Collective Phenomena in Macroscopic Systems

PREFACE

CONTENTS

Arguments are presented in favor of a possible existence of a random, force-free magnetic field. Ponderomotive forces in such a field are small, and the evolutionary time is much longer than Alfven crossing time over the vortex scale, whence the suggested term “magnetostatic.” The presence of this long-lived random magnetic field provides stiffness with respect to large-scale compressional motions. On the other hand, such a field cannot be detected by techniques involving line-of-sight averaging. It may therefore be a source of stiffness for various astrophysical objects, ranging from plasmas in clusters of galaxies to the interiors of molecular clouds in HII regions, and remaining at the same time undetectable. Analysis of large-scale motions on the background of the magnetostatic turbulence is presented; it is concluded that these large-scale motions can be roughly described by a usual hydrodynamics for the matter with an isotropic pressure; the adiabatic index is 4/3.

The onset and relaxation of turbulence, and the formation and evolution of coherent structures in an electron plasma have been studied in the Malmberg-Penning trap ELTRAP using two different experimental settings: trapped plasma and electron beam reflected by an externally applied potential barrier.

The structure and nonlinear dynamics of vortices in plasma lens for high-current ion-beam focusing have been investigated theoretically.

New aspects of collective nonlinear dust plasma interactions are presented. These are the formation of dust ion-acoustic shocks and Langmuir envelope solitons in a uniform dusty plasma, as well as self-organization of incompressible dust fluid in the form of vortical structures in a nonuniform dusty plasma. We present relevant nonlinear models and their numerical simulations for those nonlinear waves and structures. The relevance of our investigation to laboratory and space dusty plasmas is discussed.

The Weibel instability (and its beam-plasma counterpart: the current filamentation instability) is an electromagnetic instability that generates a magnetic field in the presence of particle phase-space anisotropies. These instabilities have been investigated in the case of ultra-intense and ultra-short laser pulses interacting with a plasma, but are also of primary importance in the astrophysical context relating to the formation (or to the seeding at small spatial scales) of magnetic fields. Here we shall investigate what are the typical spatial scales and structures of the magnetic field that can be expected to be generated by the development of the current filamentation instability.

In recent experiments of laser pulse interaction at relativistic intensities with a low density plasma, the proton radiography technique showed evidence of long–lived field structures generated after the self–channeling of the laser pulse.

We present 2D particle-in-cell simulations of this interaction regime, where the dynamics of similar structures has been resolved with high temporal and spatial resolution. An axially symmetrical field pattern, resembling both soliton–like and vortex structures, has been observed. A study of the physics of such structures and a comparison with experimental data is in progress.

The formation of macroscopic reconnected magnetic structures (islands) have been observed in advanced experiments on weakly collisional, well confined plasmas while established theories of the drift-tearing modes, which depend strongly on the electron temperature gradient and can describe the formation of these structures, had predicted practically inaccessible excitation thresholds for them in these regimes. The relevant theoretical dilemma is resolved as mesoscopic modes that depend critically on the ratio of the transverse (to the magnetic field) to the longitudinal thermal conductivity , can produce large scale magnetic reconnection. These modes are envisioned to emerge from a background, which can be coherent, of collisionless microscopic reconnecting modes driven by the electron temperature gradient, that create a sequence of adjacent strings of magnetic islands and increase considerably the ratio over its classical value. The mesoscopic reconnecting mode is treated by a singular perturbation analysis involving three asymptotic regions involving the small parameters and , where ε_* ≡ D_mD_A, D_m is the magnetic diffusion coefficient, , r_Te ≡ (-d InT_e/dr)^-1, K_⊥ is the transverse mode number, and D_B = cT_e/(eB).

Some recent findings about conformal invariance of isolevel lines in turbulent, two-dimensional inverse cascades are briefly reviewed.

In this paper I will review some basic aspects of the mechanism of stochastic resonance. Stochastic resonance was first introduced as a possible mechanism to explain long term climatic variation. Since then, there have been many applications of stochastic resonance in physical and biological systems. I will show that in complex system, stochastic resonance can substantially change as a function of the “system complexity”.

No abstract received.

In this paper we show how by exploiting thermophoresis in nanoparticles (NPs) aqueous dispersions it is possible to perform convection experiments at high solutal Prandtl number Pr_s. We describe the experimental tools necessary to produce and analyze the faint density modulations induced by the convective flow. The study of the transition to instability after the application of a sudden temperature gradient, allows realizing a Gedanken experiment suggested by Howard 40 years ago. The result is a measurement of the scaling exponent which relates the Nusselt number to the Rayleigh number.

One of the most interesting phenomena in the soft-matter realm consists in the spontaneous formation of super-molecular structures (microphases) in condition of thermodynamic equilibrium. A simple mechanism responsible for this self-organization or pattern formation is based on the competition between attractive and repulsive forces with different length scales in the microscopic potential, typically, a short-range attraction against a longer-range repulsion.

