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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Spinbox: tools for many-body quantum systems in a Monte Carlo context

Spinbox is a piece of software that facilitates quantum mechanical calculations relevant to Monte Carlo simulation of atomic nuclei. At the front lines of research on the nuclear many-body problem are a large number of supercomputer-scale simulation codes. These codes produce valuable results but can be hard to understand, especially for those without intimate knowledge of the relevant theoretical methods. Thus, tools that fill pedagogical roles are extremely valuable. Spinbox makes it easy for one to replicate and analyze the computational processes relevant to a Quantum Monte Carlo (QMC) simulation that may be difficult to understand/debug/analyze due to the scale of the corresponding simulation software. Spinbox is written in Python using other state-of-the-art Python modules for numerical calculations. While a number of Python libraries exist that are suited to general quantum many-body calculations, the motivation of Spinbox is quite particular. In Diffusion Monte Carlo methods (DMC, GFMC, AFDMC), the central calculation is the imaginary-time propagation of individual samples of the many-body wavefunction. Although quantum wavefunctions generally must be described by a probability distribution over a basis, DMC imbues particles (within one sample) with classical spatial coordinates. This method is unusual, so other Python packages are typically not set up to do this easily. Furthermore, the software has built-in options for nuclear systems assuming isospin symmetry, which can be set up with other libraries but is a nontrivial process to do so. Features: - numerical representation of samples of the many-body wavefunctions, including tensor-product states (used in AFDMC) - numerical representation of many-body operators, including tensor-product operators: general, spin, imaginary-time propagation, etc. - the correct associated arithmetic and algebra, implemented as class methods - classes for representing realistic nuclear two- and three-body Hamiltonians (e.g. Argonne V18, Illinois NNN) - large-scale parallel integration over random variables, crucial for the AFDMC method My goal is to make this package open source so that anyone may use it and contribute to it, particularly other researchers doing AFDMC calculations

Fox, Jordan↗
DOE OSTI2023

Effects of MOF linker rotation and functionalization on methane uptake and diffusion

The flexible degrees of freedom in metal–organic frameworks (MOFs) can have significant effects on guest molecule behavior. However, in the majority of studies applying molecular simulations to MOFs, the framework is assumed to be rigid in order to minimize computational cost. Here, in this work, we assess the significance of this assumption on a representative example of methane uptake and diffusion in UiO-66. We introduce an open-source code to modify MOFs through functionalization and linker rotation and we perform Grand Canonical Monte Carlo and molecular dynamics simulations of methane in each of the functionalized and linker-rotated derivatives of UiO-66. We find that linker rotation moderately influences methane uptake and significantly influences methane diffusion. Our assessment provides ranges of property values that serve as measures of uncertainty of these two properties associated with linker rotation. We further determine that void volume fraction and minimum pore size are the features that govern methane uptake and diffusion, respectively. These findings illustrate the impact of linker rotation on MOFs and provide design principles to guide future investigations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

SDSS-IV MaStar: [α/Fe] for the MaNGA Stellar Library from synthetic model spectra

ABSTRACT We calculate the α-enhancement ratio [α/Fe] for the Mapping Nearby Galaxies at APO (MaNGA) Stellar Library (MaStar) while also fitting for the fundamental atmospheric parameters effective temperature, surface gravity, and metallicity – Teff, log g, [Fe/H]. This approach builds upon a previous catalogue of stellar parameters, whereby only the fundamental atmospheric parameters are fit with solar-scaled models. Here, we use the same Markov Chain Monte Carlo method with the additional free parameter [α/Fe]. Using the full spectral fitting code pPXF, we are able to fit multiple lines sensitive to [α/Fe] for a more robust measurement. Quality flags based on the convergence of the sampler, errors in [α/Fe] and a cut in the χ2 of the model fit are used to clean the final catalogue, returning 17 214 spectra and values in the range of −0.25 < [α/Fe] < 0.48. Comparing our calculated [α/Fe] with literature values reveals a degeneracy in cool stars with log g ≥ ∼4; this comparison is then used to create an alternative and calibrated parameter set. We also plot the final catalogue in an [Fe/H] versus [α/Fe] diagram and recover the expected result of increasing [α/Fe] with decreasing [Fe/H] for Milky Way disc-halo stars. We apply our method to a subsample of spectra of uniform resolution and higher signal to noise that finds that our results are independent of this higher signal to noise. In the context of stellar population models, we are able to cover a parameter space for the creation of intermediate to old age models at solar-scaled [α/Fe], high [Fe/H] and enhanced [α/Fe], low [Fe/H].

