Single-shot reconstruction of core 4D phase space of high-brightness electron beams using metal grids
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To study gapped phases of 4d gauge theories, we introduce the temporal gauging of Z N 1-form symmetry in 4d quantum field theories (QFTs), thereby defining effective 3d QFTs with $\tilde{Z}_N$ × Z N 1-form symmetry. In this way, spatial fundamental Wilson and ’t Hooft loops are simultaneously genuine line operators. Assuming a mass gap and Lorentz invariant vacuum of the 4d QFT, the $\tilde{Z}_N$ × Z N symmetry must be spontaneously broken to an order-N subgroup H, and we can classify the 4d gapped phases by specifying H. This establishes the 1-to-1 correspondence between the two classification schemes for gapped phases of 4d gauge theories: one is the conventional Wilson-’t Hooft classification, and the other is the modern classification using the spontaneous breaking of 4d 1-form symmetry enriched with symmetry-protected topological states.
Accurate measurement of electron beam emittance is essential for optimizing high-brightness electron sources. The Pinhole Scan Technique measures the 4D phase space and hence the emittance by measuring the beam profile after clipping the beam using a pinhole followed by a drift section and then scanning the beam over the pinhole. This technique has been implemented in low energy (< 200 keV) beamlines at both Cornell University and Arizona State University. However, the technique poses several practical challenges. In this work, we analyze and address key issues affecting the 4D phase space and emittance measurements using this technique. We identify and investigate sources of inaccuracies like the pinhole aspect ratio, beam divergence, position-momentum correlations in the phase space, and the point-spread-function of the detector and suggest techniques to minimize them. Our findings offer a pathway to more accurate 4D phase space characterization in advanced electron beam systems.
COGENT (Continuum Gyrokinetic Edge New Technology) is a kinetic plasma simulation code that is being developed by the edge simulation laboratory (ESL) collaboration. The original version of the code has been developed in a 4D phase space (2D configuration space and 2D velocity space) to address kinetic plasma phenomena in a complex magnetic field geometry including the core, magnetic separatrix, and scrape-off layer regions. This paper is focused on extending the original 4D phase space to a 5D phase space (3D2V) to address full kinetic turbulences in a tokamak edge region. Here, we report on the current status of 5D COGENT, which presently operates in a shear-less, simple slab geometry. As a verification study, we use the problems of collision-less drift wave instability (universal instability) including its modification in the presence of collisional effects. The simulation model includes the gyrokinetic equations for ion and electron species coupled to the long-wavelength limit of the gyro-Poisson equation. Collisional effects are represented by the Krook collision model. Linear analytical results for the drift mode growth rate and real frequency are recovered, and the non-linear stage is modelled and analysed as well. In addition, extensive 5D runs have been performed to address the effects of the drift wave instability on blob/filamentary structures characteristic of a tokamak edge. Finally, a helical-shaped potential perturbation is observed to grow exponentially in time while spinning around the filament axis with electron drift frequency.
The observed population of the Milky Way satellite galaxies offers a unique testing ground for galaxy formation theory on small scales. Our novel approach was to investigate the clustering of the known Milky Way satellite galaxies and to quantify the amount of substructure within their distribution using a two-point correlation function statistic in each of three spaces: configuration space, line-of-sight velocity space, and four-dimensional (4D) phase space. These results were compared to those for three sets of subhalos in the Via Lactea II cold dark matter (CDM) simulation defined to represent the luminous dwarfs. We found no evidence at a significance level above 2{sigma} of substructure within the distribution of the Milky Way satellite galaxies in any of the three spaces. The 'luminous' subhalo sets are more strongly clustered than are the Milky Way satellites in all three spaces and over a broader range of scales in 4D phase space. Each of the 'luminous' subhalo sets are clustered as a result of substructure within their line-of-sight velocity space distributions at greater than 3{sigma} significance, whereas the Milky Way satellite galaxies are randomly distributed in line-of-sight velocity space. While our comparison is with only one CDM simulation, the inconsistencies between the Milky Way satellite galaxies and the Via Lactea II subhalo sets for all clustering methods suggest a potential new 'small-scale' tension between CDM theory and the observed Milky Way satellites. Future work will obtain a more robust comparison between the observed Milky Way satellites and CDM theory by studying additional simulations.
