在经典力学框架内和偶极近似下,引入正弦平方势,把粒子运动方程化为具有阻尼项和受迫项的广义摆方程。利用Melnikov方法讨论了沟道运动次谐分叉及其稳定性,导出了周期弯晶的临界条件和退道长度。结果表明,要试图获得高的引出效率,除了要求弯晶长度必须小于退道长度外,还必须保证沟道粒子的运动是稳定的。对临界条件的分析表明,系统的稳定性与它的参数有关,只须适当调节系统参数,就可以保证周期弯晶作为引出元件的稳定性。
In the classical mechanics frame and with a dipole approximation the particle motion equation in the periodic bent crystal is reduced to the general pendulum equation with a damping term and the forced term by using the sine-squared potential.This paper discusses the problem of the sub-harmonic bifurcation of the periodic orbit and the stabilities of the channeling motion by using Melnikov method,so as to derive the critical condition and the dechanneling length of the periodic bent crystal.The results show that channeling motion must be stable in addition that the crystal length is smaller than the dechanneling length in order to ensure higher extracted efficiency.The analysis of the critical condition shows that the system stabilities are related to its parameters.Just by properly regulating the parameters of the system,the dynamic stabilities by the use of periodic bent crystal as beam control cell can be ensured.
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