, so that ions may move freely, requires a bandwidth on the other of an inverse bounce time in the mirror. Assuming such a bandwidth, the diffusion rate in the velocity space is calculated.
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52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

Drift‐wave eigenmodes in toroidal plasmas

Liu Chen and C. Z. Cheng

Phys. Fluids 23, 2242 (1980); http://dx.doi.org/10.1063/1.862907 (8 pages) | Cited 74 times

Online Publication Date: 21 July 2008

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The eigenmode equation describing ballooning drift waves in toroidal plasmas is investigated both analytically and numerically. Two branches of eigenmodes are identified. One is slab‐like and the other is a new branch induced by finite toroidal coupling. The slab‐like eigenmodes correspond to unbounded states and experience finite shear damping. The toroidicity‐induced eigenmodes, however, can become local quasi‐bounded states with negligible shear damping. Both branches of eigenmodes may exist simultaneously. The corresponding analytical theories are also presented.
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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.)
52.55.Fa Tokamaks, spherical tokamaks
52.55.Hc Stellarators, torsatrons, heliacs, bumpy tori, and other toroidal confinement devices

Wave modulation in a nonlinear dispersive medium

Y. C. Kim, L. Khadra, and E. J. Powers

Phys. Fluids 23, 2250 (1980); http://dx.doi.org/10.1063/1.862917 (8 pages) | Cited 19 times

Online Publication Date: 21 July 2008

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A model describing the simultaneous amplitude and phase modulation of a carrier wave propagating in a nonlinear dispersive medium is developed in terms of nonlinear wave‐wave interactions between the sidebands and a low frequency wave. It is also shown that the asymmetric distribution of sidebands is determined by the wavenumber dependence of the coupling coefficient. Digital complex demodulation techniques are used to study modulated waves in a weakly ionized plasma and the experimental results support the analytical model.
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52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)

Self‐modulation of ion Bernstein waves

J. R. Myra and C. S. Liu

Phys. Fluids 23, 2258 (1980); http://dx.doi.org/10.1063/1.862918 (7 pages) | Cited 23 times

Online Publication Date: 21 July 2008

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A self‐modulation equation for coherent ion Bernstein waves is derived by a multiple‐time‐scale, perturbative expansion of the Vlasov equation. The dominant nonlinearity acting on the waves is shown to be the nonlinear ion gyrofrequency shift. The waves obey a version of the nonlinear Schrödinger equation with the dispersive terms in the three spatial directions having, in general, differing signs. If the modulation is independent of one spatial variable, the elliptic or hyperbolic two‐dimensional nonlinear Schrödinger equation results. In contrast to the elliptic case which exhibits collapse, wave energy always disperses if initially localized in the hyperbolic case.
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52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)

Nonlinear space‐charge waves on cylindrical electron beams and plasmas

Thomas P. Hughes and Edward Ott

Phys. Fluids 23, 2265 (1980); http://dx.doi.org/10.1063/1.862919 (5 pages) | Cited 7 times

Online Publication Date: 21 July 2008

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Nonlinear space‐charge waves in a strongly magnetized cylindrical plasma are investigated. Soliton and periodic wave solutions are obtained. For the case of an intense unneutralized electron beam, a significant decrease in the phase velocity of the slow space‐charge wave is found at large amplitudes. The importance of this result for some collective ion acceleration schemes is discussed.
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52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.75.Di Ion and plasma propulsion
52.27.Ny Relativistic plasmas

A two‐term approximation for growth rates of a guiding center screw pinch

Thomas E. Cayton, George Vahala, and D. C. Barnes

Phys. Fluids 23, 2270 (1980); http://dx.doi.org/10.1063/1.862920 (7 pages) | Cited 2 times

Online Publication Date: 21 July 2008

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The guiding center plasma description of an isotropic, collisionless plasma is used to study the linear stability of the diffuse screw pinch in the special case when the poloidal magnetic field component is small compared with the axial magnetic field component. A two‐term approximation for growth rates is derived from the linearized guiding center plasma equations by straightforward asymptotic expansion in terms of a small parameter that is proportional to (Bϑ/rBz)‖r=0. The two‐term approximate solution is compared with exact solutions and the range of validity of the approximations is examined. The result obtained from the guiding center plasma model is compared and contrasted with that from ideal magnetohydrodynamics. It is shown that the isotropic guiding center plasma may be more unstable or less unstable than ideal magnetohydrodynamics for the same configuration, depending on the parameters.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.55.Dy General theory and basic studies of plasma lifetime, particle and heat loss, energy balance, field structure, etc.

