Last Closed Flux Surface Research Articles

Development of an ICRH antenna system at W7-X for plasma heating and wall conditioning

An ICRH antenna system is under construction to be ready for use in the operational phase 1.2 of W7-X. A two strap antenna, with a surface adapted to the 3D shape of the Last Closed Flux Surface (LCFS) of the standard magnetic configuration (m/n=5/5), will be installed in the equatorial plane on the low field side of W7-X. The antenna system is optimised for plasma heating and wall conditioning in presence of the magnetic field in the frequency range 25–38MHz. Each strap is short-circuited on one end, is pre-matched using a tunable capacitor on the other end with connection to the RF power source about halfway in the poloidal direction. To allow optimal coupling to different magnetic configurations in W7-X the antenna can be moved radially over a distance of 350 mm. The cooling circuits in the antenna head are designed to sustain cw W7-X plasma operation in a retracted position and 2MW ICRH pulses with maximum 10s duration every 300s close to the LCFS.

Visible imaging measurement of position and displacement of the last closed flux surface in EAST tokamak

A new method for measuring the position and displacement of the last closed flux surface (LCFS) with visible imaging diagnostics has been developed in EAST. By measuring the relative intensity profiles of the green visible Li-II emission in the tangential planes of the optical systems, it is possible to infer the positions of certain points on the LCFS. This emission line is readily available in discharges with Li-coating wall routinely employed to improve the plasma performance. We describe the measuring method, giving results which are compared with those obtained by EFIT, and showing this as an effective and convenient approach to determine the position of the LCFS. This method is further applied to measure the displacements of the LCFS during application of resonant magnetic perturbation fields in the EAST tokamak.

2D distribution of hydrogen/impurity radiation and flow formation in stochastic layer during detachment transition in LHD

2D distribution of hydrogen/impurity radiation and impurity flow have been measured in the edge stochastic layer of LHD during detachment transition by using a newly developed visible spectrometer system with 130 channel optic fiber array. The spectrometer system views the edge region to resolve magnetic field structures, such as the divertor legs, the X-point, the stochastic layer, the last closed flux surface (LCFS), and the divertor plates. A clear upstream shift of CII and CIII emission from the divertor region to the X-point is observed at the detachment transition. The formation of volume recombination region is indicated by the increase in the ratio Hγ/Hβ, which is particularly enhanced around the LCFS. The flow speed distribution of C2+ is estimated from the Doppler shift of CIII spectra. The velocity of the order of 104m/s is obtained. A clear change of flow direction is observed with respect to the X-point and the density increase, and at the detachment transition.

Dirichlet boundary conditions for arbitrary-shaped boundaries in stellarator-like magnetic fields for the Flux-Coordinate Independent method

We present a technique for handling Dirichlet boundary conditions with the Flux Coordinate Independent (FCI) parallel derivative operator with arbitrary-shaped material geometry in general 3D magnetic fields. The FCI method constructs a finite difference scheme for ∇∥ by following field lines between poloidal planes and interpolating within planes. Doing so removes the need for field-aligned coordinate systems that suffer from singularities in the metric tensor at null points in the magnetic field (or equivalently, when q→∞). One cost of this method is that as the field lines are not on the mesh, they may leave the domain at any point between neighbouring planes, complicating the application of boundary conditions.The Leg Value Fill (LVF) boundary condition scheme presented here involves an extrapolation/interpolation of the boundary value onto the field line end point. The usual finite difference scheme can then be used unmodified. We implement the LVF scheme in BOUT++ and use the Method of Manufactured Solutions to verify the implementation in a rectangular domain, and show that it does not modify the error scaling of the finite difference scheme. The use of LVF for arbitrary wall geometry is outlined.We also demonstrate the feasibility of using the FCI approach in non-axisymmetric configurations for a simple diffusion model in a “straight stellarator” magnetic field. A Gaussian blob diffuses along the field lines, tracing out flux surfaces. Dirichlet boundary conditions impose a last closed flux surface (LCFS) that confines the density. Including a poloidal limiter moves the LCFS to a smaller radius.The expected scaling of the numerical perpendicular diffusion, which is a consequence of the FCI method, in stellarator-like geometry is recovered. A novel technique for increasing the parallel resolution during post-processing, in order to reduce artefacts in visualisations, is described.

