Biomedical Engineering Reference
In-Depth Information
14.4
Positron transport in water vapour
The history and current status of positron (swarm) experiments has been recently
reviewed [
12
,
13
]. One motivation for such experiments is clear - a test for the accu-
racy and completeness of the new generation of positron scattering cross-section
sets. Although there are currently no positron swarm experiments of equivalent
accuracy to their electron counter part, design considerations were outlined in
[
12
]. As experimental data for complete sets of positron cross-sections become
available [
13
,
14
], theoretical and computational techniques developed for electrons
have been adapted and applied to positrons. The macroscopic manifestations of
the microscopic differences in electron and positron cross-sections and processes
are quite striking. Of particular note is the impact of the non-conservative Ps-
formation process on the transport properties. In particular, the phenomenon of
Ps-induced negative differential conductivity (NDC) (selectively existing only for
the bulk transport coefficient- the definition is provided later on the next page),
i.e. the decrease in the drift velocity with increasing electric field strength, is now
well known in both atomic [
15
] and molecular gases [
16
]. Also, of further note is
the impact of Ps-formation on the longitudinal diffusion coefficient and excessive
skewness of spatial profiles that strongly depart from the expected Gaussians defined
by diffusion [
14
].
Future optimisation of positron-based imaging (Positron Emission Tomogra-
phy - PET) and therapies is dependent on, amongst other things, an accurate
knowledge of positron transport in human tissue or water. Using the set of positron
impact cross-sections described earlier, we have performed a study of the transport
of positrons in water vapour under the influence of an electric field [
16
]. In this
work, we use and compare two independent techniques - a multi-term solution
of Boltzmann's equation (see e.g. the review [
17
]) and a Monte-Carlo simulation
(see e.g. the review [
6
]). In Fig.
14.2
, we present the drift velocity of positrons
in water vapour. It is now well known that there are two different types of drift
velocities [
18
] (i) the flux drift velocity, which effectively measures the mean
velocity of the positrons within the swarm, and (ii) the bulk drift velocity, which
effectively measures the time rate of change of the centre-of-mass of the swarm. It is
generally the latter which is measurable in experiment, though both are calculable in
theory (although earlier theories provided mostly the flux coefficients). Differences
between the two sets manifest themselves when there are energy dependent non-
conservative (e.g. annihilation, Ps-formation) processes present and there is a
non-symmetric spatial variation in the average energy through the swarm. The
strength of the non-conservative Ps-formation processes is such that the differences
between the two sets of drift velocities can be as large as two orders of magnitude.
The bulk drift velocity is typically less than the flux drift velocity because the loss of
positrons due to Ps-formation occurs preferentially at the leading edge of the swarm
relative to the tail - a process resulting in a shift in the centre-of-mass of the swarm
in a direction opposite to the applied force. Like positron transport in other gases, we
again observe the existence of Ps-induced NDC. The combination of the increased
