正弦平方势与小振幅近似下的弯晶沟道辐射  

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

作　　者：胡西多[1] 邵明珠[1] 罗诗裕[1] 曹璎珞[2] 

机构地区：[1]东莞理工学院电子系,广东东莞523106 [2]中国矿业大学,江苏徐州213406

出　　处：《发光学报》2006年第1期18-22,共5页Chinese Journal of Luminescence

基　　金：广东省科技计划重大项目资助项目(2003A1040312)

摘　　要：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。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 1 st 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 rcsult is coincident basically with other work.

关 键 词：弯晶 沟道辐射 非线性 正弦平方势 

分 类 号：O482[理学—固体物理]