A critical issue for fusion plasma research is the erosion of the first wall of the experimental device due to impulsive heating from repetitive edge magneto-hydrodynamic (MHD) instabilities known as "edge-localized modes" (ELMs). Here, we show that the addition of small resonant magnetic field perturbations completely eliminates ELMs while maintaining a steady-state highconfinement (H-mode) plasma. These perturbations induce a chaotic behaviour in the magnetic field lines, which reduces the edge pressure gradient below the ELM instability threshold. The pressure gradient reduction results from a reduction in particle content of the plasma, rather than an increase in the electron thermal transport. This is inconsistent with the predictions of stochastic electron heat transport theory. These results provide a first experimental test of stochastic transport theory in a highly rotating, hot, collisionless plasma and demonstrate a promising solution to the critical issue of controlling edge instabilities in fusion plasma devices. Nature Physics. 3Maximizing the fusion power production in toroidally symmetric magnetic confinement devices (tokamaks 1,2 ) requires high-confinement (H-mode) plasma conditions that have high edge plasma pressures. A ubiquitous feature of these high edge pressure, steady state, H-mode tokamak plasmas is repetitive instabilities known as "edge-localized modes" (ELMs) which release a significant fraction of the thermal energy of the plasma to the first wall of the device.These instabilities are a class of ideal magneto-hydrodynamic (MHD) modes produced in a high pressure gradient region at the plasma edge (called the "pedestal") where pressure gradient driven "ballooning" modes can couple to current density driven "peeling" modes 3 . While ELMs provide a natural transport process that controls the core plasma density and edge impurity ion penetration, they also represent a significant concern for burning plasma devices such as the ! n e ped ) to achieve significant fusion power gain factors, Q ≥ 10, they must operate below ! " e * = 0.1. In this case each ELM is expected to expel up to 20% of the pedestal energy over a time interval of a few hundred µs. If allowed to reach plasma-facing wall components, energy impulses of this magnitude will cause increased erosion of plasma facing components and significantly reduce their lifetime 5,6 . Thus, controlling ELMs by replacing the energy impulses with an equivalent but more continuous transport process is a high priority issue for tokamak fusion research.A particularly appealing ELM control approach in low the RMP field causes a larger change in the edge particle balance (i.e., changes in the balance between outward particle transport and edge particle sources and sinks) rather than in the thermal transport across the pedestal is both surprising and theoretically challenging.As in previous high is satisfied, these small ELMs disappear, leaving the plasma in a very quiet state (Fig. 3a), and the pedestal density ! n e ped begins to fall w...

Large Type-I Edge Localized Modes (ELMs) are completely eliminated with small n = 3 resonant magnetic perturbations (RMP) in low average triangularity, " = 0.26, plasmas and in ITER Similar Shaped (ISS) plasmas, " = 0.53, with ITER relevant collisionalities v e " # 0.2. Significant differences in the RMP requirements and in the properties of the ELM suppressed plasmas are found when comparing the two triangularities. In ISS plasmas, the current required to suppress ELMs is approximately 25% higher than in low average triangularity plasmas. It is also found that the width of the resonant q 95 window required for ELM suppression is smaller in ISS plasmas than in low average triangularity plasmas. An analysis of the positions and widths of resonant magnetic islands across the pedestal region, in the absence of resonant field screening or a self-consistent plasma response, indicates that differences in the shape of the q profile may explain the need for higher RMP coil currents during ELM suppression in ISS plasmas. Changes in the pedestal profiles are compared for each plasma shape as well as with changes in the injected neutral beam power and the RMP amplitude. Implications of these results are discussed in terms of requirements for optimal ELM control coil designs and for establishing the physics basis needed in order to scale this approach to future burning plasma devices such as ITER.

Recent DIII-D [J. L. Luxon et al., Nucl. Fusion 43, 1813 (2003)] experiments show a correlation between the extent of overlap of magnetic islands induced in the edge plasma by perturbation coils and complete suppression of Type-I edge localized modes (ELMs) in plasmas with ITER-like electron pedestal collisionality νe*∼0.1, flux surface shape and low edge safety factor (q95≈3.6). With fixed amplitude n=3 resonant magnetic perturbation (RMP), ELM suppression is obtained only in a finite window in the edge safety factor (q95) consistent with maximizing the resonant component of the applied helical field. ELM suppression is obtained over an increasing range of q95 by either increasing the n=3 RMP strength, or by adding n=1 perturbations to “fill in” gaps between islands across the edge plasma. The suppression of Type-I ELMs correlates with a minimum width of the edge region having magnetic islands with Chirikov parameter >1.0, based on vacuum calculations of RMP mode components excluding the plasma response or rotational shielding. The fraction of vacuum magnetic field lines that are lost from the plasma, with connection length to the divertor targets comparable to an electron-ion collisional mean free path, increases throughout the island overlap region in the ELM suppressed case compared with the ELMing case.

Effects of linear plasma response currents on non-axisymmetric magnetic field perturbations from the I-coil used for Edge Localized Mode mitigation in DIII-D tokamak are analyzed with the help of a kinetic plasma response model developed for cylindrical geometry. It is shown that these currents eliminate the ergodization of the magnetic field in the core plasma and reduce the size of the ergodic layer at the edge. A simple balance model is proposed which qualitatively reproduces the evolution of the plasma parameters in the pedestal region with the onset of the perturbation.It is suggested that the experimentally observed density pump-out effect in the long mean free path regime is the result of a combined action of ion orbit losses and magnetic field ergodization at the edge.

