脉冲束六维非线性动力学方程级数解  

Series Solution for the Nonlinear Dynamic Equation of Pulsed Beams in Six Dimensional Phase Spaces

作　　者：曹少中[1] 李旸[1] 

机构地区：[1]北京印刷学院信息与机电工程学院,北京102600

出　　处：《电子学报》2011年第A03期57-60,共4页Acta Electronica Sinica

基　　金：北京市自然科学基金项目(No.4092013);北京市自然科学基金项目(No.4112019);北京市教育委员会科技计划重点项目(No.KZ201110015017)

摘　　要：针对脉冲束六维非线性动力学方程被积函数的不可积性,首先将方程的被积函数展为自变量的Taylor级数,通过直接积分获得方程关于自变量的一般级数解,然后进一步将自变量各阶项的系数对初值作Taylor展开,从而获得方程关于自变量及初值的级数解.对于脉冲束中任意粒子相对于参考粒子的相对运动动力学方程的求解问题,在方程的被积函数展为自变量的Taylor级数的基础上,将自变量的各阶项的系数进一步相对于参考粒子展开,得到了相对运动方程,经直接积分获得了方程关于自变量及相对运动初值的级数解.To unintegrable function for the nonlinear dynamic equations of pulsed beams in six dimensional phase spaces,first of all,the integrated functions of the equations are expanded as Taylor series in independent variable,the general series solution of the independent variable for the equation can be obtained by direct integration.Then the coefficients for different order items of independent variable can be expanded as Taylor series in initial value,next series solution of the independent variable and initial value for the equation can be obtained.In order to solve the dynamic equation for relative motion of any particle to reference particle,first of all expanding the integrated function as Taylor series in independent variable,then the coefficients for difference order items of independent variable can be expanded as the series of reference particle initial value,the relative motion equation can be obtained,and series solution for the independent variable and relative motion initial value of the equation can be obtained by direct integration.

关 键 词：脉冲束 六维非线性动力学方程 级数解 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]