Bifurcations leading to stochasticity in a cyclotron-maser system

Abstract

This paper is concerned with the orbital dynamics of electrons in a cyclotron maser [CO Chen, Phys. Rev. A 46,6654 (1992)] with modulated maser fields. Amplitude modulation is a natural result of wave-particle energy exchanges, and for typical system parameters, the nonlinear bifurcations of periodic orbits are investigated as the modulation level increases. Attention is focused on primary stable orbits exhibiting the same periodicity as the modulation for low modulational levels. This interest is related to the fact that the destruction of these orbits is generally associated with considerable spread of chaos over the phase space. It is found that two groups of such orbits do exist, each group located in a particular region of the phase space. As the modulation level grows, the overall behavior can be classified as a function of the modulation frequency. If this frequency is large there are two orbits in the group; one undergoes an infinite cascade of period doubling bifurcations and the other simply collapses with neighboring unstable orbits. If the frequency is small the number of orbits is larger; the collapsing orbit is still present and some of the others may fail to undergo the period doubling cascade.