Volume 28, Issue 7, July 1985
Index of content:

Nonlinear resistive g mode and electron heat conductivity in torsatron/heliotron plasmas
View Description Hide DescriptionAn electron heat conduction coefficient χ_{ e } induced by the nonlinear saturation of the resistive g mode in a stellarator is calculated. It agrees reasonably well with the anomalous χ_{ e } values inferred from Heliotron‐E [Nucl. Fusion 2 4, 305 (1984)] discharges.

The x‐ray observations of a CO_{2}‐laser‐produced plasma
View Description Hide DescriptionThe x‐ray observations of a CO_{2}‐laser‐produced plasma are reported. An underdense plasma is produced by the interaction of intense ≤10^{1} ^{4} W/cm^{2} CO_{2} laser light with a laminar gas jet target. Initial observations at moderate <10^{1} ^{3} W/cm^{2} intensities and low target density reveal an electron temperature scaling with laser intensity that is consistent with inverse bremsstrahlung absorption calculations. At higher intensities and target molecular density, a suprathermal electron temperature appears that is invariant with laser intensity. However, the variation of the detected x‐ray signal with laser intensity can be correlated to the two‐plasmon decay and stimulated Raman scattering instabilities that have been observed for this interaction.

The resistance and mobility functions of two equal spheres in low‐Reynolds‐number flow
View Description Hide DescriptionThe resistance and mobility functions which completely characterize the linear relations between the force, torque, and stresslet and the translational and rotational velocities of two spheres in low‐Reynolds‐number flow have been calculated using a boundary collocation technique. The ambient velocity field is assumed to be a superposition of a uniform stream and a linear (vorticity and rate‐of‐strain) field. This is the first compilation of accurate expressions for the entire set of functions. The calculations are in agreement with earlier results for all functions for which such results are available. The technique is successful at all sphere–sphere separations except at the almost‐touching (gaps of less than 0.005 of the sphere diameter) configuration. New results for the stresslet functions have been used to determine Batchelor and Green’s [J. Fluid Mech. 5 6, 401 (1972)] order c ^{2} coefficient in the bulk stress (7.1 instead of their 7.6). The two‐sphere functions have also been used to determine the motion of a rigid dumbbell in a linear field. We also show that certain functions have extrema.

The unsteady oblique stagnation point flow
View Description Hide DescriptionAn exact solution of the unsteady Navier–Stokes equations is found. The solution describes the stagnation region of an accelerating circular jet impinging obliquely on a flat plate.

Oscillatory and competing instabilities in a nonlinear model for Langmuir circulations
View Description Hide DescriptionA five‐mode truncation of the full partial differential equations which describe Langmuir circulations is studied. Instabilities of different kinds are possible depending on the relative strengths of a stabilizing vertical density stratification and a destabilizing vertical Stokes drift gradient. For sufficiently small buoyancy, steady convection obtains, whereas for larger values of the buoyancy oscillatory convection obtains. In addition the competition can create multiple instabilities. Techniques from dynamical systems theory are used to derive equations which describe nonlinear oscillatory convection and the multiple bifurcation, whose character has been explored in the literature. The center manifold and normal form transformations are explained in a direct and elementary manner in order to be clear to readers encountering these methods for the first time. The problem treated may also be interpreted as one of double diffusion, but with boundary conditions not usually considered. The results are discussed in terms of the physics of Langmuir circulations.

The mechanism of mixing enhancement and suppression in a circular jet under excitation conditions
View Description Hide DescriptionThe present work is a numerical study of the shear layer’s growth in a turbulent round jet under forced axisymmetric periodic disturbances. The forced oscillation is found to either enhance or reduce the momentum thickness along the jet depending on the forcing Strouhal number St, where St is defined as f d/U _{ e }. Here, f is the frequency in Hertz, d is the nozzle exit diameter, and U _{ e } is the jet exit velocity. At low Strouhal numbers (St<0.5), no subharmonic of the forced fundamental is amplified. The momentum thickness is found to increase monotonically with the forcing level, and the effect is pronounced for forcing levels higher than 0.5% of the jet exit velocity. At forcing Strouhal numbers in the range of 0.6–1.0, the first subharmonic of the fundamental is amplified. The increase in the momentum thickness caused by forcing at this Strouhal number range is proportional to the forcing level and is pronounced at low forcing levels in the range of 0.01%–1% of the jet exit velocity. If the forcing Strouhal number is close to the ‘‘shear layer instability mode,’’ St_{θ}≊0.015, several subharmonics are generated and the forcing is found to result in a reduction in the momentum thickness along the jet.

