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At least 37 records · Page 2

A test of incoherent Cerenkov radiation for VLF hiss and other magnetospheric emissions

Consideration of incoherent Cerenkov radiation from intense fluxes of electrons in the magnetosphere as a source of VLF hiss and several other emission phenomena. A procedure for calculating the Cerenkov and cyclotron radiation power from a spectrum of electrons in a test volume is outlined, as well as a ray-tracing routine for determining the path that the emitted power follows through the magnetosphere. Comparisons are made between a VLF hiss event and an energetic particle spectrum observed simultaneously with the Injun 5 spacecraft. Calculated power and fields for incoherent Cerenkov radiation are two orders of magnitude below the observed VLf hiss values, although the spectral shapes are similar. It is concluded that a partially coherent or amplified Cerenkov source or an instability is located in the altitude range from 3000 to 10,000 km. Calculations regarding Cerenkov radiation as a possible source for other wave phenomena indicate that upper hybrid resonance noise and fast hisslers may be understood in terms of incoherent Cerenkov radiation, but that V-shaped VLF hiss, saucers, ELF hiss, and Io-related Jovian decametric radiation may not.

Taylor, W. W. L.↗

On Computationally Efficient Radiative Transfer Calculations for Three-dimensional Entry Problems

The current work presents an efficient simulation framework for rigorously modeling radiative fields emanating from non-equilibrium planetary entry flows in complex three-dimensional domains. Key to this endeavor is adoption of finite-volume discretization in lieu of brute-force ray tracing. This change in conjunction with mesh sweeping and Lebedev-type quadrature for angular integration allows spatial-angular resolution of radiative transfer to be performed in a computationally tractable manner. Additionally, a new methodology has been established to build standalone reduced-order spectral databases for non-equilibrium radiative properties that can be applied to a broad range of hypersonic planetary entry problems with minimal loss in accuracy. The efficacy of the new framework has been demonstrated on the atomic nitrogen radiative system. The resulting reduced-order model requires three orders-of-magnitude fewer spectral evaluations and results in a 95% decrease in memory footprint. A comparative study for representative forebody and afterbody lines-of-sight from Stardust, FIRE II, and meteor entries into the Earth atmosphere indicates that both total intensity variation and detailed spectra can be retrieved with as few as 625 reduced-order groups (contrasting with the 100,000 frequencies in the original full set model). Similarly, three-dimensional predictions of radiative heating experienced by the Orion forebody are in excellent agreement with legacy radiation solvers while requiring only a sliver (roughly 0.5%) of computing wall time.

3D radiation↗

On Computationally Efficient Radiative Transfer Calculations for Three-Dimensional Entry Problems

The current work presents an efficient simulation framework for rigorously modeling radiative fields emanating from non-equilibrium planetary entry flows in complex three-dimensional domains. Key to this endeavor is adoption of finite-volume discretization in lieu of brute-force ray tracing. This change in conjunction with mesh sweeping and Lebedev-type quadrature for angular integration allows spatial-angular resolution of radiative transfer to be performed in a computationally tractable manner. Additionally, a new methodology has been established to build standalone reduced-order spectral databases for non-equilibrium radiative properties that can be applied to a broad range of hypersonic planetary entry problems with minimal loss in accuracy. The efficacy of the new framework has been demonstrated on the atomic nitrogen radiative system. The resulting reduced-order model requires three orders-of-magnitude fewer spectral evaluations and results in a 95% decrease in memory footprint. A comparative study for representative forebody and afterbody lines-of-sight from Stardust, FIRE II, and meteor entries into the Earth atmosphere indicates that both total intensity variation and detailed spectra can be retrieved with as few as 625 reduced-order groups (contrasting with the 100,000 frequencies in the original full set model). Similarly, three-dimensional predictions of radiative heating experienced by the Orion forebody are in excellent agreement with legacy radiation solvers while requiring only a sliver (roughly 0.5%) of computing wall time.

