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At least 379 records · Page 21

Efficient Unitary Designs from Random Sums and Permutations

A unitary k-design is an ensemble of unitaries that matches the first k moments of the Haar measure. In this work, we provide two efficient constructions of k-designs on n-qubits using new random matrix theory techniques. Our first construction is based on exponentiating sums of random i.i.d. Hermitian matrices and uses O(k2n2)-many gates. In the spirit of central limit theorems, we show that this random sum approximates the Gaussian Unitary Ensemble (GUE). We then show that the product of just two exponentiated GUE matrices is already approximately Haar random. Our second construction is based on products of exponentiated sums of random permutations and uses Õ(k poly (n)) many gates. The k dependence is optimal (up to polylogarithmic factors) and is inherited from the efficiency of existing k-wise independent permutations. Furthermore, replacing random permutations with quantum-secure pseudorandom permutations (PRPs), we also obtain a pseudorandom unitary (PRU) ensemble that is secure under nonadaptive queries. A central feature of both proofs is a new connection between the polynomial method in quantum query complexity and the large-dimension (N) expansion in random matrix theory. In particular, the first construction uses the polynomial method to control high moments of certain random matrix ensembles without requiring delicate Weingarten calculations. In doing so, we define and solve a moment problem on the unit circle, asking whether a finite number of equally weighted points can reproduce a given set of moments. In our second construction, the key step is to exhibit an orthonormal basis for irreducible representations of the partition algebra that has a low-degree large-N expansion. This allows us to show that the distinguishing probability is a low-degree rational polynomial of the dimension N.

algebra↗

Enhancing Distribution System Resilience: A First-Order Meta-RL Algorithm for Critical Load Restoration

The increasing frequency of extreme events and the integration of distributed energy resources (DERs) into modern grids have elevated the need for resilient and efficient critical load restoration strategies in distribution systems. However, the stochastic nature of renewable DERs, limited energy resource availability and the intricate nonlinearities inherent in complex grid control problem make the problem challenging. Although reinforcement learning (RL) and warm-start RL methods have shown promising results, their performance often falls short in rapidly adapting to new, unseen situations and typically requires exhaustive problem-specific tuning. To address these gaps, we propose a First-Order Meta-based RL (FOM-RL) algorithm within an online framework for adaptive and robust critical load restoration. By harnessing local DERs as the enabling technology, FOM-RL allows the RL agent to swiftly adapt to new unseen scenarios by leveraging previously acquired knowledge of different tasks. Experimental results provide evidence that proposed algorithm learns more efficiently and showcases generalization capabilities across diverse set of operational scenarios. Moreover, a rigorous theoretical analysis yields a tight sublinear regret bound, sensitive to temporal variability, with a task-averaged optimality gap bounded by O(VM+D*/(Tsquare root(M))). These results suggest that optimality improves with task similarity and an increased number of tasks M, reaffirming the efficacy and scalability of the proposed approach in addressing the complexities of critical load restoration in distribution systems.

complexity theory↗

Computing tools for effective field theories: SMEFT-Tools 2022 Workshop Report, 14–16th September 2022, Zürich

Abstract In recent years, theoretical and phenomenological studies with effective field theories have become a trending and prolific line of research in the field of high-energy physics. In order to discuss present and future prospects concerning automated tools in this field, the SMEFT-Tools 2022 workshop was held at the University of Zurich from 14th–16th September 2022. The current document collects and summarizes the content of this workshop.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Communication Lower Bounds and Optimal Algorithms for Symmetric Matrix Computations

In this article, we focus on the communication costs of three symmetric matrix computations: (i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) (ii) adding the result of the multiplication of a matrix with the transpose of another matrix and the transpose of that result, known as a symmetric rank-2k update (SYR2K) (iii) performing matrix multiplication with a symmetric input matrix (SYMM). All three computations appear in the Level 3 Basic Linear Algebra Subroutines (BLAS) and have wide use in applications involving symmetric matrices. We establish communication lower bounds for these kernels using sequential and distributed-memory parallel computational models, and we show that our bounds are tight by presenting communication-optimal algorithms for each setting. Our lower bound proofs rely on applying a geometric inequality for symmetric computations and analytically solving constrained nonlinear optimization problems. As a result, the symmetric matrix and its corresponding computations are accessed and performed according to a triangular block partitioning scheme in the optimal algorithms.

