Symmetric and asymmetric equilibria with non-parallel flows

Abstract

Several classes of analytic solutions to a generalized Grad-Shafranov equation with incompressible plasma flow non-parallel to the magnetic field are constructed. The solutions include higher transcendental functions such as the Meijer G-function and describe D-shaped and diverted configurations with either a single or double X-points. Their characteristics are examined in particular with respect to the flow parameters associated with the electric field. It turns out that the electric field makes the safety factor flatter and increases the magnitude and shear of the toroidal velocity in qualitative agreement with experimental evidence on the formation of internal transport barriers in tokamaks, thus indicating a potential stabilizing effect of the electric field.

Two-dimensional nonlinear cylindrical equilibria with reversed magnetic shear and sheared flow

“…Here the choice ρ = ρ a ( u u b − 1) 0.5 has been made for the density with ρ a = 4.0 × 10 −7 Kgr m −3 . The maximum of E increases with the flow parameter M pa but the position of the maximum is not affected by the flow in agreement with the results of [7,16]. The hollow axial current density profile in the midplane y = 0 is shown in Fig.…”

Nonlinear translational symmetric equilibria relevant to the L–H transition

“…In most of the above cases, the axisymmetric equilibria are obtained as separable solutions of GSE. A novel non-separable class of solutions was found in Kuiroukidis (2010) describing up-down symmetric configurations with incompressible flows parallel to the magnetic field and it was extended recently to include asymmetric configurations (Kuiroukidis and Throumoulopoulos 2011) and flows of arbitrary direction (Kuiroukidis and Throumoulopoulos 2012). For non-parallel flows, the question of the stability is usually not considered and this is partly due to the difficulty of the subject and the absence of a concise criterion.…”

General three-dimensional equilibria for gravitating ideal magnetohydrodynamics of field-aligned steady incompressible flows with an application to solar prominences

“…The existence of equilibrium must be ensured in order to confine the plasma by the magnetic field. Some authors investigated cylindrical and axisymmetric MHD equilibria with incompressible flows (Andreussi, Morrison & Pegoraro 2010;Shi 2011;Zhou & Yu 2011;Kuiroukidis & Throumoulopoulos 2012, 2013, 2014Moawad 2012Moawad , 2013Moawad , 2014Moawad , 2015Moawad & Ibrahim 2016;Moawad et al 2017b;Moawad, El-Kalaawy & Shaker 2017a;Adem & Moawad 2018). The equilibrium the MHD plasma reaches is governed by a generalized Grad-Shafranov equation (GGS) for the poloidal magnetic flux as well as an algebraic relation for the pressure.…”