3D radiation↗

Fast physics-based launcher optimization for electron cyclotron current drive

With the increased urgency to design fusion pilot plants, fast optimization of electron cyclotron current drive (ECCD) launchers is paramount. Traditionally, this is done by coarsely sampling the 4D parameter space of possible launch conditions consisting of (1) the launch location (constrained to lie along the reactor vessel), (2) the launch frequency, (3) the toroidal launch angle, and (4) the poloidal launch angle. For each initial condition, a ray-tracing simulation is performed to evaluate the ECCD efficiency. Unfortunately, this approach often requires a large number of simulations (sometimes millions in extreme cases) to build up a dataset that adequately covers the plasma volume, which must then be repeated every time the design point changes. Here we adopt a different approach. Rather than launching rays from the plasma periphery and hoping for the best, we instead directly reconstruct the optimal ray for driving current at a given flux surface using a reduced physics model coupled with a commercial ray-tracing code. Repeating this throughout the plasma volume requires only hundreds of simulations, constituting a significant speedup. The new method is validated on two separate example tokamak profiles, and is shown to reliably drive localized current at the specified flux surface with the same optimal efficiency as obtained from the traditional approach.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Fast HARDI Uncertainty Quantification and Visualization with Spherical Sampling

In this paper, we study uncertainty quantification and visualization of orientation distribution functions (ODF), which corresponds to the diffusion profile of high angular resolution diffusion imaging (HARDI) data. The shape inclusion probability (SIP) function is the state‐of‐the‐art method for capturing the uncertainty of ODF ensembles. The current method of computing the SIP function with a volumetric basis exhibits high computational and memory costs, which can be a bottleneck to integrating uncertainty into HARDI visualization techniques and tools. We propose a novel spherical sampling framework for faster computation of the SIP function with lower memory usage and increased accuracy. In particular, we propose direct extraction of SIP isosurfaces, which represent confidence intervals indicating spatial uncertainty of HARDI glyphs, by performing spherical sampling of ODFs. Our spherical sampling approach requires much less sampling than the state‐of‐the‐art volume sampling method, thus providing significantly enhanced performance, scalability, and the ability to perform implicit ray tracing. Our experiments demonstrate that the SIP isosurfaces extracted with our spherical sampling approach can achieve up to 8164× speedup, 37282× memory reduction, and 50.2% less SIP isosurface error compared to the classical volume sampling approach. We demonstrate the efficacy of our methods through experiments on synthetic and human‐brain HARDI datasets.

97 MATHEMATICS AND COMPUTING↗

Attribute-Aware RBFs: Interactive Visualization of Time Series Particle Volumes Using RT Core Range Queries

Smoothed-particle hydrodynamics (SPH) is a mesh-free method used to simulate volumetric media in fluids, astrophysics, and solid mechanics. Visualizing these simulations is problematic because these datasets often contain millions, if not billions of particles carrying physical attributes and moving over time. Radial basis functions (RBFs) are used to model particles, and overlapping particles are interpolated to reconstruct a high-quality volumetric field; however, this interpolation process is expensive and makes interactive visualization difficult. Existing RBF interpolation schemes do not account for color-mapped attributes and are instead constrained to visualizing just the density field. To address these challenges, we exploit ray tracing cores in modern GPU architectures to accelerate scalar field reconstruction. We use a novel RBF interpolation scheme to integrate per-particle colors and densities, and leverage GPU-parallel tree construction and refitting to quickly update the tree as the simulation animates over time or when the user manipulates particle radii. We also propose a Hilbert reordering scheme to cluster particles together at the leaves of the tree to reduce tree memory consumption. Finally, we reduce the noise of volumetric shadows by adopting a spatially temporal blue noise sampling scheme. Our method can provide a more detailed and interactive view of these large, volumetric, time-series particle datasets than traditional methods, leading to new insights into these physics simulations.

