  Planet formation via core accretion requires the production of km-sized
planetesimals from cosmic dust. This process must overcome barriers to simple
collisional growth, for which the Streaming Instability (SI) is often invoked.
Dust evolution is still required to create particles large enough to undergo
vigorous instability. The SI has been studied primarily with single size dust,
and the role of the full evolved dust distribution is largely unexplored. We
survey the Polydispserse Streaming Instability (PSI) with physical parameters
corresponding to plausible conditions in protoplanetary discs. We consider a
full range of particle stopping times, generalized dust size distributions, and
the effect of turbulence. We find that, while the PSI grows in many cases more
slowly with a interstellar power-law dust distribution than with a single size,
reasonable collisional dust evolution, producing an enhancement of the largest
dust sizes, produces instability behaviour similar to the monodisperse case.
Considering turbulent diffusion the trend is similar. We conclude that if fast
linear growth of PSI is required for planet formation, then dust evolution
producing a distribution with peak stopping times on the order of 0.1 orbits
and an enhancement of the largest dust significantly above the single power-law
distribution produced by a fragmentation cascade is sufficient, along with
local enhancement of the dust to gas volume mass density ratio to order unity.
