Fractal structures in nonlinear plasma physics

Fractal structures appear in many situations related to the dynamics of conservative as well as dissipative dynamical systems, being a manifestation of chaotic behaviour. In open area-preserving discrete dynamical systems we can find fractal structures in the form of fractal boundaries, associated to escape basins, and even possessing the more general property of Wada. Such systems appear in certain applications in plasma physics, like the magnetic field line behaviour in tokamaks with ergodic limiters. The main purpose of this paper is to show how such fractal structures have observable consequences in terms of the transport properties in the plasma edge of tokamaks, some of which have been experimentally verified. We emphasize the role of the fractal structures in the understanding of mesoscale phenomena in plasmas, such as electromagnetic turbulence.

High-frequency extensions of magnetorotational instability in astrophysical plasmas

High-frequency extensions of magnetorotational instability driven by the Velikhov effect beyond the standard magnetohydrodynamic (MHD) regime are studied. The existence of the well-known Hall regime and a new electron inertia regime is demonstrated. The electron inertia regime is realized for a lesser plasma magnetization of rotating plasma than that in the Hall regime. It includes the subregime of nonmagnetized electrons. It is shown that, in contrast to the standard MHD regime and the Hall regime, magnetorotational instability in this subregime can be driven only at positive values of dln Omega/dlnr, where Omega is the plasma rotation frequency and r is the radial coordinate. The permittivity of rotating plasma beyond the standard MHD regime, including both the Hall regime and the electron inertia regime, is calculated.

Recurrence quantification analysis of electrostatic fluctuations in fusion plasmas

We have investigated plasma turbulence at the edge of a tokamak plasma using data from electrostatic potential fluctuations measured in the Brazilian tokamak TCABR. Recurrence quantification analysis has been used to provide diagnostics of the deterministic content of the series. We have focused our analysis on the radial dependence of potential fluctuations and their characterization by recurrence-based diagnostics. Our main result is that the deterministic content of the experimental signals is most pronounced at the external part of the plasma column just before the plasma radius. Since the chaoticity of the signals follows the same trend, we have concluded that the electrostatic plasma turbulence at the tokamak plasma edge can be partially explained by means of a deterministic nonlinear system. (C) 2007 Elsevier B.V. All rights reserved.

Contributions to the theory of magnetorotational instability and waves in a rotating plasma

The one-fluid magnetohydrodynamic (MHD) theory of magnetorotational instability (MRI) in an ideal plasma is presented. The theory predicts the possibility of MRI for arbitrary 0, where 0 is the ratio of the plasma pressure to the magnetic field pressure. The kinetic theory of MRI in a collisionless plasma is developed. It is demonstrated that as in the ideal MHD, MRI can occur in such a plasma for arbitrary P. The mechanism of MRI is discussed; it is shown that the instability appears because of a perturbed parallel electric field. The electrodynamic description of MRI is formulated under the assumption that the dispersion relation is expressed in terms of the permittivity tensor; general properties of this tensor are analyzed. It is shown to be separated into the nonrotational and rotational parts. With this in mind, the first step for incorporation of MRI into the general theory of plasma instabilities is taken. The rotation effects on Alfven waves are considered.

Sound waves and solitons in hot and dense nuclear matter

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density. The equation of state is derived from a relativistic mean field model, which is a variant of the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations leads to differential equations for the density perturbation. We solve them numerically for linear and spherical perturbations and follow the propagation of the initial pulses. For linear perturbations we find single soliton solutions and solutions with one or more solitons followed by ""radiation"". Depending on the equation of state a strong damping may occur. We consider also the evolution of perturbations in a medium without dispersive effects. In this case we observe the formation and breaking of shock waves. We study all these equations also for matter at finite temperature. Our results may be relevant for the analysis of RHIC data. They suggest that the shock waves formed in the quark gluon plasma phase may survive and propagate in the hadronic phase. (C) 2009 Elseiver. B.V. All rights reserved.

Nonlinear Schrodinger equation with chaotic, random, and nonperiodic nonlinearity

In this Letter we deal with a nonlinear Schrodinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time coordinates and to check its robustness under these conditions. Here we show that the chaotic perturbation is more effective in destroying the soliton behavior, when compared with random or nonperiodic perturbation. For a real system, the perturbation can be related to, e.g., impurities in crystalline structures, or coupling to a thermal reservoir which, on the average, enhances the nonlinearity. We also discuss the relevance of such random perturbations to the dynamics of Bose-Einstein condensates and their collective excitations and transport. (C) 2010 Elsevier B.V. All rights reserved.

Canonical quantum potential scattering theory

A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find nonlinear first-order differential equations for the low-energy scattering parameters such as scattering length and effective range. They significantly simplify typical calculations, as we illustrate for atom-atom and neutron-nucleus scattering systems. A generalization to charged particle scattering is also possible.

