Equilibrium drives of the low and high field side n  =  2 plasma response and impact on global confinement

Abstract

The nature of the multi-modal n = 2 plasma response and its impact on global confinement is studied as a function of the axisymmetric equilibrium pressure, edge safety factor, collisionality, and L-versus H-mode conditions. Varying the relative phase ( Δ ϕ U L ) between upper and lower in-vessel coils demonstrates that different n = 2 poloidal spectra preferentially excite different plasma responses. These different plasma response modes are preferentially detected on the tokamak high-field side (HFS) or low-field side (LFS) midplanes, have different radial extents, couple differently to the resonant surfaces, and have variable impacts on edge stability and global confinement. In all equilibrium conditions studied, the observed confinement degradation shares the same Δ ϕ U L dependence as the coupling to the resonant surfaces given by both ideal (IPEC) and resistive (MARS-F) MHD computation. Varying the edge safety factor shifts the equilibrium field-line pitch and thus the Δ ϕ U L dependence of both the global confinement and the n = 2 magnetic response. As edge safety factor is varied, modeling finds that the HFS response (but not the LFS response), the resonant surface coupling, and the edge displacements near the X-point all share the same Δ ϕ U L dependence. The LFS response magnitude is strongly sensitive to the core pressure and is insensitive to the collisionality and edge safety factor. This indicates that the LFS measurements are primarily sensitive to a pressure-driven kink-ballooning mode that couples to the core plasma. MHD modeling accurately reproduces these (and indeed all) LFS experimental trends and supports this interpretation. In contrast to the LFS, the HFS magnetic response and correlated global confinement impact is unchanged with plasma pressure, but is strongly reduced in high collisionality conditions in both H- and L-mode. This experimentally suggests the bootstrap current drives the HFS response through the kink-peeling mode drive, though surprisingly weak or no dependence on the bootstrap current is seen in modeling. Instead, modeling is revealed to be very sensitive to the details of the edge current profile and equilibrium truncation. Holding truncation fixed, most HFS experimental trends are not captured, thus demonstrating a stark contrast between the robustness of the HFS experimental results and the sensitivity of its computation.

Three dimensional boundary displacement due to stable ideal kink modes excited by external n = 2 magnetic perturbations

“…Note, the LFS and the HFS responses of this plasma configuration have a very similar dependence on ∆ϕ UL , which is indicated in figure 7(c) and the following sections. This is a feature of the investigated plasma configuration and does not hold generally as suggested by calculations based on other ASDEX Upgrade configurations [50] and other machines [6]. One should also keep in mind that the displacement in the static experiments are expected to be roughly two times larger than the one in the rigid rotation experiments.…”

“…To increase the accuracy of the analysis, the effects of the PCS are included (section 2.4). Although the LFS response is thought to play a minor role in the ELM-mitigation [6], this comparison is very valuable to benchmark VMEC.…”

Numerically derived parametrisation of optimal RMP coil phase as a guide to experiments on ASDEX Upgrade

“…Furthermore, examining the linearised equations of ideal MHD provides a direct relation between ξ X and b 1 res [33], explaining why these three are often seen to be strongly correlated in modelling works [23,34,35]. Meanwhile, it is also shown computationally that the HFS response also shares the same ∆Φ dependence as ξ X and |b 1 res | [16,29]. Therefore in the context of optimising over ∆Φ, the figures of merit |b 1 res |, ξ X , the peeling response and the HFS response are all equivalent.…”

“…The high field side (HFS) response refers to the magnitude of the magnetic perturbation at the high field side midplane. The HFS response, both measured experimentally and predicted numerically, has been shown to correlate with density pump out and ELM suppression on DIII-D [16,29]. The edge peeling response refers to amplification of marginally stable MHD modes [30], localised near the plasma edge and with poloidal harmonic numbers above resonance (m > nq).…”

Plasma response to rotating resonant magnetic perturbations with a locked mode in the J-TEXT tokamak

“…The non-axisymmetric b r measured by LMD could be due to either the formation of a small locked island or other kinds of plasma responses, e.g. resonant field amplification (RFA) [58,59], kink mode [60], kink-ballooning or kink-peeling modes [61], etc. By superimposing a small fast rotating RMP field on the flattop of the static RMP field, the phase of the locked island could be forced to oscillate if it does exist.…”