弯晶的沟道效应

本文引入正弦平方势,将弯晶中的粒子运动方程化为常力矩作用下的摆方程,并用非线性力学方法,详细讨论了系统的相平面特征,分析了相平面上奇点分布和相对运动对系统稳定性的影响,从系统的临界状态出发导出了动力学允许的临界参数和可能偏转的最大能量;此外,还考察了小振幅近似下的粒子运动行为,发现该系统具有软弹簧特征,用Jacobian椭圆函数和第一类全椭圆积分严格求解了运动方程和振动周期,导出了低能带电粒子在弯晶中的空间分布和动量分布。 关键词：

CHANNELING EFFECTS IN BENT CRYSTAL

In this paper, the sine-squared potential is introduced, and the motion equation of particle is reduced to a pendulum equation. with constant moment; the propeties of the phase plane are described in detail by using the method in nonlinear mechanics, the effects of the singular point distribution and motion in phase plane on stability of the system are discussed, the critical parameters and maximum energy are deduced. Besides, the particle motion behaviours in the case of small amplitude approximation is analyzed. The results show that the system appears to exhibit soft-spring properties. The solution and the period are represented exaclly by Jacobian elliptic function and the 1-st kind of complete ellrptic integral. The space distribution and momentum distribution of particles are derived.