On the drift-diffusion analysis of the Pulsed Townsend experiment : a fitting algorithm and benchmark study

Abstract

Electron transport properties in gases and gas mixtures can be determined from measurements with a Pulsed-Townsend experiment. Analytical solutions of a drift-diffusion equation are fitted to the measured experimental waveforms to determine electron transport coefficients. However, it is not always unambiguously clear what the published measurement data ultimately represents, under which assumptions published transport data have been derived, and how large the uncertainty is. To address this, we first present an open source code for the analysis of the Pulsed-Townsend experiment waveforms. We then use this code to fit synthetic waveforms generated by Monte-Carlo simulations to estimate the accuracy of transport data obtained by curve fitting. Two benchmark simulation cases are considered: a representative case that closely replicates a typical Pulsed-Townsend experiment and an idealised case that replicates the assumptions that underpin the state of the art analytic solution. For each case simulations are performed for three different gases (Ar, CO 2 and SF 6 ) and over a wide range of electric field strengths (10-1000 Td), densities (10 22 - 10 24 m -3 ) and electrode spacings (10-30 mm). For the representative model, while the error in the extracted transport coefficients can be as good as 0.1%, it deteriorates with decreasing pressure, decreasing electrode gap distance and increasing electric field strength. While significantly reduced errors were found for the idealised model, errors exceeding 10% were still present in some regimes. We show that these errors are strongly correlated with the third-order transport coefficient, which calls into question the accuracy of analyses that do not account for it, especially for experiments operated at low pressures and small electrode spacings.