M. Hoelzl

Non-linear magnetohydrodynamic modeling of plasma response to resonant magnetic perturbations

The interaction of static Resonant Magnetic Perturbations (RMPs) with the plasma flows is modeled in toroidal geometry, using the non-linear resistive MHD code JOREK, which includes the X-point and the scrape-off-layer. Two-fluid diamagnetic effects, the neoclassical poloidal friction and a source of toroidal rotation are introduced in the model to describe realistic plasma flows. RMP penetration is studied taking self-consistently into account the effects of these flows and the radial electric field evolution. JET-like, MAST, and ITER parameters are used in modeling. For JET-like parameters, three regimes of plasma response are found depending on the plasma resistivity and the diamagnetic rotation: at high resistivity and slow rotation, the islands generated by the RMPs at the edge resonant surfaces rotate in the ion diamagnetic direction and their size oscillates. At faster rotation, the generated islands are static and are more screened by the plasma. An intermediate regime with static islands which sl...

Fast-ion losses induced by ELMs and externally applied magnetic perturbations in the ASDEX Upgrade tokamak

Phase-space time-resolved measurements of fast-ion losses induced by edge localized modes (ELMs) and ELM mitigation coils have been obtained in the ASDEX Upgrade tokamak by means of multiple fast-ion loss detectors (FILDs). Filament-like bursts of fast-ion losses are measured during ELMs by several FILDs at different toroidal and poloidal positions. Externally applied magnetic perturbations (MPs) have little effect on plasma profiles, including fast-ions, in high collisionality plasmas with mitigated ELMs. A strong impact on plasma density, rotation and fast-ions is observed, however, in low density/collisionality and q95 plasmas with externally applied MPs. During the mitigation/suppression of type-I ELMs by externally applied MPs, the large fast-ion bursts observed during ELMs are replaced by a steady loss of fast-ions with a broad-band frequency and an amplitude of up to an order of magnitude higher than the neutral beam injection (NBI) prompt loss signal without MPs. Multiple FILD measurements at different positions, indicate that the fast-ion losses due to static 3D fields are localized on certain parts of the first wall rather than being toroidally/poloidally homogeneously distributed. Measured fast-ion losses show a broad energy and pitch-angle range and are typically on banana orbits that explore the entire pedestal/scrape-off-layer (SOL). Infra-red measurements are used to estimate the heat load associated with the MP-induced fast-ion losses. The heat load on the FILD detector head and surrounding wall can be up to six times higher with MPs than without 3D fields. When 3D fields are applied and density pump-out is observed, an enhancement of the fast-ion content in the plasma is typically measured by fast-ion D-alpha (FIDA) spectroscopy. The lower density during the MP phase also leads to a deeper beam deposition with an inward radial displacement of ?2?cm in the maximum of the beam emission. Orbit simulations are used to test different models for 3D field equilibrium reconstruction including vacuum representation, the free boundary NEMEC code and the two-fluid M3D-C1 code which account for the plasma response. Guiding center simulations predict the maximum level of losses, ?2.6%, with NEMEC 3D equilibrium. Full orbit simulations overestimate the level of losses in 3D vacuum fields with ?15% of lost NBI ions.

Non-linear modeling of the plasma response to RMPs in ASDEX Upgrade

The plasma response to resonant magnetic perturbations (RMPs) in ASDEX Upgrade is modeled with the non-linear resistive MHD code JOREK, using input profiles that match those of the experiments as closely as possible. The RMP configuration for which edge localized modes are best mitigated in experiments is related to the largest edge kink response observed near the X-point in modeling. On the edge resonant surfaces q = m/n, the coupling between the kink component (m > nq) and the m resonant component is found to induce the amplification of the resonant magnetic perturbation. The ergodicity and the 3D-displacement near the X-point induced by the resonant amplification can only partly explain the density pumpout observed in experiments.The plasma response to resonant magnetic perturbations (RMPs) in ASDEX Upgrade is modeled with the non-linear resistive MHD code JOREK, using input profiles that match those of the experiments as closely as possible. The RMP configuration for which edge localized modes are best mitigated in experiments is related to the largest edge kink response observed near the X-point in modeling. On the edge resonant surfaces q = m/n, the coupling between the kink component (m > nq) and the m resonant component is found to induce the amplification of the resonant magnetic perturbation. The ergodicity and the 3D-displacement near the X-point induced by the resonant amplification can only partly explain the density pumpout observed in experiments.