Particle Volumes↗

Fabrication and testing of a newly designed slit system for depth-resolved X-ray diffraction measurements

A new system of slits called `spiderweb slits' have been developed for depth-resolved powder or polycrystalline X-ray diffraction measurements. The slits act on diffracted X-rays to select a particular gauge volume of sample, while absorbing diffracted X-rays from outside of this volume. Although the slit geometry is to some extent similar to that of previously developed conical slits or spiral slits, this new design has advantages over the previous ones in use for complex heterogeneous materials and in situ and operando diffraction measurements. For example, the slits can measure a majority of any diffraction cone for any polycrystalline material, over a continuous range of diffraction angles, and work for X-ray energies of tens to hundreds of kiloelectronvolts. The design is generated and optimized using ray-tracing simulations, and fabricated through laser micromachining. The first prototype was successfully tested at the X17A beamline at the National Synchrotron Light Source, and shows similar performance to simulations, demonstrating gauge volume selection for standard powders, for all diffraction peaks over angles of 2–10°. A similar, but improved, design will be implemented at the X-ray Powder Diffraction beamline at the National Synchrotron Light Source II.

depth-resolved↗

Deterministic Simulation of First-Order Scattering in a Clinical X-ray Computed Tomography Scanner - Paper 81

In nondestructive testing (NDT) and medical diagnostic x-ray imaging (photon energy<140 keV), scattered x-ray caused by Compton and Rayleigh scattering should be eliminated. Scattered x-ray photons reduce image contrast, increase image noise, and introduce artifact into the reconstructed computed tomography (CT) images. In cone-beam CT, where the coverage of the x-ray beam and the area of the detector are significantly larger than those in fan-beam CT, x-ray photon scatter is one of the major sources of image degradation. The artifacts caused by scattered x-ray photon can be divided into two categories: 1) low spatial frequency scatter profile adds a positive bias to the detected radiation signal, thus reducing the effective attenuation of the imaged object, resulting in a negative bias in the measured linear attenuation coefficient in the image; 2) a high spatial frequency scatter profile causes a differential artifact, such as shading in uniform regions. A real x-ray scan is composed of both low and high frequency scatter profiles. Thus, the key to a successful scatter correction is the ability to accurately capture the scatter profile of a real x-ray imaging scan. The most accurate method for estimating a scatter profile is the Monte Carlo simulation. However, the computation cost of the Monte Carlo method makes it unfeasible for simulating real and complex scan geometries in clinical settings. A practical yet accurate scatter profile estimation method is through ray tracing techniques, where the scatter profiles are computed by tracking rays through the object's volume. The x-ray from the source is tracked when it interacts with the material in the volume. The interaction creates scattered x-rays, in all possible directions. These rays are again either attenuated or scattered, creating cascaded scatter events. In x-ray CT, the first-order scattering (where only one scatter interaction is encountered) accounts for the most severe image artifacts since this first-order scatter contains a high frequency component of the scatter profile. Previous studies have shown that ray tracing techniques are quite effective in simulating the contribution of first-order scattering in radiological images. In this study, a similar ray tracing technique is applied to simulate the scatter profile of a real x-ray computed tomography (CT) scan in clinical settings. A good agreement has been found between the simulated scatter profile and the experimental measurement result. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗

Developing a Nuclear Quality Assurance Compliant Design Methodology for Neutronic Analysis of Xe-100 Design

The primary objective of this work is to develop a design methodology compliant with nuclear quality assurance standards for the Xe-100 neutronic design verification studies. To achieve this, a Monte Carlo model of the Xe-100 reactor was constructed using the exclusion principle, transformation technique, and universe-based level specification following Idaho National Laboratory (INL) NQA level-1 compliant standards and an NQA-1 compliant version of MCNP6. The model encompasses the entire reactor core structures, including the upper plenum, core region, and lower plenum sections, along with all sub-components. The active core section was represented using the spectral regions, each comprising a particular fuel composition and temperature averaged over the considered zone, calculated by X-energy using Very Superior Old Programs (VSOP). Additionally, a component-wise temperature map was implemented into the model, not only for the core region but also for the structural components. Temperature-dependent cross-section libraries, along with thermal scattering law libraries, generated using INL NQA-1 compliant version of NJOY21, were utilized for each isotope in the burnt fuel and the structural materials. Furthermore, the volume of each modeled component was estimated using a stochastic approach with the ray tracing method in MCNP and criticality calculations were performed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Advanced Observation Operators for GPS Radio Occultation: Validation of the 2D Ray Tracing Approach with CHAMP and SAC-C bending angle and refractivity data - Part 1

