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.

Transport control in fusion plasmas by changing electric and magnetic field spatial profiles

For magnetically confined plasmas in tokamaks, we have numerically investigated how Lagrangian chaos at the plasma edge affects the plasma confinement. Initially, we have considered the chaotic motion of particles in an equilibrium electric field with a monotonic radial profile perturbed by drift waves. We have showed that an effective transport barrier may be created at the plasma edge by modifying the electric field radial profile. In the second place, we have obtained escape patterns and magnetic footprints of chaotic magnetic field lines in the region near a tokamak wall with resonant modes due to the action of an ergodic magnetic limiter. For monotonic plasma current density profiles we have obtained distributions of field line connections to the wall and line escape channels with the same spatial pattern as the magnetic footprints on the tokamak walls. (c) 2008 Elsevier B.V. All rights reserved.

Nontwist symplectic maps in tokamaks

We review symplectic nontwist maps that we have introduced to describe Lagrangian transport properties in magnetically confined plasmas in tokamaks. These nontwist maps are suitable to describe the formation and destruction of transport barriers in the shearless region (i.e., near the curve where the twist condition does not hold). The maps can be used to investigate two kinds of problems in plasmas with non-monotonic field profiles: the first is the chaotic magnetic field line transport in plasmas with external resonant perturbations. The second problem is the chaotic particle drift motion caused by electrostatic drift waves. The presented analytical maps, derived from plasma models with equilibrium field profiles and control parameters that are commonly measured in plasma discharges, can be used to investigate long-term transport properties. (C) 2011 Elsevier B.V. All rights reserved.

Self-organized criticality in MHD driven plasma edge turbulence

We analyze long-range time correlations and self-similar characteristics of the electrostatic turbulence at the plasma edge and scrape-off layer in the Tokamak Chauffage Alfven Bresillien (TCABR), with low and high Magnetohydrodynamics (MHD) activity. We find evidence of self-organized criticality (SOC), mainly in the region near the tokamak limiter. Comparative analyses of data before and during the MHD activity reveals that during the high mHD activity the Hurst parameter decreases. Finally, we present a cellular automaton whose parameters are adjusted to simulate the analyzed turbulence SOC change with the MHD activity variation. (C) 2011 Published by Elsevier B.V.

Controle de dinâmica caótica com toros robustos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On a mathematical model arising in MHD perturbed equilibrium for Stellarator devices. A numerical approach.

Abstract?We consider a mathematical model related to the stationary regime of a plasma of fusion nuclear, magnetically confined in a Stellarator device. Using the geometric properties of the fusion device, a suitable system of coordinates and averaging methods, the mathematical problem may be reduced to a two dimensional free boundary problem of nonlocal type, where the corresponding differential equation is of the Grad?Shafranov type. The current balance within each flux magnetic gives us the possibility to define the third covariant magnetic field component with respect to the averaged poloidal flux function. We present here some numerical experiences and we give some numerical approach for the averaged poloidal flux and for the third covariant magnetic field component.

On the free-boundary for an elliptic inverse nonlocal problem arising in the nuclear fusion. A numerical approach

We consider a mathematical model related to the stationary regime of a plasma magnetically confined in a Stellarator device in the nuclear fusion. The mathematical problem may be reduced to an nonlinear elliptic inverse nonlocal two dimensional free{boundary problem. The nonlinear terms involving the unknown functions of the problem and its rearrangement. Our main goal is to determinate the existence and the estimate on the location and size of region where the solution is nonnegative almost everywhere (corresponding to the plasma region in the physical model)

Anisotropy of thermal stresses in confined dusty plasmas

Anisotropy of thermal stresses in confined dusty plasmas is considered. It is shown that in a multi-component low-temperature plasma containing electrons, ions and dust, the complicated dependence of the ion viscosity on ion temperature gradients leads to a plasma equilibrium state with anisotropic pressure. This pressure anisotropy can be of the order of the ion pressure in some limiting cases, in which the ion Larmor radius or the ion mean free path are of the order of the characteristic length of the plasma nonuniformity. For a sufficiently large dust number density, they contribute to the plasma pressure anisotropy and to its spatial dependence. Currently, it is not yet clear whether this equilibrium state is stable or not. Under these conditions, some convective plasma flows can arise in confinement devices. Therefore, this question needs special consideration.

