Analytical solutions for Tokamak equilibria with reversed toroidal current

Abstract

In tokamaks, an advanced plasma confinement regime has been investigated with a central hollow electric current with negative density which gives rise to non-nested magnetic surfaces. We present analytical solutions for the magnetohydrodynamic equilibria of this regime in terms of non-orthogonal toroidal polar coordinates. These solutions are obtained for large aspect ratio tokamaks and they are valid for any kind of reversed hollow current density profiles. The zero order solution of the poloidal magnetic flux function describes nested toroidal magnetic surfaces with a magnetic axis displaced due to the toroidal geometry. The first order correction introduces a poloidal field asymmetry and, consequently, magnetic islands arise around the zero order surface with null poloidal magnetic flux gradient. An analytic expression for the magnetic island width is deduced in terms of the equilibrium parameters. We give examples of the equilibrium plasma profiles and islands obtained for a class of current density profile.

Magnetic topology and current channels in plasmas with toroidal current density inversions

“…This is done without specifying further plasma profiles or arbitrary functions. The obtained solution agrees with several published equilibria [5][6][7][8] while providing a simple understanding of the control parameters and their relation with the current in the different channels.For axisymmetric systems the equilibrium magnetic field may be writtenwhere ψ(R, z) = RA φ (R, z) and F (R, z) = RB φ (R, z) are proportional to the poloidal magnetic flux and current respectively. B φ (R, z) and A φ (R, z) are the azimuthal components of the magnetic field and vector potential and (R, φ, z) the usual cylindrical coordinates.…”

“…This may not be appropriate for CRECs, but in a first approach a single choice of the sources p(ψ) and F (ψ) can present current density inversions and multiple magnetic families [5,6]. Other works uses successive approximations to the solution with prescribed zero-order current density models and boundary conditions [7,8].…”

Stationary MHD equilibria describing azimuthal rotations in symmetric plasmas

“…While in the static case there is no current reversal, it appears for a rotating plasma with x ¼ 1. Current reversal has been described in many static configurations, 24,25 and in our case, it has appeared due to the toroidal rotation, nevertheless, linked with the particular form of the profiles we used here. It has not been seen in other situations.…”

MHD equilibrium in Tokamaks with reversed current density

“…In recent works [31][32][33], after the choice of particular source functions, the reduction of the G-S equation to the linear case makes available analytical forms of the poloidal flux function (or the toroidal one in [31]). In the 2003 Martynov et.…”