Efficient Coupling of Fluid-Plasma and Monte-Carlo-Neutrals Models for Edge Plasma Transport

UEDGE [1] has been valuable for modeling transport in the tokamak edge and scrape-off layer due in part to its efficient \textit{fully} \textit{implicit} solution of coupled \textit{fluid} neutrals and plasma models. We are developing an implicit coupling of the kinetic Monte-Carlo (MC) code DEGAS-2 [2], as the neutrals model component, to the UEDGE plasma component, based on an extension of the Jacobian-free Newton-Krylov (JFNK) method to MC residuals [3]. The coupling components build on the methods and coding already present in UEDGE. For the linear Krylov iterations, a procedure has been developed to ``extract'' a good preconditioner from that of UEDGE. This preconditioner may also be used to greatly accelerate the convergence rate of a relaxed fixed-point iteration, which may provide a useful ``intermediate'' algorithm. The JFNK method also requires calculation of Jacobian-vector products, for which any finite-difference procedure is inaccurate when a MC component is present [3]. A semi-analytical procedure that retains the standard MC accuracy and fully kinetic neutrals physics is therefore being developed. [1] T.D. Rognlien et al., Contrib. Plasma Phys. \textbf{34}, 362. (1994). [2] D. Stotler {\&} C. Karney, Contr. Plas. Phys., 34, 392 (1994). [3] J. Willert, et al., SIAM J. Numer. Anal. \textbf{53}, 1738 (2015).