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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Roofline Analysis in the Intel® Advisor to Deliver Optimized Performance for applications on Intel® Xeon Phi™ Processor

In this session we show, in two case studies, how the roofline feature of Intel Advisor has been utilized to optimize the performance of kernels of the XGC1 and PICSAR codes in preparation for Intel Knights Landing architecture. The impact of the implemented optimizations and the benefits of using the automatic roofline feature of Intel Advisor to study performance of large applications will be presented. This demonstrates an effective optimization strategy that has enabled these science applications to achieve up to 4.6 times speed-up and prepare for future exascale architectures. # Goal/Relevance of Session The roofline model [1,2] is a powerful tool for analyzing the performance of applications with respect to the theoretical peak achievable on a given computer architecture. It allows one to graphically represent the performance of an application in terms of operational intensity, i.e. the ratio of flops performed and bytes moved from memory in order to guide optimization efforts. Given the scale and complexity of modern science applications, it can often be a tedious task for the user to perform the analysis on the level of functions or loops to identify where performance gains can be made. With new Intel tools, it is now possible to automate this task, as well as base the estimates of peak performance on measurements rather than vendor specifications. The goal of this session is to demonstrate how the roofline feature of Intel Advisor can be used to balance memory vs. computation related optimization efforts and effectively identify performance bottlenecks. A series of typical optimization techniques: cache blocking, structure refactoring, data alignment, and vectorization illustrated by the kernel cases will be addressed. # Description of the codes ## XGC1 The XGC1 code [3] is a magnetic fusion Particle-In-Cell code that uses an unstructured mesh for its Poisson solver that allows it to accurately resolve the edge plasma of a magnetic fusion device. After recent optimizations to its collision kernel [4], most of the computing time is spent in the electron push (pushe) kernel, where these optimization efforts have been focused. The kernel code scaled well with MPI+OpenMP but had almost no automatic compiler vectorization, in part due to indirect memory addresses and in part due to low trip counts of low-level loops that would be candidates for vectorization. Particle blocking and sorting have been implemented to increase trip counts of low-level loops and improve memory locality, and OpenMP directives have been added to vectorize compute-intensive loops that were identified by Advisor. The optimizations have improved the performance of the pushe kernel 2x on Haswell processors and 1.7x on KNL. The KNL node-for-node performance has been brought to within 30% of a NERSC Cori phase I Haswell node and we expect to bridge this gap by reducing the memory footprint of compute intensive routines to improve cache reuse. ## PICSAR is a Fortran/Python high-performance Particle-In-Cell library targeting at MIC architectures first designed to be coupled with the PIC code WARP for the simulation of laser-matter interaction and particle accelerators. PICSAR also contains a FORTRAN stand-alone kernel for performance studies and benchmarks. A MPI domain decomposition is used between NUMA domains and a tile decomposition (cache-blocking) handled by OpenMP has been added for shared-memory parallelism and better cache management. The so-called current deposition and field gathering steps that compose the PIC time loop constitute major hotspots that have been rewritten to enable more efficient vectorization. Particle communications between tiles and MPI domain has been merged and parallelized. All considered, these improvements provide speedups of 3.1 for order 1 and 4.6 for order 3 interpolation shape factors on KNL configured in SNC4 quadrant flat mode. Performance is similar between a node of cori phase 1 and KNL at order 1 and better on KNL by a factor 1.6 at order 3 with the considered test case (homogeneous thermal plasma).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Pre-Irradiation Comparison of W-Based Alloys for the PHENIX Campaign: Microstructure, Composition, and Mechanical Properties