Overview of diagnostic performance and results for the first operation phase in Wendelstein 7-X (invited)

Wendelstein 7-X, a superconducting optimized stellarator built in Greifswald/Germany, started its first plasmas with the last closed flux surface (LCFS) defined by 5 uncooled graphite limiters in December 2015. At the end of the 10 weeks long experimental campaign (OP1.1) more than 20 independent diagnostic systems were in operation, allowing detailed studies of many interesting plasma phenomena. For example, fast neutral gas manometers supported by video cameras (including one fast-frame camera with frame rates of tens of kHz) as well as visible cameras with different interference filters, with field of views covering all ten half-modules of the stellarator, discovered a MARFE-like radiation zone on the inboard side of machine module 4. This structure is presumably triggered by an inadvertent plasma-wall interaction in module 4 resulting in a high impurity influx that terminates some discharges by radiation cooling. The main plasma parameters achieved in OP1.1 exceeded predicted values in discharges of a length reaching 6 s. Although OP1.1 is characterized by short pulses, many of the diagnostics are already designed for quasi-steady state operation of 30 min discharges heated at 10 MW of ECRH. An overview of diagnostic performance for OP1.1 is given, including some highlights from the physics campaigns.

On the W7-X divertor performance under detached conditions

We present a theoretical/numerical predictive analysis of the performance of the W7-X island divertor under conditions of detachment characterized by intensive radiation. The analysis is based on EMC3-Eirene simulations and the earlier W7-AS experimental and numerical experience. Carbon is employed as a representative radiator. The associated drawbacks, i.e. core contamination and recycling degradation (reduced recycling flux), are evaluated by determining the carbon density at the last closed flux surface (LCFS) and the neutral pressure in the divertor chamber. Optimum conditions are explored in both configuration and plasma parameter space. This study aims to identify the key geometric/magnetic and plasma parameters that affect the performance of detached plasmas in W7-X. Emphasis is placed on what occurs when the islands are enlarged far beyond the maximum size available in W7-AS and whether an island size limit for optimal detachment operation exists, and why. Further issues addressed are the power removal ability of the W7-X edge islands, potentially limiting factors, compatibility between particle and power exhaust, and particle refueling capability of the recycling neutrals.

Guiding Center Orbit Calculation for Evaluating the Current Density Distributions of the Electrons in Electron Cyclotron Heating on QUEST

In order to evaluate the magnetic surface current density distributions, the electron guiding center orbits were calculated with the equilibrium fitting plasma equilibrium analysis. The current density distributions in electron cyclotron-heated plasma were estimated from the orbit analyses in the equilibrium plasma shaping for the fundamental and the second-harmonic resonant electrons separately. The current density distribution profiles on the equatorial plane were obtained for the electrons with initially positive and negative velocities parallel to the magnetic field direction as well as the trapped electrons. The surface averaged current density profiles of the closed flux surfaces were also evaluated. A significant amount of the positive current density distributions appeared outside the last closed flux surface (LCFS), while all the negative current density distributions were evaluated inside the LCFS. The trapped electrons being the second-harmonic electron cyclotron resonant contributed the negative current inside the LCFS. The positive current density distributions outside the LCFS were significant for the driven current density for both the fundamental and second-harmonic resonances.

Effects of magnetic ripple on 3D equilibrium and alpha particle confinement in the European DEMO

An assessment of alpha particle confinement is performed in the European DEMO reference design. 3D MHD equilibria with nested flux-surfaces and single magnetic axis are obtained with the VMEC free-boundary code, thereby including the plasma response to the magnetic ripple created by the finite number of TF coils. Populations of fusion alphas that are consistent with the equilibrium profiles are evolved until slowing-down with the VENUS-LEVIS orbit code in the guiding-centre approximation. Fast ion losses through the last-closed flux-surface are numerically evaluated with two ripple models: (1) using the 3D equilibrium and (2) algebraically adding the non-axisymmetric ripple perturbation to the 2D equilibrium. By virtue of the small ripple field and its non-resonant nature, both models quantitatively agree. Differences are however noted in the toroidal location of particles losses on the last-closed flux-surface, which in the first case is 3D and in the second not. Superbanana transport, i.e. ripple-well trapping and separatrix crossing, is expected to be the dominant loss mechanism, the strongest effect on alphas being between 100–200 KeV. Above this, stochastic ripple diffusion is responsible for a rather weak loss rate, as the stochastisation threshold is observed numerically to be higher than analytic estimates. The level of ripple in the current 18 TF coil design of the European DEMO is not found to be detrimental to fusion alpha confinement.