Non-linear MHD modeling of edge localized mode cycles and mitigation by resonant magnetic perturbations

The dynamics of a multi-edge localized mode (ELM) cycle as well as the ELM mitigation by resonant magnetic perturbations (RMPs) are modeled in realistic tokamak X-point geometry with the non-linear reduced MHD code JOREK. The diamagnetic rotation is found to be a key parameter enabling us to reproduce the cyclical dynamics of the plasma relaxations and to model the near-symmetric ELM power deposition on the inner and outer divertor target plates consistently with experimental measurements. Moreover, the non-linear coupling of the RMPs with unstable modes are found to modify the edge magnetic topology and induce a continuous MHD activity in place of a large ELM crash, resulting in the mitigation of the ELMs. At larger diamagnetic rotation, a bifurcation from unmitigated ELMs—at low RMP current—towards fully suppressed ELMs—at large RMP current—is obtained.

Nonlinear MHD simulations of Quiescent H-mode plasmas in DIII-D

In the Quiescent H-mode (QH-mode) regime, the edge harmonic oscillation (EHO), thought to be a saturated kink-peeling mode (KPM) driven unstable by current and rotation, is found in experiment to provide sufficient stationary edge particle transport to avoid the periodic expulsion of particles and energy by edge localized modes (ELMs). In this paper, both linear and nonlinear MHD modelling of QH-mode plasmas from the DIII-D tokamak have been investigated to understand the mechanism leading to the appearance of the EHO in QH-mode plasmas. For the first time nonlinear MHD simulations with low-n modes both with ideal wall and resistive wall boundary conditions have been carried out with the 3D non-linear MHD code JOREK. The results show, in agreement with the original conjectures, that in the non-linear phase, kink peeling modes are the main unstable modes in QH-mode plasmas of DIII-D and that the kink-peeling modes saturate non-linearly leading to a 3D stationary state. The characteristics of the kink-peeling modes, in terms of mode structure and associated decrease of the edge plasma density associated with them, are in good agreement with experimental measurements of the EHO in DIII-D. The effect of plasma resistivity, the role of plasma parallel rotation as well as the effect of the conductivity of the vacuum vessel wall on the destabilization and saturation of kink-peeling modes have been evaluated for experimental QH-mode plasma conditions in DIII-D.

Disruption mitigation by injection of small quantities of noble gas in ASDEX Upgrade

The most recent experiments of disruption mitigation by massive gas injection in ASDEX Upgrade have concentrated on small-relatively to the past-quantities of noble gas injected, and on the search for the minimum amount of gas necessary for the mitigation of the thermal loads on the divertor and for a significant reduction of the vertical force during the current quench. A scenario for the generation of a long-lived runaway electron beam has been established; this allows the study of runaway current dissipation by moderate quantities of argon injected. This paper presents these recent results and discusses them in the more general context of physical models and extrapolation, and of the open questions, relevant for the realization of the ITER disruption mitigation system.

