Analytic magnetohydrodynamic equilibria of a magnetically confined plasma with sheared flows

Abstract

Large-mode-number magnetohydrodynamic instability driven by sheared flows in a tokamak plasma with reversed central shear Analytic solutions of the magnetohydrodynamic equilibrium equations for a symmetric magnetically confined plasma with sheared incompressible flows associated with electric fields similar to those observed in the transition from the low-to the high-confinement mode in tokamaks are constructed in cylindrical and toroidal geometries. In particular, an exact toroidal solution is obtained which for vanishing flows reduces to the Solovév equilibrium which has been extensively employed in tokamak confinement studies. Owing to the flow, several toroidal configurations having either one or two stagnation points are possible in addition to the usual ones with a single magnetic axis. For flows pertaining to tokamak operational regime the extremum of the electric field becomes larger as flow and its shear increase, the location of the extremum being, however, nearly independent of these variations. In addition, the flow affects the safety factor profile and the shape of the magnetic surfaces and results in an increase of the magnetic shear and a decrease of the toroidal beta. The impact of plasma elongation on the above-mentioned confinement figures of merit is also evaluated.

Analytical up-down asymmetric equilibria with non-parallel flows

“…The equilibrium of an axisymmetric plasma with incompressible flow satisfies the generalized Grad-Shafranov equation 7,8 …”

Tokamak L/H mode transition

“…On the other hand, under the simplifying condition of divergence-free flows, non field-aligned rotational equilibria could be readily solved. [23][24][25] Recently, in terms of spherical coordinates, 26 the non field-aligned equilibria have been solved under a set of transformed MHD variables. 27 With these new variables, the functional dependence of the rotational Grad-Shafranov equation, plasma pressure, normal electric field, on the plasma variables are sufficiently simple and explicit to allow an understanding of the L=H mode transition through a positive feedback cycle.…”

On the Equilibrium and Stability of ITER Relevant Plasmas

“…A 4 is mostly a flow term depending on the magnitude and the shear of the flow. The flows satisfying (1) are inherently sub-Alfvénic (M 2 p < 1) because of an integral transformation involved [9]. To apply the condition we set in Eq.…”

“…Derivation of (1) and (2) is provided in [8,9,10]. Once the free functions M p (u), P s (u), Φ(u), ϱ(u) and M p (u) are assigned, Eq.…”

“…The equilibrium of an axisymmetric plasma with incompressible flow satisfies the generalized GradShafranov equation [8,9,10] …”