Helium transport in the core and stochastic edge layer in LHD

Radial profiles of the density ratio of helium to hydrogen ions are measured using charge exchange spectroscopy with a two-wavelength spectrometer in the large helical device. Helium transport at the last closed flux surface (LCFS) and stochastic magnetic field layer outside the LCFS as well as in the core plasma is studied for a wide range of helium fractions, i.e. from hydrogen-dominated plasmas up to helium-dominated plasmas. The helium density profile becomes more peaked and inward convection velocity increases in the hydrogen-dominant plasma, while it becomes flat or hollow and the convection velocity is in the outward direction in the helium-dominant plasmas. The density gradient of helium at the LCFS is twice that of hydrogen and becomes steeper as the hydrogen becomes more dominant.

Multi-purpose mid-plane manipulator for plasma surface interaction research in KSTAR

A multi-purpose mid-plane manipulator system has been developed and installed at the mid-plane of the KSTAR vacuum vessel. The system serves as user facility which allows to cover various topics of researches in plasma-surface interaction (PSI) including material sample test and PSI diagnostic. The multi-purpose mid-plane manipulator system has a 4m long cantilever structure with a 3m long moving shaft. The system is equipped with a differential pumping system for the independent installation and removal of samples and diagnostic without vacuum break of KSTAR. The sample mounting head at the end of the shaft can reach the position of the outer boundary of ∼10cm away from the last closed flux surface (LCFS). In this paper, selected PSI related experiments by using the manipulator are introduced.

Non-inductive initiation of closed flux surfaces by ECH/ECCD on KSTAR using an oblique fundamental O-mode injection from the low-field side

An experiment on non-inductive plasma current start-up by electron cyclotron (EC) heating and current drive (ECH/ECCD) has been carried out on KSTAR by injecting the fundamental O-mode wave from the low-field side obliquely to the toroidal magnetic field. A plasma current up to 14.5 kA is generated by 180 kW of 84 GHz microwave power and the magnetic measurement shows the formation of a large last-closed flux surface with a diameter of 0.4 m. The soft x-ray emission profile and fast CCD images also support the existence of closed flux surfaces. The current of the cross-field-passing electrons (CFPEs) is calculated according to the paper Nucl. Fusion 52 083008 in these experimental conditions, and it is shown that a CFPE current can produce the initial closed flux surfaces. The observed large increase of EC emission supports the generation of energetic electrons, like CFPEs. After the formation of the closed flux surfaces, the pressure-driven current and CFPE current do not flow in the closed flux surfaces. EC-driven current should flow in these surfaces and ramp up the plasma current. It is estimated that an EC-driven current of about one third of the total plasma current flows in the closed flux surface at the last stage.

Possibility of plasma position detection by means of peripheral plasma potential measurements in tokamak

In the current paper a method of plasma position measurement, alternative to magnetic diagnostics, is proposed. The method is based on determination of the last closed flux surface (LCFS) location by detecting the maximum of electrostatic potential profile. The experiments were carried out on the TUMAN- 3M tokamak in a series of similar ohmic heating shots. The method proved effective in LCFS localization; it allowed calculation of corrections for magnetic diagnostics, used routinely for plasma position detection. This method can be used in limiter and divertor tokamaks for independent check and clarification of electromagnetic plasma position diagnostics.

Full wave simulations of fast wave efficiency and power losses in the scrape-off layer of tokamak plasmas in mid/high harmonic and minority heating regimes**This article is dedicated to the memory of Cynthia K. Phillips

Several experiments on different machines and in different fast wave (FW) heating regimes, such as hydrogen minority heating and high harmonic fast waves (HHFW), have found strong interaction between radio-frequency (RF) waves and the scrape-off layer (SOL) region. This paper examines the propagation and the power loss in the SOL by using the full wave code AORSA, in which the edge plasma beyond the last closed flux surface (LCFS) is included in the solution domain and a collisional damping parameter is used as a proxy to represent the real, and most likely nonlinear, damping processes. 2D and 3D AORSA results for the National Spherical Torus eXperiment (NSTX) have shown a strong transition to higher SOL power losses (driven by the RF field) when the FW cut-off is removed from in front of the antenna by increasing the edge density. Here, full wave simulations have been extended for ‘conventional’ tokamaks with higher aspect ratios, such as the DIII-D, Alcator C-Mod, and EAST devices. DIII-D results in HHFW regime show similar behavior found in NSTX and NSTX-U, consistent with previous DIII-D experimental observations. In contrast, a different behavior has been found for C-Mod and EAST, which operate in the minority heating regime.

