Toroidal Direction Research Articles

The interaction of the ITER first wall with magnetic perturbations

Mitigation of the multiple risks associated with disruptions and runaway electrons in tokamaks involves competing demands. Success requires that each risk be understood sufficiently that appropriate compromises can be made. Here the focus is on the interaction of short timescale magnetic-perturbations with the structure in ITER that is closest to the plasma, blanket modules covered by separated beryllium tiles. The effect of this tiled surface on the perturbations and on the forces on structures is subtle. Indeterminacy can be introduced by tile-to-tile shorting. A determinate subtlety is introduced because electrically separated tiles can act as a conducting surface for magnetic perturbations that have a normal component to the surface. A practical method for including this determinate subtlety into plasma simulations is developed. The shorter the timescales and the greater the localization, particularly in the toroidal direction, the more important the magnetic effects of the tiles become.

Design of stabilizing plate of JT-60SA

The stabilizing plate (SP) of JT-60SA has been designed based on an electromagnetic and a structural analysis. The SP plays a role of both a passive stabilizer of magnetohydrodynamics (MHD) instability and a first wall at low field side in combination with a graphite tile. The SP has a double skin structure with 10 mm thickness each in order to have simultaneously high resistivity in the toroidal direction and high strength against plasma disruption as well as a seismic event. A finite element method for the calculation of the electromagnetic force induced by disruption and the structural analysis has been applied. The most serious event which is fast major disruption, is mainly considered. The eddy current reaches up to 100 MA/m2, which induces electromagnetic force < 120 MN/m3. The SP has been modified in order to satisfy the allowable membrane, bend and peak stress of SS316 L. Trial manufacture of a part of the SP has been done to investigate the effect of the weld on the deformation of the SP resulting from the contraction of the weld metal. The arrangement of heat sinks and coolant pipes, and graphite tiles has also been done, taking into account the long pulse operation of the JT-60SA plasma.

Continuum gyrokinetic simulations of edge plasmas in single-null geometries

The first continuum gyrokinetic calculations of electrostatic ion scale turbulence are presented for the case of a diverted tokamak geometry. The simulation model solves the long-wavelength limit of the full-F gyrokinetic equation for ion species coupled to the quasi-neutrality equation for electrostatic potential variations, where a fluid model is used for an electron response. In order to facilitate simulations of highly-anisotropic microturbulence in the presence of strong magnetic shear and a magnetic X-point, a numerical algorithm utilizing a locally field-aligned multiblock coordinate system has been developed and implemented in the 5D finite-volume code COGENT. In this approach, the toroidal direction is divided into blocks, such that within each block, the cells are field-aligned and a non-matching grid interface is allowed at block boundaries. The toroidal angle corresponds to the “coarse” field-aligned coordinate, whereas the poloidal cross section, comprised of the radial and poloidal directions, is finely gridded to resolve short-scale perpendicular turbulence structures and to support accurate re-mapping (interpolation) at block boundaries. The 5D simulations explore cross-separatrix ion scale turbulence in the presence of a self-consistent radial electric field and address the effects of magnetic-shear stabilization in the X-point region.

Absolute calibration of the Lyman-α measurement apparatus at DIII-D.

The LLAMA (Lyman-Alpha Measurement Apparatus) diagnostic was recently installed on the DIII-D tokamak [Rosenthal et al., Rev. Sci. Instrum. (submitted) (2020)]. LLAMA is a pinhole camera system with a narrow band Bragg mirror, a bandpass interference filter, and an absolute extreme ultraviolet photodiode detector array, which measures the Ly-α brightness in the toroidal direction on the inboard, high field side (HFS) and outboard, low field side (LFS). This contribution presents a setup and a procedure for an absolute calibration near the Ly-α line at 121.6nm. The LLAMA in-vacuum components are designed as a compact, transferable setup that can be mounted in an ex situ vacuum enclosure that is equipped with an absolutely calibrated Ly-α source. The spectral purity and stability of the Ly-α source are characterized using a vacuum ultraviolet spectrometer, while the Ly-α source brightness is measured by a NIST-calibrated photodiode. The non-uniform nature of the Ly-α source emission was overcome by performing a calibration procedure that scans the Ly-α source position and employs a numerical optimization to determine the emission pattern. Nominal and measured calibration factors are determined and compared, showing agreement within their uncertainties. A first conversion of the measured signal obtained from DIII-D indicates that the Ly-α brightness on the HFS and LFS is on the order of 1020 Ph sr-1m-2s-1. The established calibration setup and procedure will be regularly used to re-calibrate the LLAMA during DIII-D vents to monitor possible degradation of optical components and detectors.