We analyse this problem by simulations in 2D fluids. We find that, as the temperature is lowered, liquid-vapor phase separation is inhibited by the competition between attraction and repulsion, and replaced by a transition to non-homogeneous phases. The structure of the fluid shows well defined signatures of the presence of both intra- and inter-cluster correlations.

Even when the competition between attraction and repulsion is not so strong as to cause microphase formation, it still induces large density fluctuations in a wide region of the temperature-density plane. In this large-fluctuation regime, pattern formation can be triggered by a weak external modulating field.

Scale-independence of the equations of magnetohydrodynamics permits stability analysis of laboratory and astrophysical plasmas with the same techniques. This may lead to fruitful cross-fertilization, but also to paradoxes when the essential differences in plasma confinement are not accounted for.

The first point is illustrated by the analysis of an accretion disk about a black hole, which is described as a superposition of a transonically rotating ‘tokamak’ with a compact object in the center. Instabilities of the continuous spectrum, called Trans-Slow Alfvén Continuum instabilities, are found that provide an alternative route for MHD turbulence in accretion disks.

The second point is illustrated by contrasting stability of tokamaks, which is dominated by the Ansatz that the wave vector of perturbations is (nearly) perpendicular to the magnetic field, with the Parker and the magneto-rotational instability where this assumption is manifestly violated. The two view points are reconciled by analyzing the different types of plasma confinement and by fitting the instabilities in one spectral framework. This yields a new class of gravitational instabilities, called quasi-Parker instabilities, bridging the gap between the laboratory and astrophysical regimes and providing new possibilities for MHD spectroscopy to diagnose astrophysical plasmas.

We discuss results of axisymmetic magnetohydrodynamic theory and simulations of the interaction of a rapidly-rotating, aligned magnetized star with an accretion disk. The disk is considered to have a finite viscosity and magnetic diffusivity. The main parameters of the system are the star's angular velocity and magnetic moment, and the disk's viscosity, magnetic diffusivity, and mass accretion rate. We focus on the “propeller" regime where the inner radius of the disk is larger than the corotation radius. We have found two different types of magnetohydrodynamic flows: as a “weak” and “strong” propellers. The strong propellers have a powerful MHD disk wind and a collimated magnetically dominated or Poynting flux outflow from the surface of the star. The weak propellers have only weak outflows. We discuss the time-averaged characteristics of the interaction between the main elements of the system, the star, the disk, the wind from the disk, and the jet from the star. Rates of exchange of mass and angular momentum between the elements of the system are derived as a function of the main parameters. These results are applicable to the early evolution of classical T Tauri stars. They may be also used to explain the variation of angular velocity of neutron stars and cataclysmic variables.

A variety of topics related to our understanding of turbulence and angular momentum transport in astrophysical accretion disks are discussed, including (1) new numerical algorithms for magnetohydrodynamics required to study these processes, (2) turbulence and the decay of vortices in hydrodynamic disks, (3) MHD turbulence driven by the magnetorotational instability (MRI), and (4) studying the MRI through laboratory experiments. A brief outline of some of the outstanding challenges in understanding MHD turbulence in astrophysical disks is given.

In this paper, I will review the the recent progresses in understanding the nonlinear evolution of gravitationally unstable gaseous discs. Gaseous accretion discs are a fundamental ingredient in the modeling on very diverse physical systems, spanning from the large scale discs that provide the fueling for supermassive black holes (SMBH) in the nuclei of active galaxies (AGN) to the smaller scale discs surrounding young stars, which are thought to be the site where planet formation occurs. Gravitational instabilities (GI) might play an important role in determining the structure and the evolution of such discs in many cases. The advances in numerical techniques have recently made possible to run complex simulations of the non-linear behaviour of such collective phenomena, leading to a deeper understanding of important related aspects, such as fragmentation and angular momentum transport. I will also present one specific example that shows the importance of gravitational instabilities in a system of considerable astrophysical relevance: high-redshift proto-galaxies, where GI might lead to the formation of the seeds of SMBHs.

A mature sunspot is usually surrounded by a penumbra: strong vertical magnetic field in the umbra, the dark central region of sunspot, becomes more and more horizontal toward the periphery forming an ensemble of a thin magnetic filaments of varying inclinations. Recent high resolution observations with the 1-meter Swedish Solar Telescope (SST) on La Palma revealed a fine substructure of penumbral filaments and new regularities in their dynamics.¹ These findings provide both the basis and constraints for an adequate model of the penumbra whose origin still remains enigmatic. We present results of recent observations obtained with the SST. Our data, taken simultaneously in 4305 Å G-band and 4396 Å continuum bandpasses and compiled in high cadence movies, confirm previous results and reveal new features of the penumbra. We find e.g. that individual filaments are cylindrical helices with a pitch/radius ratio providing their dynamic stability. We propose a mechanism that may explain the fine structure of penumbral filaments, the observed regularities, and their togetherness with sunspot formation. The mechanism is based on the anatomy of sunspots in which not only penumbra has a filamentary structure but umbra itself is a dense conglomerate of twisted interlaced flux tubes.

