Index of content:
Volume 24, Issue 6, June 1981

Particle streak velocity field measurements in a two‐dimensional mixing layer
View Description Hide DescriptionUsing digital image processing of particle streak photography, the streamwise and perpendicular components of the velocity field were investigated, in the mid‐span plane of a two‐dimensional mixing layer, with a 6:1 velocity ratio. The Reynolds number of the flow, based on the local vorticity thickness and the velocity difference across the layer, ranged from 1360 to 2520, in the plane of observation. The significant result of this experiment was that the region of vorticity bearing fluid is confined to a small fraction of the flow. A second finding, consistent with the small regions of concentrated vorticity, was the observation of instantaneous streamwise velocity reversal, in the laboratory frame, in small regions of the flow.

Algebraic growth of disturbances in a laminar boundary layer
View Description Hide DescriptionThe temporal evolution of small three‐dimensional disturbances with a large streamwise scale in viscous, parallel, semi‐bounded flows is studied. In the limit of the initial disturbance being independent of the streamwise coordinate, the vertical velocity component consists solely of a continuous spectrum part. Tollmien–Schlichting waves do not appear in this special case. The streamwise perturbation velocity is obtained by solving a forced initial value problem. While the vertical velocity remains constant for small times, the streamwise perturbation velocity exhibits a linear growth due to the forcing. Eventually, viscous dissipation becomes dominant and the disturbance decays. Asymptotic solutions valid for small and large times are presented. The relation of these results to the longitudinal streaky structure found in many shear flows is discussed.

Stagnation regions of separation
View Description Hide DescriptionVorticity contours are used to show that two‐dimensional separation falls into three stagnation region classes for steady flows; one type on fixed walls and two others for moving walls. The existing data on laminar unsteady flows indicate that they fill the same three classes.

Stability of interface and shock wave driven by initial pressure discontinuity
View Description Hide DescriptionThe flow arising from an initial pressure discontinuity across a perturbed interface of two ideal gases is studied using analytical and numerical methods. In particular, the stability of the shock wave, the interface, and the rarefaction wave in the resulting flow are investigated. The equations of motion and the initial and boundary conditions are linearized for small perturbations, and a Fourier analysis is made in the lateral direction. The equations are then solved by the method of characteristics. The results show that the interface is unstable and its perturbations asymptotically acquire a constant rate of growth. The shock wave is stable and has rapidly damped oscillations, which appear to be unaffected by the instability of the interface.

Gasdynamics of very small Laval nozzles
View Description Hide DescriptionAn investigation of diverging supersonic nozzles with throat diameters in the range of 0.025 to 0.25 mm has been carried out using gasdynamic measurements for a variety of gases and mixtures with sulfur hexafluoride. Due to the small nozzle size, boundary layers, although thin, may constitute a major fraction of the flow or, indeed at low pressures, may be fully developed. Nevertheless these nozzles have been shown to be very efficient for production of clusters condensed from the expanding gas. They produce orders of magnitude increases in molecular beam intensities, relative to the conventional, ’’isentropic’’ free jet sources. The effects of gas properties and nozzle design on performance have been analyzed and compared to theoretical solutions of the governing equations of motion including cluster nucleation and growth.

Experimental and theoretical studies of the effects of nonuniformities in equilibrium magnetohydrodynamic flows
View Description Hide DescriptionAn experimental study of the effects of thermal and velocity nonuniformities is performed in an equilibrium plasma for a range of Hall coefficients. By introducing equally spaced cold blades in the radial flow of an electrodeless magnetohydrodynamic disk deivce, it is possible to create well‐defined two‐dimensional wake nonuniformities with strong variations of the plasma properties in the direction normal to the magnetic field and the flow. This type of nonuniformity and orientation theoretically provides the strongest reduction of Hall coefficient and effective conductivity for high values of the Hall coefficient. This degradation which reached more than 50% in some cases, is controlled by both the level of nonuniformities and the value of the ideal Hall coefficient. The former is dependent upon the number of blades (root mean square deviation of the conductivity), and the latter is dependent upon the values of the magnetic field intensities. The results provide basic quantitative information about the effects of conductivity and velocity nonuniformities on the performance of equilibrium magnetohydrodynamic generators over a wide range of Hall coefficients. The theoretical predictions are derived from a detailed two‐dimensional electrodynamic analysis and a simplified engineering model based on a generalization of Rosa’s layer model. These experiments validate the analytical studies and support the use of the theoretical layer nonuniform models in describing the effect of boundary layers on the performance of linear magnetohydrodynamic devices.