Global Positioning System (GPS) Radio Occultations (RO) bending angles and refractivity data characterize mostly the vertical structure of the Earth's atmosphere. We answer the question whether proper simulation of GPS RO data for data assimilation can be obtained with one-dimensional vertical operators, or if accounting also for horizontal atmospheric structures via ray-tracing makes a positive difference when compared with real data. We present a detailed implementation of a geometrical optics multi-plane two-dimensional (2D) ray-tracing as an observation operator to simulate GPS RO bending angles and refractivities within the Finite Volume Data Assimilation System (FVDAS). Comparisons of the outputs of that 2D observation operator with those of simpler ID observation operators are used to generate estimates of errors induced by neglecting tangent point drift (TPD) and horizontal gradients (HG). These error estimates are then confronted with errors estimates derived using 6335 real CHAMP and SAC-C occultations. The agreement for TPD-induced (HG-induced) errors is remarkably positive at altitudes 10-30 km (below 10 km). Comparisons in bending angles O - B STD of the outputs of the multi-plane 2D ray-tracer with those of a vertical Abel transform show reductions of about 8% of the usual O - B bending angle STD due to TPD in the stratosphere (3% due to HG, in the troposphere only). In terms of refractivity, the O - B STD reductions are about 1520% for TPD and 3-5% for HG in the same regions. These reductions are obtained using either 6-hour forecasts or analyses as backgrounds, and using Geometrical Optics (GO) or Canonical Transform (CT) data.

Poli, P.↗

Quasi-optical beam tracing module development for millimeter-wave high-wavenumber collective scattering on the NSTX-U and EAST tokamaks

A Python3-based beam tracing code utilizing Quasi-Optics has been developed to track both incident and receiving beams in high-k collective millimeter wave scattering systems within magnetic fusion plasmas. In contrast to existing ray tracing codes that solely consider refraction, this beam tracing code incorporates diffraction phenomena, providing a more comprehensive calculation. Here, this enhanced capability allows for a more accurate calculation of the scattering volume and spatial resolution in high-k collective scattering systems, crucial for evaluating system performance and facilitating data analysis. Unlike Geometrical Optics, Quasi-Optics employs the complex eikonal method, representing a Gaussian beam as a collection of coupled rays to accurately preserve diffraction characteristics. The developed code is intended for application in NSTX-Upgrade and EAST high-k beam tracing analyses, targeting frequencies of 693 GHz and 270 GHz, respectively. The high-k system's primary objective is the observation of electron-scale instabilities. Employing a symplectic integrator, the code ensures numerical accuracy, assessed through the conservation of the Hamiltonian. With its precision and efficiency, the code facilitates rapid inter-shot analyses.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Fully coupled simulation of cosmic reionization. I. numerical methods and tests

Here, we describe an extension of the Enzo code to enable fully coupled radiation hydrodynamical simulation of inhomogeneous reionization in large similar to(100 Mpc)(3) cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. But, we employ a simple subgrid model for star formation which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. differing principally in the operator splitting algorithm we use to advance the system of equations. Radiation transport is done in the gray flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. Finally, we illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with 3200(3) Eulerian grid cells and dark matter particles.

