X-point Height Research Articles

Statistical analysis of magnetic divertor configuration influence on H-mode transitions

DIII-D plasmas are compared for two upper divertor configurations: with the outer strike point on the small angle slot (SAS) divertor target and with the outer strike point on the horizontal divertor target (HT). Scanning the vertical distance between the magnetic null point and the divertor target over a range 0.10–0.16 m is shown to increase the threshold power, Pth , and edge plasma power, PLoss , for the low-to-high confinement (L–H) and H–L transitions respectively, by up to a factor of 1.4. The X-point height scans were performed at three L-mode core plasma line average electron densities, n¯e= 1.2, 2.2 and 3.6 ×1019m−3 , to investigate the density dependence of divertor magnetic configuration influence on Pth . The X-point height, Zx-pt , was further extended across the range 0.16–0.22 m with the more open HT divertor configuration, for which a clear decrease in Pth with increasing Zx-pt is observed. The dependence of Pth on divertor magnetic geometry is further investigated using a time-dependent probability density function (PDF) model and information geometry to elucidate the roles played by pedestal plasma turbulence and perpendicular velocity flows. The degree of stochasticity of the plasma turbulence is observed to be sensitive to the plasma heating rate. The calculated square of the information rate shows changes in the relative density fluctuations and perpendicular velocity PDFs begin 2–5 ms prior to the L–H transition for three plasmas; providing a crucial measurement of the dynamic timescale of external transport barrier formation. Additionally, both information length and rate provide potential predictors of the L–H transition for these plasmas.

Divertor power loads and scrape off layer width in the large aspect ratio full tungsten tokamak WEST

WEST is a full W tokamak with an extensive set of diagnostics for heat load measurements especially in the lower divertor. It is composed by infrared thermography, thermal measurement with thermocouples and fibre Bragg grating embedded few mm below the surface and flush mounted Langmuir probes. A large database including different magnetic equilibrium and input power is investigated to compare the heat load pattern (location, amplitude of the peak and heat flux decay length) on the inner and outer strike point regions: from the first ohmic diverted plasma (obtained during the second experimental campaign C2 in 2018) up to the high power (8 MW total injected) and high energy (up to 90 MJ injected energy in lower single null configuration) experiments performed in the last experimental campaign (C4 in 2019). Concerning the peak location, a good agreement (<1 cm) is obtained between thermal inversions and flush-mounted LP measurements. The peak heat flux from the whole set of diagnostics is in good agreement and mainly in the ±20% range, while the heat flux decay length reported on the target shows significant discrepancy between diagnostics and location in the machine (±40% range). Despite such discrepancy, heat flux decay length at target is found to scale mainly with the magnetic flux expansion through the variation of the X-point height, as expected. The improved plasma performances achieved during C4 enabled to reach significant heat load in the divertor, up to 6 MW m−2 with 4 MW of additional heating power showing the capability to reach the ITER relevant heat load (10 MW m−2 steady state) with about 7 MW of additional power in L-mode discharge. The heat load distribution is clearly asymmetric with a 3/4 and 1/4 distribution on the outer and inner strike point region respectively for the parallel heat flux.

H-Mode Power Threshold Studies on MAST

Analysis of the L–H and H–L transition power thresholds (Pth) and pedestal parameters are presented for the mega ampere spherical tokamak (MAST). The dependencies of Pth on the average, core plasma electron density, X-point height, and plasma current are described. Increasing X-point distance from the divertor floor over 10–12 cm is found to increase Pth by a factor of three, while X-point heights greater than this have no further influence. The X-point height dependence of Pth is also observed to be sensitive to the plasma current. An Ip decrease from 0.77 MA to 0.65 MA, is observed to lower Pth by a factor of three across the X-point height scan and increases the maximum X-point height at which Pth stops increasing by 3 cm. Finally, a comparison of the experimental results with the predictions by the finite beta drift wave model is made, which provides a reasonable condition for the transition into and out of the H-mode.