Al Daas, Hussam [Rutherford Appleton Laboratory, D↗

Tools for analysis of optimization models

The software is code for analyzing, debugging, and solving optimization models. The code implements several algorithms and provides convenient APIs to apply these algorithms to optimization models. The algorithms are primarily based on graph theory. They compute well-known partitions of graphs, and use these partitions to provide the user information about their optimization model, including diagnosing certain types of structural modeling errors. Some algorithms may be used as a subroutine to solve an optimization problem, and may call an optimization solver to facilitate this. Well-known linear algebra routines are called to provide further diagnostics. The software contains no data and no models other than toy models used for testing.

Parker, Robert↗

HD-Bind: Encoding of Molecular Structure with Low Precision, Hyperdimensional Binary Representations

Publicly available collections of drug-like molecules have grown to comprise tens of billions of compounds due to advances in combinatorial chemistry. Traditional methods for identifying "hit" molecules from a large collection of potential drug-like candidates have relied on biophysical theory to compute approximations to the Gibbs free energy of the binding interaction between the drug and its protein target. These approaches have the major drawback that they require exceptional computing capabilities for even relatively small collections of molecules. Hyperdimensional Computing (HDC) is a recently-proposed learning paradigm that represents data with high-dimension binary vectors; this allows the use of low-precision binary vector arithmetic to create models of the data that can be learned without the need for the gradient-based optimization required in many conventional machine learning and deep learning methods. This algorithmic simplicity allows for acceleration in hardware that has been previously demonstrated in a range of application areas. We consider existing HDC approaches for molecular property classification and introduce two novel encodings of a commonly-used molecular representation, the extended connectivity fingerprint (ECFP). We show that HDC-based inference methods are as much as 91 times more efficient than traditional machine learning methods, and achieve an acceleration of nearly nine orders of magnitude compared to molecular docking. Our results show that HDC accelerated methods retain competitive accuracy on a number of well-studied tasks such as molecular property predictions using the MoleculeNet dataset, and bind/no-bind activity classification using the DUD-E and LIT-PCBA datasets. Our work thus motivates further investigation into molecular representation learning to develop ultraefficient pre-screening tools.

Jones, William↗

US Department of Energy, Office of Science High Performance Computing Facility Operational Assessment 2019 Oak Ridge Leadership Computing Facility

Oak Ridge National Laboratory's (ORNL's) Leadership Computing Facility (OLCF) continues to surpass its operational target goals: supporting users; delivering fast, reliable computational ecosystems; creating innovative solutions for high performance computing (HPC) needs; and managing risks, safety, and security associated with operating some of the most powerful computers in the world. The results can be seen in the cutting-edge science conducted by users and the praise from the research community. Calendar year (CY) 2019 was a big year as OLCF staff ran five world-class resources (the leadershipclass computers Titan and Summit, the large analysis cluster called Eos, and the massive parallel filesystems called Atlas and Alpine)) and also began power and cooling upgrades for a 2021 exascale system called Frontier. While continuing exceptional operation of Titan, Eos, and Rhea, the OLCF released the Summit supercomputer for production on January 1, 2019. Summit debuted as the most capable and efficient system in its class and has been recognized as the most powerful system in the world for its performance on both the high performance linpack (HPL) and conjugate gradient (HPCG) benchmark applications since June 2018 according to TOP500. Summit represents the culmination of a multiyear effort between the OLCF, IBM, NVIDIA, and Mellanox to deliver a system that is unmatched for modeling, simulation, data analysis, and learning. To hit the ground running with science-ready applications on day one, application teams worked closely with the OLCF through the Center for Accelerated Application Readiness (CAAR) program for years in advance of the Summit deployment. CY 2019 was filled with outstanding results and accomplishments: a very high rating from users on overall satisfaction for the sixth year in a row; a tremendous amount of core-hours delivered to researchers from two leadership-class systems; and success in delivering on the allocation split of roughly 60%, 30%, and 10% of core-hours offered for the Innovative and Novel Computational Impact on Theory and Experiment (INCITE), Advanced Scientific Computing Research Leadership Computing Challenge (ALCC), and Director's Discretionary (DD) programs, respectively (see Operational Performance section). These accomplishments, coupled with the high utilization rates (overall and capability usage), represent the fulfillment of the promise of both leadership-class machines: efficient facilitation of leadership-class computational applications. Table ES.1 presents a summary of the 2019 OLCF metric targets and the associated results. More information can be found in the Operational Performance section for each OLCF resource. The scientific accomplishments of OLCF users are a strong indication of long-term operational success, with publications this year in such notable journals and publications as Nature, Nature Physics, Nature Plants, Physical Review X, Journal of the American Physical Society, Cell, Nano Letters, and Trends in Biotechnology. Crucial domain-specific discoveries facilitated by resources at the OLCF are described in the High Performance Computing Facility Operational Assessment 2019 Oak Ridge Leadership Computing Facility (OAR) Strategic Results section. For example, researchers used Summit to pinpoint and understand the production of proteins from genetic information, including mutations and the functional expression of disease (Section 8.2).