Dissipationless collapses in Modified Newtonian Dynamics (MOND) have been studied1 by using our MOND particle-mesh N-body code, finding that the projected density profiles of the final virialized systems are well described by Sersic profiles with index m ≲ 4 (down to m ∼ 2 for a deep-MOND collapse). The simulations provided also strong evidence that phase mixing is much less effective in MOND than in Newtonian gravity. Here we describe “ad hoc” numerical simulations with the force angular components frozen to zero, thus producing radial collapses. Our previous findings are confirmed, indicating that possible differences in radial orbit instability under Newtonian and MOND gravity are not relevant in the present context.

Accretion disks and astrophysical jets are used to model many active astrophysical objects, viz., young stars, relativistic stars, and active galactic nuclei.The problem of jet acceleration and collimation is central for understanding the physics of these objects. There is now a general consensus that jet acceleration is the result of an interplay between rotation and magnetic field. Global numerical simulations that include both the disk and jet physics have so far been limited to relatively short time scales and small ranges of viscosity and resistivity parameters that may be crucial to define the coupling of the inflow/outflow dynamics. Along these lines, we present in this paper self-consistent time-dependent simulations of supersonic jets launched from magnetized accretion disks, using high resolution numerical techniques. In particular we study the effects of the disk magnetic resistivity, parametrized through an α-presctiption, in determining the properties of the inflow/outflow system .We use the MHD FLASH code with adaptive mesh refinement, allowing us to follow the evolution of the structure for a time scale long enough to reach steady state.

The noncanonical Hamiltonian formulation of a recently derived four-field model describing collisionless reconnection is presented. The corresponding Lie-Poisson bracket is shown to be a sum of a direct and semi-direct product forms and to possess four infinite independent families of Casimir invariants. Three out of four of these families are directly associated with the existence of Lagrangian invariants of the model. Two of the invariants generalize previously discovered invariants of a two-field model for reconnection in low-β plasmas. Finally a variational principle is given for deriving general equilibrium equations and an example of an equilibrium solution is described explicitely.

To a large extent, the basic mechanism of dynamical friction remains an open problem. In fact, the classical idealized local description, given by Chandrasekhar, is known to be subject to a number of limitations, possibly related to the global nature of the collective processes that are involved. Here we present a study of the properties of dynamical friction in galaxy models, derived from a realistic distribution function, that are characterized by significant density concentration and by pressure anisotropy biased in the radial direction. The problem is addressed by means of dedicated N-body simulations. By following the fall of heavy objects inside the host galaxy, we find that the classical theory is better suited to describe dynamical friction only outside cores of models with low concentration, but fails in more concentrated models, more appropriate to describe elliptical galaxies. In turn, pressure anisotropy in the host galaxy does not appear to have significant effects.

The effects of dynamical friction on a satellite dragged in towards the center of a host elliptical galaxy have been studied mostly for the case of a satellite modeled as a rigid potential. However, under realistic conditions tidal distorsions of the satellite are expected to play an important role in the satellite–galaxy interaction. For the goal of describing such a complex stellar dynamical system, we have performed N-body simulations of the orbital evolution of a self–consistent, “live” satellite stellar system within a self–consistent, “live” host galaxy by means of the GADGET–2 code. As initial conditions, a King model for the satellite and an f^(ν) model for the host galaxy with dimensionless central potential W₀ = 7 and Ψ = 5, respectively, have been adopted; models of this type have found wide application to the description of globular clusters and elliptical galaxies. The satellite is initially placed on a quasi–circular orbit. The satellite slowly falls towards the center of the galaxy because of dynamical friction, while its mass and structure change in time as a result of the relevant tidal forces encountered along the orbit. We compare the orbital decay of this self–consistent live satellite to the orbital decay of a satellite modeled as a rigid King potential. We find that during the fall the structure of the satellite changes towards less concentrated configurations, which are interestingly well described, at any given time, as King models, but with smaller and smaller concentration parameter.

An electron plasma confined in a Malmberg-Penning trap can be a good experimental setup for the study of the two-dimensional fluid dynamics, since a magnetized plasma in this geometry behaves like an eulerian fluid in a wide range of experimental conditions. Plasma turbulence is triggered by the diocotron instability. Here, the results of a Fourier spectral analysis of the energy and enstrophy distributions are reported and interpreted using theoretical models of two dimensional turbulence.

