Line-integrated Measurements Research Articles

Validating and speeding up x-ray tomographic inversions in tokamak plasmas

X-ray tomography is a precious tool in tokamaks that provides rich information about the core plasma, such as local impurity concentration, electron temperature and density as well as magnetic equilibrium (ME) and magnetohydrodynamic activity. Nevertheless, inferring the local plasma emissivity from a sparse set of line-integrated measurements is an ill-posed problem that requires dedicated regularization and validation methods. Besides, speeding up the inversion algorithm in order to be compatible with real-time control systems is a challenging task with traditional approaches. In this contribution, in a first part we introduce tools aiming at validating and speeding up the x-ray tomographic inversions based on Tikhonov regularization, including ME constraint and parameter optimization, taking the WEST geometry as an example. In a second part, an alternative approach compatible with real-time, based on a set of neural networks is proposed and compared with the Tikhonov approach for an experimental case.

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.

Localized phase contrast imaging at the Wendelstein 7-X stellarator

In its basic form, phase contrast imaging (PCI) provides line-integrated measurements of electron density fluctuations in plasmas. As turbulent fluctuations in magnetically confined plasmas have wave vectors almost perpendicular to the background magnetic field, the signals scattered by fluctuations from different parts of the PCI line-of-sight (LoS) are spatially separated in focal planes of the plasma. This allows localized PCI measurements by placing a mask in such a plane, to only permit signals from specific parts of the LoS to reach the PCI detectors. The present paper describes modeling and design of localization masks for the PCI system at the Wendelstein 7-X (W7-X) stellarator as well as the first results obtained using the masks in the recent long-pulse W7-X experimental campaign. During this project, we have extended the theory describing the mask response within the Fraunhofer diffraction model. As a novel development, we show from first principles that the mask response is determined by the fraction of power of the scattered beam spots that passes the mask. These insights have been used to select the W7-X mask design, consisting of a circular cutout, allowing the unscattered beam spot to pass the mask, with wedges covering a fixed angular range outside the central cutout. In the recent W7-X experimental campaign, the masks have verified the location of the main turbulence features observed by the PCI system and provided new information about the location of short-wavelength magnetohydrodynamic modes.

Electron and ion temperature measurement with a new x-ray imaging crystal spectrometer on WEST.

A new x-ray imaging crystal spectrometer (XICS) has been installed, aligned, and used during experimental campaigns on the WEST tokamak. It has three interchangeable crystals for measuring the Ar XVII, Ar XVIII, and Fe XXV spectra, respectively. A patented rotating table holding the crystals is used to monitor the crystal facing the plasma remotely and without changing the position of the camera. Here, the focus is made on the Ar XVII spectrum, between 3.93 and 4.00 Å. The design of the diagnostic is presented, and a synthetic diagnostic, implemented with the Python library ToFu, is used to show the instrument's operational performance and limits. The instrument function exhibits the following two main features: a distortion for the Ar XVII spectrum, presumably due to the crystal manufacturing in two parts, and the measurement of three W spectral lines on the Ar XVI spectrum. Line of sight-integrated profiles of the electron and ion temperatures are thus extracted from the Ar XVII spectrum from two distinct spectral line ratios and from the Doppler broadening, respectively. The bremsstrahlung emission and the W line measurements are the two main limitations to compute the electron temperature. Tomographic inversions are also implemented with the library ToFu and used in order to obtain the local electron and ion temperature profiles, which are compared to other measurements from the WEST ECE (electron cyclotron emission) diagnostic. It is shown that both the XICS line-integrated and ECE Te measurements are in better agreement. Systematic differences are shown between the electron temperature profiles calculated from the two available line ratios.

