I. Introduction
Just after the initial investigations about influence of conductivity of rails on the current density distribution along the contact border [1], [2] the different propositions about application of conductor with special properties in the surface layer of rail as the method for improving of high current sliding contact properties were born. It could be, for example, a multilayer thin structure at variable conductivity from layer to layer, or thick enough surface layer with conductivity as a function of coordinates etc. Reference [1] is one of the first articles to obtain the current and magnetic field distribution in closed form. The railgun model in [3] has added the resistive layer at the rail surface, which increases from the beginning of rails to the muzzle. The concept of variable electrical conductivity as function of the rail length are also discussed in [4]–[6]. In detail, in [4], it was underlined an important role of contrast of electrical conductivity between rail and armature for improving of current distribution in the contact zone. In [5], it was proposed to dispose in the barrel of accelerator the special distributed resistors for improvement of current distribution. Later in the theoretical works [7], [8] there was shown the influence of ratio of the field diffusion coefficients (for rail/for armature) on the peak value of current density at the trailing edge of armature. In [9]–[12], the idea of variable surface conductivity of rails has been proposed as the key idea for resolution of sliding contact problems in the rail accelerator. In [9], the foundation of this idea was based on the analysis of commutation process during the motion of armature along the rail in the assumption that the variation of electrical conductivity is located exclusively in the skin depth of rails. That is a model of single surface layer with variable conductivity as a function of distance along the rail length. In [10], it was shown by author that local energy loss per unit or rail length can be constant, because the proposed reduction of the electrical conductivity is compensated by shortening of current passage time duration for each element of length in result of velocity of armature growth. In [11] and [12], a distribution of current density along the contact border has been simulated at application of multilayer structure of contact layer surface both in the rail and in the armature. It was shown there that due to special design of multilayer contact zones, the current density distribution along the contact border can be improved essentially with lowering peak of current density at trailing edge of armature up to velocity increase to 2.5 km/s.