Showing papers in "Physics of Fluids in 1980"
TL;DR: In this paper, an ignition and growth concept is used, within the framework of a one-dimensional Lagrangian hydrodynamic code, to model the shock initiation of heterogeneous solid explosives.
Abstract: An ignition and growth concept is used, within the framework of a one‐dimensional Lagrangian hydrodynamic code, to model the shock initiation of heterogeneous solid explosives. The leading shock wave of an initiating pulse is assumed to ignite a small fraction of the explosive at localized heated regions. These ignited regions then grow as material is consumed at their boundaries. The growth rate for a particular material is assumed to have the characteristic pressure dependence of high‐pressure laminar burning experiments. Results of the model calculations are in good quantitative agreement with recent manganin pressure gage and particle velocity gage measurements of the buildup of the initiating shock front to detonation for both sustained and short duration pulses in four solid explosives: PBX−9404, TATB, cast TNT, and PETN. The predicted run distances to detonation as functions of shock pressure at various initial densities and the predicted reaction zone lengths of the fully developed detonation waves also correlate well with experimental data for these four solid explosives.
587 citations
TL;DR: In this article, the authors used high toroidal mode number expansion to reduce the lowest-order system of equations to a set of ordinary (along the field line) integro-differential equations for low frequency, short perpendicular wavelength, electromagnetic perturbations in an inhomogeneous, magnetically confined plasma.
Abstract: Kinetic equations for low frequency, short perpendicular wavelength, electromagnetic perturbations in an inhomogeneous, magnetically confined plasma are developed. The analysis makes use of the recently developed high toroidal mode number expansion to reduce the lowest‐order system of equations to a set of ordinary (along the field line) integro‐differential equations. Included in these equations are the effects of finite Larmor radius, magnetic shear, trapped particles, and nonuniform magnetic curvature drifts. Perturbed fields are represented by a scalar potential and two components of the vector potential. Thus, the effects of the compressional component of the perturbed magnetic field are retained and the equations are valid for arbitrary values of the plasma pressure. The extension of the high toroidal mode number expansion to nonaxisymmetric configurations is discussed.
381 citations
TL;DR: In this article, a collisionless plasma with arbitrary ion temperature in plane geometry is formulated and the plasma-sheath equation is solved numerically with no approximation of the Debye length.
Abstract: The plasma‐sheath equation for a collisionless plasma with arbitrary ion temperature in plane geometry is formulated. Outside the sheath, this equation is approximated by the plasma equation, for which an analytic solution for the electrostatic potential is obtained. In addition, the ion distribution function, the wall potential, and the ion energy and particle flux into the sheath are explicitly calculated. The plasma‐sheath equation is also solved numerically with no approximation of the Debye length. The numerical results compare well with the analytical results when the Debye length is small.
339 citations
TL;DR: In this paper, the equations for particle drift orbits are given in a new magnetic coordinate system, which separates the fast motion along the magnetic field lines from the slow motion across the lines.
Abstract: The equations for particle drift orbits are given in a new magnetic coordinate system. This form of the equations separates the fast motion along the magnetic field lines from the slow motion across the lines. In addition, less information is required about the magnetic field structure than in alternative forms of the drift equations.
291 citations
TL;DR: In this paper, the change in kinetic energy between the initial and final states of the rollup of an infinite vortex sheet into an array of uniform vortices is calculated, and an upper limit on the pitch-to-diameter ratio of the vortex array is found.
Abstract: The change in kinetic energy between the initial and final states of the rollup of an infinite vortex sheet into an array of uniform vortices is calculated From the result, an upper limit on the pitch‐to‐diameter ratio of the vortex array is found This contrasts with a lower limit found from stability considerations by Moore and Saffman By extending the calculation to the case of elliptical vortices, it is found that a combination of energy and stability considerations is able to predict, qualitatively, a number of the observed features of the free shear layer
195 citations
TL;DR: In this paper, a vortex technique capable of calculating the Rayleigh-Taylor instability to large amplitudes in inviscid, incompressible, layered flows is introduced, whose results show the formation of a steady-state bubble at large times, whose velocity is in agreement with the theory of Birkhoff and Carter.
Abstract: A vortex technique capable of calculating the Rayleigh–Taylor instability to large amplitudes in inviscid, incompressible, layered flows is introduced. The results show the formation of a steady‐state bubble at large times, whose velocity is in agreement with the theory of Birkhoff and Carter. It is shown that the spike acceleration can exceed free fall, as suggested recently by Menikoff and Zemach. Results are also presented for instability at various Atwood ratios and for fluids having several layers.
