Line-integrated Density Research Articles

First integrated core-edge fluid simulation of ITER’s Limiter–Divertor transition with SolEdge-HDG

This work explores the Limiter–Divertor transition (L–D) during the current ramp-up of ITER’s Q = 10 baseline plasma scenario at various central line-integrated density nli values. The analysis, based on transport simulations performed with the latest version of SoleEdge-HDG, focuses on the time evolution of heat and ion particle fluxes, revealing regions of elevated temperature on the inner wall and plasma-facing components (PFCs) despite moderate loads. The investigation also delves into the effects of perpendicular convection flux terms on density build-up, comparing different formulations and their interplay with auxiliary heating sources. Furthermore, the paper shows the impact of taking into account the evolution of the parallel neutral momentum on plasma and neutral density at the targets in the context of an ITER steady-state scenario.

Density-profile imaging using a second harmonic dispersion interferometer configured with reflective-beam expanders.

A Second-Harmonic Dispersion Interferometer (SHDI) is assembled to measure the two-dimensional, line-integrated density profile of a pulsed-plasma jet using probe-beam diameters well beyond the 1mm diameters typically used in such instruments. An initial prototype demonstrated the technique using 7mm beam diameters, which are now increased to 35mm diameter using two types of beam expanders: an achromatic-beam expander (ABE) or a reflective-beam expander (RBE). ABEs were found to add a periodic background to the measured-phase image with a magnitude of the order of Δϕ ∼ 2π radians, compared to the background phase noise level in the system configured without beam expanders at Δϕbg ∼ 0.025 radians. Subtraction of the background phase in a sample image reduced the effect of the ABE phase offset to a level of Δϕ ∼ 0.1 radians, enhancing the quality of the density measurements. Reflective-beam expanders (RBEs) did not modify the background phase appreciably and were a significant improvement, allowing the instrument to be used for 2D (r, z) density-profile measurements of a 3cm diameter × 5cm long, pulsed-plasma jet. Variations in the timing parameters for the plasma gun, specifically the gas valve opening time and the gas-injection delay, for a constant discharge current were used to map the plasma gun's performance, indicating a nominal line-integrated electron density of Nedl ≳ 3 × 1015 cm-2 and a volumetric density of Ne ≃ 9 × 1015cm-3. The results obtained for the RBE configuration demonstrate that the 2D-SHDI platform may be scaled to even larger sample areas and a rep-rated system, with the ability to potentially provide for a reproducible, time-resolved (∼1 ns), high resolution (∼100μm) measurement of 2D plasma-density profiles.

Design of radial interferometer-polarimeter for internal magnetic and density fluctuation measurements at multiple space-time scales in the National Spherical Torus Experiment-Upgrade (NSTX-U).

A Faraday-effect radial interferometer-polarimeter is designed for the National Spherical Torus Experiment-Upgrade (NSTX-U) to measure multiscale magnetic and density fluctuations critical to understanding fusion plasma confinement and stability, including those originating from magnetohydrodynamic instabilities, energetic particle-driven modes, and turbulence. The diagnostic will utilize the three-wave technique with 5MHz bandwidth to simultaneously measure line-integrated magnetic and density fluctuations up to the ion-cyclotron frequency. Probe beams will be launched radially from the low-field side at the NSTX-U midplane, where the measured Faraday fluctuations mainly correspond to radial magnetic fluctuations that directly link to magnetic transport. A correlation technique will be employed to reduce the measurement noise to below 0.01° enabling detection of small amplitude fluctuations. Two toroidally displaced chords with 7° separation will be installed to measure toroidal mode numbers up to n = 25 for mode identification. Solid-state microwave sources operating at 321μm (935GHz) will be used to minimize the impact of the Cotton-Mouton effect.

A terahertz solid-state source interferometer-polarimeter designed for long pulse discharges on EAST.

A 0.65THz Solid-state Source Interferometer-Polarimeter (SSIP) with vertical viewing has been installed for line-integrated density and Faraday rotation measurements on Experimental Advanced Superconducting Tokamak (EAST). The SSIP utilizes three independent solid-state diode sources based on frequency multiplier (X48) to provide the probing beam at a fixed frequency of 0.65THz with ∼2.5 mW output power, which provide an Intermediate Frequency (IF) with wide range, and the highest IF is up to ∼10MHz. The mixers optimized for high sensitivity, ∼750 mV/mW, are used in the SSIP system, which permits multichannel interferometer-polarimeter on EAST with a low phase noise. The resolution of the integrated density is 3.3 × 1017m-2, and the Faraday rotation is about 1.5°. The density measurement has been implemented with IF ∼0.85MHz, in a plasma with plasma current ∼300kA on EAST. The line-averaged density, 3.5 × 1019m-3, measured by the SSIP shows good agreement with the results measured by the POlarimeter-INTerferometer (POINT) system and the CO2 dispersion interferometer system in the same discharge.

