Helicity dissipation in planar periodic geometries

Topological problems associated with magnetic merging in periodic geometrie s are considered. It is pointed out that although magnetic reconnection at a single site in a periodic ensemble of null points appears physically well defined, there is some difficulty in interpreting magnetic helicity. We in vestigate numerically the thought experiment of Berger [1997], in which he claims a periodic assemblage of Aux tubes may be turned inside out in weakl y resistive plasmas, thereby violating: Taylor's conjecture that the helici ty (or handedness) of the tubes should be approximately invariant. A concre te demonstration confirms the reversal of the flux tubes, and Berger's sugg ested periodic helicity measure also changes sign. We conclude that helicit y is not approximately conserved in weakly resistive periodic plasmas and t herefore that topological fidelity cannot be guaranteed. We go on to sugges t that unlike their doubly periodic counterparts, magnetic merging experime nts in singly periodic geometries may admit well-defined topological invari ants.