Abstract: Detailed computational results are presented on the stability and radial distribution of linear tearing modes in cylindrical tokamaks of various radial profiles. In the case of a skin‐current profile, a “double tearing mode”, with two points of discontinuity in the radial magnetic field perturbation is found. An analytical method is also derived for comparison of the stability of different radial profiles. It is further shown that the tearing mode can be driven by finite electron viscosity, as well as by the usual finite resistivity mechanism.

Abstract: It is shown that an electromagnetic wave interacting with a plasma is subject to instabilities leading to light filamentation. Nonlinear solutions for light filaments and light trapping are also investigated.

Abstract: The electrical conductivity, translational and reactive thermal conductivity and viscosity have been computed for ionized argon in thermodynamic equilibrium at pressues from 0.001‐1000 atm and temperatures to 35 000°K. Comparison of the values with experiments shows reasonable agreement.

Abstract: Numerical corrections are made to previous values for the power absorption coefficient and some common errors noted.

Abstract: Ion‐acoustic solitary wave (solitons) have been studied experimentally by employing a double‐plasma device. The solitary waves are found to be produced from both a single compressional pulse and a continuous wave. A rarefaction pulse also produces solitons if the pulse width is sufficiently wide. A theory based on the Schrodinger equation accounts for the number of solitons. Recurrence to the original state is observed when a continuous wave is launched. A simple wave‐wave coupling analysis for the recurrence of the original state is given.

Abstract: The instability of a circular cylindrical jet of liquid in air is studied on the assumption that the wavenumber k of the disturbance is complex while its frequency σ is real. This implies that the disturbance grows with distance along the jet, but that it does not grow with time. The occurence of such disturbances is called spatial instability, in contrast to the temporal instability studied by Rayleigh and others, in which k is real and σ is complex. It is found that there are infinitely many unstable modes for the axially symmetric case and also for each of the asymmetric cases. In the case of high velocity jets, one of these modes for the symmetric case corresponds to the mode Rayleigh found. However, it is not the most rapidly growing mode. Both analytical and numerical solutions of the dispersion equation are given for k as a function of σ and of the dimensionless jet velocity.

Abstract: A model is developed for the momentum transferred to a solid from a laser‐supported gaseous detonation wave initiated in air above the surface. One‐dimensional gasdynamic analysis is used for the detonation wave moving away from the surface and cylindrical blast‐wave theory is employed to partially account for two dimensional effects. Momentum transfer coupling coefficients (impulse/laser energy) are calculated which are functions of the laser energy flux, pulse duration, and the beam and target surface areas. Results are compared with recent experimental data obtained using a high‐power CO2 laser.

Abstract: The electrical conductivity, the translational, reactive, and internal thermal conductivity and the viscosity have been calculated for nitrogen at 1‐atm pressure and temperatures from 5000‐35 000°K. Generally satisfactory agreement is noted between the properties as computed and measured in the electric arc.

Abstract: Measurements were taken of the heat transport and vertical component of the fluid velocity in a horizontal layer of water heated from below. The heat transfer results were well correlated by a simple power law relationship and indicated the possibility of flow transitions even at relatively high Rayleigh numbers. The velocity measurements were obtained optically and compared to predictions of Kraichnan.

Abstract: A universal velocity defect law for turbulent boundary layers developing in adverse pressure gradients is proposed. The velocity scale for this law is independent of the wall shear but related instead to the local maximum in the Reynolds stress profile. The proposal and its implications are checked against a very large body of experimental results and a partial connection between the mean velocity field and the shear stress field is established. A comparison between the present theory and the mixing length theory is presented. The experimental data do not appear to support many of the assumptions nor the predictions of the mixing length theory. The distinction between equilibrium and nonequilibrium layers made by Clauser is shown to be unnecessary as all classes of layers appear to conform to the new universal velocity defect law proposed, provided that the maximum shear stress is sufficiently larger than the wall shear stress.

Abstract: A quasi‐isotropic locally homogeneous model for the two‐point double‐velocity correlation tensor is developed by the application of a plausible set of symmetry restrictions to this tensor. The two‐point correlation is related to the single‐point correlation by three independent functions, and reduces to the nonisotropic single‐point correlation and the isotropic two‐point correlation in the limiting cases. It is shown that the model implies that by the use of three independent microscales (and macroscales) it is possible to describe a matrix of 27 elements of microscales (and macroscales) which describe the nonisotropic field. The model is also used to calculate the dissipation rate of the components of the Reynolds stresses. Finally, a formula which expresses the redistribution of the velocity fluctuations due to pressure fluctuations is developed.