Stability of the noncircular screw pinch

G. Miller

Phys. Fluids 23, 2277 (1980); http://dx.doi.org/10.1063/1.862921 (6 pages) | Cited 1 time

Online Publication Date: 21 July 2008

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The magnetohydrodynamic stability of a slightly noncircular screw pinch with arbitrary cross‐sectional shape is investigated analytically and numerically using two models: the surface‐current model and the force‐free model. For the surface‐current model the noncircular correction to the instability growth rate is given in analytical form: (1) for the case nq≃m, where q is the safety factor and m and n are the azimuthal and longitudinal mode numbers of the instability, and (2) for the special case of purely transverse perturbations (n=0). For the force‐free model, the noncircular correction to the marginal stability condition is obtained. This is done analytically for nq≃m, and for fixed boundary internal modes.
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52.30.-q Plasma dynamics and flow
52.55.Ez Theta pinch

Enhanced transport in tokamaks due to toroidal ripple

Allen H. Boozer

Phys. Fluids 23, 2283 (1980); http://dx.doi.org/10.1063/1.862922 (8 pages) | Cited 65 times

Online Publication Date: 21 July 2008

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A method for evaluating transport in nonsymmetric systems is developed and applied to a previously little studied ripple collisionality regime of tokamaks. This collisionality regime, the ripple plateau, is the regime of primary importance both for present day and reactor scale tokamaks. The results can be directly applied to related systems like the toroidal Z pinch.
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52.55.Fa Tokamaks, spherical tokamaks
52.55.Hc Stellarators, torsatrons, heliacs, bumpy tori, and other toroidal confinement devices
52.25.Fi Transport properties
52.25.Dg Plasma kinetic equations

Rippling of the critical surface by four‐wave processes in a laser‐irradiated plasma

Wee Woo, J. S. DeGroot, and C. Barnes

Phys. Fluids 23, 2291 (1980); http://dx.doi.org/10.1063/1.862923 (5 pages) | Cited 4 times

Online Publication Date: 21 July 2008

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Rippling of the critical surface is investigated by a four‐wave process in which two electromagnetic waves are scattered by an ion perturbation for very high intensities in a laser‐irradiated plasma. The mechanism is the parametric oscillating two‐stream instability for the electromagnetic waves. The instability grows in the direction of the laser magnetic field; however, it hardly grows in the direction of the laser electric field. The thresholds and growth rates are obtained by a phase‐integral method, and there are optimized wavenumbers and pump fields for the growth. Results of two‐dimensional fluid and three‐dimensional particle calculations agree with the theoretical predictions. The theory also seems to be consistent with the observations in laser experiments.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.50.Jm Plasma production and heating by laser beams (laser-foil, laser-cluster, etc.)
52.25.Os Emission, absorption, and scattering of electromagnetic radiation

Local instability near the vortex point of a field‐reversed mirror

William A. Newcomb

Phys. Fluids 23, 2296 (1980); http://dx.doi.org/10.1063/1.862924 (5 pages) | Cited 26 times

Online Publication Date: 21 July 2008

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A study is made of the curvature‐driven magnetohydrodynamic instability in the neighborhood of the vortex point of a simple field‐reversed magnetic‐mirror system, with a purely poloidal magnetic field. The linearized magnetohydrodynamic equation of motion for localized modes in that neighborhood is found to be completely solvable. Two independent sets of modes are found, axial and radial, with the same spectrum of eigenfrequencies. Each set of modes, axial and radial, includes exactly one exponentially growing mode, of which the growth rate is found to be Ω, where 2πΩ−1 is the time required for one complete traversal of a closed magnetic flux line by an Alfvén‐wave signal.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.55.Jd Magnetic mirrors, gas dynamic traps
52.30.-q Plasma dynamics and flow
52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)

