Comparisons of linear and nonlinear plasma response models for non-axisymmetric perturbations

Abstract

With the installation of non-axisymmetric coil systems on major tokamaks for the purpose of studying the prospects of ELM-free operation, understanding the plasma response to the applied fields is a crucial issue. Application of different response models, using standard tools, to DIII-D discharges with applied non-axisymmetric fields from internal coils, is shown to yield qualitatively different results. The plasma response can be treated as an initial value problem, following the system dynamically from an initial unperturbed state, or from a nearby perturbed equilibrium approach, and using both linear and nonlinear models [A. D. Turnbull, Nucl. Fusion 52, 054016 (2012)]. Criteria are discussed under which each of the approaches can yield a valid response. In the DIII-D cases studied, these criteria show a breakdown in the linear theory despite the small 10−3 relative magnitude of the applied magnetic field perturbations in this case. For nonlinear dynamical evolution simulations to reach a saturated nonlinear steady state, appropriate damping mechanisms need to be provided for each normal mode comprising the response. Other issues arise in the technical construction of perturbed flux surfaces from a displacement and from the presence of near nullspace normal modes. For the nearby equilibrium approach, in the absence of a full 3D equilibrium reconstruction with a controlled comparison, constraints relating the 2D system profiles to the final profiles in the 3D system also need to be imposed to assure accessibility. The magnetic helicity profile has been proposed as an appropriate input to a 3D equilibrium calculation and tests of this show the anticipated qualitative behavior.

Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets

“…The nonlinear calculations used Fourier harmonics with m ≤ 6 and n ≤ 3. We remark that the agreement arising from this verification exercise is of unprecedented nature and may shed some light on how to reconcile the recently observed discrepancies between linear and nonlinear equilibrium codes that assume nested flux surfaces [9,10].…”

“…In particular, singular current densities at rational surfaces are predicted in equilibria with continuously-nested flux-surfaces, with and without pressure [1,[4][5][6][7]. These singular currents play a crucial role in describing (i) the plasma response to non-axisymmetric boundary perturbations [8][9][10], (ii) ideal and resistive stability [11,12], and (iii) the dynamics of reconnection phenomena, such as sawteeth [13].…”

Modelling plasma response to RMP fields in ASDEX Upgrade with varying edge safety factor and triangularity

“…The modelling is carried out using the MARS-F code [21], which has been well benchmarked [22,23] and extensively applied to model the plasma response to external 3D…”

Toroidal modelling of RMP response in ASDEX Upgrade: coil phase scan, q95 dependence, and toroidal torques

“…The basic assumption here is that the amplitude of the applied 3D RMP field is much smaller (often by several orders of magnitude) than the equilibrium field. More subtle requirements may also be imposed on the perturbative approach, both near rational surfaces as well as in terms of certain geometric constraints for the plasma displacement [24]. The full 3D equilibrium approach assumes that a full force balance condition is satisfied by the plasma response.…”