First heat flux estimation in the lower divertor of WEST with embedded thermal measurements

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 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 λqt, power spreading in the private flux region St and the strike point location x0). As a first step, five ohmic pulses have been investigated with different magnetic configuration and divertor X-point height varying from 44 to 68 mm from the surface. Despite an outboard shift, the relative displacements of the outer strike point as well as the heat flux decay length derived from the TC/FBG systems are consistent with the magnetic equilibrium reconstruction.

EDGE2D-EIRENE simulations of the impact of poloidal flux expansion on the radiative divertor performance in JET

In the past at JET, with the MkI divertor, a systematic study of the influence of X-point height and poloidal flux expansion has been conducted [1,2] showing minor differences in the radiation distribution, whereas in [3] experiment and simulations have shown enhancement of detachment as the flux expansion was increased. More recently at JET, equipped with the ITER-like wall (ILW), radiative seeded scenarios have been studied and a maximum radiation fraction 75% has been achieved. EDGE2D-EIRENE [4–6] simulations [7,8] have already shown that the divertor heat fluxes can be reduced with N2 injection, qualitatively consistent with experimental observations [9], by adjusting the impurity injection rate to reproduce the measured divertor radiation. In this paper we will present edge predictive simulations on the assessment of effects of poloidal flux expansion and recycling on radiation distribution and X-point peaking on JET-ILW nitrogen seeded plasmas.

H-mode access during plasma current ramp-up in TCV

A recent TCV experiment has investigated the dependence of the L–H transition threshold power on the plasma current ramp-rate and the X-point height above the divertor target, which both have previously been seen to affect the transition behaviour. Systematic scans in ohmically heated plasmas do not show any dependence on the plasma current ramp-up rate. In contrast, the threshold power is found to increase by a factor of two while the X-point is moved from about 10 cm up to 35 cm above the vessel floor. However, further increase, up to 60 cm, does not lead to any further increase of the required power. The Fundamenski et al model is tested against the measurements. Estimates of the Wagner number (Wa) at L–H transitions are generally close to unity, in accordance with the model. In contrast, estimates of Wa before the L–H transition, i.e. in L-mode, do not show the expected evolution towards unity.

Pfirsch–Schlüter current-driven edge electric fields and their effect on the L–H transition power threshold

An important contribution to the magnetohydrodynamic equilibrium at the tokamak edge comes from the Pfirsch–Schlüter current. The parallel electric field that can be associated with these currents is necessarily poloidally asymmetric and makes a similarly nonuniform contribution to the radial electric field on a flux surface. Here the role of the poloidal variation of this radial electric field in the L–H transition power threshold is investigated. Dependence of the resulting electric fields on magnetic topology, geometric factors such as the upper/lower triangularity and elongation, and the relative position of the X-point(s) in the poloidal plane are examined in detail. Starting with the assumption that an initially more negative radial electric field at the edge helps lower the transition power threshold, we find that our results are in agreement with a variety of experimental observations. In particular, for a ‘normal’ configuration of the plasma current and toroidal field we show the following. (i) The net radial electric field contribution by the Pfirsch–Schlüter currents at the plasma edge is negative for a lower single null and positive for a corresponding upper single null geometry. (ii) It becomes more negative as the X-point height is reduced. (iii) It also becomes more negative as the X-point radius is increased. These observations are consistent with the observed changes in the L–H transition power threshold PLH under similar changes in the experimental conditions. In addition we find that (iv) in USN with an unfavourable ion ∇B drift direction, the net radial electric field contribution is positive but decreases as the X-point radius decreases. This is consistent with the C-Mod observation that an L–I mode transition can be triggered by increasing the upper triangularity in this configuration. (v) Locally the radial electric field is positive above the outer mid-plane and reverses sign with reversal of the toroidal field, consistent with DIII-D observations in low-power L-mode discharges. Thus, taken as a whole, the Pfirsch–Schlüter current-driven fields can explain a number of observations on the L–H or L–I transition and the required power threshold PLH levels not captured by simple scaling laws. They may indeed be an important ‘hidden variable’.

