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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Preliminary verification of the MCNP perturbation and fixed-source tally sensitivity tools

Integral benchmark experiments are vital in the adjustment and validation of the nuclear data that govern predictive simulations across the nuclear community. The nuclear data sensitivity capabilities of the Monte Carlo N-Particle (MCNP ®) transport code are currently limited; however, expanding sensitivity capabilities will allow benchmark experiments to be designed to resolve compensating errors and adjust nuclear data where previously prohibitively difficult. This paper provides details of a preliminary verification for the use of (i.) the recently revised perturbation and (ii.) developmental fixed-source sensitivity tools within MCNP to calculate sensitivities of tallied responses (such as current integrated over a surface, F1, and flux averaged over a cell, F4) to nuclear data in fixed-source simulations. Energy-binned and energy-integrated sensitivities calculated with these tools are compared against sensitivities calculated using a central-difference approximation. Here, the verification is completed for four configurations of a benchmarked system using a 4.5-kg plutonium sphere surrounded by varying amounts of copper and/or polyethylene. The results show that sensitivities calculated with the perturbation and fixed-source sensitivity tools agree with the central-difference-based approach.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Introduction to SINBAD - Tutorial - 25448

With the reduction of experimental activities in several countries accompanied by closing of many experimental facilities, the need to preserve the valuable information on the performed radiation shielding benchmarks became increasingly crucial. Since the early 1990's the Organization for Economic Cooperation and Development's Nuclear Energy Agency Data Bank (OECD/NEADB) and the Radiation Safety Information Computational Center (RSICC) are working together on the Shielding Integral Benchmark Archive and Database (SINBAD) project to preserve and make available the information on the past shielding benchmark experiments. The OECD NEA Working Party on Scientific Issues of Reactor Systems (WPRS) Expert Group on Radiation Transport and Shielding (EGRTS) was started in 2011 with the mandate among others, to monitor, steer and support the continued development of the SINBAD database. The database comprises now 102 shielding benchmarks, divided into three categories, covering both low and inter-mediate energy particles applications: fission reactor shielding (48 benchmarks), fusion blanket neutronics (31), and accelerator shielding (23) benchmarks. They are fundamental to ensure that modelling tools meet the requirements of nuclear industry and licensing needs. Validation of nuclear cross-section data, nuclear codes and models as well as nuclear design components are few examples of the use of the database. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2021

Updates to Improve the Evaluated Nuclear Data of Copper Isotopes in the Resolved and Unresolved Resonance Regions

The evaluated nuclear data of the 63,65 Cu isotopes have been updated in the resolved and unresolved resonance energy regions with the goal of improving the fidelity between calculated and measured critical benchmarks. Particular focus was devoted to the 63 Cu(n, γ) cross sections because of their large sensitivity to the reactivity in the benchmark calculations. By focusing on these cross sections, the set of parameters in both resolved and unresolved resonance regions were fitted to available experimental data. The newly updated evaluations were compared to the currently available ENDF/B-VIII.0 evaluations in reactivity calculations for copper-sensitive integral benchmarks. An initial study of the sensitivity of the benchmarks to the angular distributions was performed, finding it necessary to describe the angular distributions more accurately above 100 keV. This investigation uncovered the need for more accurate data for the 63 Cu(n, γ) cross section above 100 keV. An increase in the capture cross section was found to improve agreement for the considered benchmarks.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2023

PMT-004 Validation Testing for Thermal Scattering Laws and Some Interesting Temperature-Dependent Implications [Slides]

This presentation finds that PMT-004 has four new benchmark cases highly sensitive to PE TSL (2 cases) and PMMA TSL (2 Cases). Additionally discovered was that the PE cases were well predicted using MCNP6.2 and ENDF/B-VIII.0. PMMA cases overpredicted by approximately 0.6-0.7% in k eff likely due to the lack of integral benchmarks sensitive to PMMA. The NCSU ENDF/B-VIII.1 PMMA TSL is an improvement over VIII.0. This was Accepted at last ICSBEP meeting pending comment resolution, should be published in 2024 version of the Handbook. It was found that temperature had a large impact on reactivity of the critical configuration. This has Implications for validation work for thermal cases- need to adjust TSL data to correct temperature as it can have hundreds of pcm effects for a few °C. Future thermal experiments should try and measure reactivity at multiple temperatures to add in data testing and benchmark adjustment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Neutron Pulsed Die-Away Experiments at LLNL [Slides]

