  We explore the prospects for using future supernova observations to probe the
dark energy. We focus on quintessence, an evolving scalar field that has been
suggested as a candidate for the dark energy. After simulating the observations
that would be expected from the proposed SuperNova / Acceleration Probe
satellite (SNAP), we investigate two methods for extracting information about
quintessence from such data. First, by expanding the quintessence equation of
state as w_Q(z) = w_Q(0)-alpha*ln(1+z), to fit the data, it is possible to
reconstruct the quintessence potential for a wide range of smoothly varying
potentials. Second, it will be possible, to test the basic properties of the
dark energy by constraining the parameters Omega_Q, w_Q and alpha. We show that
it may be possible, for example, to distinguish between quintessence and the
cosmological constant in this way. Further, when supernova data are combined
with other planned cosmological observations, the precision of reconstructions
and parameter constraints is significantly improved, allowing a wider range of
dark energy models to be distinguished.
