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Analysis of a noncircular diffuse pinch

The stability of incompressible columnar diffuse pinch with rectangular cross-section was studied. The results show that the operator in the transformed linear equation retains its self-adjointness, that a large number of perturbations are eliminated by the effect of the right-angled corners of the rectangle, that the flow pattern is determined by the vertical to horizontal ratio of the rectangle, and that the frequency varies with current density. It is suggested that there is an upper limit to the toroidal current when perturbations expressed by the displacement are approximated with the Fourier series truncated at high modes.