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At least 91 records · Page 5

Iron nitride powder with anisotropic shape

Techniques are disclosed for milling an iron-containing raw material in the presence of a nitrogen source to generate anisotropically shaped particles that include iron nitride and have an aspect ratio of at least 1.4. Techniques for nitridizing an anisotropic particle including iron, and annealing an anisotropic particle including iron nitride to form at least one α″-Fe16N2 phase domain within the anisotropic particle including iron nitride also are disclosed. In addition, techniques for aligning and joining anisotropic particles to form a bulk material including iron nitride, such as a bulk permanent magnet including at least one α″-Fe16N2 phase domain, are described. Milling apparatuses utilizing elongated bars, an electric field, and a magnetic field also are disclosed.

Wang, Jian-Ping↗

Time Projection Chambers instrumented with resistive MicroMegas for the SAND near detector of DUNE

The Deep Underground Neutrino Experiment (DUNE) is a next-generation long-baseline neutrino accelerator experiment aiming for precise measurements of the neutrino oscillation parameters. DUNE will include a near detector complex regrouping three different detectors among which SAND (System for on-Axis Neutrino Detection) that will be the only one permanently on the neutrino beam axis in charge of monitoring in detail the emitted neutrino beam and its stability through time, a crucial characteristic to realize accurate oscillation measurements at the percent level. SAND will reuse the superconducting magnet and the electromagnetic calorimeter of the KLOE experiment. We will describe in the following the proposal of using, as inner tracker of SAND, a large 3D matrix of 1.5cm side scintillator cubes (3DST) surrounded by 3 gaseous Time Projection Chambers. This setup allows to realize accurate beam monitoring combining the 3DST unprecedented capability of neutron detection and energy measurement with the high precision momentum resolution for charged particles offered by the TPCs. The proposed TPC design allows to reach spatial resolutions of a few hundreds of micrometers using 1 cm pads by deploying the resistive MicroMegas technology for the charge readout.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A very high energy hadron collider on the Moon

Abstract The long-term prospect of building a hadron collider around the circumference of a great circle of the Moon is sketched. A circular collider on the Moon (CCM) of ∼11 000 km in circumference could reach a proton–proton center-of-mass collision energy of 14 PeV—a thousand times higher than the Large Hadron Collider at CERN—optimistically assuming a dipole magnetic field of 20 T. Several aspects of such a project are presented, including siting, construction, availability of necessary materials on the Moon, and powering, as well as a discussion of future studies and further information needed to determine the more concrete feasibility of each. Machine parameters and vacuum requirements are explored, and an injection scheme is delineated. Other unknowns are set down. Due to the strong interest from multiple organizations in establishing a permanent Moon presence, a CCM could be the (next-to-) next-to-next-generation discovery machine for high-energy particle physics and a natural successor to next-generation machines, such as the proposed future circular collider at CERN or a super proton–proton collider in China, and other future machines, such as a collider in the Sea, in the Gulf of Mexico. A CCM would serve as an important stepping stone toward a Planck-scale collider sited in our Solar System.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Final Technical Report: Innovative Magnetron Power Sources for Superconducting RF (SRF) Accelerators

In this project, MUONS is designing and building custom magnetrons at Richardson Electronics (RELL) to test the predictions of the models and make improvements to the designs to match the needs of NP SRF accelerators and their life-cycle costs. To increase lifetime, the filament temperature is controlled by a feedback circuit that includes a model of back streaming of electrons. The gain of the magnetron is optimized by the design of an input port. A permanent magnet design with trim coil for amplitude adjustment reduces energy consumption. Moving the construction of the magnetron from prototype to manufacturing includes the utilization of RELL processes and designs. To the extent that outgassing of materials influences the lifetime of the magnetron, methods for minimizing outgassing was explored. Further experimentation of the potential of sub-critical voltage operation continues to be explored. The commercialization goal of the project will be naturally achieved as RELL already has world-wide marketing, sales, and support to exploit the assembly-line capabilities generated by this project to enable magnetron technologies for NP accelerators.

