The Bernoulli Equation and the Poloidal-sonic Singularity in an Inverse Aspect-ratio Expansion Formulation of Equilibria with Flow

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Fluid flow can play a significant role in plasma equilibrium, possibly producing transport barriers and profile pedestals. To be consistent with hot ions, finite Larmor radius (FLR) effects should be included. Ito and Nakajima have developed a formulation for calculating magnetohydrodynamic (MHD) equilibria with poloidal-sonic flow and FLR effects using an inverse aspect-ratio expansion, known as the “Ito formulation” [A. Ito and N. Nakajima, AIP Conference Proceedings 1069, 121 (2008)]. The Ito formulation typically possess a singularity when the poloidal flow varies from sub- to super-poloidal sonic, known as the “poloidal-sonic (PS) singularity.” The presence of the PS singularity prevents the Ito formulation from being directly applied to equilibria with such flows. An investigation of the single-fluid MHD model shows that the PS singularity is due to an inverse aspect-ratio expansion of the Bernoulli equation. This suggests that, in order to use the Ito formulation for an accurate calculation of MHD equilibria with poloidal-sonic flows, the Bernoulli equation must be handled non-linearly near the singularity.