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DOE OSTI2024

Localization of infrasonic sources via Bayesian back projection

SUMMARY A Bayesian framework is investigated for event-specific localization of infrasonic sources using back projection ray tracing. Direction-of-arrival information from array-based detection analysis is used to initialize a back projection ray path originating from the detecting array location and quantifying propagation characteristics from hypothetical source locations. The Fisher statistic, computed from the array’s beam coherence, is mapped into uncertainty in the launch angles of the ray path. Auxiliary parameters previously introduced for solving the Transport equation to compute geometric spreading along ray paths are used to map uncertainty in the ray launch angles into spatial and temporal uncertainties in the ray path. An atmospheric ensemble approach is applied to account for atmospheric uncertainty, and the relation between uncertainties in the atmospheric state and confidence in estimated localization are evaluated using several ensembles with specified variances. The method is evaluated using a synthetic event in the western United States constructed via forward propagation simulations as well as a single-station, multi-arrival detection from a surface explosion in the western United States. Localization results using this event-specific approach are more accurate and exhibit improved precision than existing Bayesian localization methods that leverage generalized, pre-computed propagation statistics.

58 GEOSCIENCES↗

DOE OSTI2023

Stress-induced structural changes in superconducting Nb thin films

Here we report on the analysis of stress-induced structural changes and the formation of an omega (ω) phase in polycrystalline Nb thin films deposited on Si by high-power impulse magnetron sputtering (HiPIMS) for superconducting qubits using x-ray diffraction (XRD), transmission electron microscopy (TEM), and density-functional theory (DFT). XRD analysis indicates that internal stresses in the Nb thin films lead to the formation of {112}$\langle$111$\rangle$ deformation twins and TEM analysis shows that ω phases nucleate at some of the twin boundaries in the Nb thin films. The size of ω phases ranges from 10 to 100 nm, which is comparable to the coherence length of Nb (≈40 nm), and ≈1% volume fraction of Nb grains exhibit this ω phase. The details of the formation mechanism and superconducting properties of the ω phases are investigated by DFT and potential roles of the ω phase in Nb as a source of decoherence in superconducting qubits are also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Universality of Collective Density Fluctuations in Liquids at and away from Equilibrium – An Integrated Neutron Scattering, Theoretical, and Computational Study (Final Technical Report)

Liquids, ubiquitous on earth, are prototypical disordered condensed matter. As the mediate phase between non-structured gases and ordered solids, liquids p ossess intriguing complexities that are absent on either extreme counter phase, especially when they are driven away from equilibrium. Despite decades of studies, the physics of liquids still keeps surprising us and challenges our understanding of condensed matter, emergent phenomena, and complex systems. Among the many interesting properties, the nature of collective dynamics in liquids remains elusive because of both the presence of strong interactions and the absence of translational invariance. This project studied the universal features of collective density fluctuations (or collective modes), which include both phonon-like excitations and collective relaxations, in the Q-dependent generalized hydrodynamic regime in liquids and liquid-like matter both at and away from equilibrium. We performed systematic studies of the fast collective dynamics (including both phonon-like excitations and collective relaxations) of four classes of liquids characterized by different fragilities and interactions using synergistically integrated coherent neutron scattering experiments (Inelastic Neutron Scattering (INS), Quasi-Elastic Neutron Scattering (QENS), and Neutron Spin Echo (NSE)), a ViscoElastic Hydrodynamics theory we have been developing, andMolecular Dynamics (MD) simulations and our analysis package LiquidLib. The transformative knowledge of the collective dynamics in liquids is important to understand and ultimately control the transport of mass, energy, and charge in liquids, both at and away from thermal equilibrium, which may will likely impact a wide range of disciplines.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Measuring Loss Tangents of Substrates for Superconducting Qubits with Part-per-Billion Precision

We report precision measurements of dielectric loss tangents in substrates for superconducting qubits using an ultra-high quality factor niobium SRF cavity operating at millikelvin temperatures and low electric fields. Multiple substrate types and surface treatments are compared to assess how processing impacts microwave dissipation. The RF results are correlated with materials analysis, including ToF-SIMS and XPS, to identify dominant loss mechanisms. This combined study links microscopic surface chemistry to macroscopic performance and provides a framework for materials-driven improvements in qubit coherence and device design.

