RESUMO
Recent evidence shows that heteroclinic bifurcations in magnetic islands may be caused by the amplitude variation of resonant magnetic perturbations in tokamaks. To investigate the onset of these bifurcations, we consider a large aspect ratio tokamak with an ergodic limiter composed of two pairs of rings that create external primary perturbations with two sets of wave numbers. An individual pair produces hyperbolic and elliptic periodic points, and its associated islands, that are consistent with the Poincaré-Birkhoff fixed-point theorem. However, for two pairs producing external perturbations resonant on the same rational surface, we show that different configurations of isochronous island chains may appear on phase space according to the amplitude of the electric currents in each pair of the ergodic limiter. When one of the electric currents increases, isochronous bifurcations take place and new islands are created with the same winding number as the preceding islands. We present examples of bifurcation sequences displaying (a) direct transitions from the island chain configuration generated by one of the pairs to the configuration produced by the other pair, and (b) transitions with intermediate configurations produced by the limiter pairs coupling. Furthermore, we identify shearless bifurcations inside some isochronous islands, originating nonmonotonic local winding number profiles with associated shearless invariant curves.
RESUMO
We analyze nonlinear aspects of the self-consistent wave-particle interaction using Hamiltonian dynamics in the single wave model, where the wave is modified due to the particle dynamics. This interaction plays an important role in the emergence of plasma instabilities and turbulence. The simplest case, where one particle (N=1) is coupled with one wave (M=1), is completely integrable, and the nonlinear effects reduce to the wave potential pulsating while the particle either remains trapped or circulates forever. On increasing the number of particles ( N=2, M=1), integrability is lost and chaos develops. Our analyses identify the two standard ways for chaos to appear and grow (the homoclinic tangle born from a separatrix, and the resonance overlap near an elliptic fixed point). Moreover, a strong form of chaos occurs when the energy is high enough for the wave amplitude to vanish occasionally.
RESUMO
We study the dynamics of a relativistic charged particle in the presence of a uniform magnetic field and a stationary electrostatic wave that propagates at an arbitrary angle. The wave is considered as a series of periodic pulses which allows us to derive an exact map for the system. In particular, we investigate the heating process of an initially low-energy particle. It is found that abrupt changes in the maximum energy attained by the particle may occur as the angle between the wave propagation and the magnetic field varies. To determine what is the mechanism behind this phenomenon a reduced Hamiltonian that retains the important dynamical features is obtained. Using both Poincaré plots and perturbation theory, we identify that a separatrix reconnection is the key mechanism for the abrupt change in particle response.
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We analyze the dynamics of a relativistic particle moving in a uniform magnetic field and perturbed by a standing electrostatic wave. We show that a pulsed wave produces an infinite number of perturbative terms with the same winding number, which may generate islands in the same region of phase space. As a consequence, the number of isochronous island chains varies as a function of the wave parameters. We observe that in all the resonances, the number of chains is related to the amplitude of the various resonant terms. We determine analytically the position of the periodic points and the number of island chains as a function of the wave number and wave period. Such information is very important when one is concerned with regular particle acceleration, since it is necessary to adjust the initial conditions of the particle to obtain the maximum acceleration.
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We analyze the behavior of a relativistic particle moving under the influence of a uniform magnetic field and a stationary electrostatic wave. We work with a set of pulsed waves that allows us to obtain an exact map for the system. We also use a method of control for near-integrable Hamiltonians that consists of the addition of a small and simple control term to the system. This control term creates invariant tori in phase space that prevent chaos from spreading to large regions, making the controlled dynamics more regular. We show numerically that the control term just slightly modifies the system but is able to drastically reduce chaos with a low additional cost of energy. Moreover, we discuss how the control of chaos and the consequent recovery of regular trajectories in phase space are useful to improve regular particle acceleration.
Assuntos
Aceleração , Campos Eletromagnéticos , Retroalimentação , Modelos Teóricos , Dinâmica não Linear , Teoria Quântica , Simulação por ComputadorRESUMO
We investigate the concept of a standard map for the interaction of relativistic particles and electrostatic waves of arbitrary amplitudes, under the action of external magnetic fields. The map is adequate for physical settings where waves and particles interact impulsively, and allows for a series of analytical result to be exactly obtained. Unlike the traditional form of the standard map, the present map is nonlinear in the wave amplitude and displays a series of peculiar properties. Among these properties we discuss the relation involving fixed points of the maps and accelerator regimes.
RESUMO
We detected an outbreak of American cutaneous leishmaniasis in the Jequitinhonha River Valley, Minas Gerais, Brazil. Clinical and epidemiological aspects were studied for a period of two years. Data include results of physical examinations, Montenegro skin test and serology. In total 72 of the 299 individuals evaluated presented active lesions. Only one case out of these 72 patients showed the mucosal form of the disease. The precarious sanitary conditions, low educational level and low income found in the population studied demonstrated that, as with the other parasitic diseases, cutaneous leishmaniasis occurs with greater frequency in needy populations. A canine serological survey detected 20.3% (30/148) of dogs reactive to the Leishmania antigen. Lutzomyia intermedia was the predominant phlebotomine species and the majority of the specimens (84.9%) were captured in the peridomicile. Four samples from human and three from canine cases were isolated and characterised by PCR and isoenzymes as being Leishmania (Viannia) braziliensis. The peridomiciliary nature of the disease is discussed.