Abstract Details
Abstracts
Author: Bradley R Andrew
Requested Type: Poster
Submitted: 2023-03-23 13:55:33
Co-authors: E.G. Kostadinova, D.M. Orlov
Contact Info:
Auburn University
380 Duncan Drive
Auburn, Alabama 36849
United States
Abstract Text:
The Nonlinear Fokker Planck (NLFP) equations are useful in plasma physics when the evolution of the density is affected by nonlinear behavior, nonlocal interactions, and/or anomalous diffusion. In some cases, the power-law NLFP equation admits q-Gaussian solutions, where the q-parameter quantifies the degree of non-extensivity of the distribution function. Difficulty arises in solving NLFP equations due to the power-law dependence of the density function in the diffusion term. An alternative approach is substituting the nonlinear diffusion term with a Factional Laplacian operator acting on the distribution. This new equation is linear and called the Fractional Laplacian Diffusion (FLD) equation. We conjecture that scaling relations exist between the fraction on the Laplacian, s, in the FLD equation and the power on the distribution, (2-q), in the (no-drift) NLFP equation. Specifically, for the family of q-Gaussian solutions satisfying q ϵ (1,3), we propose the scaling relation s=((3-q))1⁄2.
To examine this conjecture, we investigate the spectrum of an Anderson-type Hamiltonian with a Fractional Laplacian for а range of s values corresponding to known solutions of the NLFP equation in terms of q-Gaussian distributions. We discuss the conditions when it is possible to replace the nonlinear NLFP equation by the linear FLD equation. To test this theory, we present preliminary analysis of DIII-D data from experiments where energetic electrons have been detected. Data from various diagnostics (TS, ECE, GRI, HXR) is used to reconstruct the non-Maxwellian electron distribution. Then, a q-Gaussian is fitted to extract the values of q and the corresponding s. Finally, the Fractional Laplacian Spectral (FLS) model is used to calculate the probability for transport as a function of spatial scale. The FLS predictions are compared against experimental observations to assess the validity of the q-s scaling relation.
DE-FC02-04ER54698, DE- FG02-05ER54809, DE-SC0023061.
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