Interpretative 3D MHD modelling of deuterium SPI into a JET H-mode plasma

The pre-thermal quench (pre-TQ) dynamics of a pure deuterium ( D2 ) shattered pellet injection (SPI) into a 3MA / 7MJ JET H-mode plasma is studied via 3D non-linear MHD modelling with the JOREK code. The interpretative modelling captures the overall evolution of the measured density and radiated power. The simulations also identify the importance of the drifts of ablation plasmoids towards the tokamak low field side (LFS) and the impurities in the background plasma in fragment penetration, assimilation, radiative cooling and MHD activity in D2 SPI experiments. It is found that plasmoid drifts lead to an about 70% reduction of the central line-integrated density (compared to a simulation without drifts) in the JET D2 SPI discharge considered. Impurities that pre-exist before the SPI as well as those from possible impurity influxes related to the SPI are shown to dominate the radiation in the considered discharge. With inputs from JOREK simulations, modelling with the Lagrangian particle-based pellet code PELOTON reproduces the deviation of the SPI fragments in the direction of the major radius as observed by the fast camera. This confirms the role of rocket effects and plasmoid drifts in the considered discharge and reinforces the validity of the JOREK modelling. The limited core density rise due to plasmoid drifts and the strong radiative cooling and MHD activity with impurities (depending on their species and concentration) could limit the effectiveness of LFS D2 SPI in runaway electron avoidance and are worth considering in the design of the ITER disruption mitigation system.

Forward modelling of the Cotton-Mouton effect polarimetry on EAST tokamak

Measurement of plasma electron density by far-infrared laser polarimetry has become a routine and indispensable tool in magnetic confinement fusion research. This article presents the design of a Cotton-Mouton polarimeter interferometer, which provides a reliable density measurement without fringe jumps. Cotton-Mouton effect on Experimental Advanced Superconducting Tokamak (EAST) is studied by Stokes equation with three parameters . It demonstrates that under the condition of a small Cotton-Mouton effect, parameter contains information about Cotton-Mouton effect which is proportional to the line-integrated density. For a typical EAST plasma, the magnitude of Cotton-Mouton effects is less than 2 for laser wavelength of 432 . Refractive effect due to density gradient is calculated to be negligible. Time modulation of Stokes parameters ( , ) provides heterodyne measurement. Due to the instabilities arising from laser oscillation and beam refraction in plasmas, it is necessary for the system to be insensitive to variations in the amplitude of the detection signal. Furthermore, it is shown that non-equal amplitude of X-mode and O-mode within a certain range only affects the DC offset of Stokes parameters ( , ) but does not greatly influence the phase measurements of Cotton-Mouton effects.

Improved filters for angular filter refractometry

Angular filter refractometry is an optical diagnostic that measures the absolute contours of a line-integrated density gradient by placing a filter with alternating opaque and transparent zones in the focal plane of a probe beam, which produce corresponding alternating light and dark regions in the image plane. Identifying transitions between these regions with specific zones on the angular filter (AF) allows the line-integrated density to be determined, but the sign of the density gradient at each transition is degenerate and must be broken using other information about the object plasma. Additional features from diffraction in the filter plane often complicate data analysis. In this paper, we present an improved AF design that uses a stochastic pixel pattern with a sinusoidal radial profile to minimize unwanted diffraction effects in the image caused by the sharp edges of the filter bands. We also present a technique in which a pair of AFs with different patterns on two branches of the same probe beam can be used to break the density gradient degeneracy. Both techniques are demonstrated using a synthetic diagnostic and data collected on the OMEGA EP (extended performance) laser.