This presentation discusses why PNDA is ideal for TSL validations as it does not require fissile material, it has very simple target shapes and compositions, it is only sensitive to absorption and scattering of target medium, and that well conducted experiments have uncertainties of 0.1% - 0.5%. The presentation concludes by examining PNDA’s advantages and its role in nuclear data validations as it offers a cost-effective experiment for an integral benchmark, it provides the ability to focus on specific cross section data validation including thermal neutron absorption and thermal scattering laws, and the low experimental uncertainty makes it an excellent benchmark candidate. Additionally, it is easily tunable and can facilitate temperature dependent cross section validation by cooling or heating up targets.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Preliminary NoMAD Results of the MUSIC Experiment

The Measurement of Uranium Subcritical and Critical (MUSiC) experiment was carried out from December 2020 through April 2021 at the National Criticality Experiments Research Center (NCERC). This measurement campaign featured bare configurations of the Rocky Flats highly-enriched uranium (HEU) shells, with each configuration having different numbers of these shells. The goal of the experiment was to test multiple neutron multiplicity detectors and measurement methods for a large range of neutron multiplication values, to see when the combination of detectors and methods break down as the configurations reach the delayed supercritical window. Adding subcritical integral benchmarks gives additional validation to nuclear data. These benchmarks provide additional parameters against which to validate the data. While critical benchmarks have just a single value, $K_{eff}$ , subcritical benchmarks can be used to infer multiple parameters. As an example, recent subcritical benchmarks utilizing the Hage-Cifarelli formalism have three quantities of interest ($R_{1}$, $R_{2}$, and $M_{L}$). This gives nuclear data evaluators additional data to use when performing their evaluations, and allows for these benchmarks to be useful for additional types of nuclear data.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Verification of Upcoming MCNP Features For Estimating Nuclear Data Sensitivities in Fixed Source Simulations [Abstract]

Predictive simulation codes, like the Monte Carlo N-Particle (MCNP) transport code, are used throughout the nuclear community. These simulations are based on nuclear data. Maximizing the accuracy and precision of nuclear data maximizes the accuracy and precision of the overall simulation. This is imperative to applications that rely on simulations. For example, improving nuclear data for special nuclear material improves simulation accuracy in stockpile stewardship applications, which results in larger safety margins and decreased operational costs. The improvement and validation of nuclear data is completed through integral benchmark experiments. Past benchmarks have primarily been limited to focus on the effective multiplication factor ($\kappa$ eff ); broadening the purview of benchmarks beyond $\kappa$ eff -dependent nuclear data addresses nuclear data deficiencies. Different response types depend on different areas of nuclear data. This dependence is quantified as nuclear data sensitivity: the change in response due to perturbation of a contributing parameter. The larger the nuclear data sensitivity of a response, the more the experiment is influenced by the uncertainties of the nuclear data. The optimization of nuclear data sensitivities in future benchmarks would result in more detailed validation of lesser studied areas of nuclear data. Currently, direct sensitivity capabilities are not easily found for all experiment types and parameters. An MCNP tool to directly estimate the cross section sensitivities of tallied values is under development. Additionally, updates have been made to the perturbation feature of MCNP, which can be used in a less direct approach to estimating sensitivities. This work verifies these features to estimate nuclear data sensitivities in fixed source simulations of a 4.5-kg sphere of alpha- phase weapons-grade plutonium surrounded by differing amounts of copper and polyethylene. Integrated estimates made using MCNP’s tools were found to statistically agree with integrated estimates made from manual perturbation of nuclear data proving the validity of the MCNP tools.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Preliminary Design of a New Pulsed-Neutron Die--Away Experiments with Absorbers (IER-552 CED-1)

