Session ZM05: Mini-Conference on Transport in Non-Ideal, Multi-Species Plasmas II

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In the hydrodynamic description of plasmas, a large number of transport processes, such as thermal and electrical conductivity, temperature relaxation and stopping power are dominated by electrons, where the physics of these processes is captured in the corresponding transport coefficients. We present a model for these coefficients that have been numerically computed using an effective screening potential approach. Within the framework of the Boltzmann collision operator, accurate fits for the relevant cross sections and collision integrals are calculated. The results are then validated by both experimental results as well as simulations from higher-fidelity theoretical models.   

Live

A multitemperature Bhatnagar-Gross-Krook kinetic model is developed that includes partial degeneracy for the electrons. The model is constructed to satisfy the basic conservation laws with an H-theorem, generalized to mixed statistics (i.e., Maxwell-Boltzmann, Fermi-Dirac), that yields the desired equilibrium limit. From this model, we obtain a moment-based quantum hydrodynamics formulation closed through a Chapman-Enskog expansion to yield expressions for the transport coefficients, including electron-ion temperature relaxation and electronic thermal conductivity. The transport coefficients include both electron-electron and electron-ion collisions with degeneracy corrections valid from zero temperature to the classical limit. Comparisons in modeling philosophy and results are made with the Lee-More model.   

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Rotating plasma systems present novel possibilities for control of plasma parameters by varying the angular frequency of the vessel, thereby creating shear and driving cross-field transport. Furthermore, the existence of multiple ion species introduces additional cross-field transport effects which enrich the solution space and give rise to unique phenomena. We investigate experimentally-accessible profiles in a collisional magnetized plasma and discuss their merits for common applications of such systems.   

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Computational models are formulated in hierarchies of variable fidelity, often with no quantitative rule for defining the fidelity boundaries. We have constructed a dataset from a wide range of atomistic computational models to reveal the accuracy boundary between higher-fidelity models and a simple, lower-fidelity model. The symbolic decision boundary is discovered by optimizing a support vector machine on the data through iterative feature engineering. This data-driven approach reveals two important results: (1) a symbolic rule emerges that is independent of the algorithm, and (2) the symbolic rule provides a deeper understanding of the fidelity boundary. Specifically, our dataset is composed of radial distribution functions from seven high-fidelity methods that cover wide ranges in the features (element, density and temperature); high-fidelity results are compared with a simple pair-potential model to discover the nonlinear combination of the features, and the machine learning approach directly reveals the central role of atomic physics in determining accuracy. From the learned symbolic rule, transferability of the result is used to understand accuracy boundaries for diffusion and viscosity calculations in non-ideal plasmas.   

Live

Macroscopic models of non-ideal plasmas rely on closure information in the form of equations of state and transport coefficients. Unfortunately, our highest-fidelity models (e.g. Kohn-Sham molecular dynamics) remain very expensive to compute, especially at elevated temperatures where transport is most important. Lower fidelity models such as pair-potential molecular dynamics and analytic theories are orders of magnitude faster but lack the accuracy of the high-fidelity models. By using machine learning tools, we combine data at the various levels of fidelity to make high-fidelity predictions where it is impossible for the high-fidelity codes to operate. Here, we examine both multi-fidelity Gaussian process regression (GPR) and deep learning to predict transport coefficients (i.e., diffusion and viscosity) at high temperatures using calculations done at low temperature with Kohn-Sham molecular dynamics. We find excellent predictions, as measured through a cross validation procedure. Moreover, GPR adds additional value in that it "suggests" the most important new high-fidelity calculations by reporting confidence intervals throughout the extent of the prediction.