Dynamics of a Resistive Sheet Pinch

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Abstract
The dynamic evolution and the saturated state of a long sheet pinch subject to growth of resistive tearing modes was investigated by numerical solution of the 2D MHD equations. Both the compressible and the incompressible equations were used, and the difference is found to be negligible. The necessity of considering a resistive equilibrium is stressed. The paper concentrates on a static equilibrium maintained by an external electric field and requiring a special distribution of the resistivity η. In addition the dynamics of the resistivity plays an important part. Assuming η to be time independent, the sheet pinch develops a number of soliton-like magnetic islands, which coalesce. The final state consists of a single soliton, while the generation of further sol-itons is inhibited by a strong shear flow allong the current sheet. When allowance is made for parallel diffusion of the resistivity such that η is essentially a flux function, the final state is quite different. Here the longest wavelength dominates, leading to a single, large island and completely destroying the original sheet pinch

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