Abstract. In this paper the manipulation of power deposition on divertor targets at DIII-D by application of resonant magnetic perturbations (RMPs) for suppression of large Type-I edge localized modes (ELMs) is analysed. We discuss the modification of the ELM characteristics by the RMP applied. It is shown, that the width of the deposition pattern in ELMy H-mode depends linearly on the ELM deposited energy, whereas in the RMP phase of the discharge those patterns are controlled by the externally induced magnetic perturbation. It was also found that the manipulation of heat transport due to application of small, edge resonant magnetic perturbations (RMP) depends on the plasma pedestal electron collisionality . We compare in this analysis RMP and no RMP phases with and without complete ELM suppression. At high , the heat flux during the ELM suppressed phase is of the same order as the inter-ELM and the no-RMP phase. However, below this collisionality value, a slight increase of the total power flux to the divertor is observed during the RMP phase. This is most likely caused by a more negative potential at the divertor surface due to hot electrons reaching the divertor surface from the pedestal area along perturbed, open field lines and/or the density pump out effect.

Abstract. A study of three-dimensional perturbed magnetic field structures and transport for edge localized mode control experiments with resonant magnetic perturbations at DIII-D is presented. We focus on ITER-Similar Shape plasmas at ITER relevant electron pedestal collisionalities ν * e ∼ 0.2. This study is performed in comparison to results from TEXTOR-Dynamic Ergodic Divertor circular limiter plasmas. For both experiments the magnetic field structure is analyzed in the vacuum paradigm -superimposing the external RMP field on the unperturbed equilibrium. At TEXTOR this description holds for normalized poloidal flux Ψ N > 0.7 without tearing modes driven by the RMP field. For DIII-D H-mode plasmas the validity of this approach still needs to be established. In this paper a method is discussed to diagnose the degree of edge stochastization based on a comparison between modeled magnetic footprints on the divertor targets and experimental data. Clear evidence is presented for the existence of a generic separatrix perturbation causing striation of target particle fluxes. However, heat fluxes into these striations are small. This observation can be explained by accounting for the different heat and particle source locations and the 3D trajectories of the open, perturbed field lines towards the divertor target. Analysis of the transport characteristics filling the perturbed separatrix lobes based on initial EM C3/EIREN E modeling suggests the existence of open field lines connecting the stochastic edge to the target pattern. However, the width and inward most extent of the stochastic layer can not yet be quantified.

Small edge resonant magnetic perturbations are used to control the pedestal transport and stability in low electron collisionality ( e * ), ITER relevant, poloidally diverted plasmas. The applied perturbations reduce the height of the density pedestal and increase its width while increasing the height of the electron pedestal temperature and its gradient.The effect of the perturbations on the pedestal gradients is controlled by the current in the perturbation coil, the poloidal mode spectrum of the coil, the neutral beam heating power and the divertor deuterium fueling rate. Large pedestal instabilities, referred to as edge as an array of higher frequency electromagnetic waves and turbulence [7]. Outside the plasma, sources such as field-errors from asymmetries in toroidal and poloidal magnetic field coils, magnetic materials, vacuum vessel image and return currents [8], external control coils used to stabilize plasma modes, and correction coils [9] used to minimize perturbations from known field-errors on low integer rational surfaces all contribute to the structure of the magnetic field in which the plasma resides. At the edge of the plasma where the safety factor [ q ( ) defined as the rate of change in toroidal magnetic flux with poloidal magnetic flux ] increases rapidly, all of these perturbations contribute to the creation of closely spaced resonant magnetic islands which may result in the formation of edge stochastic layers. In a poloidally diverted tokamak, the high magnetic shear q across the edge of the plasma results in an increased density of island states and a significantly higher probability of forming open stochastic layers that connect magnetic field lines to plasma facing material surfaces [10]. Thus, the edge plasma is immersed in a dynamically complex magnetic topology over the same region where substantial radial flows of mass and energy, driven by large gradients, compete with strong turbulent transport in highly sheared toroidal and poloidal plasma flow fields. Large radial gradients in the plasma pressure are often established by a strong reduction in turbulent 4 transport due to sheared plasma flow. The large edge gradients are a key factor in the establishment of good confinement levels that make the tokamak the leading candidate for fusion reactors. However, they also lead to the instabilities known as ELMs which drive impulsive energy losses that can be detrimental to plasma facing surfaces. It is easy to understand why the development of tools to control the pedestal transport and stability is a compelling issue for improving the performance and operational safety of high energy density tokamak based fusion confinement systems.A strong motivation for understanding the physics of edge stochastic layers is to enable the development of predictable and reliable tools for controlling key fusion plasma pedestal processes such as: the plasma temperature and pressure at the top of the pedestal, the size and frequency of ELMs, the energy and particle exhaust rate in steady-state cond...

A kinetic transport simulation for the first 4 ms of the vacuum resonant magnetic perturbations (RMPs) application has been performed for the first time in realistic diveted DIII-D tokamak geometry [J. Luxon, Nucl. Fusion 42, 614 (2002)], with the self-consistent evaluation of the radial electric field and the plasma rotation. It is found that, due to the kinetic effects, the stochastic parallel thermal transport is significantly reduced when compared to the standard analytic model