Bafia, Daniel [Fermilab]↗

DOE OSTI2026

Measuring Loss Tangents of Substrates for Superconducting Qubits with Part-per-Billion Precision

Bafia, Daniel [Fermilab]↗

DOE OSTI2020

Variational fast forwarding for quantum simulation beyond the coherence time

Abstract Trotterization-based, iterative approaches to quantum simulation (QS) are restricted to simulation times less than the coherence time of the quantum computer (QC), which limits their utility in the near term. Here, we present a hybrid quantum-classical algorithm, called variational fast forwarding (VFF), for decreasing the quantum circuit depth of QSs. VFF seeks an approximate diagonalization of a short-time simulation to enable longer-time simulations using a constant number of gates. Our error analysis provides two results: (1) the simulation error of VFF scales at worst linearly in the fast-forwarded simulation time, and (2) our cost function’s operational meaning as an upper bound on average-case simulation error provides a natural termination condition for VFF. We implement VFF for the Hubbard, Ising, and Heisenberg models on a simulator. In addition, we implement VFF on Rigetti’s QC to demonstrate simulation beyond the coherence time. Finally, we show how to estimate energy eigenvalues using VFF.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Pedestal formation via different trajectories in the stability space in response to the timing scan of neutral beam heating in DIII-D

The frequency of type-I ELMs decreases as the initiation of the neutral beam injection (NBI) heating is delayed with respect to the time when plasma current (I p ) reaches flat-top in the ITER Baseline Scenario discharges in DIII-D. Henceforth, the time gap between the NBI initiation and I p flat-top will be referred to as “heating delay.” As the heating delay is modified, pedestal formation follows different trajectories in the edge current density–pedestal pressure gradient (j edge -∇p e ped ) space from the L-H transition toward the first ELM event. During the stationary phase after the first ELM, the ELM frequency (f ELM ) decreases by a factor of ~2 as the heating delay is increased. A longer pedestal recovery time in the inter-ELM period is observed for the low f ELM discharges as compared to the high f ELM discharges. Both low and high f ELM discharges show nearly identical profiles of electron density and temperature and have a similar MHD stability just before an ELM crash. However, a marked difference is observed in the magnetic spectrogram of the high and low f ELM discharges in response to the variation in the heating delay. The main difference is in the 200–400 kHz range of the magnetic spectra. A quasi-coherent mode (QCM) at 220 kHz and weaker broadband fluctuations are observed in the high f ELM discharges, while only strong broadband fluctuations are prevalent in the low f ELM discharges. ELM-synchronized analysis shows that the time evolution of these modes is different for the high and low f ELM discharges. The localization of both these modes is confirmed at the maximum gradient region of the pedestal. We hypothesize that these modes cause important pedestal transport and that the difference in the pedestal recovery of the high and low f ELM discharges is a result of the difference in transport driven by these modes, as they change with changes in the heating delay. It is demonstrated experimentally for the first time that discharges with similar pedestal parameters can carry the history of the heating delay into the stationary phase and that changes in turbulent-driven transport are a likely cause of changes in f ELM observed with variations of heating delay.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Detection of coherent optical phonons in a thin bismuth film by ultrafast electron diffraction

Coherent dynamics of lattice oscillations in a ∼20-nm-thick film obtained by thermal sputtering of bismuth is studied using ultrashort electron bunches synchronised with femtosecond laser pulses irradiating the sample. The Fourier analysis of ultrafast electron diffraction (UED) data shows that the observed modulation of the signal is due to the ensemble of modes corresponding to optical phonons with frequencies of approximately 3, 6 and 9 THz. A conclusion is made that these peaks correspond to the manifestation of the bismuth A{sub 1g} mode (three-terahertz peak), as well as its first and second overtones, which is probably due to quantum confinement in a 20-nm Bi nanostructure. The possibility of a detailed study of the quantum-size effect in bismuth with the help of a transmission UED is analysed. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Nonsteady Load Responses of Wind Turbines to Atmospheric and Mountain-Generated Turbulence Eddies, With Impacts on the Main Bearing: A Validation Study

