Improved Abel Method for Low Sampling Points Situation and Experimental Verification of Electron Density Distribution Microwave Diagnosis

This article presents a developed algorithm applied in the microwave diagnostics of electronic density distribution. The method is specifically designed for accurately reconstructing electron density distributions in column-symmetric plasmas with a low number of sampling points. The main work is to propose a new fitting method (FM) based on the existing Abel inverse transformation method. Unlike previous methods that perform polynomial fitting on experimentally measured electron density path integrals, this approach represents the target electron density distribution using a polynomial with undetermined coefficients. It utilizes the integral function along the path as the fitting formula to fit the measured values. The undetermined coefficients are determined through the least squares FM, thus obtaining the target electron density distribution function. Notably, this method does not involve smoothing or interpolation of the measured data, effectively avoiding the significant reduction in reconstruction accuracy caused by a limited number of data points. Verification through numerical calculations demonstrates that FM achieves higher reconstruction accuracy compared with the cubic interpolation (CI) method when the number of sampling points is small. The effect of both methods is compared in experiments. As electromagnetic propagation waves in the plasma boundary region are influenced by diffraction and other phenomena, and the CI integral equation is prone to accumulating errors, FM is more suitable for microwave diagnosis than CI under the condition of sparse sampling points.