Pressure Driven Currents Near Magnetic Islands in mD MHD Equilibria: Effects of Pressure Variation Within Flux Surfaces and of Symmetry
Authors: A. Reiman
Abstract: In toroidal, magnetically confined
plasmas, the heat and particle transport is strongly anisotropic,
with transport along the field lines sufficiently strong
relative to cross-field transport that the equilibrium
pressure can generally be regarded as constant on the flux
surfaces in much ofthe plasma. The regions near small
magnetic islands, and those near the X-lines of larger islands,
are exceptions, having a significant variation of the
pressure within the flux surfaces. It is shown here that the
variation of the equilibrium pressure within the flux
surfaces in those regions has significant consequences for
the pressure driven currents. It is further shown that the
consequences are strongly affected by the symmetry of the magnetic
field if the field is invariant under combined reflection in the
poloidal and toroidal angles. (This symmetry property is called
"stellarator symmetry".) In non-stellarator-symmetric
equilibria, the pressure-driven currents have logarithmic
singularities at the X-lines. In stellarator-symmetric
MHD equilibria, the singular components of the
pressure-driven currents vanish. These equilibria are to be
contrasted with equilibria having B
p = 0,
where the singular components of the pressure-driven
currents vanish regardless of the symmetry. They are also to be
contrasted with 3D MHD equilibrium solutions that are
constrained to have simply nested flux surfaces, where the
pressure-driven current goes like 1 I x near rational
surfaces, wherex is the distance from the rational
surface. (Except in the case of quasi-symmetric flux
surfaces.) For the purpose of calculating the
pressure-driven currents near magnetic islands, we work with a
closed subset of the MHD equilibrium equations that involves
only perpendicular force balance, and is decoupled from parallel
force balance. It is not correct to use the parallel
component of the conventional MHD force balance equation, B
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