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Using the nonlinear 3D MHD code JOREK with reduced MHD equations (visco-resistive MHD), we have successfully simulated a recent n = 2 resonant magnetic perturbation (RMP)- driven edge localized mode (ELM) suppression in KSTAR. We have found that such ELM suppression has been attributable not only to the degraded pedestal but also to the direct coupling between the peeling-ballooning mode (PBM) and RMP-driven plasma response. Notably, the pedestal pressure gradient is reduced as the radial transport is enhanced because of the formation of the stochastic layer and increased convection fluxes due to tearing and the kink-peeling mode driven by RMPs. The increased transport in the stochastic layer is due to the parallel transport across the stochastic fields, described by the Braginskii model in the simulation. While the linear stability of the PBM improves owing to the degraded pedestal, it is not a sole contributor to ELM suppression, in that the nonlinear mode coupling plays a more critical role. This outcome is consistent with previous studies where mode coupling affects the ELM mitigation or suppression. In addition, PBM locking has been numerically achieved during the ELM suppression phase, which may support the relationship between VE×B ≈ 0 at the pedestal and the onset of ELM suppression. We suggest that PBM locking can enhance the mode interactions between RMPs and PBMs, which is significant for ELM suppression.

We present global linear and nonlinear simulations of ion temperature gradient instabilities based on a fluid formulation, with an adapted version of the JOREK code. These simulations are performed in realistic global tokamak equilibria based on the solution of the Grad-Shafranov equation. Benchmarking of linear growth rates was successfully completed with respect to previously published data. We find two distinct types of eigenstructures, depending on the magnetic shear. For high shear, when the coupling of poloidal harmonics is strong, ballooning-type eigenmodes are formed, which are up-down asymmetric with a finite ballooning angle, θ0. The poloidal harmonics which form the global eigenmode are found to demonstrate a radial shift, being centered well outside of their corresponding rational surface. Stronger diamagnetic effects increase both θ0 and proportionately shift the m harmonics to larger radii (by as much as two rational surfaces). In the low shear regime, the unstable eigenmodes become narrowly localized between neighboring pairs of rational surfaces, and exhibit no up-down asymmetry. Our simulations also show the generation of finite Reynolds stress due to nonlocal/global profile effects. This stress possesses both poloidally symmetric (n = m = 0) and asymmetric (finite-m) components. Turbulent saturation in nonlinear simulations is demonstrated for both shear regimes.

In nonlinear MHD simulations of DIII-D QH-mode plasmas it has been found that low n kink/peeling modes (KPMs) are unstable and grow to a saturated external kink mode. The features of the dominant saturated KPMs, which are localized toroidally by non-linear coupling of harmonics, such as mode frequencies, density fluctuations and their effect on pedestal particle and energy transport, are in good agreement with the observations of the Edge Harmonic Oscillation (EHO) typically present in DIII-D QH-mode experiments. The non-linear evolution of MHD modes with toroidal mode numbers n from 0 to 10, including both kink-peeling modes and ballooning modes, is investigated through MHD simulations by varying the pedestal current and pressure relative to the initial conditions of DIII-D QH-mode plasma. The edge current and pressure at the pedestal are key parameters for the plasma either saturating to a QH-mode regime or a ballooning mode dominant regime. The influence of E×B flow and its shears on QH-mode plasma has been investigated. The behavior of QH-mode with different flow shear shows E×B rotation has strong stabilization effects on the medium to high-n modes but destabilizing for n=2. The QH-mode extrapolation results of an ITER Q=10 plasma show that the pedestal currents are large enough to destabilize an n=1-5 kink/peeling mode, leading to a saturated kink-peeling mode.

