Controlling chaos in wave-particle interactions

Alternate islands of multiple isochronous chains in wave-particle interactions

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.

Chaotic particle heating due to an obliquely propagating wave in a magnetized plasma

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.