43 PARTICLE ACCELERATORS↗

Rare earth metals production using alternative feedstock that eliminates HF

This work reports the successful production of rare earth (RE) metal using Na-RE-F. Presently, RE metals are primarily produced using RE-fluoride due to its higher air and moisture stability compared to RE-chloride. However, its preparation requires the use of corrosive and hazardous chemicals, such as hydrofluoric acid (HF) or ammonium bifluoride (NH 4 HF 2 ). The present study demonstrates that Na-RE-F is an alternative salt to the typically used RE-fluoride. The Na-RE-F for this work is produced via a scalable hydrometallurgical approach using three different RE salts as feedstock, including acetate, nitrate, and chloride. HF is neither used nor generated during the salt preparation process. Furthermore, the Na-RE-F powder dries in air (without dry HF), and only water evolves during the drying process. Analyses of the Na-RE-F show that NaF liberates as a flux during the heating process, which lowers the salt reduction temperature to <900 °C, thus minimizing or eliminating the need for additional flux. Calciothermic reduction of the Na-RE-F salt is successfully employed to obtain RE metal. This work represents a safer, greener, and more widely deployable approach for producing the RE metals needed for permanent magnets which support the transition to a cleaner society through the decarbonization of the transportation industry.

36 MATERIALS SCIENCE↗

An experimental platform for investigating astrophysically relevant magnetized plasma jets on the COBRA facility

A new platform has been developed for the 1-MA COBRA generator to investigate the physical processes affecting the formation, collimation, and stability of high-speed outflows in magnetically driven laboratory plasma jets. Such experiments serve as diagnostically accessible surrogates for astrophysical jets under the assumption that the underlying dynamics are scale invariant. In contrast to previous current driven high energy density laboratory jet experiments that use radial/conical wire arrays or foils, the platform described here uses azimuthally symmetric gas-puff injection. This avoids the ablation phase from a solid target, allowing the jets to develop earlier and be driven longer without depleting their mass source and disrupting. A permanent magnet provides an initial poloidal magnetic field, which links the two concentric electrodes and mimics the boundary conditions of a star-accretion disk system. Extended magnetohydrodynamic effects can be assessed using a polarity convolute, which allows for reversal of the electrode bias. The resulting plasma jets exhibit remarkable stability, persisting for hundreds of nanoseconds and achieving aspect ratios ≳30:1.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Spectral characterization of flash and high flux x-ray radiographic sources with a magnetic Compton spectrometer

In this article, we present a new analysis method applied to revitalize permanent magnet Compton spectrometers used to measure photon energy spectra in the MeV range. The inversion of the measured electron distribution to determine the original photon distribution is achieved via a method of consistent coupled radiation transport and magnetic field mapping of the input photon spectra to the measured electron distribution. The method of linear least squares was used to perform the unfolding of the electron distribution to the initial photon spectra, without any assumptions made regarding the electron distribution. We present an application of this method to data from a nominal 19.4 MeV flash radiographic source (the first axis of the Dual Axis Radiographic Hydro-Test Facility) capable of generating 500 R @ 1 m in ~60 ns and a medical therapy source (a Scanditronix M22, Microtron) capable of variable energies with nominal endpoints of 6, 10, 15, and 20 MeV and an output of ~1000–2000 R/min @ 1 m. The results provide agreement between the modeled and unfolded experimentally measured photon spectra as quantified by statistical tests, from 1.5 to 20 MeV. Experimental results are presented as well as a discussion of the novel MCNP6-based simulations and methods for reconstruction of the spectra.

47 OTHER INSTRUMENTATION↗

Feasibility of FDEM cross-dipole and TDEM loop sources for monitoring CO 2 at the Kemper CarbonSAFE site

Electromagnetics has been shown to be a viable tool to monitor CO 2 plumes embedded in saline reservoirs. However, the majority of studies focus on measuring the electric field, which requires cumbersome equipment in the field and it is difficult to install permanent measurement stations. Magnetic field receivers offer an opportunity to reduce the form factor of the survey and increase the mobility by utilizing upcoming technologies, such as drones. We explore the use of frequency-domain electric dipole sources, and timedomain loops with a focus on measuring the secondary magnetic field at the surface for a conceptual injection scenario based on the Kemper CarbonSAFE site. We find that electric dipole sources give a response above the sensitivity of current sensor technology and, therefore, be a viable tool for CO 2 monitoring. The time domain loop source does provide fields that are useful for determining the location of the CO 2 plume, however the field magnitude is below the sensitivity of the current generation of instruments. To explore the use of a potential borehole receiver we generate a map of the magnetic field at depth to explore potential borehole placement for monitoring efforts. Finally, we limit the spatial extent of the electric dipole survey to a single parcel of land to help understand how the fields change with survey geometry. We find that the shape of the secondary fields change slightly with the small transmitter, but are still measurable provided that the cultural noise at the site is low. Thus, we conclude that at the Kemper site a frequency-domain cross-dipole source with magnetometer receivers is suitable to monitor the expansion of the CO 2 plume in the saline reservoir, even with a limited transmitter footprint on the surface.

