“…where compared to the two-component VPB system (1.1), the dynamical equation of electrons and the ions-electrons collisions have been omitted, and the number density n e = R 3 f e dξ has been replaced by an analogue of the classical Boltzmann relation n e = exp{φ/T e }, or a general function depending on the potential function φ. We remark that the Boltzmann relation has been recently extensively visited in a lot of studies of kinetic and related fluid dynamic equations, for instance, [16,47,48,49,50,72]. Inspired by our previous works [25,26,28], we expect in the paper to further consider the much more physical two-component VPB system, particularly extending the results in [42,44] to the case of perturbations of the non-constant equilibrium state.…”