Tungsten is the material of choice as the plasma-facing material in future plasma-burning fusion reactors. During operation, plasma-facing materials will be simultaneously exposed to 14-MeV neutrons, low-energy D/He particles, and high heat loads. Neutron irradiation of tungsten results in bulk material damage, including knock-on damage causing loops and voids, and transmutation reactions leading to the transmutation of tungsten to rhenium and osmium. Under irradiation to high dose, Re and Os atoms can amalgamate into precipitates that drastically alter the material properties, noticeably increasing the hardness. However, the early-stage development of Re and Os precipitates under a fast neutron spectrum has not been investigated.In this work, the microstructure and hardening behavior of W-Re alloys containing 0 to 2.2 wt% Re, TiC-doped W, and powder-injection-molded W are investigated prior to neutron irradiation at 500ºC and 800ºC to ~0.1 displacement per atom in the High Flux Isotope Reactor (HFIR) to establish a baseline understanding of the starting microstructures.Transmission electron microscopy analysis indicates a dislocation-heavy microstructure, and scanning transmission electron microscopy–energy dispersive spectroscopy shows no spatial segregation of Re and W. Similarly, surface compositional studies performed with electron backscatter diffraction and X-ray photoelectron spectroscopy showed no presence of Re, indicating the Re did not segregate or form new phases during fabrication. Here, the alloys in their as-fabricated state showed no Re segregation or second-phase development, with no significant differences between their microstructures and Vickers hardness values.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Generation and Control of Self-Organized Nonlinear Kinetic Structures in High Energy Density Plasmas in the Presence of Intense Magnetic Fields and Ultrashort Laser Pulses

Goals were to study the interplay between electron plasma waves (EPW), KEEN waves and externally generated magnetic fields. In particular, the Weibel instability B field generation process and its interrelationship with the existence of nonlinear EPWs in high energy density plasmas. We focused on a number of models of how Kinetic, Nonlinear Electron Plasma Waves, KNL-EPW and KEEN waves create anisotropic electron velocity distribution functions, e- VDF, and how these anisotropic e- VDFs in turn drive the Weibel instability and generate B fields. Our goal is to control the SRS and SKEENS processes that generate the KNL-EPW, control the anisotropy, and thus also control the dynamics of the resulting B fields, their influence on the transport coefficients and heat transport that results, their modification of SRS itself and the reinforced anisotropy driven loop gain.

(Kinetic electrostatic electron nonlinear) KEEN wa↗
DOE OSTI2024

Impact of structural biology and the protein data bank on us fda new drug approvals of low molecular weight antineoplastic agents 2019–2023

Abstract Open access to three-dimensional atomic-level biostructure information from the Protein Data Bank (PDB) facilitated discovery/development of 100% of the 34 new low molecular weight, protein-targeted, antineoplastic agents approved by the US FDA 2019–2023. Analyses of PDB holdings, the scientific literature, and related documents for each drug-target combination revealed that the impact of structural biologists and public-domain 3D biostructure data was broad and substantial, ranging from understanding target biology (100% of all drug targets), to identifying a given target as likely druggable (100% of all targets), to structure-guided drug discovery (>80% of all new small-molecule drugs, made up of 50% confirmed and >30% probable cases). In addition to aggregate impact assessments, illustrative case studies are presented for six first-in-class small-molecule anti-cancer drugs, including a selective inhibitor of nuclear export targeting Exportin 1 (selinexor, Xpovio), an ATP-competitive CSF-1R receptor tyrosine kinase inhibitor (pexidartinib,Turalia), a non-ATP-competitive inhibitor of the BCR-Abl fusion protein targeting the myristoyl binding pocket within the kinase catalytic domain of Abl (asciminib, Scemblix), a covalently-acting G12C KRAS inhibitor (sotorasib, Lumakras or Lumykras), an EZH2 methyltransferase inhibitor (tazemostat, Tazverik), and an agent targeting the basic-Helix-Loop-Helix transcription factor HIF-2α (belzutifan, Welireg).

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

Neural network reconstruction of the DIII-D tokamak plasma boundary using a reduced set of diagnostics

This study investigates the feasibility of reconstructing the last closed flux surface in the DIII-D tokamak using neural network models trained on reduced input feature sets, addressing an ill-posed task. Two models are compared: one trained solely on coil currents and another incorporating coil currents, plasma current and loop voltage. The model trained exclusively on coil currents achieved a mean point displacement of $0.04$ m on a held-out test set, while the inclusion of plasma current and loop voltage reduced the error to $0.03$ m. This comparison highlights the trade-offs between input feature complexity and reconstruction accuracy, demonstrating the potential of machine learning algorithms to perform effectively in data-limited environments, such as those expected in fusion power plants due to diagnostic constraints imposed by the presence of blankets and shielding.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Understanding Formation of Irradiation-Induced Defects through 4D-STEM, Electron Tomography, and WBDF-STEM

