L\'evy flights on a comb and the plasma staircase

We formulate the problem of confined L\'evy flight on a comb. The comb represents a sawtooth-like potential field $V(x)$, with the asymmetric teeth favoring net transport in a preferred direction. The shape effect is modeled as a power-law dependence $V(x) \propto |\Delta x|^n$ within the sawtooth period, followed by an abrupt drop-off to zero, after which the initial power-law dependence is reset. It is found that the L\'evy flights will be confined in the sense of generalized central limit theorem if (i) the spacing between the teeth is sufficiently broad, and (ii) $n > 4-\mu$, where $\mu$ is the fractal dimension of the flights. In particular, for the Cauchy flights ($\mu = 1$), $n>3$. The study is motivated by recent observations of localization-delocalization of transport avalanches in banded flows in the Tore Supra tokamak and is intended to devise a theory basis to explain the observed phenomenology.Comment: 13 pages; 3 figures; accepted for publication in Physical Review

Fusion, collapse, and stationary bound states of incoherently coupled waves in bulk cubic media

We study the interaction between two localized waves that propagate in a bulk (two transverse dimensions) Kerr medium, while being incoherently coupled through cross-phase modulation. The different types of stationary solitary wave solutions are found and their stability is discussed. The results of numerical simulations suggest that the solitary waves are unstable. We derive sufficient conditions for when the wave function is bound to collapse or spread out, and we develop a theory to describe the regions of different dynamical behavior. For localized waves with the same center we confirm these sufficient conditions numerically and show that only when the equations and the initial conditions are symmetric are they also close to being necessary conditions. Using Gaussian initial conditions we predict and confirm numerically the power-dependent characteristic initial separations that divide the phase space into collapsing and diffracting solutions, and further divide each of these regions into subregions of coupled (fusion) and uncoupled dynamics. Finally we illustrate how, close to the threshold of collapse, the waves can cross several times before eventually collapsing or diffracting

Impurity transport in plasma edge turbulence

The turbulent transport of minority species/impurities is investigated in 2D drift-wave turbulence as well as in 3D toroidal drift-Alfven edge turbulence. The full effects of perpendicular and -- in 3D -- parallel advection are kept for the impurity species. Anomalous pinch effects are recovered and explained in terms of Turbulent EquiPartition (TEP)Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

Stretched exponential relaxation and ac universality in disordered dielectrics

This paper is concerned with the connection between the properties of dielectric relaxation and ac (alternating-current) conduction in disordered dielectrics. The discussion is divided between the classical linear-response theory and a self-consistent dynamical modeling. The key issues are, stretched exponential character of dielectric relaxation, power-law power spectral density, and anomalous dependence of ac conduction coefficient on frequency. We propose a self-consistent model of dielectric relaxation, in which the relaxations are described by a stretched exponential decay function. Mathematically, our study refers to the expanding area of fractional calculus and we propose a systematic derivation of the fractional relaxation and fractional diffusion equations from the property of ac universality.Comment: 8 pages, 2 figure

Generic features of modulational instability in nonlocal Kerr media

The modulational instability (MI) of plane waves in nonlocal Kerr media is studied for a general, localized, response function. It is shown that there always exists a finite number of well-separated MI gain bands, with each of them characterised by a unique maximal growth rate. This is a general property and is demonstrated here for the Gaussian, exponential, and rectangular response functions. In case of a focusing nonlinearity it is shown that although the nonlocality tends to suppress MI, it can never remove it completely, irrespectively of the particular shape of the response function. For a defocusing nonlinearity the stability properties depend sensitively on the profile of the response function. It is shown that plane waves are always stable for response functions with a positive-definite spectrum, such as Gaussians and exponentials. On the other hand, response functions whose spectra change sign (e.g., rectangular) will lead to MI in the high wavenumber regime, provided the typical length scale of the response function exceeds a certain threshold. Finally, we address the case of generalized multi-component response functions consisting of a weighted sum of N response functions with known properties.Comment: 9 pages, 5 figure

Numerical Simulations of Intermittent Transport in Scrape-Off Layer Plasmas

Two-dimensional fluid simulations of interchange turbulence for geometry and parameters relevant for the scrape-off layer of confined plasmas are presented. We observe bursty ejection of particles and heat from the bulk plasma in the form of blobs. These structures propagate far into the scrape-off layer where they are lost due to transport along open magnetic field lines. From single-point recordings it is shown that the blobs have asymmetric conditional wave forms and lead to positively skewed and flat probability distribution functions. The radial propagation velocity may reach one tenth of the sound speed. These results are in excellent agreement with recent experimental measurements.Comment: 8 pages, 7 figure

Intermittent transport in edge plasmas

The properties of low-frequency convective fluctuations and transport are investigated for the boundary region of magnetized plasmas. We employ a two-dimensional fluid model for the evolution of the global plasma quantities in a geometry and with parameters relevant to the scrape-off layer of confined toroidal plasmas. Strongly intermittent plasma transport is regulated by self-consistently generated sheared poloidal flows and is mediated by bursty ejection of particles and heat from the bulk plasma in the form of blobs. Coarse grained probe signals reveal a highly skewed and flat distribution on short time scales, but tends towards a normal distribution at large time scales. Conditionally averaged signals are in perfect agreement with experimental measurements.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France