1. Progress in Fluxon modeling C.E. DeForest, SwRI LWS workshop, March 2004 Fluxons are discrete field lines. Fluxons have many advantages over existing MHD codes. The SwRI fluxon code is nearly ready for scientific application.

2. Gripes about existing MHD codes... ● Eulerian grids are too resistive. ● Lagrangian grids fail in evolving systems. ● 3-D models choke even huge computers.

3. What are fluxons, and what makes them so great? ● Fluxons are quantized field lines that interact at a distance. ● They are modeled as lists of nodes located in 3-space. ● Forces are calculated via analytic geometry. ● Current code: finds force-free fields by magnetofriction. ● Future code: quasi-stationary MHD, then full MHD. ● Fluxon models are divergence-free by construction. ● Boundaries: none (no box!) ● Reconnection: none unless you add it, which is easily done. ● Node count scales as O(L 2.1 )-O(L 2.4 ) for 3-D simulation.

4. Adapting Maxwell's Equations to Fluxons... Magnetic energy in a volume: Force resolves to the magnetic pressure and curvature forces: How to estimate B from the geometry?

5. Voronoi mathematics deals with related problems. Finding the 3-D neighborhood is tractable but expensive. Voronoi Analysis: 3-D The B field is just each fluxon's flux, divided by the cross-section of its neighborhood and directed along the fluxon.

6. Voronoi Analysis: 2-D (Cross-sectional Plane) Working in the cross- sectional plane makes finding the Voronoi neighborhood affordable. The geometry of the neighborhood gives both the magnetic pressure and its gradient.

7. Simple 3-D Relaxations Fluxon relaxation in simple cases yields familiar answers. Potential field animationSimple current animation

8. Interacting flux A low (freshly emerged?) potential field bipole interacts with a simple current-carrying loop.

9. More views of the interacting flux

10. Performance, and future milestones: ● Those relaxations used 20 - 45 min. on a 1GHz Pentium laptop; 500-1,000 nodes each. ● Not optimized for speed. 10x-30x speedup feasible. ● 10 4 -10 5 nodes: OK for workstation. ('toy' problems) ● 10 6 -10 7 nodes: OK for big iron. (AR or global models) ● Validate code; write easier front-end. ● Augment to track tension build-up as boundary evolves. ● Add reconnection criteria. ● Add non-magnetic forces. ● Add inertial forces.

11. Some applications (Tomorrow, the world!)... ● Effect of magnetic carpet on corona ● Heating and evolution of active regions ● Aly-Sturrock conjecture (in-)validation ● CME onset; filament stability, formation, & support ● Interaction of plasmoids with the magnetosphere ● Real-time CME prediction (using HVMI & AIA)