Nonmonotonic maps and related bifurcations in laser accelerators

In this paper we analyze the orbital dynamics of electrons in a laser accelerator whose high-frequency laser wave is slowly modulated both in space and time. Slow modulations are a natural result of modulational instabilities and wave-particle energy exchanges, and for typical system parameters we focus our study on stability and bifurcations of periodic orbits. It is found out that the orbital nonlinear frequencies are nonmonotonic functions of the system energy. This leads to the appearance of peculiar reconnection processes and associated inverse saddle-node bifurcations, in addition to the more usual period doubling cascades preceding chaos.