  Streamer discharges pose basic problems in plasma physics, as they are very
transient, far from equilibrium and have high ionization density gradients;
they appear in diverse areas of science and technology. The present paper
focuses on the derivation of a high order fluid model for streamers. Using
momentum transfer theory, the fluid equations are obtained as velocity moments
of the Boltzmann equation; they are closed in the local mean energy
approximation and coupled to the Poisson equation for the space charge
generated electric field. The high order tensor in the energy flux equation is
approximated by the product of two lower order moments to close the system. The
average collision frequencies for momentum and energy transfer in elastic and
inelastic collisions for electrons in molecular nitrogen are calculated from a
multi term Boltzmann equation solution. We then discuss, in particular, (1) the
correct implementation of transport data in streamer models; (2) the accuracy
of the two term approximation for solving Boltzmann's equation in the context
of streamer studies; and (3) the evaluation of the mean-energy-dependent
collision rates for electrons required as an input in the high order fluid
model. In the second paper in this sequence, we will discuss the solutions of
the high order fluid model for streamers, based on model and input data derived
in the present paper.
