Cantorian structures in discharge plasma double layers. Theoretical and experimental aspects of basic processes

Using a one-dimensional nonlinear diffusion equation we show that the oscillation modes of a discharge plasma are cnoidal. By their degeneration, we get striations, solitons, etc., the last corresponding to quasi-autonomous structures of a double layer (DL) type. Considering of the DL as a superconducting structure, its inside dynamics is given both by expelling the electrostatic field and by focusing the charge particle beam. In two dimensions, the cnoidal oscillation modes of the discharge plasma DLs assimilated to a superconducting lattice impose the Cantorian structure of space-time. In this context it results in a direct relationship between the high-dimensional fractal string and theory [see Solitons & Fractals 12 (2001) 875] via the electromagnetic fine structure constant. The theoretical model is validated by experimental studies of plasma DLs, through electrical and spectral methods.