Numerical study of tearing mode seeding in tokamak X-point plasma

A detailed understanding of island seeding is crucial to avoid (N)TMs and their negative consequences like confinement degradation and disruptions. In the present work, we investigate the growth of 2/1 islands in response to magnetic perturbations. Although we use externally applied perturbations produced by resonant magnetic perturbation (RMP) coils for this study, results are directly transferable to island seeding by other MHD instabilities creating a resonant magnetic field component at the rational surface. Experimental results for 2/1 island penetration from ASDEX Upgrade are presented extending previous studies. Simulations are based on an ASDEX Upgrade L-mode discharge with low collisionality and active RMP coils. Our numerical studies are performed with the 3D, two fluid, non-linear MHD code JOREK. All three phases of mode seeding observed in the experiment are also seen in the simulations: first a weak response phase characterized by large perpendicular electron flow velocities followed by a fast growth of the magnetic island size accompanied by a reduction of the perpendicular electron velocity, and finally the saturation to a fully formed island state with perpendicular electron velocity close to zero. Thresholds for mode penetration are observed in the plasma rotation as well as in the RMP coil current. A hysteresis of the island size and electron perpendicular velocity is observed between the ramping up and down of the RMP amplitude consistent with an analytically predicted bifurcation. The transition from dominant kink/bending to tearing parity during the penetration is investigated

Effect of divertor plasma conditions & drifts on ELM power fluxes at the ITER divertor targets

\u3cp\u3eThe effect of divertor recycling, in/out recycling asymmetries and ion ∇B drift direction on in/out divertor power and particle flux asymmetries for stationary plasma conditions and during ELMs have been modelled with the 2-D PARASOL PIC kinetic code. The direction of the ion ∇B drift has a strong effect on the steady-state in/out heat/particle flux divertor asymmetries and this effect is even larger for ELMs. The modelled changes of the in/out divertor asymmetries with ∇B for steady state conditions are contrary to experimental findings (the inner divertor heat flux does not become similar to outer one when ∇B direction is reversed). Simulations of ELMs find that the energy load to the inner divertor is largest for normal ∇B and smallest for reversed ∇B for an ELM energy loss of δW\u3csub\u3eELM\u3c/sub\u3e/W-12%. This finding is robust to modelling assumptions (recycling value, in/out recycling ratio, ELM energy loss magnitude and plasma collisionality). This is good qualitative agreement with experiment, although magnitude of the predicted changes is much larger than in experiment. The magnitude of δW\u3csub\u3eELM\u3c/sub\u3e/W itself is also found to affect the in/out ELM energy deposition asymmetry and E\u3csub\u3ein\u3c/sub\u3e/E\u3csub\u3eout\u3c/sub\u3e increases with δW\u3csub\u3eELM\u3c/sub\u3e/W for normal ∇B while it decreases with reversed ∇B for low collisionalities. Further 2-D PARASOL simulations to study the role of drifts, recycling and thermoelectric currents are in progress to refine these findings.\u3c/p\u3

Progress in the modelling of 3-D effects on MHD stability with the PB3D numerical code and implications for ITER

Introduction\u3cbr/\u3eThe theory of magnetohydrodynamics (MHD) is valuable because it leads to baseline considerations for toroidal magnetic configurations, even when the parameter ranges in which these configurations are situated often don’t strictly satisfy the assumptions behind the MHD theory. The reason for this lies in the strong anisotropy of these configurations, where the dynamics perpendicular to the magnetic field lines is often indeed well-described by the theory, even though the direction parallel to the magnetic\u3cbr/\u3efield lines is not. This work is situated in the study of fluted or high-n modes, which are normal modes that fit in the theory of MHD stability, that show very fast variation accross the magnetic field lines, as compared to the behavior along them. High-n MHD stability is important by itself as it can describe phenomena that are known to be important for the current and next generation of nuclear fusion devices, such as ELMs, which can be interpreted as due to two types of high-n instabilities: ballooning modes and peeling modes. In the view of studying these phenomena in enough detail, the two ingredients that this work combines within the world of high-n stability are the inclusion of a possible vacuum perturbation,\u3cbr/\u3ewhich is necessary for peeling modes to exist in the absence of resistivity; and the correct treatment of 3-D effects, which are important not only for stellarators, but also for tokamaks. An example thereof can be found in the well-known consequences that toroidal field (TF) ripples can have on confinement [Sai+07; Wey+17]; but also in the application of resonant magnetic perturbation (RMP) coils to control ELMs by destabilizing them [Eva+06]. After briefly summarizing the theory of ideal linear 3-D MHD\u3cbr/\u3estability and the advancements of the PB3D (Peeling-Ballooning in 3-D) code over the past year in 2, this work then treats its application to the study of 3-D ballooning stability when applying RMPs in tokamaks\u3cbr/\u3ein 3 and 4. Finally, in section 5, conclusions are phrased as well as the plans for future work