58 GEOSCIENCES↗

Accelerating the discovery of novel magnetic materials using machine learning–guided adaptive feedback

Magnetic materials are essential for energy generation and information devices, and they play an important role in advanced technologies and green energy economies. Currently, the most widely used magnets contain rare earth (RE) elements. An outstanding challenge of notable scientific interest is the discovery and synthesis of novel magnetic materials without RE elements that meet the performance and cost goals for advanced electromagnetic devices. Here, we report our discovery and synthesis of an RE-free magnetic compound, Fe 3 CoB 2 , through an efficient feedback framework by integrating machine learning (ML), an adaptive genetic algorithm, first-principles calculations, and experimental synthesis. Magnetic measurements show that Fe 3 CoB 2 exhibits a high magnetic anisotropy ( K 1 = 1.2 MJ/m 3 ) and saturation magnetic polarization ( J s = 1.39 T), which is suitable for RE-free permanent-magnet applications. Our ML-guided approach presents a promising paradigm for efficient materials design and discovery and can also be applied to the search for other functional materials.

36 MATERIALS SCIENCE↗

Plasma-based particle sources

High-brightness particle beams generated by advanced accelerator concepts have the potential to become an essential part of future accelerator technology. In particular, high-gradient accelerators can generate and rapidly accelerate particle beams to relativistic energies. The rapid acceleration and strong confining fields can minimize irreversible detrimental effects to the beam brightness that occur at low beam energies, such as emittance growth or pulse elongation caused by space charge forces. Due to the high accelerating gradients, these novel accelerators are also significantly more compact than conventional technology. Advanced accelerators can be extremely variable and are capable of generating particle beams with vastly different properties using the same driver and setup with only modest changes to the interaction parameters. So far, efforts have mainly been focused on the generation of electron beams, but there are concepts to extend the sources to generate spin-polarized electron beams or positron beams. The beam parameters of these particle sources are largely determined by the injection and subsequent acceleration processes. Although, over the last decade there has been significant progress, the sources are still lacking a sufficiently high 6-dimensional (D) phase-space density that includes small transverse emittance, small energy spread and high charge, and operation at high repetition rate. This is required for future particle colliders with a sufficiently high luminosity or for more near-term applications, such as enabling the operation of free-electron lasers (FELs) in the X-ray regime. Major research and development efforts are required to address these limitations in order to realize these approaches for a front-end injector for a future collider or next-generation light sources. In particular, this includes methods to control and manipulate the phase-space and spin degrees-of-freedom of ultrashort plasma-based electron bunches with high accuracy, and methods that increase efficiency and repetition rate. These efforts also include the development of high-resolution diagnostics, such as full 6D phase-space measurements, beam polarimetry and high-fidelity simulation tools. A further increase in beam luminosity can be achieve through emittance damping. Emittance cooling via the emission of synchrotron radiation using current technology requires kilometer-scale damping rings. For future colliders, the damping rings might be replaced by a substantially more compact plasma-based approach. Here, plasma wigglers with significantly stronger magnetic fields are used instead of permanent-magnet based wigglers to achieve similar damping performance but over a two orders of magnitude reduced length.

