Index of content:
Volume 24, Issue 2, February 1981

Stochastic model theory for coherent turbulent structures in circular jets
View Description Hide DescriptionA stochastic model based on a linearized theory is developed. It is assumed that the large scale structure of the turbulence is created randomly at the jet orifice and that its subsequent convection downstream may be described in terms of quantities predicted by a linearized inviscid stability theory for slowly diverging flows. The process of the generation of turbulence is modeled by the imposition of a stochastic initial condition for the corresponding stability problem. The application of this condition secures the homogeneity of mean values of the turbulent quantities with respect to the angular coordinate; the contribution of each spiral mode is then proportional to a certain spectral function, the latter being an unknown function within the framework of the present study. Since experiments have shown that the turbulence of jets is far from being adequately represented by white noise conditions, the spectral functions must be determined by fitting to experimental data. It is shown that the model is capable of predicting the experimental trends for circumferential and radial coherence functions fairly well. However, complications arise with respect to the axial coherence functions and an attempt is made to alleviate the difficulties by either a cutoff assumption or by a process of continuation of the inviscid quantities.

Two‐point probability density function closure applied to a diffusive‐reactive system
View Description Hide DescriptionThe Ievlev multipoint probability density function closure proposal is applied at the two‐point level to the mass balance equation for a single stochastically distributed reactant undergoing molecular diffusion and nonlinear reaction. The solution is shown to satisfy the major realizability properties of a probability density function and to be unique. In the case of a linear reaction, it produces the exact solution for an initially multivariate normal distribution. By short‐time numerical integration of a second‐order reaction with diffusion, the solution is shown to represent molecular mixing more satisfactorily than do existing one‐point theories.

Rayleigh–Taylor stability with mass and heat transfer
View Description Hide DescriptionA nonlinear analysis of the Rayleigh–Taylor stability of two thermally conducting fluids is presented. Mass transfer across the interface due to the evaporation and condensation process is explicitly taken into account. The method of multiple scale expansion is employed for the analysis. The stability criterion is expressible in terms of various competing parameters representing the equilibrium heat flux, latent heat of evaporation, vapor pressure, gravity, surface tension, densities of the fluids, and thermal properties of the fluids. It is found that when the heat flux is strong enough and when the heat transfer mechanism is efficient enough, the system can be stabilized in the regimes where it would be linearly unstable. The study has also shed light on the validity of the quasi‐equilibrium approximation employed in a previous nonlinear study of the stability problem. The implication for the phenomenon of boiling heat transfer is also discussed.

Mixture approach to a model for sediment transport
View Description Hide DescriptionA mixture of heat‐conducting viscous inert fluids is given the structure of material with hidden variables. As a consequence, a model for sediment transport is elaborated within the approximation of sediments as a dilute suspension. Such a model turns out to be hyperbolic and allows for exceptional transverse waves.

Elongational flow of dilute drag reducing fluids in a falling jet
View Description Hide DescriptionAn elongational flow of dilute polymer solution in a falling jet was studied. Measurements were made of the stress and velocity distribution along the falling jet by means of a photographic technique. The results show that the relaxation time in dilute drag reducing fluids is much longer than those predicted in a simple shear flow, and suggest the possibility of using a very high value of the relaxation time in a wall turbulence model. Also, the increase in Trouton ratios determined for a simple elongational flow is possibly as high as 27 000.

Stimulated and spontaneous emission of acoustic waves from shock fronts
View Description Hide DescriptionIn certain materials, shock waves of sufficient intensity spontaneously emit transverse rarefaction waves and are therefore unstable. A criterion is derived by calculating the relative amplitudes of reflected acoustic waves incident on the shock from behind. This criterion is found to delimit the conditions under which both acoustic amplification and acoustic emission can occur; it agrees with earlier results by Kontorovich.

Multi‐shock solutions of random phase three‐wave interactions
View Description Hide DescriptionExplicit solutions of the equations describing the space–time interaction of three random phase wave packets are presented. The solutions describe the collision and decay of previously known shock‐like solutions. Stability of the solutions to a perturbation in initial conditions is also analyzed. For those solutions which are unstable, a closed form solution of the nonlinear evolution of the interaction is given.

Discrete spectrum for ideal magnetohydrodynamic channel flow
View Description Hide DescriptionSufficient conditions are derived for the stability of cylindrically symmetric plasma equilibria with steady flow when the magnetic field is unidirectional and the flow is tangential to the field. The stability criteria involve only the flow, sound, and Alfvén speeds.

Finite‐beta modifications of drift and trapped‐electron modes
View Description Hide DescriptionA previous two‐dimensional electrostatic calculation for the spatial structure of drift and trapped‐electron modes is extended to include finite‐β effects. Specifically, the parallel perturbed vector potential, and the parallel Ampere’s law are added to the calculation. Illustrative results are presented. The effect of increasing β can be either stabilizing or destabilizing, depending on the parameter values chosen. For present tokamak β values, the finite‐β effects are small.

Trapped electron modifications to tearing modes in the low collision frequency limit
View Description Hide DescriptionIn the limit of weak collisions, a narrow boundary layer forms at the trapped/untrapped boundary in velocity space. When the electron collision frequency ν_{ e } is small compared with the wave frequency ω times the inverse aspect ratio ε, a realistic collision operator must be employed to evaluate the response of the boundary layer electrons. The parallel current carried by the barely circulating boundary layer electrons results in tearing mode modifications which are evaluated from a slab model in the banana regime (ν_{ e }<εω) by using a Lorentz model collision operator.

