Biomedical Engineering Reference
In-Depth Information
state determined by a balance between power input from an applied electric field
E
and energy loss rate via collisions between electrons in the swarm and particles
of a neutral gas of density
n
0
. A similar definition applies for positron swarms.
Various configurations of swarm experiments exist [
4
]. It is important to understand
that swarm experiments differ significantly from beam-based methodologies: swarm
experiments are many scattering experiments while beam experiments are single
scattering experiments. By applying a field, the swarm is driven out of thermal
equilibrium and the velocity distributions are distinctly non-Maxwellian. The swarm
may be in equilibrium with electric field (energy and momentum gained from the
field are dissipated in collisions) or be in the so-called non-hydrodynamic (non-
equilibrium) regime whereby the distribution is both space and time dependent.
It is worth noting that most gas filled traps including the Surko trap start with
a mono-energetic distribution of positrons and, after several collisions, develop a
broad swarm-type distribution.
Variations in the applied field allow one to selectively assess various energy
regions in the cross-sections. Initially swarm experiments were designed to indi-
rectly extract complete sets of cross-sections, and although the number of swarm
experiments has declined in recent years, these experiments still continue to
provide important information for electron systems. Completeness and accuracy
of the cross-section set (which includes the momentum transfer cross-section,
rotational cross-sections, vibrational cross-sections etc. for all energetically allowed
excitations) is determined by correspondence of the measured transport coefficients
with those calculated or simulated. These transport coefficients include e.g. the
drift velocity
W
, transverse and longitudinal diffusion coefficients
D
T
and
D
L
respectively and the rate coefficients for a range of applied reduced fields
E=n
0
(see e.g. [
4
] for details). The textbook by Robson [
5
] gives an overview of modern
charged particle transport theory and for a recent review of swarm experiments and
swarm transport data the reader is referred to [
6
].
For modeling radiation damage in biological matter, establishing an accurate
and complete set of electron - water cross-sections is paramount. Recently a
recommended “best set” of cross-sections in water vapour has been compiled [
3
].
Of particular importance for radiation damage is the low-energy range up to about
20 eV, corresponding to secondary electrons from primary ionization. In this region,
there exists experimental swarm data for electrons in water vapour [
7
-
9
]. When
combined with the current transport theory or simulation that is of equal (or better
accuracy), the process can provide a definitive test on the accuracy and completeness
of the current sets of cross-sections for electrons in water vapour. One of the
impediments to a true test has been the differences in the transport coefficient
definition and measurement techniques that exist between the various groups.
Robson et al. [
10
] have recently reconciled the differences, outlining procedures for
true comparisons of recently measured drift velocities of electrons in water vapour
[
9
]. A recent study [
11
] has made comment on the accuracy of recommended cross-
section sets, exploring the impact of variations and sensitivities in the recommended
sets of cross-sections including the anisotropic nature of the scattering.
