Crystalline undulator radiation and motion behavior in the vicinity of the resonance line

Abstract

Searching for new light source, especially short wave-length coherence light source has attracted extensive attention. The using of the crystalline undulator radiation as a short wave-length coherence light source is most likely to be one of the options. From the viewpoints of potential and field, the centrifugal force generated by periodic bent crystal is regarded as centrifugal potential, the particle motion equation is reduced to Mathieu equation with Duffing-type, and from the energy viewpoint the stability of the system is discussed. The behaviors of particles in the vicinity of the resonance are analyzed by perturbation method; the jump phenomena and instable behavior are revealed. The results show that the stability of the system is related to its parameters, and only properly adjusting these parameters, the bifurcation and instability for the system can be avoided in principle.