F. Orain

Screening of resonant magnetic perturbations by flows in tokamaks

The non-linear reduced four-field RMHD model in cylindrical geometry was extended to include plasma rotation, neoclassical poloidal viscosity and two fluid diamagnetic effects. Interaction of the static resonant magnetic perturbations (RMPs) with the rotating plasmas in tokamaks was studied. The self-consistent evolution of equilibrium electric field due to RMP penetration is taken into account in the model. It is demonstrated that in the pedestal region with steep pressure gradients, mean flows perpendicular to the magnetic field, which includes and electron diamagnetic components plays an essential role in RMP screening by plasma. Generally, the screening effect increases for lower resistivity, stronger rotation and smaller RMP amplitude. Strong screening of central islands was observed limiting RMP penetration to the narrow region near the separatrix. However, at certain plasma parameters and due to the non-linear evolution of the radial electric field produced by RMPs, the rotation can be compensated by electron diamagnetic rotation locally. In this case, RMPs can penetrate and form magnetic islands. Typical plasma parameters and RMPs spectra on DIII-D, JET and ITER were used in modelling examples presented in the paper.

Three-dimensional distortions of the tokamak plasma boundary: boundary displacements in the presence of resonant magnetic perturbations

The three-dimensional plasma boundary displacements induced by applied non-axisymmetric magnetic perturbations have been measured in ASDEX Upgrade, DIII-D, JET, MAST and NSTX. The displacements arising from applied resonant magnetic perturbations (RMPs) are measured up to +/- 5% of the minor radius in present-day machines. Good agreement can be found between different experimental measurements and a range of models-be it vacuum field line tracing, ideal three-dimensional MHD equilibrium modelling, or nonlinear plasma amplification. The agreement of the various experimental measurements with the different predictions from these models is presented, and the regions of applicability of each discussed. The measured displacement of the outboard boundary from various machines is found to correlate approximately linearly with the applied resonant field predicted by vacuum modelling (though it should be emphasized that one should not infer that vacuum modelling accurately predicts the displacement inside the plasma). The RMP-induced displacements foreseen in ITER are expected to lie within the range of those predicted by the different models, meaning less than +/- 1.75% (+/- 3.5 cm) of the minor radius in the H-mode baseline and less than +/- 2.5% (+/- 5 cm) in a 9MA plasma. Whilst a displacement of 7 cm peak-to-peak in the baseline scenario is marginally acceptable from both a plasma control and heat loading perspective, it is important that ITER adopts a plasma control system which can account for a three-dimensional boundary corrugation to avoid an n = 0 correction which would otherwise locally exacerbate the displacement caused by the applied fields.

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.

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.

Experimental studies of high-confinement mode plasma response to non-axisymmetric magnetic perturbations in ASDEX Upgrade

The interaction of externally applied small non-axisymmetric magnetic perturba16 tions (MP) with tokamak high-confinement mode (H-mode) plasmas is reviewed and illus17 trated by recent experiments in ASDEX Upgrade. The plasma response to the vacuum MP 18 field is amplified by stable ideal kink modes with low toroidal mode number n driven by the 19 H-mode edge pressure gradient (and associated bootstrap current) which is experimentally 20 evidenced by an observable shift of the poloidal mode number m away from field alignment 21 (m = qn, with q being the safety factor) at the response maximum. A torque scan experiment 22 demonstrates the importance of the perpendicular electron flow for shielding of the resonant 23 magnetic perturbation, as expected from a two-fluid MHD picture. Two significant effects of 24 MP occur in H-mode plasmas at low pedestal collisionality, νped ≤ 0.4: (a) a reduction of the 25 global plasma density by up to 50% and (b) a reduction of the energy loss associated with edge 26 localised modes (ELMs) by a factor of up to 10. A comprehensive database of ELM mitigation 27 pulses at low ν∗ in ASDEX Upgrade shows that the degree of ELM mitigation correlates with 28 the reduction of pedestal pressure which in turn is limited and defined by the onset of ELMs, 29 i. e. a modification of the ELM stability limit by the magnetic perturbation. 30 PACS numbers: 52.55.Fa, 52.55.Tn, 52.65.Kj 31 2

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.