Plasma modelling results and shape control improvements for NSTX

New shape control implementations and dynamics studies on the National Spherical Torus eXperiment (NSTX) (Ono et al 2000 Nucl. Fusion 40 557–61) are summarized. In particular, strike point position, X-point height and squareness control, and two new system-identification methods/control-tuning algorithms were put into operation. The PID controller for the strike point was tuned by analysing the step response of the strike point position to the poloidal coil currents, employing the Ziegler–Nichols method. An offline system identification of the plasma response to the control inputs based on ARMAX (Ljung 1999 System Identification: Theory for the User (Englewood Cliffs, NJ: Prentice-Hall)) input–output models was implemented. With this tool, rough estimates of the improvements were realized and several control improvements were identified. An online automatic relay-feedback PID tuning algorithm, which has the advantage of tuning the controller in one shot, was implemented, thus optimizing the use of experimental time. Using these new capabilities, all four upper/lower/inner/outer strike points were simultaneous controlled and a combined X-point height, strike point radius control was implemented. The new and improved control with better accuracy and robustness enabled successful plasma operations with the liquid lithium divertor. Additionally this year, the first independent squareness control was developed. This will enable better optimization of the NSTX shape for stability and high performance in the future.

L–H transition studies on DIII-D to determine H-mode access for operational scenarios in ITER

A comprehensive set of L–H transition experiments has been performed on DIII-D to determine the requirements for access to H-mode plasmas in ITER's first (non-nuclear) operational phase with H and He plasmas and the second (activated) operational phase with D plasmas. The H-mode power threshold, PTH, was evaluated for different operational configurations and auxiliary heating methods for the different main ion species. Helium plasmas have significantly higher PTH than deuterium plasmas at low densities for all heating schemes, but similar PTH as deuterium plasmas at high densities except for H-neutral beam injection-heated discharges, which are still higher. Changes in PTH are observed when helium concentration levels in deuterium plasmas exceed 40%. There is a strong dependence of PTH on the magnetic geometry in the vicinity of the divertor. The trend of decreasing PTH with decreasing X-point height is observed for all of the main ion species irrespective of the heating method, which appears to indicate that there is a common physics process behind this effect for all of the ion species. Helium and deuterium plasmas exhibit a significant increase in PTH for strong resonant magnetic perturbations. The application of a local magnetic ripple of 3% from test blanket module mock-up coils did not change PTH in deuterium plasmas.

The torque dependence of the H-mode power threshold in hydrogen, deuterium and helium plasmas in DIII-D

On DIII-D, the H-mode power threshold has been determined for hydrogen, deuterium and helium plasmas heated by neutral beam injection and/or by electron cyclotron heating and as a function of the applied torque plasmas for plasma configurations in the favourable ion grad-B drift direction. The H-mode threshold power has been determined to increase with input torque for all the main ion species (hydrogen, deuterium and helium). The H-mode threshold power for similar plasma parameters and configurations is the least for deuterium, followed by helium and hydrogen in that order. The plasma geometry also affects the power threshold, which is dependent on the X-point height.

Solar coronal heating by magnetic cancellation – II. Disconnected and unequal bipoles

Two-dimensional numerical magnetohydrodynamic simulations of a cancelling magnetic feature (CMF) and the associated coronal X-ray bright point (XBP) are presented. Coronal magnetic reconnection is found to produce the Ohmic heating required for a coronal XBP. During the BP phase where reconnection occurs above the base, about 90–95 per cent of the magnetic flux of the converging magnetic bipole cancels at the base. The last ≈5 to 10 per cent of the base magnetic flux is cancelled when reconnection occurs at the base. Reconnection happens in a time-dependent way in response to the imposed converging footpoint motions. A potential field model gives a good first approximation to the qualitative behaviour of the system, but the magnetohydrodynamics (MHD) experiments reveal several quantitative differences: for example, the effects of plasma inertia and a pressure build-up in-between the converging bipole are to delay the onset of coronal reconnection above the base and to lower the maximum X-point height.

