El Naschie’s ε(∞) space–time and patterns in plasma discharge

Abstract It is shown that the dynamics of the double layer implies fractal space–time. Then, through the spontaneous symmetry breaking the Langmuir’s relations, the distributions of the potential, field, charge densities and the evolution to chaos through period doubling have been obtained. Assimilating the double layer with a plasma–plasma interface and using the scale relativity theory, the breaking frequency and the hysteresis have been analyzed. The correspondence with El Naschie’s e (∞) space–time implies the particles phase correlation in the double layer. The model was also verified by means of our experimental data.