One of the important aspects of the ectonic theory of vacuum discharge is the question of the emergence of new (or secondary) explosion centers - ectons, which would provide self-discharge. In this direction, a two-dimensional non-stationary model of initiation of new explosion emission centers in the interaction of the plasma of the cathode spot of the vacuum arc with the micro-steps of the cathode surface is proposed and developed. In this model, we assume that above the cathode surface there is a cathode spot plasma with the concentration of ions at the boundary of the space charge layer n_i and the electron temperature T_e. The shape of the microarray surface is given by the Gauss function z_s=hexp(-(r/d)²), where h is the height, d is the radius of the base r_mm, which is determined at z_s=0.1h. The micro-step geometry is conveniently characterized by the current density gain B_i=S/pi*r_m², where S is the surface area. In view of the fact that the thickness of the layer of space charge is much smaller than the characteristic dimensions of microvista, the parameters of the layer are considered one-dimensional (local) approximation. Calculation of the temperature field in the cathode is based on the heat equation. The ohmic electric field U and the current density in the cathode are determined on the basis of the continuity equation, which allows to calculate the Joule Heat source. To calculate the current density of ions, we assume that the ions are monoenergetic particles coming from the boundary of the spatial charge layer with a "bomovskoy" speed. In this case, all ions recombine on the cathode surface. The flow of ions from the plasma brings energy to the cathode, which causes a corresponding contribution to the surface heat source. Emission characteristics are calculated numerically in the WKB approximation taking into account the shift of the chemical potential due to a significant increase in the cathode temperature. To calculate the electric field on the cathode surface, the generalized McCone equation is used, taking into account the volume charge of electrons moving from the plasma to the cathode.

Numerical simulation of the micro-step heating process has shown that the process of energy absorption by the micro-step due to the flow of ions from the cathode spot plasma and the presence of the electric field of the spatial charge layer near the cathode surface provide the necessary "priming" power of the heat flow for the development of the Joule micro-step heating process and the subsequent micro-explosion at the ion current density values at the cathode 10⁶~10⁷ A·cm^-2 and the micro-step current density gain in several units.

Fig. 1. The geometry of the problem and the schematic diagram of the fluxes of charged particles on the boundary of cathode plasma.

Fig. 2. Spatial distribution of temperature (right) and current density module (left) at different times of thermal instability development. Calculation parameters: n_i =10²⁶ m^-3, T_e=2 eV, (j_i=5.6*10¹⁰ A/m²), =4.

Fig. 3. The dependence of the delay time before the explosion of microarray geometry: green – n_i=10²⁶ m^-3 T_e=2 eV (j_i=5.6*10¹⁰ A/m²), purple - n_i =1.8*10²⁶ m^-3, T_e=2 eV (j_i=1.1*10¹¹ A/m²).