S. Pamela

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...

Resistive MHD simulation of edge-localized-modes for double-null discharges in the MAST device

Recent development of the nonlinear magneto hydrodynamic (MHD) code JOREK has enabled the alignment of its two-dimensional finite-element grid along poloidal flux surfaces for double-null Grad–Shafranov equilibria. In previous works with the JOREK code, only single X-point plasmas were studied. The fast-camera diagnostic on MAST, which gives a global view of the pedestal filamentation during an ELM crash, clearly shows filaments travelling far into the scrape-off layer, as far as the first wall. Simulation of such a filament dynamics in MAST double-null plasmas is presented here and compared with experimental observations. In addition to direct comparison with the fast-camera images, general aspects of filaments are studied, such as their radial speed and composition. A qualitative validation of simulations is carried out against other diagnostics, such as the Thomson-scattering profiles or the infra-red camera images. Simulations are found to reproduce experimental edge localized modes in a reasonable manner, with similar energy losses and divertor heat-flux profiles. However, the MHD model used for those simulations is a reduced MHD model, which is likely approaching the limit of its applicability for the MAST device. Also, the absence of diamagnetic drift terms in the present MHD model results in nonlinear simulations being dominated by the highest mode number, and thus coupling with lower mode numbers is not observed.

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.

Electron Kinetics Inferred from Observations of Microwave Bursts During Edge Localized Modes in the Mega-Amp Spherical Tokamak

Recent measurements of microwave and x-ray emission during edge localized mode (ELM) activity in tokamak plasmas provide a fresh perspective on ELM physics. It is evident that electron kinetics, which are not incorporated in standard (fluid) models for the instability that drives ELMs, play a key role in the new observations. These effects should be included in future models for ELMs and the ELM cycle. The observed radiative effects paradoxically imply acceleration of electrons parallel to the magnetic field combined with rapid acquisition of perpendicular momentum. It is shown that this paradox can be resolved by the action of the anomalous Doppler instability which enables fast collective radiative relaxation, in the perpendicular direction, of electrons accelerated in the parallel direction by inductive electric fields generated by the initial ELM instability.

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.

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=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.

Recent progress in understanding the processes underlying the triggering of and energy loss associated with type I ELMs

The type I ELMy H-mode is the baseline operating scenario for ITER. While it is known that the type I edge-localized mode (ELM) ultimately results from the peeling–ballooning instability, there is growing experimental evidence that a mode grows up before the ELM crash that may modify the edge plasma, which then leads to the ELM event due to the peeling–ballooning mode. The triggered mode results in the release of a large number of particles and energy from the core plasma but the precise mechanism by which these losses occur is still not fully understood and hence makes predictions for future devices uncertain. Recent progress in understanding the processes that trigger type I ELMs and the size of the resultant energy loss are reviewed and compared to experimental data and ideas for further development are discussed.

Towards understanding edge localised mode mitigation by resonant magnetic perturbations in MAST

Type-I Edge Localised Modes (ELMs) have been mitigated in MAST through the application of n = 3; 4, and 6 resonant magnetic perturbations. For each toroidal mode number of the non-axisymmetric applied fields, the frequency of the ELMs has been increased significantly, and the peak heat flux on the divertor plates reduced commensurately. This increase in ELM frequency occurs despite a significant drop in the edge pressure gradient, which would be expected to stabilise the peeling-ballooning modes thought to be responsible for type-I ELMs. Various mechanisms which could cause a destabilisation of the peeling-ballooning modes are presented, including pedestal widening, plasma rotation braking, three dimensional corrugation of the plasma boundary, and the existence of radially extended lobe structures near to the X-point. This leads to a model aimed at resolving the apparent dichotomy of ELM control, which is to say ELM suppression occurring due to the pedestal pressure reduction below the peeling-ballooning stability boundary, whilst the reduction in pressure can also lead to ELM mitigation, which is ostensibly a destabilisation of peeling-ballooning modes. In the case of ELM mitigation, the pedestal broadening, 3d corrugation, or lobes near the X-point degrade ballooning stability so much that the pedestal recovers rapidly to cross the new stability boundary at lower pressure more frequently, whilst in the case of suppression, the plasma parameters are such that the particle transport reduces the edge pressure below the stability boundary, which is only mildly affected by negligible rotation braking, small edge corrugation or short, broad lobe structures.

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

An increase in ELM frequency has been demonstrated in MAST by applying resonant magnetic perturbations (RMPs) with toroidal mode number, nRMP = 2, 3, 4, 6. It has been observed that the mitigated ELM frequency increases with the amplitude of the applied field provided it is above a critical threshold. This threshold value depends on the mode number of the RMP, with higher nRMP having a larger critical value. For the same ELM frequency, the reduction in the peak heat load on the divertor plates is approximately the same for all RMP configurations. The RMPs give rise to perturbations to the plasma shape, with lobe structures occurring due to the tangled magnetic fields near the X-point, and corrugations of the plasma boundary at the midplane. The X-point lobe length increases linearly with the applied field when above a threshold, with RMPs of higher toroidal mode number giving rise to longer lobes for the same applied resonant field. Similarly, the midplane displacements increase with the applied field strength, though the corrugation amplitude is less dependent upon the RMP configuration. For all nRMP, the RMPs result in enhanced particle transport and a reduction in the pedestal pressure gradient caused by an increased pedestal width, which is found to be consistent with a decrease in the critical pressure at which infinite-n ballooning modes are driven unstable in non-axisymmetric plasmas. The plasma rotation braking is strongest for lowest nRMP whilst the degradation of access to H-mode resultant from the application of RMPs are non-monotonic in nRMP, with the optimal case for both occurring for nRMP = 4. Whilst there are advantages and disadvantages for all RMP configurations, the configurations found to be optimised in terms of pedestal degradation, access to H-mode, plasma rotation and distortion to the plasma configuration in MAST are nRMP = 3 or 4, consistent with the configurations anticipated for use in ITER.

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...