This report presents the preliminary design (CED-1) of IER-552, pulsed-neutron die-away (PNDA) experiments with absorbers, to be conducted by Lawrence Livermore National Laboratory (LLNL). The goal of the PNDA experiments with absorbing materials is to produce high-quality, low-cost integral benchmarks that can be used to validate cross sections that are high priority nuclear data for the Department of Energy’s Nuclear Criticality Safety Program (NCSP). PNDA experiments can be used to generate nuclear data validation benchmarks quickly and cheaply, as they do not require fissile material or a nuclear facility to conduct them. The original PNDA experiments were set up at LLNL under IER-501. Extending the PNDA experiments to include absorbing materials leverages existing facilities and resources at LLNL to validate cross sections, with a basic experiment design that uses a neutron generator to impinge a short, mono-energetic neutron pulse on a poisoned, moderating target sample. The neutron pulse lasts 100 µs, after which the neutron population in the sample reaches thermal equilibrium and later spatial equilibrium. In this fully equilibrized state, the neutron population has a characteristic decay-time eigenvalue. The eigenvalue can be used as an integral parameter to validate nuclear data involved with neutron scattering and absorption. Two observables can be measured: the neutron population and the population of secondary γ-rays produced by inelastic and capture reactions. This report explores the feasibility of both approaches. For γ-ray measurements, this allows for direct measurement of reactions of interest for validation. During the neutron burst time, inelastic (prompt) γ-rays dominate, and these data can be isolated for validation of neutron inelastic scattering data. After the pulse ends, neutron capture (delayed) γ-rays dominate and are produced by many reaction channels as neutrons slow down to thermal energies. Two sets of γ-ray spectra (inelastic, capture) can be produced for validation. Additionally, the time-dependent decay of the capture γ-ray population when the neutron population is thermalized and in its fundamental mode can be used for validation. Two experiments can be imagined where pulsed neutrons are used to validate the nuclear data of absorbing materials. The first integrates well into the existing PNDA testbed at LLNL. The absorber material would be introduced into a moderating target and the same neutron generator, neutron detectors, electronics, and shielding box used for IER-501 would be employed. From the same experimental setup, many absorbing materials can be validated by simply changing the neutron poison in the moderator. The only significant modification would be the introduction of a γ-ray detector. Such an experiment would primarily serve to validate nuclear data in the thermal energy range. The second kind of experiment would validate the fast and epithermal energy range. It would involve pulsing neutron into a bare assembly of the absorber material and measuring the die-away of neutrons. The fast leakage of such an assembly requires nanosecond neutron-generator pulse widths and fast detectors/electronics that could measure ~200 ns die-away curves. This kind of experiment would ideally be performed at a cyclotron, like that available at Lawrence Berkeley National Laboratory.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Towards an Era of Low-Temperature Integral Critical Experiments: Surrogate Testing of Low-Temperature TEX Configurations

United States and IAEA regulations for the transportation of radioactive materials require that fissile materials must be subcritical under expected ambient temperatures ranging from -40°C to 38°C. While historical experiments have been conducted at room and elevated temperatures, no criticality integral benchmarks exist for temperatures below room temperature. The Low-Temperature Thermal Epithermal eXperiments (LT-TEX) aim to provide benchmark evaluations down to -40°C. The LT-TEX design incorporates stacked HEU plates interspersed with varying thicknesses of polyethylene disks to provide varying levels of moderation, with five configurations at 20°C having already been benchmarked. A novel vacuum/cryogenic chamber was fabricated to contain the LT-TEX configurations in a thermally isolated environment and cool it to -40°C. Prior to testing with fissile materials, testing with surrogate fuel plates was performed to characterize the thermal properties of the system, ensure no condensation forms on the stack, and to test that the uranium plates would not warp, or fracture during the thermal cycling. Surrogate testing has characterized the cryogenic chamber and verified its viability to perform the benchmark experiments, allowing for the next steps in the LT-TEX experimental campaign. The results of the surrogate testing are discussed and compared to heat transfer calculations performed as part of the experiment design process, to establish confidence in the thermal behavior of the system.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Neutron Noise Analysis of the Neptunium Subcritical Observation (NESO) Experiment

