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In this paper, we derive a Vlasov type kinetic model for diatomic plasma inwhich each ion consists of two atoms bonded through an oscillatoryintermolecular force given by a singular Hooke potential. We then consider theexistence and uniqueness of the classical solution to the proposed model. Acareful analysis of the oscillatory behavior of atoms near singular points ofthe Hooke potential is carried out to extend the local-in-time solution to theglobal solution.

One-dimensional diatomic Vlasov-Poisson system with oscillatory molecular bonds