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

We use a three-dimensional Cartesian resistive MHD code to investigate thre e-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 mag netic flux tubes that follow the system. evolution to a final steady state. The energy evolution and reconnection rate for flux tubes with both parall el and antiparallel axial fields and with equal and nonequal strengths are studied. For the first time, we calculate a gauge-invariant relative magnet ic 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 signif icantly for different cases, and it may be comparable with the energy dissi pation rate. The footpoints of the interacting flux tubes were held fixed o r allowed to move to simulate different conditions in the solar photosphere . The cases with fixed footpoints had lower magnetic energy release and rea ched a steady state faster than cases with moving footpoints. For all compu ted cases the magnetic energy was released mostly through work done on the plasma by the electromagnetic forces rather than through resistive dissipat ion. The reconnection rate of the poloidal magnetic held is faster for the case with antiparallel flux tubes than for the case with parallel flux tube s, consistent with laboratory experiments. We find that during reconnection supersonic (but sub-Alfvenic) flows develop, and it may take a considerabl y 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 moment um equation; the plasma pressure may be significant for the final equilibri um steady state even with low-beta initial conditions, and the work done on the plasma by compression is important in energy exchange.