The Neptunium Subcritical Observation (NeSO) experiment was a subcritical integral benchmark experiment. This experiment was designed in 2017-2018 and was performed at the National Criticality Experiments Research Center (NCERC) in 2019. Eight different subcritical configurations were measured with varying Nickel reflector thickness. For all configurations, a 3 He detection system was used to record neutron events. The focus of this work is to share neutron noise results of the measured data.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

Calculation of state-to-state differential and integral cross sections for atom-diatom reactions with transition-state wave packets

A recently proposed transition-state wave packet method [R. Welsch, F. Huarte-Larrañaga, and U. Manthe, J. Chem. Phys. 136, 064117 (2012)] provides an efficient and intuitive framework to study reactive quantum scattering at the state-to-state level. It propagates a few transition-state wave packets, defined by the eigenfunctions of the low-rank thermal flux operator located near the transition state, into the asymptotic regions of the reactant and product arrangement channels separately using the corresponding Jacobi coordinates. The entire S-matrix can then be assembled from the corresponding flux-flux cross-correlation functions for all arrangement channels. Since the transition-state wave packets can be defined in a relatively small region, its transformation into either the reactant or product Jacobi coordinates is accurate and efficient. Furthermore, the grid/basis for the propagation, including the maximum helicity quantum number K, is much smaller than that required in conventional wave packet treatments of state-to-state reactive scattering. This approach is implemented for atom-diatom reactions using a time-dependent wave packet method and applied to the H + D{sub 2} reaction with all partial waves. Excellent agreement with benchmark integral and differential cross sections is achieved.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Validation of Thermal Scattering Laws for Light Water at Elevated Temperatures with Diffusion Experiments

Light water is the most important neutron moderator in many reactor applications. Thermal neutron scattering kernels for H bound in H 2 O are represented by ENDF-format thermal scattering laws (TSLs) evaluated at discrete temperatures T . Nuclear data evaluations are conventionally validated utilizing a combination of critical benchmarks and experimental cross section data. Existing public critical benchmarks may be inadequate for testing water TSLs over the full range of T of interest in reactor applications, and experimental thermal scattering cross section data for water is sparse at elevated T . In this work, MC21 is used to simulate the decay of the equilibrium thermal neutron flux in light-water spheres of several radii. The fundamental-mode time eigenvalue $\mathcal{a}$ is calculated at 22 °C and 227 °C (at saturation pressure) for each sphere using three different H-H 2 O TSLs. Fitting $\mathcal{a}$ to a polynomial function of geometric buckling allows calculation of the thermal neutron diffusion length L . Extrapolation lengths are treated as a function of the transport mean free path and geometry. Experimental L data from 25 publications at 49 temperatures (from 10 °C to 295 °C), computed by several different time-dependent and space-dependent decay methods, is used to develop an empirical fit of L vs. T . The MC21-calculated L for the TSLs tested are within ±1% of the predicted values at 22 °C and 227 °C. This validation approach, which may be repeated at arbitrary T , constitutes an integral benchmark specific to and characterizing the detailed physics of the thermal scattering kernel applied.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Nuclear Data – Benchmarking 19 F(α,n) Yield Data for Nuclear Safeguards