Edge localized modes (ELMs) are magnetohydrodynamic (MHD) instabilities that cause fast periodic relaxations of the strong edge pressure gradient in tokamak fusion plasmas. A novel diagnostic method allows the extraction of toroidal mode numbers, rotation velocities and spatial information during the ELM cycle including the crash. While mode number branches n = 3-6 and n = 8-10 are dominant just before the ELM crash, during the ELM crash n = 2-5 are observed in typical discharges with type-I ELMs in the tokamak experiment. These findings are compared to results from nonlinear MHD simulations. Although n = 6 is linearly dominant, nonlinear coupling in which n = 1 is particularly important leads to the dominance of n = 3-5 during the ELM crash, in excellent agreement with experimental observations. The simultaneous occurrence of these modes over a wide radial region leads to high stochasticity and thus increased transport.

The explanation of the existence of the rotating MHD modes in the pedestal region before Type I edge localized mode (ELM) crash and in the inter-ELM periods (ELM precursors) observed in KSTAR is provided for the first time in the present paper. The dynamics of ELMs, observed using electron cyclotron emission imaging (ECEI) in KSTAR tokamak, is compared to the modelling results of the non-linear reduced resistive MHD code JOREK. The realistic KSTAR pulse parameters and geometry including X-point and scrape off layer (SOL) were used. The full ELM crash modelling was performed using JOREK code for single and multi-harmonic representation and in multi-cycles ELMy regimes including relevant flows. The most unstable toroidal modes numbers (n = 5–8), velocity (~5 km s−1 for n = 8 mode) and the direction of the mode rotation were reproduced in modelling. The two fluid diamagnetic effects and toroidal rotations included in the model were found to be the most important factors in explaining the experimentally observed rotation of the ballooning modes before the ELM crash and in the inter-ELM phase. In multi-harmonic multi-cycle simulations the spectrum of temperature fluctuations is similar to the experimental one in the inter-ELM phase, where several rotating modes with medium n numbers were detected in 5–30 kHz frequency range. The rotating modes can contain single or several harmonics which last from 0.2 ms to few ms in time, and can appear and disappear in the inter ELM period or persist until a new ELM crash.

Time-dependent nonlinear simulation using the BOUT++ 3-field model is performed for a study of edge localized mode (ELM) dynamics in KSTAR H-mode plasmas. The simulated results of the ELM evolution are directly compared with the 2D ELM structures, measured by electron cyclotron emission imaging systems, from the initial growth to crash phase. The simulation results are qualitatively in good agreement with the observations. Specifically, it is notable in simulation and experiment that higher-n modes in a quasi-steady state phase evolve into lower-n modes close to the ELM-crash in time. It suggests that lower-n modes may be responsible for the onset of the crash. A postanalysis supports that nonlinear mode coupling between toroidal harmonics may drive the lower-n mode.

In order to reduce the risks for ITER Plasma Facing Components (PFCs), it is proposed to equip Tore Supra with a full tungsten divertor, benefitting from the unique long pulse capabilities, the high installed RF power and the long experience with actively cooled high heat flux components of the Tore Supra platform. The transformation from the current circular limiter geometry to the required X-point configuration will be achieved by installing a set of copper poloidal coils inside the vacuum vessel. The new configuration will allow for H-mode access, providing relevant plasma conditions for PFC technology validation. Furthermore, attractive steady-state regimes are expected to be achievable. The lower divertor target design will be closely based on that currently envisaged for ITER (W monoblocks), while the upper divertor region will be used to qualify the main first wall heat sink technology adopted for the ITER blanket modules (CuCrZr copper/stainless steel) with a tungsten coating (in place of the Be tiles which ITER will use). Extended plasma exposure will provide access to ITER critical issues such as PFC lifetime (melting, cracking, etc.), tokamak operation on damaged metallic surfaces, real time heat flux control through PFC monitoring, fuel retention and dust production.