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1985

The gamma-ray telescope Gamma-1

French and Soviet specialists have designed and built the gamma-ray telescope GAMMA-1 to detect cosmic gamma rays above 50 MeV. The sensitive area of the detector is 1400 sq cm, energy resolution is 30% at 300 MeV, and angular resolution 1.2 deg at 300 MeV (and less than 20' arc when a coded aperture mask is used). Results on calibration of the qualification model and Monte-Carlo calculations are presented.

Akimov, V. V.↗
NASA NTRS2006

A Detailed FLUKA-2005 Monte Carlo Simulation for the ATIC Detector

We have performed a detailed Monte Carlo (MC) calculation for the Advanced thin Ionization Calorimeter (ATIC) detector using the MC code FLUKA-2005 which is capable of simulating particles up to 10 PeV. The ATIC detector has completed two successful balloon flights from McMurdo, Antarctica lasting a total of more than 35 days. ATIC is designed as a multiple, long duration balloon Bight, investigation of the cosmic ray spectra from below 50 GeV to near 100 TeV total energy; using a fully active Bismuth Germanate @GO) calorimeter. It is equipped with a large mosaic of silicon detector pixels capable of charge identification and as a particle tracking system, three projective layers of x-y scintillator hodoscopes were employed, above, in the middle and below a 0.75 nuclear interaction length graphite target. Our calculations are part of an analysis package of both A- and energy-dependences of different nuclei interacting with the ATIC detector. The MC simulates the responses of different components of the detector such as the Simatrix, the scintillator hodoscopes and the BGO calorimeter to various nuclei. We also show comparisons of the FLUKA-2005 MC calculations with a GEANT calculation and data for protons, He and CNO.

Gunasingha, R. M.↗
NASA NTRS2007

Comparison of Fluka-2006 Monte Carlo Simulation and Flight Data for the ATIC Detector

We have performed a detailed Monte Carlo (MC) simulation for the Advanced Thin Ionization Calorimeter (ATIC) detector using the MC code FLUKA-2006 which is capable of simulating particles up to 10 PeV. The ATIC detector has completed two successful balloon flights from McMurdo, Antarctica lasting a total of more than 35 days. ATIC is designed as a multiple, long duration balloon flight, investigation of the cosmic ray spectra from below 50 GeV to near 100 TeV total energy; using a fully active Bismuth Germanate(BGO) calorimeter. It is equipped with a large mosaic of.silicon detector pixels capable of charge identification, and, for particle tracking, three projective layers of x-y scintillator hodoscopes, located above, in the middle and below a 0.75 nuclear interaction length graphite target. Our simulations are part of an analysis package of both nuclear (A) and energy dependences for different nuclei interacting in the ATIC detector. The MC simulates the response of different components of the detector such as the Si-matrix, the scintillator hodoscopes and the BGO calorimeter to various nuclei. We present comparisons of the FLUKA-2006 MC calculations with GEANT calculations and with the ATIC CERN data and ATIC flight data.

Gunasingha, R.M.↗
DOE OSTI2020

Gamma ray Imaging Based Methods to Improve the Accuracy of Uranium Holdup Quantification

