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AbstractAbstract
[en] Asymptotic solutions of the magnetohydrostatic equations Δx(JxB)=0, ΔxB=0, J=ΔxB (with single-valued ∫dxxJxB) have been recently obtained to all orders in a torus with arbitrary section for a quasi-axisymmetric, quasi-azimuthal field configuration and quasi-vacuum B. In this paper it is considered a much weaker asymptotic ansatz, namely: i) the spatial domain where the solution is sought merely belongs to the torus homology class, ii) a vacuum, closed-line B dominates together with a parallel J; it is also proved that the corresponding problem of constructing an asymptotic solution can be reduced to solving a weakly singular Hammerstein integral equation to the lowest significant order and a weakly singular nonhomogeneous Fredholm integral equation of the 2nd kind of each of the subsequent orders
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Nuovo Cim., B; v. 32(1); p. 1-39
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