Abstract:
Test modes on turbulent magnetized plasmas are studied taking into account the ion trapping that characterizes the E x B drift in the background turbulence. We show that trappyng provides the physical mechanism for the formation of large scale potential structures (inverse cascade) observed in drift turbulence. Trapping combined with the motion of the potential with the diamagnetic velocity determines ion flows in opposite directions, which reduce the growth rate and eventually damps the drift modes. It also determine transitory zonal flow modes in connection with compressibility effect due to the polarization drift in the background turbulence.

Abstract:
The two-dimensional ideal (Euler) fluids can be described by the classical fields of streamfunction, velocity and vorticity and, in an equivalent manner, by a model of discrete point-like vortices interacting in plane by a self-generated long-range potential. This latter model can be formalized, in the continuum limit, as a field theory of scalar matter in interaction with a gauge field, in the $su(2) $ algebra. This description has already offered the analytical derivation of the \emph{sinh}-Poisson equation, which was known to govern the stationary coherent structures reached by the Euler fluid at relaxation. In order this formalism to become a familiar theoretical instrument it is necessary to have a better understanding of the physical meaning of the variables and of the operations used by the field theory. Several problems will be investigated below in this respect.

Abstract:
The large scale atmospheric vortices (tropical cyclones, tornadoes) are complex physical systems combining thermodynamics and fluid-mechanical processes. The well known tendency of vorticity to self-organization, an universal property of the two-dimensional fluids, is part of the full dynamics, but its description requires particular methods. The general framework for the thermodynamical and mechanical processes is based on conservation laws while the vorticity self-organization needs a variational approach. It is difficult to estimate to what extent the vorticity self-organization (a purely kinematic process) have influenced the characteristics of the tropical cyclone at stationarity. If this influence is substantial it is expected that the stationary state of the tropical cyclone has the same nature as the vortices of many other systems in nature: ideal (Euler) fluids, superconductors, Bose - Einstein condensate, cosmic strings, etc. In previous works we have formulated a description of the $2D$ vorticity self-organization in terms of a classical field theory. The field theoretical (FT) formulation finds that the quasi-coherent form of the atmospheric vortex (tropical cyclone) at stationarity is an expression of the Self-Duality. In the present work we examine a strong property of the tropical cyclone, which arises in the FT formulation in a natural way: the equality of the masses of the particles associated to the matter field and respectively to the gauge field in the FT model is translated into the equality between the maximum radial extension of the tropical cyclone and the Rossby radius. For the cases where the FT model is a good approximation we calculate characteristic quantities of the tropical cyclone and find good comparison with observational data.

Abstract:
The special problem of transport in 2-dimensional divergence-free stochastic velocity fields is studied by developing a statistical approach, the nested subensemble method. The nonlinear process of trapping determined by such fields generates trajectory structures whose statistical characteristics are determined. These structures strongly influence the transport.

Abstract:
In a two-dimensional model of the planetary atmosphere the compressible convective flow of vorticity represents a strong nonlinearity able to drive the fluid toward a quasi-coherent vortical pattern. This is similar to the highly organised motion generated at relaxation in ideal Euler fluids. The problem of the atmosphere is however fundamentally different since now there is an intrinsic length, the Rossby radius. Within the Charney Hasegawa Mima model it has been derived a differential equation governing the stationary, two-dimensional, highly organised vortical flows in the planetary atmosphere. We present results of a numerical study of this differential equation. The most characteristic solution shows a strong similarity with the morphology of a tropical cyclone. Quantitative comparisons are also favorable and several relationships can be derived connecting the characteristic physical parameters of the tropical cyclone: the radius of the eye-wall, the maximum azimuthal velocity and the radial extension of the vortex.

Abstract:
Evolving from turbulent states the 2D fluids and the plasmas reach states characterized by a high degree of order, consisting of few vortices. These asymptotic states represent a small subset in the space of functions and are characterised by properties that are difficult to identify in a direct approach. The field theoretical approach to the dynamics and to the asymptotic states of fluids and plasmas in 2D provides a considerable extension of the usual perspective. The present works discusses a series of consequences of the field theoretical approach, when it is applied to particular problems. The discussion is developed around known physical problems: the current density profiles in cylindrical plasma, the density pinch in tokamak and the concentration of vorticity.

Abstract:
Strong electrostatic turbulence in magnetically confined plasmas is characterized by trapping or eddying of particle trajectories produced by the $E\times B$ stochastic drift. Trapping is shown to produce strong effects on test particles and on test modes. It determines non-standard statistics of trajectories: non-Gaussian distribution, memory effects and coherence. Trapped trajectories form quasi-coherent structure. Trajectory trapping has strong nonlinear effects on the test modes on turbulent plasmas. We determine the growth rate of drift modes as function of the statistical characteristics of the background turbulence. We show that trapping provides the physical mechanism for the inverse cascade observed in drift turbulence and for the zonal flow generation.

Abstract:
The effects of the resonant magnetic perturbations (RMPs) on the turbulent transport are analyzed in the framework of the test particle approach using a semi-analytical method. The normalized RMP amplitude $P_{b}$ extends on a large range, from the present experiments to ITER conditions. The results are in agreement with the experiments at small $P_{b}.$ The predictions for ITER strongly depend on the type of turbulent transport. A very strong increase of the turbulent transport is obtained in the nonlinear regime, while the effects of the RMPs are much weaker for the quasilinear transport.

Abstract:
Fundamental Lagrangian, frozen-in and topological invariants can be useful to explain systematic connections between plasma parameters. At high plasma temperature the dissipation is small and the robust invariances are manifested. We invoke a frozen-in invariant which is an extension of the Ertel's theorem and connects the vorticity of the large scale motions with the profile of the safety factor and of particle density. Assuming ergodicity of the small scale turbulence we consider the approximative preservation of the invariant for changes of the vorticity in an annular region of finite radial extension (i.e. poloidal rotation). We find that the ionization-induced rotation triggered by a pellet requires a reversed-$q$ profile. In the $H$-mode, the invariance requires a accumulation of the current density in the rotation layer. Then this becomes a vorticity-current sheet which may explain experimental observations related to the penetration of the Resonant Magnetic Perturbation and the filamentation during the Edge Localized Modes.

Abstract:
At incident powers much higher than the threshold for filamentation a pulse from a high-power laser generates in the transversal plane a complex structure. It consists of randomly meandering stripes defining connected regions where the field intensity is high; and, the complementary regions dominated by diffusive plasma with defocusing property. The pattern is similar to an ensemble of clusters of various extensions. We provide evidence that there is a correlation between this filamentation and the {\it labyrinth} instability in reaction-diffusion systems. Besides the similarity of the spatial organization in the two cases, we show that the differential equations that describe these two dynamical processes lead to effects that can be mutually mapped. For the laser beam at high power the Non-linear Schrodinger Equation in a regime of strong self-focusing and ionization of the air leads to multiple filamentation and the structure of clusters. Under the effect of the {\it labyrinth} instability a model of activator-inhibitor leads to a similar pattern. The origin of this connection must be found in the fact that both optical turbulence and the activator-inhibitor dynamics have the nature of competition between two phases of the same system.