Showing papers in "Physics of Fluids in 1974"
TL;DR: In this article, a simple formalism for the parametric decay of an intense, coherent electromagnetic wave into an electrostatic wave and scattered electromagnetic waves in a homogeneous plasma is developed.
Abstract: A simple formalism for the parametric decay of an intense, coherent electromagnetic wave into an electrostatic wave and scattered electromagnetic waves in a homogeneous plasma is developed. Various instabilities including Brillouin and Raman scattering, Compton scattering, filamentational and modulational instabilities are derived and discussed in a systematic manner. Growth rates as a function of the incident pump power are shown.
656 citations
TL;DR: In this article, a simple physical approximation is developed for the effect of viscosity for stable interfacial waves and for the unstable interacial waves which correspond to Rayleigh-Taylor instability.
Abstract: A simple, physical approximation is developed for the effect of viscosity for stable interfacial waves and for the unstable interfacial waves which correspond to Rayleigh‐Taylor instability. The approximate picture is rigorously justified for the interface between a heavy fluid (e.g., water) and a light fluid (e.g., air) with negligible dynamic effect. The approximate picture may also be rigorously justified for the case of two fluids for which the differences in density and viscosity are small. The treatment of the interfacial waves may easily be extended to the case where one of the fluids has a small thickness; that is, the case in which one of the fluids is bounded by a free surface or by a rigid wall. The theory is used to give an explanation of the bioconvective patterns which have been observed with cultures of microorganisms which have negative geotaxis. Since such organisms tend to collect at the surface of a culture and since they are heavier than water, the conditions for Rayleigh‐Taylor instability are met. It is shown that the observed patterns are quite accurately explained by the theory. Similar observations with a viscous liquid loaded with small glass spheres are described. A behavior similar to the bioconvective patterns with microorganisms is found and the results are also explained quantitatively by Rayleigh‐Taylor instability theory for a continuous medium with viscosity.
436 citations
TL;DR: In this paper, a collisionless toroidal plasmas with smooth nonuniformities is considered and a heating scheme based on the spatial resonance of shear Alfven waves is proposed.
Abstract: Heating of a collisionless plasma by utilizing the spatial resonance of shear Alfven waves is proposed and application to toroidal plasmas is discussed. The resonance exists due to the nonuniform Alfven speed. This heating scheme is analyzed in one dimension including the effects of a shear magnetic field and plasma compressibility. For plasmas with smooth nonuniformities (| k⊥l | ≫ 1, k⊥ is the wavenumber prependicular to the ambient magnetic field and the nonuniformity direction, and l is the scale length of the nonuniformity), the energy absorbed per unit surface area per driving cycle is [b02(μ0k⊥)−1]. Here, b0 is the flux density of the driving magnetic field evaluated at the resonant point. With sharp nonuniformities (| k⊥l | ≪ 1), absorption is large if the surface eigenmode is excited. The corresponding value is [b02(μ0k⊥)−1(k⊥l)−1]. Otherwise, it is [b02(μ0k⊥)−1(k⊥l)].
365 citations
TL;DR: In this article, Ramaman and Brillouin scattering of an electromagnetic wave in an inhomogeneous, expanding plasma were studied for the application of laser-pellet irradiation.
Abstract: Raman and Brillouin scattering of an electromagnetic wave in an inhomogeneous, expanding plasma are studied. Application to laser‐pellet irradiation is considered.
312 citations
TL;DR: In this article, the microcanonical ensemble for two-dimensional interacting line vortices is explored for the regime of total positive interaction energy, which should be above the Onsager negative temperature threshold.
Abstract: The dynamics of two-dimensional interacting line vortices is identical to that of the two-dimensional electrostatic guiding center plasma. Both are Hamiltonian systems and are therefore susceptible to statistical mechanical treatments. The predictions of the microcanonical ensemble are explored for this system. Interest focuses primarily on the regime of total positive interaction energy, which should be above the Onsager negative temperature threshold. Calculations of the probability distribution for a component by means of the central limit theorem are carried out in the manner of Khinchin. The probability distribution of a component reduced to the usual Gibbs distribution in the regime of positive temperatures, and is still explicitly calculable for negative temperatures. The negative temperature states are neither quiescent nor spatially uniform. Expressions for the temperature are explicitly provided in terms of the total particle energy and particle number. A BBGKY hierarchy can be derived for both temperature regimes. Numerical simulations involving solutions of the equations of motion of 4008 particles are presented.