97 MATHEMATICS AND COMPUTING↗

Designing Catalysts for Dehydrogenation of Methane for Reducing Greenhouse Gas during Natural Gas Extraction

Catalytic conversion of methane (CH 4 ) into useful products is critical for maximizing the utility of natural gas output and for reducing green house gas release associated with flaring (burning off CH 4 at natural gas extraction sites). One particular useful technique is methane dry reforming (DRM), which involves the chemical reaction of CH 4 with carbon dioxide (CO 2 ) to generate carbon monoxide (CO), hydrogen gas (H 2 ), and subsequently other useful products. New and improved catalysts are required to facilitate efficient dry methane reforming. In this report, we apply the Density Functional Theory (DFT) computational technique to investigate a catalyst consisting of small nickel clusters (Ni n , n < 10) on ceria (Ce0 2 (111) surfaces) support. One main thrust of this project is to study the initial CH 4 and CO 2 reactions with the catalyst. We find that CH 4 exhibits barrierless reactive adsorption on to the catalyst. In order words, this step is likely not the rate-determining step. A second thrust is to perform detailed studies of the catalyst itself and examine the role of oxygen vacancies. Using a specific DFT method and a hypothesis about the absence of the Ce(III) redox state, we obtain predictions about oxygen vacancies in good agreement with experimental observations.

03 NATURAL GAS↗

A trait-based framework for linking microbial communities with carbon transformations under precipitation change

Droughts are common throughout the world. As the climate changes, droughts may become more frequent and intense. Still, scientists are uncertain about how drought will affect the natural world, particularly the bacteria, fungi, and other microbes that live in soils. These tiny life forms are crucial because they control the Earth’s flows of carbon and essential nutrients. Researchers at the University of California, Irvine, and Lawrence Berkeley National Laboratory teamed up to study how the microbiome, or collection of bacteria and fungi in the soil, deals with drought. Since 2007, the researchers have used shelters with retractable roofs to prevent nearly half of normal rainfall from reaching grass and shrub ecosystems, and their soil microbiomes, in Southern California. The study team discovered that microbes have some clever tricks up their sleeve for surviving drought. When growing on dead grass as a food source, microbes ramp up production of specialized chemicals called osmolytes that keep their cells from drying out. But microbes growing on dead shrubs face another problem. Unlike grass, shrub leaves are a lousy food source. To digest and consume shrub leaves, microbes have to exude more enzymes, which act like biochemical chef knives that chop complex leaf molecules into bite-sized pieces. Carbon is the coin of the microbial realm, earned via enzyme action or slurping up dead plant juices. Microbes growing under normal conditions on tasty dead grass have it easy: they can spend most of their carbon currency on growth. With drought, life gets harder as microbes need to pay up for osmolytes and ramp down their growth. It gets worse with shrub leaves because microbes have to multi-task among growth, enzyme secretion, and osmolyte production. When drought hits, microbes on shrub leaves forgo the osmolytes, probably because losing the carbon revenue from enzyme investment would be a deal-breaker for survival. The next question tackled by the researchers asked how the genes controlling microbial lifestyles sort out across the tree of life. Most microbiologists thought these lifestyles would correspond to rather large branches on the tree. But the study team found that in fact, very closely related microbes differ in important and interesting ways. For example, bacteria that have nearly identical housekeeping genes respond distinctively to warming, rainfall, and plant chemistry. As a result, soil microbiomes are much richer in diversity than originally thought. And studying microbial diversity in much greater detail could open up many more possibilities for how microbial life deals with changing environmental conditions. Trying to understand microbial life without the fine details of genetic diversity is like trying to stream Netflix on a dial-up connection. By looking across the landscape, the researchers revealed that microbial diversity is absolutely critical for maintaining the planet’s flows of carbon and nutrients. The study team designed a new technology—microbial cages—for transplanting intact microbiomes. With the cages, the researchers could move microbiomes to novel environments and compare their ability to cycle carbon and nutrients. In some cases, performance tailed off when microbiomes found themselves in a new environment, but in other cases, performance rivaled or even exceeded that of the resident microbiome. And even the low performers eventually caught up to the native microbiomes if given sufficient time. These findings mean that microbiomes—at least in Southern California—may be resilient to climate shifts due to a high diversity of microbial lifestyles. Coping with heat and drought may literally be in their DNA. The last piece of the research puzzle, and a “Holy Grail” for microbial ecologists, is to forecast the behavior of diverse microbiomes. To meet this challenge, the study team developed new theory and computer models. For the first time, these models account for hundreds of different microbes and how their intricate lifestyles cope with drought. The models are starting to connect the tiniest microbes with the global cycles that sustain Earth’s farms, fields, and forests. With that connection, it will be easier for society to plan for a world with more droughts and other climate disruptions.

