正弦平方势与环形加速器的弯晶束流引出
Sinesquared Potential and Beam Extraction in Circulation Accelerator by Bent Crysta
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摘要: 在经典力学框架内和偶极近似下， 引入正弦平方势， 把粒子在弯晶中的运动方程化为具有固定力矩的摆方程。 利用Jacobian椭圆函数和椭圆积分分析了系统的相平面特征。 导出了弯晶的最大偏转能量、 退道系数和退道长度。 计算结果表明， 对于曲率半径为1 m， 能量为1.0 GeV的质子， Si(110)面沟道的引出效率为70%； 对于MeV范围的粒子， 退道长度大约是μm量级； 对于TeV范围的粒子， 退道长度可达1 m以上。 In the classical mechanics frame and the dipole approximation the particle motion equation in bent crystal is reduced to the pendulum equation with a constant momentum by using the sinesquared potential.The phase planar properties are analysed by means of Jacobian elliptic function and the elliptic integral. The maximum deflected energy, the dechanneling factor and the dechanneled length are derived. The results show that the extrated efficiency is 70% for a proton beam with energy E=1.0 GeV moved in the channel on Si(110) if a radius of curvature R=1 m; and dechanneled length is of the order of μm for the particles with MeV energy; the dechanneled length is above 1 meter for the particle with TeV energy.
Abstract: In the classical mechanics frame and the dipole approximation the particle motion equation in bent crystal is reduced to the pendulum equation with a constant momentum by using the sinesquared potential.The phase planar properties are analysed by means of Jacobian elliptic function and the elliptic integral. The maximum deflected energy, the dechanneling factor and the dechanneled length are derived. The results show that the extrated efficiency is 70% for a proton beam with energy E=1.0 GeV moved in the channel on Si(110) if a radius of curvature R=1 m; and dechanneled length is of the order of μm for the particles with MeV energy; the dechanneled length is above 1 meter for the particle with TeV energy.
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