A major challenge in advancing nuclear materials for next-generation fission and proposed fusion reactors is to comprehensively understand the formation of irradiation-induced defects. Here it is essential to correlate the evolution of irradiation-induced defects and the degradation of mechanical properties, as they collectively dictate the material's lifespan and ensure nuclear safety. Scanning transmission electron microscopy (STEM) based techniques have emerged as indispensable tools for irradiation-induced defect characterization, offering high spatial resolution imaging and chemical analysis, such as electron energy loss spectroscopy (EELS) and energy dispersive X-ray spectroscopy (EDXS). These techniques have been effectively used to obtain an atomic-scale view of the defect structure. Recent advances in electron microscopy, particularly in 4D-STEM, offer detailed insight into microstructural evolution by capturing full 2D diffraction patterns at every pixel position. Using high-speed direct electron detectors, this technology generates a four-dimensional dataset, overcoming the limitations of traditional STEM imaging.

36 MATERIALS SCIENCE↗
DOE OSTI2024

On a class of selection rules without group actions in field theory and string theory

We discuss a class of selection rules which i) do not come from group actions on fields, ii) are exact at tree level in perturbation theory, iii) are increasingly violated as the loop order is raised, and iv) eventually reduce to selection rules associated with an ordinary group symmetry. We start from basic field-theoretical examples in which fields are labeled by conjugacy classes rather than representations of a group, and discuss generalizations using fusion algebras or hypergroups. We also discuss how such selection rules arise naturally in string theory, such as for non-Abelian orbifolds or other cases with non-invertible worldsheet symmetries.

Kaidi, Justin (ORCID:0000000161440729)↗
DOE OSTI2021

Estimation of sensor measurement errors in reactor coolant systems using multi-sensor fusion

A nuclear power plant is typically instrumented with a variety of sensors to continually monitor its variables, and their sensor’s measurements may be used to assess the plant state and initiate safety actions, if needed. Errors in sensor measurements, due to factors such as calibration drifts, critically affect such state assessments. Here, we address a problem of estimating sensor errors using physics-informed machine learning methods that use measurements collected under known plant conditions. For a given sensor, we propose an information fusion method that uses measurements from other sensors to estimate its output assuming it is error-free and provides its difference from an actual measurement as an error estimate. We present the ensemble of trees and support vector machine fusers, and evaluate their performance using measurements collected over an emulated test loop of a pressurized water reactor. The plant variables are related to each other through the underlying physical laws under inertial constraints that place bounds on their derivatives, which analytically justify the applicability of machine learning methods for computing these fusers. Under twenty scenarios, we assess their sensor error estimates for pressure sensors of the heat exchanger of a reactor’s primary coolant system. Multiple types of errors are captured by both fusers under externally induced calibration drifts, blockages, minor leaks and air gaps in sensing lines, and electromagnetic interference; the root mean square error of the estimation of error is under 2.2% percent of the maximum measurement. We present generalization equations, in the framework of statistical learning theory, for these methods that characterize the confidence probability that the estimation error is bounded by a specified parameter in future test scenarios.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Validation of prediction capability of operating space for plasma initiation in MAST-U

DYON is a plasma initiation modelling code that solves the differential equation system of the full circuit equations (plasma current, active coil currents and eddy currents in full passive structures) and 0D global energy and particle balance equations (Kim 2022 Nucl. Fusion 62 126012). In order to test the capability of the full electromagnetic plasma initiation model to predict individual discharges in experiments and thus the operating space in the device, a dedicated experimental database was built in MAST-U by scanning the prefilled gas pressure p 0 and the induced loop voltage V loop . In the experimental operating space of p 0 and V loop the lower and the upper limits of p 0 are determined by the plasma breakdown failure and the plasma burn-through failure, respectively. The lower limit of V loop is determined by the plasma burn-through failure. By directly reading the control room data used in each discharge (i.e. currents in the solenoid, poloidal field coils, and toroidal field coils, p 0 , and gas puffing rate), the full electromagnetic DYON consistently predicted the failed breakdown, failed burn-through, and successful plasma initiation discharges in the experimental database, demonstrating its capability to predict the operating space for inductive plasma initiation. The Paschen curve calculated with the effective connection length in MAST-U indicates a much higher p 0 required for plasma breakdown than the experimental data, indicating that individual field line evaluation is necessary to calculate the quantitative requirements for Townsend breakdown. The demonstration in this paper shows that the full electromagnetic DYON could be a useful simulation tool to assess the feasibility of inductive plasma initiation and to optimise operating scenarios in future devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