194 citations
TL;DR: In this paper, the shapes and properties of two equal corotating uniform vortices, rotating steadily about each other, are calculated and an integrodifferential equation for the bounding contour is solved numerically, using Newton's method.
Abstract: The shapes and properties of two equal corotating uniform vortices, rotating steadily about each other, are calculated. An integrodifferential equation for the bounding contour is solved numerically, using Newton’s method. The results compare well with those obtained from a simple model. It is shown that steady solutions do not exist if the vortices are too close. The stability to two‐dimensional disturbances is discussed qualitatively and the critical separation at which the system becomes unstable is calculated. Some comments are made on the stability of a vortex pair of equal counter rotating uniform vortices.
187 citations
TL;DR: In this article, the influence of fluctuations in the rate of local turbulent energy dissipation on higher-order structure functions for small separation distances r and on moments of turbulent velocity derivatives is examined using the hypotheses of Kolmogoroff and Obukhov for the probability density and variance of the dissipation fluctuations.
Abstract: The influence of fluctuations in the rate of local turbulent energy dissipation on higher‐order structure functions for small separation distances r and on moments of turbulent velocity derivatives is examined using the hypotheses of Kolmogoroff and Obukhov for the probability density and variance of the dissipation fluctuations. The predicted variation of the skewness and flatness factors with Rλ represents the available experimental data fairly well over a relatively wide range of Rλ when the constant μ introduced in the variance hypothesis is suitably chosen. The predicted variation of S with K fits the data very well. The present analysis breaks down for moments of sufficiently high order probably due to basic shortcomings of the hypotheses.
187 citations
TL;DR: In this article, small-angle CO2 laser scattering techniques are described which provide detailed information about density fluctuations in plasmas, and the theories of the scattering and the heterodyne and homodyne detection processes are described in detail for the case of smallangle scattering.
Abstract: Small‐angle CO2 laser scattering techniques are described which provide detailed information about density fluctuations in plasmas. These techniques are nonperturbative and measure the frequencies, wave vectors, and amplitudes of the density fluctuations. The theories of the scattering and the heterodyne and homodyne detection processes are described in detail for the case of small‐angle scattering. Several models are developed to describe recent experiments involving both coherent and stochastic fluctuations. The laser, detector, and physical arrangement used in the experiments are described in detail. Experimental studies of driven Bernstein waves, ion acoustic turbulence in a positive column discharge, and fluctuations in tokamaks are described to illustrate these techniques. It is demonstrated that CO2 laser scattering is useful in studying fluctuations with wavelengths between 0.01 and 1 cm and frequencies from 1 kHz to tens of giga‐Hertz in plasmas with mean densities ranging from 1010 to 1017 cm−3.
181 citations
TL;DR: In this paper, the interaction of solitary-wave solutions of a model equation for long waves in dispersive media is examined numerically, and two new solitary waves, having slightly different amplitudes from the original waves, together with a small dispersive tail are generated as a result of the interaction.
Abstract: The interaction of solitary‐wave solutions of a model equation for long waves in dispersive media is examined numerically. It is found that the waves do not emerge from the interaction unscathed. Instead, two new solitary waves, having slightly different amplitudes from the original waves, together with a small dispersive tail are generated as a result of the interaction.
173 citations
TL;DR: In this article, the mean rate of dissipation of a plane jet and three circular jets was measured along the axes of a single plane jet, covering good ranges of the jet Reynolds number Ujd/ν and the downstream distance x. The results confirmed the universal relations, derived from requirements of self-preservation, between e and x, for both the circular jet and the plane jet.
Abstract: The mean rate of dissipation e is measured along the axes of a plane jet and three circular jets, covering good ranges of the jet Reynolds number Ujd/ν and the downstream distance x. The data confirm the universal relations, derived from requirements of self‐preservation, between e and x, for both the circular jet and the plane jet. For either type of jet, the turbulence Reynolds number Rλ and the local Reynolds number Rc (based on local velocity and length scales) are found to be related as Rλ∼2.3Rc1/2.
TL;DR: In this article, an electromagnetic ion cyclotron instability was proposed as the wave generation mechanism; this theory was tested by evaluating the linear growth integrals under the measured anisotropic hot ion distribution.
