Integrable maps with non-trivial topology: application to divertor configurations

We explore a method for constructing two-dimensional area-preserving, integrable maps associated with Hamiltonian systems, with a given set of fixed points and given invariant curves. The method is used to find an integrable Poincare map for the field lines in a large aspect ratio tokamak with a poloidal single-null divertor. The divertor field is a superposition of a magnetohydrodynamic equilibrium with an arbitrarily chosen safety factor profile, with a wire carrying an electric current to create an X-point. This integrable map is perturbed by an impulsive perturbation that describes non-axisymmetric magnetic resonances at the plasma edge. The non-integrable perturbed map is applied to study the structure of the open field lines in the scrape-off layer, reproducing the main transport features obtained by integrating numerically the magnetic field line equations, such as the connection lengths and magnetic footprints on the divertor plate.

Chaotic transport in reversed shear tokamaks

For tokamak models using simplified geometries and reversed shear plasma profiles, we have numerically investigated how the onset of Lagrangian chaos at the plasma edge may affect the plasma confinement in two distinct but closely related problems. Firstly, we have considered the motion of particles in drift waves in the presence of an equilibrium radial electric field with shear. We have shown that the radial particle transport caused by this motion is selective in phase space, being determined by the resonant drift waves and depending on the parameters of both the resonant waves and the electric field profile. Moreover, we have shown that an additional transport barrier may be created at the plasma edge by increasing the electric field. In the second place, we have studied escape patterns and magnetic footprints of chaotic magnetic field lines in the region near a tokamak wall, when there are resonant modes due to the action of an ergodic magnetic limiter. A non-monotonic safety factor profile has been used in the analysis of field line topology in a region of negative magnetic shear. We have observed that, if internal modes are perturbed, the distributions of field line connection lengths and magnetic footprints exhibit spatially localized escape channels. For typical physical parameters of a fusion plasma, the two Lagrangian chaotic processes considered in this work can be effective in usual conditions so as to influence plasma confinement. The reversed shear effects discussed in this work may also contribute to evaluate the transport barrier relevance in advanced confinement scenarios in future tokamak experiments.

Plasma confinement in tokamaks with robust torus

We present a non-linear symplectic map that describes the alterations of the magnetic field lines inside the tokamak plasma due to the presence of a robust torus (RT) at the plasma edge. This RT prevents the magnetic field lines from reaching the tokamak wall and reduces, in its vicinity, the islands and invariant curve destruction due to resonant perturbations. The map describes the equilibrium magnetic field lines perturbed by resonances created by ergodic magnetic limiters (EMLs). We present the results obtained for twist and non-twist mappings derived for monotonic and non-monotonic plasma current density radial profiles, respectively. Our results indicate that the RT implementation would decrease the field line transport at the tokamak plasma edge. (C) 2010 Elsevier B.V. All rights reserved.

Mean Motion in Stochastic Plasmas With a Space-Dependent Diffusion Coefficient

Radial transport in the tokamap, which has been proposed as a simple model for the motion in a stochastic plasma, is investigated. A theory for previous numerical findings is presented. The new results are stimulated by the fact that the radial diffusion coefficients is space-dependent. The space-dependence of the transport coefficient has several interesting effects which have not been elucidated so far. Among the new findings are the analytical predictions for the scaling of the mean radial displacement with time and the relation between the Fokker-Planck diffusion coefficient and the diffusion coefficient from the mean square displacement. The applicability to other systems is also discussed. (c) 2009 WILEY-VCH GmbH & Co. KGaA, Weinheim