Simulation of the loss of passing fast ions induced by magnetic islands in EAST tokamak plasmas

The loss of beam ions due to magnetic islands is investigated in a tokamak. The perturbed guiding-center drifts of passing particles including the effect of the finite orbit width are demonstrated. The widths of the drift islands under resonant conditions are studied theoretically and numerically. The ORBIT code is used to simulate the action of the neoclassical tearing mode with a toroidal mode number n = 1 and poloidal mode number m = 2 on passing fast ions generated by neutral beam injection in the Experimental Advanced Superconducting Tokamak. Two loss channels for passing fast ions are identified as the resonant interaction and the stochastic interaction. The lost fast ions in the loss detector zone (LDZ) to simulate the fast-ion loss detector assemble around two regions in phase space, namely, (i) a pitch angle of θ = 28° both with and without the mode and (ii) θ = 59° when the mode amplitude is large enough, where θ=arccosv∥/v. The number of these lost ions in the LDZ evolves in the period of the mode. The fraction of the total lost ions evolves in the period of the n = 1 oscillation in the toroidal direction. The fraction of lost beam ions has a linear relationship with the mode amplitude in first 10 µs and a quadratic one thereafter. The corresponding characteristics of the lost beam ions in phase space are also discussed.

Computational studies on fast wave current drive in high beta SST-1 and SST-2 plasmas

The non-inductive current drive in low toroidal beta (β) steady-state superconducting tokamak-1 (SST-1) is obtained using slow waves or Lower Hybrid waves (LHW). If β of the plasma is increased either by increasing the plasma parameters (density/temperature) or by decreasing the toroidal magnetic field, the non-inductive current drive may be supported by Fast Waves (FWs), as wave accessibility is limited for slow waves at these high β plasmas. Non-inductive current drive using FWs is explored for these high β plasmas to identify the optimized parameters (operating frequency and parallel refractive index (n||)) of the fast wave. The studies indicate that FWs may be launched with an operating frequency of 0.5 GHz RF source and n|| around 4 in SST-1 plasma. The GENRAY code is employed to carry out detailed studies on Fast Wave Current Drive (FWCD) analysis using ray tracing techniques. Computational studies on FWCD are carried out where central electron density (ne0) and central electron temperature (Te0) of 6×1019m−3 and 3 keV respectively is assumed. The FWCD displays central depositions of RF power and is attributed to fast radial propagation compared to the parallel propagation along the toroidal magnetic field, resulting in ray transits with large number of reflections. The off-axis current drive in SST-1 plasma requires reduced radial penetration of the wave and demands unrealistic plasma parameter in terms of β. However, for SST-2 plasmas, having enhanced plasma parameters (βN∼1.8), it is found that if FWs are launched with n||∼3 and f∼1.5 GHz, the radial penetration of the wave is impeded and single pass absorption in toroidal direction is observed, thus providing conducive condition for off axis current drive. It indicates that FWs would drive plasma current of 11 kA/MW at ρ∼0.7 for ne0∼2.2×1020m−3 and Te0∼7.7 keV values.

