A one dimensional model of a peculiar configuration of charged layers in equilibrium composed by one electron rich layer surrounded by two ion rich layers adjacent to plasmas at distinct potentials and which is formed in a low pressure arc discharge (usually know as a triple layer) has been constructed using the BGK method [1] viz., with the help of the Poisson-Vlasov's system of equations applied to the free and reflected populations of electrons and ions in a supposedly existing electrostatic potential with the free populations assumed to be monoenergetic beams and the reflected ones obeying the Maxwell-Boltzmann distribution. Sagdeev potentials derived for the charged region and matched by appropriate plasma boundary conditions are numerically integrated to obtain the electrostatic potential for some set of free input parameters, compatible with those of a specific group of experiments. Limitations of the model are addressed to.