Heating of a toroidal plasma by a nonuniform radio frequency field

Y. Amagishi, A. Hirose, and H. M. Skarsgard

Phys. Fluids 23, 2301 (1980); http://dx.doi.org/10.1063/1.862925 (7 pages) | Cited 1 time

Online Publication Date: 21 July 2008

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Nonuniform electric fields created by an oscillating (1.8 MHz) dipole magnetic field are applied to a preformed, argon plasma in a torus with major radius R=19 cm, minor radius a=2.5 cm, and a toroidal magnetic field Ba=0.3 T. The induced rf plasma current flows in opposite toroidal directions in the outer (larger major radius) and inner regions of the plasma. Spatially and temporally resolved measurements are made of the electron density and temperature as well as the induced electric field and current density. Heating of both the electrons and the ions is observed. Maximum temperatures Te∼100 eV and t→Ti∼35 eV are found at a density of 1018 m−3. Rapid electron heat conduction toward the plasma center occurs, with a characteristic time of several μsec. The ion heating rate correlates with the growth rate for ion acoustic waves, calculated from measured plasma parameters.
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52.50.Gj Plasma heating by particle beams
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)

Resonant parametric excitations driven by lower‐hybrid fields

E. Villalón

Phys. Fluids 23, 2308 (1980); http://dx.doi.org/10.1063/1.862926 (10 pages) | Cited 4 times

Online Publication Date: 21 July 2008

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Three‐wave parametric excitation in inhomogeneous plasmas is examined in a two‐dimensional geometry relevant to supplementary rf heating of tokamaks. The stabilization of resonant parametric excitation due to a linear mismatch in wavenumbers and to the Landau‐damping rates of the decay waves is analyzed, assuming that the magnitude of the pump field is constant in time and in the spatial region where the resonant interaction takes place. Both types of temporally growing modes and spatially amplified instabilities are studied, using a WKB analysis. It is shown that either by increasing the strength of the mismatch K′ or the width of the pump L, the growth rate of the fastest growing normal mode will decrease. When the excited waves are slightly damped, it is shown that there exists a finite value of the product K′L, such that, above it, no temporal normal modes are excited. The amount of spatial amplification is also reduced by the mismatch in wavenumbers and by the damping rates of the excited waves. Because of the finite spatial extent of the pump electric field, the amplification length is found to be smaller than or equal to L, depending on the strength of the mismatch and damping rates.
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52.50.Gj Plasma heating by particle beams
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.55.Fa Tokamaks, spherical tokamaks
52.55.Hc Stellarators, torsatrons, heliacs, bumpy tori, and other toroidal confinement devices

Thermal and radiation losses in a linear device

Philip Rosenau and David Degani

Phys. Fluids 23, 2318 (1980); http://dx.doi.org/10.1063/1.862927 (8 pages)

Online Publication Date: 21 July 2008

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An analysis is presented of the electron temperature in a linear device which includes the effect of thermal conduction, heat flux limit, radiation, and end plugs. It is found that the thermal conduction and the heat flux limit are dominant in the initial phase of cooling, while the later phase is almost completely controlled by radiation that spatially homogenizes the temperature distribution. In the case of bremsstrahlung, within the frame of the present model, the temperature decays to zero in a finite time. This process takes the form of a cooling wave that moves from the ends of the column to the center. Impurities cause a milder, exponential decay, which is still much faster than the algebraic conduction decay. The thermal effectiveness of the end plugs is described by a convective transfer coefficient hp. Its scaling law (in terms of the coupled plamsa‐plug system) reveals that a very high plug‐plasma density ratio provides a simple way to significantly retard the cooling.
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52.55.Ez Theta pinch
52.25.Kn Thermodynamics of plasmas
52.25.Fi Transport properties
52.25.Os Emission, absorption, and scattering of electromagnetic radiation
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