Turbulent flow structure in the near field of a swirling round free jet
View Description Hide DescriptionTurbulent flow structure in the near field of a swirling round free jet is experimentally and theoretically investigated in a low‐speed wind tunnel. The experiments are conducted in a slightly heated swirling jet with an irrotational, low‐speed, coflowing stream. Velocity and temperature are simultaneously measured using a laser Doppler anemometer and a resistance thermometer, respectively. The results show that in a strongly swirling jet, the ambient fluid is rapidly entrained into the jet in the region near the convergent nozzle exit. The entrainment rate shows a value about twice as large as that in a nonswirling jet, even in the immediate vicinity of the nozzle exit. This rapid entrainment is attributed to the recirculating flow which is formed by the adverse pressure induced to balance the strong centrifugal force. The flow structure is compared with the numerical predictions based on a two‐equation model of the type k‐ε. The predictions and experimental results both agree well.

Testing a closure for velocity/pressure‐gradient correlations in nonuniform turbulent flow
View Description Hide DescriptionCertain velocity/pressure‐gradient correlations arise in the Reynolds stress equation through the interaction of the turbulent velocity field with the mean strain rate field. An existing, rational closure representation for these correlations is extended here and then tested. The closure permits good agreement to be obtained between observed and computed Reynolds stress components as they evolve under the influence of uniform shear and plane strain.

Solution to the piecewise linear continuous random initial value problem for Burgers’ equation
View Description Hide DescriptionA closed form solution to Burgers’ equation on an infinite domain has been obtained for ‘‘random sawtooth’’ continuous initial conditions defined on a finite domain. The ‘‘turbulent’’ solution is than used to compute statistical measures such as skewness and flatness factors, energy decay rates, and the temporal evolution of velocity autocorrelations and energy spectra.

Double layer formation caused by contact between different temperature plasmas
View Description Hide DescriptionThe formation of an electrical potential difference between hot and cold plasmas is studied by means of a particle simulation. It is found that a double layer structure is formed on the hot‐plasma side of the contact surface between the cold and hot plasmas. The potential difference is given approximately by φ_{DL}∼T _{eh}/2e, where T _{eh} and e are the hot‐electron temperature and the electronic charge, respectively. The double layer is accompanied by a negative potential dip on the low potential side (cold plasma) of the double layer, the depth of which is φ_{dip}∼2T _{ec}/e, where T _{ec} is the cold‐electron temperature. Interestingly, however, the positive potential difference and the negative potential dip are created independently.

Numerical simulations of current‐limited double layers observed in a linear mirror device
View Description Hide DescriptionSimulations based on the Vlasov–Poisson scheme are carried out to observe the temporal and spatial development of dopuble layers (DLs) in a linear mirror field. Simulation results show that the magnetic mirrors have a substantial effect in reducing the current passing through the DL. Development of a negative potential region on the low potential side of the DL is also observed, in agreement with the experimental results. The observed strong DLs appear to be formed, triggered by the ion‐acoustic instability.

Particle simulations of the low‐α Pierce diode
View Description Hide DescriptionThe evolution of small initial perturbations of the uniform equilibrium of the ‘‘classical’’ Pierce diode [J. Pierce, J. Appl. Phys. 1 5, 721 (1944)] is studied using particle simulations. These simulations have been performed with the new bounded‐plasma code PDW1 [Wm. S. Lawson (private communication)] and cover the parameter range 0<α<3π, where α=ω_{ p } L/v _{0}. In the linear regime, three stages (initial transit, adjustment, and dominant eigenmode) are distinguished; oscillation frequencies, growth/damping rates, and potential profiles of the dominant eigenmode as well as oscillation frequencies of the next‐to‐dominant eigenmode are recovered and shown to agree quantitatively with recent analytical results. In the linearly unstable cases, the system evolves nonlinearly to a final state which may be either a new, nonuniform dc equilibrium, or a state of large‐amplitude oscillations. In particular, for α=1.5π the character of the final state is found to depend on the details of the initial conditions.

Scattering of ion‐acoustic solitons
View Description Hide DescriptionA series of experiments is described that is designed to ascertain the properties of the scattering of planar ion‐acoustic solitons from objects of various shapes. The scattered solitons are compared with those radiated from the same objects.

Strong ion acceleration by a collisionless magnetosonic shock wave propagating perpendicularly to a magnetic field
View Description Hide DescriptionA 2 1/2 ‐dimension, fully relativistic, fully electromagnetic particle code is used to study the time evolution of a nonlinear magnetosonic pulse propagating in a direction perpendicular to a magnetic field. The pulse is excited by an instantaneous piston acceleration, and evolves in a totally self‐consistent manner. A large amplitude pulse traps some ions and accelerates them parallel to the wave front. They are detrapped when their velocities become of the order of the sum of the E×B drift velocity and the wave phase velocity, where E is the electric field in the direction of the wave propagation. The pulse develops into a quasishock wave in a collisionless plasma because of dissipation caused by the resonant ion acceleration. A simple nonlinear wave theory for a cold plasma describes the shock properties observed in the simulation except for the effects of resonant ions. In particular, the magnitude of an electric potential across the shock region is derived analytically and is found to be in good agreement with our simulations. The potential jump is proportional to B ^{2}, and hence the E×B drift velocity of the trapped ions is proportional to B.