MCNP Models for Tokamak Cooling Water System Equipment Evaluations

Heat generated in the ITER fusion reactor is deposited in the tokamak vacuum vessel, in-vessel components, and in the components of the neutral beam injector during plasma operations and during subsequent decay of activation products. This heat is managed by the tokamak cooling water system (TCWS). The stainless steel material in the integrated loop of blanket edge-localized mode vertical stabilization coils and divertor (IBED) components (e.g., piping, heat exchangers (HXs), and pumps) contains activation sources because of its exposure primarily to neutron radiation from the decay of 17 N, which is a short-lived radionuclide produced by neutron capture reactions with oxygen nuclei in the IBED primary heat transfer system (PHTS) cooling water during plasma operations. A detailed geometry model of the IBED stainless steel components and neutron radiation sources is required for an accurate assessment of the gamma activation sources on level 3 of the tokamak building. In the baseline design, each of the eight IBED PHTS cooling trains has two shell-and-tube heat exchangers (HXs) connected in series. Because these HXs are very large and contain a large amount of radioactive water, the possibility of using compact HXs of the welded shell-and-plate type is under investigation. This paper presents two Monte Carlo N-Particle (MCNP) TCWS geometry models, one model for each HX type, along with the associated piping. These models were obtained by automatic geometry conversion from TCWS computer-aided design models. In conclusion, the TCWS geometry models and neutron source definitions were incorporated into a baseline MCNP model of the Tokamak Complex.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Temperature-dependent model of helium bubble expansion and bursting in tungsten

Continuum-scale models that can reliably predict the behavior of helium in tungsten are of interest to the fusion community due to the projected impact of these materials on fusion reactor operation. In this work, we perform molecular dynamics simulations of spherical helium bubbles of various sizes in tungsten at different temperatures and depths with the goal of determining a mathematical model of the pressure and density at which the bubbles initially expand or burst as a function of depth, size, temperature, and surface orientation. The bubbles are small enough that their loop-punching pressures cannot be accurately predicted with continuum mechanics, and their expansion behavior is important, as it appears to cause many of the features observed on helium-irradiated tungsten surfaces. We vary the temperature, bubble size, bubble depth, and surface orientation in each case, recording the bubble pressure and density that result in bubble expansion. An exponential function with three adjustable parameters is found to fit the results well; the parameters that best fit our results are provided.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Development of a Scanning Microscale Fast Neutron Irradiation Platform for Examining the Correlation Between Local Neutron Damage and Graphite Microstructure