Measurement of ion temperature and toroidal flow during magnetic reconnection with a large guide field

Ion temperature and toroidal flow along the guide field direction are measured using a new ion tomographic diagnostic on the Magnetic Reconnection eXperiment (MRX) during magnetic reconnection with a guide field strength of about 1.4 and 2.1 times the strength of the reconnecting component. Strong toroidal flows, beyond what has been measured in anti-parallel and lower guide field conditions on MRX, are observed. Sustained ion heating with no discernible structure within the measurement region is also observed. Probe measurements including Langmuir and Mach probe measurements are made to support the tomographic inversion of line-integrated measurements, as well as to provide local measurements of plasma parameters. Measurements of toroidal velocity and ion temperature are supported with time series data. Energy flow into and out of the X-line region is estimated using a guiding center framework and presented in the Appendix of this manuscript, suggesting an outsized role played by parallel electric field in energizing ions. The guiding center approximation is not well satisfied in the region of interest; however, the estimates provide a springboard for future, further experimentation.

Characterization of cesium and H−/D− density in the negative ion source SPIDER

The Heating Neutral Beam Injectors (HNBs) for ITER will have to deliver 16.7 MW beams of H/D particles at 1 MeV energy. The beams will be produced from H−/D− ions, generated by a radiofrequency plasma source coupled to an ion acceleration system. A prototype of the ITER HNB ion source is being tested in the SPIDER experiment, part of the ITER Neutral Beam Test Facility at Consorzio RFX. Reaching the design targets for beam current density and fraction of coextracted electrons is only possible by evaporating cesium in the source, in particular on the plasma facing grid (PG) of the acceleration system. In this way the work function of the surfaces decreases, significantly increasing the amount of surface reactions that convert neutrals and positive ions into H−/D−. It is then of paramount importance to monitor the density of negative ions and the density of Cs in the proximity of the PG. Monitoring the Cs spatial distribution along the PG is also essential to guarantee the uniformity of the beam current. In SPIDER, this is possible thanks to the Cavity Ringdown Spectroscopy (CRDS) and the Laser absorption Spectroscopy diagnostics (LAS), which provide line-integrated measurements of negative ion density and neutral, ground state Cs density, respectively. The paper discusses the CRDS and LAS measurements as a function of input power and of the magnetic and electric fields used to reduce the coextraction of electrons. Negative ion density data are in qualitative agreement with the analogous measurements in Cs-free conditions. In agreement with simulations, Cs density is peaked in the center of the source; a top/bottom non uniformity is also present. Several effects of plasma on Cs deposition and negative ion production are presented.

Regressive Tomography and Direct Regressive Reconstruction: A Research Note

Two related methods for inverting line-integrated measurements are presented in this research paper in the context of the recent deuterium-tritium experiments in the JET tokamak. Unlike traditional methods of tomography, these methods rely on making use of a family of model distributions defining a functional space within which a solution of the inversion problem is expected to exist. This is a stronger assumption than that underlying traditional methods of tomography and requires that suitable models for the expected distribution be available. In return, the methods offer computationally efficient and robust reconstructions. Regressive tomography, as applied to the data from the JET neutron cameras, involves calculating a set of 100 or more two-dimensional (2-D) neutron emission distributions in a representative variety of conditions using the ASCOT and AFSI Monte Carlo fast ion orbit and fusion reaction codes. The distributions are line integrated to represent synthetic measurements from the 19 channels of this two-camera system. An inversion matrix is then obtained by regressing the 2-D distributions corresponding to each of the voxels against these line integrals. The second method, direct regressive reconstruction, bypasses the calculation of line integrals altogether by regressing experimental camera data against calculated neutron emission distributions. This method does not require the cameras to be calibrated, not even relatively between channels. The inversion matrices obtained by any of the two methods can then be used to provide neutron emission profiles for which ASCOT/AFSI calculations are not available.

High-fidelity inference of local impurity profiles in C-2W using Bayesian tomography.

In C-2W (also called "Norman") [1], beam-driven field reversed configuration plasmas embedded in a magnetic mirror are produced and sustained in a steady state. A multi-chord passive Doppler spectroscopy diagnostic provides line-integrated impurity emission measurements near the center plane of the confinement vessel with fast time resolution. The high degree of plasma non-uniformity across optical sightlines can preclude direct fitting of the measured line-integrated spectra. To overcome this challenge, local impurity profiles are inferred using Bayesian tomography, a superior analysis technique based on a complete forward model of the diagnostic. The measured emission of O4+ triplet lines near 278.4nm is modeled assuming two independent populations: thermal and beam ions. Gaussian processes are used to generate and infer local profiles. The inference incorporates details of the geometrical arrangement of the diagnostic, instrument function, intensity calibration, and a noise model. Markov chain Monte Carlo (MCMC) sampling of the posterior distribution of solutions provides high-fidelity uncertainty estimates. The reconstructed O4+ impurity profiles are consistent with data from other diagnostics and show good agreement with expected physics based on previously developed models of biasing circuit and impurity transport.