Bi-Maxwellian electron energy distribution function in the vicinity of the last closed flux surface in fusion plasma

The first-derivative probe technique was applied to derive data for plasma parameters from the IV Langmuir probe characteristics measured in the plasma boundary region in the COMPASS tokamak and in the TJ-II stellarator. It is shown that in the COMPASS tokamak in the vicinity of the last closed flux surface (LCFS) the electron energy distribution function (EEDF) is bi-Maxwellian with the low-temperature electron fraction predominating over the higher temperature one, whereas in the far scrape-off layer (SOL) the EEDF is Maxwellian. In the TJ-II stellarator during NBI heated plasma the EEDF in the confined plasma and close to the LCFS is bi-Maxwellian while in the far SOL the EEDF is Maxwellian. In contrast, during the ECR heating phase of the discharge both in the confined plasma and in the SOL the EEDF is bi-Maxwellian. The mechanism for the appearance of a bi-Maxwellian EEDF in the vicinity of the LCFS is discussed. The comparison of the results from probe measurements with ASTRA package and EIRENE code calculations suggests that the main reason of the appearance of a bi-Maxwellian EEDF in the vicinity of the LCFS is the ionization of the neutral atoms. Results for the electron temperatures and densities obtained by the first-derivative probe technique in the COMPASS tokamak and in the TJ-II stellarator were used to evaluate the radial distribution of the parallel power flux density. It is shown that in the SOL the radial distribution of the parallel power flux density is a double exponential. It is pointed out that in the calculations of the parallel power flux density at the LCFS the energy losses from ionization mechanisms must be taken into account.

Plasma flows and fluctuations with magnetic islands in the edge plasmas of J-TEXT tokamak

The first comprehensive measurements of plasma flows and fluctuations nearby static magnetic islands driven by resonant magnetic perturbations are presented. These experiments were performed using multiple Langmuir probe arrays on the edge plasmas of the J-TEXT tokamak. Controlled variations of the island size and location are explored. This study aims to understand the interaction between turbulence and magnetic islands, and to elucidate magnetic island effects on edge turbulence and flow intensity profiles, edge electric fields, and thus confinement regime transitions. Turbulence and low frequency flows (LFFs) all drop inside the magnetic island, but increase at its boundary, as island width increases. The geodesic acoustic mode is damped in most of the edge area with magnetic islands. The sign of the radial electric field changes from negative to positive within the islands. The gradient of turbulent stresses vanishes at the island center, and becomes steeper at the boundaries of the islands. The particle transport induced by the turbulence is reduced inside the magnetic islands. The magnetic island effects on flows and turbulence can lead to an increase in LFFs and enhance Reynolds stresses near the last closed flux surface (LCFS). A stronger radial electric field layer can be formed near the LCFS when magnetic islands are present. The results suggest that magnetic islands can be used as a tool to enhance edge turbulence and flows, edge electric fields, and thus to trigger confinement regime transitions.

A set-up for a biased electrode experiment in ADITYA Tokamak

An experimental set-up to investigate the effect of a biased electrode introduced in the edge region on ADITYA tokamak discharges is presented. A specially designed double-bellow mechanical assembly is fabricated for controlling the electrode location as well as its exposed length inside the plasma. The cylindrical molybdenum electrode is powered by a capacitor-bank based pulsed power supply (PPS) using a semiconductor controlled rectifier (SCR) as a switch with forced commutation. A Langmuir probe array for radial profile measurements of plasma potential and density is fabricated and installed. Standard results of improvement of global confinement have been obtained using a biased electrode. In addition to that, in this paper we show for the first time that the same biasing system can be used to avoid disruptions through stabilisation of magnetohydrodynamic (MHD) modes. Real time disruption control experiments have also been carried out by triggering the bias-voltage on the electrode automatically when the Mirnov probe signal exceeds a preset threshold value using a uniquely designed electronic comparator circuit. Most of the results related to the improved confinement and disruption mitigation are obtained in case of the electrode tip being kept at ~3 cm inside the last closed flux surface (LCFS) with an exposed length of ~20 mm in typical discharges of ADITYA tokamak.