43 PARTICLE ACCELERATORS↗

Modelling pulsed field magnetization of iron-based bulk superconductors

Abstract Bulk superconductors can be used as super-strength quasi-permanent magnets capable of providing magnetic flux densities considerably superior to conventional permanent magnets. This makes them attractive for several engineering applications that rely on strong magnetic fields like rotating machines, NMR/MRI and magnetic drug delivery systems. Recently, the authors reported a record trapped magnetic field in an iron-based bulk superconductor: 2.83 T was trapped in potassium-doped barium iron arsenide (Ba, K)Fe 2 As 2 (or Ba122) at 5 K. Of particular significance is that the strength and temporal stability of this magnetic field exceeds the requirements of MRI machines, indicating iron-based bulks can now perform at levels demanded by engineering applications. One crucial challenge for their practical use, however, is the need to apply and remove an external magnetic field to magnetize them. Pulsed field magnetization (PFM) shows great promise as a practical method of magnetizing bulks, but the process generates heat in the bulk that is detrimental to its superconducting performance and ability to act as a super-strength magnet. In this paper, coupled electromagnetic–thermal numerical models are used to simulate the PFM of iron-based bulk superconductors. Here we focus on the recent-record-breaking, fine-grain polycrystalline K-doped Ba122 bulks. The impact that the specific J c ( B ) characteristics and thermal properties of the Ba122 material—all of which have been experimentally measured from state-of-the-art samples—have on the magnetic flux dynamics and thermal behaviour during PFM, including the final trapped field, is investigated. We show that because the thermal properties are similar to those of REBa 2 Cu 3 O 7 −δ bulks, a similar response to pulsed fields is obtained. A maximum trapped field of ∼0.81 T (∼43.3% of the maximum trapped field capability under ideal, field-cooling conditions) was simulated at 5 K, with a magnetization efficiency of ∼54%. The modelling framework provides a fast and flexible tool for optimising the practical PFM process at different operating temperatures to maximise the trapped field in state-of-the-art Ba122 bulks and to guide the design of future experiments.

bulk superconductors↗

Exploring the Nature of f-Element Soft Donor Interactions Using Electronically Tunable Azolate Ionic Liquids

This project was undertaken to advance the understanding of how f-elements interact with moderately soft donors, a heavily investigated yet open question which is of prime importance in spent nuclear fuel processing and fundamental inorganic chemistry. During the course of the project, based on exciting results, a stretch goal was developed to study the hydrolysis products of transuranic actinide metals, a somewhat understudied field even with its significance in nuclear fuel cycle and impacts in environmental chemistry. The stretch goal was to take our serendipitous discovery of an easy route to isolation of crystalline multinuclear ƒ-element hydrolysis products, and apply it to gaining a mechanistic understanding of Pu(III/IV) colloid formation. The simplicity of our techniques should lend themselves to the remote handling required for study of many transuranic elements. We developed several methodologies using azolium azolate chemistry to overcome ƒ-element hydrolysis problems that prohibit the isolation of ƒ-element soft donor complexes and to build a crystallographic library of ƒ-element N-donor complexes as a means to understand the fundamental differences between actinide and lanthanide interactions with moderately soft donor ligands. Our next major endeavor will be to transfer this chemistry from 4ƒ elements to transuranic elements, particularly in the study of hydrolysis of Pu(III/IV). While our work is fundamental in nature, applications of the knowledge we are generating should be felt in such diverse fields as catalysis, separations in general, nuclear waste remediation specifically, and many other applications in f-element magnetic and luminescent properties. The potential ramifications of the consistent and robust formation of hydrolysis controlled hexanuclear lanthanide structures are enormous, with future uses being catalyst formation, higher-nuclearity structure synthesis using our hexanuclear motif as a fundamental building block, Pu waste remediation, separations, and many other potential applications resulting from characteristic magnetic and luminescent properties of lanthanide polynuclear structures. Three synthetic methodologies (direct mixing with variable stoichiometries, use of volatile solvent, metathesis) were developed starting with 7 acidic and 6 basic azoles to obtain ionic liquids suitable for f-element coordination. Proton transfer by acidic/basic azole combination led to suitable low melting salts and two cocrystals. Acid/base reaction of azoles with soft-donor permanent cations of ([X 4444 ][OH] (where [X 4444 ] + = tetrabutylammonium [N 4444 ] + or tetrabutylphosphonium [P 4444 ] + ) with weakly acidic azoles including imidazole, 1,2,3-triazole, 1,2,4-triazole, 5-aminotetrazole, 4,5-dicyanoimidazole, and 2-amino-4,5-dicyanoimidazole) revealed several suitable low-melting salts. Metathesis reactions of Na(azolate) were conducted by first using weakly acidic azoles including 4,5-dicyanoimidazole, 2-amino-4,5-dicyanoimidazole, 5-aminotetrazole, and 1,2,4-triazole to form sodium or lithium salts using group(I) hydroxides in methanolic solutions. The best results were obtained by reacting the basic and acidic azoles directly in 1:1 or 3:1 ratios at elevated temperatures. Twenty-two azole mixtures were identified which are either low melting solids or room temperature liquids. Each of the low melting solids was confirmed to be a new solid phase, each of which is being further characterized. The liquids and solids are anticipated to be ILs, eutectics, or partially ionized systems, all of which will be suitable for the dissolution of f-element salts. Five new synthetic methodologies were developed to finding suitable crystallization conditions for f-element complexation with the goal of finding simple one pot reaction syntheses and crystallization strategies that could be used under the demanding conditions of transuranic chemistries. These synthetic methods yield many new crystalline phases which were studied by single crystal X-ray diffraction.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

