Fluctuation Diagnostics Research Articles

Real-time confinement regime detection in fusion plasmas with convolutional neural networks and high-bandwidth edge fluctuation measurements

A real-time detection of the plasma confinement regime can enable new advanced plasma control capabilities for both the access to and sustainment of enhanced confinement regimes in fusion devices. For example, a real-time indication of the confinement regime can facilitate transition to the high-performing wide-pedestal (WP) quiescent H-mode, or avoid unwanted transitions to lower confinement regimes that may induce plasma termination. To demonstrate real-time confinement regime detection, we use the 2D beam emission spectroscopy (BES) diagnostic system to capture localized density fluctuations of long wavelength turbulent modes in the edge region at a 1 MHz sampling rate. BES data from 330 discharges in either L-mode, H-mode, quiescent H (QH)-mode, or WP QH-mode were collected from the DIII-D tokamak and curated to develop a high-quality database to train a deep-learning classification model for real-time confinement detection. We utilize the 6×8 spatial configuration with a time window of 1024 µs and recast the input to obtain spectral-like features via fast Fourier transform preprocessing. We employ a shallow 3D convolutional neural network for the multivariate time-series classification task and utilize a softmax in the final dense layer to retrieve a probability distribution over the different confinement regimes. Our model classifies the global confinement state on 44 unseen test discharges with an average F 1 score of 0.94, using only ∼1 ms snippets of BES data at a time. This activity demonstrates the feasibility for real-time data analysis of fluctuation diagnostics in future devices such as ITER, where the need for reliable and advanced plasma control is urgent.

Gyrokinetic turbulence modeling of a high performance scenario in JT-60SA

Local gyrokinetic simulations are used to model turbulent transport for the first time in a representative high-performance plasma discharge projected for the new JT-60SA tokamak. The discharge features a double-null separatrix, 41 MW of combined neutral beam heating and electron cyclotron heating, and a high predicted ratio of the normalized plasma kinetic to magnetic pressure β. When considering input parameters computed from reduced transport models, gyrokinetic simulations predict a turbulent heat flux well below the injected 41 MW. Increasing the background gradients, on the other hand, can trigger a non-zonal transition (NZT), causing heat fluxes to no longer saturate. Furthermore, when considering fast ions in the simulations, a high-frequency mode is destabilized that substantially impacts the turbulence. The NZT is avoided by reducing the electron pressure by 10% below its nominal value, and the fast-ion resonance is removed by reducing the fast-ion temperature. The thus-obtained simulation features broadband frequency spectra and density and temperature fluctuation levels δn/n≈1% –2%, δT/T≈1% –6% that should be measurable with fluctuation diagnostics planned for JT-60SA. The temperature profile is fixed by the critical main-ion temperature gradient as a consequence of the high stiffness; heat fluxes increase by a factor of ten when increasing the main ion temperature gradient by 17%. Despite large gradients, it is demonstrated that, due to the large β, retaining compressional magnetic field fluctuations and in particular, the contribution of the pressure gradient in the ∇B drifts, is crucial to achieving non-zero heat fluxes.

Particle-hole asymmetric lifetimes promoted by nonlocal spin and orbital fluctuations in SrVO3 monolayers

The two-dimensional nature of engineered transition-metal ultrathin oxide films offers a large playground of yet to be fully understood physics. Here, we study pristine ${\mathrm{SrVO}}_{3}$ monolayers that have recently been predicted to display a variety of magnetic and orbital orders. We find that nonlocal magnetic (orbital) fluctuations lead to a strong (weak to moderate) momentum differentiation in the self-energy, particularly in the scattering rate. In the one-band 2D Hubbard model, momentum selectivity on the Fermi surface (``$k={k}_{F}$'') is known to lead to pseudogap physics. Here instead, in the multiorbital case, we evidence a differentiation between momenta on the occupied (``$k<{k}_{F}$'') and the unoccupied side (``$k>{k}_{F}$'') of the Fermi surface. Based on the dynamical vertex approximation, and introducing a ``binaural fluctuation diagnostics'' tool, we advance the understanding of spectral signatures of nonlocal fluctuations. Our work calls to (re)examine ultrathin oxide films and interfaces with methods beyond dynamical mean-field theory and may point to correlation-enhanced thermoelectric effects.

