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 SF6, highlighting also estimates of the differences.
Highlights
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
It is important to understand that different swarm experiments operate in different regimes—time of flight (TOF) and pulsed-Townsend (PT) for example in the hydrodynamic regime, where the space-time dependence of all quantities can be projected onto the number density, n (r, t) [55], while the steady state Townsend (SST) approach operates in the non-hydrodynamic regime, where one has to treat the space (r) and time (t) dependence more generally [47, 56]
We have shown that the governing equation traditionally used to analyse the PT experiment—the Brambring representation of the equation of continuity—is fundamentally flawed, and transport properties subsequently defined through that equation do not have a clear representation in terms of the distribution function
Summary
Physics, from atmospheric processes through to medical imaging and therapies [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]. A general solution of the full diffusion equation has long been available in the literature [73, 74], and in section 3 we show how it can be adapted to the PT experiment to extract the standard definitions of the transport coefficients with firm foundations in kinetic theory. Transformation of existing measured PT transport properties, for the particular examples of Ar and SF6, are presented in section 4 and compared with the bulk transport coefficients extracted from TOF experiments and calculated using a multi-term solution of Boltzmann’s equation.
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