Unambiguity of matching of the fields of a nonlinear ionizing electromagnetic wave at a discontinuity near a plasma resonance point

The selection of solutions (discontinuous near the plasma-resonance point) of the locally nonlinear electrodynamic problem of the action of a strong ionizing high-frequency electromagnetic wave is considered. To this end, the locally nonlinear problem is treated from the viewpoint of a more complete but singularly perturbed problem, that of finding the field, the temperature, and the density of the electrons. To select the solutions of the locally nonlinear problem it is proposed to use a criterion from the theory of singularly perturbed equations, namely choose from among all its solutions only the one which is simultaneously a solution of the initial problem. For solutions with jumps whose structure is determined by the equation of heat conduction (through the point of the plasma resonance due to superheating of the plasma, disregarding diffusion), this criterion calls for satisfaction of a certain integral condition that leads to continuity of the heat flux through the jump. This integral equation is expounded in detail for a jump through the point of the plasma resonance that appears in the field of a strong high-frequency ionizing electromagnetic wave