  Reissner-Nordstr\"om Anti-de Sitter (RNAdS) black holes are unstable against
the charged scalar field perturbations due to the well-known superradiance
phenomenon. We present the time domain analysis of charged scalar field
perturbations in the RNAdS black hole background in general dimensions. We show
that the instabilities of charged scalar field can be explicitly illustrated
from the time profiles of evolving scalar field. By using the Prony method to
fit the time evolution data, we confirm the mode that dominates the long time
behavior of scalar field is in accordance with the quasinormal mode from the
frequency domain analysis. The superradiance origin of the instability can also
be demonstrated by comparing the real part of the dominant mode with the
superradiant condition of charged scalar field. It is shown that all the
unstable modes are superradiant, which is consistent with the analytical result
in the frequency domain analysis. Furthermore, we also confirm there exists the
rapid exponential growing modes in the RNAdS case, which makes the RNAdS black
hole a good test ground to investigate the nonlinear evolution of superradiant
instability.
