Curvilinear formulation of anti-symmetric plasmas models

The anti-symmetry formalism is a new representation of the fluid equations that retains important symmetries of the force operator, and that also leads to simple discrete energy conservation theorems by simple analogy with their continuous form [1]. We extend and adapt the anti-symmetry fluid formalism to curvilinear geometry, determining the curvilinear form of the plasma fluid equations, and demonstrating that the anti-symmetry of the force operator is still retained after a coordinate transformation. It is found that the curvilinear equations retain the same structure as in Cartesian coordinates, however recast in terms of generalized variables rescaled by the metric coefficients. Special attention is needed to treat the metrics in a manner such that their derivatives do not introduce artificial forces. The first tests in cylindrical coordinates are carried out using the magnetized Rayleigh-Taylor instability using a Hall-MHD model, demonstrating the numerical robustness of the approach.

[1] F.D Halpern and R.E. Waltz, Phys. Plasmas 25, 060703 and Phys. Plasmas 27, 042303