Model for screening of resonant magnetic perturbations by plasma in a realistic tokamak geometry and its impact on divertor strike points
Pavel Cahyna, Eric Nardon
备注：
Accepted in the Proceedings of the 19th International Conference on Plasma Surface Interactions, to be published in Journal of Nuclear Materials. Version 2: minor formatting and text improvements, more results mentioned in the conclusion and abstract
This work addresses the question of the relation between strike-point splitting and magnetic stochasticity at the edge of a poloidally diverted tokamak in the presence of externally imposed magnetic perturbations. More specifically, ad-hoc helical current sheets are introduced in order to mimic a hypothetical screening of the external resonant magnetic perturbations by the plasma. These current sheets, which suppress magnetic islands, are found to reduce the amount of splitting expected at the target, which suggests that screening effects should be observable experimentally. Multiple screening current sheets reinforce each other, i.e. less current relative to the case of only one current sheet is required to screen the perturbation.
General formula describing both the divertor strike point splitting and width of magnetic islands created by resonant magnetic perturbations (RMPs) in a poloidally diverted tokamak equilibrium is derived. Under the assumption that the RMP is produced by coils at the low-field side such as those used to control edge localized modes (ELMs) it is demonstrated that the width of islands on different magnetic surfaces at the edge and the amount of divertor splitting are related to each other. Explanation is provided of aligned maxima of the perturbation spectra with the safety factor profile - an ef…
Nitrogen seeded detachment has been achieved in the Tokamak a Configuration Variable (TCV) in advanced divertor configurations (ADCs), namely X-divertor and X-point target, with and without baffles in H-mode plasmas with high core confinement. Both ADCs show a remarkable reduction in the inter-ELM particle and heat fluxes to the target compared to the standard divertor configuration. 95-98% of the peak heat flux to the target is mitigated as a synergetic effect of ADCs, baffling, and nitrogen seeded detachment. The effect of divertor geometry and baffles on core-divertor compatibility is inves…
The survivability of dust being transported in the magnetized sheath near the divertor plate of a tokamak and its impact on the desired balance of erosion and redeposition for a steady-state reactor are investigated. Two different divertor scenarios are considered. The first is characterized by an energy flux perpendicular to the plate $q_0\simeq 1$ MW/m$^2$ typical of current short-pulse tokamaks. The second has $q_0\simeq 10$ MW/m$^2$ and is relevant to long-pulse machines like ITER or DEMO. It is shown that micrometer dust particles can survive rather easily near the plates of a divertor pl…
The characteristics of wall recycling with different divertor configurations were investigated in this study, focusing on the observations of the spatial distributions of deuterium atomic emissions in the Balmer series (D_α, D_β, D_γ, and D_δ) with different magnetic field configurations in the Experimental Advanced Superconducting Tokamak. The observed D_α and D_β emissions were primarily relatively close to the divertor targets, while the D_γ and D_δ emissions were primarily relatively close to the X-point. The distributions of the emissions close to the divertor targets and X-point changed …
Intermittent positive bursts of plasma density detected by Langmuir probes at the edge of the TEXTOR tokamak are investigated. Burst statistical properties and temporal characteristics together with their radial dependence are studied in two different regimes - with electrode biasing and dynamic ergodic divertor (DED). Similar modification of intermittent burst characteristics are observed. Namely, the average burst rate increases and the average burst duration decreases compared to Ohmic conditions. Statistical properties are also modified in the same way in both regimes. The reason is that b…
In-situ, two-dimensional (2D) Langmuir probe measurements across a large part of the TCV divertor are reported in L-mode discharges with and without divertor baffles. This provides detailed insights into time averaged profiles, particle fluxes, and fluctuations behavior in different divertor regimes. The presence of the baffles is shown to substantially increase the divertor neutral pressure for a given upstream density and to facilitate the access to detachment, an effect that increases with plasma current. The detailed, 2D probe measurements allow for a divertor particle balance, including i…
The XGC1 edge gyrokinetic code is used for a high fidelity prediction for the width of the heat-flux to divertor plates in attached plasma condition. The simulation results are validated against the empirical scaling $λ_q \propto B_P^{-γ}$ obtained from present tokamak devices, where $λ_q$ is the divertor heat-flux width mapped to the outboard midplane and $γ_q=1.19$ as defined by T. Eich et al. [Nucl. Fusion 53 (2013) 093031], and $B_P$ is the magnitude of the poloidal magnetic field at outboard midplane separatrix surface. This empirical scaling predicts $λ_q \leq 1mm$ when extrapolated to I…
