Leppink E, Lau C, Lin Y, Wukitch S J
MIT Plasma Science and Fusion Center, Cambridge, Massachusetts 02139, USA.
Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA.
Rev Sci Instrum. 2023 Jun 1;94(6). doi: 10.1063/5.0132246.
The Abel transform is often used to reconstruct plasma density profiles from O-Mode polarized reflectometry diagnostics. However, standard numerical trapezoidal evaluation of the Abel inversion integral can be computationally expensive for a large number of evaluation points, and an endpoint singularity exists on the upper-bound of the integral, which can result in an increased error. In this work, Chebyshev-Gauss quadrature is introduced as a new method to evaluate the Abel inversion integral for the problem of O-Mode plasma reflectometry. The method does not require numerical evaluation of an integral singularity and is shown to have similar accuracy compared to existing methods while being computationally efficient.
阿贝尔变换常用于从O模偏振反射测量诊断中重建等离子体密度分布。然而，对于大量的评估点，阿贝尔反演积分的标准数值梯形评估在计算上可能很昂贵，并且积分上限存在端点奇异性，这可能导致误差增加。在这项工作中，引入了切比雪夫-高斯求积法作为一种新方法来评估O模等离子体反射测量问题中的阿贝尔反演积分。该方法不需要对积分奇异性进行数值评估，并且与现有方法相比具有相似的精度，同时计算效率高。