Previous computational and field experiments identify three characteristic time scales in the aerodynamic responses of utility-scale wind turbine loads to atmospheric boundary layer (ABL) turbulence: a 30-90 second time scale for the passage of high/low speed "streaks" through the rotor plane, the blade and rotor rotation time scales (approximately 1 to 5 seconds), and a sub-second time scale created by blade rotation through gradients within eddy coherent structure. In the current study we compare aerodynamic load responses from daytime ABL turbulence quantified with large-eddy simulation and a actuator line model of the NREL 5 MW wind turbine with analysis of field data from the NREL/GE 1.5 MW wind turbine 5 kilometers east of the Rocky Mountain Front Range in Colorado. In addition, we contrast the responses to the passage of the mountain-generated eddies embedded within the westerly winds with the ABL eddies embedded within northerly/southerly winds. These analyses are in context with the nonsteady forcing of the main bearing by the aerodynamic generation of nontorque bending moments on the main shaft. Potentially relevant to main bearing failure mechanisms, both computational and field data show that the magnitudes of turbulence-generated nontorque bending moments, that we show generate nonsteady force on the main bearing, are of order, and often larger than, torque (which underlies power). However, the temporal variations in these two responses are uncorrelated, implying that the aerodynamic mechanisms that drive power and main bearing response are fundamentally different. We find this to be the case in the field with both mountain-generated eddies (westerly winds) and ABL-generated eddies (northerly/southerly winds). Whereas the time and length scales are comparable, the mountain eddies were somewhat more energetic than the northerly/southerly ABL eddies. Interestingly, however, the fluctuations in nontorque bending moment that force the main bearing were found to be stronger when forced by the ABL eddies than the mountain eddies. The field studies validate the key results from the computational study and show even stronger response in the nontorque bending moment than in the computer simulations. In all cases, the torque and nontorque bending moments are temporally uncorrelated, torque and power are driven by time variations in rotor-averaged horizontal wind velocity and nontorque bending moments are driven by time changes in the degree of nonuniformity in the distribution of velocity over the rotor plane. Thus the results generalize the mechanisms underlying nonsteady aerodynamic forcing to classes of turbulence eddy types with strength of order or stronger than ABL eddies with transverse scale of order the wind turbine rotor. These include atmospheric turbulence eddies, topography-generated turbulence eddies and, by extension, impacts of turbine-wake-scale turbulence eddies on downstream wind turbine rotors.

17 WIND ENERGY↗

DOE OSTI2021

Characterization of Alloy 709 Commercial Heats

The creep-resistant austenitic stainless steel Alloy 709 (Fe-20Cr-25Ni (wt%) based steel) is being investigated as a candidate structural material for the next generation of advanced reactors. Unlike conventional solid solution strengthened austenitic stainless steels, Alloy 709 develops a variety of precipitates during aging at different temperatures and times. In this study, precipitate evolution during short-term aging at 775°C was characterized. The effect of aging time (e.g., 10 vs. 100 hours) and cooling after aging (e.g., water quench vs. air cool) on grain size and precipitates have been investigated using light optical microscopy (OM), electron backscatter diffraction (EBSD), transmission electron microscopy (TEM), and energy-dispersive X-ray spectroscopy (EDS). MX (Ni,Tb)(C,N) and M23C6 (Cr,Mo)C precipitates were observed in all the statically-aged samples. The grain size distribution in the sample aged for 10 hours and water quenched (10Q) versus the one aged for 100 hours and air cooled (100A) were comparable. This indicates that grain structure was fairly stable when aging at 775°C for up to 100 hours. In contrast, the sample aged for 10 hours and air cooled (10A) showed the smallest and the most uniform grain size distribution. This phenomenon was observed in only one sample. More studies on duplicate samples are needed to confirm the results obtained. The cooling medium (e.g., water quench vs. air cool) was not observed to impact the size nor the distribution of the MX and M23C6 precipitates. Increasing the aging time resulted in the following: (1) a decrease in dislocations as well as the number density of small precipitates; (2) an increase in the ratio of free precipitates that were not pinning dislocations; (3) relatively higher N, Nb, and Ti concentration in MX precipitate; (4) some increase in length of M23C6 carbides which were located on the coherent boundaries; and (5) the introduction of Sienriched M6X precipitates. The tensile tests at room temperature showed similar properties for each of the static aging treatments, indicating that the differences observed in the microstructural analysis did not have a significant impact on the tensile properties.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Synchrotron infrared nano-spectroscopy and -imaging

