Grid image refractometry (GIR) is proposed as a technique for determining the two-dimensional density profiles of long scale-length laser-produced plasmas. Its distinctive feature is that an optical probe beam is broken up into ‘‘rays’’ by being passed through a grid before traversing the plasma. The refraction angles of the rays are measured by imaging the plasma at two or more object planes and are integrated to yield the phase front. For cylindrically symmetric plasmas the density profile is then determined using Abel inversion. The feasibility of GIR is illustrated by an experiment in which a thick CH target was irradiated with ∼100 J of 527 nm radiation and diagnosed with a 20 ps, 263 nm probe. The resulting density profile is substantially larger than any that have previously been reported using interferometry and compares quite closely with hydrodynamic simulations.

In this work the effect of ray stochasticity on the multipass absorption of lower-hybrid waves, used to drive current in tokamaks, is considered. In toroidal geometry, stochasticity arises as an intrinsic property of the Hamiltonian ray trajectories for lower-hybrid waves. Based on the wave kinetic equation, a diffusion equation is derived, with damping and sources, for the wave energy density in the stochastic layer. This equation is solved simultaneously with the electron Fokker–Planck equation to describe the quasilinear flattening of the electron distribution function and the subsequent modification of the wave damping. Steady-state solutions of this system (obtained numerically) indicate that the spectral gap is filled in a self-regulating manner, so that the boundaries of the diffused wave spectrum are independent of the level of ray stochastic diffusion. This allows the development of a simple (semianalytic) model for the self-consistent wave spectrum and the radial profile of absorbed power.

The theory of Onsager symmetry is reconsidered from the point of view of its application to nonequilibrium, possibly turbulent steady states. A dynamical formalism based on correlation and response functions is used; understanding of its relationship to more conventional approaches based on entropy production enables one to resolve various confusions about the proper use of the theory, even near thermal equilibrium. Previous claims that ‘‘kinematic’’ flows must be excluded from considerations of Onsager symmetry are refuted by showing that suitably defined reversible and irreversible parts of the Onsager matrix separately obey the appropriate symmetry; fluctuating hydrodynamics serves as an example. It is shown that Onsager symmetries are preserved under arbitrary covariant changes of variables; the Weinhold metric is used as a fundamental tensor. Covariance is used to render moot the controversy over the proper choice of fluxes and forces in neoclassical plasma transport theory. The fundamental distinction between the fully contravariant Onsager matrix Lij and its mixed representation Lij is emphasized and used to explain why some previous workers have failed to find Onsager symmetry around turbulent steady states. The generalized Onsager theorem of Dufty and Rubí [Phys. Rev. A 36, 222 (1987)] is reviewed. An explicitly soluble Langevin problem is shown to violate Onsager’s original symmetry but to obey the generalized theorem. The physical content of the generalized Onsager symmetry is discussed from the point of view of Nosé–Hoover dynamics. A set of extended Graham–Haken potential conditions are derived for Fokker–Planck models and shown to be consistent with the generalized Onsager relations. Finally, for quite general, possibly turbulent steady states it is argued that realizable Markovian statistical closures with underlying Langevin representations must also obey the generalized theorem. In the special case in which all state variables have even parity and there are no external parameters that change sign under time reversal, the steady-state energy balance fully determines the Onsager matrix, which is guaranteed to be symmetric.

The nonlinear behavior of the two-dimensional Bénard problem with periodic boundary conditions in the horizontal direction is studied with particular emphasis on the role of self-consistent chaotic advection. The results show a complex interplay between vortices driven by the Bénard (Rayleigh–Taylor) instability and shear flow, which is driven by the vortices [J. Drake et al., Phys. Fluids B 4, 4881 (1992)] and which causes their decay. Chaotic advection occurs in the transition from the low Rayleigh number (Ra) regime to the high Ra regime [J. Finn, Phys. Fluids B 5, 415 (1993)]. For the former, vortex flow and shear flow coexist, possibly with slow relaxation oscillations. In the high Ra regime there are vortices localized near the upper and lower boundaries with a shear flow in between. As Ra is decreased from the high Ra regime, these vortices broaden, eventually overlapping, causing self-consistent Lagrangian chaos. This onset of chaos is responsible for several properties of the transition state between the low Ra and the high Ra regimes, most notably the damping of the relaxation oscillations involving vortex and shear flow. It is also observed that the Nusselt number Nu has a peak with respect to Ra in this transition regime characterized by Lagrangian chaos. In the low Ra regime, on the other hand, the relaxation oscillations are on a much slower time scale than the eddy turnover time and the Lagrangian behavior is described by separatrix crossing.

