Tokamak MHD equilibria with reversed magnetic shear and sheared flow

Abstract

Analytic solutions of the magnetohydrodynamic equilibrium equations for a cylindrically symmetric magnetically confined plasma with reversed magnetic shear, s < 0, and sheared flow are constructed by prescribing the safety factor-, poloidal velocity-and axial velocity-profiles consistently with experimental ones. On the basis of the solutions obtained in most of the cases considered it turns out that an increase of |s| and of the velocity components result in larger absolute values for the radial electric field, E r , its shear, |dE r /dr| ≡ |E ′ r |, and the E × B velocity shear, ω E×B = |d/dr(E × B/B2 )|, which may play a role in the formation of Internal Transport Barriers (ITBs) in tokamaks. In particular for a constant axial magnetic field, ω E×B at the point where E ′ r = 0 is proportional to 1 − s. Also, |E ′ r | and ω E×B increase as the velocity shear takes larger values. The results clearly indicate that s < 0 and sheared flow act synergetically in the formation of ITBs with the impact of the flow, in particular the poloidal one, being stronger than that of s < 0.

Magnetohydrodynamic counter-rotating vortices and synergetic stabilizing effects of magnetic field and plasma flow

“…It may be noted here that certain synergetic action of the magnetic field and flow for the formation of internal transport barriers in terms of reversed magnetic shear and flow shear was found theoretically in Refs. [11,12] and observed recently in JET (Ref. [29]).…”

“…In particular, analytic equilibrium solutions have been obtained as solutions to generalized Grad-Shafranov equations (Refs. [3,4,6,7,9,10,11,13]). An impact of the equilibrium flow related to the convective term in the momentum equation is that the isobaric surfaces deviate from the magnetic surfaces.…”

Two-fluid tokamak equilibria with reversed magnetic shear and sheared flow

“…A discussion on this issue is made in the Introduction of Ref. [12]. Also, the experimental and theoretical knowledge on discharges with ITBs was reviewed recently in Refs.…”

“…Discrepancy of the measured poloidal velocities from neoclassical predictions before, during and after the transport bifurcation associated with enhanced reversed shear plasmas was reported in [16,17]. Further discussion on these issues is made in the Introduction of [18]. Also, the experimental and theoretical knowledge on discharges with ITBs was reviewed recently in [11] and [19].…”

“…Also, the experimental and theoretical knowledge on discharges with ITBs was reviewed recently in [11] and [19]. In a previous work [18] we studied tokamak magnetohydrodynamic (MHD) equilibrium states with reversed magnetic shear and sheared flow in cylindrical geometry. In particular, presuming that E r , E r and ω E×B are of relevance to the formation of ITBs we examined how these quantities are affected by the magnetic shear and sheared flow and found that the latter quantities act synergetically in increasing ω E×B with the impact of the flow, in particular the poloidal flow, being stronger than that of the magnetic shear, s. In view of complicated experimental evidence and incomplete theoretical understanding, the present work aims as a first step at extending our previous MHD study [18] to the framework of the two-fluid model.…”