Foundations and interpretations of the pulsed-Townsend experiment

M. J.E. Casey, P. W. Stokes, D. G. Cocks, D. Bošnjaković, I. Simonović, M. J. Brunger, S. Dujko, Z. Lj Petrović, R. E. Robson, R. D. White

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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 SF6, highlighting also estimates of the differences.

Original languageEnglish
Article number035017
Number of pages11
JournalPlasma Sources Science and Technology
Issue number3
Publication statusPublished - 25 Mar 2021


  • Brambring s equation
  • kinetic theory
  • pulsed townsend experiment
  • pulsed townsend governing equation
  • transport coefficient definition


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