Spontaneous ion‐acoustic generation in a high power, multifilament ion source
View Description Hide DescriptionUnder certain operating conditions, a high power, multifilament ion source can effectively function as a spontaneously excited ion‐acoustic resonator. The fluctuations, initially excited by a current‐driven instability at the thermionic source cathode, exhibit a Lorentzian spectral profile where the resonant frequency is solely determined by the spatial cathode configuration, and the resonance half‐width is set by the mean plasma ion lifetime. The ion wave‐cathode interaction, responsible for the resonant behavior, entails a feedback mechanism dependent on the electrostatic wave scattering properties of thermionic filaments operated under space‐charge‐limited conditions. Fluctuation amplitude levels are insufficient to significantly perturb the ions and consequently, the instability does not affect the performance of a multifilament source neutral beam system.

Recurrence of initial state of nonlinear ion waves
View Description Hide DescriptionBy solving the Korteweg–deVries equation in a wide range of the ratio between the nonlinearity and the dispersion, the recurrence of the initial state of the ion wave is examined. The recurrence is assured of taking place only when the dispersion of the initial ion wave predominates over the nonlinearity. If the initial wave has strong nonlinearity compared with the dispersion, the recurrence is indistinct, and the initial monochromatic wave evolves to a turbulent state.

Kink and displacement instabilities in imploding wire arrays
View Description Hide DescriptionCylindrical arrays of parallel wires can be imploded by the magnetic forces generated by currents through the wires to form hot, dense Z‐pinch plasmas. Analytic growth rates of displacements and deformations of wires in imploding wire arrays are calculated. Arrays of six or more wires are reasonably stable against asymmetric displacements. The growth rate of the kink instability on a single wire of linear mass density μ, radius a, and carrying current I peaks at λ_{max} = 0.7I/μ^{1/2} c a at a kink wavelength of about 4a. The most unstable kink modes of n‐wire arrays are the symmetric (l = 0) radial modes and antisymmetric (l = n/2) tangential modes. The effect of a center wire is to tend to destabilize radial kink modes and stabilize tangential modes. In the experimental parameter range of the largest current generators, the number of kink growth times before collision is insensitive to values of maximum current and current pulse width. In general, the kink instability will grow nonlinearly if the initial array radius is more than a few plasma wire radii. In the limit of long wavelengths, the kink instability is shown to be equivalent to the displacement instability.

Observation of a decay instability of an ion beam‐plasma system
View Description Hide DescriptionA decay type instability is observed in a linearly stable ion beam‐plasma system. The spatial development of the instability agrees with the solution of the mode coupling equations describing a three‐wave interaction.

Numerical simulations of electrostatic hydrogen cyclotron instabilities
View Description Hide DescriptionBoth one‐ and two‐dimensional particle simulation models have been used to study the nonlinear behavior of the electrostatic hydrogen cyclotron instabilities driven by the electron current along the magnetic field. It is found that the instability saturates as a result of electron velocity space diffusion along the magnetic field. The cyclotron waves remain highly coherent in the nonlinear stage. When the electron drift speed is comparable to the thermal speed, substantial ion heating as well as particle cross‐field diffusion comparable to Bohm diffusion has been observed. Comparisons of the simulation results with the theoretical predictions and the observations in both laboratory and space plasmas are discussed.

Current‐driven microinstabilities in a neutral sheet
View Description Hide DescriptionComputer simulation is used to investigate current‐driven microinstabilities in a simple reversed field (neutral sheet) configuration. A long wavelength, predominantly electromagnetic, instability develops at the reversal point as a consequence of the lower hybrid drift instability, which is excited away from the reversal point where the density gradients are steep. The resulting anomalous resistivity is much smaller at the null point.

