Generalized random walk model of cathode spot motion

Cathode spots in a cathodic arc discharge exhibit complex dynamical motion. Traditionally, this motion has been modeled as a simple random walk with fixed-step size and time, but this approach fails to reconcile the large variations in experimental measurements of step size and time and it also fails to explain the temporal self-similarity of the cathode spot process in the burning voltage noise. We propose a generalized random walk model based on a diffusive continuous time random walk, allowing step size and time to be governed by evolving probability distributions. The proposed model resolves the inconsistencies in earlier models and successfully reproduces the fractal features seen in experiments, namely, the Brownian noise in the spectral power density of the burning voltage and in light emission.