Fluorine compounds of U and Pu are ubiquitous in the nuclear fuel cycle, so F(α,n) neutrons are an important signature and quantitative source term that needs to be understood for physics-based interpretation of nondestructive assay measurements. Historically there have been large differences in the basic nuclear data for this reaction reported by various groups. UF 6 is the most prominent material in the nuclear fuel cycle, with the potential for short-term production into weaponizable form. Verification of bulk quantities, natural feed, depleted tails, and especially low enriched product in cylinders is particularly important. The principal physical measurement is neutron counting. For enriched material, the 19 F(α,n) reaction, driven by 234U, is the dominant source of neutrons. Basic nuclear data, cross sections, needed to calculate the yield, as well as information on the source spectrum for sensitivity studies are sparse and highly discrepant. This limits defensible physics-based performance evaluations. The same applies to holdup and criticality studies in which hydrated uranyl fluoride is the material of interest which accumulates in enrichment facilities. In the future we anticipate that the physics community will have made improved accelerator-based measurements and undertaken a more thorough evaluation and adjustment of all relevant available data. But in the short term, this does not help the safeguards community face the pressing real-world nondestructive assay requirements. To address this need, we have performed quality neutron measurements on UF6 materials using well-known material and high-capability neutron counters. A robust determination of the n/s/g of 234 U in UF 6 was generated along with a scientifically defensible uncertainty analysis. The weighted average value of the neutron yield is 509 n/s/g 234 U with a random uncertainty of approximately 1%. Dominant sources of systematic uncertainty are in the efficiency determination where we incur approximately 1.1% relative standard deviation associated with the 252 Cf reference source and about 0.9% uncertainty coming from the uncertainty in the F(α,n) spectrum. The stated uncertainties are an order of magnitude better than current data based on accelerator data reported in the literature. Aside from being of immediate and direct use by the safeguards community, this result will serve as an enduring integral benchmark for subsequent data evaluations that will need to match it in order to be credible. In addition to yield normalization, safeguards users of F(α,n) data also need guidance of the neutron emission spectrum. We have generated a neutron emission using a modified version of the well-known SOURCES 4C code, updated with new alpha stopping power coefficients, and a blended microscopic cross section data set. The yield and spectra are available in a form that MCNP users can readily use.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Advancing Inverse Sensitivity/Uncertainty Methods for Nuclear Fuel Cycle Applications

The inverse sensitivity/uncertainty quantification (IS/UQ) method has recently been implemented in the Inverse Sensitivity/UnceRtainty Estimator (INSURE) module of the AMPX cross section processing system [M.E. Dunn and N.M. Greene, “AMPX-2000: A Cross-Section Processing System for Generating Nuclear Data for Criticality Safety Applications,” Trans. Am. Nucl. Soc. 86, 118–119 (2002)]. The IS/UQ method aims to quantify and prioritize the cross section measurements along with uncertainties needed to yield a given nuclear application(s) target response uncertainty, and doing this at a minimum cost. Since in some cases the extant uncertainties of the differential cross section data are already near the limits of the present-day state-of-the-art measurements, requiring significantly smaller uncertainties may be unrealistic. Therefore, we have incorporated integral benchmark experiments (IBEs) data into the IS/UQ method using the generalized linear least-squares method, and have implemented it in the INSURE module. We show how the IS/UQ method could be applied to systematic and statistical uncertainties in a self-consistent way and how it could be used to optimize uncertainties of IBEs and differential cross section data simultaneously. We itemize contributions to the cost of differential data measurements needed to define a realistic cost function.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

GENESIS: Gamma Energy Neutron Energy Spectrometer for Inelastic Scattering

Improved neutron inelastic scattering cross section data are needed to inform integral benchmark studies and advance applications in a wide variety of areas including nuclear energy, stockpile stewardship, nonproliferation, and space exploration. Neutron inelastic scattering also serves as a non-selective probe of low-lying nuclear structure. To help meet these needs, the Gamma Energy Neutron Energy Spectrometer for Inelastic Scattering (GENESIS) was constructed at the 88-Inch Cyclotron at Lawrence Berkeley National Laboratory. This array couples high-resolution γ-ray detectors and fast neutron detectors to achieve single and coincident n/γ detection over a broad energy range. The current configuration of the array includes 26 organic liquid scintillators and four high-purity germanium detectors (two single-crystal and two four-crystal CLOVER detectors with two-fold segmentation). The array was constructed with minimal supporting material and designed to cover a wide range of secondary particle angles and energies with limited inter-element scattering. Data acquisition is accomplished using Mesytec MDPP-16 multi-channel high-resolution digital pulse processing modules. The array characteristics, including γ-ray and neutron energy resolution, timing resolution, and detection efficiency were measured and used to validate a Geant4 model of the array. Furthermore, the primary sources of neutron background and the uncertainties in the determination of incident and secondary neutron energy were assessed. GENESIS provides a new capability to address nuclear data needs and facilitates the advancement of a wide range of nuclear applications.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