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Defined as nuclear reactors with a power output up to 300 megawatts electrical (MWe) by the International Atomic Energy Agency (IAEA) and targeted for multipurpose applications, small modular reactors (SMRs) have been recognized as a very promising, clean, affordable, and sustainable energy source by many countries. At present, more than 80 SMRs are under design, development, demonstration, deployment, and beyond (4D+) phases worldwide. This study focuses on the current world status of SMRs and focuses on the necessary developments to accelerate the process of adopting SMRs as a major energy source globally. SMRs are not a new concept, but they do represent a new vision for older concepts if the challenges inherent within them are mitigated with strategic and realistic solution approaches. The major challenges for SMRs 4D+ like any new reactors are: (a) qualifying the advanced fuel-to-reactor design; (b) supporting rapid scaled/prototypic experimentations; (c) maintaining local and global codes, standards, and licensing; (d) supply chain issues;(e) effective cradle-to-grave nuclear fuel cycle and fuel material transportation, and (f) mitigating financial and environmental risks. These upfront challenges can be mitigated with a synergistic solution approach among the various stakeholders: industry, academia, research, government, and international entities.
Defined as nuclear reactors with a power output up to 300 megawatts electrical (MWe) by the International Atomic Energy Agency (IAEA) and targeted for multipurpose applications, small modular reactors (SMRs) have been recognized as a very promising, clean, affordable, and sustainable energy source by many countries. At present, more than 80 SMRs are under design, development, demonstration, deployment, and beyond (4D+) phases worldwide. This paper focuses on the current world status of SMRs and focuses on the necessary developments to accelerate the process of adopting SMRs as a major energy source globally. SMRs are not a new concept, but they do represent a new vision for older concepts if the challenges inherent within them are mitigated with strategic and realistic solution approaches. The major challenges for SMRs 4D+ like any new reactors are: (a) qualifying the advanced fuel-to-reactor design; (b) supporting rapid scaled/prototypic experimentations; (c) maintaining local and global codes, standards, and licensing; (d) supply chain issues; (e) effective cradle-to-grave nuclear fuel cycle and fuel material transportation, and (f) mitigating financial and environmental risks. These upfront challenges can be mitigated with a synergistic solution approach among the various stakeholders: industry, academia, research, government, and international entities.
Defined as nuclear reactors with a power output up to 300 megawatts electrical (MWe) by the International Atomic Energy Agency (IAEA) and targeted for multipurpose applications, small modular reactors (SMRs) have been recognized as a very promising, clean, affordable, and sustainable energy source by many countries. At present, more than 80 SMRs are under design, development, demonstration, deployment, and beyond (4D+) phases worldwide. This study focuses on the current world status of SMRs and focuses on the necessary developments to accelerate the process of adopting SMRs as a major energy source globally. SMRs are not a new concept, but they do represent a new vision for older concepts if the challenges inherent within them are mitigated with strategic and realistic solution approaches. The major challenges for SMRs 4D+ like any new reactors are: (a) qualifying the advanced fuel-to-reactor design; (b) supporting rapid scaled/prototypic experimentations; (c) maintaining local and global codes, standards, and licensing; (d) supply chain issues;(e) effective cradle-to-grave nuclear fuel cycle and fuel material transportation, and (f) mitigating financial and environmental risks. These upfront challenges can be mitigated with a synergistic solution approach among the various stakeholders: industry, academia, research, government, and international entities.
Characterizing the phase space distribution of particle beams in accelerators is a central part of accelerator understanding and performance optimization. However, conventional reconstruction-based techniques either use simplifying assumptions or require specialized diagnostics to infer high-dimensional (> $2D$) beam properties. In this Letter, we introduce a general-purpose algorithm that combines neural networks with differentiable particle tracking to efficiently reconstruct high-dimensional phase space distributions without using specialized beam diagnostics or beam manipulations. Furthermore, we demonstrate that our algorithm accurately reconstructs detailed 4D phase space distributions with corresponding confidence intervals in both simulation and experiment using a single focusing quadrupole and diagnostic screen. This technique allows for the measurement of multiple correlated phase spaces simultaneously, which will enable simplified 6D phase space distribution reconstructions in the future.
Purpose: To report an approach to quantify the normal tissue sparing for 4D robustly-optimized versus PTV-optimized IMPT plans. Methods: We generated two sets of 90 DVHs from a patient’s 10-phase 4D CT set; one by conventional PTV-based optimization done in the Eclipse treatment planning system, and the other by an in-house robust optimization algorithm. The 90 DVHs were created for the following scenarios in each of the ten phases of the 4DCT: ± 5mm shift along x, y, z; ± 3.5% range uncertainty and a nominal scenario. A Matlab function written by Gay and Niemierko was modified to calculate EUD for each DVH for the following structures: esophagus, heart, ipsilateral lung and spinal cord. An F-test determined whether or not the variances of each structure’s DVHs were statistically different. Then a t-test determined if the average EUDs for each optimization algorithm were statistically significantly different. Results: T-test results showed each structure had a statistically significant difference in average EUD when comparing robust optimization versus PTV-based optimization. Under robust optimization all structures except the spinal cord received lower EUDs than PTV-based optimization. Using robust optimization the average EUDs decreased 1.45% for the esophagus, 1.54% for the heart and 5.45% for the ipsilateral lung. The average EUD to the spinal cord increased 24.86% but was still well below tolerance. Conclusion: This work has helped quantify a qualitative relationship noted earlier in our work: that robust optimization leads to plans with greater normal tissue sparing compared to PTV-based optimization. Except in the case of the spinal cord all structures received a lower EUD under robust optimization and these results are statistically significant. While the average EUD to the spinal cord increased to 25.06 Gy under robust optimization it is still well under the TD50 value of 66.5 Gy from Emami et al. Supported in part by the NCI U19 CA021239.
