  Numerical studies of primordial star formation suggest that the first stars
in the universe may have been very massive. Stellar models indicate that
non-rotating Population III stars with initial masses of 140-260 Msun die as
highly energetic pair-instability supernovae. We present new two-dimensional
simulations of primordial pair-instability supernovae done with the CASTRO
code. Our simulations begin at earlier times than previous multidimensional
models, at the onset of core collapse, to capture any dynamical instabilities
that may be seeded by collapse and explosive burning. Such instabilities could
enhance explosive yields by mixing hot ash with fuel, thereby accelerating
nuclear burning, and affect the spectra of the supernova by dredging up heavy
elements from greater depths in the star at early times. Our grid of models
includes both blue supergiants and red supergiants over the range in progenitor
mass expected for these events. We find that fluid instabilities driven by
oxygen and helium burning arise at the upper and lower boundaries of the oxygen
shell $\sim$ 20 - 100 seconds after core bounce. Instabilities driven by
burning freeze out after the SN shock exits the helium core. As the shock later
propagates through the hydrogen envelope, a strong reverse shock forms that
drives the growth of Rayleigh--Taylor instabilities. In red supergiant
progenitors, the amplitudes of these instabilities are sufficient to mix the
supernova ejecta.
