Magnetohydrodynamically generated velocities in confined plasma

Abstract

Abstract. It is shown numerically that both toroidal and poloidal rotational flows are intrinsic to a rigid toroid confining a conducting magnetofluid in which a current is driven by the application of externally-supported electric and magnetic fields. The computation involves no microscopic instabilities or kinetic theory and is purely magnetohydrodynamic (MHD) in nature. The properties and intensity of the rotations are regulated by dimensionless numbers (Lundquist, viscous Lundquist, and Hartmann) that contain the resistivity and viscosity of the magnetofluid. The computation makes use of the recently developed "penalization method" to enforce visco-resistive boundary conditions. The point is not that other more exotic kinetic effects may not also contribute to rotational effects in toroidal laboratory devices, but rather that at the most simple magnetohydrodynamic level (uniform mass density and incompressible magnetofluids), they are not necessary. Rotational flows are an irreducible effect inherent in toroidal, driven MHD by itself, without necessary kinetic complications.

The effect of toroidicity on reversed field pinch dynamics

“…The poloidal magnetic field is calculated from the current density distribution j 0 T (R). For more details about its numerical generation in general geometries we refer to [32]. For the cylindrical geometry the imposed axial magnetic and electric field are uniform.…”

“…For more details about its numerical generation in general geometries we refer to [32]. For the cylindrical geometry the imposed axial magnetic and electric field are uniform.…”

Steady-state flows in a visco-resistive magnetohydrodynamic model of tokamak plasmas with inhomogeneous heating

“…There is then the possibility to determine the steady-state velocity field from a numerical resolution of the weak form of the Navier-Stokes equation coupled to Maxwell equations for the electromagnetic field. This line of research was initiated by Montgomery and co-workers (Montgomery, Bates & Li 1997;Kamp & Montgomery 2003a, 2004Morales et al 2015). The original visco-resistive system of equations possesses up-down symmetry properties (Oueslati & Firpo 2020) with respect to the tokamak horizontal midplane so that a tokamak having an up-down symmetric border possesses a naturally antisymmetric toroidal velocity field, which results in a net zero toroidal flow, unless the up-down symmetry is broken.…”