Suppression of beam losses is essential for successful operation of high-intensity linac. Historically, the values of the field amplitudes and phases of the side-coupled, 805-MHz LANSCE linac modules are maintained using a well-known delta-t tuning procedure. Transverse matching of the beam with accelerator is performed through adjustments of beam ellipses in 4D phase space with accelerator lattice using matching quadrupoles. Control of the beam-energy ramp along the length of a proton linear accelerator is required to improve tune of accelerator and decrease beam losses. Time-of-flight measurements of the H - beam energy are now being used to confirm and improve the overall control of the energy ramp along the linac. The time-of-flight method utilizes absolute measurements of beam energy using direct signals from beam at an oscilloscope, as well as the difference in RF phases measured as the beam passes installed delta-t pickup loops. A newly developed BPPM data acquisition system is used. Beam energy measurement along accelerator together with phase scans, klystrons output power control, and delta-t method, allow tuning of accelerator much more close to original design and reduce losses generated by linac. Details of the upgraded tuning procedure and results of tuning and operation are presented here.
Previous works on reconstructing the 4D phase space using tomography require optimal selection of projection views to achieve accurate reconstruction. In 2D reconstruction, the process is straightforward, as an object can be evenly sampled by dividing the angles evenly. However, extending this concept from 2D to 4D is not intuitive. This work demonstrates that quaternions can be used to more effectively describe views in 4D and introduces the Fibonacci Flower algorithm and repulsive force algorithm to evenly space views in 4D space in order to achieve higher reconstruction accuracy.
The arrival of direct electron detectors (DED) with high frame-rates in the field of scanning transmission electron microscopy has enabled many experimental techniques that require collection of a full diffraction pattern at each scan position, a field which is subsumed under the name four dimensional-scanning transmission electron microscopy (4D-STEM). DED frame rates approaching 100 kHz require data transmission rates and data storage capabilities that exceed commonly available computing infrastructure. Current commercial DEDs allow the user to make compromises in pixel bit depth, detector binning or windowing to reduce the per-frame file size and allow higher frame rates. This change in detector specifications requires decisions to be made before data acquisition that may reduce or lose information that could have been advantageous during data analysis. The 4D Camera, a DED with 87 kHz frame-rate developed at Lawrence Berkeley National Laboratory, reduces the raw data to a linear-index encoded electron event representation (EER). Here we show with experimental data from the 4D Camera that linear-index encoded EER and its direct use in 4D-STEM phase contrast imaging methods enables real-time, interactive phase-contrast from large-area 4D-STEM datasets. Furthermore, we detail the computational complexity advantages of the EER and the necessary computational steps to achieve real-time interactive ptychography and center-of-mass differential phase contrast using commonly available hardware accelerators.