79 ASTRONOMY AND ASTROPHYSICS↗

An Analytical Model for the Prediction of a Micro-Dosimeter Response Function

A rapid analytical procedure for the prediction of a micro-dosimeter response function in low Earth orbit (LEO), correlated with the Space Transportation System (STS, shuttle) Tissue Equivalent Proportional Counter (TEPC) measurements is presented. The analytical model takes into consideration the energy loss straggling and chord length distribution of the detector, and is capable of predicting energy deposition fluctuations in a cylindrical micro-volume of arbitrary aspect ratio (height/diameter) by incoming ions through both direct and indirect (ray) events. At any designated (ray traced) target point within the vehicle, the model accepts the differential flux spectrum of Galactic Cosmic Rays (GCR) and/or trapped protons at LEO as input. On a desktop PC, the response function of TEPC for each ion in the GCR/trapped field is computed at the average rate of 30 seconds/ion. The ionizing radiation environment at LEO is represented by O'Neill fs GCR model (2004), covering charged particles in the 1 less than or equal to Z less than or equal to 28. O'Neill's free space GCR model is coupled with the Langley Research Center (LaRC) angular dependent geomagnetic cutoff model to compute the transmission coefficient in LEO. The trapped proton environment is represented by a LaRC developed time dependent procedure which couples the AP8MIN/AP8MAX, Deep River Neutron Monitor (DRNM) and F10.7 solar radio frequency measurements. The albedo neutron environment is represented by the extrapolation of the Atmospheric Ionizing Radiation (AIR) measurements. The charged particle transport calculations correlated with STS 51 and 114 flights are accomplished by using the most recent version (2005) of the LaRC deterministic High charge (Z) and Energy TRaNsport (HZETRN) code. We present the correlations between the TEPC model predictions (response function) and TEPC measured differential/integral spectra in the lineal energy (y) domain for both GCR and trapped protons, with the conclusion that the model correctly accounts for the increase in flux at low y values where energetic ions are the primary contributor. We further discuss that, even with the incorporation of angular dependency in the cutoffs, comparison of the GCR differential/integral flux between STS 51 and 114 TEPC measured data and current calculations indicates that there still exists an underestimation by the simulations at low to mid range y values. This underestimation is partly related the exclusion of the secondary pion particle production from the current version of HZETRN.

Badavi, Francis F.↗

Parametric study of beam refraction problems across laser anemometer windows

The experimenter is often required to view flows through a window with a different index of refraction than either the medium being observed or the medium that the laser anemometer is immersed in. The refraction that occurs at the window surfaces may lead to undesirable changes in probe volume position or beam crossing angle and can lead to partial or complete beam uncrossing. This report describes the results of a parametric study of this problem using a ray tracing technique to predict these changes. The windows studied were a flat plate and a simple cyclinder. For the flat-plate study: (1) surface thickness, (2) beam crossing angle, (3) bisecting line - surface normal angle, and (4) incoming beam plane surface orientation were varied. For the cylindrical window additional parameters were also varied: (1) probe volume immersion, (2) probe volume off-radial position, and (3) probe volume position out of the R-theta plane of the lens. A number of empirical correlations were deduced to aid the interested reader in determining the movement, uncrossing, and change in crossing angle for a particular situation.

Owen, A. K.↗

A parametric study of the beam refraction problems across laser anemometer windows

The experimenter is often required to view flows through a window with a different index of refraction than either the medium being observed or the medium that the laser anemometer is immersed in. The refraction that occurs at the window surfaces may lead to undesirable changes in probe volume position or beam crossing angle and can lead to partial or complete beam uncrossing. This report describes the results of a parametric study of this problem using a ray tracing technique to predict these changes. The windows studied were a flat plate and a simple cylinder. For the flat-plate study: (1) surface thickness, (2) beam crossing angle, (3) bisecting line - surface normal angle, and (4) incoming beam plane surface orientation were varied. For the cylindrical window additional parameters were also varied: (1) probe volume immersion, (2) probe volume off-radial position, and (3) probe volume position out of the r-theta plane of the lens. A number of empirical correlations were deduced to aid the reader in determining the movement, uncrossing, and change in crossing angle for a particular situations.

Owen, Albert K.↗

SU-E-T-397: Evaluation of Planned Dose Distributions by Monte Carlo (0.5%) and Ray Tracing Algorithm for the Spinal Tumors with CyberKnife

Purpose: To analyze and evaluate dose distribution between Ray Tracing (RT) and Monte Carlo (MC) algorithms of 0.5% uncertainty on a critical structure of spinal cord and gross target volume and planning target volume. Methods: Twenty four spinal tumor patients were treated with stereotactic body radiotherapy (SBRT) by CyberKnife in 2013 and 2014. The MC algorithm with 0.5% of uncertainty is used to recalculate the dose distribution for the treatment plan of the patients using the same beams, beam directions, and monitor units (MUs). Results: The prescription doses are uniformly larger for MC plans than RT except one case. Up to a factor of 1.19 for 0.25cc threshold volume and 1.14 for 1.2cc threshold volume of dose differences are observed for the spinal cord. Conclusion: The MC recalculated dose distributions are larger than the original MC calculations for the spinal tumor cases. Based on the accuracy of the MC calculations, more radiation dose might be delivered to the tumor targets and spinal cords with the increase prescription dose.

