Current sheet formation due to nonlinear kink modes in periodic and line-tied configurations

The full magnetohydrodynamic evolution of kink instabilities in cylindrical geometry is computed. The equilibria investigated serve as generic models of coronal loops. The effects of both periodic and line-tying boundary conditions at the axial ends of the cylinder are compared and contrasted. The net axial current, which is distributed internally to the loop, can be varied from case to case. It is found that one effect of the line-tying boundary condition is that the minimum length for the onset of a kink instability is increased. For line-tied loops, resonant surfaces do not exist, though linear analysis shows that there may or may not occur quasi-resonant regions, i.e., regions of strong gradients, which, however, are confined to the loop apex, far from the line-tied boundaries. When such a region is present for the linear mode, the formation and nonlinear development of current layers is confined to the central region of the loop. In a case where no such regions exist for the linear mode (corresponding to k . B not equal 0 in the periodic cylinder!, current concentrations appear two thirds of the way from the center of the loop. This effect disappears in the axially periodic case. The consequences of these results for solar physics are discussed. (C) 1998 American Institute of Physics. [S1070-664X(98)01010-6].