On Fractal Properties of Equipotentials over a Real Rough Surface Faced to Plasma in Fusion Devices

We consider a sheath region bounded by a corrugated surface of material conductor and a flat boundary held to a constant voltage bias. The real profile of the film deposited from plasma on a limiter in a fusion device was used in numerical solving of the Poisson's equation to find a profile of electrostatic potential. The rough surface influences the equipotential lines over the surface. We characterized a shape of equipotential lines by a fractal dimension. The long-range correlation in the potential field is imposed by the non-trivial fractal structure of the surface. Dust particles bounced in such irregular potential field can accelerate due to the Fermi acceleration.