An FFT overlap method for high bandwidth far-infrared laser Interferometer in HL-2A

A novel Real-Time High Bandwidth Phasemeter (RHBP) system has been developed for far-infrared laser interferometer in HL-2A tokamak. To meet the requirement of high-precision electron density fluctuation diagnostics, the system is based on the FFT overlap method, which can suppress the measurement error in high-bandwidth mode. The system consists of four Real-time Signal Conditioning (RSC) Modules and four RHBP Modules for high spatial resolution. Benefiting from the field-programmable gate array (FPGA) platform, the proposed method can be implemented with low noise and low cost. Experimental results suggest that the density resolution is 1.79× 1015/m-3 in high-bandwidth mode, which indicates that the proposed RHBP system achieves high performance for high-frequency fluctuation measurement.

System-on-chip upgrade of millimeter-wave imaging diagnostics for fusion plasma.

Monolithic, millimeter wave "system-on-chip" technology has been employed in chip heterodyne radiometers in a newly developed Electron Cyclotron Emission Imaging (ECEI) system on the DIII-D tokamak for 2D electron temperature and fluctuation diagnostics. The system employs 20 horn-waveguide receiver modules each with customized W-band (75-110GHz) monolithic microwave integrated circuit chips comprising a W-band low noise amplifier, a balanced mixer, a ×2 local oscillator (LO) frequency doubler, and two intermediate frequency amplifier stages in each module. Compared to previous quasi-optical ECEI arrays with Schottky mixer diodes mounted on planar antennas, the upgraded W-band array exhibits >30 dB additional gain and 20× improvement in noise temperature; an internal eight times multiplier chain is used to provide LO coupling, thereby eliminating the need for quasi-optical coupling. The horn-waveguide shielding housing avoids out-of-band noise interference on each module. The upgraded ECEI system plays an important role for absolute electron temperature and fluctuation measurements for edge and core region transport physics studies. An F-band receiver chip (up to 140GHz) is under development for additional fusion facilities with a higher toroidal magnetic field. Visualization diagnostics provide multi-scale and multi-dimensional data in plasma profile evolution. A significant aspect of imaging measurement is focusing on artificial intelligence for science applications.

Ab initio phonon self-energies and fluctuation diagnostics of phonon anomalies: Lattice instabilities from Dirac pseudospin physics in transition metal dichalcogenides

We present an ab initio approach for the calculation of phonon self-energies and their fluctuation diagnostics, which allows us to identify the electronic processes behind phonon anomalies. Application to the transition-metal-dichalcogenide monolayer 1H-TaS$_2$ reveals that coupling between the longitudinal-acoustic phonons and the electrons from an isolated low-energy metallic band is entirely responsible for phonon anomalies such as the mode softening and associated charge-density waves observed in this material. Our analysis allows us to distinguish between different mode-softening mechanisms including matrix-element effects, Fermi-surface nesting, and Van Hove scenarios. We find that matrix-element effects originating from a peculiar type of Dirac pseudospin textures control the charge-density-wave physics in 1H-TaS$_2$ and similar transition metal dichalcogenides.

Fluctuation diagnostics of the finite-temperature quasi-antiferromagnetic regime of the two-dimensional Hubbard model

We study the finite temperature Fermi-liquid to non-Fermi-liquid crossover in the 2D Hubbard model for a range of dopings using the self-consistent ladder dual fermion method. We consider relatively high temperatures where we identify a suppression of the density of states near the Fermi level caused by a quasi-antiferromagnetic behaviour that is itself characterized by a long, but finite, correlation length scale. We perform fluctuation diagnostics to decompose the single-particle self energy into scattering $q$-vector and bosonic frequency contributions. Within this framework we find that the key contributions to the single-particle self energy that give non-Fermi-liquid character, even at weak coupling, are caused by relatively sharp $q=(\pi,\pi)$ spin fluctuations, while the decomposition in the bosonic frequency channel shows a complicated dependence on the relative strengths of zero, positive and negative frequency contributions. Finally, variation in density suggests that the tendency towards non-Fermi-liquid behavior is not substantially different for electron or hole doped systems.

Dynamical charge susceptibility in the Hubbard model

We compute the dynamical charge susceptibility in the two-dimensional Hubbard model within the dynamical cluster approximation. In order to understand the connection between charge susceptibility and pseudogap, we investigate the momentum, doping, and temperature dependence. We find that as a function of frequency, the dynamical charge susceptibility is well represented by a single peak at a characteristic frequency. It shows little momentum or temperature dependence, while the doping dependence is more evident, and no clear signature of the pseudogap is observed. Data for the doping evolution of the static susceptibility and for fluctuation diagnostics are presented. Our susceptibilities should be directly measurable in future Momentum-resolved electron energy-loss spectroscopy experiments.