The modulational instability development of Langmuir waves is investigated in highly collisional plasmas where the characteristic frequency Ω of the modulated perturbations is much less than νeff, the effective electron collision frequency. It is demonstrated that the modulational instability for the situation considered is mostly determined by collisional effects (differential Joule heating nonlinearity), in contrast to the well-known modulational instability in collisionless plasmas (where ponderomotive force nonlinearity dominates). Rates and thresholds of the instability are found in various limits. The modulational instability is most effective when the angles between a pump wave vector and wave vectors of the modulational perturbations are of order unity.

The effects of nonlocal heat transport on stimulated scattering instabilities of electromagnetic waves are investigated employing the recently derived expression for the electron number density perturbations that are driven by the ponderomotive and thermal forces in high Zi collisional plasmas. The growth rates and the threshold conditions for stimulated Brillouin and stimulated Compton scattering, as well as modulational instabilities, are obtained. It is found that the growth rates of the scattering instabilities of electromagnetic waves are considerably enhanced due to nonlocal electron heat conduction in collisional plasmas.

The propagation of a high-irradiance laser beam in a plasma whose optical index depends nonlinearly on the light intensity is investigated through both theoretical and numerical analyses. The nonlinear effects examined herein are the relativistic decrease of the plasma frequency and the ponderomotive expelling of the electrons. This paper is devoted to focusing and defocusing effects of a beam assumed to remain cylindrical and for a plasma supposed homogeneous along the propagation direction but radially inhomogeneous with a parabolic density profile. A two-parameter perturbation expansion is used; these two parameters, assumed small with respect to unity, are the ratio of the laser wavelength to the radial electric-field gradient length and the ratio of the plasma frequency to the laser frequency. The laser field is described in the context of a time envelope and spatial paraxial approximations. An analytical expression is provided for the critical beam power beyond which self-focusing appears; it depends strongly on the plasma inhomogeneity and suggests the plasma density tailoring in order to lower this critical power. The beam energy radius evolution is obtained as a function of the propagation distance by numerically solving the paraxial equation given by the two-parameter expansion. The relativistic mass variation is shown to dominate the ponderomotive effect. For strong laser fields, self-focusing saturates due to corrections of fourth order in the electric field involved by both contributions.

The stability of electromagnetic ballooning modes is investigated using a toroidal two-fluid model allowing for arbitrary Ln/LB (the characteristic scale lengths of density and magnetic-field inhomogeneities). The ballooning mode equation is solved numerically and the two-fluid and magnetohydrodynamic stability properties are discussed and compared. The perpendicular compressibility strongly reduces the growth rate and for Ln/LB∼Ln/LT∼1, the mode is completely stabilized.

A kinetic theory is developed which unifies the concept of radio-frequency (rf) current drive and wave helicity injection. It is shown that wave helicity injection and transport can be incorporated into the more general concept of rf forces. Moreover, the part related to wave helicity has the same form as a mean field dynamo. Present result suggests that the evaluation of rf current drive by conventional methods may leave out some important effects. The theory may also simplify the study of rf influence on transport and stability.

A general theoretical approach has been formulated for analyzing two-dimensional structures of high-n toroidal Alfvén eigenmodes (TAE) in large aspect-ratio, finite-β tokamaks. Here, n is the toroidal wave number and β is the ratio between plasma and magnetic pressures. The present approach generalizes the standard ballooning-mode formalism and is capable of treating eigenmodes with extended global radial structures, as well as finite coupling between discrete and continuous spectra. Employing the well-known (s,α) model equilibrium and assuming a linear equilibrium profile, the present approach has been applied to the calculation of the resonant continuum damping rate of TAE modes. Here, s and α denote, respectively, the strengths of magnetic shear and pressure gradients. In particular, it is found that there exists a critical α value, αc(s), such that, as α→αc, the continuum damping rate is significantly enhanced and, thus, could suppress the potential TAE instability.