276 citations
TL;DR: In this paper, the phenomenology of thermonuclear burn in deuterium-tritium microspheres at high densities is described, and numerical results characterizing the burn for a broad range of initial conditions are given.
Abstract: The phenomenology of thermonuclear burn in deuterium‐tritium microspheres at high densities is described, and numerical results characterizing the burn for a broad range of initial conditions are given. The fractional burnup, bootstrap‐heating, and depletion of the DT fuel, its expansive disassembly, and thermonuclear ignition by propagating burn from central hot spots in the microspheres are discussed. Extensive numerical results from a 3 T Lagrangian simulation code are presented. The yields Y0 from uniform 10, 1, and 0.1 μg microspheres with densities ρ = 1 to 4 × 104 g/cm3 and temperatures Te = Ti = 1.8 to 100 keV are given. It is shown that Y0 ∼ ρR, ρR < 0.3 (R is the microsphere radius) or, equivalently, Y0 ∼ ρ2/3 for spheres of fixed mass m. The gain‐factor G0 ≡ Y0/mI0 (I0 is the internal energy) is shown to measure burn efficiency in uniform microspheres. More than a four‐fold increment in the gain factor is shown to derive from apportionment of the internal energy in a central hot spot. The limit...
233 citations
TL;DR: In this paper, the spectral variance transverse and parallel to the direction of axisymmetry is characterized by two parameters, and the dependence of these energy components on wave vector orientation is developed into a spherical harmonic expansion, and only low order terms are examined in detail.
Abstract: The approach of axisymmetric, homogeneous turbulence to isotropy using the direct interaction approximation is investigated. The turbulence is characterized by two parameters, the spectral variance transverse and parallel to the direction of axisymmetry. The dependence of these energy components on wave vector orientation is developed into a spherical harmonic expansion, and only low order terms are examined in detail. In terms of this characterization of the theory, the general qualitative nature of the relaxation to isotropy is discussed and numerical results for the energy spectrum and transfer functions are presented. It is shown that the simplest characterization of the theory leads to an almost linear relaxation to isotropy. The numerical results at moderate Reynolds numbers are compared to the phenomenological theory of Rotta [J. C. Rotta, Z. Physik 129, 547 (1951)]. A simple analytic estimate of the Rotta relaxation rate is also presented.
209 citations
TL;DR: In this paper, it was shown that for a cylindrical equilibrium of a perfectly conducting plasma, the magnetohydrodynamic spectrum contains at most two continua, and that the spectrum is at most twice continuous.
Abstract: It is shown that, for a cylindrical equilibrium of a perfectly conducting plasma, the magnetohydrodynamic spectrum contains at most two continua.
197 citations
TL;DR: In this paper, the nonlinear evolution of plane hydromagnetic fluctuations propagating along the unperturbed magnetic field direction is considered and explicit expressions are derived for the asymptotic state and for the characteristic lines which describe the evolution toward that state.
Abstract: The nonlinear evolution of plane hydromagnetic fluctuations propagating along the unperturbed magnetic field direction is considered. From an expansion of the ideal magnetohydrodynamic equations and the hydromagnetic shock jump conditions, it is shown that a wave in which the magnitude of the magnetic field is nonconstant steepens into a shock and subsequently evolves toward a purely Alfvenic fluctuations of lower mean energy density. Explicit expressions are derived for the asymptotic state and for the characteristic lines which describe the evolution toward that state. A class of fluctuations which includes linearly polarized waves is shown to evolve into rotational discontinuities. The results are applied to observations of hydromagnetic fluctuations in the solar wind.
184 citations
TL;DR: In this paper, the driftkinetic equation is considered from the viewpoint of the ion parallel flow U and the radial gradients of density, temperature, and electrostatic potential; this relation is derived and compared to similar relations for collisionless regimes.
