参数共振与晶体摆动场中粒子运动的稳定性

Parametric Resonance and Stability of Particle Motion in Crystalline Undulator

从倒置摆方程出发讨论了无扰动系统的相平面特征,并用Jacobi椭圆函数和椭圆积分解析地描述了带电粒子的电磁辐射;用多尺度法导出了扰动系统的频率响应、临界条件和一阶近似解,揭示了系统不可逆性、不稳定性和弛豫行为。用拉莫公式讨论了带电粒子的辐射强度。指出了适当调节参数可以保证系统的稳定性。

Starting from the inverted pendulum equation, the phase plane characteristics of the unperturbed system were discussed, and the electromagnetic radiation of the charged particle was described analytically by Jaeobi elliptic function and elliptic integral. The frequency response, critical condition and first order approximation solution of the perturbed system were derived by the multiseale method, thus the irreversibility, instability and relaxation behavior of the system were revealed. The radiation intensity of the charged particles was discussed by Ramo＇s formula. It is pointed out that the stability of the system can he ensured by adjusting the parameters properly.