Abstract: Examples of propagating electromagnetic Alfven/ion cyclotron waves in plasma particle and magnetic field data observed by the ATS-6 geostationary satellite are discussed. These waves were viewed mainly near the afternoon and dusk regions of the earth's magnetosphere with normalized frequencies in the 0.05 to 0.5 range. Two wave events were analyzed: both appeared coincidentally with the encounter of cool plasma populations which joined the hot populations already present. An electromagnetic ion cyclotron instability was proposed as the wave generation mechanism; this theory was tested by evaluating the linear growth integrals under the measured anisotropic hot ion distribution.
TL;DR: In this paper, the authors investigated the linear behavior of the double-tearing mode within the framework of magnetohydrodynamics and derived the dispersion relation for the mode.
Abstract: The linear behavior of the double‐tearing mode is investigated within the framework of magnetohydrodynamics. A two‐space‐scale analysis in which resistive solutions valid near the rational surfaces are joined to ideal solutions outside these regions is performed and used to derive the dispersion relation for the mode. If the separation of the rational surfaces at x=±xs is sufficiently small [xs/a<(kya)−7/9S−1/9], the growth rate is predicted to scale as S−1/3, and the structure of the mode proves to be essentially identical with that of the m=1 tearing mode in cylindrical geometry. With increasing separation, the mode makes a transition to the S−3/5 scaling and structure of the standard tearing mode. These predictions are confirmed by direct numerical solution of the magnetohydrodynamic equations, and the S−1/3 scaling is shown to be correlated with violations of the constant‐ψ approximation. Possible physical implications of the double‐tearing mode are discussed.
TL;DR: In this article, the nonlocal structure of the lower-hybrid-drift instability in a reversed field configuration is investigated and the effects of this instability on magnetic energy dissipation and its role in the Los Alamos field reversed theta pinch are discussed.
Abstract: The nonlocal structure of the lower‐hybrid‐drift instability is investigated in a reversed field configuration. The calculation includes electromagnetic effects and ∇B electron orbit modifications, which must be considered in the high β region of the current sheet. The eigenmodes are trapped in a potential well centered symmetrically on either side of the neutral layer at ‖x‖∼λ (λ is the scale length of the current sheet). The fundamental mode is well localized away from the neutral line with a half‐width Δx∼ (λ/ky)1/2<<λ, where ky∼Ωe(Ti/me)1/2 for the fastest growing mode. Higher order modes, however, have growth rates comparable to the fundamental mode and are much more global. In the cold electron limit (Te=0), the higher order modes with ∂/∂x∼ky can propagate throughout the entire sheet. In the warm electron limit (Te≠0), the electron ∇B drift‐wave resonance damps the mode and prevents the penetration of the mode closer than ‖x‖p∼λ (Te/2Ti) 1/2 of the neutral line. The effects of this instability on magnetic energy dissipation and its role in the Los Alamos field reversed theta pinch are discussed.
TL;DR: In this paper, a theoretical model describing the spatial structure and scaling laws of laser driven ablative implosions is presented, under conditions when heat flow is fluxlimited at the critical surface and suprathermal electrons do not form a dominant energy transport mechanism.
Abstract: A theoretical model is presented describing the spatial structure and scaling laws of laser driven ablative implosions. The effect of inhibited electron thermal transport is explicitly included. The theory is in excellent agreement with results from a computer hydrodynamics code, under conditions when heat flow is flux‐limited at the critical surface and suprathermal electrons do not form a dominant energy transport mechanism.
Abstract: A simple model of nonlinear saturation of an unstable mode is studied. The model consists of the resonant three‐wave coupling equations with the highest frequency wave linearly unstable and the two lower frequency waves damped. As the damping of the stable waves is increased, the solutions go through an interesting succession of qualitative changes, including bifurcations to increasingly complex periodic solutions and the appearance of apparently chaotic (i.e., aperiodic) solutions. These qualitative features are shown to be explainable on the basis of a one‐dimensional mapping which is numerically derivable from the original system of differential equations.
TL;DR: In this article, conservation of angular momentum and conservation of energy were used to place an upper bound on the fraction of electrons that can ever reach the wall of a perfectly conducting and perfectly absorbing cylindrical wall.
Abstract: 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.
TL;DR: In this article, the Euler-Tricomi equation and Chaplygin's equation were generalized to the relativistic regime and the adiabatic index was generalized by Γ≡ Γ/(1−β2s).