Abstract: The nonlinear saturation spectrum of the decay instability is obtained in the limit of small spontaneous emission, for comparable ion and electron temperatures, from numerical solutions of a kinetic equation based on an accurate expression for the nonlinearity. The spectral energy occupies several pairs of isolated saucer‐shaped regions in wave‐vector space. The regions increase in thickness, angular diameter, and number as the pump power is increased. The theory thus predicts the generation of waves propagating in directions which can differ substantially from the direction of the pump field. Ionospheric observations confirm this prediction; they were difficult to reconcile with the predictions of previous theories based on an approximate expression for the nonlinearity. The present work also corrects the results of previous one‐dimensional theories that used an accurate expression for the nonlinearity and predicted “spectral lines” in the limit of vanishing spontaneous emission. Excitation of the purely growing instability is predicted for pump powers greater than about 2.5 times the threshold of the decay instability.

Abstract: The nature of equilibrium states of inviscid two‐dimensional “turbulence” is discussed. Results of numerical simulations are presented to clarify the theory.

Abstract: The nonlinear evolution of the decay instability in a plasma driven by an externally imposed pump field oscillating near the electron plasma frequency is considered. For a plasma with comparable electron and ion temperatures and for weak pump fields, nonlinear Landau damping of electron plasma waves on the ions is the dominant nonlinearity. It is demonstrated that a one‐dimensional wave kinetic equation describes the dominant interactions for spectral intensities whose characteristic angular width is small. This equation is solved numerically with the exact form for the matrix element which describes the coupling. An analytical solution is found for the spectral intensity in the limit in which the (small) spontaneous emission term is neglected. The plasma wave energies obtained both numerically and analytically are in good agreement. General characteristics of the plasma wave spectrum agree with observations in the ionosphere. The enhanced dissipation rate of the pump due to the presence of the fluctuations agrees with that observed in a laboratory experiment.

Abstract: One‐dimensional and joint probability density distributions for longitudinal components of turbulent velocities as well as higher‐order correlations are measured in a turbulent boundary layer on a flat plate using hot‐wire anemometry and high‐speed computing methods. The effect of the nonlinear response of the hot‐wire is taken into account. Data pertaining to the general nature of the turbulent boundary layer are presented and comparison is made between the measured correlations and those corresponding to a Gaussian probability distribution of turbulent velocities as well as to non‐Gaussian distributions of the Gram‐Charlier type. Similar comparisons are made of the measured one‐dimensional and joint probability distributions. Probability distributions in the boundary layer are also compared to those measured downstream of a grid. The closure of the tails of the probability distribution and its effect on the accuracy of the measurements of higher‐order moments is considered.

Abstract: The collisional regime of neoclassical transport theory is investigated, using a moment equation approach as well as a method based on the drift kinetic equation. Allowing for both density and temperature gradients, and an externally induced toroidal electric field, the transport coefficients describing particle and energy flux perpendicular to the magnetic field of an axisymmetric confinement system are derived. Relations between the parallel and perpendicular fluxes, which are exact in the collisional regime, are also derived. Charge neutrality is used to obtain the electrostatic potential variation on a magnetic surface.

Abstract: Using numerical simulation, it was found that, with the inclusion of thermally‐generated magnetic fields, about 3 × 104 neutrons are produced in 2 nsec and the electron temperature rose as high as 15 keV in a target heated by a 4‐nsec, 80‐J laser pulse.

Abstract: From numerical and analytical solutions of the normal mode equation for drift waves in a sheared magnetic field, the critical shear S c for the onset of instability and the normal mode growth rates at subcritical shear are obtained. At low beta and without a parallel current it is shown that approximately twice the previously indicated shear is required for stability and the (m e / m i)1/3 scaling of S c is confirmed. The addition of a parallel plasma current is shown to increase initially the critical shear quadratically with current and then linearly at larger currents. The effect of electron and ion temperature gradients is studied with equal density and temperature gradients resulting in aproximately a 50% reduction in S c. Finally, the effect of finite beta on the critical shear is studied.

Abstract: A derivation is given for the nonrelativistic equation of motion of a fully ionized isothermal plasma in the presence of an intense electromagnetic wave, such as laser light. The result can be expressed in a form similar to an equation used in the microwave confinement of plasmas. Applications of the result are made to the evaluation of self‐focusing effects. The forces exerted on the plasma are found to be significant magnitude at contemporary intensity levels for neodymium laser radiation at λ = 1.06 μm.

Abstract: Finite aspect ratio modifications to neoclassical transport theory are considered. In the general case of arbitrary flux surface geometry, a closed set of macroscopic equations is derived. These include the equation which determines the time evolution of the flux surfaces. In the large aspect ratio case, the O (r /R ) corrections to the order O (r )1/2)R (1/2)) transport coefficients, calculated previously, are obtained. In particular, an expression for the electrical conductivity is obtained which may be regarded as exact for all experimentally interesting aspect ratios.