Results of calculations of resonant magnetic perturbation spectra on the COMPASS tokamak are presented. Spectra of the perturbations are calculated from the vacuum field of the perturbation coils. Ergodization is then estimated by applying the criterion of overlap of the resulting islands and verified by field line tracing. Results show that for the chosen configuration of perturbation coils an ergodic layer appears in the pedestal region. The ability to form an ergodic layer is similar to the theoretical results for the ELM suppression experiment at DIII-D; thus, a comparable effect on ELMs can be expected.

Results from three-dimensional modeling of plasma edge transport and plasma–wall interactions during application of resonant magnetic perturbation (RMP) fields for control of edge-localized modes in the ITER standard 15 MA Q = 10 H-mode are presented. The full 3D plasma fluid and kinetic neutral transport code EMC3-EIRENE is used for the modeling. Four characteristic perturbed magnetic topologies are considered and discussed with reference to the axisymmetric case without RMP fields. Two perturbation field amplitudes at full and half of the ITER ELM control coil current capability using the vacuum approximation are compared to a case including a strongly screening plasma response. In addition, a vacuum field case at high q 95 = 4.2 featuring increased magnetic shear has been modeled. Formation of a three-dimensional plasma boundary is seen for all four perturbed magnetic topologies. The resonant field amplitudes and the effective radial magnetic field at the separatrix define the shape and extension of the 3D plasma boundary. Opening of the magnetic field lines from inside the separatrix establishes scrape-off layer-like channels of direct parallel particle and heat flux towards the divertor yielding a reduction of the main plasma thermal and particle confinement. This impact on confinement is most accentuated at full RMP current and is strongly reduced when screened RMP fields are considered, as well as for the reduced coil current cases. The divertor fluxes are redirected into a three-dimensional pattern of helical magnetic footprints on the divertor target tiles. At maximum perturbation strength, these fingers stretch out as far as 60 cm across the divertor targets, yielding heat flux spreading and the reduction of peak heat fluxes by 30%. However, at the same time substantial and highly localized heat fluxes reach divertor areas well outside of the axisymmetric heat flux decay profile. Reduced RMP amplitudes due to screening or reduced RMP coil current yield a reduction of the width of the divertor flux spreading to about 20–25 cm and cause increased peak heat fluxes back to values similar to those in the axisymmetric case. The dependencies of these features on the divertor recycling regime and the perpendicular transport assumptions, as well as toroidal averaged effects mimicking rotation of the RMP field, are discussed in the paper.

International audience; With WEST (Tungsten Environment in Steady State Tokamak) (Bucalossi et al 2014 Fusion Eng. Des. 89 [http://dx.doi.org/10.1016/j.fusengdes.2014.01.062] 907?12 ), the Tore Supra facility and team expertise (Dumont et al 2014 Plasma Phys. Control. Fusion 56 [http://dx.doi.org/10.1088/0741-3335/56/7/075020] 075020 ) is used to pave the way towards ITER divertor procurement and operation. It consists in implementing a divertor configuration and installing ITER-like actively cooled tungsten monoblocks in the Tore Supra tokamak, taking full benefit of its unique long-pulse capability. WEST is a user facility platform, open to all ITER partners. This paper describes the physics basis of WEST: the estimated heat flux on the divertor target, the planned heating schemes, the expected behaviour of the L?H threshold and of the pedestal and the potential W sources. A series of operating scenarios has been modelled, showing that ITER-relevant heat fluxes on the divertor can be achieved in WEST long pulse H-mode plasmas.

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.

International audience; The full dynamics of a multi-edge-localized-mode (ELM) cycle is modeled for the first time in realistic tokamak X-point geometry with the nonlinear reduced MHD code JOREK. The diamagnetic rotation is found to be instrumental to stabilize the plasma after an ELM crash and to model the cyclic reconstruction and collapse of the plasma pressure profile. ELM relaxations are cyclically initiated each time the pedestal gradient crosses a triggering threshold. Diamagnetic drifts are also found to yield a near-symmetric ELM power deposition on the inner and outer divertor target plates, consistent with experimental measurements.

