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Elliptic and hyperelliptic magnetohydrodynamic equilibria

H. Tasso·G. N. Throumoulopoulos
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Abstract

The present study is a continuation of a previous one on "hyperelliptic" axisymmetric equilibria started in [Tasso and Throumoulopoulos, Phys. Plasmas 5, 2378 (1998)]. Specifically, some equilibria with incompressible flow nonaligned with the magnetic field and restricted by appropriate side conditions like "isothermal" magnetic surfaces, "isodynamicity" or P + B^2/2 constant on magnetic surfaces are found to be reducible to elliptic integrals. The third class recovers recent equilibria found in [Schief, Phys. Plasmas 10, 2677 (2003)]. In contrast to field aligned flows, all solutions found here have nonzero toroidal magnetic field on and elliptic surfaces near the magnetic axis.

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H. Tasso, G. N. Throumoulopoulos. 2004-04-14. Elliptic and hyperelliptic magnetohydrodynamic equilibria. https://doi.org/10.1393/ncb%2Fi2004-10130-x

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