54 ENVIRONMENTAL SCIENCES↗

Helicity Injected Torus (HIT): Sustainment of Stable Equilibria Through Self-organization

This is the Final Progress Report of the Helicity Injected Torus (HIT) program covering May 2016 through December 2020. During this final period the HIT program continued to make advancements in computational modeling, theory, and experimental studies of global self-organization and inductively sustained spheromaks. This included many valuable contributions to the fusion, plasma and physics community, through peer-reviewed publications, PhD theses and conference presentations and posters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

US Department of Energy, Office of Science High Performance Computing Facility Operational Assessment 2021: Oak Ridge Leadership Computing Facility

Oak Ridge National Laboratory’s (ORNL’s) Leadership Computing Facility (OLCF) continues to surpass its operational target goals of supporting users; delivering fast, reliable computational ecosystems; creating innovative solutions for high-performance computing (HPC) needs; contributing to the community to build the next generation HPC workforce, and managing risks, safety, and security associated with operating some of the most powerful computers in the world. The results can be seen in the cutting-edge science conducted by users and the praise from the research community. Calendar year (CY) 2021 saw continued excellence in research supported by the OLCF’s leadership-class computing resources, including Summit (the nation’s most powerful supercomputer), the global scratch file system Alpine, the Scalable Protected Infrastructure (SPI), the Exploratory Visualization Environment for Research in Science and Technology (EVEREST), and the archival mass-storage resource High-Performance Storage System (HPSS). While maintaining access and exceptional user support for Summit, the OLCF continued to make progress on the installation and deployment of Frontier, which will be the nation’s first exascale system when it comes online at the start of CY 2023. Users have already begun running and optimizing scientific codes on Crusher, the OLCF test and development system equipped with Frontier’s architecture. Throughout the year, the OLCF maintained a strong culture of operational excellence, including risk management, workplace safety, and cybersecurity. The OLCF’s rigorous risk management strategy anticipated and mitigated risks, and at this time there are no high-priority operational risks. Similarly, ORNL and the OLCF were committed to operating under the US Department of Energy’s (DOE’s) safety regulations that ensure a safe workplace. Technical staff tracked and monitored existing threats and vulnerabilities within the OLCF while continually developing tools and practices to enhance operations without increasing the facility’s risk. CY 2021 was filled with outstanding results and accomplishments, including a very high rating from users on overall satisfaction for the eighth consecutive year; a tremendous number of node hours delivered to 1,671 researchers on Summit; and the successful delivery of the allocation split of roughly 60%, 20%, and 20% of core-hours offered for the Innovative and Novel Computational Impact on Theory and Experiment (INCITE), Advanced Scientific Computing Research Leadership Computing Challenge (ALCC), and Director’s Discretionary (DD) programs, respectively (Section 2). COVID-19 research remained a focus in 2021, and the ALCC and DD programs allocated over 1 million Summit hours to the COVID-19 High Performance Computing Consortium. These accomplishments, coupled with the high utilization rates (i.e., overall and capability usage), represent the fulfillment of the promise of leadership class machines: efficient facilitation of leadership-class computational applications.