International audience; A possible mechanism of edge localized modes (ELMs) mitigation by resonant magnetic perturbations (RMPs) is proposed based on the results of nonlinear resistive magnetohydrodynamic modeling using the JOREK code, realistic JET-like plasma parameters and an RMP spectrum of JET error-field correction coils (EFCC) with a main toroidal number n ¼ 2 were used in the simulations. Without RMPs, a large ELM relaxation is obtained mainly due to the most unstable medium-n ballooning mode. The externally imposed RMP drives nonlinearly the modes coupled to n ¼ 2 RMP which produce small multimode relaxations, mitigated ELMs. The modes driven by RMPs exhibit a tearinglike structure and produce additional islands. Mitigated ELMs deposit energy into the divertor mainly in the structures ("footprints") created by n ¼ 2 RMPs, however, slightly modulated by other nonlinearly driven even harmonics. The divertor power flux during a ELM phase mitigated by RMPs is reduced almost by a factor of 10. The mechanism of ELM mitigation by RMPs proposed here reproduces generic features of high collisionality RMP experiments, where large ELMs are replaced by small, much more frequent ELMs or magnetic turbulence. Total ELM suppression was also demonstrated in modeling at higher RMP amplitude.

Progress in the definition of the requirements for edge localized mode (ELM) control and the application of ELM control methods both for high fusion performance DT operation and non-active low-current operation in ITER is described. Evaluation of the power fluxes for low plasma current H-modes in ITER shows that uncontrolled ELMs will not lead to damage to the tungsten (W) divertor target, unlike for high-current H-modes in which divertor damage by uncontrolled ELMs is expected. Despite the lack of divertor damage at lower currents, ELM control is found to be required in ITER under these conditions to prevent an excessive contamination of the plasma by W, which could eventually lead to an increased disruptivity. Modelling with the non-linear MHD code JOREK of the physics processes determining the flow of energy from the confined plasma onto the plasma-facing components during ELMs at the ITER scale shows that the relative contribution of conductive and convective losses is intrinsically linked to the magnitude of the ELM energy loss. Modelling of the triggering of ELMs by pellet injection for DIII-D and ITER has identified the minimum pellet size required to trigger ELMs and, from this, the required fuel throughput for the application of this technique to ITER is evaluated and shown to be compatible with the installed fuelling and tritium re-processing capabilities in ITER. The evaluation of the capabilities of the ELM control coil system in ITER for ELM suppression is carried out (in the vacuum approximation) and found to have a factor of ∼2 margin in terms of coil current to achieve its design criterion, although such a margin could be substantially reduced when plasma shielding effects are taken into account. The consequences for the spatial distribution of the power fluxes at the divertor of ELM control by three-dimensional (3D) fields are evaluated and found to lead to substantial toroidal asymmetries in zones of the divertor target away from the separatrix. Therefore, specifications for the rotation of the 3D perturbation applied for ELM control in order to avoid excessive localized erosion of the ITER divertor target are derived. It is shown that a rotation frequency in excess of 1 Hz for the whole toroidally asymmetric divertor power flux pattern is required (corresponding to n Hz frequency in the variation of currents in the coils, where n is the toroidal symmetry of the perturbation applied) in order to avoid unacceptable thermal cycling of the divertor target for the highest power fluxes and worst toroidal power flux asymmetries expected. The possible use of the in-vessel vertical stability coils for ELM control as a back-up to the main ELM control systems in ITER is described and the feasibility of its application to control ELMs in low plasma current H-modes, foreseen for initial ITER operation, is evaluated and found to be viable for plasma currents up to 5–10 MA depending on modelling assumptions.