The fast particle radiation damage effect of graphite, a main material in current and future nuclear reactors, has significant influence on the utilization of this material in fission and fusion plants. Atoms on graphite crystals can be easily replaced or dislocated by fast protons and result in interstitials and vacancies. The currently accepted model indicates that after most of the interstitials recombine with vacancies, surviving interstitials form clusters and furthermore gather to create loops with each other between layers. Meanwhile, surviving vacancies and interstitials form dislocation loops on the layers. The growth of these inserted layers cause the dimensional increase, i.e. swelling, of graphite. Interstitial and vacancy dislocation loops have been reported and they can easily been observed by electron microscope. However, observation of the intermediate atom clusters becomes is paramount in helping prove this model. We utilize fast protons generated from the University of Missouri Research Reactor (MURR) cyclotron to irradiate highly- oriented pyrolytic graphite (HOPG) as target for this research. Post-irradiation examination (PIE) of dosed targets with high-resolution transmission electron microscopy (HRTEM) has permit observation and analysis of clusters and dislocation loops to support the proposed theory. Another part of the research is to validate M.I. Heggie’s Ruck and Tuck model, which introduced graphite layers may fold under fast particle irradiation. Again, we employed microscopy to image irradiated specimens to determine how the extent of Ruck and Tuck by calculating the number of folds as a function of dose. Our most significant accomplishment is the invention of a novel class of high-intensity pure beta-emitters for long-term lightweight batteries. We have filed four invention disclosure records based on the research conducted in this project. These batteries are lightweight because they consist of carbon and tritium and can be fabricated to conform to many geometric shapes. In addition, we have published eight peer-reviewed American Nuclear Society (ANS) transactions, and presented our findings at ANS National Meetings, and several universities.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Optimizing the Design of Diatom Biosilica-Targeted Fusion Proteins in Biosensor Construction for Bacillus anthracis Detection

In vivo functionalization of diatom biosilica frustules by genetic manipulation requires careful consideration of the overall structure and function of complex fusion proteins. Although we previously had transformed Thalassiosira pseudonana with constructs containing a single domain antibody (sdAb) raised against the Bacillus anthracis Sterne strain, which detected an epitope of the surface layer protein EA1 accessible in lysed spores, we initially were unsuccessful with constructs encoding a similar sdAb that detected an epitope of EA1 accessible in intact spores and vegetative cells. This discrepancy limited the usefulness of the system as an environmental biosensor for B. anthracis. We surmised that to create functional biosilica-localized biosensors with certain constructs, the biosilica targeting and protein trafficking functions of the biosilica-targeting peptide Sil3T8 had to be uncoupled. We found that retaining the ER trafficking sequence at the N-terminus and relocating the Sil3T8 targeting peptide to the C-terminus of the fusion protein resulted in successful detection of EA1 with both sdAbs. Homology modeling of antigen binding by the two sdAbs supported the hypothesis that the rescue of antigen binding in the previously dysfunctional sdAb was due to removal of steric hindrances between the antigen binding loops and the diatom biosilica for that particular sdAb.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

O'Hare Airport roadway traffic prediction via data fusion and Gaussian process regression

This study proposes an approach of leveraging information gathered from multiple traffic data sources at different resolutions to obtain approximate inference on the traffic distribution of Chicago's O'Hare Airport area. Specifically, it proposes the ingestion of traffic datasets at different resolutions to build spatiotemporal models for predicting the distribution of traffic volume on the road network. Due to its good adaptability and flexibility for spatiotemporal data, the Gaussian process (GP) regression was employed to provide short-term forecasts using data collected by loop detectors (sensors) and supplemented by telematics data. The GP regression is used to make predictions of the distribution of the proportion of sensor data traffic volume represented by the telematics data for each location of the sensors. Consequently, the fitted GP model can be used to determine the approximate traffic distribution for a testing location outside of the training points. Policymakers in the transportation sector can find the results of this work helpful for making informed decisions relating to current and future transportation conditions in the area.

42 ENGINEERING↗
DOE OSTI2025

Design Overview of a High-Pressure Helium Flow Visualization Apparatus for Blanket Cooling Studies

Cooling of the fusion blanket first wall remains a significant challenge given the adverse conditions of heat and particle flux encountered near the plasma. Helium emerges as an attractive cooling candidate because of its chemical and neutronic inertness and separability from hydrogenic species (e.g. tritium). Because of the low thermal mass of helium, optimization of these coolant channels is warranted to provide high heat transfer performance at low pumping costs. Increasingly, computational fluid dynamics (CFD) simulations are employed to model and optimize these flow channels, and accompanying experimental data are needed to validate the predictions of these models. To provide the aforementioned experimental data, a high-pressure helium flow visualization upgrade has been designed for the Helium Flow Loop Experiment facility. This apparatus was built to American Society of Mechanical Engineers boiler and pressure vessel standards to withstand operating pressure of 4 MPa and mated to high-pressure glass windows. Seedless flow visualization is performed via high-speed background oriented schlieren (BOS), with image correlation used for time-resolved two-dimensional velocimetry at frequencies in excess of 60 kHz. Rectangular flow channel test articles are additively manufactured via laser powder bed fusion and installed into this visualization apparatus, with one-sided heating supplied by resistive heaters. In conclusion, the chosen test geometries were informed by prior CFD simulations, and the helium flow structures observed via BOS (detachment, recirculation, etc.) will be used for the validation of these accompanying models, in support of the design and optimization of blanket cooling channel configurations.

