[Table of Contents]

Plasma and Fusion Research

Volume 6, 2403044 (2011)

Regular Articles

The Bernoulli Equation and the Poloidal-sonic Singularity in an Inverse Aspect-ratio Expansion Formulation of Equilibria with Flow
Daniel RABURN and Atsushi FUKUYAMA
Kyoto University, Kyoto 606-8501, Japan
(Received 6 December 2010 / Accepted 10 February 2011 / Published 27 July 2011)


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.


magnetohydrodynamics, equilibrium, flow, poloidal-sonic singularity, Bernoulli equation, two-fluid model, finite Larmor radius

DOI: 10.1585/pfr.6.2403044


  • [1] T.S. Taylor, H.S.T. John, A.D. Turnbull et al., Plasma Phys. Control. Fusion 36, B229 (1994).
  • [2] R. Betti and J.P. Freidberg, Phys. Plasmas 7(6), 2439 (2000).
  • [3] L. Guazzotto, R. Betti, J. Manickam and S. Kaye, Phys. Plasmas 11(2), 604 (2004).
  • [4] R. Iacono, A. Bondeson, F. Troyon and R. Gruber, Phys. Fluids B 2, 1794 (1990).
  • [5] A. Ito and N. Nakajima, AIP Conference Proceedings 1069, 121 (2008).
  • [6] D. Raburn and A. Fukuyama, Phys. Plasmas 17(2), 122504 (2010).
  • [7] A. Ito, J.J. Ramos and N. Nakajima, Plasma Fusion Res. 3, 034 (2008).
  • [8] A. Ito and N. Nakajima, Plasma Phy. Control. Fusion 51, 035007 (2009).
  • [9] E. Hameiri, Phys. Fluids 26(1), 230 (1983).
  • [10] J.J. Ramos, Phys. Plasmas 12, 112301 (2005).

This paper may be cited as follows:

Daniel RABURN and Atsushi FUKUYAMA, Plasma Fusion Res. 6, 2403044 (2011).