Abstract: Steady two‐dimensional flow of an ideal compressible fluid is studied in the context of special‐relativistic gasdynamics. The Newtonian equations for potential flow, including the equation of characteristics, Chaplygin’s equation, and the Euler–Tricomi equation, are generalized. It is found that these equations can have the same form in the Newtonian and the relativistic regimes if their parameters are defined in the local rest‐frame of the fluid. The Mach number thus defined, M≡[β/(1−β2)1/2]×[βs/(1−β2s)1/ 2]−1, where β and βs are, respectively, the speed of the fluid and the speed of sound relative to the fluid (in units of the speed of light), is shown to have the same properties as M=β/βs in Newtonian theory. The Newtonian expressions for oblique plane shock waves in a perfect gas can similarly be generalized in certain cases (which include, in particular, the extreme‐relativistic limit), and it is shown that the adiabatic index Γ in these expressions is generalized by Γ≡ Γ/(1−β2s). Some applications ...
TL;DR: Fully nonlinear planar ion-acoustic solitary waves moving obliquely to an external magnetic field were studied in this article. But the results were limited to the case of a single wave.
Abstract: Fully nonlinear planar ion‐acoustic solitary waves moving obliquely to an external magnetic field are studied.
TL;DR: In this article, the interaction physics and hydrodynamic motion of thin-foil targets irradiated by long, low-flux Nd-laser pulses (3 nsec, 1012-1015 W/cm2) are studied experimentally and compared with theoretical models.
Abstract: The interaction physics and hydrodynamic motion of thin‐foil targets irradiated by long, low‐flux Nd‐laser pulses (3 nsec, 1012–1015 W/cm2) are studied experimentally and compared with theoretical models. Laser light absorption is high (80%–90%) and thin‐foil targets are accelerated up to 107 cm/sec with good (20%) hydrodynamic efficiency in the 1012–1013 W/cm2 range. These results agree with a simple rocket ablation model. Details of thermal heat flow, both axially (related to ablation depth) and laterally (related to beam uniformity requirements), are also presented.
TL;DR: The first analytical solution of the trapped ion vortex state known since the early days of computer simulations was presented in this article, which appears as a nonlinear saturated state of the ion ion two-stream instability and represents, macroscopically, a plasma (ion) hole moving near the ion thermal velocity.
Abstract: The first analytical solution of the trapped ion‐vortex state known since the early days of computer simulations is presented. It appears as a nonlinear saturated state of the ion‐ion two‐stream instability and represents, macroscopically, a plasma (ion) hole moving near the ion thermal velocity. Both electron and ion densities are locally depressed.
TL;DR: The linear stability theory of an electron temperature gradient driven microtearing mode, an instability recently proposed as a possible cause for anomalous electron thermal transport in tokamaks, is considered in this article.
Abstract: The linear stability theory of an electron temperature gradient driven microtearing mode, an instability recently proposed as a possible cause for anomalous electron thermal transport in tokamaks, is considered. The theory is electromagnetic and is carried out within the context of a slab model with a sheared magnetic field. In contrast to the linear theory of drift waves, where any magnetic shear is completely stabilizing, shear may actually increase the growth rate of microtearing modes. The crucial feature required for instability is the energy dependence of electron‐ion collisions. The mode is shown to be unstable for electron temperature gradients and degrees of collisionality typical of present day tokamaks. It is found that previous theories of these modes were based on assumptions which are not, in general, justified; a case in point being the fact that the usually neglected electrostatic effects are actually quite important in producing instability.
TL;DR: In this article, the second-order theory for electrostatic microinstabilities driven by currents both across and parallel to a uniform magnetic field in a Vlasov plasma is considered, where both electrons and ions are taken as magnetized, and propagation is in the plane defined by the drift velocities and the magnetic field.
Abstract: The second‐order theory for electrostatic microinstabilities driven by currents both across and parallel to a uniform magnetic field in a Vlasov plasma is considered. Both electrons and ions are taken as magnetized, and propagation is in the plane defined by the drift velocities and the magnetic field. A consistent procedure is used to compare wave‐particle exchange frequencies of momentum and energy for the lower hybrid density drift, ion cyclotron electron density drift, universal density drift, ion acoustic current, and ion cyclotron current instabilities. In this model, resistivities and heating frequencies of the universal instability are substantially greater than those due to the other drift modes, and wave‐particle transport due to the ion cyclotron electron density drift instability is larger than that of the lower hybrid density drift instability at Te≳Ti.