Collisionless tearing instability in a non‐Maxwellian neutral sheet: An integrodifferential formulation
View Description Hide DescriptionAn integro‐differential formalism is developed to study the collisionless tearing instability in a non‐Maxwellian neutral sheet. The exact unperturbed particle orbits are used analytically in the orbit integrals. The treatment is linear, self‐consistent, and kinetic for both ions and electrons. The analysis is carried out for low‐frequency, purely growing electromagnetic perturbations (‖ω‖≪ω_{ c i }). Using the Galerkin method, the integro‐differential equation is solved to obtain the dispersion relation and the eigenmode structure. A sufficient condition for instability is given on the basis of a quadratic form and the eigenvalues of a self‐adjoint integro‐differential operator. The formalism is applied to a specific model distribution. For the case where the electrons and ions are both non‐Maxwellian, it is found that the instability is dominated by the axis‐crossing electrons and that the eigenmode is strongly localized to a region of the order of ( ρ_{ e } z _{ p })^{1} ^{/} ^{2} at the null plane, where ρ_{ e } is a measure of the electron gyroradius in the asymptotic magnetic field and z _{ p } is the sheet thickness. It is shown that the growth rate can be enhanced by several orders of magnitude over the isotropic case and that short wavelength perturbations are strongly preferred. The dispersion relation has the general form γ/k v _{ e∥}=const where k∥B _{0} and v _{ e∥} is the electron thermal velocity along B _{0}, the equilibrium magnetic field.

Theory of resistivity‐gradient‐driven turbulence
View Description Hide DescriptionA theory of the nonlinear evolution and saturation of resistivity‐driven turbulence, which evolves from linear rippling instabilities, is presented. The nonlinear saturation mechanism is identified both analytically and numerically. Saturation occurs when the turbulent diffusion of the resistivity is large enough so that dissipation caused by parallel electron thermal conduction balances the nonlinearly modified resistivity gradient driving term. The levels of potential, resistivity, and density fluctuations at saturation are calculated. A combination of computational modeling and analytic treatment is used in this investigation.

Wave‐particle resonance broadening in a Langmuir turbulence
View Description Hide DescriptionA new resonance broadening theory formulated in the Fokker–Planck framework shows agreement with numerical analyses in which particle diffusion in velocity space is studied against a background of prescribed Langmuir turbulence, much better than the Dupree–Weinstock theory. The deviation from the quasilinear theory because of modification of particle orbits is stronger than previously conjectured.

Multiple Raman up‐conversion of radiation from pre‐existing Langmuir turbulence
View Description Hide DescriptionThe equilibrium states described by a damped and driven kinetic equation governing the evolution of the spectrum of radiation in a stationary Langmuir‐turbulent plasma are studied. Both Langmuir and transverse spectra are assumed to be one‐dimensional in wavenumber space. A source of radiation at the plasma frequency and a uniform rate of dissipation at the higher harmonics are assumed. The radiation is characterized by an effective temperature z, proportional to the Langmuir energy density and inversely proportional to the dissipation rate of the transverse waves. If z<1 the equilibrium photon spectrum decreases with increasing frequency as a power law in z. If z>1, photons scattered out of certain regions of phase space may return at a significant rate, and the spectrum is found to have a global maximum above the plasma frequency ω_{ p }. The location of this maximum is proportional to z ^{1} ^{/} ^{3} ω_{ p }, which may be many times the plasma frequency. Applications to a laser‐plasma experiment and to the solar wind environment are discussed.

Three‐drift‐wave interaction at finite parallel wavelength: Bifurcations and transition to turbulence
View Description Hide DescriptionThe generic properties of the nonlinear interaction of three drift waves with finite k _{∥} are investigated. The different types of stationary or quasistationary states are characterized by the bifurcation diagram in γ_{1}, κ parameter space, where γ_{1} measures the mode excitation and κ the parallel wavenumber. The transition to turbulence corresponds exactly to the Ruelle–Takens picture: steady state→periodic solution→doubly periodic solution→turbulence, in contrast to the period‐doubling route usually observed in low‐dimensional dynamic systems. The transition to k _{∥}=0, the model of Horton and Terry [Phys. Fluids 2 5, 491 (1982)], occurs at very small values of k _{∥}.

A nonlocal analysis of drift and drift‐cyclotron waves in cylindrical geometry
View Description Hide DescriptionAn analysis of electron drift waves and drift‐cyclotron waves has been carried out in cylindrical geometry using a k‐space integral equation. The model assumes a low‐β electrostatic plasma in a straight magnetic field with a Gaussian density profile. Above the threshold for the drift‐cyclotron instability, a complicated spectrum of modes is found, with the fundamental radial eigenmode not necessarily the most unstable. In solving the integral equation, improved computational efficiency is obtained by decomposing the eigenfunctions on an associated Laguerre polynomial basis, a method which works best for low‐azimuthal (m<25) and low‐radial (n<10) mode numbers.