Benchmarking kinetic calculations of resistive wall mode stability

Abstract

Validating the calculations of kinetic resistive wall mode (RWM) stability is important for confidently predicting RWM stable operating regions in ITER and other high performance tokamaks for disruption avoidance. Benchmarking the calculations of the Magnetohydrodynamic Resistive Spectrum-Kinetic (MARS-K) [Y. Liu et al., Phys. Plasmas 15, 112503 (2008)], Modification to Ideal Stability by Kinetic effects (MISK) [B. Hu et al., Phys. Plasmas 12, 057301 (2005)], and Perturbed Equilibrium Nonambipolar Transport (PENT) [N. Logan et al., Phys.Plasmas 20, 122507 (2013)] codes for two Solov'ev analytical equilibria and a projected ITER equilibrium has demonstrated good agreement between the codes. The important particle frequencies, the frequency resonance energy integral in which they are used, the marginally stable eigenfunctions, perturbed Lagrangians, and fluid growth rates are all generally consistent between the codes. The most important kinetic effect at low rotation is the resonance between the mode rotation and the trapped thermal particle's precession drift, and MARS-K, MISK, and PENT show good agreement in this term. The different ways the rational surface contribution was treated historically in the codes is identified as a source of disagreement in the bounce and transit resonance terms at higher plasma rotation. Calculations from all of the codes support the present understanding that RWM stability can be increased by kinetic effects at low rotation through precession drift resonance and at high rotation by bounce and transit resonances, while intermediate rotation can remain susceptible to instability. The applicability of benchmarked kinetic stability calculations to experimental results is demonstrated by the prediction of MISK calculations of near marginal growth rates for experimental marginal stability points from the National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)]. V C 2014 AIP Publishing LLC. [http://dx.

Modelling of 3D fields due to ferritic inserts and test blanket modules in toroidal geometry at ITER

“…This is essentially a MHD-kinetic hybrid model, based on the so called non-perturbative approach. The code implementation (MARS-K) benchmarking results were reported in [23] and validated against experiments [24,14]. The quasi-linear extension, implemented to model the external 3D field induced toroidal flow damping of the plasma, was reported in [18].…”

Rotational stabilization of the resistive wall modes in tokamaks with a ferritic wall

“…In a search of more plausible reasons aside from ideal plasmas or walls, several theories for the rotational stabilization have been proposed that rely on some dissipation in the plasma and incorporate a magnetically thin wall. 3,15,[28][29][30][31][32][33][34][35][36][37] The latter means that the wall is described as resistive, but with utmost simplicity assuming that the induced electric field E is constant across the wall. This is a step ahead compared to the ideal-wall or no-wall approaches but can be justified for slow modes only with xs sk < 1, where s sk l 0 rd 2 w ;…”

Three-Dimensional Drift Kinetic Response of High-βPlasmas in the DIII-D Tokamak

“…mars-f only solves the linearized ideal M HD equations to obtain the fluid plasm a response [8]. The upgraded mars-k/ f codes, with improved numerical stability, have been benchm arked with the ipec-pent [29,30] and misk codes [31]. Figure 1 com pares the com puted radial plasm a displace ment £ ■ V s between the fluid and the kinetic approaches, based on DIII-D discharge 135773, where the plasma pressure is close to = 2.25.…”