  We study the effect of an inhomogeneous gas density on positive streamer
discharges in air using a 3D fluid model with stochastic photoionization,
generalizing earlier work with a 2D axisymmetric model by Starikovskiy and
Aleksandrov (2019 Plasma Sources Sci. Technol. 28 095022). We consider various
types of planar and (hemi)spherical gas density gradients. Streamers propagate
from a region of density n0 towards a region of higher or lower gas density n1,
where n0 corresponds to 300 K and 1 bar. We observe that streamers can always
propagate into a region with a lower gas density. When streamers enter a region
with a higher gas density, branching can occur at the density gradient, with
branches growing in a flower-like pattern over the gradient surface. Depending
on the gas density ratio, the gradient width and other factors, narrow branches
are able to propagate into the higher-density gas. In a planar geometry, we
find that such propagation is possible up to a gas density slope of 3.5n0/mm,
although this value depends on a number of conditions, such as the gradient
angle. Surprisingly, a higher applied voltage makes it more difficult for
streamers to penetrate into the high-density region, due to an increase of the
primary streamer's radius.