Experimental characterization of the effect of E × B shear on edge-harmonic oscillation mode structure

The edge-harmonic oscillation (EHO) mode is one of the characteristic modes that provides an edge transport channel during high-confinement ELM-free phase (the so-called Quiescent High-confinement phase). Recent theoretical work and extensive experimental observations have suggested that the large rotational E × B shear is the key to destabilize an EHO. As the eigenmode grows to large amplitude, it will exert a drag on the rotation, resulting in EHO’s saturation (Snyder et al 2007 Nucl. Fusion 47 961). However, detailed mechanisms concerning this process remain vague. We have performed continuous tracking on how the E × B shear affects the EHO mode structure to search for a possible explanation of the saturation mechanism. Two edge density fluctuation diagnostics are employed to observe the eigenmode structure evolution of EHO in the pedestal region in the radial and poloidal directions, respectively. Our results show that the EHO mode’s radial wavenumber is strongly correlated with the E × B shear rate, while the poloidal wavenumber is unaffected by the E × B shear rate. During the EHO existence, with the E × B shearing rate ramping down, the radial wavenumber is also observed to be decreasing.

Complementary views on electron spectra: From fluctuation diagnostics to real-space correlations

We study the relation between the microscopic properties of a many-body system and the electron spectra, experimentally accessible by photoemission. In a recent paper [Phys. Rev. Lett. 114, 236402 (2015)], we introduced the "fluctuation diagnostics" approach, to extract the dominant wave vector dependent bosonic fluctuations from the electronic self-energy. Here, we first reformulate the theory in terms of fermionic modes, to render its connection with resonance valence bond (RVB) fluctuations more transparent. Secondly, by using a large-U expansion, where U is the Coulomb interaction, we relate the fluctuations to real space correlations. Therefore, it becomes possible to study how electron spectra are related to charge, spin, superconductivity and RVB-like real space correlations, broadening the analysis of an earlier work [Phys. Rev. B 89, 245130 (2014)]. This formalism is applied to the pseudogap physics of the two-dimensional Hubbard model, studied in the dynamical cluster approximation. We perform calculations for embedded clusters with up to 32 sites, having three inequivalent K-points at the Fermi surface. We find that as U is increased, correlation functions gradually attain values consistent with an RVB state. This first happens for correlation functions involving the antinodal point and gradually spreads to the nodal point along the Fermi surface. Simultaneously a pseudogap opens up along the Fermi surface. We relate this to a crossover from a Kondo-like state to an RVB-like localized cluster state and to the presence of RVB and spin fluctuations. These changes are caused by a strong momentum dependence in the cluster bath-couplings along the Fermi surface. We also show, from a more algorithmic perspective, how the time-consuming calculations in fluctuation diagnostics can be drastically simplified.

Parquet decomposition calculations of the electronic self-energy

The parquet decomposition of the self-energy into classes of diagrams, those associated with specific scattering processes, can be exploited for different scopes. In this work, the parquet decomposition is used to unravel the underlying physics of non-perturbative numerical calculations. We show the specific example of dynamical mean field theory (DMFT) and its cluster extensions (DCA) applied to the Hubbard model at half-filling and with hole doping: These techniques allow for a simultaneous determination of two-particle vertex functions and self-energies, and hence, for an essentially "exact" parquet decomposition at the single-site or at the cluster level. Our calculations show that the self-energies in the underdoped regime are dominated by spin scattering processes, consistent with the conclusions obtained by means of the fluctuation diagnostics approach [Phys. Rev. Lett. 114, 236402 (2015)]. However, differently from the latter approach, the parquet procedure displays important changes with increasing interaction: Even for relatively moderate couplings, well before the Mott transition, singularities appear in different terms, with the notable exception of the predominant spin-channel. We explain precisely how these singularities, which partly limit the utility of the parquet decomposition, and - more generally - of parquet-based algorithms, are never found in the fluctuation diagnostics procedure. Finally, by a more refined analysis, we link the occurrence of the parquet singularities in our calculations to a progressive suppression of charge fluctuations and the formation of an RVB state, which are typical hallmarks of a pseudogap state in DCA.

Fluctuation Diagnostics of the Electron Self-Energy: Origin of the Pseudogap Physics.

