Erratum: “Exact nonlinear analytic Vlasov–Maxwell tangential equilibria with arbitrary density and temperature profiles” [Phys. Plasmas 10, 2501 (2003)]

The tangential layers are characterized by a bulk plasma velocity and amagnetic field that are perpendicular to the gradient direction. They have beenextensively described in the frame of the Magneto-Hydro-Dynamic (MHD) theory.But the MHD theory does not look inside the transition region if the transitionhas a size of a few ion gyroradii. A series of kinetic tangential equilibria,valid for a collisionless plasma is presented. These equilibria are exactanalytical solutions of the Maxwell-Vlasov equations. The particle distributionfunctions are sums of an infinite number of elementary functions parametrizedby a vector potential. Examples of equilibria relevant to space plasmas areshown. A model for the deep and sharp density depletions observed in theauroral zone of the Earth is proposed. Tangential equilibria are also relevantfor the study of planetary environments and of remote astrophysical plasmas