Edge localised modes (ELMs) are a concern for future devices as they can limit the operational lifetime of the divertor. The mitigation of ELMs can be performed by the application of resonant magnetic perturbations (RMPs) which act to degrade the pressure gradient in the edge of the plasma. Investigations of the effect of RMPs on MAST have been performed in a range of plasmas using perturbations with toroidal mode numbers of n=3, 4 and 6. It has been seen that the RMPs increase the ELM frequency, which gives rise to a corresponding decrease in the ELM energy. The reduced ELM energy decreases t…
The guiding-center kinetic neoclassical transport code, XGC0, [C.S. Chang et. al, Phys. Plasmas 11, 2649 (2004)] is used to compute the heat fluxes and the heat-load width in the outer divertor plates of Alcator C-Mod and DIII-D tokamaks. The dependence of the width of heat-load fluxes on neoclassical effects, neutral collisions and anomalous transport is investigated using the XGC0 code. The XGC0 code includes realistic X-point geometry, a neutral source model, the effects of collisions, and a diffusion model for anomalous transport. It is observed that width of the XGC0 neoclassical heat-loa…
Following the analysis on linear spectra of shear Alfvén fluctuations excited by energetic particles (EPs) in the Divertor Tokamak Test (DTT) facility plasmas [T. Wang et al., Phys. Plasmas 25, 062509 (2018)], in this work, nonlinear dynamics of the corresponding mode saturation and the fluctuation induced EP transport is studied by hybrid magnetohydrodynamic-gyrokinetic simulations. For the reversed shear Alfvén eigenmode driven by magnetically trapped EP precession resonance in the central core region of DTT plasmas, the saturation is mainly due to radial decoupling of resonant trapped EPs. …
We analyze a Hamiltonian model with five wire loops that delineates the magnetic surfaces of the tokamak ITER, including a similar safety factor profile and the X-point related to the presence of a poloidal divertor. Non-axisymmetric magnetic perturbations are added by external coils, similar to the correction coils installed at the tokamak DIII-D and those that will be installed at ITER. To show the influence of magnetic perturbations on the field line escape, we integrate numerically the field line differential equations and obtain the footprints and deposition patterns on the divertor plate…
Nowadays, divertors are used in the main tokamaks to control the magnetic field and to improve the plasma confinement. In this article, we present analytical symplectic maps describing Poincaré maps of the magnetic field lines in confined plasmas with a single null poloidal divertor. Initially, we present a divertor map and the tokamap for a diverted configuration. We also introduce the Ullmann map for a diverted plasma, whose control parameters are determined from tokamak experiments. Finally, an explicit, area-preserving and integrable magnetic field line map for a single-null divertor tokam…
A free-boundary Tokamak Equilibrium Solver (TES), developed for advanced study of tokamak equilibra, is described with two distinctive features. One is a generalized method to resolve the intrinsic axisymmetric instability, which is encountered after all in equilibrium calculation with a free-boundary condition. The other is an extension to deal with a new divertor geometry such as snowflake or X divertors. For validations, the uniqueness of a solution is confirmed by the independence on variations of computational domain, the mathematical correctness and accuracy of equilibrium profiles are c…
Reduction of the peak heat loads on the plasma facing components is essential for the success of the next generation of high fusion power tokamaks such as the International Thermonuclear Experimental Reactor (ITER) 1 . Many present concepts for accomplishing this involve the use of atomic processes to transfer the heat from the plasma to the main chamber and divertor chamber walls and much of the experimental and theoretical physics research in the fusion program is directed toward this issue. The results of these experiments and calculations are the result of a complex interplay of many proce…
Divertor strike point splitting induced by resonant magnetic perturbations (RMPs) has been observed on MAST for a variety of RMP configurations in a plasma scenario with Ip=750kA where those configurations all have similar resonant components. Complementary measurements have been obtained with divertor Langmuir probes and an infrared camera. Clear splitting consistently appears in this scenario only in the even configuration of the perturbation coils, similarly to the density pump-out. These results present a challenge for models of plasma response to RMPs.
We present simulated figures of the diverted magnetic field lines of the tokamak ITER, obtained by numerically integrating a Hamiltonian model with electrical currents in five wire loops and control coils. We show evidences of a sticky island embedded in the chaotic region near the divertor plates, which traps magnetic field lines for many toroidal turns increasing their connection lengths to these plates.