Toroidal drift modes driven by ion pressure gradients
View Description Hide DescriptionIon pressure gradient‐driven drift modes are analyzed for their parametric dependence on the shear, the toroidal aspect ratio, and the pressure gradient using the ballooning toroidal mode theory. An approximate formula for the anomalous ion thermal conductivity is derived for the turbulent regime.

Stability of multipoles to ballooning modes with large toroidal mode number
View Description Hide DescriptionThe stability of multipoles having a purely poloidal field to ballooning modes of high toroidal mode number is studied. First, a perturbation theory based on large m is discussed, and it is found that the first‐order correction to the β limit is of order 1/m. Next, the equations for a linear quadrupole and octopole are solved and the results are compared with recent multipole experiments.

Stability of a diffuse linear pinch with axial boundaries
View Description Hide DescriptionA formulation of the stability behavior of a finite‐length pinch is presented. A general initial perturbation is expressed as a uniformly convergent sum over a complete discrete k set. A variational calculation is then performed, based on the energy principle, in which the end‐boundary conditions appear as constraints. The requisite Lagrange multipliers mutually couple the elemental periodic excitations. The resulting extended form of δW still admits a proper second‐variation treatment so that the minimization and stability considerations of Newcomb remain applicable. Comparison theorems are discussed as is the relevance of this end‐effect model to the stability of solar coronal loops.

Electron‐cyclotron resonance heating in plasmas with arbitrary stratification of the magnetic field
View Description Hide DescriptionCyclotron resonance absorption in a plasma with arbitrary stratification of the magnetic field is considered. Using the absorption coefficient derived for perpendicular stratification, simple analytic estimates of the absorption can be made for artrary stratification.

Relativistic limit on resonance at oblique incidence
View Description Hide DescriptionIn a collisionless cold plasma, the limit has been obtained of a resonance electric field peak at oblique incidence of a p‐polarized electromagnetic wave upon an inhomogeneous plasma as a result of the nonlinear relativistic treatment of plasma waves.

Turbulent heating of parametric instabilities in unmagnetized plasmas
View Description Hide DescriptionConsideration of the effect of a uniform pump field on the particle orbits in a Vlasov plasma leads to a modified diffusion coefficient. When the particles oscillate in the pump field, the turbulent wave phase velocity seen by the particles is Doppler shifted by multiples of ω_{0}/k (ω_{0} is the pump frequency). Hence, strong interactions between the particles and various components of the turbulent field will take place. It is shown that when the pump field is sufficiently strong: E _{0}⩾(4πn _{0} T _{ e })^{1/2}, bulk heating can dominate over tail heating and excitation of electrons to energy levels higher than the normal suprathermal values is possible. This field strength is within the range of laser fusion.

Toroidal effects on propagation, damping, and linear mode conversion of lower hybrid waves
View Description Hide DescriptionA common simplifying assumption made in the consideration of radio‐frequency heating of tokamaks near the lower hybrid frequency is that the wavelength imposed by the coupling device parallel to the magnetic field is not modified by gradients along the field. In the present calculation, the parallel wavelength is allowed to vary, and important effects are found on wave penetration and damping if the toroidal aspect ratio (R _{major}/r _{minor}) is less than approximately five. The calculation shows that heating at the center of a small aspect ratio torus is inhibited by a decrease in k _{∥} if waves are launched at the outside, and that it may be possible to change the plasma current via electron Landau damping with a coupler of symmetric power spectrum by placing the coupler at the top (or bottom) of the torus.

Irreversibility and transport in the lower hybrid drift instability
View Description Hide DescriptionThe dynamics of electrons in a low‐frequency wave propagating perpendicular to a uniform magnetic field are studied and the implications of these results for transport and heating by the lower hybrid drift instability are explored. Below a threshold eφ/T _{ i }≊ 0.25–1.0, all electron energy exchange with the wave is reversible and no plasma transport is possible. Above this threshold, trapping of electrons by the wave potentials takes place and causes irreversible electron heating and diffusion. These results imply that anomolous transport in inhomogeneous plasma with weak drifts (diamagnetic velocity less than the ion thermal velocity) may be substantially less than previously predicted.