Line integrated density measurements on the Versatile Experiment Spherical Torus (VEST) using frequency sweep interferometer

A frequency sweep interferometer (FSI) operating in the frequency range of 50–75 GHz is installed in the versatile experiment spherical torus spherical tokamak to measure the line integrated density (LID). FSI measures the time derivative of phase to calculate the group delay, which is proportional to the LID under the condition that the microwave frequency is much higher than the plasma frequency. Since the group delay is calculated from the time derivative of phase and the frequency sweep rate, FSI is very sensitive to the measurement noise. In the view point of signal processing, derivative exaggerates the measurement noise. Therefore, sophisticated techniques for phase measurement and frequency linearization are required to obtain meaningful results with FSI. The detailed techniques and the hardware setup are explained in the paper. The LID measured by FSI is benchmarked with the LID measured by a conventional 94 GHz heterodyne interferometer. The two measurements agree well. A conventional interferometer can no longer provide LID when severe phase errors occur. This is because phase errors propagate to subsequent measurements. However, FSI provides LID during the entire discharge time successfully regardless of frequent measurement failure because the LID is obtained in FSI from the time derivative of phase rather than the phase. In this sense, FSI is suitable as a diagnostics for steady state plasmas. The main cause for the phase errors is identified as the beam path displacement due to the refraction of the plasma.

Digital holographic interferometry for diagnosing the density profile of laser-produced collisionless shock

A digital holographic interferometry based on Fresnel biprism has been developed to measure the electron density profile of laser-produced collisionless shocks in laboratory, which used the Fourier transform method to solve the wrapped phase. The discontinuous surfaces of shocks will produce the break and split of the interference fringes, which cannot be processed by the conventional path-following phase unwrapping algorithm when reconstructing the real phase of the plasma. Therefore, we used a least-squares method to extract the real phase, which is proportional to the line-integrated electron density. We obtained fine density profiles of collisionless shocks in the line-integrated density region around 1018 cm−2 with a density resolution of 3.38 × 1016 cm−2. The shock structure is in well agreement with that measured by the dark-field schlieren methods and that predicted by shock jump condition. Synthetic holograms are used to confirm the effectiveness of our algorithm, and it is shown that correct results can still be obtained even if part of the diagnostic light is refracted out of the optical system by the shock.

Study of plasma parameters in high enthalpy ICP-heated wind tunnel by using single Langmuir probe

In this paper, a single probe (SP) has been designed for study plasma parameters of High enthalpy ICP-heated wind tunnel. It is found that the electron temperature in the core region is about 2.4 eV and that in the edge region is about 3–4 eV. At the maximum power of the High Enthalpy ICP-heated wind tunnel, the electron density reach 4.34 × 1013 cm-3. Meanwhile, the radial electron density distribution of SP is numerically integrated to calculate the line integral density, which is compared with the line integral density measured by 890 GHz HCN laser interferometer. The results show that the probe diagnosis results have the same trend as the laser diagnosis results. The line integral electron density measured by SP is 0.8 times higher than that measured by the HCN interferometer.

ITER Toroidal Interferometer and Polarimeter (TIP) beam refraction in 3D density profiles

Calculations of the expected refraction of the five ITER Toroidal Interferometer and Polarimeter (TIP) chords are presented for a range of conditions including high-density axisymmetric, ELMing H-mode cases and shattered pellet disruption mitigation cases. The calculations are carried out with a newly developed ray tracing code capable of following TIP’s 10.59μm laser beams through arbitrary 3D electron density profiles. Using JOREK simulations of ELM density perturbations in a 15MA ITER baseline plasma, it is shown that refraction from ELMs is expected to be negligible. It is found, however, that TIP interferometers will be able to clearly resolve the line-integrated density perturbation from ELMs and contribute to the ITER measurement requirement “14. H-mode, ELMs and L-H mode transition indicator”. Calculations of the expected refraction in a NIMROD simulated shattered pellet disruption mitigation scenario with peak local electron densities of ne=3.7×1021 m−3 (max line-averaged densities of navg=1.3×1021 m−3) also show tolerable refraction and it is likely that most, if not all chords, would avoid signal loss. For both axisymmetric and structured plasmas with line-averaged densities in the mid to upper 1021 m−3 range, values likely present only during disruption mitigation, refraction becomes significant and could limit the ability of TIP to make reliable density measurements.

Local current shrinkage induced by the MARFE in L mode discharges on EAST tokamak

In this study, the multifaceted asymmetric radiation from the edge (MARFE) was observed in high-density discharges or during impurity gas injection on the EAST tokamak. The MARFE onset indicated by spectral and radiation signals can also be detected by the POlarimeter-INTerferometer (POINT) diagnostic, which measures the horizontal line-integrated density and the Faraday rotation. The fluctuation amplitude of the density signal resulting from the MARFE oscillation increases with the edge safety factor, which is consistent with the thermal instability theory. By combining density and the Faraday rotation, the local current shrinkage in the MARFE region is observed during the MARFE movement. The density and the current profile calculated by the POINT become more peak during the MARFE, which may lead to a strong magnetohydrodynamic instability that can result in disruption.

