基于基函数展开方法处理具有陡峭界面的Abel反演问题  

An Abel inversion method based on basis set expansion for discontinuous radial distribution problems

作　　者：韩丹[1] 晏卓阳 张天奎[1] 陈佳[1] 于明海 吴玉迟[1,2] 谷渝秋[1,2] 

机构地区：[1]中国工程物理研究院激光聚变研究中心等离子体物理重点实验室,四川绵阳621900 [2]上海交通大学IFSA协同创新中心,上海200240

出　　处：《强激光与粒子束》2016年第9期45-50,共6页High Power Laser and Particle Beams

基　　金：国家自然科学基金项目(11174259;11375161;11405159;11505166);等离子体物理重点实验室基金项目(9140C680301150C68297;9140C680302130C68242)

摘　　要：在激光聚变研究中,存在大量具有陡峭不连续界面特性的靶丸等离子体诊断问题,需要借助Abel反演方法对结果进行分析。提出了一种基于基函数展开处理不连续径向分布的Abel反演方法,采用带约束的Landweber迭代法求得优化结果。利用该算法可以对不连续阶跃分布进行比较准确的反演,获得阶跃结构特征。在理想情况下,针对不连续阶跃分布的反演方差好于10-4,即使在存在一定噪声的情况下也仍然可以获得较好的结果。该方法可用于对激光聚变研究中压缩过程中球壳的背光照相、自发光成像、光谱测量等诊断结果的数据分析。Diagnostics of fusion capsule plasma which usually has a discontinuous radial distribution is a basic problem in la-ser fusion plasma researches.An Abel inversion method based on basis set expansion was proposed to handle this discontinuous Abel inverse problem.This method expands the radial distribution on a set of basis functions,and then the measurement data can be approximated by a linear combination of Abel transforms of the basis functions.The weighted coefficients of the basis functions were obtained by projected Landweber iteration method.Numerical simulations demonstrate that the proposed method is suffi-ciently accurate to reconstruct discontinuous radial distribution,and variance of reconstructed result can reach 10 -4 for ideal sig-nal.Although some noise were added in measurement data,the inversion result can still reflect discontinuous property of radial distribution accurately.

关 键 词：Abel反演 基函数展开 等离子体诊断 非连续分布 X射线成像 

分 类 号：O536[理学—等离子体物理] O241[理学—物理]