正弦平方势与晶体摆动场辐射的非线性特征

在经典力学框架内和偶极近似下,引入正弦平方势讨论了系统非线性对摆动场辐射的影响。首先,把粒子在弯晶中的运动方程化为具有周期外力作用的摆方程,用Jacobian椭圆函数和椭圆积分解析地描述了粒子运动行为;用多尺度度法和三角函数的广义Bessel展开,找到了受迫摆方程的近似解。而后,在超相对论情况下讨论了系统的瞬时辐射强度和平均辐射强度,并对两种辐射的强度比进行了讨论。结果表明,摆动场辐射强度与摆动场振幅平方成正比,振幅越大摆动场辐射强度越强。

The Sine-squared Potential and Nonlinear Properties of Crystalline Undulator Field Radiation

Based on the framework of classical mechanics and dipole approximation,the sine-squared potential was introduced to discuss the nonlinear effects of crystalline undulator field radiation.First,the particles motion equation in the bent crystal was reduced to the pendulum equation with a periodic external force,the behavior of the particle motion was analytically described by Jacobian elliptic functions and elliptic integrals.Approximate solution of the forced pendulum equation is resolved by using the multi-scale method and the generalized Bessel expansion of trigonometric functions.Then,in the ultra-relativistic case,the system’s instantaneous radiation intensity and average radiation intensity are discussed and compared.The results show that the radiation intensity is proportional to the amplitude square of the crystalline Undulator field.