Parametric X ray Radiation of Charged Particle and Stabilities in Bent Crystal
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Abstract
An exploration of a new light source by PXR as Laser gived rise to extensive attention. The particle motion must be stable in order to obtain coherent PXR source. But, an instability of system is possible due to the effect of bent crystal， thus the reflection, the diffraction, the focus and the spectral distribution of PXR will be effected.In the classical mechanics frame and dipole approximation the particle motion equation in bent crystal is reduced to the pendulum equation with a constant momentum by the sinesquared potential.The phase planar properties are analysed by means of Jacobian elliptic function and the elliptic integral. It shows that the stability of the system is related to the curvature Q of the bent crystal. When the condition 0≤Q<1 is satisfied, the system is stable。
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