The Need for a New LLNL Pulsed Sphere Neutron Leakage Spectra Series

Here, it is shown that spectra measured as part of the Lawrence Livermore National Laboratory Pulsed Sphere (LPS) program offer decisive information to locate formatting or physics issues in nuclear data of key interest for fusion reactor simulations. However, experiments from this measurement series are not benchmarks. For instance, their uncertainties are incomplete. There are also many open questions—e.g., on the setup, the detector response, and whether LPS are accurately modeled—that cannot be answered anymore given the limited documentation and that many of the experimenters are no longer actively working. This limited knowledge has implications when one tries to adjust nuclear data to LPS spectra. Usually, one adjusts to benchmarks representing an application with the hope to get more precise nuclear data for the application of interest where differential data might be scarce and/or to reduce nuclear data uncertainties in the application simulations. However, it is demonstrated that adjustment with LPS spectra without accounting for missing uncertainties and modeling potential biases in the experimental data leads to adjusted data that are highly unphysical. That means adjusted data differ significantly from evaluated data based on information from differential experiments; also, application quantities predicted with the adjusted data deviate distinctly from experimental ones. While we can approximate our limited knowledge on these experiments with Gaussian processes in the adjustment process, this modeling of bias is arbitrary rather than based on a physics explanation, calling into doubt the validity of resulting adjusted data. Thus, we discuss here the need for a new measurement series, learning from the strengths and weaknesses of the LPS program, to yield decisive and well-benchmarked integral experiments to support fusion reactor research.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Benchmark calculations of electron impact electronic excitation of the hydrogen molecule

We present benchmark integrated and differential cross-sections for electron collisions with H 2 using two different theoretical approaches, namely, the R-matrix and molecular convergent close-coupling. This is similar to comparative studies conducted on electron–atom collisions for H, He and Mg. Electron impact excitation to the ${\mathrm{b}}^{3}{{\Sigma}}_{\mathrm{u}}^{+}$, ${\mathrm{a}}^{3}{{\Sigma}}_{\mathrm{g}}^{+}$, ${\mathrm{B}}^{1}{{\Sigma}}_{\mathrm{u}}^{+}$, c3Πu, ${\mathrm{E}\mathrm{F}}^{1}{{\Sigma}}_{\mathrm{g}}^{+}$, C1Πu, ${\mathrm{e}}^{3}{{\Sigma}}_{\mathrm{u}}^{+}$, ${\mathrm{h}}^{3}{{\Sigma}}_{\mathrm{g}}^{+}$, ${\mathrm{B}}^{\prime 1}{{\Sigma}}_{\mathrm{u}}^{+}$ and d3Πu excited electronic states are considered. Calculations are presented in both the fixed nuclei and adiabatic nuclei approximations, where the latter is shown only for the ${\mathrm{b}}^{3}{{\Sigma}}_{\mathrm{u}}^{+}$ state. Good agreement is found for all transitions presented. Where available, we compare with existing experimental and recommended data.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2017

Particle simulation of radio frequency waves with fully-kinetic ions and gyrokinetic electrons

A toroidal particle-in-cell (PIC) code, suitable for investigating nonlinear phenomena in radio frequency (RF) heating and current drive, is developed and verified thereafter through a series of fidelity tests for field solvers and single particle motions in toroidal geometry, where simulation results show good coincidence with analytical prediction. The RF capability is then demonstrated through the integrated benchmarks with linear lower hybrid wave and ion Bernstein wave theory in cylindrical geometry, where the analytic result is easily available. The frequency and mode structure in the simulations agree well with the theoretical prediction.

Lin, Jingbo↗