First results from three-dimensional modeling of the divertor heat and particle flux pattern during application of resonant magnetic perturbation fields as ELM control scheme in ITER with the EMC3-Eirene fluid plasma and kinetic neutral transport code are discussed. The formation of a helical magnetic footprint breaks the toroidal symmetry of the heat and particle fluxes. Expansion of the flux pattern as far as 60 cm away from the unperturbed strike line is seen with vacuum RMP fields, resulting in a preferable heat flux spreading. Inclusion of plasma response reduces the radial extension of the heat and particle fluxes and results in a heat flux peaking closer to the unperturbed level. A strong reduction of the particle confinement is found. 3D flow channels are identified as a consistent reason due to direct parallel outflow from inside of the separatrix. Their radial inward expansion and hence the level of particle pump out is shown to be dependent on the perturbation level.

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...

19th International Conference on Plasma-Surface Interactions in Controlled Fusion Devices (PSI), Univ Calif, Gen Atom, San Diego, CA, MAY 24-28, 2010; International audience; Massive gas injection was used on Tore Supra to study disruption mitigation. The cooling time between the injection and the thermal quench drops to 2 ms for larger gas flow rates (similar to 5e24 atoms/s) limiting the radiated energy to similar to 10% of the plasma thermal energy content. A significant reduction of the heat load on the limiter is nevertheless observed in the mitigated cases. The broadening factor of the power decay length in the scrape-off layer during the thermal quench estimated around 10 (+/-5) does not change significantly between mitigated and unmitigated. Reached densities with He injections are sufficient to suppress primary runaway electrons (dominant on Tore Supra) but still far too low to avoid avalanche process (dominant in ITER). The extension of the current quench time, which is observed in mitigated disruptions (typically by 50%), could be an attractive feature to reduce the requirements on the density. (C) 2011 Elsevier B.V. All rights reserved.

The main results of the Tore Supra experimental programme in the years 2007–2008 are reported. They document significant progress achieved in the domain of steady-state tokamak research, as well as in more general issues relevant for ITER and for fusion physics research. Three areas are covered: ITER relevant technology developments and tests in a real machine environment, tokamak operational issues for high power and long pulses, and fusion plasma physics. Results presented in this paper include test and validation of a new, load-resilient concept of ion cycotron resonance heating antenna and of an inspection robot operated under ultra-high vacuum and high temperature conditions; an extensive experimental campaign (5 h of plasma) aiming at deuterium inventory and carbon migration studies; real-time control of sawteeth by electron cyclotron current drive in the presence of fast ion tails; ECRH-assisted plasma start-up studies; dimensionless scalings of transport and turbulence; transport experiments using active perturbation methods; resistive and fast-particle driven MHD studies. The potential role of Tore Supra in the worldwide fusion programme before the start of ITER operation is also discussed.

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.

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.

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.

Operating ITER in the reference inductive scenario at the design values of Ip = 15 MA and QDT = 10 requires the achievement of good H-mode confinement that relies on the presence of an edge transport barrier whose pedestal pressure height is key to plasma performance. Strong gradients occur at the edge in such conditions that can drive magnetohydrodynamic instabilities resulting in edge localized modes (ELMs), which produce a rapid energy loss from the pedestal region to the plasma facing components (PFC). Without appropriate control, the heat loads on PFCs during ELMs in ITER are expected to become significant for operation in H-mode at Ip = 6–9 MA; operation at higher plasma currents would result in a very reduced life time of the PFCs. Currently, several options are being considered for the achievement of the required level of ELM control in ITER; this includes operation in plasma regimes which naturally have no or very small ELMs, decreasing the ELM energy loss by increasing their frequency by a factor of up to 30 and avoidance of ELMs by actively controlling the edge with magnetic perturbations. Small/no ELM regimes obtained by influencing the edge stability (by plasma shaping, rotational shear control, etc) have shown in present experiments a significant reduction of the ELM heat fluxes compared to type-I ELMs. However, so far they have only been observed under a limited range of pedestal conditions depending on each specific device and their extrapolation to ITER remains uncertain. ELM control by increasing their frequency relies on the controlled triggering of the edge instability leading to the ELM. This has been presently demonstrated with the injection of pellets and with plasma vertical movements; pellets having provided the results more promising for application in ITER conditions. ELM avoidance/suppression takes advantage of the fact that relatively small changes in the pedestal plasma and magnetic field parameters seem to have a large stabilizing effect on large ELMs. Application of edge magnetic field perturbation with non-axisymmetric fields is found to affect transport at the plasma edge and thus prevent the uncontrolled rise of the plasma pressure gradients and the occurrence of type-I ELMs. This paper compiles a brief overview of various ELM control approaches, summarizes their present achievements and briefly discusses the open issues regarding their application in ITER.