97 MATHEMATICS AND COMPUTING↗

Basic Research in Edge and Scrape-Off Layer Fusion Plasmas (Final Report)

U.S. Department of Energy (DOE) supported work at Lodestar Research Corporation under grant DE-FG02-97ER54392 is summarized in this final report. The research conducted under this grant addressed key scientific issues associated with boundary plasmas in fusion energy experimental devices. Harnessing the energy that is released in fusion reactions would provide a safe and abundant source of power to meet the growing energy needs of the world population. Lodestar investigated the important cm-scale region near the edge of these devices where hot plasma, close to one million degrees, meets material surfaces in what is known as a scrape-off layer (SOL). This critical region is subject to plasma turbulence and plasma flows which must be understood to optimize fusion performance on future machines. Strong interactions of applied RF waves is also observed to occur in this region, and must be understood to mitigate unwanted effects and enhance overall performance. The work employed theoretical models and theory-based computational models for validation. The models were applied to understand experimental results and to carry out basic theoretical investigations relevant to the production of fusion energy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Advanced Closures for Nonlinear Fluid Simulations of Plasmas (Final Report)

Advanced Closures for Nonlinear Fluid Simulations of Plasmas E. Held, Utah State University (Principal Investigator) J.-Y. Ji, Utah State University (Co-Investigator) Utah State University (USU) continued to develop and apply closures for hybrid fluid/kinetic simulations of magnetized fusion plasmas. The closures developed by USU's fusion theory and computation group use the drift ordering and are referred to as "continuum" and "general moment" approaches. They differ in their representation for the distribution functions which probabilistically describe the density of particles in 5 dimensional phase space. The two chosen velocity variables, needed in studies of kinetic physics for magnetized plasmas, are the speed and the component of a particle's velocity along the magnetic field. In magnetized plasmas, the charged particle trajectories are tied closely to the magnetic field lines. Both approaches account for binary interactions between particles using the Coulomb collision operator. Theoretical and computational development along both lines provided avenues for verification between the two approaches. This funding allowed USU to further develop physically accurate and numerically efficient models that advance our understanding of kinetic physics in experiments like the International Thermonuclear Experimental Reactor (ITER). The ITER device will likely prove the physical practicality of thermonuclear fusion by producing 500 megawatts of clean, abundant fusion power. This work helped to realize this goal by advancing our simulation capability using hybrid fluid/kinetic models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Tunable Few-Layer van der Waals Crystals and Heterostructures as Emerging Energy and Quantum Materials (Final Technical Report)

2D and layered (van der Waals) semiconductors offer extraordinary opportunities for manipulating optically excited charge carriers, many-body excitations, and non-charge based quantum numbers. To date, research has focused on a limited group of materials, mostly transition metal dichalcogenides in the monolayer limit. Other van der Waals semiconductors, and especially few-layer to multilayer crystals and their heterostructures, carry large potential for the discovery of phenomena of interest for future energy and information technologies. But they remain largely unexplored, often due to a lack of access to high-quality materials and approaches for measuring their properties at the relevant scales. The goal of this project was to develop an EPSCoR-State/National Laboratory Partnership that addresses the challenges of preparing high-quality van der Waals semiconductors and of probing their structure, composition, and especially their optoelectronic and photonic properties, near the atomic scale using electron microscopy techniques. A central component of the project was the development of advanced methods for electron microscopy and electron-excited spectroscopy, taking advantage of unique samples as well as leading capabilities and expertise at the partner institutions. Efforts to advance leading-edge techniques was supported by ancillary developments, such as precision sample preparation for electron microscopy/spectroscopy, coordinated chemical imaging, and analytical electron microscopy. Experiments in materials synthesis and technique development were closely linked to theory and computation. The results obtained under this project yielded multifaceted benefits to the involved partners and their institutions, DOE-BES, the wider scientific community, and society at large, particularly in the State of Nebraska through dividends from knowledge and human capital generated under the project.

