Scaling properties and cascades bifurcations in one-dimensional discrete maps
Chaos in mathematical models of cancer - how and why it occurs. An approach from t...
| Grant number: | 15/05186-0 |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| Effective date (Start): | December 01, 2015 |
| Effective date (End): | September 30, 2020 |
| Field of knowledge: | Physical Sciences and Mathematics - Physics - Classical Areas of Phenomenology and Applications |
| Principal Investigator: | Iberê Luiz Caldas |
| Grantee: | Meirielen Caetano de Sousa |
| Host Institution: | Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
| Associated research grant: | 18/03211-6 - Non linear dynamics, AP.TEM |
| Associated scholarship(s): | 19/23366-7 - Electron acceleration by surface plasma waves, BE.EP.PD |
Abstract We consider the interaction between charged particles and electrostatic waves, and we study the regular particle acceleration that occurs in the resonant islands. Regular particle acceleration is strongly influenced by the presence of chaos in phase space, which destroys regular trajectories. In this project, we investigate new methods that are able to control chaos with a low energy cost, as part of an ongoing collaboration with the Federal University of Rio Grande do Sul. For low density beams, we analyze methods that act locally in phase space, since they may be more efficient when they require less energy to be implemented. In the case of high density beams, we use methods that are able to control chaos in the dynamics of the beam envelope. This project also aims to strengthen the collaboration between the Universities of São Paulo and Aix-Marseille, France. Through this collaboration, we analyze the dynamics of electron beams for a better understanding of wave-particle interactions, including the validation of numerical codes and analytical models, and the development of new and robust models to describe self-consistent effects. Besides controlling chaos and self-consistent effects, we analyze the perturbations that act on the system and their superposition in order to determine how the parameters change the configuration of phase space, specially the quantity and the position of the island chains in which the particles are accelerated. We also consider the successive isochronous bifurcations that alter the number of island chains and play a key hole in the dynamics of the system. | |
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