Deposits in commercial uranium processing facilities of interest to nuclear safeguards are predominantly low enriched uranium (LEU). The shapes and sizes of holdup deposits can vary significantly, thus making it difficult to model the deposits accurately for calibration purposes. This presents a challenge to currently employed methods such as the Generalized Geometry Holdup (GGH) that rely on quantifying 235U mass by simplifying deposit shapes as a point, a line, or an area. In this work, gamma ray imaging using high energy resolution Germanium Gamma Imagers (GeGI™) is employed to determine the distribution of uranium inside the source containment. Two types of imaging methods are employed; coded-aperture imaging and Compton imaging. Gamma-ray emissions seen in different regions of the image are quantified using an inverse gamma-ray transport solver being developed at ORNL. Using measured data, the inverse method will be used to solve for unknown source parameters such as source matrix thickness, density, and attenuation due to container wall and shielding. The intrinsic efficiency of the detector is determined based on a library of built-in response functions and key dimensions of the detector (e.g., thickness and radius of the detector crystal). Measurements are performed in both imaging modalities using uranium sources of well-known masses and enrichments configured inside mocked-up holdup fixtures. Results from the two imaging modalities are intercompared. The paper presents preliminary results of the imaging measurements and the progress made in the computational methods to quantify uranium mass.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2016

Use of Monte Carlo simulation to quantify CIPS risk

Crud Induced Power Shift (CIPS), caused by the accumulation of boron compounds in corrosion product deposits on high power fuel assemblies, is an important operational issue for Pressurized Water Reactors (PWRs). The Boron-induced Offset Analysis (BOA) computer code has been developed by EPRI in collaboration with Westinghouse to help utility engineers avoid onset of CIPS. The code, used with an established procedure, predicts the maximum boron mass that will be accumulated in the upcoming cycle for a given core design and plant chemistry and operating program. The calculated boron mass above a given threshold predicts the risk of CIPS to the upcoming cycle. BOA has been successful in correctly predicting the risk for onset or lack of CIPS in many cycles. However, like most codes modeling complex physical phenomena, it is subject to uncertainties in several of the inputs used to describe these phenomena. The current BOA procedure results in a single 'best estimate' prediction, which has been judged to provide engineers with a practical way to assess CIPS risk. As such, however, there is a probability that the actual plant CIPS performance may be underestimated. This paper describes a method to assess the probability (with an associated confidence level) of no CIPS, mild to moderate CIPS, or severe CIPS using BOA for a given core design. This is accomplished through the use of a Monte Carlo simulation. The simulation is applied to several plant examples, and the results are evaluated in terms of the likelihood of mild or severe CIPS. A suggested set of criteria for decision making regarding CIPS risk is presented in the conclusion. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2018

RAINIER: A simulation tool for distributions of excited nuclear states and cascade fluctuations

In this paper, a new code has been developed named RAINIER that simulates the γ-ray decay of discrete and quasi-continuum nuclear levels for a user-specified range of energy, angular momentum, and parity including a realistic treatment of level spacing and transition width fluctuations. A similar program, DICEBOX, uses the Monte Carlo method to simulate level and width fluctuations but is restricted in its initial level population algorithm. On the other hand, modern reaction codes such as TALYS and EMPIRE populate a wide range of states in the residual nucleus prior to γ-ray decay, but do not go beyond the use of deterministic functions and therefore neglect cascade fluctuations. This combination of capabilities allows RAINIER to be used to determine quasi-continuum properties through comparison with experimental data. Finally, several examples are given that demonstrate how cascade fluctuations influence experimental high-resolution γ-ray spectra from reactions that populate a wide range of initial states.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

An Efficient Sampling-Based Method for Sensitivity and Uncertainty Analysis Through RAVEN

Sensitivity analysis (SA) and uncertainty quantification (UQ) are now widely recognized as essential parts of analyses for complex nuclear systems. Plenty of well-established methodologies are already available for performing SA and UQ, such as Monte Carlo analysis, adjoint-based method, and variance decomposition. The focus of this summary is on developing an efficient sampling-based approach to perform SA and UQ through RAVEN. RAVEN (Risk Analysis and Virtual control Environment) is a software framework able to perform SA and UQ, currently under development at the Idaho National Laboratory. In literature, a number of approaches have been developed to accelerate the process of SA and UQ for large complex systems, such as principal component analysis (PCA) of input space, input-output correlation analysis, and intersection subspace methods. The fundamental idea is to identify the dominant active directions in the parameter space prior to conducting SA and UQ. The premise is that the number of active directions is much less than the dimensionality of input space. In this work, the PCA or Karhunen-Loeve expansion or SVD method is implemented in RAVEN to identify the active directions. This approach is also combined with the forward sampling approaches, such as Monte Carlo, Grid, Latin Hypercube, and Response Surface Design sampling approaches that are currently available in RAVEN, to perform SA and UQ more efficiently. The summary is organized as follows. In the following section, we present the PCA-based forward sampling approach. The effectiveness and efficiency are discussed in the numerical results section. The paper then ends with a concluding summary. In this summary, we have presented PCA-based forward sampling approach to perform SA and UQ. The goal is to reduce the computational overhead for repetitive executions of complex nuclear systems that are generally required when performing SA and UQ. The control of correlations between input parameters is implemented in RAVEN to better represent the input relationships. In addition, we are currently examining our implementations with more realistic models, and we are also focusing on implementation of some new high-dimensional input reduction techniques in RAVEN. (authors)

