Analytic high-beta tokamak equilibria with poloidal-sonic flow

A reduced set of equations for high-beta tokamak equilibria with flow comparable to the poloidal sound velocity is solved analytically. The solution includes higher-order terms of asymptotic expansions in terms of the inverse aspect ratio and indicates the modification of the magnetic structure and the departure of the pressure surfaces from the magnetic surfaces by sub- or super-poloidal-sonic flows. The analytical representation for the shift of the magnetic axis from the geometrical axis (the Shafranov shift) and that of the pressure maximum and the equilibrium beta limit are also obtained. The Shafranov shift is enhanced by a slightly super-poloidal-sonic flow and it produces a forbidden region of equilibrium by the poloidal-sonic flow. The physical mechanism of the shift of the pressure maximum from the magnetic axis due to the poloidal-sonic flow is discussed in analogy to those of the geodesic acoustic mode and the slow magnetosonic wave.