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.