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2015

A Study of Neutron Leakage in Finite Objects

A computationally efficient 3DHZETRN code capable of simulating High charge (Z) and Energy (HZE) and light ions (including neutrons) under space-like boundary conditions with enhanced neutron and light ion propagation was recently developed for simple shielded objects. Monte Carlo (MC) benchmarks were used to verify the 3DHZETRN methodology in slab and spherical geometry, and it was shown that 3DHZETRN agrees with MC codes to the degree that various MC codes agree among themselves. One limitation in the verification process is that all of the codes (3DHZETRN and three MC codes) utilize different nuclear models/databases. In the present report, the new algorithm, with well-defined convergence criteria, is used to quantify the neutron leakage from simple geometries to provide means of verifying 3D effects and to provide guidance for further code development.

Wilson, John W.↗
NASA NTRS2004

Unified Models of Turbulence and Nonlinear Wave Evolution in the Extended Solar Corona and Solar Wind

The PI (Cranmer) and Co-I (A. van Ballegooijen) made substantial progress toward the goal of producing a unified model of the basic physical processes responsible for solar wind acceleration. The approach outlined in the original proposal comprised two complementary pieces: (1) to further investigate individual physical processes under realistic coronal and solar wind conditions, and (2) to extract the dominant physical effects from simulations and apply them to a 1D model of plasma heating and acceleration. The accomplishments in Year 2 are divided into these two categories: 1a. Focused Study of Kinetic Magnetohydrodynamic (MHD) Turbulence. lb. Focused Study of Non - WKB Alfven Wave Rejection. and 2. The Unified Model Code. We have continued the development of the computational model of a time-study open flux tube in the extended corona. The proton-electron Monte Carlo model is being tested, and collisionless wave-particle interactions are being included. In order to better understand how to easily incorporate various kinds of wave-particle processes into the code, the PI performed a detailed study of the so-called "Ito Calculus", i.e., the mathematical theory of how to update the positions of particles in a probabilistic manner when their motions are governed by diffusion in velocity space.

Cranmer, Steven R.↗
DOE OSTI2021

Neutronics Calculation Advances at Los Alamos: Manhattan Project to Monte Carlo

The history and advances of neutronics calculations at Los Alamos during the Manhattan Project through the present are reviewed. Substantial improvements to neutron diffusion methods and the invention of both the Monte Carlo neutron transport methods in 1947 and deterministic discrete ordinates Sn in 1953 were all made at Los Alamos just after the Manhattan Project. We briefly summarize early simpler and more approximate neutronics methods and then describe the need to better predict neutronics behavior through consideration of theoretical equations, models and algorithms, experimental measurements, and available computing capabilities and their limitations. This paper briefly covers key advances in deterministic methods during the Manhattan Project. These capabilities, coupled with increasing postwar defense needs and the invention of electronic computing with the Electronic Numeric Integrator and Computer, known as ENIAC, and the Mathematical Analyzer Numerical Integrator and Automatic Computer Model, known as MANIAC, led to the creation of Monte Carlo and deterministic discrete ordinates neutronics transport methods. We note the important role that the scientific comradery between the Los Alamos scientists played in the process. This paper briefly covers the early methods, algorithms, computers, and electronic and women pioneers that enabled Monte Carlo to spread to all areas of science. We focus heavily on these early developments and the subsequent creation of the MCNP® code, advances in its associated nuclear data, and its applications to problems of national defense at Los Alamos.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

