Experiments are under way at the University of New England to measure
the optical absorption of excited gas particles in a pre-breakdown dis
charge. Such measurements can be used to deduce the number density of
electrons in the discharge. By comparing this experimental density map
with the predictions of theory, electron transport parameters may be
determined. In this paper, new theoretical expressions are derived for
the number density distributions of electrons in a uniform electric f
ield. These are found by solving the electron diffusion equation in a
plane parallel electrode geometry with a radially symmetric cathodic c
urrent source. The contribution of ion-induced secondary current is in
cluded, and problems posed by non-equilibrium conditions near the elec
trodes are addressed. Techniques of data reduction are discussed with
a particular emphasis on the avoidance of these problems.