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This paper brings further insight into the recently published N-bodydescription of Debye shielding and Landau damping [Escande D F, Elskens Y andDoveil F 2014 Plasma Phys. Control. Fusion 57 025017]. Its fundamental equationfor the electrostatic potential is derived in a simpler and more rigorous way.Various physical consequences of the new approach are discussed, and thisapproach is compared with the seminal one by Pines and Bohm [Pines D and Bohm D1952 Phys. Rev. 85 338--353].

N-body description of Debye shielding and Landau damping