Local moderate magnetically induced hyperthermia using an implant formed in situ in a mouse tumor model.

Purpose: We investigate a new heat delivery technique for the local treatment of solid tumors. The technique involves injecting a formulation that solidifies to form an implant in situ. This implant entraps superparamagnetic iron oxide nanoparticles (SPIONs) embedded in silica microbeads for magnetically induced moderate hyperthermia. Particle entrapment prevents phagocytosis and distant migration of SPIONs. The implant can be repeatedly heated by magnetic induction. Methods: We evaluated heating and treatment efficacies by means of thermometry and survival studies in nude mice carrying subcutaneous human colocarcinomas. At day 1, we injected the formulation into the tumor. At day 2, a single 20-min hyperthermia treatment was delivered by 141-kHz magnetic induction using field strengths of 9 to 12 mT under thermometry. Results: SPIONs embedded in silica microbeads were effectively confined within the implant at the injection site. Heat-induced necro-apoptosis was assessed by histology on day 3. On average, 12 mT resulted in tumor temperature of 47.8 degrees C, and over 70% tumor necrosis that correlated to the heat dose (AUC = 282 degrees C.min). In contrast, a 9-mT field strength induced tumoral temperature of 40 degrees C (AUC = 131 degrees C.min) without morphologically identifiable necrosis. Survival after treatment with 10.5 or 12 mT fields was significantly improved compared to non-implanted and implanted controls. Median survival times were 27 and 37 days versus 12 and 21 days respectively. Conclusion: Five of eleven mice (45%) of the 12 mT group survived one year without any tumor recurrence, holding promise for tumor therapy using magnetically induced moderate hyperthermia through injectable implants.

Relativistic high-current electron-beam stopping-power characterization in solids and plasmas: collisional versus resistive effects.

We present experimental and numerical results on intense-laser-pulse-produced fast electron beams transport through aluminum samples, either solid or compressed and heated by laser-induced planar shock propagation. Thanks to absolute K� yield measurements and its very good agreement with results from numerical simulations, we quantify the collisional and resistive fast electron stopping powers: for electron current densities of � 8 � 1010 A=cm2 they reach 1:5 keV=�m and 0:8 keV=�m, respectively. For higher current densities up to 1012 A=cm2, numerical simulations show resistive and collisional energy losses at comparable levels. Analytical estimations predict the resistive stopping power will be kept on the level of 1 keV=�m for electron current densities of 1014 A=cm2, representative of the full-scale conditions in the fast ignition of inertially confined fusion targets.

Direct Vlasov simulations of electron-attracting cylindrical Langmuir probes in flowing plasmas

Current collection by positively polarized cylindrical Langmuir probes immersed in flowing plasmas is analyzed using a non-stationary direct Vlasov-Poisson code. A detailed description of plasma density spatial structure as a function of the probe-to-plasma relative velocity U is presented. Within the considered parametric domain, the well-known electron density maximum close to the probe is weakly affected by U. However, in the probe wake side, the electron density minimum becomes deeper as U increases and a rarified plasma region appears. Sheath radius is larger at the wake than at the front side. Electron and ion distribution functions show specific features that are the signature of probe motion. In particular, the ion distribution function at the probe front side exhibits a filament with positive radial velocity. It corresponds to a population of rammed ions that were reflected by the electric field close to the positively biased probe. Numerical simulations reveal that two populations of trapped electrons exist: one orbiting around the probe and the other with trajectories confined at the probe front side. The latter helps to neutralize the reflected ions, thus explaining a paradox in past probe theory.

