This paper studies the construction of the exact solution for parabolic coupled systems of the type , , , , , and , where , , , and are arbitrary matrices for which the block matrix is nonsingular, and is a positive stable matrix.

Using 80 miniature soft-X-ray detectors viewing along chords through a plasma cross-section at one toroidal location, tomographic reconstructions of emissivity have been obtained without the need for assuming any symmetry or rotation of the plasma. In one class of plasma discharges, it is found that a large m = 1 oscillation, which previously had been ascribed to the rotation of an MHD instability, actually is not rotating at all.