Purpose: Respiratory-correlated positron emission tomography (PET/CT) 4D PET/CT is used to mitigate errors from respiratory motion; however, the optimal CT attenuation correction (CTAC) method for 4D PET/CT is unknown. The authors performed a phantom study to evaluate the quantitative performance of CTAC methods for 4D PET/CT in the ground truth setting. Methods: A programmable respiratory motion phantom with a custom movable insert designed to emulate a lung lesion and lung tissue was used for this study. The insert was driven by one of five waveforms: two sinusoidal waveforms or three patient-specific respiratory waveforms. 3DPET and 4DPET images of the phantom under motion were acquired and reconstructed with six CTAC methods: helical breath-hold (3DHEL), helical free-breathing (3DMOT), 4D phase-averaged (4DAVG), 4D maximum intensity projection (4DMIP), 4D phase-matched (4DMATCH), and 4D end-exhale (4DEXH) CTAC. Recovery of SUV{sub max}, SUV{sub mean}, SUV{sub peak}, and segmented tumor volume was evaluated as RC{sub max}, RC{sub mean}, RC{sub peak}, and RC{sub vol}, representing percent difference relative to the static ground truth case. Paired Wilcoxon tests and Kruskal–Wallis ANOVA were used to test for significant differences. Results: For 4DPET imaging, the maximum intensity projection CTAC produced significantly more accurate recovery coefficients than all other CTAC methods (p < 0.0001 over all metrics). Over all motion waveforms, ratios of 4DMIP CTAC recovery were 0.2 ± 5.4, −1.8 ± 6.5, −3.2 ± 5.0, and 3.0 ± 5.9 for RC{sub max}, RC{sub peak}, RC{sub mean}, and RC{sub vol}. In comparison, recovery coefficients for phase-matched CTAC were −8.4 ± 5.3, −10.5 ± 6.2, −7.6 ± 5.0, and −13.0 ± 7.7 for RC{sub max}, RC{sub peak}, RC{sub mean}, and RC{sub vol}. When testing differences between phases over all CTAC methods and waveforms, end-exhale phases were significantly more accurate (p = 0.005). However, these differences were driven by the patient-specific respiratory waveforms; when testing patient and sinusoidal waveforms separately, patient waveforms were significantly different between phases (p < 0.0001) while the sinusoidal waveforms were not significantly different (p = 0.98). When considering only the subset of 4DMATCH images that corresponded to the end-exhale image phase, 4DEXH, mean and interquartile range were similar to 4DMATCH but variability was considerably reduced. Conclusions: Comparative advantages in accuracy and precision of SUV metrics and segmented volumes were demonstrated with the use of the maximum intensity projection and end-exhale CT attenuation correction. While respiratory phase-matched CTAC should in theory provide optimal corrections, image artifacts and differences in implementation of 4DCT and 4DPET sorting can degrade the benefit of this approach. These results may be useful to guide the implementation, analysis, and development of respiratory-correlated thoracic PET/CT in the radiation oncology and diagnostic settings.
Purpose: To quantify the impact of 4D PET/CT on PERCIST metrics in lung and liver tumors in NSCLC and colorectal cancer patients. Methods: 32 patients presenting lung or liver tumors of 1–3 cm size affected by respiratory motion were scanned on a GE Discovery 690 PET/CT. The bed position with lesion(s) affected by motion was acquired in a 12 minute PET LIST mode and unlisted into 8 bins with respiratory gating. Three different CT maps were used for attenuation correction: a clinical helical CT (CT-clin), an average CT (CT-ave), and an 8-phase 4D CINE CT (CT-cine). All reconstructions were 3D OSEM, 2 iterations, 24 subsets, 6.4 Gaussian filtration, 192×192 matrix, non-TOF, and non-PSF. Reconstructions using CT-clin and CT-ave used only 3 out of the 12 minutes of the data (clinical protocol); all 12 minutes were used for the CT-cine reconstruction. The percent change of SUVbw-peak and SUVbw-max was calculated between PET-CTclin and PET-CTave. The same percent change was also calculated between PET-CTclin and PET-CTcine in each of the 8 bins and in the average of all bins. A 30% difference from PET-CTclin classified lesions as progressive metabolic disease (PMD) using maximum bin value and the average of eight bin values. Results: 30 lesions in 25 patients were evaluated. Using the bin with maximum SUVbw-peak and SUVbw-max difference, 4 and 13 lesions were classified as PMD, respectively. Using the average bin values for SUVbw-peak and SUVbw-max, 3 and 6 lesions were classified as PMD, respectively. Using PET-CTave values for SUVbw-peak and SUVbw-max, 4 and 3 lesions were classified as PMD, respectively. Conclusion: These results suggest that response evaluation in 4D PET/CT is dependent on SUV measurement (SUVpeak vs. SUVmax), number of bins (single or average), and the CT map used for attenuation correction.
We describe a new spatial discretization of a continuum gyrokinetic Vlasov model in axisymmetric tokamak edge plasma geometries. The geometries are represented using a multiblock decomposition in which logically distinct blocks are smoothly mapped from rectangular computational domains and are aligned with magnetic flux surfaces to accommodate strong anisotropy induced by the magnetic field. We employ a fourth-order, finite-volume discretization in mapped coordinates to mitigate the computational expense associated with discretization on 4D phase space grids. Applied to a conservative formulation of the gyrokinetic system, a finite-volume approach expresses local conservation discretely in a natural manner involving the calculation of normal fluxes at cell faces. In the approach presented here, the normal fluxes are computed in terms of face-averaged velocity normals in such a way that (i) the divergence-free property of the gyrokinetic velocity is preserved discretely to machine precision, (ii) the configuration space normal velocities are independent of mapping metrics, and (iii) the configuration space normal velocities are computed from exact pointwise evaluation of magnetic field data except for one term. The algorithms described in this paper form the foundation of a continuum gyrokinetic edge code named COGENT, which is used here to perform a convergence study verifying the accuracy of the spatial discretization.