Experimental observation of heat flux mitigation during divertor detachment in the DIII-D small angle slot divertor

Abstract Employing an array of surface eroding thermocouples (SETCs), the heat flux measured at the outer strike point of the DIII-D Small Angle Slot (SAS) divertor was found to be reduced by ~50% when the plasma reached the detachment regime compared to the attached state. Reduction in heat flux of similar magnitude has been found in both toroidal field directions (obtained by ramping up the plasma density) but with different characteristics: With the ion B × ∇B drift direction toward the SAS divertor, the heat flux measured by the SETCs first increased as plasma density increased, which may due to reduction in energy losses in the upstream and hence increase in the power flow into the divertor, and then began to roll over concurrent with a reduction in ion saturation current density on nearby Langmuir probes. In contrast, with the ion B × ∇B drift directed away from the SAS, the heat flux began at a higher value but decreases monotonically with increasing plasma density. This leads to lower heat flux in this BT direction at up to 20% lower line-averaged density. These significant differences in the onset of detachment in opposing BT directions are believed to be largely determined by the impacts of E × B drifts. Because ITER’s divertor must be operated with some degree of plasma detachment to radiate most of the power arriving in the scrape-off-layer, it is crucial to further understand the impact of magnetic drifts on plasma detachment behavior in a tight divertor geometry.

Extended Solov'ev type equilibria for rotating plasmas with positive and negative triangularity

The Solov'ev ansatz is employed to solve the equilibrium equation for plasmas rotating in the toroidal direction. The plasma shape can be controlled by fixing the values of the aspect ratio, elongation, triangularity, and curvature at the equatorial points. In addition, it is possible to set the values of the plasma current, total β, and Mach number. Analytic expressions for the shape coefficients and examples of equilibria with positive and negative triangularity are presented.

Statistical characteristics of the SOL turbulence in the first divertor plasma operation of W7-X using a reciprocating probe

The statistical characteristics of the scrape-off layer (SOL) turbulence have been investigated in the first divertor plasma operation of W7-X using a reciprocating probe. The turbulence spectra, auto-correlation time and the statistical parameters are analyzed in three magnetic configurations. In standard and high mirror configurations, the SOL turbulence can be classified into four patterns from the outer SOL to the inner SOL, and each pattern is characterized by the poloidal cross correlation spectrum and the turbulence propagation property. A strong dependence of the SOL turbulence on the magnetic topology is demonstrated experimentally. In high iota configuration, the SOL island is relatively narrow and consequently the fluctuation level of turbulence is weak in the far SOL but enhanced significantly in the near SOL. In the reversed field case, the SOL turbulence reveals similar propagation properties and statistical parameters with those in the normal field case, demonstrating the same turbulence structure in both toroidal field directions.

Reactance Regulation Using Coils with Perpendicular Magnetic Field in the Tubular Core design

This article presents an efficient method for prosumer connection to the distribution line. The prosumers can be connected to the distribution line using specially designed controllable reactive impedance. The reactive impedance is controlled using specially designed coils and magnetic core. The internal coil is wound in the toroidal direction (across the z-axis) and creates a toroidal shape. A thin ferromagnetic strip is coiled on this toroidal shape in the poloidal direction to form the ferromagnetic core. Then, an external coil is wound on this ferromagnetic core in the poloidal direction. The internal coil is controlled by the inductive impedance of the external coil, which is related to the anisotropic properties of ferromagnetic strips. The internal coil is connected between the power supply line and a prosumer. This arrangement confirms the magnetic independence of coils and the symmetry of the current in the internal coil. The magnetic coupling between both coils is very low (~0.015–0.017) and appropriate for engineering applications. It is approved that the impedance of the internal coil is changed due to the anisotropic magnetic properties of the core material.

