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注意到晶体摆动场辐射是基于沟道粒子的横向运动,而晶体的周期弯曲则等效为作用在粒子上的力。把晶体的周期弯曲视为相互作用势,并考虑在周期摆动场中粒子的“同步辐射”。在经典力学框架内和偶极近似下,把粒子的纵向运动方程化为摆方程,并在小振幅近似下,把它进一步化为Duffing方程。用Jacobian椭圆函数和第一类椭圆积分严格地给出了粒子轨道和它的运动周期;讨论了沟道辐射、摆动场辐射和“同步辐射”能量(频率)。结果表明,三种辐射之间的频率差别比较大,在实验上很容易将他们分开。选择如下一组参数V0=0.5eV,波长λp=100nm,能量γ=104,计算结果表明,“同步辐射”频率Ω=8.83×1019,已进入X-能区。
Note that the crystal swing field radiation is based on the lateral movement of the channel particles, while the periodic bending of the crystal is equivalent to the force acting on the particles. The periodic bending of the crystal is considered as the interaction potential and the “synchrotron radiation” of the particle in the periodic wobble field is taken into account. In the framework of classical mechanics and dipole approximation, the longitudinal motion of particles is transformed into a pendulum equation, which is further reduced to a Duffing equation with a small amplitude approximation. The particle orbit and its period of motion are given strictly by the Jacobian elliptic function and the first kind of elliptic integral; the channel radiation, the oscillating field radiation and the “synchrotron radiation” energy (frequency) are discussed. The results show that there is a large difference in the frequencies between the three types of radiation and that they can be easily separated experimentally. Select a set of parameters V0 = 0.5eV, wavelength λp = 100nm, energy γ = 104, the calculated results show that the “synchrotron radiation” frequency Ω = 8.83 × 1019, has entered the X-energy zone.