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The motion of a collisionless plasma is described by the Vlasov-Poissonsystem, or in the presence of large velocities, the relativistic Vlasov-Poissonsystem. Both systems are considered in one space and one momentum dimension,with two species of oppositely charged particles. A new identity is derived forboth systems and is used to study the behavior of solutions for large times.

Decay in Time for a One-Dimensional Two-Component Plasma