Manipulation of E×B drifts in a slot divertor with advanced shaping to optimize detachment

SOLPS-ITER edge code analysis including drifts shows that optimization of divertor target shaping in a small angle slot (SAS) can strongly influence E× B drift particle fluxes, potentially improving divertor detachment for both toroidal field directions. This is enabled by directing recycling neutrals toward the separatrix from both the common flux region (CFR) and the private flux region (PFR) walls of the slot with a V-shape target in the slot (SAS-V), leading to two separate reinforcing effects, each individually involving positive feed-back: (a) increase of neutral recycling at the PFR wall of the slot due to—and causing—strong radial E× B ion flux from the CFR to the PFR; (b) decrease of E× B loss of ions out of the outer divertor into the inner divertor via the PFR due to reduction of the radial gradient of electron temperature at the outer target caused by the increased particle retention in the outer divertor. This circumvents the general problem for divertor operation with ion B ×∇B toward the X-point: E× B loss of particles from the outer divertor CFR plasma tends to keep it hot and attached. This work identifies a strong interaction between divertor geometry and drifts, a potentially important effect for optimizing advanced divertors for power exhaust in fusion reactors.

Plasma Profiles Modifications by Upgraded Power of IBW Heating System in HT-7 Tokamak

The enhancement in local and globalized electron heating has been observed after upgrading of ion Bernstien waves (IBWs) heating system in HT-7 tokamak. The overall capability of injection power has been upgraded from 350 to 600 kW (15–30 MHz) for best and active control of pressure and current density profiles, and to discover the new phenomena of plasma heating for good energy and particle confinement. A new quadruple T-type IBWs coupling antenna has been utilized which has been mounted in the toroidal direction on low field side in the device. The electron heating on both on-axis and off-axis electrons not delete has been observed. Not delete The change in direct electron heating via electron Landau damping (ELD) from IBWs has been investigated, while the bulk electron temperature showed a large rise with a heating factor, ∆(Tene)/Prf, up to 9.3 × 1019 eV m–3 kW–1 with central electron density (ne) 3.7 × 1019 m–3. The particle confinement has also been achieved with IBW injection power of 550 kW at frequency of 27 MHz and with toroidal magnetic field of 1.92 T. The modifications observed in electron temperature and other plasma profiles are discussed under various plasma conditions. The improved energy confinement has also been observed in this scenario.

Optimization of the chamfering structures for ITER-like W/Cu monoblocks to avoid the leading edge-induced melting in EAST

EAST has installed a full ITER-like W divertor with W/Cu monoblocks for targets in the upper part of vacuum chamber since 2014. Although the dual chamfer shaping structure with 1 mm cutting in both toroidal and radial directions (1 mm × 1 mm) has been employed to mitigate the leading edge-induced thermal effect, severe leading edge-induced melting was widely observed on both inner and outer targets. All melting only occurred at the leading edges between neighboring cassette modules (inter-CMs), while it was not found at the leading edges between neighboring monoblocks within one cassette module (intra-CM). To optimize the chamfering structure for avoiding melting, thermal analysis of W/Cu monoblocks was performed by finite element method. It is identified that the current dual chamfer shaping structure (1 mm × 1 mm) does not work for inter-CMs due to the large radial misalignment which was hardly controlled and could even reached up to 3 mm. With such large misalignment, the maximum surface steady state heat load is only 1.2 MW m−2 for current structure. Thus, a symmetric structure of CMs which survive EAST operations requirement with two different toroidal magnetic fields has been proposed to improve the thermal performance and avoid melting. At inter-CMs, the optimized chamfering structure suitable for larger misalignments and heat fluxes has been suggested. And, the current dual chamfer shaping structure is remained at intra-CM after thermal evaluation. Such symmetric CMs should ensure EAST operate with heat flux up to 3 MW m−2 with 3 mm misalignment level. And, further improvement to withstand a higher heat flux is also proposed and discussed.

Quasi-analytical equilibria with toroidal rotation and shape control

Quasi-analytical equilibrium solutions for plasmas rotating in the toroidal direction are presented. The formalism provides control of the plasma shape (aspect ratio, elongation and triangularity) and allows to independently set the values of the rotation velocity (Mach number) and the plasma current and β. Explicit expressions for the shape coefficients and examples of equilibria calculated with this method are presented.

