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We study the production dynamics of charm quarks in the parton cascade modelfor relativistic heavy ion collisions at RHIC and LHC energies. The model iseminently suited for a study of the pre-equilibrium dynamics of charm quarks atmodest transverse momenta. The treatment is motivated by QCD parton picture anddescribes the dynamics of an ultra-relativistic heavy-ion collision in terms ofcascading partons which undergo scattering and multiplication whilepropagating. 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 importantfor an accurate determination of energy loss suffered by charm quarks whiletraversing the thermalized quark gluon plasma.

Medium Modification of Charm Production in Relativistic Heavy Ion  Collisions due to Pre-equilibrium Dynamics of Partons at $\sqrt{s_{\textrm  {NN}}}$= 0.2--5.02 TeV