Abstract: Plasma rotation in the collisional regime is considered from the viewpoint of the driftkinetic equation, using orderings which have become standard in neoclassical transport theory. Kinetic arguments require a unique relation between the ion parallel flow U and the radial gradients of density, temperature, and electrostatic potential; this relation is derived and compared to similar relations for collisionless regimes. The off‐diagonal stress tensor component, which governs the time evolution of U is also calculated. This component does not resemble a viscous stress, and dominates classical viscosity by roughly the usual Pfirsch‐Schluter factor.
180 citations
TL;DR: In this article, the Schrodinger equation was used to describe the long time slow modulation of the complex wave amplitude for a wide class of nonlinear dispersive waves including magneto-acoustic and electron plasma waves.
Abstract: The Krylov‐Bogoliubov‐Mitropolsky perturbation method is applied to systems of nonlinear dispersive waves including plasma waves such as ion‐acoustic, magneto‐acoustic, and electron plasma waves. It is found that long time slow modulation of the complex wave amplitude can be described by the nonlinear Schrodinger equation for a very wide class of nonlinear dispersive waves.
TL;DR: In this article, the dispersion relation for parametric instabilities near the lower hybrid frequency is derived and analyzed, and the driving mechanism for this instability is shown to be analogous to nonlinear Landau damping in perturbation theory.
Abstract: The dispersion relation for parametric instabilities near the lower‐hybrid frequency is derived and analyzed. It is found that for propagation angles cos2θ(mi/me) < 1 resonant decay into ion acoustic (ion‐cyclotron) waves does not occur; rather, decay into nonresonant quasi‐ion modes and lower‐hybrid waves occurs. The driving mechanism for this instability is shown to be analogous to nonlinear Landau damping in perturbation theory. The large amplitude dispersion relation is analyzed numerically for a number of typical experimental regimes, and growth rates and thresholds are obtained for both the purely growing mode and the newly found quasi‐ion modes.
TL;DR: In this article, the magnetic field dependence of the thermal conductivity of laser-produced plasmas has been investigated and it was shown that B fields, with their attendant nonuniform heating effects, will occur even in uniformly irradiated spherical pellets or plane slabs.
Abstract: The intense thermal energy flux emanating from the critical layer in laser‐produced plasmas is shown to generate an instability that derives from the magnetic field dependence of the thermal conductivity. This implies that B fields, with their attendant nonuniform heating effects, will occur even in uniformly irradiated spherical pellets or plane slabs. These fields may play a role in attempts to compress pellets for fusion, for example, by being partially trapped and amplified by compression in the interior of a pellet.
TL;DR: In this article, a simulation of particle diffusion on a numerically integrated, decaying isotropic turbulent flow field is presented, where the diffusion of both fluid particles and small spherical particles is studied.
Abstract: Results are presented of computer simulations of particle diffusion on a numerically integrated, decaying isotropic turbulent flow field. The diffusion of both fluid particles and “small” spherical particles is studied. Comparisons are made of the various temporal autocorrelation coefficients. It is found that for “short” times, the Lagrangian (fluid point) velocity correlation is larger than the Eulerian correlation, while for longer times the opposite is true. It is also found in the “small” spherical particle case that as the response time of the particle is increased, the velocity autocorrelation coefficient increases.
TL;DR: In this paper, an exact relativistic self-consistent equilibrium is found for the electron sheath which is expected to form under the condition where the applied magnetic field is sufficiently strong to prevent electrons from flowing between the electrodes.
Abstract: An investigation is made of the behavior of a high voltage diode for the situation where the cathode‐anode gap is initially filled with a transverse magnetic field. An exact relativistic self‐consistent equilibrium is found for the electron sheath which is expected to form under the condition where the applied magnetic field is sufficiently strong to prevent electrons from flowing between the electrodes. The condition on the magnetic field for “insulation” is found to be (eBy0d/mc2)2 > 2|eV0/mc2| + (eV0/mc2)2, where By0 is the applied magnetic field, V0 is the voltage across the diode, d is the cathode‐anode separation in the x direction, and —e and m are the electron charge and rest mass, respectively.