In some conditions, I-mode plasmas can feature pedestal relaxation events (PREs) that transiently enhance the energy reaching the divertor target plates. To shed light into their appearance, characteristics and energy reaching the divertor targets, a comparative study between two tokamaks $-$ Alcator C-Mod and ASDEX Upgrade $-$ is carried out. It is found that PREs appear only in a subset of I-mode discharges, mainly when the plasma is close to the H-mode transition. Also, the nature of the triggering instability is discussed by comparing measurements close to the separatrix in both devices. T…
Advanced divertors are magnetic geometries where a second X-point is added in the divertor region to address the serious challenges of burning plasma power exhaust. Invoking physical arguments, numerical work, and detailed model magnetic field analysis, we investigate the magnetic field structure of advanced divertors in the physically relevant region for power exhaust - the Scrape-Off Layer (SOL). A primary result of our analysis is the emergence of a physical "metric", the Divertor Index DI, that quantifies the flux expansion increase as one goes from the main X-point to the strike point. It…
The formation of the radial electric field, $E_{\rm r}$ in the SOL has been experimentally studied for attached divertor conditions in stellarator W7-X. The main objective of this study is to test the validity in a complex 3D island divertor of simple models, typically developed in tokamaks, relating $E_{\rm r}$ to the sheath potential drop gradient at the target. Additionally, we investigate the effect of the edge $E_{\rm r}$ shear on the reduction of density fluctuation amplitude, a well-established phenomenon according to the existing bibliography. The main diagnostic for measurements in th…
High flux expansion divertor studies have been carried out in the National Spherical Torus Experiment using steady-state X-point height variations from 22 to 5-6 cm. Small-ELM H-mode confinement was maintained at all X-point heights. Divertor flux expansions from 6 to 26-28 were obtained, with associated reduction in X-point connection length from 5-6 m to 2 m. Peak divertor heat flux was reduced from 7-8 MW/m$^2$ to 1-2 MW/m$^2$. In low X-point configuration, outer strike point became nearly detached. Among factors affecting deposition of parallel heat flux in the divertor, the flux expansion…
Power exhaust is one of the major challenges for a future fusion device. Applying a non-axisymmetric external magnetic perturbation is one technique that is studied in order to mitigate or suppress large edge localized modes which accompany the high confinement regime in tokamaks. The external magnetic perturbation brakes the axisymmetry of a tokamak and leads to a 2D heat flux pattern on the divertor target. The 2D heat flux pattern at the outer divertor target is studied on ASDEX Upgrade in stationary L-Mode discharges. The amplitude of the 2D characteristic of the heat flux depends on the a…
Shaping of magnetic flux surfaces is found to have a strong impact on turbulence and transport in tokamak edge plasmas. A series of axisymmetric equilibria with varying elongation and triangularity, and a divertor configuration are implemented into a computational gyrofluid turbulence model. The mechanisms of shaping effects on turbulence and flows are identified. Transport is mainly reduced by local magnetic shearing and an enhancement of zonal shear flows induced by elongation and X-point shaping.
Non-resonant stellarator divertors have magnetic flux tubes, called magnetic turnstiles, that cross cantori, which are fractal remnants of destroyed invariant tori with holes, that lie outside the outermost confining surface. The exiting and entering flux tubes can be adjacent as is generally expected but can also have the unexpected feature of entering or exiting at separate locations of the cantori. Not only can there be two types of turnstiles, but pseudo turnstiles can also exist. A pseudo turnstile is formed when a cantorus has a sufficiently large, although limited, radial excursion to s…
Non-axisymmetric stationary magnetic perturbations lead to the formation of homoclinic tangles near the divertor magnetic saddle in tokamak discharges. These tangles intersect the divertor plates in static helical structures that delimit the regions reached by open magnetic field lines reaching the plasma column and leading the charged particles to the strike surfaces by parallel transport. In this article we introduce a non-axisymmetric rotating magnetic perturbation to model the time development of the three-dimensional magnetic field of a single-null DIII-D tokamak discharge developing a ro…
The SMARDDA software library is used to model plasma interaction with complex engineered surfaces. A simple flux-tube model of power deposition necessitates the following of magnetic fieldlines until they meet geometry taken from a CAD (Computer Aided Design) database. Application is made to 1) models of ITER tokamak limiter geometry and 2) MASTU tokamak divertor designs, illustrating the accuracy and effectiveness of SMARDDA, even in the presence of significant nonaxisymmetric ripple field. SMARDDA's ability to exchange data with CAD databases and its speed of execution also give it the poten…
