  We study the production dynamics of charm quarks in the parton cascade model
for relativistic heavy ion collisions at RHIC and LHC energies. The model is
eminently suited for a study of the pre-equilibrium dynamics of charm quarks at
modest transverse momenta. The treatment is motivated by QCD parton picture and
describes the dynamics of an ultra-relativistic heavy-ion collision in terms of
cascading partons which undergo scattering and multiplication while
propagating. We find considerable suppression of charm quarks production in
$AA$ collisions compared to those for $pp$ collisions at the same
$\sqrt{s_{\text {NN}}}$ scaled by number of collisions. This may be important
for an accurate determination of energy loss suffered by charm quarks while
traversing the thermalized quark gluon plasma.