TL;DR: In this article, it was shown that the classical inward diffusion of high-Z impurities in toroidal plasmas is enhanced by the PfirschSchluter effect, and numerical transport coefficients were evaluated.
Abstract: It is shown that the classical inward diffusion of high‐Z impurities in toroidal plasmas is enhanced by the Pfirsch‐Schluter effect. Numerical transport coefficients are evaluated. Typically, both density and temperature gradients are found to produce inward impurity diffusion.
TL;DR: In this article, the authors measured the spatial development of disturbance pressure waves in a low-speed axisymmetric turbulent free jet and found that the wave characteristics follow closely the linear stability theory of an inviscid diverged shear flow.
Abstract: Measurements of the spatial development of disturbance pressure waves in a low‐speed axisymmetric turbulent free jet have been carried out. The results show that the wavenumbers of the pressure waves increase monotonically, while the phase velocities decrease as the Strouhal number of the jet increases. The pressure disturbance grows to a maximum at some distance downstream from the nozzle and then decays. The distributions of the amplitude of the pressure waves along the jet are similar if the data are plotted against a normalized distance St x/D. The most amplified mode is at a Strouhal number of 0.5 for the shear layer and 0.35 for the center line. The wave characteristics follow closely the linear stability theory of an inviscid diverged shear flow.
TL;DR: In this article, the Lagrangian formulation is used to solve for the electron trajectories in some simple magnetic cusp configurations, and a threshold energy for transmission through the cusp is found, and confirmed experimentally.
Abstract: Single‐particle motion of relativistic electrons in a cusped magnetic field has been studied both analytically and experimentally. The Lagrangian formulation is used to solve for the electron trajectories in some simple magnetic cusp configurations. A threshold energy for transmission through the cusp is found, and confirmed experimentally. Two different electron orbit off‐centering mechanisms are discussed; one arising from a nonzero radial component of particle velocity on the upstream side of the cusp transition, and another arising from the finite width of the cusp transition. Experiments are reported confirming the existence of these off‐centering mechanisms, and the results are compared with theoretical expectations.
TL;DR: In this paper, a finite length slow wave source having a potential distribution phi ~ cosk0z is found to generate spatial oscillations having a well-defined wavelength, which are confined to regions bounded by conical curves originating at the ends of the source, and the axial distance of rf energy propagation to the lower hybrid layer is greater than the radial distance of propagation by a factor of the order (mi/me)1/2.
Abstract: The propagation of electrostatic plasma waves, and their subsequent conversion into hot plasma waves at the lower hybrid frequency is calculated for realistic density profiles and finite rf sources in a slab geometry. A finite length slow wave source having a potential distribution phi ~ cosk0z is found to generate spatial oscillations having a well-defined wavelength. These oscillations are confined to regions bounded by conical curves originating at the ends of the source. The axial distance of rf energy propagation to the lower hybrid layer is found to be greater than the radial distance of propagation by a factor of the order (mi/me)1/2. The conversion at the lower hybrid layer of the electrostatic cold plasma waves excited by a finite source into propagating hot plasma waves is calculated. It is shown that collisional damping at the lower hybrid layer may predominate over mode conversion even for relatively low collision frequencies.
TL;DR: In this article, two familiar functional formalisms in turbulence are applied to the simultaneous turbulent mixing and chemical reaction of scalar fields, and the problem is formally posed in terms of initial and boundary conditions.
Abstract: The two familiar functional formalisms in turbulence are applied to the simultaneous turbulent mixing and chemical reaction of scalar fields. One‐step, second‐order, irreversible, exothermic chemical reactions with an Arrhenius‐type rate constant are considered. The problem is formally posed in terms of initial and boundary conditions. For the special case of equal mass‐diffusivities and a Lewis number of one the functional equations are decoupled into a turbulent binary mixing study and a reactive problem. The Lewis‐Kraichnan formalism is used in order to obtain exact functional solutions of the binary mixing case in final period turbulence. Driving forces are included in the thermal energy equation. These solutions are used to obtain detailed information about the binary mixing problem and the behavior of very rapidly reacting species in the final period.
