Index of content:
Volume 24, Issue 10, October 1981

A differentiable trajectory approximation to turbulent diffusion
View Description Hide DescriptionThe problem of turbulent diffusion is posed as determining the time evolution of the probability density of the concentration given those for the fluid velocity components, sources, and the initial concentration. At each time, all variables are elements of the Hilbert space L _{ R } ^{2}(R ^{3}), and a finite‐dimensional approximation based on expansions in orthonormal basis functions is developed. An expression for the joint probability density of all the Fourier coefficients is derived, the evaluation of which is shown to be particularly straightforward. Diffusion of material from a single source in an unbounded mildly turbulent fluid is considered as an application.

Structure functions of turbulence in an adverse pressure gradient
View Description Hide DescriptionLongitudinal and transverse structure functions of turbulent velocity fluctuations up to the fourth order have been measured in an adverse pressure gradient and compared with the original ideas of Kolmogoroff and with other experimental results. The results show the existence of an inertial subrange for a separation range of about one decade, and in turn the predictions of Kolmogoroff’s original theory have some validity even for a flow that is subjected to an adverse pressure gradient.

Viscous buckling of slender horizontal jets
View Description Hide DescriptionExperimental results are presented describing the buckling type of instability in jets of very viscous liquids that flow from vertical slit‐type orifices. Under certain conditions, the jet may buckle in a manner similar to the buckling of a cantilever beam. The governing dimensionless parameters are identified and their critical values determined.

Electrohydrodynamic stability in the presence of a thermal gradient
View Description Hide DescriptionThe effect of a temperature‐dependent dielectric constants is considered in the stability analysis of a liquid layer subjected to an electric field, weak unipolar injection, and temperature gradient.

Resonant shadowgraph and schlieren studies of magnetized laser‐produced plasmas
View Description Hide DescriptionResonant shadowgraph and schlieren techniques provide instantaneous photographs of a laser‐produced barium plasma flowing across a transverse magnetic field. The field is seen to impose considerable structure upon the expanding plasma. The flow separates into several well‐defined regions, according to velocity. The slow plasma component displays internal striations. These are interpreted as shock waves excited by plasma flow across the field.

Nonlinear evolution equations, recurrence and stochasticity
View Description Hide DescriptionPerturbative, spatially–periodic solutions of the Korteweg–deVries, the modified Korteweg–deVries, and the nonlinear Schrödinger equations are shown to be recurrent and nonstochastic, densely covering parts of the phase space bounded by level surfaces of the constants of motion. The connection of this result with the numerical phenomena of recurrences and the slow randomization of nonlinear systems is discussed.

Alfvén wave excitation of the magnetostatic mode
View Description Hide DescriptionIt is shown that the magnetostatic mode can be excited by kinetic Alfvén waves. The growth rates are calculated for various limits of interest in plasma diffusion studies as well as Alfvén wave plasma heating experiments.

Excitation of convection cells by ion‐cyclotron waves
View Description Hide DescriptionIt is shown that convective cells can be excited by large‐amplitude propagating ion‐cyclotron waves in a plasma. Using the two‐fluid model, a coupled set of differential equations is obtained. A nonlinear dispersion relation for the modulational instability is then derived. This relation is investigated for different parameter regimes and expressions for the growth rates are obtained analytically. Relevance of the work to space physics as well as magnetically confined plasmas is discussed.

Nonlinear evolution of the ion beam mode
View Description Hide DescriptionThe nonlinear evolution of the wave envelope of the fast ion beam mode has been studied experimentally. At large amplitudes above threshold, the beam mode is observed to be self‐amplitude‐modulated. When the self‐ modulation has fully evolved, the wave splits into a train of wave packets. Finally, it is shown that the self‐modulation observed can be explained by a theory for the modulational instability.

Generation and collapse of Langmuir solitons in a nonuniform plasma
View Description Hide DescriptionThis numerical study considers the effect of a zero‐order density gradient on the development of Langmuir wave collapse in two dimensions. Two different situations are considered; (1) an initial soliton is pertubed in a direction transverse to the density gradient, and (2) the plasma is resonantly driven by an external pump electric field in the presence of transverse density fluctuations. The principal finding is that the density gradient can inhibit the development of Langmuir collapse for both the initial soliton and the externally driven cases. Over the limited parameter space surveyed it is found that collapse occurs for values of the scaled gradient parameter g≲2.5; where g = (9/8)(M/m)^{3/2}(λ_{D}/L), M is the ion mass, m is the electron mass, λ_{D} is the Debye length, and L is the gradient scale length. For larger values of g, collapse is not observed.

Simple criteria for the absence of the beam‐Weibel instability
View Description Hide DescriptionRigorously sufficient and approximately necessary conditions for the absence of the beam‐Weibel instability are derived. These conditions include previously known stability criteria and resolve the seeming contradiction that these modes can be stabilized by beam temperature when the plasma is cold, but they cannot be stabilized by beam temperature when the plasma has infinitesimally small temperature.