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.

Mm-wave polarimeter and profilometry design study for retrieving plasma density in the PANDORA experiment

In the recent past, the possibility to use a superconducting trap confining a hot and dense plasma as a tool to investigate radioactivity in astrophysical scenarios has been proposed. Making possible these kind of unprecedented measurements is the main aim of the PANDORA (Plasmas for Astrophysics Nuclear Decays Observation and Radiation for Archaeometry) project. In this context, it is planned to build a compact and flexible magnetic plasma trap where plasma reaches an electron density ne ∼ 1011–1013 cm−3, and an electron temperature, in units of kT, kTe ∼ 0.1–30 keV. The setup is conceived to be able to measure, for the first time, nuclear β-decay rates in stellar-like conditions in terms of ionization states. In this paper, the design study of a mm-wave polarimeter for the PANDORA plasma line-integrated electron density measurement is presented. The paper highlights the method of this type of measurements for the first time proposed for a magneto-plasma trap which represents an “intermediate” case between the ultra-compact plasma ion sources and the large-size thermonuclear fusion devices. Preliminary measurements at scaled microwave frequencies have carried out both on a “free-space” setup by using a wire-grid polarizer and a rotable Ka-band OMT + horn antennas system, and on a compact trap (called Flexible Plasma Trap) installed at INFN-LNS and used as PANDORA down-sized testbench are described. The polarimeter technique will support β-decay investigation by simultaneous measurements of the total plasma density, which is crucial to carefully evaluate the decay-constant and to extrapolate the laboratory observed data to the astrophysical scenarios. Moreover, this work proposes to adopt an electromagnetic inverse-scattering-based technique-based method to retrieve the electron density profile along the probing antennas line-of-sight. Numerical results of this so-called “inverse profilometry” are also shown.

Characterization of Cs-free negative ion production in the ion source SPIDER by cavity ring-down spectroscopy

The neutral beam injectors of the ITER experiment will be based on negative ion sources for the generation of beams composed by 1 MeV H/D particles. The prototype of these sources is currently under testing in the SPIDER experiment, part of the Neutral Beam Test Facility of Consorzio RFX, Padua, Italy. Among the targets of the experimentation in SPIDER, it is of foremost importance to maximize the beam current density produced by the accelerator. The SPIDER operating conditions can be optimized thanks to a cavity ring-down spectroscopy diagnostic, which provides line-integrated measurements of negative ion density in proximity of the accelerator apertures. The specific implementation in SPIDER shows a drift in ring down time measurements, which develops in a time scale of few hours, thus possibly affecting the negative ion density estimates in plasma pulses of 1 h duration, as required by ITER. Possible causes and solutions are discussed. Regarding the source performance, this paper presents how negative ion density is influenced by the RF power used to sustain the plasma, and by the magnetic filter field present in SPIDER to limit the amount of co-extracted electrons. In this study, SPIDER was operated in hydrogen and deuterium, in Cs-free conditions.

Enteric methane emission estimates for Kenyan cattle in a nighttime enclosure using a backward Lagrangian Stochastic dispersion technique

This study provides methane (CH4) emission estimates for mature female African beef cattle in a semi-arid region in Southern Kenya using open-path laser spectroscopy together with a backward Lagrangian Stochastic (bLS) dispersion modeling technique. We deployed two open-path lasers to determine 10-min averages of line-integrated CH4 measurements upwind and downwind of fenced enclosures (so-called bomas: a location where the cattle are gathered at night) during 14 nights in September/October 2019. The measurements were filtered for wind direction deviations and friction velocity before the model was applied. We compared the obtained emission factors (EFs) with the Intergovernmental Panel on Climate Change (IPCC) Tier 1 estimates for the Sub-Saharan African (SSA) countries, which were mostly derived from studies carried out in developed countries and adapted to the conditions in Africa. The resulting EF of 75.4 ± 15.99 kg year−1 and the EFs calculated from other studies carried out in Africa indicate the need for the further development of region-specific EFs depending on animal breed, livestock systems, feed quantity, and composition to improve the IPCC Tier 1 estimates.

