Magnetic Flux Cancellation and Coronal Magnetic Energy

I investigate the processes at work in the cancellation of normal mag- netic ∞ux in solar magnetograms, and study the relationships between cancellation and the budget of free magnetic energy in the coronal mag- netic fleld that can power solar ∞ares and CMEs. After deflning cancel- lation mathematically, I derive equations that quantify the evolution of free magnetic energy in response to arbitrary plasma ∞ows on the bound- ary, including ∞ows consistent with cancellation. While cancellation can reduce the magnetic energy in both the actual coronal fleld and the poten- tial fleld matching the same normal fleld boundary condition, cancellation can, in the process, increase the difierence between the two, i.e., cancel- lation can increase the free magnetic energy in the corona. By making simple assumptions based upon typical observed fleld conflgurations in fllament channels, I show that cancellation tends to add free energy to these flelds. Finally, I discuss the implications of this fact, as well as wider applications of the free energy ∞ux formalism developed here. I also brie∞y address related issues, including the relationship of cancellation to Taylor's hypothesis.