Modelling of three dimensional equilibrium and stability of MAST plasmas with magnetic perturbations using VMEC and COBRA

Abstract

Abstract. It is known that magnetic perturbations can mitigate edge localized modes (ELMs) in experiments, for example MAST (Kirk et al 2013 Nucl. Fusion 53 043007 ). One hypothesis is that the magnetic perturbations cause a three dimensional corrugation of the plasma and this corrugated plasma has different stability properties to peeling-ballooning modes compared to an axisymmetric plasma. It has been shown in an up-down symmetric plasma that magnetic perturbations in tokamaks will break the usual axisymmetry of the plasma causing three dimensional displacements (Chapman et al 2012 Plasma Phys. Control. Fusion 54 105013). We produce a free boundary three-dimensional equilibrium of a lower single null MAST relevant plasma using VMEC (S P Hirshman and J C Whitson 1983 Phys. Fluids 26 3553). The current and pressure profiles used for the modelling are similar to those deduced from axisymmetric analysis of experimental data with ELMs. We focus on the effect of applying n = 3 and n = 6 magnetic perturbations using the RMP coils. A midplane displacement of over ±1 cm is seen when the full current is applied. The current in the coils is scaned and a linear relationship between coil current and midplane displacement is found. The effect of this non-axisymmetric equilibrium on infinite n ballooning stability is investigated using COBRA ( R Sanchez et al 2000 J. Comput. Phys. 161 576-588). The infinite n ballooning stability is analysed for two reasons; it may give an indication of the effect of non-axisymmetry on finite n peeling-ballooning modes, responsible for ELMs; and infinite n ballooning modes are correlated to kinetic ballooning modes (KBMs) which are thought to limit the pressure gradient of the pedestal (Snyder et al 2009 Phys. Plasmas 16 056118). The equilibria with midplane displacements due to RMP coils have a higher ballooning mode growth rate than the axisymmetric case and the possible implications are discussed.

Effect of resonant magnetic perturbations on microturbulence in DIII-D pedestal

“…Using a local 3D equilibrium model, the 3D modulation of the local magnetic shear was found to modify the infinite-n ideal MHD ballooning stability boundary in the α − s parameter space [6]. The enhancement of the high-n ballooning mode instability by n = 3 RMP was also reported in ideal MHD COBRA simulations using local geometry in radial and toroidal angle space [7]. The enhanced zonal flow damping by 3D magnetic fields has been shown in the resistive drift wave turbulence using an extended Hasegawa-Wakatani fluid model [8].…”

Assessing the merits of resonant magnetic perturbations with different toroidal mode numbers for controlling edge localised modes

“…Figure 14 shows the n = ∞ ballooning mode growth rate-as a proxy for kinetic ballooning mode stability-across the radial extent of the pedestal. Here, the growth rate is shown for a toroidal position where instability is exacerbated, though in a different toroidal phase the n = ∞ growth rate is decreased relative to the case without RMPs [57]. The non-axisymmetric perturbation of the pedestal exacerbates kinetic ballooning mode instability, widening the region over which infinite-n modes are unstable and enhancing the mode growth rate.…”

“…The region over which the infinite-n ballooning modes become unstable, and the enhancement in their growth rate, is similar for all RMP configurations, consistent with the pedestal structure being similar for all n RMP . When an n RMP = 3 field is applied, the pedestal pressure must be reduced by 30% for the infinite-n ballooning mode growth rate in the toroidal position of greatest instability to equal that in the case with no RMPs [57]. The reduction in the pedestal pressure to reach marginal stability may be different for other RMP mode numbers [57].…”

“…When an n RMP = 3 field is applied, the pedestal pressure must be reduced by 30% for the infinite-n ballooning mode growth rate in the toroidal position of greatest instability to equal that in the case with no RMPs [57]. The reduction in the pedestal pressure to reach marginal stability may be different for other RMP mode numbers [57].…”

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

“…Secondly, the plasma response leads to 3D deformation of an otherwise 2D axi-symmetric tokamak equilibrium, eventually forming a 3D equilibrium [13,14]. This may have several consequences, in particular, in terms of the ELM control physics, on the stability of the underlying peeling-ballooning modes [15]. Finally, toroidal torques, of various physics origins, can be generated as a result of the plasma response, that may in turn act on the plasma by changing the toroidal flow [16,17,18].…”