Model of pulsed electric discharge expansion in dense gas, taking into account electron and radiative thermal conductivities. V. Invariants of the set of equations describing the pulsed discharge

Similarity exponents of physical quantities of pulsed electric discharges in gases (at atmospheric pressure and above) and their dimensional invariants with respect to the linear coordinate and time transformation x' (i) = sx (i) , t' = st (s is the compression/stretching coefficient) are determined. Their dimensionless invariants are found from the invariance of the dimensionless continuity, motion, and energy balance equations with respect to the linear coordinate and time transformation. The values of the dimensionless invariants are determined from the condition of the uniform distribution of the plasma pressure in the discharge channel. Using these invariants, it became possible to reduce partial differential equations to ordinary differential equations solutions to which are used to determine the time dependences of the discharge channel radius and the time dependences of the plasma density and temperature (on the discharge channel axis) for the initial discharge stage.