Related papers: Classification of Orbits in Poincar\'e Maps using …
Many important qualities of plasma confinement devices can be determined via the Poincar\'e plot of a symplectic return map. These qualities include the locations of periodic orbits, magnetic islands, and chaotic regions of phase space.…
Nowadays, divertors are used in the main tokamaks to control the magnetic field and to improve the plasma confinement. In this article, we present analytical symplectic maps describing Poincar\'e maps of the magnetic field lines in confined…
Poincar\'e maps for toroidal magnetic fields are routinely employed to study gross confinement properties in devices built to contain hot plasmas. In most practical applications, evaluating a Poincar\'e map requires numerical integration of…
Tokamak plasmas are confined by a magnetic field that limits the particle and heat transport perpendicular to the field. Parallel to the field the ionised particles can move freely, so to obtain confinement the field lines are "closed" (ie.…
The confinement of plasmas in tokamaks and stellarators depends on magnetic field lines lying in nested toroidal surfaces. The transition near the plasma edge away from the lines lying in magnetic surfaces defines properties of divertors.…
Experimental diagnostics, analysis tools and simulations represent particle distributions in various forms and coordinates. Algorithms to manage these data are needed on platforms like the ITER Integrated Modelling & Analysis Suite (IMAS),…
In magnetically confined plasma, it is possible to qualitatively describe the magnetic field configuration via phase spaces of suitable symplectic maps. These phase spaces are of mixed type, where chaos coexists with regular motion, and the…
It is shown that applying manifold learning techniques to Poincar\'e sections of high-dimensional, chaotic dynamical systems can uncover their low-dimensional topological organization. Manifold learning provides a low-dimensional embedding…
The paper suggests certain regimes of fusion plasma with magnetic confinement, when the Larmor radius $\lambda$ and the angle $\alpha$ (determining the orientation of the local coordinates) form an analytic function $w=\lambda e^{i\alpha}$…
Topological analysis of the magnetic field in simulated plasmas allows the study of various physical phenomena in a wide range of settings. One such application is magnetic reconnection, a phenomenon related to the dynamics of the magnetic…
The accurate construction of tokamak equilibria, which is critical for the effective control and optimization of plasma configurations, depends on the precise distribution of magnetic fields and magnetic fluxes. Equilibrium fitting codes,…
Despite many of the most common chaotic dynamical systems being continuous in time, it is through discrete time mappings that much of the understanding of chaos is formed. Henri Poincar\'e first made this connection by tracking consecutive…
The emergence and dynamics of filamentary structures associated with edge-localized modes (ELMs) inside tokamak plasmas during high-confinement mode is regularly studied using Electron Cyclotron Emission Imaging (ECEI) diagnostic systems.…
Poincar\'e maps play a fundamental role in nonlinear dynamics and chaos theory, offering a means to reduce the dimensionality of continuous dynamical systems by tracking the intersections of trajectories with lower-dimensional section…
This overview presents a tutorial introduction to the theory of magnetic plasma confinement in toroidal confinement systems with particular emphasis on axisymmetric equilibrium geometries, and tokamaks. The discussion covers three important…
Studying 2 degree-of-freedom (DOF) Hamiltonian dynamical systems often involves the computation of stable & unstable manifolds of periodic orbits, due to the homoclinic & heteroclinic connections they can generate. Such study is generally…
This study extends the functional perturbation theory~(FPT) of dynamical systems, which was initially developed for investigating the shifts of magnetic field line trajectories within the chaotic edge region of plasma when subjected to…
In this work, we propose a novel physics informed neural network based algorithm for real time plasma boundary reconstruction in tokamak devices. The approach is based on a single Extreme Learning Machine network used to solve the…
Chaotic transport is related to the complex dynamical evolution of chaotic trajectories in Hamiltonian systems, which models various physical processes. In magnetically confined plasma, it is possible to qualitatively describe the…
In this work, we provide an overview of various control strategies aimed at steering plasma toward desired configurations using an external magnetic field. From a modeling perspective, we focus on the Vlasov equation in a two-dimensional…