Needleless electrospinning. I. A comparison of cylinder and disk nozzles

In this study, we demonstrated the needleless electrospinning of poly(vinyl alcohol) (PVA) nanofibers with two nozzles, a rotating disk and a cylinder, and examined the effect of the nozzle shape on the electrospinning process and resultant fiber morphology. The disk nozzle needed a relatively low applied voltage to initiate fiber formation, and the fibers were mainly formed on the top disk edge. Also, the PVA concentration had little influence on the disk electrospinning process (up to 11 wt %). In comparison, the cylinder electrospinning showed a higher dependence on the applied voltage and polymer concentration. The fibers were initiated from the cylinder ends first and then from the entire cylinder surface only if the applied voltage were increased to a certain level. With the same polymer solution, the critical voltage needed to generate nanofibers from the disk nozzle was lower than that needed to generate nanofibers from the cylinder. Both electrospinning systems could produce uniform nanofibers, but the fibers produced from the disk nozzle were finer than those from the cylinder when the operating conditions were the same. A thin disk (8 cm in diameter and 2 mm thick) could produce nanofibers at a rate similar to that of a cylinder of the same diameter but 100 times wider (i.e., 20 cm long). Finite element analysis of electric field profiles of the nozzles revealed a concentrated electric field on the disk edge. For the cylinder nozzle, an uneven distribution of the electric field intensity profile along the nozzle surface was observed. The field lines were mainly concentrated on the cylinder ends, with a much lower electric field intensity formed in the middle surface area. At the same applied voltage, the electric field intensity on the disk edge was much higher than that on the cylinder end. These differences in the electric field intensity profiles could explain the differences in the fiber fineness and rate of the nanofibers produced from these two nozzles. These findings will benefit the design and further development of large-scale electrospinning systems for the mass production of nanofibers for advanced applications.

Particle trapping using dielectrophoretically patterned carbon nanotubes

This study presents the dielectrophoretic (DEP) assembly of multi-walled carbon nanotubes (MWCNTs) between curved microelectrodes for the purpose of trapping polystyrene microparticles within a microfluidic system. Under normal conditions, polystyrene particles exhibit negative DEP behaviour and are repelled from microelectrodes. Interestingly, the addition of MWCNTs to the system alters this situation in two ways: first, they coat the surface of particles and change their dielectric properties to exhibit positive DEP behaviour; second, the assembled MWCNTs are highly conductive and after the deposition serve as extensions to the microelectrodes. They establish an array of nanoelectrodes that initiates from the edge of microelectrodes and grow along the electric field lines. These nanoelectrodes can effectively trap the MWCNT-coated particles, since they cover a large portion of the microchannel bottom surface and also create a much stronger electric field than the primary microelectrodes as confirmed by our numerical simulations. We will show that the presence of MWCNT significantly changes performance of the system, which is investigated by trapping sample polystyrene particles with plain, COOH and goat anti-mouse IgG surfaces.

Alternative Model of Three-Phase Transmission Line Theory-Based Modal Decomposition

In this paper is shown the development of a transmission line, based on discrete circuit elements that provide responses directly in the time domain and phase. This model is valid for ideally transposed rows represent the phases of each of the small line segments are separated in their modes of propagation and the voltage and current are calculated at the modal field. However, the conversion phase-mode-phase is inserted in the state equations which describe the currents and voltages along the line of which there is no need to know the user of the model representation of the theory in the field lines modal.

SPH simulations of clumps formation by dissipative collisions of molecular clouds - II. Magnetic case

We performed computer simulations of interstellar cloud-cloud collisions using the three-dimensional smoothed particle magnetohydrodynamics method. In order to study the role of the magnetic field on the process of collision-triggered fragmentation, we focused our attention on head-on supersonic collisions between two identical spherical molecular-clouds. Two extreme configurations of the magnetic field were adopted: parallel and perpendicular to the initial clouds motion. The initial magnetic field strength was approximately 12.0 muG. In the parallel case, much more of the collision debris were retained in the shocking region than in the non-magnetic case where gas escaped freely throughout the symmetry plane. Differently from the non-magnetic case, eddy-like vortices were formed. The regions of highest vorticity and the the regions of highest density are offset. We found clumps formation only in the parallel case, however, they were larger, hotter and less dense than in the analogous non-magnetic case. In the perpendicular case, the compressed field works as a magnetic wall, preventing a stronger compression of the colliding clouds. This last effect inhibits direct contact of the two clouds. In both cases, we found that the field lines show a chaotic aspect in large scales. Also, the field magnitude is considerably amplified in the shock layer. However, the field distribution is almost coherent in the higher density regions.

