The article covers workability of the density functional theory in systems consisting of two subsystems which include two various types of Fermi particles. At the description of similar systems, in particular, molecules and nanoclusters, the density functional method is carried out in the assumption that system properties can be described while considering the basic condition of non-uniform electronic gas moving in the potential created by motionless nuclear kernels. In this work it was shown that such an approach results in an error in definition of the basic energy of the system. Ways of quantitative estimation of this error were specified.

The paper considers problems of complex experimental research of high-beat states of electrode assemblies for electroarc devices working in a wide range of controlled environment pressures. The author describes methods and means of diagnostics of devices with hot cathodes (models with hollow cathode and with tungsten core cathode).  The experimental setup consisted of different diagnostic equipment which allowed to determine both local and integral thermophysical characteristics of the voltaic arc, namely: high temperature of the cathode (up to 3000 K) and its longitudinal distribution, large heat fluxes into the anode (QA ≥ 1 kW) and its distribution on the working electrode surface. The results of diagnostics of electrodes thermal states were discussed, and recommendations on their use in technological electroarc devices were given in this article.