TL;DR: In this article, the relationship between nonlinear wave coupling and the properties of the bispectrum is investigated for the case of three-wave coupling, in particular, the dependence of the phase of the Bispectrum, the direction of power flow between modes, and the sign of the skewness parameter, on the nonlinear amplitude variation and coupling coefficient.
Abstract: The relationship between nonlinear wave coupling and the properties of the bispectrum are investigated for the case of three‐wave coupling. In particular, the dependence of the phase of the bispectrum, the direction of power flow between modes, and the sign of the skewness parameter, on the nonlinear amplitude variation and coupling coefficient, is analytically investigated and found to be in good agreement with experimental observations.
TL;DR: In this paper, the authors investigated low frequency wave and transport in a plasma consisting almost purely of electrons and found that the modal frequencies agree well with linear theory, but the damping is governed by nonlinear effects.
Abstract: Investigations of low frequency waves and transport in a plasma consisting almost purely of electrons are presented here. This plasma is trapped in a cylindrical system with radial confinement supplied by a strong axial magnetic field and axial confinement supplied by electrostatic fields. Very long containment times are possible. Classical transport due to electron‐neutral collisions has been investigated and good agreement with the theory of Douglas and O’Neil is obtained. Externally launched diocotron waves are investigated. The modal frequencies agree well with linear theory, but the damping is governed by nonlinear effects. Experimental scaling laws for the damping rates are given. Measurements of spatial transport due to these modes are also presented. A signature of this process is that the transport is strongly localized spatially.
TL;DR: In this paper, the nonlinear interaction of tearing modes of different helicity in tokamaks is studied for realistic values of resistivity and parallel heat conduction, and the self-consistent evolution of the resistivity is taken into account through the electron heat-conduction equation.
Abstract: The nonlinear interaction of tearing modes of different helicity in tokamaks is studied for realistic values of resistivity and parallel heat conduction. The self‐consistent evolution of the resistivity is taken into account through the electron heat conduction equation. For equilibrium q profiles inferred from electron temperature profiles measured before a tokamak disruption, the essential result is that the (m=2;n=1) mode nonlinearly destabilizes other modes on a rapid time scale. Because of the development of magnetic islands of different helicity, the toroidal current density is severely deformed. These islands overlap and field lines become stochastic in a sizable plasma volume, flattening the temperature profile in this region through parallel heat transport. The deformation of the toroidal current produces a rapid decrease in the self‐inductance of the plasma, and the voltage at the limiter decreases, becoming increasingly negative. An extensive survey of equilibria and initial conditions has been conducted and a simple prescription for their nonlinear stability properties is given.
TL;DR: In this article, a method for evaluating transport in nonsymmetric systems is developed and applied to a previously little studied ripple collisionality regime of tokamaks, the ripple plateau.
Abstract: 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.
TL;DR: In this article, the formation of the low potential region on the basis of the space charge is explained by the electron drift current, and the particle distribution in the stable double layer establishes a potential profile, which creates electron and ion beams that excite plasma instabilities.
Abstract: Experiments on both stationary and propagating double layers and a related analytical model are described. Stationary double layers with eΔφ/kTe≳1 were produced in a multiple plasma device, in which an electron drift current was present. An investigation of the plasma parameters for the stable double layer condition is described. The particle distribution in the stable double layer establishes a potential profile, which creates electron and ion beams that excite plasma instabilities. The measured characteristics of the instabilities are consistent with the existence of the double layer. Propagating double layers are formed when the initial electron drift current is large. The slopes of the transition region increase as they propagate. A physical model for the formation of a double layer in the experimental device is described. This model explains the formation of the low potential region on the basis of the space charge. This space charge is created by the electron drift current. The model also accounts f...
TL;DR: In this paper, the steady-state helical trajectories for the electrons in a free electron laser with an axial guide magnetic field were considered and the stability against perturbations and accessibility of such steady states was considered.
Abstract: The propagation of a cold relativistic electron beam in a free electron laser with an axial guide magnetic field is considered. The possibility of several steady‐state helical trajectories for the electrons is shown, and the stability against perturbations and accessibility of such steady states is considered. Necessary and sufficient conditions for the stability are derived and indicate the importance of the transition region at the entrance of the laser. Possible modes of operation of the laser in different steady‐state regimes are suggested and illustrated by numerical examples.
TL;DR: In this paper, the eigenmode equation describing ballooning drift waves in toroidal plasmas is investigated both analytically and numerically, and two branches of eigenmodes are identified.
Abstract: 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.