Standard map in magnetized relativistic systems: fixed points and regular acceleration

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.Comment: Work to appear in Phys. Rev. E. 2 figure

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.Comment: Submitte

Statistical Mechanics of Unbound Two Dimensional Self-Gravitating Systems

We study, using both theory and molecular dynamics simulations, the relaxation dynamics of a microcanonical two dimensional self-gravitating system. After a sufficiently large time, a gravitational cluster of N particles relaxes to the Maxwell-Boltzmann distribution. The time to reach the thermodynamic equilibrium, however, scales with the number of particles. In the thermodynamic limit, $N\to\infty$ at fixed total mass, equilibrium state is never reached and the system becomes trapped in a non-ergodic stationary state. An analytical theory is presented which allows us to quantitatively described this final stationary state, without any adjustable parameters

Multiple Island Chains in Primary Resonances.

We analyse the dynamics of a relativistic particle moving in a uniform magnetic field\ud and perturbed by a stationary electrostatic wave. We show that a pulsed wave produces an\ud infinite number of perturbing terms with the same winding number. The perturbation coupling\ud alters the number of island chains as a function of the parameters of the wave. We also observe\ud that the number of chains in is always even if the number of islands in each chain is odd