Helium flow↗
DOE OSTI2022

Demonstration of RELAP5-3D for transient analysis of a dual coolant lead lithium fusion blanket concept

Our research aims to build a multiphysics framework for transient analysis of the Dual- Coolant Lead-Lithium (DCLL) blanket design of the proposed Fusion Nuclear Science Facility (FNSF) for all Onticipated Operational Occurrences (AOOs) using Reduced Order Models (ROMs). This paper presents an assessment of using RELAP5-3D for transient thermal-hydraulic blanket analysis of the DCLL design. Preliminary validation studies for the RELAP5-3D properties were conducted using a representative vertical flow loop model and a comparison study using experimental data from the thermal convection corrosion loops at ORNL. These studies inspected the thermal hydraulic response of Lead-Lithium Eutectic (PbLi) systems within the RELAP5-3D code; mainly pressure drop and heat transfer, as compared to analytical calculations and experimental data. The Magnetohydrodynamic (MHD) pressure drop effect for liquid metal under the effects of a uniform magnetic field was implemented into our models using an equivalent forms loss coefficient based on the phasic momentum equations. We verified our implementation of MHD pressure drop within RELAP5-3D using a systematic approach consisting of two studies. Models were developed to perform comparison studies based on experimental data from the Argonne Liquid metal EXperiment (ALEX) facility and the Magnetohydrodynamic PbLi Experiment (MaPLE) facility. Using the developed validation basis, we built a simplified DCLL channel model within RELAP5-3D, inspected MHD pressure drop and performed transient temperature analysis. The DCLL channel model used radial heating data from the International Thermonuclear Experimental Reactor (ITER) which was normalized to the FNSF design. Here, a representative startup transient was performed using a relative power curve from the initial ramp up of a long-term power pulse of the Tore Supra reactor. This study demonstrated that RELAP5-3D ROMs are capable of accurate transient analysis of the DCLL blanket. We have since utilized MCNP to develop heating profiles based on the FNSF design and are working toward implementing them into our DCLL model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Helicon waves in uniform plasmas. II. High m numbers

Helicons are whistler modes with azimuthal wave numbers. They have been studied in solids and plasmas where boundaries play a role. The present work shows that very similar modes exist in unbounded gaseous plasmas. Instead of boundaries, the antenna properties determine the topology of the wave packets. The simplest antenna is a magnetic loop which excites m = 0 or m = 1 helicons depending on whether the dipole moment is aligned parallel or perpendicular to the ambient background magnetic field B{sub 0}. While these low order helicons have been described by J. M. Urrutia and R. L. Stenzel [“Helicon modes in uniform plasmas. I. Low m modes,” Phys. Plasmas 22, 092111 (2015)], the present work focuses on high order modes up to m = 8. These are excited by antenna arrays forming magnetic multipoles. Their wave magnetic field has been measured in space and time in a large and uniform laboratory plasma free of boundary effects. The observed wave topology exhibits m pairs of unique field line spirals which may have inspired the name “helicon” to this mode. All field lines converge into these nested spirals which propagate like corkscrews along B{sub 0}. The field lines near the axis of helicons are perpendicular to B{sub 0} and circularly polarized as in parallel whistlers. Helical antennas couple to these transverse fields but not to the spiral fields of helicons. Using a circular antenna array of phased m = 0 loops, right or left rotating or non-rotating multipole antenna fields are generated. They excite m < 0 and m > 0 modes, showing that the plasma supports both modes equally well. The poor excitation of m < 0 modes is a characteristic of loops with dipole moment across B{sub 0}. The radiation efficiency of multipole antennas has been found to decrease with m.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