Hamiltonian chaos: from galactic dynamics to plasma physics
| dc.contributor.advisor | Skokos, Haris | |
| dc.contributor.author | Tenaw , Henok | |
| dc.date.accessioned | 2025-12-18T07:49:07Z | |
| dc.date.available | 2025-12-18T07:49:07Z | |
| dc.date.issued | 2025 | |
| dc.date.updated | 2025-12-18T07:45:31Z | |
| dc.description.abstract | The primary focus of this thesis is the numerical investigation of the influence of chaos in Hamiltonian models describing the behavior of charged particle orbits in plasma, the motion of stars in barred galaxies, and the diffusion of trajectories in multidimensional maps. First, we systematically explore the interplay between magnetic and kinetic chaos in toroidal fusion plasmas, where non-axisymmetric perturbations disrupt smooth magnetic flux surfaces, generating complex particle trajectories. Using the Generalized Alignment Index (GALI) method of chaos detection, we efficiently quantify chaos, compare the behavior of magnetic field lines and particle orbits, visualize the radial distribution of chaotic regions, and offer the GALI method as a valuable tool for studying the dynamics of plasma physics models. Next, we study the evolution of phase space structures in a three-dimensional (3D) barred galactic potential, following successive 2D and 3D pitchfork and period-doubling bifurcations of periodic orbits. By employing the so-called 'color and rotation' technique to visualize the four-dimensional Poincare surface ยด of sections of the system, we reveal distinct structural patterns. We further investigate the long-term diffusion transport and chaos properties of single and coupled standard maps, focusing on parameters that induce anomalous diffusion through the presence of accelerator modes exhibiting ballistic transport. Using different ensembles of initial conditions in chaotic regions influenced by these modes, we examine asymptotic diffusion rates and their corresponding time scales, identifying conditions that suppress anomalous transport and lead to long-term convergence to normal diffusion across various coupled map arrangements. Lastly, we perform the first comprehensive investigation into the behavior of the GALI indices for various attractors in continuous and discrete-time dissipative systems, extending the application of the method to non-Hamiltonian systems. A key aspect of our work involves analyzing and comparing the performance of the GALI method with the computation of Lyapunov Exponents for non-Hamiltonian dissipative systems exhibiting hyperchaotic motion. | |
| dc.identifier.apacitation | Tenaw , H. (2025). <i>Hamiltonian chaos: from galactic dynamics to plasma physics</i>. (). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/42450 | en_ZA |
| dc.identifier.chicagocitation | Tenaw , Henok. <i>"Hamiltonian chaos: from galactic dynamics to plasma physics."</i> ., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2025. http://hdl.handle.net/11427/42450 | en_ZA |
| dc.identifier.citation | Tenaw , H. 2025. Hamiltonian chaos: from galactic dynamics to plasma physics. . University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. http://hdl.handle.net/11427/42450 | en_ZA |
| dc.identifier.ris | TY - Thesis / Dissertation AU - Tenaw , Henok AB - The primary focus of this thesis is the numerical investigation of the influence of chaos in Hamiltonian models describing the behavior of charged particle orbits in plasma, the motion of stars in barred galaxies, and the diffusion of trajectories in multidimensional maps. First, we systematically explore the interplay between magnetic and kinetic chaos in toroidal fusion plasmas, where non-axisymmetric perturbations disrupt smooth magnetic flux surfaces, generating complex particle trajectories. Using the Generalized Alignment Index (GALI) method of chaos detection, we efficiently quantify chaos, compare the behavior of magnetic field lines and particle orbits, visualize the radial distribution of chaotic regions, and offer the GALI method as a valuable tool for studying the dynamics of plasma physics models. Next, we study the evolution of phase space structures in a three-dimensional (3D) barred galactic potential, following successive 2D and 3D pitchfork and period-doubling bifurcations of periodic orbits. By employing the so-called 'color and rotation' technique to visualize the four-dimensional Poincare surface ยด of sections of the system, we reveal distinct structural patterns. We further investigate the long-term diffusion transport and chaos properties of single and coupled standard maps, focusing on parameters that induce anomalous diffusion through the presence of accelerator modes exhibiting ballistic transport. Using different ensembles of initial conditions in chaotic regions influenced by these modes, we examine asymptotic diffusion rates and their corresponding time scales, identifying conditions that suppress anomalous transport and lead to long-term convergence to normal diffusion across various coupled map arrangements. Lastly, we perform the first comprehensive investigation into the behavior of the GALI indices for various attractors in continuous and discrete-time dissipative systems, extending the application of the method to non-Hamiltonian systems. A key aspect of our work involves analyzing and comparing the performance of the GALI method with the computation of Lyapunov Exponents for non-Hamiltonian dissipative systems exhibiting hyperchaotic motion. DA - 2025 DB - OpenUCT DP - University of Cape Town KW - applied mathematics LK - https://open.uct.ac.za PB - University of Cape Town PY - 2025 T1 - Hamiltonian chaos: from galactic dynamics to plasma physics TI - Hamiltonian chaos: from galactic dynamics to plasma physics UR - http://hdl.handle.net/11427/42450 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/42450 | |
| dc.identifier.vancouvercitation | Tenaw H. Hamiltonian chaos: from galactic dynamics to plasma physics. []. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2025 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/42450 | en_ZA |
| dc.language.rfc3066 | eng | |
| dc.publisher.department | Department of Mathematics and Applied Mathematics | |
| dc.publisher.faculty | Faculty of Science | |
| dc.publisher.institution | University of Cape Town | |
| dc.subject | applied mathematics | |
| dc.title | Hamiltonian chaos: from galactic dynamics to plasma physics | |
| dc.type | Thesis / Dissertation | |
| dc.type.qualificationlevel | Doctoral | |
| dc.type.qualificationlevel | PhD |