Symplectic Maps for Diverted Plasmas Caldas, Ibere Luiz; Bartoloni, Bruno F.; Ciro, David ...
IEEE transactions on plasma science,
2018-July, 2018-7-00, 2018-07-01, Letnik:
46, Številka:
7
Journal Article
Recenzirano
Odprti dostop
Nowadays, divertors are used in the main tokamaks to control the magnetic field and to improve the plasma confinement. In this paper, we present analytical symplectic maps describing Poincaré maps of ...the magnetic field lines in confined plasmas with a single-null poloidal divertor. Initially, we present a divertor map and the tokamap for a diverted configuration. We also introduce the Ullmann map for a diverted plasma, whose control parameters are determined from tokamak experiments. Finally, an explicit, area-preserving, and integrable magnetic field line map for a single-null divertor tokamak is obtained using a trajectory integration method to represent toroidal equilibrium magnetic surfaces. In this method, we also give examples of onset of chaotic field lines at the plasma edge due to resonant perturbations.
The geomagnetic field's dipole undergoes polarity reversals in irregular time intervals. Particularly long periods without reversals (of the order of 10^{7} yr), called superchrons, have occurred at ...least three times in the Phanerozoic (since 541 million years ago). We provide observational evidence for high non-Gaussianity in the vicinity of a transition to and from a geomagnetic superchron, consisting of a sharp increase in high-order moments (skewness and kurtosis) of the dipole's distribution. Such an increase in the moments is a universal feature of crisis-induced intermittency in low-dimensional dynamical systems undergoing global bifurcations. This implies a temporal variation of the underlying parameters of the physical system. Through a low-dimensional system that models the geomagnetic reversals, we show that the increase in the high-order moments during transitions to geomagnetic superchrons is caused by the progressive destruction of global periodic orbits exhibiting both polarities as the system approaches a merging bifurcation. We argue that the non-Gaussianity in this system is caused by the redistribution of the attractor around local cycles as global ones are destroyed.
In Hamiltonian systems subjected to periodic perturbations the stable and unstable manifolds of the unstable periodic orbits provide the dynamical "skeleton" that drives the mixing process and bounds ...the chaotic regions of the phase space. Determining the behavior of these objects is valuable in physical applications involving asymmetric solenoidal fields or time-dependent Hamiltonian systems. Here we introduce a simple method to calculate an unstable periodic orbit given an initial guess on its position. Then we present an efficient adaptive method to build its high-resolution invariant manifolds to arbitrary length and compare it to a random sampling method with the same computational cost. The adaptive method gives a high-quality representation of the manifolds and reveals fine details that become lost in the random sampling method. Finally, we introduce an approximation to the adaptive method to build the manifolds avoiding redundant calculations and reducing logarithmically the number of computations needed to represent these surfaces.
In this work we study the magnetic field modeling of realistic non-axisymmetric plasma equilibrium configurations and the heat flux patterns on the plasma facing components of tokamak divertor ...discharges. We start by establishing the relation between generic magnetic configurations and Hamiltonian dynamical systems. We apply the concept of magnetic helicity, used to establish topological bounds for the magnetic field lines in ideal plasmas, and to understand the self-consistency of reconnected magnetic surfaces in non-axisymmetric configurations. After this theoretical discussion, we present some results on magnetohydrodynamic equilibrium and the use of analytical solutions to the Grad-Shafranov equation for describing real tokamak discharges based on the experimental diagnostics and realistic boundary conditions. We also compare the equilibrium reconstruction of a DIII-D discharge obtained with a numerical reconstruction routine, developed as part of this research, and the EFIT code used by several tokamak laboratories around the world. The magnetic topology and plasma profiles obtained with our method are in considerable agreement with the numerical reconstruction performed with the other code. Then, we introduce a simplified description of the generic non-axisymmetric magnetic field created by known sources and implement it numerically for describing the magnetic field due to external coils in tokamak devices. After that, we use this routines to develop a numerical procedure to adjust a suitable set of non-linear parameters of internal filamentary currents, which are intended to model the plasma response based on the magnetic field measurements outside the plasma. Finally, these methods are used to model the magnetic field created by a slowly rotating plasma instability in a real DIII-D discharge. The plasma response modeling is based on the magnetic probe measurements and allow us to calculate the magnetic field in arbitrary locations near the plasma edge. Using this information we determine the non-axisymmetric plasma edge through the magnetic invariant manifolds routine developed during this work. The intersection of the calculated invariant manifold with the tokamak chamber agrees considerably well with the heat flux measurements for the same discharge at the divertor plates, indicating the development of a rotating manifold due to the internal asymmetric plasma currents, giving quantitative support to our simplified description of the magnetic field and the plasma edge definition through the invariant manifolds.