We demonstrate how to identify which physical processes dominate the low-energy spectral functions of correlated electron systems. We obtain an unambiguous classification through an analysis of the equation of motion for the electron self-energy in its charge, spin, and particle-particle representations. Our procedure is then employed to clarify the controversial physics responsible for the appearance of the pseudogap in correlated systems. We illustrate our method by examining the attractive and repulsive Hubbard model in two dimensions. In the latter, spin fluctuations are identified as the origin of the pseudogap, and we also explain why d-wave pairing fluctuations play a marginal role in suppressing the low-energy spectral weight, independent of their actual strength.

Grating spectrometer system for beam emission spectroscopy diagnostics using high-energy negative-ion-based neutral beam injection on LHD

A beam emission spectroscopy (BES) system was developed for density gradient and fluctuation diagnostics in the Large Helical Device (LHD). In order to cover the large Doppler shift of the Hα beam emission because of the high-energy negative-ion-based neutral beam atom (acceleration voltage V(acc)=90-170 kV) and the large motional Stark splitting due to the large v×B field (magnetic field B=3.0 T), a grating spectrometer was used instead of a conventional interference filter system. The reciprocal linear dispersion is about 2 nm/mm, which is sufficient to cover the motional Stark effect spectra using an optical fiber with a diameter of 1 mm.

Overview of LHD Plasma Diagnostics

The Large Helical Device (LHD) is the world’s largest heliotron-type device with l = 2, m = 10 continuous superconducting helical coils and three pairs of superconducting poloidal coils. The major and minor radii of the plasma are 3.6 to 3.9 and 0.6 to 0.65 m, respectively. A plasma with an elliptic cross section confined in the helical magnetic field rotates poloidally along the magnetic axis and has no axial symmetry. For the installation of various kinds of diagnostic instruments, large-sized ports are equipped. The diameter of the largest horizontal ports is 2410 mm, which enables us to easily access the full plasma cross section with multichannel viewing chords aligned parallel to one another. For the precise measurement of plasma quantities in a three-dimensional helical plasma, an extensive set of diagnostics has been developed with national and international collaborators and is routinely operated in LHD. The diagnostic system now consists of [approximately]50 measuring instruments and includes many challenging diagnostics that have been developed and operated for the study of LHD plasma confinement. These are classified as profile diagnostics, fluctuation diagnostics, and advanced diagnostics, some of which are selected for introduction in this article. In addition, diagnostics for the divertor and for energetic particles are discussed, along with topics that are somewhat unique to helical devices such as diagnosing three-dimensional phenomena and flux surface mapping. This large number of diagnostics in LHD rely on a data acquisition system that has broken world records for the amount of information accumulated in one shot. Finally, looking to the near future, countermeasures have been taken to protect diagnostics from the neutrons and gamma fluxes anticipated during deuterium-deuterium experiments, such as placing much of the diagnostic instrumentation behind a 2-m-thick concrete biological shield encompassing the LHD test cell.

Experiments with liquid metal walls: Status of the lithium tokamak experiment

Abstarct Liquid metal walls have been proposed to address the first wall challenge for fusion reactors. The lithium tokamak experiment (LTX) at the Princeton Plasma Physics Laboratory (PPPL) is the first magnetic confinement device to have liquid metal plasma-facing components (PFC's) that encloses virtually the entire plasma. In the current drive experiment-upgrade (CDX-U), a predecessor to LTX at PPPL, the highest improvement in energy confinement ever observed in ohmically heated tokamak plasmas was achieved with a toroidal liquid lithium limiter. The LTX extends this liquid lithium PFC by using a conducting conformal shell that almost completely surrounds the plasma. By heating the shell, a lithium coating on the plasma-facing side can be kept liquefied. A consequence of the low-recycling conditions from liquid lithium walls is the need for efficient plasma fueling. For this purpose, a molecular cluster injector is being developed. Future plans include the installation of a neutral beam for core plasma fueling, and also ion temperature measurements using charge-exchange recombination spectroscopy (CHERS). Low edge recycling is also predicted to reduce temperature gradients that drive drift wave turbulence. Gyrokinetic simulations are in progress to calculate fluctuation levels and transport for LTX plasmas, and new fluctuation diagnostics are under development to test these predictions.