Global gyrokinetic particle simulations of microturbulence in W7-X and LHD stellarators

Global gyrokinetic particle simulations of electrostatic ion temperature gradient (ITG) instability show that the most unstable eigenmode is localized to some magnetic fieldlines or discrete locations on the poloidal plane in the Wendelstein 7-X (W7-X) stellarator due to its mirror-like magnetic fields, which vary strongly in the toroidal direction and induce coupling of more toroidal harmonics (n) to form the linear eigenmode than in the Large Helical Device (LHD) stellarator. Nonlinear electrostatic simulation results show that self-generated zonal flows are the dominant saturation mechanism for the ITG instabilities in both the LHD and W7-X. Furthermore, radial widths of the fluctuation intensity in both the LHD and W7-X are significantly broadened from the linear phase to the nonlinear phase due to turbulence spreading. Finally, nonlinear spectra in the W7-X are dominated by low-n harmonics, which can be generated both by nonlinear toroidal coupling of high-n harmonics and by linear toroidal coupling with large amplitude zonal flows due to the 3D equilibrium magnetic fields.

On thermal axisymmetric liquid-metal divertors

Abstract Motivated by liquid-metal divertor concepts, we consider a detailed model of a thin liquid-metal film flowing down a toroidally-symmetric solid substrate, driven by gravity as well as thermal and mechanical interaction with the SOL. In the relevant physical limit where the film is thin relative to the divertor extent, and the induced magnetic field is weaker than the applied field, the governing equations may be approximated asymptotically to yield tractable reduced-order dynamics. The analysis incorporates gravitational, thermocapillary and thermoelectric forces, and reveals several nontrivial findings. Firstly, we find that the influence on the liquid metal flow of the toroidal component of the applied field is negligible compared to that of the poloidal component. This has important ramifications for the behaviour of the liquid metal. Secondly, we identify a “spiral-type flow” due to a flow component in the toroidal direction. This flow has been previously reported in the literature in the isothermal case when using extreme parameters. Our analysis explains why these extreme parameter choices were required to observe the isothermal flow, and reveals that, for typical parameters in the thermal case, the flow becomes significant due to thermoelectric forces. Thirdly, we deduce full dimensional velocity scalings. Finally, we present a case study that employs the reduced-order model to explore the effects of sweeping the plasma strike point up and down the divertor. We simulate fully transient dynamics within the divertor and demonstrate how, in some regions of parameter space, the sweeping might promote dry-out or droplet ejection of the liquid metal. We discuss how the case study can inform both divertor material choice as well as tokamak operating parameters.

Stationary high-performance grassy ELM regime in EAST

A stationary, high-performance grassy edge-localized mode (ELM) regime has been successfully accessed on the EAST tokamak since the 2016 campaign. increase via increase of heating power or q95 are both found to facilitate a higher grassy ELM frequency. Edge measurement of absolute extreme ultraviolet radiation indicates that the affected area by grassy ELMs is localized at the pedestal region and the perturbations there induced by grassy ELMs can be 90% smaller than that by type-I ELMs. Parameter scan demonstrates that the grassy ELM regime has good density control capacity, and the access to the grassy ELM regime is independent of the toroidal field direction and low-hybrid-wave power. Statistical analysis indicates that the grassy ELM regime is highly reproducible in a wide parameter space when edge safety factor and poloidal beta are simultaneously high enough ( and ). High triangularity contributes to the increase of grassy ELM frequency while the requirement on high internal inductance in the JET tokamak for grassy ELMs cannot be found in EAST. The operational space in pedestal top collisionality for the EAST grassy ELMs is in the range of . The exploration towards lower is mainly limited by the available heating power. Evolution of a coherent mode at pedestal top suggests that grassy ELMs most likely generate in the steep-gradient region of the pedestal, rather than on the pedestal top or near the separatrix. The grassy ELM regime offers a highly promising approach for further exploration of long-pulse high-performance H-mode operations in EAST, with potential application to the Chinese Fusion Engineering Test Reactor (CFETR) as the baseline scenario and a primary solution for the control of ELMs.

