  High resolution N-body simulations have revealed the survival of considerable
substructure within galactic halos. Assuming that the predicted dark matter
clumps are composed of annihilating neutralinos, we examine their detectability
via Atmospheric Cherenkov Telescopes (ACTs). Depending on their density
profile, individual neutralino clumps should be observable via their gamma-ray
continuum and line emissions. We find that the continuum signal is the most
promising signal for detecting a neutralino clump, being significantly stronger
than the monochromatic signals. Limits from the line detectability can help
lift degeneracies in the supersymmetric (SUSY) parameter space. We show that by
combining the observations of different mass clumps, ACTs can explore most of
the SUSY parameter space. ACTs can play a complementary role to accelerator and
gamma-ray satellite limits by exploring relatively large neutralino masses and
less concentrated clumps. We develop a strategy for dark matter clump studies
by future ACTs based on VERITAS specifications and encourage the development of
techniques to identify primaries. This can reduce the background by an order of
magnitude.