Measurement error due to self-absorption in calibration-free laser-induced breakdown spectroscopy

Self-absorption of spectral lines is known to lower the performance of analytical measurements via calibration-free laser-induced breakdown spectroscopy. However, the error growth due to this effect is not clearly assessed.Here we propose a method to quantify the measurement error due to self-absorption based on the calculation of the spectral radiance of a plasma in local thermodynamic equilibrium. Validated through spectroscopic measurements for a binary alloy thin film of compositional gradient, the method evidences that measurement performance lowering due to self-absorption depends on the spectral shape of the analytical transition and on the intensity measurement method. Thus, line-integrated intensity measurements of Stark broadened lines enable accurate analysis, even at large optical thickness, if line width and plasma size are precisely known. The error growth due to self-absorption is significantly larger for line shapes dominated by Doppler broadening and for line-center intensity measurements. The findings present a significant advance in compositional measurements via calibration-free laser-induced breakdown spectroscopy, as they enable straightforward selection of most appropriate analytical lines.

Implementing an X-ray tomography method for fusion devices

In fusion devices, the X-ray plasma emissivity contains essential information on the magnetohydrodynamic activity, the magnetic equilibrium and on the transport of impurities, in particular for tokamaks in the soft X-ray (SXR) energy range of 0.1–20 keV. In this context, tomography diagnostics are a key method to estimate the local plasma emissivity from a given set of line-integrated measurements. Unfortunately, the reconstruction problem is mathematically ill-posed, due to very sparse and noisy measurements, requiring an adequate regularization procedure. The goal of this paper is to introduce, with a didactic approach, some methodology and tools to develop an X-ray tomography algorithm. Based on a simple 1D tomography problem, the Tikhonov regularization is described in detail with a study of the optimal reconstruction parameters, such as the choice of the emissivity spatial resolution and the regularization parameter. A methodology is proposed to perform an in situ sensitivity and position cross-calibration of the detectors with an iterative procedure, by using the information redundancy and data variability in a given set of reconstructed profiles. Finally, the basic steps to build a synthetic tomography diagnostics in a more realistic tokamak environment are introduced, together with some tools to assess the capabilities of the 2D tomography algorithm.

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.

Development and first operation of a cavity ring down spectroscopy diagnostic in the negative ion source SPIDER.

The neutral beam injectors of the ITER experiment will rely on negative ion sources to produce 16.7MW beams of H/D particles accelerated at 1MeV. The prototype of these sources was built and is currently operated in the SPIDER (Source for the Production of Ions of Deuterium Extracted from a Radio frequency plasma) experiment, part of the Neutral Beam Test Facility of Consorzio RFX, Padua. In the SPIDER, the H-/D- ion source is coupled to a three grid, 100 kV acceleration system. One of the main goals of the experimentation in SPIDER is to uniformly maximize the extracted current density; to achieve this, it is important to study the density of negative ions available in the proximity of the ion acceleration system. In SPIDER, line-integrated measurements of negative ion density are performed by a cavity ring down spectroscopy diagnostic. Its principle of operation is based on the absorption of the photons of a laser beam pulse by H-/D- photo-detachment; the absorption detection is enhanced by trapping the laser pulse in an optical cavity, containing the absorbing medium (i.e., negative ions). This paper presents and discusses the CRDS diagnostic setup in the SPIDER, including the first measurements of negative ion density, correlated with the main source parameters.