Assuming a magnetic field perpendicular to ion extraction axis x, a selfconsistent model of the plasma and of the ion beam, including all the structures in-between (presheath, sheath and meniscus), is written and numerically solved in two dimension x, y. A series expansion of the one dimensional solution is used to represent most of the plasma analytically and to precise boundary conditions. Five field variables are used to treat the positive ion case, namely the three fluid velocities V, the ion density profile n and the adimensional potential u. Collisional effect and their implication on equation kind and stability are discussed, as well as correction to fluid approximation.

Generation of plasma perturbations because of collisionless super–Alfvénic dense plasma clouds expanding through and decelerating in an ambient plasma background is studied. Using an universal hybrid kinetic-hydrodynamical description, the calculations are made for a 2D and 3D expansion of a spherical cloud into an initially uniform background with uniform magnetic field.

A fully three dimensional Particle in Cell model of the plasma fiber had been developed. The code is written in FORTRAN 95, implementation CVF (Compaq Visual Fortran) under Microsoft Visual Studio user interface. Five particle solvers and two field solvers are included in the model. The solvers have relativistic and non-relativistic variants. The model can deal both with periodical and non-periodical boundary conditions. The mechanism of the surface turbulences generation in the plasma fiber was successfully simulated with the PIC program package.

In order to derive a quantum dynamics which takes intrinsically into account many-body long-range forces and collective effects, we formulate a generalized Schrödinger equation which satisfies, under an appropriate generalization of the operators properties, the basic quantum mechanics assumptions. Such an equation of motion can be viewed as the quantum stochastic counterpart of a generalized classical kinetic equation, reproducing the stationary distribution of the Tsallis non-extensive thermostatistics.

One mechanism of filling of electrostatic plasma lens for high-current ion-beam-focusing by electrons against direction of electric field due to non-linear vortex behavior has been considered.

The self-consistent formation, observed in experiments, of the solitary barrier for plasma electrons and ions has been analytically described.

The properties and excitation of the solitary forerunner and solitary wake-field by electron bunch are investigated.

We consider the possibility of enhancing the ionization charge states of beam ions by electron vortices excited in cylindrically symmetric plasma optical systems of finite length with crossed radial electric and longitudinal magnetic fields.

The mechanism has been offered and the observed formation of the ion crystal near the electrical probe has been analytically described.

The behavior of the two plasma flows, propagating towards each other along axis of the cylindrically symmetrical cusp kind of the magnetic field, is considered. It is shown that for fixed plasma flow velocity and radius and for fixed radius of the magnetic field line curvature there is the most effective value of the magnetic field for the best control of plasma flows.

We derive a fractional relaxation equation in a setting which refers to the universal conductivity response of homogeneously disordered solid materials. Initial-time behavior of the decay function is a stretched exponential the so-called Kohlrausch-Williams-Watts (KWW) function, ρ(t) ∝ exp [–(t/τ)^β].

We report on an analytical approach to deduce the critical angular velocities for the appearance of a finite number of vortices and their degrees in rotating 2D Bose-Einstein condensates in the Thomas-Fermi regime of large coupling strength between the particles. Moreover, we derive the distribution of vortices in the condensate i.e. the vortex pattern.

A practical method for distinguishing stochastic and regular subsystems in the entire set of particles for numerical modeling of the development of physical instabilities in collisionless systems with self-consistent fields is proposed. The method of subdividing the phase space into subsystems is based on the comparison of the results of two computational experiments with identical initial conditions but different realizations of rounding errors. An example of establishing the spatial and temporal domains of the development of collective instability and determining the instability increments is offered by a gravitating disk.

No abstract received.

An innovative argument is presented in order to explain the formation of Quasi-Single-Helicity (QSH) states in Reversed-Field-Pinches (RFPs) as result of a tearing perturbation of a force-free equilibrium. In particular it is shown that force-free equilibria with a piecewise constant ratio between the current density and the magnetic field can be tearing unstable to modes with helicity corresponding to the one observed during QSH states, whereas they are stable with respect to modes with other helicities. It is suggested that RFPs could reach such equilibria as a consequence of an evolution of the system from a relaxed Taylor state toward a non-reversed force-free state on resistive time scales.

In this paper is showed the way how to solve movement of electric charged particles where the energy loss by radiation is taken into account. Obviously the calculation of movement with energy loss is made by solving of relativistic or non-relativistic equation of motion. The interaction with proper electric field of the particle is added subsequently as the corrections given by statistic formulas depending on the particle concentration and on the temperature of plasma. The alternative way presented in this paper is based on solving of Lorentz-Dirac (LD) equation in which the reaction force from the radiation is included. Because of known nonuniqueness of the original LD equation, the modified LD equation based on their integro–differential form is used and this is only of the second order in comparison with the third order original LD equation. The restrictions for validity of modified LD equation are mentioned. Tests of accuracy of proposed numerical scheme under various conditions are made.

LIST OF PARTICIPANTS