  Negative streamer ionization fronts in nitrogen under normal conditions are
investigated both in a particle model and in a fluid model in local field
approximation. The parameter functions for the fluid model are derived from
swarm experiments in the particle model. The front structure on the inner scale
is investigated in a 1D setting, allowing reasonable run-time and memory
consumption and high numerical accuracy without introducing super-particles. If
the reduced electric field immediately before the front is >= 50kV/(cm bar),
solutions of fluid and particle model agree very well. If the field increases
up to 200kV/(cm bar), the solutions of particle and fluid model deviate, in
particular, the ionization level behind the front becomes up to 60% higher in
the particle model while the velocity is rather insensitive. Particle and fluid
model deviate because electrons with high energies do not yet fully run away
from the front, but are somewhat ahead. This leads to increasing ionization
rates in the particle model at the very tip of the front. The energy overshoot
of electrons in the leading edge of the front actually agrees quantitatively
with the energy overshoot in the leading edge of an electron swarm or avalanche
in the same electric field.