Inversion technique to obtain local ion temperature profiles for an axisymmetric plasma with toroidal and radial velocities

A matrix inversion technique is derived to calculate local ion temperature from line-integrated measurements of an extended emission source in an axisymmetric plasma which exactly corrects for both toroidal velocity and radial velocity components. Local emissivity and toroidal velocity can be directly recovered from line-integrated spectroscopic measurements, but an independent measurement of the radial velocity is necessary to complete the temperature inversion. The extension of this technique to handle the radial velocity is relevant for magnetic reconnection and merging compression devices where temperature inversion from spectroscopic measurements is desired. A simulation demonstrates the effects of radial velocity on the determination of ion temperature.

EMC3-EIRENE simulation of first wall recycling fluxes in W7-X with relation to H-alpha measurements

In the Wendelstein 7-X stellarator, the main locations of particle sources are expected to be the carbon divertors, baffles and graphite heat shield first wall. In this paper, the heat shield is implemented in EMC3-EIRENE to understand the expected areas and magnitudes of the recycling flux to this component. It is found that in the simulation the heat shield is not a significant source of recycling neutrals. The areas of simulated recycling flux are shown to correlate well with footprints of plasma-wetting seen in post-experimental campaign in-vessel inspection photos. EMC3-EIRENE reconstruction of line-integrated H-alpha measurements at the heat shield indicate that the majority of emission does not come from local recycling neutrals. Rather, the H-alpha signals at the heat shield are dominated by ionization of neutrals which have leaked from the divertor/baffle region into the midplane. The magnitude of the H-alpha line emission from the synthetic reconstruction is consistent with the experiment, indicating that a large overestimation of heat shield recycling would occur if these measurements were assumed to be from local recycling sources. In the future, it may be possible to obtain some information of local recycling from the heat shield since it was found that the majority of the recycling flux occurs on two well-localized areas.

Plasma parameter profile inference from limited data utilizing second-order derivative priors and physic-based constraints

A Bayesian framework has been used to improve the quality of inferred plasma parameter profiles. An integrated data analysis allows for coherent combinations of different diagnostics, and Gaussian process regression provides a reliable regularization process and systematic uncertainty estimation. In this paper, we propose a new profile inference framework that utilizes our prior knowledge about plasma physics, along with integrated data analysis and a Gaussian process. In order to facilitate the use of the Markov chain Monte Carlo sampling, we use a Gaussian process to define quantities corresponding to the second derivatives of the profiles. We validate the analysis technique by using a synthetic one-dimensional plasma, in which the transport properties are known and demonstrate that the proposed analysis technique can infer plasma parameter profiles from line-integrated measurements only. Furthermore, we can even infer unknown parameters in our physics models when our physics knowledge on the system is incomplete. This analysis framework is applicable to laboratory plasmas and provides a means to investigate plasma parameters, to which standard diagnostics are not directly sensitive.

Ammonia emissions from an uncovered dairy slurry storage tank over two years: Interactions with tank operations and meteorological conditions

The storage of slurry substantially contributes to the ammonia (NH3) released from livestock production. This study quantified farm-scale NH3 emissions from a circular open tank storing dairy cow slurry by means of continuous measurements over two years. Emissions were determined by scaling the product of line-integrated concentration measurements across the tank and wind speed measurements at 10 m height. The resulting data were calibrated to emissions determined using the integrated horizontal flux method. The data analysis was structured according to the main influencing factors: natural crust and meteorological conditions. The average annual emission was 0.065 g NH3 m−2 h−1 with a maximum of 1.67 g NH3 m−2 h−1. Annual emissions scaled to total ammoniacal nitrogen (TAN) were 3.3% of the TAN flow into the store. A natural crust on the slurry surface, which was strongly affected by agitation of the tank, diminished the gas release. An increasing time span after agitation led to correspondingly lower emissions. A greater filling level enhanced crust formation and induced an additional drop in emissions. Precipitation reduced emissions by 64%–86% compared to dry weather conditions. Higher wind speed and temperatures increased emissions. The emissions were highest in periods with weak or no crusting of the slurry surface, which covered 40% of the study time, but produced 61% of total emissions. The response of NH3 emissions to the interactions of influencing factors, which might vary considerably between stores, suggests that these factors require consideration for the determination of emission factors used for inventory reporting.