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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.

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.

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.

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...

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 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.