TL;DR: In this paper, a modified energy principle is obtained by means of which the stability of plasma confinement systems can be tested for times of thermonuclear interest, instead of the infinitely long times which are pertinent to the usual stability analysis.
Abstract: An equilibrium is called σ stable if growth faster than exp (σt) does not occur. On the basis of this definition a modified energy principle is obtained by means of which the stability of plasma confinement systems can be tested for times of thermonuclear interest, instead of the infinitely long times which are pertinent to the usual stability analysis. The theory is applied to the diffuse linear pinch, a theorem for σ stability is derived, and the connection with the normal‐mode analysis is shown to be given with the Sturmian property, which holds for the unstable side of the spectrum, whereas the stable side consists of Sturmian and anti‐Sturmian point spectra separated by continuous spectra. Growth rates and eigen‐functions of Suydam modes are numerically calculated, and it is shown that violation of Suydam's criterion in the high and intermediate shear case leads to nonlocalized rapidly growing m = 1 modes. Consequently, this criterion obtains new relevance in the σ‐stability analysis for this regime.
TL;DR: In this article, the wavelength of singly periodic Taylor vortices in the steady state after a sudden start was studied experimentally, and it was found that the preferred wavelength was smaller than the critical wavelength.
Abstract: The wavelength of steady Taylor vortices established through a sudden start of the inner cylinder has been studied experimentally. The sudden start procedure gives the fluid a choice in the selection of the wavelength. It was found that the preferred wavelength of singly periodic vortices in the steady state after a sudden start is smaller than the critical wavelength, with a minimum at around T / Tc = 15. When the Taylor number to which the sudden start was made was increased to around 60 Tc, then the preferred wavelength approached the critical wavelength. A wavelength once established through a sudden start did not change its value if afterwards the Taylor number was maintained for a very long time or if the Taylor number was varied over larger intervals, provided the flow was singly periodic. However, this rule does not hold when the critical Taylor number is approached from above with a flow created through a sudden start to a higher Taylor number. In this case the wavelength increases to approach th...
TL;DR: In this article, temperature measurements made in the slightly heated, plane turbulent wake at stations 400 and 500 diam downstream from a heated cylinder at a Reynolds number of 2800 were presented.
Abstract: Results are presented of temperature measurements made in the slightly heated, plane turbulent wake at stations 400 and 500 diam downstream from a heated cylinder at a Reynolds number of 2800. The results include transverse distributions of the first four moments of the temperature obtained using both conventional and conditional sampling and averaging techniques, the downstream distribution of the root mean square temperature fluctuations on the wake centerline and the probability density function of the temperature. Additionally, there are obtained, as a function of distance from the interface, temperature moments which indicate that there is a definite thermal structure associated with the interface.
TL;DR: In this article, the hydrodynamic stability of a free-boundary pinch with noncircular cross section was investigated and the analysis was restricted to nonflute modes, and the stability conditions for a pinch with elliptical cross section and flat current density were obtained.
Abstract: The hydrodynamic stability of a free‐boundary pinch with noncircular cross section is investigated. The analysis is restricted to nonflute modes. The stability conditions for a pinch with elliptical cross section and flat current density are obtained. For arbitrary shapes and current profiles, an asymptotic stability criterion is given for kink and tearing modes of large azimuthal wavenumbers.
TL;DR: In this paper, an appropriate kinetic equation which contains the angular scattering, friction, and diffusion of the energetic ions by the background particles, charge exchange on the background neutrals, and acceleration of the ion by the electric field has been derived by using the WKBJ method.
Abstract: The energetic ion distribution resulting from the injection of high‐energy neutrals into a toroidal plasma has been derived. An appropriate kinetic equation which contains the angular scattering, friction, and diffusion of the energetic ions by the background particles, charge exchange on the background neutrals, and acceleration of the ions by the electric field has been solved analytically by use of the WKBJ method. Collisions of the energetic ions with the faster moving electrons results in some of the ions increasing their energy above the injection energy. The width of this ``high‐energy tail'' is shown to depend upon the electron temperature and the electric field. An estimate of the effect upon the width of this tail of collisions between the energetic ions themselves is also given. Finally, illustrated examples of the various significant physical processes are presented.