Turbulence in collisionless plasmas: statistical analysis from numerical simulations with pressure anisotropy

In recent years, we have experienced increasing interest in the understanding of the physical properties of collisionless plasmas, mostly because of the large number of astrophysical environments (e. g. the intracluster medium (ICM)) containing magnetic fields that are strong enough to be coupled with the ionized gas and characterized by densities sufficiently low to prevent the pressure isotropization with respect to the magnetic line direction. Under these conditions, a new class of kinetic instabilities arises, such as firehose and mirror instabilities, which have been studied extensively in the literature. Their role in the turbulence evolution and cascade process in the presence of pressure anisotropy, however, is still unclear. In this work, we present the first statistical analysis of turbulence in collisionless plasmas using three-dimensional numerical simulations and solving double-isothermal magnetohydrodynamic equations with the Chew-Goldberger-Low laws closure (CGL-MHD). We study models with different initial conditions to account for the firehose and mirror instabilities and to obtain different turbulent regimes. We found that the CGL-MHD subsonic and supersonic turbulences show small differences compared to the MHD models in most cases. However, in the regimes of strong kinetic instabilities, the statistics, i.e. the probability distribution functions (PDFs) of density and velocity, are very different. In subsonic models, the instabilities cause an increase in the dispersion of density, while the dispersion of velocity is increased by a large factor in some cases. Moreover, the spectra of density and velocity show increased power at small scales explained by the high growth rate of the instabilities. Finally, we calculated the structure functions of velocity and density fluctuations in the local reference frame defined by the direction of magnetic lines. The results indicate that in some cases the instabilities significantly increase the anisotropy of fluctuations. These results, even though preliminary and restricted to very specific conditions, show that the physical properties of turbulence in collisionless plasmas, as those found in the ICM, may be very different from what has been largely believed.

Comparative electron temperature measurements of Thomson scattering and electron cyclotron emission diagnostics in TCABR plasmas

We present the first simultaneous measurements of the Thomson scattering and electron cyclotron emission radiometer diagnostics performed at TCABR tokamak with Alfven wave heating. The Thomson scattering diagnostic is an upgraded version of the one previously installed at the ISTTOK tokamak, while the electron cyclotron emission radiometer employs a heterodyne sweeping radiometer. For purely Ohmic discharges, the electron temperature measurements from both diagnostics are in good agreement. Additional Alfven wave heating does not affect the capability of the Thomson scattering diagnostic to measure the instantaneous electron temperature, whereas measurements from the electron cyclotron emission radiometer become underestimates of the actual temperature values. (C) 2010 American Institute of Physics. [doi:10.1063/1.3494379]

Alfveacuten continuum deformation by kinetic geodesic effect in rotating tokamak plasmas

Using a quasitoroidal set of coordinates with coaxial circular magnetic surfaces, Vlasov equation is solved for collisionless plasmas in drift approach and a perpendicular dielectric tensor is found for large aspect ratio tokamaks in a low frequency band. Taking into account plasma rotation and charge separation parallel electric field, it is found that an ion geodesic effect deform Alfveacuten wave continuum producing continuum minimum at the rational magnetic surfaces, which depends on the plasma rotation and poloidal mode numbers. In kinetic approach, the ion thermal motion defines the geodesic effect but the mode frequency also depends on electron temperature. A geodesic ion Alfveacuten mode predicted below the continuum minimum has a small Landau damping in plasmas with Maxwell distribution but the plasma rotation may drive instability.

Melting and freezing of spherical bismuth nanoparticles confined in a homogeneous sodium borate glass

The melting temperature and the crystallization temperature of Bi nanoclusters confined in a sodium borate glass were experimentally determined as functions of the cluster radius. The results indicate that, on cooling, liquid Bi nanodroplets exhibit a strong undercooling effect for a wide range of radii. The difference between the melting temperature and the freezing temperature decreases for decreasing radius and vanishes for Bi nanoparticles with a critical radius R = 1.9 nm. The magnitude of the variation in density across the melting and freezing transitions for Bi nanoparticles with R = 2 nm is 40% smaller than for bulk Bi. These experimental results support a basic core-shell model for the structure of Bi nanocrystals consisting of a central crystalline volume surrounded by a structurally disordered shell. The volume fraction of the crystalline core decreases for decreasing nanoparticle radius and vanishes for R = 1.9 nm. Thus, on cooling, the liquid nanodroplets with R < 1.9 nm preserve, across the liquid-to-solid transformation, their homogeneous and disordered structure without crystalline core.