The line integrated density measurement by using a frequency sweep interferometer

Frequency modulated continuous wave (FMCW) reflectometer has been widely used to measure the plasma density profile by launching linear frequency modulated microwave into the plasma and measuring the group delay of the microwave reflected at the cutoff density. For a certain frequency range, the microwave just passes through the plasma and reflects back from the vacuum inner wall. By analyzing the phase information of the passing-through microwave, the line integrated density (LID) can be obtained. An FMCW reflectometer operating in this particular regime is called a frequency sweep interferometer (FSI). If the microwave frequency is much higher than the plasma frequency, the group delay of FSI is directly proportional to the LID. This is why a THz interferometer is needed for high density plasma diagnostics in fusion experiments. For a frequency range slightly above the plasma frequency, the FSI measurements depend not only on the LID but also on the details of the plasma density profile. It is analytically shown that the group delay of FSI can be expanded as a Taylor series of inverse frequency squares. The coefficients of the Taylor series correspond to the multiple moments of LID. Therefore LID can be obtained by polynomial fitting the group delay as a function of inverse frequency squares even if the microwave frequency is not much higher than the plasma frequency. This algorithm is tested by simulating the response of the FSI to the given density profile as sweeping the microwave frequency over wide ranges. This algorithm works well even if the microwave frequency is just 3–4 times higher than the plasma frequency and it can be applied for the steady state plasmas.

Measurement of 2D density profiles using a second-harmonic, dispersion interferometer.

A second-harmonic, dispersion interferometer is used to image large-area (≃5cm2) plasma-jet and gas-jet density profiles. Achromatic telescopes magnify the diameters of the primary-laser beam (1064nm) and its second-harmonic (532nm) before probing the sample and de-magnify the beam diameters after the sample, where the primary beam transfers its phase change to a second, second-harmonic beam, allowing the sample's dispersive-phase change to be measured between two, orthogonally polarized second harmonic beams. The telescopes produce an azimuthally symmetric, dispersive-phase shift in the sample + background phase-change image and in the background phase-change image, which is removed by digital subtraction. The interferometer's performance was verified using standard-optical components as dispersive elements (BK7 lenses and wedge plates), resolving a minimum, phase-change sensitivity of Δϕmin ≳ 15 mrad and spatial resolution of Δxres ≃ 100μm. The phase change produced by unknown-density objects (a pulsed-plasma-jet and a pulsed-gas-jet) was measured, and their data were used to recover the original, 2D density profiles using an inverse Abel transform: peak-number density, Ngas ≃ 6 × 1020cm-3 and Ne ≃ 5 × 1016cm-3; line-integrated density, ∫Ngasdl ∼ 2 × 1019cm-2 and ∫Nedl ∼ 1 × 1016cm-2. The techniques and methods developed here are scalable to even larger probe-beam diameters and frame-capture rates, leading to a diagnostic capability that is well-suited for applications involving the real-time measurement of density.

Electron density profile reconstruction with convolutional neural networks

Convolutional neural networks are introduced into reconstructing electron density profiles from line-integrated density measurements of interferometers in the EAST tokamak. Diagnostic data from the polarimeter/interferometer and the hydrogen cyanide interferometer diagnostic systems are integrated to improve the reconstruction performance. By training and optimization with unreliable measurements in the data set, the robustness of this algorithm is enhanced. The established model can predict the probability distribution of density profiles accurately, fast, and robustly to noise and interference. This algorithm is not restricted to specific equilibrium configurations and can be transferred easily between different fusion devices.

Validation of theory-based integrated modeling and new insights for a high-performance steady-state scenario with only RF heating on EAST

Theory-based integrated modeling is validated against high-performance steady-state core plasmas on EAST in the high poloidal beta (β p) regime with only RF heating. Reasonably good agreement between the modeling results and experimental measurements is obtained not only for the temperature profiles but also for the 11-chord line-integrated densities and Faraday angles for the first time. This validation effort demonstrates that the safety factor profiles can be non-reversed in high β p experiments on EAST. The inaccessibility for LH waves observed in conventional ray-tracing simulations for some high β p experiments is effectively mitigated by including the modeling of wave propagation in the scrape-off layer. The observed confinement improvement with density increasing (Gong et al 2019 Nucl. Fusion 59 086030) can be attributed to the reduction of turbulent transport by the collisional stabilization in trapped electron modes, rather than by the Shafranov shift stabilization effect which was proposed to be the major cause of confinement enhancement in previous literature. Based on the successful validation and newly gained physical insights, predictive modeling is performed for core plasma considering the future upgrade capacity of LH wave system and shows that the high-performance steady-state H-mode scenario on EAST can be extended to the regime with q 95 to be ITER relevant.

