Nonlinear dynamics of the relativistic standard map

The acceleration and heating of charged particles by electromagnetic fields has been extensively investigated by the standard map. The question arises as to how the relativistic effects change the dynamical behavior described with the classical standard map. The relativistic standard map is a two-parameter (K,\ensuremath{\beta}=\ensuremath{\omega}/kc) family of dynamical systems reduced to the standard map when \ensuremath{\beta}\ensuremath{\rightarrow}0. For \ensuremath{\beta}\ensuremath{\ne}0 the relativistic mass increase suppresses the onset of stochasticity. It is shown that the speed of light limits the rate of advance of the phase in the relativistic standard map and introduces Kolmogorov-Arnold-Moser surfaces persisting in the high-momentum region. An intricate structure in the higher-order periodic orbits and chaotic orbits is analyzed using the symmetry properties of the relativistic standard map. An interchange of the stability of the periodic orbits is observed and explained by the local linear stability of the periodic orbits.

Hali tarjima qilinmagan