Using Nonextensive Statistics and Spectral Theory to Characterize Anomalous Diffusion in Fusion Plasmas

Anomalous diffusion is commonly observed in tokamaks and stellarators in the form of energetic electrons, which can sometimes escape confinement and lead to wall damage. These sub-populations of energetic particles lead to non-Maxwellian distribution functions for the electron position, velocity, and energy. Here we apply nonextensive statistics to study energetic electrons in fusion plasmas. The nonextensive statistics is a formulation in which the typical distributions are q-Gaussian where quantifies how much the distribution deviates from a Gaussian or a Maxwellian. Here we reconstruct histograms of electron displacements from particle tracing simulations using data from the DIII-D and NSTX-U tokamaks. We fit a q-Gaussian distribution to these histograms to extract for different plasma conditions. The value of is then used to determine the fraction on a Fractional Laplacian through an analytically derived scaling relation. Finally, a Fractional Laplacian Spectral code is used to find the probability for electron diffusion at different spatial scales.