Fluxon Modeling of Low-Beta Plasmas
  We have developed a new, quasi-Lagrangian approach for numerical modeling of magnetohydrodynamics in low to moderate $\beta$ plasmas such as the solar corona. We introduce the concept of a ``fluxon'', a discretized field line. Fluxon models represent the magnetic field as a skeleton of such discrete field lines, and interpolate field values from the geometry of the skeleton where needed, reversing the usual direction of the field line transform. The fluxon skeleton forms the grid for a collection of 1-D Eulerian models of plasma along individual flux tubes. Fluxon models have no numerical resistivity, because they preserve topology explicitly. Our prototype code, \emph{FLUX}, is currently able to find 3-D nonlinear force-free field solutions with a specified field topology, and work is ongoing to validate and extend the code to full magnetohydrodynamics. FLUX has significant scaling advantages over conventional models: for ``magnetic carpet'' models, with photospheric line-tied boundary conditions, FLUX simulations scale in complexity like a conventional 2-D grid although the full 3-D field is represented. The code is free software and is available online. In this current paper we introduce fluxons and our prototype code, and describe the course of future work with the code. 
Craig E. DeForest, Charles C. Kankelborg