Non-linear Simulations of MHD Instabilities in Tokamaks Including Eddy Current Effects and Perspectives for the Extension to Halo Currents

The dynamics of large scale plasma instabilities can be strongly influenced by the mutual interaction with currents flowing in conducting vessel structures. Especially eddy currents caused by time-varying magnetic perturbations and halo currents flowing directly from the plasma into the walls are important. The relevance of a resistive wall model is directly evident for Resistive Wall Modes (RWMs) or Vertical Displacement Events (VDEs). However, also the linear and non-linear properties of most other large-scale instabilities may be influenced significantly by the interaction with currents in conducting structures near the plasma. The understanding of halo currents arising during disruptions and VDEs, which are a serious concern for ITER as they may lead to strong asymmetric forces on vessel structures, could also benefit strongly from these non-linear modeling capabilities. Modeling the plasma dynamics and its interaction with wall currents requires solving the magneto-hydrodynamic (MHD) equations in realistic toroidal X-point geometry consistently coupled with a model for the vacuum region and the resistive conducting structures. With this in mind, the non-linear finite element MHD code JOREK [1, 2] has been coupled [3] with the resistive wall code STARWALL [4], which allows us to include the effects of eddy currents in 3D conducting structures in non-linear MHD simulations. This article summarizes the capabilities of the coupled JOREK-STARWALL system and presents benchmark results as well as first applications to non-linear simulations of RWMs, VDEs, disruptions triggered by massive gas injection, and Quiescent H-Mode. As an outlook, the perspectives for extending the model to halo currents are described.

Edge localized mode rotation and the nonlinear dynamics of filaments

Edge Localized Modes (ELMs) rotating precursors were reported few milliseconds before an ELM crash in several tokamak experiments. Also, the reversal of the filaments rotation at the ELM crash is commonly observed. In this article, we present a mathematical model that reproduces the rotation of the ELM precursors as well as the reversal of the filaments rotation at the ELM crash. Linear ballooning theory is used to establish a formula estimating the rotation velocity of ELM precursors. The linear study together with nonlinear magnetohydrodynamic simulations give an explanation to the rotations observed experimentally. Unstable ballooning modes, localized at the pedestal, grow and rotate in the electron diamagnetic direction in the laboratory reference frame. Approaching the ELM crash, this rotation decreases corresponding to the moment when the magnetic reconnection occurs. During the highly nonlinear ELM crash, the ELM filaments are cut from the main plasma due to the strong sheared mean flow that is non...

Non-linear MHD simulations of ELMs in JET and quantitative comparisons to experiments

A subset of JET ITER-like wall (ILW) discharges, combining electron density and temperature as well as divertor heat flux measurements, has been collected for the validation of non-linear magnetohydrodynamic (MHD) simulations of edge-localised-modes (ELMs). This permits a quantitative comparison of simulation results against experiments, which is required for the validation of predicted ELM energy losses and divertor heat fluxes in future tokamaks like ITER. This paper presents the first results of such a quantitative comparison, and gives a perspective of what will be necessary to achieve full validation of non-linear codes like JOREK. In particular, the present study highlights the importance of pre-ELM equilibria and parallel energy transport models in MHD simulations, which form the underlying basis of ELM physics.

Electromagnetic thin-wall model for simulations of plasma wall-touching kink and vertical modes

The understanding of plasma disruptions in tokamaks and predictions of their effects require realistic simulations of electric currents excitation in 3-dimensional vessel structures by the plasma touching the walls. As it was discovered at JET in 1996 (Litunovski 1995; Noll et al. 1996) the wall touching kink modes are frequently excited during the Vertical Displacement Events (VDE) and cause big sideways forces on the vacuum vessel which are difficult to confront in large tokamaks. In disruptions, the sharing of electric current between the plasma and the wall plays an important role in plasma dynamics and determines the amplitude and localization of the sideways force (Riccardo, Noll et al. 2000; Riccardo and Walker 2000; Zakharov 2008; Riccardo at al. 2009; Bachmann at al. 2011). This paper describes a flat triangle representation of electric circuits of a thin conducting wall of arbitrary 3-dimensional geometry. Implemented into the Shell Simulation Code (SHL) and the Source Sink Current code (SSC), this model is suitable for modelling the electric currents excited in the wall inductively and through the current sharing with the plasma.