High Temperature Sodium Submersible Flowmeter Design and Analysis

This work details the design and analysis of a permanent magnet flowmeter designed to be submerged in a pool type sodium fast reactor environment. Recently developed Samarium Cobalt rare earth magnets were utilized that have demonstrated resilience to temperature and neutron flux up to 550 °C and 10 18 n/cm 2 , respectively. This paper will discuss the theory, design, calibration and uncertainty quantification of the flowmeter. The flowmeter was calibrated over a flowrate range of 11.4 - 90.9 LPM at temperatures of 220 and 400 °C, yielding an uncertainty in calibration of 2-3.6%. Here, a finite element model was developed and validated experimentally, yielding <; 3.2% error.

47 OTHER INSTRUMENTATION↗

Solvent-driven fractional crystallization for atom-efficient separation of metal salts from permanent magnet leachates

Abstract This work reports a dimethyl ether-driven fractional crystallization process for separating rare earth elements and transition metals. The process has been successfully applied in the treatment of rare earth element-bearing permanent magnet leachates as an atom-efficient, reagent-free separation method. Using ~5 bar pressure, the solvent was dissolved into the aqueous system to displace the contained metal salts as solid precipitates. Treatments at distinct temperatures ranging from 20–31 °C enable crystallization of either lanthanide-rich or transition metal-rich products, with single-stage solute recovery of up to 95.9% and a separation factor as high as 704. Separation factors increase with solution purity, suggesting feasibility for eco-friendly solution treatments in series and parallel to purify aqueous material streams. Staged treatments are demonstrated as capable of further improving the separation factor and purity of crystallized products. Upon completion of a crystallization, the solvent can be recovered with high efficiency at ambient pressure. This separation process involves low energy and reagent requirements and does not contribute to waste generation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Concept of circular-linear energy recovery accelerator to probe the energy frontier

Energy-frontier accelerators provide powerful tools performing high precision measurements confirming the fundamentals of the physics and broadening new research horizons. Such machines are either driven by circular or linear accelerators. The circular machines, having the centre-of-mass (CM) energy values reaching 200 GeV (for leptons) and above, experience beam energy loss and quality dilution, for example, due to synchrotron radiation, limiting the overall CM energy achievable and requiring a constant energy top-up to compensate the loss and the beam quality dilution. Linear colliders overcome these limitations, while the finite capabilities of generating high average current beams limits the luminosity. This is partially compensated by the quality of the colliding beams. In this work, we suggest a novel design of circular-linear accelerator based on the merging of the “non-emitting”, low-energy storage rings and energy recovery linear accelerators. We suggest using the recently considered dual-axis asymmetric cavities to enable the operation of such a system, and in particular the energy recovery from spent, high-intensity beams. The machine considered, under the scope of the SNOWMASS-2021 initiative, can be potentially used to reach ultimate energy frontiers in high-energy physics as well as to drive next generation light sources. The merging of circular and linear systems, and applications of dual axes cavities, should allow the maintaining of high beam quality, high luminosity, and high energy efficiency, while offering a flexible energy management and opening clear opportunity for reducing the running cost. We note that the numbers shown in the paper are for illustration purpose and can be improved further.

