Related papers: Classification of Orbits in Poincar\'e Maps using …
A new class of static magnetohydrodynamic (MHD) magnetic island bifurcations is identified in rotating spherical tokamak plasmas during single- and two-fluid resistive MHD simulations. As the magnitude of an externally applied…
The Poincar\'e map is widely used to study the qualitative behavior of dynamical systems. For instance, it can be used to describe the existence of periodic solutions. The Poincar\'e map for dynamical systems with impulse effects was…
In the presented field line map approach the simulation domain of a tokamak is covered with a cylindrical grid, which is Cartesian within poloidal planes. Standard finite-difference methods can be used for the discretisation of…
The penalization method is used to take account of obstacles, such as the limiter, in a tokamak. Because of the magnetic confinement of the plasma in a tokamak, the transport occurs essentially in the direction parallel to the magnetic…
This work is concerned with planar real analytic differential systems with an analytic inverse integrating factor defined in a neighborhood of a regular orbit. We show that the inverse integrating factor defines an ordinary differential…
Statistics of Poincar\' e recurrence for a class of circle maps, including sub-critical, critical, and super-critical cases, are studied. It is shown how the topological differences in the various types of the dynamics are manifested in the…
Three novel applications of computational topology in the field of fusion science are developed. A procedure for the automatic classification of the orbits of magnetic field lines into topologically distinct classes using Vietoris-Rips…
In this paper, a method to construct topological template in terms of symbolic dynamics for the diamagnetic Kepler problem is proposed. To confirm the topological template, rotation numbers of invariant manifolds around unstable periodic…
We are interested in arrangements of circles and the regions surrounded by them. {\it Poincar\'e-Reeb graphs} have been fundamental and strong tools in studying shapes of regions surrounded by real algebraic curves, since around 2020. They…
The available magnetic field data from the terrestrial magnetosphere, solar wind and planetary magnetospheres exceeds over $10^6$ hours. Identifying plasma waves in these large data sets is a time consuming and tedious process. In this…
Fusion-graded plasmas are one of the physically complex systems, resulting in continuous establishment of plasma theories for unclarified physical phenomena in order to thoroughly control nuclear fusion reactors. Deep learning has drawn…
This paper deals with fundamental properties of Poincar\'e half-maps defined on a straight line for planar linear systems. Concretely, we focus on the analyticity of the Poincar\'e half-maps, their series expansions (Taylor and…
In order to identify complicated systems, more prominent and promising methods are needed among which we may refer to fractional order differential equations. The aim of this paper is to propose a fractional order nonlinear model to predict…
Self-consistent equations for intrinsic rotation in tokamaks with small poloidal magnetic field $B_p$ compared to the total magnetic field $B$ are derived. The model gives the momentum redistribution due to turbulence, collisional transport…
In the quest for controlled thermonuclear fusion, tokamaks present complex challenges in understanding burning plasma dynamics. This study introduces a multi-region multi-timescale transport model, employing Neural Ordinary Differential…
The method of using neural networks (NNs) for turbulent transport prediction in a simplified model of tokamak plasmas is explored. The NNs are trained on a database obtained via test-particle simulations of a transport model in the…
Mission designers must study many dynamical models to plan a low-cost spacecraft trajectory that satisfies mission constraints. They routinely use Poincar\'e maps to search for a suitable path through the interconnected web of periodic…
Analytic results for (Q)ED processes in external fields are limited to a few special cases, such as plane waves. However, the strong focussing of intense laser fields implies a need to go beyond the plane wave model. By exploiting…
We present various techniques that make orbit-following Monte Carlo simulations faster and more reliable when assessing collisionless fast particle losses due to magnetic field perturbations. These techniques are based on identifying…
The growing amount of data produced by simulations and observations of space physics processes encourages the use of methods rooted in Machine Learning for data analysis and physical discovery. We apply a clustering method based on…