基于三次样条函数算法的逆阿贝尔变换

Inverted Abel transform based on cubic spline functions

等离子体有关参数的径向分布 ,在等离子体研究中十分有意义的。只要等离子体具有轴对称和光性薄的性质 ,那么利用 Abel逆变换便可以从所测量得到的某种物理量 ,沿测量方向的积分求出径向分布值。激光等离子体实验中的轴对称的 X光体发射强度分布及通过多通道方法可测量电子密度和温度分布 ,需要采用逆阿贝尔 ( Abel)变换。本文采用三次样条函数近似方法计算逆 Abel变换 ,并对两种有代表性的分布进行了计算 ,数值模拟结果表明 :此方法反演的精度高 ,计算也比较简便 ,程序实现很容易。

The radial distributions of plasma parameters are very important in plasma physics. If the plasma distribution is axial symmetrical and optically thin, the radial distribution of some physical parameters are obtainded by using Abel inversion from measured integral value along radial direction. The inverted Abel transform is necessarily used to compute the X ray emission radial distribution and measure the electronic temperature and density through multichannel method in laser produced plasma expeirments. Using the cubic spline function method, the inverted Abel transform is numerically calculated from two typical distribution that are gaussian and off axial distribution. The simulated results show that this algorithm is high accurate, convenient to compute and easy to program.