43 PARTICLE ACCELERATORS↗

Universal Electronic‐Structure Relationship Governing Intrinsic Magnetic Properties in Permanent Magnets

An electronic-structure-centered perspective is presented on permanent-magnet (PM) design, highlighting two key levers, that is, saturation magnetization (M s ), governed by 3d-band filling and exchange physics, and magnetocrystalline anisotropy energy (MAE), arising from spin-orbit coupling (SOC) on anisotropic orbital populations. Reviewing current practices, including DFT-based MAE/J ij extraction, atomistic-spin and micromagnetic modeling, and high-throughput machine learning (ML) pipelines, three bottlenecks limiting predictive discovery is identified that is i) electronic-structure accuracy for small MAE (sensitive to functional choice, Hubbard U, and many-body effects), ii) finite-temperature and kinetic realism (phonon/magnon renormalization, ordering kinetics), and iii) descriptor and multiscale decoupling (lack of SOC-weighted and orbital-resolved fingerprints). Deep dives into the electronic-structure of Nd─Fe─B and Fe─N show how these fingerprints govern magnetic performance, motivating DFT- and quantum-mechanics-based descriptors for discovery. Unbiased, structure-driven exploration, coupled with high-throughput simulations, ML, generative AI, and reasoning models, accelerates candidate identification and propagates insights across scales. Addressing supply-chain risks, on future needs of designing “critical-element-free” magnets with tailored microstructure and high energy products is emphasized. By integrating electronic fingerprints, AI reasoning, and multiscale modeling, a practical roadmap is provided for rare-earth-lean or rare-earth free, high-performance, sustainable PMs.

Singh, Prashant [Ames Laboratory, and Iowa State U↗

Design and Optimization of Processes for Recovering Rare Earth Elements from End-of-Life Hard Disk Drives

In this poster, we first provide motivation for why rare earth elements as rare earth permanent magnets (REPM) are increasing in demand. We then highlight some of the recent work that has been done by several national labs (National Renewable Energy Laboratory (NREL), Environmental Protection Agency (EPA), Critical Minerals Institute (CMI)) on recycling rare earth elements from end-of-life hard disk drives (EOL). Then, we mention our long-term plan to design a feedstock agnostic process to recover rare earth elements as rare earth oxides from many different EOL products at once. Next, we discuss how we quantified the rare earth elements available for recycling from EOL hard disk drives from consumer desktops and laptops. We then discuss how we used superstructure optimization to design the optimal pathway. The proposed superstructure was modeled as a MILP optimization problem, selecting the net present value as the objective function. Costing data from the literature was used to inform this model whenever possible. However, due to the novelty of this research area, data were often unavailable, thus requiring the generation of flowsheets implemented in Aspen Plus.

Laliwala, Chris↗

A Real-Time Testbed for Smart Inverter Cyber Security Studies

Distributed energy resources (DER) have become a popular solution to modern-day issues surrounding the efficiency and reliability of power generation, as well as climate change concerns. Energy centers are shifting towards incorporating smart inverters with embedded functionalities such as high voltage ride through (HVRT), low voltage ride through (LVRT), active and reactive power compensation. However, the integration of smart inverters leave DER systems highly vulnerable to cybersecurity threats. The distributed network protocol 3 (DNP3) is a common method of communication between grid-tied hardware. Despite its popularity, the level of security leaves all hardware connected to the grid at risk of severe cyber-attacks. Thus, it is important to study any potential cybersecurity threats towards grid-tied smart inverters to mitigate cybersecurity vulnerabilities and refine existing cyber-security protections. This report describes the proposed testbed design to study cybersecurity threats to smart inverters. The testbed utilizes a real-time simulation case in RSCAD that includes a grid-tied wind turbine (WT) topology featuring two back-to-back two-level voltage source converters (BTB,2L-VSCs) and a permanent magnet synchronous machine (PMSM). The simulated case runs within the NovaCor real time digital simulator (RTDS). This report focuses on the design and implementation of a single module of the GTNETx2 card as a distributed network protocol and the configuration of an IEEE 1518 DNP database file that includes input and output variables mapped to different connection points in the grid that transmit and receive discrete, analog, and binary signals on command. This allows realistic emulation of the communication between the smart inverter and the grid for cybersecurity studies.

97 MATHEMATICS AND COMPUTING↗