El Naschie’s self-organization of the patterns in a plasma discharge: Experimental and theoretical results

Abstract

Abstract Using the finite differences method it is shown that a diffusion equation can generate but not maintain a double layer (DL). Instead of these, a reaction–diffusion equation system induces a Koch-type fractal which leads to a self-organization scenario of plasma–plasma interface as a DL. Using the scale relativity theory (SRT) it was shown that a plasma–plasma interface behaves as a junction of Josephson type: a negative differential resistance is its self-structuring condition, it has memory through hysterezis and work in two oscillation regimes. The correspondence with El Naschie’s e (∞) space time is achieved, through the generation of the harmonics of Cantorian fractal type, as well as through the separation of the oscillation regimes, i.e. the intermittent self-organization. In the linear regime of oscillation, the plasma–plasma interface works as a string of Cantorian-fractal type (El Naschie’s string). The model was verified by means of our experimental data too.