PB3D: a new code for edge 3-D ideal linear peeling-ballooning stability

A new numerical code PB3D (Peeling-Ballooning in 3-D) is presented. It implements and solves the intermediate-to-high-n ideal linear magnetohydrodynamic stability theory extended to full edge 3-D magnetic toroidal configurations in previous work [1]. The features that make PB3D unique are the assumptions on the perturbation structure through intermediate-to-high mode numbers n in general 3-D configurations, while allowing for displacement of the plasma edge. This makes PB3D capable of very efficient calculations of the full 3-D stability for the output of multiple equilibrium codes. As first verification, it is checked that results from the stability code MISHKA [2], which considers axisymmetric equilibrium configurations, are accurately reproduced, and these are then successfully extended to 3-D configurations, through comparison with COBRA [3], as well as using checks on physical consistency. The non-intuitive 3-D results presented serve as a tentative first proof of the capabilities of the code

Influence of toroidal ripple on peeling-ballooning stability in the pedestal of H-mode plasmas

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A wall-aligned grid generator for non-linear simulations of MHD instabilities in tokamak plasmas

\u3cp\u3eBlock-structured mesh generation techniques have been well addressed in the CFD community for automobile and aerospace studies, and their applicability to magnetic fusion is highly relevant, due to the complexity of the plasma-facing wall structures inside a tokamak device. Typically applied to non-linear simulations of MHD instabilities relevant to magnetically confined fusion, the JOREK code was originally developed with a 2D grid composed of isoparametric bi-cubic Bézier finite elements, that are aligned to the magnetic equilibrium of tokamak plasmas (the third dimension being represented by Fourier harmonics). To improve the applicability of these simulations, the grid-generator has been generalised to provide a robust extension method, using a block-structured mesh approach, which allows the simulations of arbitrary domains of tokamak vacuum vessels. Such boundary-aligned grids require the adaptation of boundary conditions along the edge of the new domain. Demonstrative non-linear simulations of plasma edge instabilities are presented to validate the robustness of the new grid, and future potential physics applications for tokamak plasmas are discussed. The methods presented here may be of interest to the wider community, beyond tokamak physics, wherever imposing arbitrary boundaries to quadrilateral finite elements is required.\u3c/p\u3

Edge stability analysis of ITER baseline plasma simulations

A stability analysis using equilibria from CORSICA transport simulations finds that the maximum stable pedestal pressure in ITER 15 MA baseline plasma is 110 kPa corresponding to a pedestal temperature of 5.9 keV. The height of the stable pedestal is robust for the assumption of the pedestal height varying only by about 10% if the width of the pedestal is varied by 30%. A conducting first wall has a stabilizing effect on the peeling-ballooning modes that limit the edge pressure. However, the stabilization is unlikely to significantly change the stability limits, but could affect the ELM dynamics by lowering the growth rate of the ELM triggering peeling-ballooning modes. The entire pedestal region is stable against n = ∞ ballooning modes for all studied pedestal temperatures. This is due to the high bootstrap current keeping the magnetic shear in the region of large pressure gradient

Evaluation of core beta effects on pedestal MHD stability in ITER and consequences for energy confinement

\u3cp\u3eThe maximum stable pedestal pressure has been shown to increase with core pressure and in combination with profile stiffness this can lead to a positive feedback mechanism. However, the effect is shown to saturate for high β in ASDEX-Upgrade [1]. This paper investigates whether this effect appears in ITER scenarios, using ideal MHD numerical codes HELENA and MISHKA for different ITER scenarios from inductive 7.5-15 MA plasmas to steady-state scenarios at 10 MA. No pedestal pressure saturation is found for inductive scenarios; on the contrary for the 10MA steady-state scenario the pedestal pressure is the same for a wide range of total β and is limited by low n kink-peeling modes. Finally, a comparison of the achievable pressure for various levels of core profile stiffness is made with the IPB98(y,2) scaling law.\u3c/p\u3

MHD stability of the pedestal in ITER scenarios

The linear ideal magnetohydrodynamic (MHD) limits of the pedestal in ITER scenarios associated with the preparation and realization of the nominal fusion gain Q = 10 (inductive scenario at 15 MA/5.3 T, half-field/half-current and intermediate H-mode scenario at 10 MA/3.5 T), as well as the hybrid scenario at 12 MA/5.3 T, are investigated in this work. The accessible part of the MHD stability diagram is determined by computing the bootstrap current and self-consistently evaluating the corresponding pedestal current. This procedure shows that only a small part of peeling-ballooning diagrams is physically accessible. Uncertainties about the foreseen plasma profiles motivate studies evaluating the impact of various parameters on the pedestal limits. We have addressed issues such as the pedestal width, the global performance, pressure peaking, edge current density, internal inductance and plasma shaping. A scaling law for the maximum pedestal pressure in the ITER scenarios is proposed, highlighting that the main dependences are on the plasma current, the edge safety factor, the pedestal width and the internal inductance