Self-Affine Fractality of Bifurcating Arc Trail in Magnetized Plasma

Fractality of the arc trail in magnetized plasma is investigated on the basis of an experimental observation and numerical simulation. When the trail of a unipolar arc on a tungsten electrode is analyzed in detail, the global fractal dimension is observed to reach unity, while the local dimension is considerably high, typically 1.65. This indicates that the arc trail in magnetized plasma has self-affine fractality. Physically, this is because global motion is controlled by the magnetic field, though the arc spot moves randomly on a smaller scale. A Monte Carlo simulation is introduced to model the arc spot motion by considering the self-avoiding effect, directional movement, and bifurcation effect. This reveals that the effect of the magnetic field increases the probability of reignition in the direction of global motion by several tens percent, assuming that the stride size of the random walk is consistent with the trail width of 10 µm.