COMMENTS ON THE EXTENDED ENERGY PRINCIPLE

The present analysis concerns a plasma confined in a magnetic field, which consists of one part due to the plasma current density and one part due to steady currents in fixed external conductors. Unrestricted free-boundary displacements are studied that lead to an unbalanced pressure force at the plasma boundary and to a corresponding change in potential energy. Thus the total change in energy is due to two factors: (i) the work done against the plasma volume forces, and (ii) the work done against the unbalanced pressure forces at the plasma boundary. These two contributions can be of comparable magnitude. As a consequence, the conventional extended energy principle has to be reconsidered. This reconsideration applies in particular to its final formulation, where unrestricted displacements are made to replace restricted ones in an expression for the potential energy change deduced from the work of the plasma volume force only. The final formulation therefore leads to an incomplete and incorrect result, as caused by a logical jump in the argument when making such a replacement. The conventional MHD analysis on perturbed plasmas thus has to be revised, by taking induced surface currents properly into account. This applies to all plasmas in inhomogeneous externally applied magnetic fields.