A Vlasov code developed by Denavit [Phys. Fluids 28, 2773 (1985)] was modified and used to study long-time behavior of the single-mode bump-on-tail instability. Large oscillations, which interrupted his original runs at ω0 T≊1300 shortly after reaching the O’Neil trapping level (OTL), were identified and controlled by heating the cold background electrons. A run to ω0T =30 000 showed growth well beyond the OTL and eventually saturated at about the level predicted by Simon and Rosenbluth (SR) [Phys. Fluids 19, 1567 (1976)], before oscillations set in. A run with warmer background electrons was again interrupted by oscillations. A weakly unstable case was followed to ω0T =60 000; it also showed growth well beyond the OTL but saturated at an amplitude that was significantly below that predicted by SR. In all cases, the velocity distribution developed strong ripples near v=0. These are shown to be caused by a numerical grid effect, and they may be responsible for the eventual development of the large oscillations and for the low level of saturation in the weakly unstable case.

Linear tearing instability is studied in the banana collisionality regime in tokamak geometry. Neoclassical effects produce significant modifications of Ohm’s law and the vorticity equation, so that the growth rate of tearing modes driven by Δ′ is dramatically reduced compared to the usual resistive magnetohydrodynamic values. Consequences of this result, regarding the presence of pressure-gradient-driven neoclassical resistive interchange instabilities and the evolution of magnetic islands in the Rutherford regime, are discussed.

The linear stability of two immiscible liquid layers heated from below through a rigid perfectly conducting boundary with a free deformable upper surface and a deformable liquid–liquid interface is examined. Three modes of instability are allowed simultaneously in the analysis: surface tension driven at each of the two interfaces, buoyancy driven because of the presence of adverse density gradients in each liquid, and an interfacial mode (the Rayleigh–Taylor instability), related to the density difference and interfacial tension at the interfaces. For purely surface tension driven convection, the presence of a middle interface that can suppress normal deformations makes the two liquid layers more stable than a single layer of the same total depth. The interaction of the buoyancy and interfacial modes leads to overstability when the physical properties of the two liquids are only slightly different from each other. For certain Rayleigh numbers, both stationary and oscillatory modes display positive growth constants over a certain range of wavenumbers. As the Marangoni number is increased, the coupling between the surface tension and buoyancy mechanisms makes the system more unstable but removes the oscillatory eigenmodes. The addition of trace amounts of insoluble surface active agents at the two interfaces has a very strong stabilizing influence by introducing the expected hydrodynamic rigidity to the surfaces. However, their more interesting effect is their ability to change the nature of the most unstable eigenmode from stationary to oscillatory.

Hot alpha particles and thermalized helium ash particles in tokamaks can have significant effects on high toroidal mode number instabilities such as the trapped-electron drift mode and the kinetically calculated magnetohydrodynamic ballooning mode. In particular, the effects can be stabilizing, destabilizing, or negligible, depending on the parameters involved. In high-temperature tokamaks capable of producing significant numbers of hot alpha particles, the predominant interaction of the mode with the alpha particles is through resonances of various sorts. In turn, the modes can cause significant anomalous transport of the alpha particles and the helium ash. Here, results of comprehensive linear eigenfrequency–eigenfunction calculations are presented for relevant realistic cases to show these effects.

A kinetic formalism of sideband excitation at the multiples of bounce and cyclotron frequencies of electrons trapped in the ponderomotive potential well and a guide field is developed. A positive (negative) slope of the distribution function with parallel energy is necessary for the excitation of upper (lower) sidebands of the bounce frequency. The cyclotron harmonic sideband excitation requires large perpendicular energy; the latter, however, tends to lower the growth rate of bounce harmonic sidebands. In either case the growth rate falls off rapidly with the harmonic number.

The hydrodynamic transport properties of hard-sphere dispersions are calculated for volume fractions (φ) spanning the dilute limit up to the fluid–solid transition at φ=0.49. Particle distributions are generated by a Monte Carlo technique and the hydrodynamic interactions are calculated by Stokesian dynamics simulation. The effects of changing the number of particles in the simulation cell are investigated, and the scaling laws for the finite-size effects are determined. The effects of using various levels of approximation in computing both the far- and near-field hydrodynamic interactions are also examined. The transport properties associated with porous media—permeabilities and hindered diffusion coefficients—are determined here. The corresponding properties of freely mobile suspensions are determined in a companion paper [Phys. Fluids 31, xxxx (1988)].

The equilibrium and stability of three-dimensional (3-D) ionospheric plasma clouds is investigated. The equilibrium density profile is assumed to be a 3-D water bag with a circular cross section transverse to B, and an ellipsoidal cross section parallel to B. The equilibrium potential consists of two parts: a polarization potential driven by a uniform neutral wind, and an ambipolar potential driven by parallel electron pressure. The latter potential is shown to cause sheared azimuthal plasma flows perpendicular to B. A stability analysis of this equilibrium is carried out. It is found that the E×B instability, which causes the structuring of ionospheric plasma clouds, can be stabilized by the shear in the azimuthal flow. A marginal stability criterion is derived. On the basis of this stability criteria, striations of barium clouds in the ionospheric F region should be stable to further bifurcation, as is observed

A relativistic electron beam in the presence of a whistler wave excites a negative-energy beam space charge mode and a high frequency laser radiation (ω1≫ωc). The instability is explosive for a copropagating beam and the whistler pump, resulting in the excitation of an intense laser in a short pulse. The explosion time τ={(4/kv0)[(ω1−k1vb−ωc) γ0ω1/(ω1−k1vb)ω′pb]1/2}. For both the counterpropagating beam and the whistler wave, the instability is nonexplosive. The laser frequency in this case is somewhat larger, whereas the exponentiation time is comparable to the explosion time of the earlier case.

A model calculation is presented to study turbulence at moderate Reynolds number, Re. In conformity with recent measurements, it is proposed that in the energy cascade the fractional volume occupied by eddies of various sizes depends on Re. By introducing a Re-dependent parameter in the random beta model, it is shown that the scaling behavior of the small-velocity fluctuations at moderate Re can be characterized by a single Re-dependent scaling exponent α0. The calculated Re dependence of α0 is consistent with the experimental data. Corrections to this scaling are calculated using the multifractal concept. The Reynolds number dependence of other multifractal properties in turbulent flows is also calculated.

The nonlinear interaction of three waves propagating in an infinite plasma with a finite spectral bandwidth is studied. A Hamiltonian formulation of the interaction is used and, with the help of a projection operator method, generalized Langevin equations are derived for the wave field amplitudes. A simple form of the evolution equations, more complete than the usual fixed-phase equations, is obtained when the ballistic term and higher-order corrections of the memory effects in the Langevin equations are neglected. Approximate analytical solutions are derived using a multiple time scale method. These are compared with the results of numerical integration. A number of new qualitative features related to the finite spectral bandwidth are discussed in detail.