Cylindrical Viscous Boundary Layer For Transonic Equilibrium*

Transonic equilibria have been studied in the past in a number of papers, see e.g. [1-4]. They occur in tokamak geometry when the core region of the plasma has slow (with respect to the poloidal sound speed, Csp = CsBp/B) poloidal rotation, while the edge has supersonic (vp > Csp) rotation, a realistic condition in H-mode tokamak plasmas. In the single-fluid MHD model transonic equilibria are characterized by a radial discontinuity in density, pressure and velocity. Physical intuition dictates that including fluid viscosity in the problem will relax the discontinuity to a sharp-gradient layer between the slow- and fast- flowing regions. We use a high aspect ratio expansion of the equilibrium to build a cylindrical model of the viscous, compressible transonic boundary layer. The formulation requires a series expansion in the poloidal angle θ, but only a few terms are needed for good accuracy. The resulting system of nonlinear ODEs is more complex than formally similar problems in classical fluid-dynamics, but it can still be solved numerically with standard methods.

[1] L. Guazzotto, R. Betti, J. Manickam, S. Kaye, Physics of Plasmas 11 2, 604-614

[2] L. Guazzotto, R. Betti, Physics of plasmas 12 5, 056107

[3] L. Guazzotto, E. Hameiri, Physics of Plasmas 21 2, 022512

[4] L. Guazzotto, R. Betti, S.C. Jardin, Physics of Plasmas 20 4, 042502