SU-G-206-05: A Comparison of Head Phantoms Used for Dose Determination in Imaging Procedures

Purpose: To determine similarities and differences between various head phantoms that might be used for dose measurements in diagnostic imaging procedures. Methods: We chose four frequently used anthropomorphic head phantoms (SK-150, PBU-50, RS-240T and Alderson Rando), a computational patient phantom (Zubal) and the CTDI head phantom for comparison in our study. We did a CT scan of the head phantoms using the same protocol and compared their dimensions and CT numbers. The scan data was used to calculate dose values for each of the phantoms using EGSnrc Monte Carlo software. An .egsphant file was constructed to describe these phantoms using a Visual C++ program for DOSXYZnrc/EGSnrc simulation. The lens dose was calculated for a simulated CBCT scan using DOSXYZnrc/EGSnrc and the calculated doses were validated with measurements using Gafchromic film and an ionization chamber. Similar calculations and measurements were made for PA radiography to investigate the attenuation and backscatter differences between these phantoms. We used the Zubal phantom as the standard for comparison since it was developed based on a CT scan of a patient. Results: The lens dose for the Alderson Rando phantom is around 9% different than the Zubal phantom, while the lens dose for the PBU-50 phantom was about 50% higher, possibly because its skull thickness and the density of bone and soft tissue are lower than anthropometric values. The lens dose for the CTDI phantom is about 500% higher because of its totally different structure. The entrance dose profiles are similar for the five anthropomorphic phantoms, while that for the CTDI phantom was distinctly different. Conclusion: The CTDI and PBU-50 head phantoms have substantially larger lens dose estimates in CBCT. The other four head phantoms have similar entrance dose with backscatter hence should be preferred for dose measurement in imaging procedures of the head. Partial support from NIH Grant R01-EB002873 and Toshiba Medical Systems Corp.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Information criteria for quantifying loss of reversibility in parallelized KMC

Parallel Kinetic Monte Carlo (KMC) is a potent tool to simulate stochastic particle systems efficiently. However, despite literature on quantifying domain decomposition errors of the particle system for this class of algorithms in the short and in the long time regime, no study yet explores and quantifies the loss of time-reversibility in Parallel KMC. Inspired by concepts from non-equilibrium statistical mechanics, we propose the entropy production per unit time, or entropy production rate, given in terms of an observable and a corresponding estimator, as a metric that quantifies the loss of reversibility. Typically, this is a quantity that cannot be computed explicitly for Parallel KMC, which is why we develop a posteriori estimators that have good scaling properties with respect to the size of the system. Through these estimators, we can connect the different parameters of the scheme, such as the communication time step of the parallelization, the choice of the domain decomposition, and the computational schedule, with its performance in controlling the loss of reversibility. From this point of view, the entropy production rate can be seen both as an information criterion to compare the reversibility of different parallel schemes and as a tool to diagnose reversibility issues with a particular scheme. As a demonstration, we use Sandia Lab's SPPARKS software to compare different parallelization schemes and different domain (lattice) decompositions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Tycho: Realistically Simulating Exoplanets within Stellar Clusters. I. Improving the Monte Carlo Approach

To fully understand the diverse population of exoplanets, we must study their early lives within open clusters, the birthplace of most stars with masses >0.5M {sub ⊙} (including those currently in the field). Indeed, when we observe planets within clustered environments, we notice highly eccentric and odd systems that suggest the importance of dynamical pathways created by interactions with additional bodies (as in the case of HD 285507b). However, it has proven difficult to investigate these effects, as many current numerical solvers for the multi-scale N-body problem are simplified and limited in scope. To remedy this, we aim to create a physically complete computational solution to explore the role of stellar close encounters and interplanetary interactions in producing the observed exoplanet populations for both open cluster stars and field stars. We present a new code, Tycho, which employs a variety of different computational techniques, including multiple N-body integration methods, close encounter handling, modified Monte Carlo scattering experiments, and a variety of empirically informed initial conditions. We discuss the methodology in detail, and its implementation within the AMUSE software framework. Approximately 1% of our systems are promptly disrupted by star-star encounters contributing to the rogue planets occurrence rate. Additionally, we find that close encounters which that perturb long-period planets lead to 38.3% of solar-system-like planetary systems becoming long-term unstable.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