Infrared (IR) spectroscopy has evolved into a powerful analytical technique to probe molecular and lattice vibrations, low-energy electronic excitations and correlations, and related collective surface plasmon, phonon, or other polaritonic resonances. In combination with scanning probe microscopy, near-field infrared nano-spectroscopy and -imaging techniques have recently emerged as a frontier in imaging science, enabling the study of complex heterogeneous materials with simultaneous nanoscale spatial resolution and chemical and quantum state spectroscopic specificity. Here, we describe synchrotron infrared nano-spectroscopy (SINS), which takes advantage of the low-noise, broadband, high spectral irradiance, and coherence of synchrotron infrared radiation for near-field infrared measurements across the mid- to far-infrared with nanometer spatial resolution. This powerful combination provides a qualitatively new form of broadband spatio-spectral analysis of nanoscale, mesoscale, and surface phenomena that were previously difficult to study with IR techniques, or even any form of micro-spectroscopy in general. We review the development of SINS, describe its technical implementations, and highlight selected examples representative of the rapidly growing range of applications in physics, chemistry, biology, materials science, geology, and atmospheric and space sciences.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

Coherent detection of hidden spin–lattice coupling in a van der Waals antiferromagnet

Strong interactions between different degrees of freedom lead to exotic phases of matter with complex order parameters and emergent collective excitations. Conventional techniques, such as scattering and transport, probe the amplitudes of these excitations, but they are typically insensitive to phase. Therefore, novel methods with phase sensitivity are required to understand ground states with phase modulations and interactions that couple to the phase of collective modes. Here, by performing phase-resolved coherent phonon spectroscopy (CPS), we reveal a hidden spin–lattice coupling in a vdW antiferromagnet FePS 3 that eluded other phase-insensitive conventional probes, such as Raman and X-ray scattering. With comparative analysis and analytical calculations, we directly show that the magnetic order in FePS 3 selectively couples to the trigonal distortions through partially filled t 2 g orbitals. This magnetoelastic coupling is linear in magnetic order and lattice parameters, rendering these distortions inaccessible to inelastic scattering techniques. Our results not only capture the elusive spin–lattice coupling in FePS 3 but also establish phase-resolved CPS as a tool to investigate hidden interactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Near-field radiative heat transfer between irregularly shaped dielectric particles modeled with the discrete system Green's function method

Near-field radiative heat transfer (NFRHT) between irregularly shaped dielectric particles made of SiO 2 and morphology characterized by Gaussian random spheres is studied. Particles are modeled using the discrete system Green's function (DSGF) approach, which is a volume integral numerical method based on fluctuational electrodynamics. This method is applicable to finite, three-dimensional objects, and all system interactions are defined independent of thermal excitation by a generalized system Green's function. The DSGF method is deemed suitable to model NFRHT between irregularly shaped particles after verification against the analytical solution for chains of two and three SiO 2 spheres. The NFRHT results reveal that geometric irregularity in particles leads to a reduction of the total conductance from that of comparable perfect spheres at vacuum separation distances smaller than the particle size, a regime in which NFRHT is a surface phenomenon. At vacuum separation distances larger than the particle size, NFRHT becomes a volumetric process, and the total conductance between irregularly shaped particles converges to that of comparable perfect spheres. Spectral analysis reveals, however, that particle irregularity leads to damping and broadening of resonances at all separation distances, thereby highlighting the importance of the DSGF method for spectral engineering in the near field. The reduced spectral coherence when particle size is larger than the vacuum separation distance is attributed to coupling of surface phonon-polaritons within the randomly generated, distorted particle features. For particle size smaller than the vacuum separation distance, resonance broadening and damping are linked with the multiple localized surface phonon modes supported by the composite spherical harmonic morphologies of the Gaussian random spheres. In conclusion, this paper has direct implications for thermal management of packed particle systems, with applications in radiative property control, electronics, energy conversion, and nanomanufacturing.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Gluon distributions and their applications to Ioffe-time distributions

