SPATIALLY RESOLVED ION CURRENT DENSITY MEASUREMENTS WITH A TRANSIENT INSERTION LANGMUIR PROBE

This work presents a novel technique for constructing spatially resolved ion densities from Transient Insertion Langmuir Probe (TIL Probe) measurements in a flame. Similar to a tomographic transformation, this technique is used to deduce the spatial distribution of ions in a flame from many individual measurements that are integrated along a probe's length. We demonstrate the approach in the oxyfuel cutting torch preheat flame, which presents two severe challenges for electrical measurements: (1) temperatures over 3,000K destroy most probes made from alloys with appropriate chemical stability, and (2) the relevant length scales are on the order 0.15 mm. Presented here are (1) a Fourier series formulation for the current density, (2) a least-square problem for calculating the coefficients, (3) criteria for the highest wavenumber allowed in the expansion, (4) description of an experiment used to measure probe currents in an oxyfuel cutting torch preheat flame, (5) solution for spatially resolved current density in the oxyfuel cutting torch flame. Images of ion current density are produced with a resolution of 0.15 mm (0.0059 in), exhibiting peak current densities around 14 mu A/mm. It is found that low-signal regions in the "shadow" of high-signal regions can suffer from signal-to-noise ratio problems due to natural fluctuations in the flame, and improvements are proposed to mitigate the effect. It is found that the numerical cost of setting up the resulting Hermitian-matrix linear problem far exceeds the numerical cost of inversion. High-level packages like Python and MATLAB are far too slow, so a multi-threaded algorithm is implemented in C, and the LAPACKE C library is used for efficient linear algebra support.