Implementation and application of two synthetic diagnostics for validating simulations of core tokamak turbulence

The deployment of multiple high-resolution, spatially localized fluctuation diagnostics on the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] opens the door to a new level of core turbulence model validation. Toward this end, the implementation of synthetic diagnostics that model physical beam emission spectroscopy and correlation electron cyclotron emission diagnostics is presented. Initial results from their applications to local gyrokinetic simulations of two locations in a DIII-D L-mode discharge performed with the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] are also discussed. At normalized toroidal flux ρ=0.5, we find very good agreement between experiment and simulation in both the energy flows and fluctuation levels measured by both diagnostics. However, at ρ=0.75, GYRO underpredicts the observed energy flows by roughly a factor of 7, with rms fluctuation levels underpredicted by a factor of 3. Interestingly, at both locations we find good agreement in the shapes of the radial and vertical density correlation functions and in the shapes of the frequency power spectra. At both locations, the attenuation of the GYRO-predicted fluctuations due to the spatial averaging imposed by the diagnostics’ spot sizes is significant, and its incorporation via the use of synthetic diagnostics is shown to be essential for quantitative comparisons such as these.

In search of zonal flows by using direct density fluctuation measurements

A method for zonal flow study by using direct density fluctuation measurements is proposed. When ambient drift-wave turbulence is modulated by zonal flows (i.e. in the drift-wave-zonal flow systems), an envelope of the ambient density fluctuations has spectral peaks around zonal flow frequencies. A spectral peak at the geodesic acoustic mode (GAM) frequency is observed in the envelope of the ambient density fluctuations measured in edge plasma of the JFT-2M tokamak. The significant cross-bicoherence is also found between the ambient density fluctuations and its envelope in the GAM frequency. This result demonstrates that we can measure the GAM only by using density fluctuation data. This method provides a possibility of zonal flow research in burning core plasma by density fluctuation diagnostics such as microwave reflectometry.

Coupling of global toroidal Alfvén eigenmodes and reversed shear Alfvén eigenmodes in DIII-D

Reversed shear Alfvén eigenmodes (RSAEs) are typically thought of as being localized near the minima in the magnetic safety factor profile, however, their spatial coupling to global toroidal Alfvén eigenmodes (TAEs) has been observed in DIII-D discharges. For a decreasing minimum magnetic safety factor, the RSAE frequency chirps up through that of stable and unstable TAEs. Coupling creates a small gap at the frequency degeneracy point forming two distinct global modes. The core-localized RSAE mode structure changes and becomes temporarily global. Similarly, near the mode frequency crossing point, the global TAE extends deeper into the plasma core. The frequency splitting and spatial structure of the two modes throughout the various coupling stages, as measured by an array of internal fluctuation diagnostics, are in close agreement with linear ideal MHD calculations using the NOVA code. The implications of this coupling for eigenmode stability is also investigated and marked changes are noted throughout the coupling process.

Improved conditional averaging technique for plasma fluctuation diagnostics

Conditional averaging is one of the standard methods to detect large-scale structures in turbulent flows. By means of synthetic and experimental data it is shown that the usual trigger conditions are not sufficient to obtain reliable structure amplitudes. Our analysis shows that the amplitude reduction is caused by trigger jitter and a finite probability for trigger errors to occur. Using an improved conditional averaging scheme based upon a cross-correlation analysis, the possibility to remove these errors and to obtain correct amplitudes is shown.

Core barrier formation near integer q surfaces in DIII-D

Recent DIII-D experiments have significantly improved the understanding of internal transport barriers (ITBs) that are triggered close to the time when an integer value of the minimum in q is crossed. While this phenomenon has been observed on many tokamaks, the extensive transport and fluctuation diagnostics on DIII-D have permitted a detailed study of the generation mechanisms of q-triggered ITBs as pertaining to turbulence suppression dynamics, shear flows, and energetic particle modes. In these discharges, the evolution of the q profile is measured using motional Stark effect polarimetry and the integer qmin crossings are further pinpointed in time by the observation of Alfvén cascades. High time resolution measurements of the ion and electron temperatures and the toroidal rotation show that the start of improved confinement is simultaneous in all three channels, and that this event precedes the traversal of integer qmin by 5–20ms. There is no significant low-frequency magnetohydrodynamic activity prior to or just after the crossing of the integer qmin and hence magnetic reconnection is determined not to be the precipitant of the confinement change. Instead, results from the GYRO code point to the effects of zonal flows near low order rational q values as playing a role in ITB triggering. A reduction in local turbulent fluctuations is observed at the start of the temperature rise and, concurrently, an increase in turbulence poloidal flow velocity and flow shear is measured with the beam emission spectroscopy diagnostic. For the case of a transition to an enduring internal barrier the fluctuation level remains at a reduced amplitude. The timing and nature of the temperature, rotation, and fluctuation changes leading to internal barriers suggests transport improvement due to increased shear flow arising from the zonal flow structures.