TL;DR: In this paper, a general dispersion relation for parametric instabilities caused by a large amplitude pump wave which couples high and low frequency modes of a magnetized plasma is derived, which contains decay instabilities, purely growing instabilities and modulational instabilities.
Abstract: A general dispersion relation is derived for parametric instabilities caused by a large amplitude pump wave which couples high and low frequency modes of a magnetized plasma. The nonlinear effects coupling the high and low frequency waves are: (1) the low‐frequency pondermotive force due to the coupling of the pump with the high frequency perturbations, and (2) the high frequency nonlinear source current density produced by coupling of the pump with the low frequency perturbations. The dispersion relation contains decay instabilities, purely growing instabilities, modulational instabilities, self‐focusing and nonlinear Landau damping. As examples the dispersion relation is applied to self‐focusing, magnetosonic decay and purely growing instabilities, whistler decay and nonlinear Landau dumping of electron plasma waves and transverse electromagnetic waves.
TL;DR: In this paper, the magnetohydrodynamic stability of a straight plasma column with elliptic cross section, carrying a uniform axial current, is investigated by extremizing the Lagrangian of the system using a natural coordinate system based on the magnetic field lines.
Abstract: The magnetohydrodynamic stability of a straight plasma column with elliptic cross section, carrying a uniform axial current, is investigated by extremizing the Lagrangian of the system using a natural coordinate system based on the magnetic field lines. Stability criteria are derived and growth rates are obtained analytically for systems with a uniform mass density inside the plasma. It is shown that the coupling between kink modes and Alfven waves produced by noncircularity is a destabilizing effect. A technique for solving the problem numerically is also discussed and used to demonstrate the effect of a spatially varying plasma density on the growth rate.
TL;DR: In this article, a criterion for predicting the transverse spacing dimensions in gas phase detonations is developed, which depends upon the collision of wave fronts to form new reaction centers which eventually lead to the formation of new cells.
Abstract: A criterion for predicting the transverse spacing dimensions in gas phase detonations is developed. The criterion depends upon the collision of wave fronts to form new reaction centers which eventually lead to the formation of new cells. Calculated values of transverse spacing over a wide range of pressure, dilution and degree of overdrive in the hydrogen‐oxygen‐argon system are compared to experimental data for stoichiometric mixtures. The predicted values of spacing with no overdrive are about twice the experimental values. A minimum in the predicted spacing is found with overdrive as well as a cutoff value of overdrive for which the predicted spacing becomes infinite.
TL;DR: In this paper, a three velocity and one-space dimensional nonrelativistic electromagnetic particle simulation code employing the fast Fourier transform algorithm is described and used to simulate the amplification of electromagnetic radiation by an electron beam passed over a rippled static magnetic field.
Abstract: A three velocity and one‐space dimensional nonrelativistic electromagnetic particle simulation code employing the fast Fourier transform algorithm is described and used to simulate the amplification of electromagnetic radiation by an electron beam passed over a rippled static magnetic field. In the beam frame the rippled magnetic field looks like an intense electromagnetic pump and thus a parametric instability can be produced. In one case, it was observed that 30% of the beam energy was converted to electromagnetic radiation.
TL;DR: In this paper, a set of model equations for the parametric instability that consist of damped harmonic oscillators coupled with a stochastic oscillatory driver is considered, and a solution for the average response of the oscillators is derived.
Abstract: A set of model equations for the parametric instability that consist of damped harmonic oscillators coupled with a stochastic oscillatory driver is considered. With the assumption that the autocorrelation time of the stochastic part of the driver is very short, a solution for the average response of the oscillators is derived. This solution holds for arbitrary damping rates, unlike the results of previous authors. Threshold levels and growth rates for the parametric decay and oscillating two‐stream instabilities are found as a function of driver bandwidth.