Three-dimensional magnetohydrodynamic simulations of the interaction of magnetic flux tubes

We use a three-dimensional Cartesian resistive MHD code to investigate three-dimensional aspects of the interaction of magnetic flux tubes as observed in the solar atmosphere and studied in laboratory experiments. We present here the first results from modeling the reconnection of two Gold-Hoyle magnetic flux tubes that follow the system. evolution to a final steady state. The energy evolution and reconnection rate for flux tubes with both parallel and antiparallel axial fields and with equal and nonequal strengths are studied. For the first time, we calculate a gauge-invariant relative magnetic helicity of the system and compare its evolution for all the above cases. We observed that the rate at which helicity is dissipated may vary significantly for different cases, and it may be comparable with the energy dissipation rate. The footpoints of the interacting flux tubes were held fixed or allowed to move to simulate different conditions in the solar photosphere. The cases with fixed footpoints had lower magnetic energy release and reached a steady state faster than cases with moving footpoints. For all computed cases the magnetic energy was released mostly through work done on the plasma by the electromagnetic forces rather than through resistive dissipation. The reconnection rate of the poloidal magnetic field is faster for the case with antiparallel flux tubes than for the case with parallel flux tubes, consistent with laboratory experiments. We find that during reconnection supersonic (but sub-Alfvenic) flows develop, and it may take a considerably longer time for the system to reach a steady state than for magnetic Bur to reconnect. It is necessary to retain the pressure gradient in the momentum equation; the plasma pressure may be significant for the final equilibrium steady state even with low-beta initial conditions, and the work done on the plasma by compression is important in energy exchange.