JET divertor geometry and plasma shape effects on the L–H transition threshold

Results from recent experiments to study the effects of divertor geometry and increased plasma shaping on the L–H transition threshold on JET are reported. Equivalent septum configurations run with the new septum replacement plate (SRP) in the MkII Gas Box divertor have shown that the presence of the septum lowers the L–H transition power threshold, Pth, by 20%. For X-point to virtual septum top distances of less than 6 cm, the SRP plasmas also demonstrate a significant decrease of the L–H Pth and pedestal electron temperature, Te with reduced X-point height. Although, the SRP plasma's Pth remains above that with the septum, there is no difference in the pedestal Te at the L–H transition. The influence of plasma shaping on the L–H transition has also been investigated for the first time on JET in a series of density scans at Ip/Bt of 2.5 MA/2.7 T. While keeping the lower triangularity, δlower, and divertor geometry constant, the upper triangularity, δupper, has been increased from 0.23 to 0.34 with no effect on Pth or the pedestal Te or Ti. In a separate edge ne scan, two configurations with different δupper/δlower values of 0.23/0.23 and 0.43/0.33 have been compared. A large difference in the transition threshold is observed at values of edge ne above 1.8 × 1019 m−3, with the higher δ plasmas characterized by Pth of up to 25% lower at the highest densities scanned. This is thought to be the result of lowered X-point and outer strike point heights with increased δ.

Performance of high triangularity plasmas as the volume of the secondary divertor is varied in DIII-D

This paper examines the sensitivity of edge pedestal and divertor performance parameters to changes in the volume of a secondary divertor that tends to form inside the vacuum chamber in high triangularity plasma shapes. The sensitivity was examined by varying the vertical distance of the secondary X-point from the target plate, Z S X , while holding the primary X-point height fixed. The ion ∇ B drift was in the direction of the primary divertor. Discharges with and without active primary divertor cryo-pumping were examined. The effective rate of rise of the core density at the L–H transition increased 80% as Z S X was reduced. At high density achieved by gas injection, the core line-averaged density at the H–L back transition decreased by 30% as Z S X was reduced. Both of these results indicate that performance may be affected when core plasma screening of neutrals in the secondary divertor is reduced as Z S X decreases. The peak heat flux in the secondary divertor decreased as Z S X was reduced due to increased flux expansion until a threshold was reached at Z S X ∼3 cm where it remained constant. This indicated that the high recycling character of the plasma above the target in the secondary divertor was lost when the length of the outer divertor leg was reduced below a critical value.

Particle control and behaviour of neutrals in the pumped W-shaped divertor of JT-60U

As a trial for an active particle control, simultaneous feedback control of the divertor neutral pressure and main plasma density by the dual locations of gas puff is performed in the W-shaped divertor of JT-60U. At a relatively low gas-puffing rate, the divertor neutral pressure and main density are well controlled as pre-programmed. Lowering the X-point height is effective for isolation of the main plasma from divertor neutral particles. Simultaneous control has some difficulty at a high gas-puffing rate due to an increase of the cross-term coupling with each gas puff. Particle flux from the neutral beam also makes it difficult to control divertor neutral pressure and density. The simultaneous controllability depends on the operational region of the divertor neutral pressure and the main density. The coupling of the divertor neutral pressure with gas puff becomes larger in the high flux region, so that core fuelling in order to minimise the coupling is necessary for an effective particle isolation.

