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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了具有阻尼项和受迫项的摆方程。用Hamiltonian原理和相平面方法讨论了系统的稳定性,并对系统的退道系数、退道长度进行了分析。结果表明,电子和正电子面沟道辐射除了能量适用范围不同外,二者非常类似。它们都可以利用声学方法、机械方法或梯度掺杂法等方法将晶体周期弯曲,而且可以利用现有的加速器提供所需要的粒子束。
In the framework of classical mechanics and dipole approximation, the sine-squared potential is introduced to transform the particle motion equation into a pendulum equation with damped and forced terms. The stability of the system is discussed by the Hamiltonian principle and the phase plane method. The retreat coefficient and the retreat length of the system are analyzed. The results show that both the electron and the positron emission are very similar, except for the different energy ranges. They all can bend the crystal cycle using methods such as acoustical methods, mechanical methods or gradient doping methods, and the existing accelerators can be used to provide the desired particle beam.