Foundations and interpretations of the pulsed-Townsend experiment

Abstract

The pulsed-Townsend (PT) experiment is a well known swarm technique used to measure transport properties from a current in an external circuit, the analysis of which is based on the governing equation of continuity. In this paper, the Brambring representation (1964 Z. Phys. 179 532) of the equation of continuity often used to analyse the PT experiment, is shown to be fundamentally flawed when non-conservative processes are operative. The Brambring representation of the continuity equation is not derivable from Boltzmann's equation and consequently transport properties defined within the framework are not clearly representable in terms of the phase-space distribution function. We present a re-analysis of the PT experiment in terms of the standard diffusion equation which has firm kinetic theory foundations, furnishing an expression for the current measured by the PT experiment in terms of the universal bulk transport coefficients (net ionisation rate, bulk drift velocity and bulk longitudinal diffusion coefficient). Furthermore, a relationship between the transport properties previously extracted from the PT experiment using the Brambring representation, and the universal bulk transport coefficients is presented. The validity of the relationship is tested for two gases Ar and SF 6 , highlighting also estimates of the differences.

Cross sections and transport coefficients for electrons in C2H6O and its mixtures with Ar and Ne

“…In accordance with the analysis of Casey et al [44], we have shown only the bulk drift velocities in our plots. As for the difference between the two-term and multiterm/MC results [27], it has been represented as the difference between the lines and the corresponding points labeled MC.…”

Toward a complete and comprehensive cross section database for electron scattering from NO using machine learning

“…When performing a Boltzmann equation swarm analysis, it is essential to precisely interpret what is being measured in each swarm experiment under consideration [34,57]. In this regard, many of the earlier electron-NO measurements are inadequate as they are obtained using a "magnetic deflection" experiment [58] that measures a drift velocity that is distinct from the bulk (centre-ofmass) drift velocity measured in pulsed-Townsend experiments [57] and provided by our Boltzmann solver.…”

“…When performing a Boltzmann equation swarm analysis, it is essential to precisely interpret what is being measured in each swarm experiment under consideration [34,57]. In this regard, many of the earlier electron-NO measurements are inadequate as they are obtained using a "magnetic deflection" experiment [58] that measures a drift velocity that is distinct from the bulk (centre-ofmass) drift velocity measured in pulsed-Townsend experiments [57] and provided by our Boltzmann solver. Ultimately, we choose to calculate comparisons to the drift velocities and longitudinal diffusion coefficients of Takeuchi et al [33], the ionisation coefficients of Lakshminarasimha et al [55], the attachment coefficients of Parkes et al [54], the transverse characteristic energies of Lakshminarasimha et al [55] and Mechlińska-Drewko et al [56], and the longitudinal characteristic energies of Mechlińska-Drewko et al [56] and Takeuchi et al [33] (calculated using their drift and diffusion measurements).…”

An improved set of electron-THFA cross sections refined through a neural network-based analysis of swarm data

“…Typical uncertainties for W , α eff and D L were ±2%, ±6% and ±12%, respectively. Note that these transport coefficients can be related to the net ionisation frequency, R net , the bulk drift velocity, W B , and the bulk diffusion coefficient, D B,L , via [98]:…”