Computational study of the internal kink mode evolution and associated magnetic reconnection phenomena

Numerical study of plasma relaxation and self-organization in two-dimensional incompressible magnetohydrodynamic (MHD) systems is presented. A large semi-periodic tearing unstable reversed magnetic field configuration in flat Cartesian geometry and a driven tokamak-like kink-unstablescrew pinch in helical geometry are considered. Special emphasis is made on the coupling between global and local scales by way of magnetic reconnection. The influence of the global system's size and geometry on the magnetic reconnection phenomenon and associated current sheet dynamics are evaluated in different collisionality regimes. Questions of plasmoid formation by way of current sheet break-up and onset of fast reconnection in a semi-collisional regime are investigated. Visco-resistive, electron and Hall MHD plasma fluid models are employed in the study. In helical geometry, application of Ohmic current drive to the periodic screw-pinch with large axial magnetic field and hollow resistivity profile are shown to result in "sawtooth-like" limit cycle behavior which is independent of the exact initial conditions. Incomplete reconnection saw-teeth, maintaining the value of safety factor q in the central plasma region below unity throughout the cycle, are demonstrated for the first time in numerical simulations. Sensitivity of sawtooth characteristics to a number of plasma parameters is evaluated. The initial value problems described above are solved with an adaptive fully implicit parallel macroscopic modeling code SEL, which is capable of evolving a large range of extended MHD equations. The structure, key features, and thorough testing of the code are described in detail.