Regularization Methods for Extracting Doppler Broadening From Hall Thruster Plasma

Abstract

Extracting Doppler broadening from laser-induced fluorescence (LIF) measurements is essential for determining species temperature in the plasma. The fluorescence signal is a convolution of many broadening effects of which Doppler broadening is the most significant, but several others contribute as well: collisional (pressure) broadening (particle-to-particle interactions), natural lifetime broadening, and power broadening. The process that extracts Doppler broadening is an <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ill-posed</b> inverse problem. The regularization approach addresses the <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ill-posed</b> problem to ensure a unique and stable solution with the best possible accuracy. This study reported the Xe II temperature by applying truncated singular value decomposition (TSVD) and Tikhonov regularization (zeroth, first and second-order) methods for deconvolution of Doppler broadening. Tikhonov first-order and TSVD employing the generalized cross-validation (GCV) method provide accurate reconstruction within 2.0%–8.0% of the actual measurements.