Development of the neutral model in the nonlinear MHD code JOREK:Application to e × B drifts in ITER PFPO-1 plasmas

The prediction of power fluxes and plasma-wall interactions impacted by MHD processes during ITER operation [disruption, Edge Localized Modes (ELMs), 3D magnetic fields applied for ELM control, etc.] requires models that include an accurate description of the MHD processes themselves, as well as of the edge plasma and plasma-wall interaction processes. In this paper, we report progress on improving the edge plasma physics models in the nonlinear extended MHD code JOREK, which has capabilities to simulate the MHD response of the plasma to the applied external 3D fields, disruptions and ELMs. The extended MHD model includes E × B drifts, diamagnetic drifts, and neoclassical flows. These drifts can have large influences, on e.g., divertor asymmetries. Realistic divertor conditions are important for impurity sputtering, transport, and their effect on the plasma. In this work, we implemented kinetic and fluid neutral physics modules, investigated the influence of poloidal flows under divertor conditions in the ITER PFPO-1 (1.8T/5MA) H-mode plasma scenario, and compared the divertor plasma conditions and heat flux to the wall for both the fluid and kinetic neutral model (in JOREK) to the well-established 2D boundary plasma simulation code suite SOLPS-ITER. As an application of the newly developed model, we investigated time-dependent divertor solutions and the transition from attached to partially detached plasmas. We present the formation of a high-field-side high-density-region and how it is driven by poloidal E × B drifts.</p

A generalised formulation of G-continuous Bezier elements applied to non-linear MHD simulations

The international tokamak ITER is progressing towards assembly completion and first-plasma operation, which will be a physics and engineering challenge for the fusion community. In the preparation for ITER experimental scenarios, non-linear MHD simulations are playing an essential role to actively understand and predict the behaviour and stability of tokamak plasmas in future fusion power plant. The development of MHD codes like JOREK is a key aspect of this research effort, and provides invaluable insight into the plasma stability and the control of global and localised plasma events, like Edge-Localised-Mode and disruptions. In this paper, we present an operational implementation of a new, generalised formulation of Bezier finite-elements applied to the JOREK code, a significant advancement from the previously G1-continuous bi-cubic Bezier elements. This new mathematical method enables any polynomial order of Bezier elements, with a guarantee of G-continuity at the level of (n−1)/2, for any odd n, where n is the order of the Bezier polynomials. The generalised method is defined, and a rigorous mathematical proof is provided for the G-continuity requirement. Key details on the code implementation are mentioned, together with a suite of tests to demonstrate the mathematical reliability of the finite-element method, as well as the practical usability for typical non-linear tokamak MHD simulations. A demonstration for a state-of-the-art simulation of an Edge-Localised-Mode instability in the future ITER tokamak, with realistic grid geometry, finalises the study.</p

Modelling of high-field-side high-density region with the nonlinear MHD code JOREK with kinetic neutrals

In this contribution, we have presented a benchmark of JOREK-without drifts-with kinetic neutrals against SOLPS-ITER (without drifts) and the development of the HFSHD-region in JOREK simulations with kinetic neutrals for early ITER operation (the PFPO-1 phase). Ramping up the fueling rate (in the divertor) decreases gradually the heat flux towards the divertor target. Once the ionisation front comes off the wall, cross field transport moves neutrals and plasma across the separatrix. Building up the (off-separatrix) density in the high field side. Around a critical upstream density, the plasma undergoes a sharp transition to form the HFSHD-region carried by the formation of an →−E×→−B vortex. This →−E×→−B vortex increases in strength and displaces the inner target ion flux upwards. Switching off →−E×→−B drifts strongly reduces cross-field transport and thus does not allow for the density buildup at the high-field-side. With more accurate divertor solution, JOREK can now better study the consequences in the divertor as a result of MHD instabilities, such as ELMs.</p

Modelling of high-field-side high-density region with the nonlinear MHD code JOREK with kinetic neutrals

