正弦平方势与小振幅近似下的弯晶沟道辐射

在理想情况下和经典力学框架内,引入正弦平方势,把粒子在弯晶中的运动方程化为具有外力矩的摆方程。并对系统的相平面特征进行了数值分析。在小振幅近似下,把粒子运动方程化为具有硬特性的弹簧-振子系统,用Jacobian椭圆函数和椭圆积分解析地给出系统的解和粒子运动周期。讨论了弯晶沟道辐射频率、无量纲偏转角和辐射谱的一般特征。指出利用沟道辐射作为激光的可能性。以正电子在碳单晶中沟道辐射为例进行了具体计算,得到了与其他工作基本一致的结果。

Sine-squared Potential and Channelling Radiation of Bent Crystal in Small Amplitude Approximation

A charged particle moving along the direction of the low crystal face index can penetrates through the crystal as easily as it does through a channel. This phenomenon is so-called channeling effect. The classical physics points out that an accelerated charged particle radiates energy spontaneously when moving in an electromagnetic field. The analogous situation occurs in crystal channel. When a charged particle moves in an accelerated way through a lattice field, the radiation energy can be produced. The behaviours of the charged particles moved in a crystal channel are controlled by the interaction potential between a charged particles and the crystal. Usual interaction potential is Lindhad potential, Moliere potential and Sine-squared potential. The channeling radiation is described analytically by using the sine-squared potential. The bend of the crystal is equivalent to constant moment. Thus in a framework of the classical mechanics the motion equation of a particles in a bent crystal is reduced to pendulum equation with a constant moment by using the sine-squared potential.The phase planar properties of the system are analyzed by the numerical method.In the small amplitude approximation the motion equation of a particles is reduced to the equation for the hard spring-oscillator.The solution of the equation and the period of the particle motion are expressed exactly by means of Jacobian elliptic function and 1st kind elliptic integral.The properties of the radiation spectrum is discussed.It pointed out it is possible to take channeling radiation as a new γ-Laser.As example, maximum radiation frequence,deflective angle ψ of a positron in the carbon crystal are calculated.The result is coincident basically with other work.