  We discuss the prospects for the detection of gamma-ray bursts (GRBs) by the
Cherenkov Telescope Array (CTA), the next generation, ground-based facility of
imaging atmospheric Cherenkov telescopes (IACTs) operating above a few tens of
GeV. By virtue of its fast slewing capabilities, the lower energy threshold
compared to current IACTs, and the much larger effective area compared to
satellite instruments, CTA can measure the spectra and variability of GRBs with
excellent photon statistics at multi-GeV energies. Employing a model of the GRB
population whose properties are broadly consistent with observations by the
Gamma-ray Burst Monitor (GBM) and Large Area Telescope (LAT) onboard Fermi, we
simulate follow-up observations of GRBs with the Large Size Telescopes (LSTs),
the component of CTA with the fastest slew speed and the best sensitivity at
energies below a few hundred GeV. For our fiducial assumptions, we foresee that
the LSTs can detect ~0.1 GRBs per year during the prompt phase and ~0.5 per
year in the afterglow phase, considering only one array site and both GBM and
the Space-based multi-band astronomical Variable Object Monitor (SVOM) as the
alert instruments. The detection rates can be enhanced by a factor of about 5
and 6 for the prompt emission and the afterglow, respectively, assuming two
array sites with the same sensitivity and that the GBM localization error can
be reduced to less than 1 deg. The expected distribution of redshift and photon
counts are presented, showing that despite the modest event rate, hundreds or
more multi-GeV photons can be anticipated from a single burst once they are
detected. We also study how the detection rate depends on the intrinsic GRB
properties and the delay time between the burst trigger and the follow-up
observation.