Abstract: An analysis was performed on the incompressible, unsteady, magnetohydrodynamic boundary layer on a semi‐infinite flat plate mounted in a duct. The stream unsteadiness was composed of a small sinusoidally oscillating component superimposed on a constant value, while the constant magnetic field was normal to both the stream and the plane of the plate. Solutions to the momentum and energy equations were obtained by numerical integration for the unsteady magnetic interaction effects, including dissipation, using a product series expansion in the Strouhal number s and a Hartmann‐Reynolds number parameter χ. A time and distance dependent boundary condition at the edge of the thermal layer was properly satisfied using this expansion procedure. The results show that, while increases in skin friction and heat transfer occur both with the steady magnetic case (s = 0,0 < χ ⩽ 0.2) and with the unsteady nonmagnetic case (0 < s ⩽ 0.6, χ = 0), the full unsteady magnetic interaction produces amplitude increases in these ...

Abstract: Simulation calculations and theory which show that a very strong electric field with a frequency near the plasma frequency parametrically excites electrostatic turbulence are presented. The plasma is strongly heated with the electrons receiving most of the energy. A simple electron trapping theory accounts for the saturation electric field. After the plasma becomes turbulent, the real part of the frequency of the ion mode is drastically changed from the linear value.

Abstract: Previous models of the BGK type for ion‐electron collisions are modified to produce the correct relation between the time scales for ion‐electron momentum exchange and ion thermalization.

Abstract: A nonlinear theory of the current‐driven ion‐acoustic instability is presented. The saturation mechanism is the perturbation of the ion orbits by the turbulent waves, which results in a broadening of the resonant interaction between the ions and the waves. The angular spectrum and rms field fluctuation energy are calculated and compared both with experiment and two‐dimensional computer simulations. An approximate expression for the angular spectrum, obtained in three dimensions, predicts a broad angular spectrum as well as a fluctuation level which is in order of magnitude agreement with two recent experiments. More complete numerical results in two dimensions also predict a broad angular spectrum in agreement with the two‐dimensional simulations, and a fluctuation level in very good numerical agreement with the simulations.

Abstract: The Benard problem of the radiating nongray fluids is examined in terms of the Eddington approximation. The nongrayness of radiation is prescribed by the ratio and product of the Planck and Rosseland means of the absorption coefficient, η = (αP/αR)1/2 and αM = (αPαR)1/2, respectively. Effects of radiation on the classical problem are then characterized by four parameters: the Planck number, P0 (the ratio of conduction to radiation), optical thickness, τ = αMd (d being the distance between the plates) nongrayness of the fluid η and the emissivity of boundaries e0 and e1, respectively. The radiation in general has a stabilizing effect; decreasing P0, increasing degree of nongrayness for η > 1, changing color of boundaries from black to mirror all delay the onset of instability. The boundary color and nongrayness of gas are responsible for the extrema observed in stability curves. Accuracy of the Eddington approximation is checked with the exact solution and the convergence of the approximate solution is stu...

Abstract: Shock structure during ionization of a hydrogen-helium mixture was studied using hydrogen line and continuum emission measurements. A reaction scheme is proposed which includes hydrogen dissociation and a two-step excitation-ionization mechanism for hydrogen ionization by atom-atom and atom-electron collisions. Agreement was achieved between numerical calculations and measurements of emission intensity as a function of time for shock velocities from 13 to 20 km/sec in a 0.208 H2 - 0.792 He mixture. The electron temperature was found to be significantly different from the heavy particle temperature during much of the ionization process. Similar time histories for H beta and continuum emission indicate upper level populations of hydrogen in equilibrium with the electron concentration during the relaxation process.

Abstract: Neutral injection of fast atoms into a toroidal plasma can produce, after ionization, a double‐humped velocity distribution with appreciable spatial inhomogeneity in the fast‐ion component. Fluid instability may be excited in the Kelvin‐Helmholtz and temperature gradient drift modes, and microinstability may appear in the drift wave and in the quasiperpendicular acoustic mode.

Abstract: An experimental study was made of the instability of an accelerated water‐air interface. The measured growth rate agreed with theory. The method of analysis of the data reduced scatter in the results and allowed the growth rate of second order waves to be determined. The growth rate of second‐order waves agreed reasonably well with theory of Emmons, Chang, and Watson.

Abstract: A theory is given to explain the observed dependence on Reynolds number of the decay of turbulent line vortices. It is argued that the turbulent vortex has a triple structure. There is an outer region for r > r1 (r1 is the radius of maximum tangential velocity) with a logarithmic distribution of circulation, and for r < r1 an inner region and viscous core in both of which the motion is close to solid body rotation. It is predicted that r1 ~ (vT1 t2)1/4, where 1 is the circulation at r1. Further, T1/T0 is predicted to be a slowly decreasing function of T0/v, where T0 is the strength of the vortex. The development of an overshoot of circulation in the outer region is discussed, and the axial velocities produced by growth of a trailing vortex are calculated.