We study a particular class of asymptotic solutions of the magnetohydrostatic equations, precisely in the limit where:i) both the magnetic and current density fields are quasi-symmetric about an axis and quasi-parallel to the corresponding azimuth direction;ii) a vacuum magnetic field dominates. The construction of these solutions, to any order n, is reduced to the problem of solving an elliptic semi-linear (n=0) or linear (n ⩾ 1) equation in the meridian plane. The overall asymptotic problem turns out to be intrinsically under-determined from the boundary: that is, it is impossible to single out a unique solution by prescribing conveniently strong conditions on the boundary of the domain where the solution itself is sought. This study arises from the attempt to explain the quasi equilibrium occurring in fusion devices of the « Tokamak » type in terms of a purely magnetohydrostatic model. Comments and clarifications about this aspect of the problem may be found in , together with a suitably abridged version of the mathematical formalism.
Magnetic Field Unique Solution Mathematical Formalism Asymptotic Solution Strong Condition
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