  A major obstacle for the understanding of long electrical discharges is the
complex dynamics of streamer coronas, formed by many thin conducting filaments.
Building macroscopic models for these filaments is one approach to attain a
deeper knowledge of the discharge corona. Here we present a one-dimensional,
macroscopic model of a propagating streamer channel. We represent the streamer
as an advancing finite-conductivity channel with a surface charge density at
its boundary. This charge evolves self-consistently due to the electric current
that flows through the streamer body and within a thin layer at its surface. We
couple this electrodynamic evolution with a field-dependent set of chemical
reactions that determine the internal channel conductivity. With this
one-dimensional model we investigate how key properties of a streamer affect
the channel's evolution. The ultimate objective of our model is to construct
realistic models of streamer coronas in order to understand better the physics
of long electrical discharges.