A novel approach for mitigating disruptions using biased electrode in Aditya tokamak

Disruptions, induced in Aditya tokamak by hydrogen gas puffing, are successfully mitigated through stabilization of magnetohydrodynamic (MHD) modes by applying a bias voltage to an electrode placed inside the last-closed flux surface prior to the gas injection. Above a threshold voltage sheared Er × Bφ rotation of the plasma generated by the edge biasing leads to substantial reduction in the growth of MHD modes (m/n = 3/1, 2/1), which causes avoidance of disruptions through prevention of mode overlapping and subsequent ergodization of magnetic field lines.

First EMC3‐EIRENE Simulations with Divertor Legs of LHD in Realistic Device Geometry

AbstractAn extended mesh system for EMC3‐EIRENE has been developed to simulate peripheral plasma including the ergodic and the divertor leg regions of LHD. Both the open and the closed divertor configurations are available. A series of simulations for 8MW input power, five different electron densities at the LCFS (last closed flux surface) and the open/closed configurations were carried out. Approximately 10 times larger neutral pressure was observed under the dome structure compared with the open configuration, which is in good agreement with experimental measurements. In the case of the closed configuration, the leg regions have a large contribution of ionization to hydrogen recycling. In the case of high density discharges, however, electron temperature in the legs becomes low and the major contribution of ionization moves to the ergodic region. Significant influence of configurations is observed in the inboard side of LHD, where closed divertor components are installed but little influence is seen near the LCFS. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Scaling of the scrape-off layer width during inter-ELM H modes on MAST as measured by infrared thermography

The power load to the divertor surfaces is a key concern for future devices such as ITER, due to the thermal limits on the material surface. One factor that characterizes the heat flux to the divertor is the fall off length in the scrape-off layer (SOL), which recent empirical scalings have shown could be as small as 1 mm. These predictions are based on a multi-machine scaling of the heat flux width fitted using an expression for the divertor heat flux profile which includes a term for the exponential decay in the SOL and diffusion about the last closed flux surface (LCFS) in the private flux region. This expression has been used to fit a database of inter-ELM H mode profiles at the upper divertor and extract the fall off length, λq, for a range of different plasma parameters in double null plasmas. The midplane separation between the primary and secondary LCFS (δrsep) of the double null plasma used in the study are in the range 2 ⩽ δrsep ⩽ 7 mm and no correlation is seen between the fall off length and the δrsep. The MAST data shows good agreement with the formula, with the fitted fall off length spanning a range of 5–11 mm in the data base generated. Regression of this data has shown that the fall off length has the strongest dependence on the plasma current (or equivalently, the poloidal magnetic field at the outboard midplane) to the power −0.71. The scaling with the smallest χ2 error utilizes the poloidal magnetic field at the outboard midplane (Bpol,omp) and the power crossing the SOL in the relation with χ2 = 3.46 and R2 = 0.56 as a goodness of fit. The equivalent scaling with plasma current is with χ2 = 3.84 and R2 = 0.55. The moderate goodness of fit suggests that additional plasma parameters are required to accurately reproduce the observed variation in λq.

Edge transport studies in the edge and scrape-off layer of the National Spherical Torus Experiment with Langmuir probes

Transport and turbulence profiles were directly evaluated using probes for the first time in the edge and scrape-off layer (SOL) of NSTX [Ono et al., Nucl. Fusion 40, 557 (2000)] in low (L) and high (H) confinement, low power (Pin∼ 1.3 MW), beam-heated, lower single-null discharges. Radial turbulent particle fluxes peak near the last closed flux surface (LCFS) at ≈4×1021 s−1 in L-mode and are suppressed to ≈0.2×1021 s−1 in H mode (80%–90% lower) mostly due to a reduction in density fluctuation amplitude and of the phase between density and radial velocity fluctuations. The radial particle fluxes are consistent with particle inventory based on SOLPS fluid modeling. A strong intermittent component is identified. Hot, dense plasma filaments 4–10 cm in diameter, appear first ∼2 cm inside the LCFS at a rate of ∼1×1021 s−1 and leave that region with radial speeds of ∼3–5 km/s, decaying as they travel through the SOL, while voids travel inward toward the core. Profiles of normalized fluctuations feature levels of 10% inside LCFS to ∼150% at the LCFS and SOL. Once properly normalized, the intermittency in NSTX falls in similar electrostatic instability regimes as seen in other devices. The L-H transition causes a drop in the intermittent filaments velocity, amplitude and number in the SOL, resulting in reduced outward transport away from the edge and a less dense SOL.