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| Author(s): |
Meirielen Caetano de Sousa
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Física (IF/SBI) |
| Defense date: | 2015-07-31 |
| Examining board members: |
Ibere Luiz Caldas;
Zwinglio de Oliveira Guimarães Filho;
Rafael Ribeiro Dias Vilela de Oliveira;
Jose Danilo Szezech Junior;
Ricardo Luiz Viana
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| Advisor: | Ibere Luiz Caldas |
| Abstract | |
In this thesis, we analyze the dynamics of a relativistic particle moving under the influence of a uniform magnetic field and a stationary electrostatic wave given as a series of periodic pulses. The map that describes the time evolution of the system is explicit, and it can be considered as a magnetized relativistic version of the classical standard map. We calculate analytically the approximate position of the periodic points and we use this information to study the primary resonances. For the system under study, we observe that most of its resonances exhibit more than one island chain. It occurs because the system presents an infinite number of resonant terms with the same winding number that may generate islands in the same position of phase space. We verify that this superposition of resonant terms makes the number of chains vary as a function of the parameters of the wave. For sufficiently large values of the wave period or wave number, all the primary resonances present two or more island chains in phase space. We use the islands of primary resonances in this thesis to regularly accelerate particles. In particular, we consider the main resonance of the system, for which the initial energy of the particle can be very close to its rest energy if the parameters of the wave are adequate. Furthermore, we apply a method of control of chaos for near-integrable Hamiltonians that consists in the addition of a simple control term with low amplitude to the system. This control term creates invariant tori in the whole phase space that confine the chaotic trajectories to small regions, making the controlled dynamics more regular. We verify numerically that the control term drastically reduces the chaotic regions. Moreover, we observe that the control of chaos and the consequent recovery of periodic and quasiperiodic trajectories in phase space can be used to improve the process of regular particle acceleration. (AU) | |
| FAPESP's process: | 11/20794-6 - Chaos in magnetized relativistic systems: regular acceleration and control of chaos |
| Grantee: | Meirielen Caetano de Sousa |
| Support Opportunities: | Scholarships in Brazil - Doctorate (Direct) |