Asymptotic-preserving Lagrangian approach for modeling anisotropic transport in magnetized plasmas

Modeling electron transport in magnetized plasmas is extremely challenging due to the extreme anisotropy between parallel (to the magnetic field) and perpendicular directions (the transport-coefficient ratio $\chi_{\parallel}/\chi_{\perp} \sim 10^{10}$ in fusion plasmas). Recently, a novel Lagrangian Green's function method has been proposed\footnote{D. del-Castillo-Negrete, L. Chac\'on, \emph{PRL}, {\bf 106}, 195004 (2011); D. del-Castillo-Negrete, L. Chac\'on, \emph{Phys. Plasmas}, submitted (2011)} to solve the local and non-local \emph{purely} parallel transport equation in general 3D magnetic fields. The approach avoids numerical pollution, is inherently positivity-preserving, and is scalable algorithmically (i.e., work per degree-of-freedom is grid-independent). In this poster, we discuss the extension of the Lagrangian Green's function approach to include perpendicular transport terms and sources. We present an asymptotic-preserving numerical formulation, which ensures a consistent numerical discretization temporally and spatially for {\em arbitrary} $\chi_{\parallel}/\chi_{\perp}$ ratios. We will demonstrate the potential of the approach with various challenging configurations, including the case of transport across a magnetic island in cylindrical geometry.