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.

Non-linear reduced MHD modelling of the toroidally rotating plasma response to resonant magnetic perturbations (RMPs) is presented for DIII-D and ITER-like typical parameter and RMP coils. The non-linear cylindrical reduced MHD code was adapted to take into account toroidal rotation and plasma braking mechanisms such as resonant one (∼j × B) and the neoclassical toroidal viscosity (NTV) calculated for low collisionality regimes (‘1/ν’ and ‘ν’). Counter toroidal rotation by NTV is predicted for ITER with the proposed RMP coils in 1/ν-limit. Resonant braking is localized near resonant surfaces and is weak compared with NTV in the 1/ν regime for typical DIII-D and ITER parameters. Toroidal rotation leads to the effective screening of RMPs that is larger for stronger rotation and lower resistivity, resulting mainly in central islands screening. Non-resonant helical harmonics (q ≠ m/n) in RMP spectrum are not influenced by plasma rotation, and hence penetrate and are important in NTV mechanism.

The effects of orbit squeezing are important to neoclassical and anomalous transport fluxes in the region where plasma confinement is improved. This occurs in the edge region after the transition from the low confinement mode (L-mode) to the high confinement mode (H-mode) or in the vicinity of low-order rational surfaces. Neoclassical toroidal viscosity in tokamaks induced by the broken toroidal symmetry resulting from the activity of magnetohydrodynamic instabilities or error fields is calculated to include orbit squeezing effects. It is found that in the 1∕ν regime, the magnitude of the neoclassical toroidal viscosity is enhanced by a factor of ∣S∣3∕2, where ν is the collision frequency and S is the orbit squeezing factor; while in the ν regime, it is reduced by a factor of ∣S∣1∕2. A boundary layer analysis is performed to remove the singularity in the vicinity of the trapped-circulating boundary in the ν regime. As a result, the well-known ν regime is recovered. Orbit squeezing has little effect in the...

It is demonstrated that the pitch angle integrals in the transport fluxes in the ν regime calculated in K. C. Shang [Phys. Plasmas 10, 1443 (2003)] are divergent as the trapped-circulating boundary is approached. Here, ν is the collision frequency. The origin of this divergence results from the logarithmic dependence in the bounce averaged radial drift velocity. A collisional boundary layer analysis is developed to remove the singularity. The resultant pitch angle integrals now include not only the original physics of the ν regime but also the boundary layer physics. The transport fluxes, caused by the particles inside the boundary layer, scale as ν.

The response of an H-mode plasma to Resonant Magnetic Perturbations (RMPs) generated by so-called “I-coils” in DIII-D experiments on type I edge localized modes suppression is modelled using the nonlinear reduced magnetohydrodynamics (with zero-β, i.e. zero plasma temperature, in the version used here) code JOREK in X-point geometry. JOREK self-consistently advances in time the magnetic flux, vorticity, and plasma density in the presence of the RMPs. Without any toroidal rotation, the magnetic response from the plasma does not significantly modify the islands widths. A radial convective E×B plasma transport is observed to occur in the presence of the RMPs. The possibility that this mechanism could explain the enhanced density transport observed experimentally in DIII-D is discussed. Simulations with a rigid-body-like rotation at a fixed velocity shows evidence of a screening of the RMPs. The extension of our results to realistic parameters is discussed.