Linear waves and instabilities on magnetically insulated gaps
View Description Hide DescriptionA linear, fully relativistic and electromagnetic analysis of waves perturbing the Brillouin flow state on planar, magnetically insulated gaps is presented. Three independent classes of waves are treated individually; transverse‐magnetic waves propagating normal to the insulating magnetic field, transverse‐electric waves propagating in the same direction, and a set of waves propagating along the magnetic field. Dispersion relations governing discrete modes of oscillation for each class are found and solved for some cases of interest. Only the transverse‐magnetic waves are found to be unstable due to the existence of a Doppler‐shifted plasma reasonance layer at frequencies above the plasma frequency. The scaling of the growth rate for this instability with respect to parameters characterizing the equilibrium state is examined. In addition to these discrete modes, spectral continua associated with localized resonance phenomena in the electron sheath bounding the cathode are described and explained.

Nonlinear saturation of the lower‐hybrid‐drift instability: Axis encircling model
View Description Hide DescriptionThe nonlinear evolution of the lower‐hybrid‐drift instability is considered in the guiding‐centers‐on‐axis model. Extremely rapid radial quasi‐linear diffusion of electrons leads to the buildup of a radial electric field E_{ r }. Saturation occurs when the E_{ r }×B electron drift velocity equals the local ion rotational velocity. Due to the rapid linear growth rate, the unmagnetized ions are unable to shield out E_{ r }, which becomes significant long before density profile flattening occurs.

Theory of two‐point correlation function in a Vlasov plasma
View Description Hide DescriptionA self‐consistent theory of phase‐space granulations, called ’’clumps’’, has been derived. These fluctuations are produced when regions of different phase‐space density are mixed by the fluctuating electric fields. The source term and turbulent scattering operator for these fluctuations are obtained through a renormalization of the one‐ and two‐point equations for a Vlasov plasma. The proper treatment of the singular behavior exhibited by the two‐point equation, coupled with the self‐consistent approach leads to a number of significant changes compared with previous formulations. The case of electrostatic turbulence is considered throughout this paper. The method of solution is based on the concept of two disparate time scales which allow the treatment of the equal time two‐point equation as an initial condition for its two‐time counterpart. The picture of a ’’test’’ clump emerges quite naturally within such a framework. The source term for the clump correlation function is identified and certain intrinsic properties determined. Physical interpretations of the coefficients in the renormalization are given and their role in energy and momentum conservation demonstrated. The theory is reminiscent of Fokker–Planck analysis with which numerous parallels are drawn.

Cross‐field diffusion and fluctuation spectra in a levitated octupole in the presence of a toroidal field
View Description Hide DescriptionThe diffusion coefficient D _{⊥} for a collisionless hydrogen plasma was measured in the levitated octupole when a weak toroidal field was added. A twenty‐fold decrease in the anomalous diffusion was observed with B _{ t }/B _{ p }≳0.1. This reduced level of diffusion was still two orders of magnitude larger than the classical value and the residual level of convective cell activity was responsible for the enhanced transport. Locally trapped particles in the poloidal field mirrors allow the convective cell activity (f<600 Hz) to persist even when the toroidal field was added. The principal effect of the added toroidal field was observed to be a localization of the convective cells in the region where particles are trapped and a shift in the k _{⊥} spectrum to shorter wavelengths.

Transport studies in reversed field theta pinches
View Description Hide DescriptionAnomalous transport in a reversed field theta pinch is examined. The principal effects are anomalous resistivity and rotation generation. Similarity solutions for the resistive decay are found which agree qualitatively with experiment. Also, it is shown that the spin up and anomalous resistivity may be the effect of a single underlying cause, a current‐driven microinstability.

Anomalous decay of induced electron currents in field‐reversed systems
View Description Hide DescriptionInduced electron currents are studied in systems which are field‐reversed due to ion currents, with no toroidal magnetic field. In such systems, electron flow is induced in the region of closed field lines, with a large velocity shear that can drive a Kelvin–Helmholtz type instability. Analysis of the nonlinear evolution suggests that the instability leads to a rapid dissipation of electron currents. Rough estimates show that the instability is likely to be of importance in field‐reversed ion ring and mirror experiments.

Bifurcation of elliptical equilibria
View Description Hide DescriptionIt is shown that a bifurcation of the equilibrium solutions for straight elliptical plasma columns with a diffuse current profile exists for a suitable choice of the currents in the external conductors.

Fast ion production by suprathermal electrons in laser fusion plasmas
View Description Hide DescriptionThe acceleration of ions by two isothermal species of electrons, thermal and suprathermal, in a laser‐fusion plasma is investigated. The disassembly of an initially stationary plasma slab, including charge separation effects, is described. Before the rarefaction wave has penetrated appreciably into the slab, an interior Debye sheath which separates the suprathermal and thermal electrons, as well as an exterior sheath at the ion‐vacuum interface is found. As the rarefaction approaches the center of the slab, the dynamics is modified due to the conservation of species number and total energy. The energetics of the long‐time evolution is described by a quasi‐neutral similarity solution appropriate to finite two‐electron species systems.

Ion emission from laser‐produced, multi‐ion species, two‐electron temperature plasmas
View Description Hide DescriptionA model for ion emission from (CH)_{ n } and (CH_{2})_{ n } laser‐produced plasmas containing both hot and cold electron populations is presented. Computed Faraday cup current traces illustrate the point that separate C^{6+} and H^{+} ion current peaks cannot be resolved, showing that care should be excercised when interpreting the total ion current observed experimentally. The slow C^{6+} ions are found to carry most of the ion momentum. A small number of fast C^{6+} and H^{+} ions containing a substantial fraction of the total ion energy are produced. Fast ions, corresponding to those observed experimentally, can thus be generated without the need to invoke inhibition of heat flux into the target, as has been suggested.