60 APPLIED LIFE SCIENCES↗

Population of 224 realistic human subject-based computational breast phantoms

Purpose: To create a database of highly realistic and anatomically variable 3D virtual breast phantoms based on dedicated breast computed tomography (bCT) data. Methods: A tissue classification and segmentation algorithm was used to create realistic and detailed 3D computational breast phantoms based on 230 + dedicated bCT datasets from normal human subjects. The breast volume was identified using a coarse three-class fuzzy C-means segmentation algorithm which accounted for and removed motion blur at the breast periphery. Noise in the bCT data was reduced through application of a postreconstruction 3D bilateral filter. A 3D adipose nonuniformity (bias field) correction was then applied followed by glandular segmentation using a 3D bias-corrected fuzzy C-means algorithm. Multiple tissue classes were defined including skin, adipose, and several fractional glandular densities. Following segmentation, a skin mask was produced which preserved the interdigitated skin, adipose, and glandular boundaries of the skin interior. Finally, surface modeling was used to produce digital phantoms with methods complementary to the XCAT suite of digital human phantoms. Results: After rejecting some datasets due to artifacts, 224 virtual breast phantoms were created which emulate the complex breast parenchyma of actual human subjects. The volume breast density (with skin) ranged from 5.5% to 66.3% with a mean value of 25.3% ± 13.2%. Breast volumes ranged from 25.0 to 2099.6 ml with a mean value of 716.3 ± 386.5 ml. Three breast phantoms were selected for imaging with digital compression (using finite element modeling) and simple ray-tracing, and the results show promise in their potential to produce realistic simulated mammograms. Conclusions: This work provides a new population of 224 breast phantoms based on in vivo bCT data for imaging research. Compared to previous studies based on only a few prototype cases, this dataset provides a rich source of new cases spanning a wide range of breast types, volumes, densities, and parenchymal patterns.

61 RADIATION PROTECTION AND DOSIMETRY↗

SU-F-T-53: Treatment Planning with Inhomogeneity Correction for Intraoperative Radiotherapy Using KV X-Ray Beams

Purpose: The current standard in dose calculation for intraoperative radiotherapy (IORT) using the ZEISS Intrabeam 50 kV x-ray system is based on depth dose measurements in water and no heterogeneous tissue effect has been taken into account. We propose an algorithm for pre-treatment planning including inhomogeneity correction based on data of depth dose measurements in various tissue phantoms for kV x-rays. Methods: Direct depth dose measurements were made in air, water, inner bone and cortical bone phantoms for the Intrabeam 50 kV x-rays with a needle applicator. The data were modelled by a function of power law combining exponential with different parameters. Those phantom slabs used in the measurements were scanned to obtain CT numbers. The x-ray beam initiated from the source isocenter is ray-traced through tissues. The corresponding doses will be deposited/assigned at different depths. On the boundary of tissue/organ changes, the x-ray beam will be re-traced in new tissue/organ starting at an equivalent depth with the same dose. In principle, a volumetric dose distribution can be generated if enough directional beams are traced. In practice, a several typical rays traced may be adequate in providing estimates of maximum dose to the organ at risk and minimum dose in the target volume. Results: Depth dose measurements and modeling are shown in Figure 1. The dose versus CT number is shown in Figure 2. A computer program has been written for Kypho-IORT planning using those data. A direct measurement through 2 mm solid water, 2 mm inner bone, and 1 mm solid water yields a dose rate of 7.7 Gy/min. Our calculation shows 8.1±0.4 Gy/min, consistent with the measurement within 5%. Conclusion: The proposed method can be used to more accurately calculate the dose by taking into account the heterogeneous effect. The further validation includes comparison with Monte Carlo simulation.

60 APPLIED LIFE SCIENCES↗