Abstract
The recent stage of the magnetohydrodynamic energy principle applied to laboratory and space plasmas is briefly reviewed. In detail, the energy principle is presented for an internally homogeneous pinch in a perfectly conducting wall. The plasma is separated from the wall by a vacuum. The principle is applied to ITER-type and lightning systems. Thereat, a system of mathematical equations of motion for fluid elements is derived using a cylindrical coordinate system. But the obtained equations may be also applied to plasmas with disturbances of non-cylindrical symmetry. From the equations of motion, an analytical relation for the radial displacements of the fluid elements is presented, which describes magnetohydrodynamic waves as e.g. sausage and kink ones. The numerical results here presented are, as a first step, only performed for plasma disturbances with cylindrical symmetry and outer azimuthal magnetic fields directed parallely to the conducting wall. Thus, the dispersion relations for sausage instabilities in ITER-type and lightning plasmas are solved. It is shown for which values of the inner and external magnetic fields of the systems instabilities occur. In case of lightnings, the radial displacements in the plasma are estimated.
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