SU-G-TeP1-03: Beam Quality Correction Factors for Linear Accelerator with and Without Flattening Filter

Purpose: The impact of removing the flattening filter on absolute dosimetry based on IAEA’s TPR-398 and AAPM’s TG-51 was investigated in this study using Monte Carlo simulations. Methods: The EGSnrc software package was used for all Monte Carlo simulations performed in this work. Five different ionization chambers and nine linear accelerator heads have been modeled according to technical drawings. To generate a flattening filter free radiation field the flattening filter was replaced by a 2 mm thick aluminum layer. Dose calculation in a water phantom were performed to calculate the beam quality correction factor k{sub Q} as a function of the beam quality specifiers %dd(10){sub x}, TPR{sub 20,10} and mean photon and electron energies at the point of measurement in photon fields with (WFF) and without flattening filter (FFF). Results: The beam quality correction factor as a function of %dd(10){sub x} differs systematically between FFF and WFF beams for all investigated ionization chambers. The largest difference of 1.8% was observed for the largest investigated Farmer-type ionization chamber with a sensitive volume of 0.69 cm{sup 3}. For ionization chambers with a smaller nominal sensitive volume (0.015 – 0.3 cm{sup 3}) the deviation was less than 0.4% between WFF and FFF beams for %dd(10){sub x} > 62%. The specifier TPR{sub 20,10} revealed only a good correlation between WFF and FFF beams (< 0.3%) for low energies. Conclusion: The results confirm that %dd(10){sub x} is a suitable beam quality specifier for FFF beams with an acceptable bias. The deviation depends on the volume of the ionization chamber. Using %dd(10){sub x} to predict k{sub Q} for a large volume chamber in a FFF photon field may lead to not acceptable errors according to the results of this study. This bias may be caused by the volume effect due to the inhomogeneous photon fields of FFF linear accelerators.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-C-201-07: Towards Clinical Cherenkov Emission Dosimetry: Stopping Power-To-Cherenkov Power Ratios and Beam Quality Specification of Clinical Electron Beams

Purpose: We propose a Cherenkov emission (CE)-based reference dosimetry method, which in contrast to ionization chamber-based dosimetry, employs spectrum-averaged electron restricted mass collision stopping power-to-Cherenkov power ratios (SCRs), and we examine Monte Carlo-calculated SCRs and beam quality specification of clinical electron beams. Methods: The EGSnrc user code SPRRZnrc was modified to compute SCRs instead of stopping-power ratios (single medium: water; cut-off: CE threshold (observing Spencer-Attix conditions); CE power: Frank-Tamm). SCRs are calculated with BEAMnrc for realistic electron beams with nominal energies of 6–22 MeV from three Varian accelerators (TrueBeam Clinac 21EX, Clinac 2100C/D) and for mono-energetic beams of energies equal to the mean electron energy at the water surface. Sources of deviation between clinical and mono-energetic SCRs are analyzed quantitatively. A universal fit for the beam-quality index R{sub 50} in terms of the depth of 50% CE C{sub 50} is carried out. Results: SCRs at reference depth are overestimated by mono-energetic values by up to 0.2% for a 6-MeV beam and underestimated by up to 2.3% for a 22-MeV beam. The variation is mainly due to the clinical beam spectrum and photon contamination. Beam angular spread has a small effect across all depths and energies. The influence of the electron spectrum becomes increasingly significant at large depths, while at shallow depths and high beam energies photon contamination is predominant (up to 2.0%). The universal data fit reveals a strong linear correlation between R{sub 50} and C{sub 50} (ρ > 0.99999). Conclusion: CE is inherent to radiotherapy beams and can be detected outside the beam with available optical technologies, which makes it an ideal candidate for out-of-beam high-resolution 3D dosimetry. Successful clinical implementation of CE dosimetry hinges on the development of robust protocols for converting measured CE to radiation dose. Our findings constitute a key step towards clinical CE dosimetry.

60 APPLIED LIFE SCIENCES↗