Validity of the similarity law for the glow discharges in non-plane-parallel gaps

The glow discharges in the gaps geometrically similar to that used in glow discharge cleaning of the International Thermonuclear Experimental Reactor (ITER) were numerically simulated based on a two-dimensional fluid model in which the linear dimensions of gap A are two times that of gap B and the pressure of gap A is half that of gap B. Under an applied voltage of 1000 V, the physical parameters at the corresponding point pz in these two gaps were compared. It was found that the electric potential U(pz), the reduced field E(pz)/p and the electron temperature Te(pz) are equal in values for these two gaps, but the electron density ne(pz) and ion density ni(pz) for gap B are four times that of gap A. All these parameter ratios are the same as that defined by similarity law, which confirmed that the similarity law is valid for the glow discharges in non-plane-parallel gaps.