Edge localised modes (ELMs) are a concern for future devices, such as ITER, due to the large transient heat loads they generate on the divertor surfaces which could limit the operational time of the device. This paper discusses the application of resonant magnetic perturbations (RMPs) as a mechanism for ELM control on MAST. Experiments have been performed using an n=3 toroidal mode number perturbation and measurements of the strike point splitting performed. The measurements have been made using both infrared and visible imaging to measure the heat and particle flux to the divertor. The measur…
Tokamak plasmas are confined by a magnetic field that limits the particle and heat transport perpendicular to the field. Parallel to the field the ionised particles can move freely, so to obtain confinement the field lines are "closed" (ie. form closed surfaces of constant poloidal flux) in the core of a tokamak. Towards, the edge, however, the field lines begin to intersect physical surfaces, leading to interaction between neutral and ionised particles, and the potential melting of the material surface. Simulation of this interaction is important for predicting the performance and lifetime of…
High-power TCV scenario for conventional and alternative divertor studies
Max Planck Institute for Plasma Physics（马克斯·普朗克等离子体物理研究所）；Eindhoven University of Technology（埃因霍温理工大学）；DIFFER - Dutch Institute for Fundamental Energy Research（荷兰基础能源研究院）
First divertor exposure experiments of a renewable boron pebble aggregate in DIII-D
University of California San Diego（加州大学圣迭戈分校）；Thea Energy, Inc.（Thea能源公司）；University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）；Sandia National Laboratories（桑迪亚国家实验室）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Oak Ridge National Laboratory（橡树岭国家实验室）；General Atomics（通用原子能公司）；Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）；Aalto University（阿尔托大学）
Understanding and predicting divertor heat-load width $λ_q$ is a critically important problem for an easier and more robust operation of ITER with high fusion gain. Previous predictive simulation data for $λ_q$ using the extreme-scale edge gyrokinetic code XGC1 in the electrostatic limit under attached divertor plasma conditions in three major US tokamaks [C.S. Chang et al., Nucl. Fusion 57, 116023 (2017)] reproduced the Eich and Goldston attached-divertor formula results [formula #14 in T. Eich et al., Nucl. Fusion 53, 093031 (2013); R.J. Goldston, Nucl. Fusion 52, 013009 (2012)], and further…
It is found that the X-Divertor (XD) configuration [1-3] can be made with the conventional PF coil set on ITER[4], where all PF coils are outside the TF coils. Desirable configurations are possible where the PF currents are below the present maximum design limits on ITER, and where the baseline divertor cassette is used. It is possible that the XD could be used to assist in high-power operation on ITER, but some further issues need examination. Note that the increased major radius of the Super X-Divertor (SXD) [5-8] is not a feature of the XD geometry. In addition, we present an XD configurati…
The application of resonant magnetic perturbations (RMPs) produces splitting of the divertor strike point due to the interaction of the RMP field and the plasma field. The application of a rotating RMP field causes the strike point splitting to rotate, distributing the particle and heat flux evenly over the divertor. The RMP coils in MAST have been used to generate a rotating perturbation with a toroidal mode number n=3. The ELM frequency is doubled with the application of the RMP rotating field, whilst maintaining the H mode. During mitigation, the ELM peak heat flux is seen to be reduced by …
Spacecraft heat shield study in the DIII-D tokamak
University of California San Diego（加州大学圣迭戈分校）；Auburn University（奥本大学）；General Atomics（通用原子能公司）；Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）；Baylor University（贝勒大学）；University of Stuttgart（斯图加特大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
An analytical model previously developed to study the structure of the magnetic field for the TEXTOR-DED [S.S. Abdullaev et al. Phys. Plasmas, 6, 153 (1999)] is applied to the similar study of the Ergodic Divertor of Tore Supra tokamak [Ph. Ghendrih, Plasma Phys. Control. Fusion, 38, 1653 (1996)]. The coil configuration of ED Tore Supra consists of six modules equidistantly located along the toroidal direction on the low-field-side of the torus with given toroidal and poloidal extensions. The Hamiltonian formulation of field line equations in straight-field-line coordinates (Boozer coordinates…
The present paper deals with the surface heat flux estimation with thermocouples (TC) and fiber Bragg grating (FBG) embedded in the plasma facing components (PFC) of the WEST tokamak. A 2D heat transfer model combined with the conjugate gradient method (CGM) and the adjoint state is used to estimate the plasma heat flux deposited on the PFC. The plasma heat flux is characterized by the time evolution of its amplitude and spatial shape on the target (heat flux decay length $λ^t_q$, power spreading in the private flux region $S^t$ and the strike point location $x_0$). As a first step, five ohmic…