36 MATERIALS SCIENCE↗

Ocean Energy Systems Wave Energy Modeling Task 10.4: Numerical Modeling of a Fixed Oscillating Water Column

This paper reports on an ongoing international effort to establish guidelines for numerical modeling of wave energy converters, initiated by the International Energy Agency Technology Collaboration Program for Ocean Energy Systems. Initial results for point absorbers were presented in previous work, and here we present results for a breakwater-mounted Oscillating Water Column (OWC) device. The experimental model is at scale 1:4 relative to a full-scale installation in a water depth of 12.8 m. The power-extracting air turbine is modeled by an orifice plate of 1–2% of the internal chamber surface area. Measurements of chamber surface elevation, air flow through the orifice, and pressure difference across the orifice are compared with numerical calculations using both weakly-nonlinear potential flow theory and computational fluid dynamics. Both compressible- and incompressible-flow models are considered, and the effects of air compressibility are found to have a significant influence on the motion of the internal chamber surface. Recommendations are made for reducing uncertainties in future experimental campaigns, which are critical to enable firm conclusions to be drawn about the relative accuracy of the numerical models. It is well-known that boundary element method solutions of the linear potential flow problem (e.g., WAMIT) are singular at infinite frequency when panels are placed directly on the free surface. This is problematic for time-domain solutions where the value of the added mass matrix at infinite frequency is critical, especially for OWC chambers, which are modeled by zero-mass elements on the free surface. A straightforward rational procedure is described to replace ad-hoc solutions to this problem that have been proposed in the literature.

16 TIDAL AND WAVE POWER↗

Testing Classical Properties from Quantum Data

Many properties of Boolean functions can be tested far more efficiently than the function itself can be learned. However, this dramatic advantage often disappears when testers are limited to random samples of ƒ instead of adaptively chosen queries to f. In this work we investigate the quantum version of this restriction: quantum algorithms that test properties of a Boolean function f solely from copies of either the function state |ƒ⟩ ∝ ∑ x |x, ƒ(x)⟩ or the phase state |(-1) ƒ ⟩ ∝ ∑ x (-1) ƒ(x) |x⟩. For monotonicity, symmetry, and triangle-freeness, we show passive quantum testers are unboundedly or super-polynomially better than their classical passive testing counterparts. They are competitive with classic query -based testers in each case. Our new testers use techniques beyond quantum Fourier sampling, and it turns out this is necessary: we show a certain class of bent functions can be tested from 𝒪(1) function states but has a sample complexity lower bound of 2 Ω(n) for any tester relying exclusively on Fourier and classical samples. Our passive quantum testers are competitive with classical query -based testers, but this isn't universal: we exhibit a testing problem that can be solved from 𝒪(1) classical queries but requires Ω(2 n/2 ) function state copies. The Forrelation problem provides a separation of the same magnitude in the opposite direction, so we conclude that quantum data and classical queries are "maximally incomparable" resources for testing. We also begin the study of lower bounds for testing from quantum data. For quantum monotonicity testing, we prove that the ensembles of [Goldreich et al., 2000; Black, 2024], which give exponential lower bounds for classical sample-based testing, do not yield any nontrivial lower bounds for testing from quantum data. New insights specific to quantum data will be required for proving copy complexity lower bounds for testing in this model.

Boolean Functions↗

Diffraction of radio-frequency waves by plasma turbulence in the edge of a tokamak

The Mie-Lorenz-Debye theory of scattering of radio frequency waves (RF) by filamentary structures in the edge of a tokamak plasma has been established in prior publications. These results have been verified. Theory and computations show that RF can be reflected, refracted, and diffracted by turbulence. Furthermore, the filamentary structures lead to side scattering of waves and excitation of wave modes different from the launched RF. It is important to quantify the overall effect of turbulence on the propagation of RF since efficiency of heating and current drive by RF waves depends upon the wave characteristics. The commonly used RF ranges vary from the low frequency ion-cyclotron (IC) waves, to medium frequency lower-hybrid (LH) waves, to high-frequency electron cyclotron (EC) waves with wavelengths respectively, large, comparable, or smaller than the radial dimensions of the filaments. Currently, we discuss the scattering as well as the forces exerted by different RF in the edge plasma. Also, we present a code for 3D full wave scattering analysis of arbitrary tensor permittivity and plasma density profiles. The study is applicable to ITER-like plasmas, as well as to plasmas in medium sized tokamaks such as TCV, ASDEX-U and DIII-D and high field concepts like SPARC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