Lower‐hybrid propagation cones and tail heating of electrons and ions
View Description Hide DescriptionPlasma heating by lower‐hybrid waves has been studied using a two‐and‐one‐half‐dimensional electrostatic code with more realistic plasma and source models than previously used. Mode couplings between wavenumber modes of opposite sign occur when two propagation cones meet. The resulting smaller k _{∥} and/or higher ω modes propagate in the interior. These modes appear to be plausible mechanisms for tail heating of electrons and ions.

Time‐dependent nonlinear Langmuir waves
View Description Hide DescriptionThe existence of nonlinear periodic Langmuir waves that are time dependent in any frame of reference is demonstrated, the phase and amplitude modulations being induced by the oscillating motion of trapped particles. Large amplitude modulations can be found even for weak trapped particles densities. Sideband instabilities are strongly modified by the oscillating motion when the energy dependence of the bounce frequency is taken into account.

Limit cycle behavior of the bump‐on‐tail instability
View Description Hide DescriptionThe nonlinear dynamics of the bump‐on‐tail instability is considered. The eigenmodes have discrete k because of finite periodic boundary conditions. Increasing a critical parameter (the number density) above its neutral stable value by a small fractional amount Δ^{2}, one mode becomes unstable. The nonlinear dynamics of the unstable mode is determined by means of the multiple time scale method. Usually, limit cycle behavior is found. A short comparison with quasi‐linear theory is given, and the results are compared with experiment.

Ballooning and interchange stability in axisymmetric field reversed equilibria
View Description Hide DescriptionThe magnetohydrodynamic stability of axisymmetric field reversed equilibria (compact tori) without a toroidal magnetic field is studied. It is shown that axis encircling ions do not interact with modes having a short wavelength in the toroidal (symmetry) direction. A large toroidal aspect ratio equilibrium with nearly circular flux surfaces is found to be stable to ballooning modes if the axis encircling ions carry more than half the current. In the opposite limit, e.g., elliptical flux surfaces with aspect ratio as large as 5, ninety percent of the current must be carried by axis‐encircling ions. In a thermal plasma (a reversed field theta pinch, for example) only a fraction of the outer flux surfaces are unstable if ρ_{ i }/L, the ratio of ion gyroradius to scale length, is greater than 0.3, and if the flux surfaces are not too elongated.

Transport of a trace impurity in a dirty plasma in the Pfirsch–Schlüter regime
View Description Hide DescriptionParticle transport rates for a trace impurity are calculated for a Pfirsch–Schlüter regime plasma consisting of a main ion and all the charge states of a background impurity. The main ion is taken to be much lighter than all impurities, but masses and charges are otherwise arbitrary. Qualitative trends of the transport rates with variations in the trace impurity mass and background impurity concentrations are discussed.

Bumpy torus transport in the low collision frequency limit
View Description Hide DescriptionA variational formulation of transport for a closed field line, large aspect ratio bumpy torus in the low collision frequency limit is presented. The relatively large radial excursions made by those particles with canceling magnetic and electric poloidal drifts requires generalization of previous neoclassical techniques. General expressions for the transport coefficients of both charge species are given. Explicit numerical coefficients are evaluated under certain simplifying assumptions for both the banana and nonbanana species.

Enhanced current penetration in tokamaks
View Description Hide DescriptionThe rate at which current penetrates to the interior of a plasma during the current rise phase of a discharge is found to be greatly enhanced by anomalous viscosity due to electromagnetic turbulence.

Laser induced density profiles in an isothermal plasma
View Description Hide DescriptionThe absorption and scattering of laser light in laser fusion targets is very dependent on the exact form of the laser induced density profiles. The possible profiles that can exist are examined using a simple isothermal model. It is shown that four different structures are possible. The flow speed profiles and the speed of the critical surface are determined for each of these structures. It is shown that two of these structures are locally overdense and can exist in an underdense plasma, and thus may have a large effect on the amount of light reaching the critical surface.

Enhancement of free electron laser radiation by applying a direct current electric field
View Description Hide DescriptionThe intensity of the electromagnetic radiation produced by a free electron laser can be substantially increased by applying a dc electric field at the time of saturation. By using a proper dc electric field strength, a substantial number of trapped electrons can become clamped in the decelerating phase and continuously transfer the dc electric field energy into the locked high frequency radiation. A modulational instability is observed when the radiation intensity exceeds some threshold, and ultimately terminates the conversion process.

Radial losses in high‐β multiple mirror plasmas
View Description Hide DescriptionThe importance of radial losses in collisional multiple mirror confinement is investigated for arbitrary values of β. Classical radial diffusion and complete fluid stability are assumed. Analytical and numerical solutions of the coupled axial and radial diffusion problem are found. The results can be characterized in terms of a single parameter α∼(τ_{ z }/τ_{ x })^{1/2} where τ_{ z } and τ_{ x } are average values of the axial and radial confinement times. Radial losses are unimportant for α≲0.5 and improvement in overall confinement can be achieved by increasing β for these small values of α. When applied to existing reactor designs, the theory shows that radial losses are significant for one‐component reactors but can be made negligible for two‐component (wetwood burner) reactors.