A 3-D MHD equilibrium description of nonlinearly saturated ideal external kink/peeling structures in tokamaks

Abstract

Novel free boundary magnetohydrodynamic equilibrium states with spontaneous three-dimensional (3-D) deformations of the plasma-vacuum interface are computed. The structures obtained look like saturated ideal external kink/peeling modes. Large edge pressure gradients yield toroidal mode number n = 1 distortions when the edge bootstrap current is large and higher n corrugations when this current is small. Linear ideal MHD stability analyses confirm the nonlinear saturated ideal kink equilibrium states produced and we can identify the Pfirsch-Schlüter current as the main linear instability driving mechanism when the edge pressure gradient is large. The dominant non-axisymmetric component of this Pfirsch-Schlüter current drives a near resonant helical parallel current density ribbon that aligns with the near vanishing magnetic shear region caused by the edge bootstrap current. This current ribbon is a manifestation of the outer mode previously found on JET (Solano 2010). We claim that the equilibrium corrugations describe structures that are commonly observed in quiescent H-mode tokamak discharges.

Analytic study on low- external ideal infernal modes in tokamaks with large edge pressure gradients

“…In addition we point out that in the tanh model, contrarily to the step case, the shape of the eigenfunctions depends on the value of δq (and so on the corresponding growth rate). We note that the radial structure of the main and sidebands harmonics closely resembles what has been found numerically in three-dimensional equilibria simulations (Cooper et al 2015(Cooper et al , 2016a and in MHD stability calculations (Medvedev et al 2006;Zheng et al 2013a,b). We shall now consider the case with a resistive wall.…”

“…We note that the radial structure of the main and sidebands harmonics closely resembles what has been found numerically in three-dimensional equilibria simulations (Cooper et al. 2015, 2016 a , b ) and in MHD stability calculations (Medvedev et al. 2006; Zheng et al.…”

“…Three-dimensional free boundary MHD equilibria simulations of Joint European Torus (JET) and Tokamak à Configuration Variable (TCV)-like plasmas, in which a large edge bootstrap current flattens the safety factor, recovered saturated ideal kink/peeling structures (Cooper et al. 2015, 2016 a , b ). The computed equilibrium state is characterised by a distorted boundary with a dominant Fourier component where the corrugation is driven mainly by non-axisymmetric components of the parallel current density.…”

Analytic stability criteria for edge MHD oscillations in high performance ELM free tokamak regimes

“…Equation ( 14) is evaluated by means of ( 6) and ( 7) while ( 15) is obtained from (4) (see [28]). Evaluating (10) at r * and a gives respectively X ± (r * ) = r ±m * L ± /(2 ± m + C ± ) and X ± (a) = a ±m L ± /(2 ± m + B ± ) having used (12). Integration of equation (10) from r * to a finally gives ) , where β = 2p * q 2 /B 2 0 , ε p = r p /R 0 and [23]:…”

“…Three dimensional free boundary Analytic stability criteria for edge MHD oscillations in high performance ELM free tokamak regimes D. Brunetti 1 , J.P. Graves 2 , E. Lazzaro 1 , A. Mariani 2,a , S. Nowak 1 , W.A. Cooper 2 and C. Wahlberg 3 MHD equilibria simulations of JET and TCV-like plasmas with large edge bootstrap current exhibit a distorted boundary with a dominant n = 1 Fourier component driven mainly by non axisymmetric contributions to the parallel current density [12][13][14]. Nonlinear simulations of QH-mode DIII-D plasma discharges showed that medium-n (∼3, 4, 5) harmonics are linearly the most unstable modes but the nonlinear phase is dominated by saturated stationary low-n modes [15].…”