  Previous theoretical works have shown that in optically thin disks, dust
grains are photoelectrically stripped of electrons by starlight, heating nearby
gas and possibly creating a dust clumping instability, the photoelectric
instability (PeI), that significantly alters global disk structure. In the
current work, we use the Pencil Code to perform the first numerical models of
the PeI that include stellar radiation pressure on dust grains in order to
explore the parameter regime in which the instability operates. In models with
gas surface densities greater than $\sim$$10^{-4}~\mathrm{g}~\mathrm{cm}^{-2}$,
we see a variety of dust structures, including sharp concentric rings and
non-axisymmetric arcs and clumps that represent dust surface density
enhancements of factors of $\sim$$5-20$ depending on the run parameters. The
gas distributions show various structures as well, including clumps and arcs
formed from spiral arms. In models with lower gas surface densities, vortices
and smooth spiral arms form in the gas distribution, but the dust is too weakly
coupled to the gas to be significantly perturbed. In one high gas surface
density model, we include a large, low-order gas viscosity, and, in agreement
with previous radiation pressure-free models, find that it observably smooths
the structures that form in the gas and dust, suggesting that resolved images
of a given disk may be useful for deriving constraints on the effective
viscosity of its gas. Broadly, our models show that radiation pressure does not
preclude the formation of complex structure from the PeI, but the qualitative
manifestation of the PeI depends strongly on the parameters of the system. The
PeI may provide an explanation for unusual disk morphologies such as the moving
blobs of the AU Mic disk, the asymmetric dust distribution of the 49 Ceti disk,
and the rings and arcs found in the disk around HD 141569A.