We investigate unpolarized and polarized gluon distributions and their applications to the Ioffe-time distributions, which are related to lattice QCD calculations of parton distribution functions. Guided by the counting rules based on the perturbative QCD at large momentum fraction x and the color coherence of gluon couplings at small x, we parametrize gluon distributions in the helicity basis. By fitting the unpolarized gluon distribution, the inferred polarized gluon distribution from our parametrization agrees with the one from global analysis. A simultaneous fit to both unpolarized and polarized gluon distributions is also performed to explore the model uncertainty. The agreement with the global analysis supports the (1 - x) power suppression of the helicity-antialigned distribution relative to the helicity-aligned distribution. The corresponding Ioffe-time distributions and their asymptotic expansions are calculated from the gluon distributions. Our results of the Ioffe-time distributions can provide guidance to the extrapolation of lattice QCD data to the region lacking precise gluonic matrix elements. Therefore, they can help regulate the ill-posed inverse problem associated with extracting the gluon distributions from discrete data from first-principle calculations, which are available in a limited range of the nucleon momentum and the spatial separation between the gluonic currents. Given various limitations in obtaining lattice QCD data at large Ioffe time, phenomenological approaches can provide important complementary information to extract the gluon distributions in the entire momentum fraction region, especially at small x. The possibility of investigating higher-twist effects and other systematic uncertainties in the contemporary first-principle calculations of parton distributions from phenomenologically well-determined Ioffe-time distributions in the large Ioffe-time region is also discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

A TCN-Based Hybrid Forecasting Framework for Hours-Ahead Utility-Scale PV Forecasting

This paper presents a Temporal Convolutional Network (TCN) based hybrid PV forecasting framework for enhancing hours-ahead utility-scale PV forecasting. The hybrid framework consists of two forecasting models: a physics-based trend forecasting (TF) model and a data-driven fluctuation forecasting (FF) model. Three TCNs are integrated in the framework for: i) blending the inputs from different Numerical Weather Prediction sources for the TF model to achieve superior performance on forecasting hourly PV profiles, ii) capturing spatial-temporal correlations between detector sites and the target site in the FF model to achieve more accurate forecast of intra- hour PV power drops, and iii) reconciling TF and FF results to obtain coherent hours-ahead PV forecast with both hourly trends and intra-hour fluctuations well preserved. To automatically identify the most contributive neighboring sites for forming a detector network, a scenario-based correlation analysis method is developed, which significantly improves the capability of the FF model on capturing large power fluctuations caused by cloud movements. Here, the framework is developed, tested, and validated using actual PV data collected from 95 PV farms in North Carolina. Simulation results show that the performance of 6 hours ahead PV power forecasting is improved by 20% - 30% compared with state-of-the-art methods.

42 ENGINEERING↗

DOE OSTI2024

Wasatch Fault Structure from Machine Learning Arrival Times and High-Precision Earthquake Locations

Abstract On 18 March 2020, a magnitude 5.7 earthquake hit the Salt Lake valley in the state of Utah, United States. Using a dense geophone deployment and machine learning (ML), an additional several thousand events were detected and located. Currently, both the mainshock and the majority of the aftershocks are suspected to have occurred on or near a deeper portion of the Salt Lake segment of the Wasatch fault—part of a large range-bounding fault system thought to be capable of generating an Mw 7.2 earthquake. However, a small subset of aftershocks may have occurred on a portion of the more steeply, eastward dipping, and poorly understood West Valley fault. Unfortunately, the catalog locations and lack of focal mechanisms for this subset of aftershocks provide only a crude constraint on the true fault structure. To better illuminate fault structure, we relocate the ML-generated catalog with a range of magnitudes from −2 to 4.6, using: (1) NonLinLoc, a nonlinear location algorithm, (2) source-specific station terms, and (3) waveform coherence. We further compute first-motion focal mechanisms for 68 events. Results of the relocation suggest a simpler, minimally listric Wasatch fault geometry, contrary to what has been previously proposed. We also find that analysis of the focal mechanisms and waveform similarity indicates minimal event similarity throughout the Magna sequence, suggesting a highly complex and heterogeneous rupture zone, as opposed to rupture on a single plane. These findings suggest an increased seismic hazard due to the overall shallowness of the earthquake sequence and highly varied rupture mechanisms.