The Schenberg spherical gravitational wave detector: the first commissioning runs

Here we present a status report of the first spherical antenna project equipped with a set of parametric transducers for gravitational detection. The Mario Schenberg, as it is called, started its commissioning phase at the Physics Institute of the University of Sao Paulo, in September 2006, under the full support of FAPESP. We have been testing the three preliminary parametric transducer systems in order to prepare the detector for the next cryogenic run, when it will be calibrated. We are also developing sapphire oscillators that will replace the current ones thereby providing better performance. We also plan to install eight transducers in the near future, six of which are of the two-mode type and arranged according to the truncated icosahedron configuration. The other two, which will be placed close to the sphere equator, will be mechanically non-resonant. In doing so, we want to verify that if the Schenberg antenna can become a wideband gravitational wave detector through the use of an ultra-high sensitivity non-resonant transducer constructed using the recent achievements of nanotechnology.

Magnetic-field asymmetry of nonlinear transport in a small ring

We have investigated the magnetic-field asymmetry of the conductance in the nonlinear regime in a small Aharonov-Bohm ring. We have found that the odd-in B and linear in V (the DC bias) correlation function of the differential conductance exhibits periodical oscillations with the Aharonov-Bohm flux. We have deduced the electron interaction constant and analyzed the phase rigidity of the Aharonov-Bohm oscillations in the nonlinear regime. Copyright (C) EPLA, 2009

Experimental characterization of nonlinear systems: a real-time evaluation of the analogous Chua`s circuit behavior

This paper presents an experimental characterization of the behavior of an analogous version of the Chua`s circuit. The electronic circuit signals are captured using a data acquisition board (DAQ) and processed using LabVIEW environment. The following aspects of the time series analysis are analyzed: time waveforms, phase portraits, frequency spectra, Poincar, sections, and bifurcation diagram. The circuit behavior is experimentally mapped with the parameter variations, where are identified equilibrium points, periodic and chaotic attractors, and bifurcations. These analysis techniques are performed in real-time and can be applied to characterize, with precision, several nonlinear systems.

Gravitational field of a straight cosmic string in the framework of higher-derivative gravity

The gravitational properties of a straight cosmic string are studied in the linear approximation of higher-derivative gravity. These properties are shown to be very different from those found using linearized Einstein gravity: there exists a short range gravitational (anti-gravitational) force in the nonrelativistic limit; in addition, the derection angle of a light ray moving in a plane orthogonal to the string depends on the impact parameter.

Degenerate Two-Photon Absorption in All-Trans Retinal: Nonlinear Spectrum and Theoretical Calculations

In this work we investigate the degenerate two-photon absorption spectrum of all-trans retinal ill ethanol employing the Z-scan technique with femtosecond pulses, The two-photon absorption (2PA) spectrum presents a monotonous increase as the excitation wavelength approaches the one-photon absorption band and it peak at 790 nm. We attribute the 2PA hand to the mixing of states (1)B(u)+-like and vertical bar S(1)>, which are strongly allowed by one- and two-photon, respectively. We modeled the 2PA spectrum by using the sum-over-states approach and obtained spectroscopic parameters of the electronic transitions to vertical bar S >, vertical bar S(2)> (""(1)Bu(+)""), vertical bar S(3)>, and vertical bar S(4)> singlet-excited states. The results were compared with theoretical predictions of one- and two-photon transition calculations using the response Functions formalism within the density functional theory framework with the aid of the CAM-B3LYP functional.

Action of the gravitational field on the dynamical Casimir effect

In this paper, we analyze the action of the gravitational field on the dynamical Casimir effect. We consider a massless scalar field confined in a cuboid cavity placed in a gravitational field described by a static and diagonal metric. With one of the plane mirrors of the cavity allowed to move, we compute the average number of particles created inside the cavity by means of the Bogoliubov coefficients computed through perturbative expansions. We apply our result to the case of an oscillatory motion of the mirror, assuming a weak gravitational field described by the Schwarzschild metric. The regime of parametric amplification is analyzed in detail, demonstrating that our computed result for the mean number of particles created agrees with specific associated cases in the literature. Our results, obtained in the framework of the perturbation theory, are restricted, under resonant conditions, to a short-time limit.

Nonlinear spectrum effect on the coherent control of molecular systems

This work demonstrates that the detuning of the fs-laser spectrum from the two-photon absorption band of organic materials can be used to reach further control of the two-photon absorption by pulse spectral phase manipulation. We investigate the coherent control of the two-photon absorption in imidazole-thiophene core compounds presenting distinct two-photon absorption spectra. The coherent control, performed using pulse phase shaping and genetic algorithm, exhibited different growth rates for each sample. Such distinct trends were explained by calculating the two-photon absorption probability considering the intrapulse interference mechanism, taking into account the two-photon absorption spectrum of the samples. Our results indicate that tuning the relative position between the nonlinear absorption and the pulse spectrum can be used as a novel strategy to optimize the two-photon absorption in broadband molecular systems. (C) 2011 Elsevier B.V. All rights reserved.

Nonlinear refractive index of RECOB (RE = Gd and La) crystals

The Z-scan technique is employed to obtain the nonlinear refractive index (n (2)) of the Ca(4)REO(BO(3))(3) (RECOB, where RE = Gd and La) single crystals using 30 fs laser pulses centered at 780 nm for the two orthogonal orientations determined by the optical axes (X and Z) relative to the direction of propagation of the laser beam (k//Y// crystallographic b-axis). The large values of n (2) indicate that both GdCOB and LaCOB are potential hosts for Yb:RECOB lasers operating in the Kerr-lens mode locking (KLM) regime.