Comparison of a drift effect model with measured H-mode power thresholds

The H-mode power threshold has a weak but positive dependence when the ion drift is away from the X-point, in contrast to the nearly linear dependence when the ion drift is toward the X-point. This indicates that geometry plays an important role in the H-mode power threshold scaling. A simple model of the drift effect failed to predict this behaviour, but successfully predicted the sign change of gas puffing and low X-point height on the power threshold. The difference between the threshold power required for sawtooth and non-sawtooth-triggered transitions can be substantial. This effect may contribute to the observed B scaling of the H-mode power threshold.

Ideal interchange instability near the separatrix in the SOL and its relation to ELMs

The linear stability of the `scrape-off-layer' (SOL) with respect to interchange-type modes is studied using the reduced MHD model and applying a ballooning approximation to the perturbations. `Line-tying' boundary conditions are used at the target plates. Employing a metric determined by the magnetic field geometry, the influence of the X-point on stability is assessed. The effect of relevant parameters like X-point height, magnetic shear and plasma shaping is qualitatively determined. It is demonstrated that the calculations for experimental configurations and those based on an analytical equilibrium model yield good qualitative agreement. It is shown that the SOL plasma just outside the separatrix can become unstable more easily (i.e. for lower pressure gradients) than the plasma just inside the separatrix where the magnetic well is stabilizing. This finding can be important for explaining the occurrence of giant ELMs. The interchange instability in the SOL may act as a precursor and is mainly localized near the X-point, but may also have a strong signature just above the outer midplane. The scaling of the ELM repetition time with heating power and current is derived.

Reciprocating and fixed probe measurements of density and temperature in the DIII-D divertor

This paper describes divertor density and temperature measurements using both a new reciprocating Langmuir probe (XPT-RCP) which plunges vertically above the divertor floor up to the X-point height and swept, single, Langmuir probes fixed horizontally across the divertor floor. These types of measurements are important for testing models of the SOL and divertor which then are used to determine engineering design criteria for plasma facing components in reactor size tokamaks. The 6 mm diameter fixed single probes (19 domed and 2 flat at radially equivalent locations) are incorporated into the lower divertor floor at 19 radial locations and swept at 250 Hz. These probes are critical for determining plasma detachment from the floor during operation with high density, highly radiating divertors. By sweeping the divertor strike point across the fixed probes, different regions of the target plate incident flux profile can be sampled and a high resolution spatial profile can be obtained from each probe tip as the strike point moves past. The X-point reciprocating probe (XPT-RCP) provides n e and T e profiles with high spatial (2 mm) and temporal (0.5 ms) resolution from the target plate to the X-point along a single vertical chord at the same radial location as a fixed probe tip at a different azimuthal location. The probe n e and T e are compared to the divertor Thomson scattering (DTS) n e and T e (eight vertical points at 20 Hz, R Thomson = R X- point- rcp ). Recent observations have also shown divertor densities from 3 × 10 19 to 4 × 10 20 m −3 near the target plate with the highest densities observed with D 2 gas puffing. Electron temperature is typically of the order of 15–25 eV at the target rising to about 70 eV near the X-point. Lower temperature, higher density plasmas are observed along the inner leg. Generally good agreement among the XPT-RCP, the fixed floor probes, and the DTS is observed. Differences between these diagnostic measurements will also be discussed with respect to different operating regimes and conditions.

Divertor configuration studies on JET

In the 1994/1995 JET experimental campaign, with the MkI divertor, a systematic study of the influence of X-point height, flux expansion and target orientation on the plasma performance was executed. Various plasma configurations were tested under a number of different conditions, including Ohmic density limits, L-mode with 3 MW of NBI, H-mode at 10 MW of NBI.and divertor seeding with nitrogen at 10 MW of NBI. The behaviour of the main plasma for the various configurations was quite similar, although there were small differences, for example in impurity control and fuelling efficiency. The paper describes the details of the experiment and presents the results, comparing the findings to the results of simulations using the EDGE2 D plasma boundary code.