In this contribution, we have presented a benchmark of JOREK-without drifts-with kinetic neutrals against SOLPS-ITER (without drifts) and the development of the HFSHD-region in JOREK simulations with kinetic neutrals for early ITER operation (the PFPO-1 phase). Ramping up the fueling rate (in the divertor) decreases gradually the heat flux towards the divertor target. Once the ionisation front comes off the wall, cross field transport moves neutrals and plasma across the separatrix. Building up the (off-separatrix) density in the high field side. Around a critical upstream density, the plasma undergoes a sharp transition to form the HFSHD-region carried by the formation of an →−E×→−B vortex. This →−E×→−B vortex increases in strength and displaces the inner target ion flux upwards. Switching off →−E×→−B drifts strongly reduces cross-field transport and thus does not allow for the density buildup at the high-field-side. With more accurate divertor solution, JOREK can now better study the consequences in the divertor as a result of MHD instabilities, such as ELMs.</p

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

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

Magnetic nuclear fusion devices are a promising candidate for the confinement of thermonuclear plasmas but various instabilities set important limits on their operation. Peeling-ballooning perturbations, which can be described appropriately using high-n linear ideal MHD stability theory, are two of them, where high-n indicates that the perturbations are localized along the magnetic field lines [1]. A new numerical code, called PB3D (Peeling Ballooning in 3D) was written to investigate the stability of these instabilities in a fast and reliable way, solving the generalized eigensystem presented first in [8]. The important new aspect of this theory is that it describes stability of full 3-D equilibrium configurations that are allowed to perturb the plasma edge, in contrast with previous treatments such as used in the ELITE [9] or MISHKA code [5] that both treat the stability of axisymmetric equilibria. 3D effects are important for numerous reasons: In tokamaks axisymmetry is often broken, either deliberately, such as when RMP techniques are used to suppress periodic plasma relaxations called ELMs, or due to imperfections in the axisymmetric design, such as the toroidal ripple introduced by discrete toroidal field coils. Stellarators devices, on the other hand, are inherently 3D and cannot be approximated using axisymmetric theory. In this work, the verification of PB3D with stability results for axisymmetric equilibria is presented, indicating that these are accurately reproduced, and non-intuitive first 3-D results are given.</p

Electron acceleration in a JET disruption simulation

Runaways are suprathermal electrons having sufficiently high energy to be continuously accelerated up to tens of MeV by a driving electric field [1]. Highly energetic runaway electron (RE) beams capable of damaging the tokamak first wall can be observed after a plasma disruption [2]. Therefore, it is of primary importance to fully understand their generation mechanisms in order to design mitigation systems able to guarantee safe tokamak operations. In a previous work, [3], a test particle tracker was introduced in the JOREK 3D non-linear MHD code and used for studying the electron confinement during a simulated JET-like disruption. It was found in [3] that relativistic electrons are not completely deconfined by the stochastic magnetic field taking place during the disruption thermal quench (TQ). This is due to the reformation of closed magnetic surfaces at the beginning of the current quench (CQ). This result was obtained neglecting the inductive electric field in order to avoid the unrealistic particle acceleration which otherwise would have happened due to the absence of collision effects. The present paper extends [3] analysing test electron dynamics in the same simulated JET-like disruption using the complete electric field. For doing so, a simplified collision model is introduced in the particle tracker guiding center equations. We show that electrons at thermal energies can become RE during or promptly after the TQ due to a combination of three phenomena: a first REs acceleration during the TQ due to the presence of a complex MHD-induced electric field, particle reconfinement caused by the fast reformation of closed magnetic surfaces after the TQ and a secondary acceleration induced by the CQ electric field

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

The 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.</p

Three-dimensional non-linear magnetohydrodynamic modeling of massive gas injection triggered disruptions in JET

JOREK 3D non-linear MHD simulations of a D2 Massive Gas Injection (MGI) triggered disruption in JET are presented and compared in detail to experimental data. The MGI creates an overdensity that rapidly expands in the direction parallel to the magnetic field. It also causes the growth of magnetic islands (m=n ¼ 2=1 and 3/2 mainly) and seeds the 1/1 internal kink mode. O-points of all island chains (including 1/1) are located in front of the MGI, consistently with experimental observations. A burst of MHD activity and a peak in plasma current take place at the same time as in the experiment. However, the magnitude of these two effects is much smaller than in the experiment. The simulated radiation is also much below the experimental level. As a consequence, the thermal quench is not fully reproduced. Directions for progress are identified. Radiation from impurities is a good candidate.EURATOM 63305