Physics of Magnetohydrodynamic Rossby Waves in the Sun

Abstract Evidence of the existence of hydrodynamic and MHD Rossby waves in the Sun is accumulating rapidly. We employ an MHD Rossby wave model for the Sun in simplified Cartesian geometry, with a uniform toroidal field and no differential rotation, to analyze the role of each force that contributes to Rossby wave dynamics, and compute fluid particle trajectories followed in these waves. This analysis goes well beyond the traditional formulation of Rossby waves in terms of conservation of vorticity. Hydrodynamic Rossby waves propagate retrograde relative to the rotation of the reference frame, while MHD Rossby waves can be both prograde and retrograde. Fluid particle trajectories are either clockwise or counterclockwise spirals, depending on where in the wave pattern they are initiated, that track generally in the direction of wave propagation. Retrograde propagating MHD Rossby waves move faster than their hydrodynamic counterparts of the same wavelength, becoming Alfvén waves at very high field strengths. Prograde MHD Rossby waves, which have no hydrodynamic counterpart, move more slowly eastward than retrograde MHD Rossby waves for the same toroidal field, but with a speed that increases with toroidal field, in the high field limit again becoming Alfvén waves. The longitude and latitude structures of all these waves, as seen in their velocity streamlines and perturbation field lines as well as fluid particle trajectories, are remarkably similar for different toroidal fields, rotation, longitudinal wavelength, and direction of propagation.

A high-order non field-aligned approach for the discretization of strongly anisotropic diffusion operators in magnetic fusion

In this work we present a hybrid discontinuous Galerkin scheme for the solution of extremely anisotropic diffusion problems arising in magnetized plasmas for fusion applications. Unstructured meshes, non-aligned with respect to the dominant diffusion direction, allow an unequalled flexibility in discretizing geometries of any shape, but may lead to spurious numerical diffusion. Curved triangles or quadrangles are used to discretize the poloidal plane of the machine, while a structured discretization is used in the toroidal direction. The proper design of the numerical fluxes guarantees the correct convergence order at any anisotropy level. Computations performed on well-designed 2D and 3D numerical tests show that non-aligned discretizations are able to provide spurious diffusion free solutions as long as high-order interpolations are used. Introducing an explicit measure of the numerical diffusion, a careful investigation is carried out showing an exponential increase of this latest with respect to the non-alignment of the mesh with the diffusion direction, as well as an exponential decrease with the polynomial degree of interpolation. A brief assessment of the method with respect to two finite-difference schemes using non-aligned discretization, but classically used in fusion modeling, is also presented. Program summaryProgram Title: Laplace-HDG (Laplace Hybrid Discontinuous Galerkin)CPC Library link to program files:http://dx.doi.org/10.17632/c3dhycyvj8.1Licensing provisions: GPLv3Programming language: Fortran 95Nature of problem: Anisotropic Laplace problem in 2D with Dirichlet boundary conditionsSolution method: Hybrid discontinuous Galerkin scheme

Direct Observation of Flatband Loop States Arising from Nontrivial Real-Space Topology.

Topological properties of lattices are typically revealed in momentum space using concepts such as the Chern number. Here, we study unconventional loop states, namely, the noncontractible loop states (NLSs) and robust boundary modes, mediated by nontrivial topology in real space. While such states play a key role in understanding fundamental physics of flatband systems, their experimental observation has been hampered because of the challenge in realizing desired boundary conditions. Using a laser-writing technique, we optically establish photonic kagome lattices with both an open boundary by properly truncating the lattice, and a periodic boundary by shaping the lattice into a Corbino geometry. We thereby demonstrate the robust boundary modes winding around the entire edge of the open lattice and, more directly, the NLSs winding in a closed loop akin to that in a torus. We prove that the NLSs due to real-space topology persist in ideal Corbino-shaped kagome lattices of arbitrary size. Our results could be of great importance for our understanding of the singular flatbands and the intriguing physics phenomenon applicable for strongly interacting systems.