Neste trabalho estuda-se a modelagem do campo magnético em configurações realistas de plasmas em equilíbrio não-axissimétrico e o fluxo de calor nos componentes em contato com o plasma em descargas de tokamaks com desviadores poloidais. Começa-se estabelecendo a relação entre configurações magnéticas arbitrárias e sistemas dinâmicos Hamiltonianos. Então aplicamos o conceito de helicidade magnética, que é usado para estabelecer limitações topológicas sobre as linhas de campo magnético em plasmas ideais, assim como para compreender a auto-consistência das superfícies magnéticas reconectadas em configurações não-axissimétricas. Após esta discussão teórica, apresentam-se alguns resultados sobre o equilíbrio magnetohidrodinâmico e o uso de soluções analíticas à equação de Grad-Shafranov para descrever descargas reais em tokamaks, com base em diagnósticos experimentais e condições de contorno realistas. Também realiza-se uma comparação entre a reconstrução do equilíbrio de uma descarga do DIII-D, obtida mediante uma rotina numérica desenvolvida para esta pesquisa, com a obtida mediante o código EFIT, usado amplamente em diversos tokamaks. Após isso, apresenta-se uma descrição simplificada do campo magnético não-axissimétrico, criado por fontes determinadas, e a sua implementação para descrever o campo magnético devido às correntes externas em tokamaks. Então, usam-se estas rotinas para desenvolver um procedimento numérico que ajusta um conjunto adequado de parâmetros não-lineares de correntes filamentares internas, com as quais pretende-se modelar a resposta do plasma com base nas medidas de campo magnético fora do plasma. Finalmente, estes métodos são utilizados para modelar o campo magnético criado por uma instabilidade com rotação lenta numa descarga do DIII-D. Com base nas medidas das sondas magnéticas é possível modelar os campos criados em regiões arbitrárias próximas da borda do plasma. Usando esta informação é possível determinar a borda não-axissimétrica do plasma mediante as invariantes magnéticas calculadas com a utilização de uma rotina desenvolvida durante este trabalho. A intersecção da superfície invariante com a câmara do tokamak coincide satisfatoriamente com as medidas de fluxo de calor nas placas do divertor para a mesma descarga, indicando o desenvolvimento de uma variedade giratória criada pelas correntes de plasma não-axissimétricas, e sustentando quantitativamente a nossa descrição simplificada do campo magnético, assim como a definição da borda do plasma mediante as invariantes magnéticas.
It is shown that nonlocal interactions and phenomena can be achieved through local considerations, in which the departure of some scalar field from an harmonic one in a point changes as a function of ...the field itself in such point. After discretizing the equation of motion, it is shown that the shape of the nonlocal interaction function depends deeply on the choice of boundary conditions. As a physical implementation, the found interactions describes the evolution for the inductively coupled nonlinear networks. A qualitative analysis suggests that under such interactions the system self-organizes quite naturally, finally this is evidenced through the numerical solution of the equations of motion in the case of local cubic nonlinearities for two different boundary conditions.
The figure of the 'other' is fundamental to the concept of communication. Online or offline, communication, which is commonly defined as the act of sending or imparting information to others, is only ...possible in the face of others. In fact, the reason we communicate is to interact with others—to talk to another, to share our thoughts and insights with them, or to respond to their needs and requests. No matter how it is structured or conceptualized, communication is involved with addressing the other and dealing with the ontological, epistemological, and ethical questions of otherness or alterity. But who or what can be other? Who or what can be the subject of communication? Is the other always and only another human? Or can the other in these communicative interactions be otherwise? This book is about others (and other kinds of others). It concerns the current position and status of the other in the face of technological innovations that can, in one way or another distort, mask, or even deface the other. Ten innovative essays, written by an international team of experts, individually and in collaboration with each other, seek to diagnose the current situation with otherness, devise innovative solutions to the questions of alterity, and provide insight for students, teachers and researchers trying to make sense of the opportunities and challenges of the 21st century.
Atmospheric blockings are persistent large-scale climate patterns with duration between days and weeks. In principle, blockings might involve a large number of modes interacting non-linearly, and a ...conclusive description for their onset and duration is still elusive. In this paper we introduce a simplified account for this phenomena by means of a single-triad of Rossby-Hawritz waves perturbed by one topography mode. It is shown that the dynamical features of persistent atmospheric patterns have zero measure in the phase space of an unperturbed triad, but such measure becomes finite for the perturbed dynamics. By this account we suggest that static inhomogeneities in the two-dimensional atmospheric layer are required for locking flow patterns in real space.
Eur. Phys. J. Special Topics 229, 1507 (2020) Stickiness is a well known phenomenon in which chaotic orbits expend an
expressive amount of time in specific regions of the chaotic sea. This
phenomenon ...becomes important when dealing with area-preserving open systems
because, in this case, it leads to a temporary trapping of orbits in certain
regions of phase space. In this work, we propose that the different scenarios
of dynamical trapping can be explained by analyzing the crossings between
invariant manifolds. In order to corroborate this assertion, we use an adaptive
refinement procedure to approximately obtain the sets of homoclinic and
heteroclinic intersections for the area-preserving H\'enon map, an archetype of
open systems, for a generic parameter interval. We show that these sets have
very different statistical properties when the system is highly influenced by
dynamical trapping, whereas they present similar properties when stickiness is
almost absent. We explain these different scenarios by taking into
consideration various effects that occur simultaneously in the system, all of
which are connected with the topology of the invariant manifolds.
The changeover from normal to super diffusion in time dependent billiards is explained analytically. The unlimited energy growth for an ensemble of bouncing particles in time dependent billiards is ...obtained by means of a two dimensional mapping of the first and second moments of the velocity distribution function. We prove that for low initial velocities the mean velocity of the ensemble grows with exponent ~1/2 of the number of collisions with the border, therefore exhibiting normal diffusion. Eventually, this regime changes to a faster growth characterized by an exponent ~1 corresponding to super diffusion. For larger initial velocities, the temporary symmetry in the diffusion of velocities explains an initial plateau of the average velocity.
PDF
