A representation of toroidal MHD in terms of stream functions and potentials

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Abstract
An exact representation of toroidal magneto-hydrodynamics is proposed, in which the electro-magnetic and the velocity fields are represented in terms of stream functions and potentials, without assuming any spatial symmetries. Two important features of this representation are the use of a time-independent but otherwise arbitrary reference field B0, and the fact that the vector product of the velocity V with B0, and not V itself, is represented in terms of stream functions. In this way the equations take a form which allows relatively easy physical interpretation and is well suited for deriving reduced MHD equations for particular stability problems.