The non-twist standard map with robust tori

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Plasma confinement in tokamaks with robust torus

We present a non-linear symplectic map that describes the alterations of the magnetic field lines inside the tokamak plasma due to the presence of a robust torus (RT) at the plasma edge. This RT prevents the magnetic field lines from reaching the tokamak wall and reduces, in its vicinity, the islands and invariant curve destruction due to resonant perturbations. The map describes the equilibrium magnetic field lines perturbed by resonances created by ergodic magnetic limiters (EMLs). We present the results obtained for twist and non-twist mappings derived for monotonic and non-monotonic plasma current density radial profiles, respectively. Our results indicate that the RT implementation would decrease the field line transport at the tokamak plasma edge. © 2010 Elsevier B.V. All rights reserved.

Diagnostics of equatorial and low latitude ionosphere by TEC mapping over Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Analysis on the formation of a FRC by flux measurements and MHD simulations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Reconnection current sheet structure in a turbulent medium

In the presence of turbulence, magnetic field lines lose their dynamical identity and particles entrained on field lines diffuse through space at a rate determined by the amplitude of the turbulence. In previous work (Lazarian and Vishniac, 1999; Kowal et al., 2009; Eyink et al., 2011) we showed that this leads to reconnection speeds which are independent of resistivity. In particular, in Kowal et al. (2009) we showed that numerical simulations were consistent with the predictions of this model. Here we examine the structure of the current sheet in simulations of turbulent reconnection. Laminar flows consistent with the Sweet-Parker reconnection model produce very thin and well ordered currents sheets. On the other hand, the simulations of Kowal et al. (2009) show a strongly disordered state even for relatively low levels of turbulence. Comparing data cubes with and without reconnection, we find that large scale field reversals are the cumulative effect of many individual eddies, each of which has magnetic properties which are not very different from turbulent eddies in a homogeneous background. This implies that the properties of stationary and homogeneous MHD turbulence are a reasonable guide to understanding turbulence during large scale magnetic reconnection events. In addition, dissipation and high energy particle acceleration during reconnection events take place over a macroscopic volume, rather than being confined to a narrow zone whose properties depend on microscopic transport coefficients.

Effective transport barriers in nontwist systems

In fluids and plasmas with zonal flow reversed shear, a peculiar kind of transport barrier appears in the shearless region, one that is associated with a proper route of transition to chaos. These barriers have been identified in symplectic nontwist maps that model such zonal flows. We use the so-called standard nontwist map, a paradigmatic example of nontwist systems, to analyze the parameter dependence of the transport through a broken shearless barrier. On varying a proper control parameter, we identify the onset of structures with high stickiness that give rise to an effective barrier near the broken shearless curve. Moreover, we show how these stickiness structures, and the concomitant transport reduction in the shearless region, are determined by a homoclinic tangle of the remaining dominant twin island chains. We use the finite-time rotation number, a recently proposed diagnostic, to identify transport barriers that separate different regions of stickiness. The identified barriers are comparable to those obtained by using finite-time Lyapunov exponents.

Shearless transport barriers in magnetically confined plasmas

Shearless transport barriers appear in confined plasmas due to non-monotonic radial profiles and cause localized reduction of transport even after they have been broken. In this paper we summarize our recent theoretical and experimental research on shearless transport barriers in plasmas confined in toroidal devices. In particular, we discuss shearless barriers in Lagrangian magnetic field line transport caused by non-monotonic safety factor profiles. We also discuss evidence of particle transport barriers found in the TCABR Tokamak (University of Sao Paulo) and the Texas Helimak (University of Texas at Austin) in biased discharges with non-monotonic plasma flows.