Geochemistry & Geophysics↗

DOE OSTI2025

Numerical Analysis of High-Order Modes in SRF Resonators for Particle Accelerators

Over the past decades, superconducting technology has rapidly evolved towards high accelerating gradients and low surface resistance, making it possible to operate particle accelerators with high average beam currents and large duty factors. However, RF losses due to coherent excitation of the HOM become the limiting factor for these regimes. Unlike the cavity operating mode, which is tuned separately, the HOM parameters can significantly vary from one cavity to another due to finite mechanical tolerances during the manufacturing process. Thus, it is of utmost importance to know the HOM parameter spread in advance in order to predict unexpected cryogenic losses, overheating of beam line components and maintain stable beam dynamics. In this paper, we present a method for generating cavity geometry with an arbitrary spread of mechanical imperfections and numerically evaluating HOM statistics. Knowing the spread of HOM parameters, we calculated the probability of resonant HOM losses in SRF accelerating cavities used in CW beam current machines such as the PIP-II and LCLS-II linacs, as well as for the SRF crab-cavity for the ILC project. Finally, we present experimental results of HOM spectra measurements in hundreds of 1.3 GHz cavities installed in LCLS-II cryomodules. Studying the effects of HOM excitation results in specifications of the SRF cavity and cryomodule and can significantly impact the efficiency and reliability of the machine operation.

Lunin, Andrei [Fermilab] (ORCID:0000000290096792)↗

DOE OSTI2023

Sensitivity analysis of the effect of wind and wake characteristics on wind turbine loads in a small wind farm

Abstract. Wind turbines are designed using a set of simulations to determine the fatigue and ultimate loads, which are typically focused solely on unwaked wind turbine operation. These structural loads can be significantly influenced by the wind inflow conditions. Turbines experience altered inflow conditions when placed in the wake of upstream turbines, which can additionally influence the fatigue and ultimate loads. It is important to understand the impact of uncertainty on the resulting loads of both unwaked and waked turbines. The goal of this work is to assess which wind-inflow-related and wake-related parameters have the greatest influence on fatigue and ultimate loads during normal operation for turbines in a three-turbine wind farm. Twenty-eight wind inflow and wake parameters are screened using an elementary effects sensitivity analysis approach to identify the parameters that lead to the largest variation in the fatigue and ultimate loads of each turbine. This study uses the National Renewable Energy Laboratory (NREL) 5 MW baseline wind turbine, simulated with OpenFAST and synthetically generated inflow based on the International Electrotechnical Commission (IEC) Kaimal turbulence spectrum with the IEC exponential coherence model using the NREL tool TurbSim. The focus is on sensitivity to individual parameters, though interactions between parameters are considered, and how sensitivity differs between waked and unwaked turbines. The results of this work show that for both waked and unwaked turbines, ambient turbulence in the primary wind direction and shear are the most sensitive parameters for turbine fatigue and ultimate loads. Secondary parameters of importance for all turbines are identified as yaw misalignment, streamwise integral length, and the exponent and streamwise components of the IEC coherence model. The tertiary parameters of importance differ between waked and unwaked turbines. Tertiary effects account for up to 9.0 % of the significant events for waked turbine ultimate loads and include veer, non-streamwise components of the IEC coherence model, Reynolds stresses, wind direction, air density, and several wake calibration parameters. For fatigue loads, tertiary effects account for up to 5.4 % of the significant events and include vertical turbulence standard deviation, lateral and vertical wind integral lengths, non-streamwise components of the IEC coherence model, Reynolds stresses, wind direction, and all wake calibration parameters. This information shows the increased importance of non-streamwise wind components and wake parameters in the fatigue and ultimate load sensitivity of downstream turbines.

17 WIND ENERGY↗