A quasi-optical microwave interferometer for the XuanLong-50 experiment

A quasi-optical Mach-Zehnder microwave interferometer operating at 140 GHz has been developed for the ENN's spherical tokamak XuanLong-50 (EXL-50), for the purposes of line-integral electron density measurement and plasma density real-time feedback control input. The EXL-50 is designed for long pulse operation (over 5 s) and the electron density of phase I is estimated below 1019 m-3. Thus, the well-known microwave interferometer is suitable for the advantage of cost effectiveness and good stability. One of the major errors of the interferometer is vibration. To reduce it, the entire interferometer is supported by sand-filled stainless-steel columns of 0.3 m inner diameter and the vibration modes are calculated by finite elements analysis. Other sources of error, such as noise and thermal drift, are carefully handled. To reduce noise, the interferometer including cables and digitizers are carefully shielded and grounded. The phase error due to source frequency thermal drift, manifested due to uneven probe beam and reference beam path lengths, is observed in long term operation and explained by model calculation. A continuous 100 s test shows that it is reduced to about 0.04 °/s when the Gunn oscillators are temperature controlled by Peltier coolers with the industrial Proportional-Integral-Derivative control method to maintain the frequency stability. The system has been in routine operation since August 2019, with 1016 m-2 line-integral density resolution. The technical details of the interferometer and experimental results are presented.

Homodyne interferometry using a phase rotator for calibration of sine-cosine phase detection of a 70GHz probe beam through a plasma.

Homodyne interferometry using a motorized phase rotator for calibration of sine-cosine detection of the phase shift of a 70 GHz probe beam through a plasma has been developed. Four interferometers based on this interferometry have been installed on the low aspect ratio torus experiment (LATE) device with four horizontal probe beams on the mid-plane, which has measured the line-integrated electron densities with a time resolution of 10 μs and a resolution of line-integrated density of 5 × 1015m-2.

First neutral beam experiments on Wendelstein 7-X

In the previous divertor campaign, the Wendelstein 7-X (W7-X) device injected 3.6 MW of neutral beam heating power allowing for the achievement of densities approaching 2 × 1020 m−3, and providing the first initial assessment of fast ion confinement in a drift optimized stellarator. The neutral beam injection (NBI) system on W7-X is comprised of two beam boxes with space for four radio frequency sources each. The 3.6 MW of heating reported in this work was achieved with two sources in the NI21 beam box. The effect of combined electron-cyclotron resonance heating (ECRH) and NBI was explored through a series of discharges varying both NBI and ECRH power. Discharges without ECRH saw a linear increase in the line-integrated plasma density, and strong peaking of the core density, over the discharge duration. The presence of 1 MW of ECRH power was found to be sufficient to control a continuous density rise during NBI operation. Simulations of fast ion wall loads were found to be consistent with experimental infrared camera images during operation. In general, NBI discharges were free from the presence of fast ion induced Alfvénic activity, consistent with low beam betas. These experiments provide data for future scenario development and initial assessment of fast-ion confinement in W7-X, a key topic of the project.

Phase contrast imaging measurements and numerical simulations of turbulent density fluctuations in gas-fuelled ECRH discharges in Wendelstein 7-X

The fundamental nature of turbulent density fluctuations in standard Wendelstein 7-X (W7-X) stellarator discharges is investigated experimentally via phase contrast imaging (PCI) in combination with gyrokinetic simulations with the code GENE. We find that density fluctuations are ion-temperature-gradient-driven and radially localised in the outer half of the plasma. It is shown that the line-integrated PCI measurements cover the right range of wavenumbers and a favourable toroidal and poloidal location to capture some of the strongest density fluctuations in W7-X. Due to the radial localisation of fluctuations, measured wavenumber–frequency spectra exhibit a dominant phase velocity, which can be related to the$\boldsymbol {E\times B}$rotation velocity at the radial position of a well in the neoclassical radial electric field. The match is robust against variations of heating power and line-integrated density, which is partly due to the localisation of fluctuations and partly due to effects of the radial gradient in the$\boldsymbol {E\times B}$velocity profile on the wavenumber–frequency spectrum. The latter effect is studied with a newly built synthetic PCI diagnostic and global gyrokinetic simulations with GENE-3D.