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At least 433 records · Page 24

Thermal and electromechanical response of ultra-thin carbon-strip polarimeter targets in relativistic bunched beams

Thin carbon-strip targets provide fast relative hadron beam polarimetry, but their response in intense relativistic bunched beams is not governed by local stopping-power heating alone. We develop a coupled response model that combines beam-target overlap, secondary-electron escape, retained heat, target motion, transient heat transport, RF-induced strip-end heating, beam-induced forces, resistance changes, and slack-strip deformation. RHIC target observations constrain the relevant motion, force, and nonlocal-heating scales and show that target survival depends on both beam-center heating and electromagnetic boundary conditions near the strip ends. Applying the model to Booster, AGS, RHIC, and EIC proton and 3 He cases shows that the RHIC proton lifetime scale is reproduced at the order-of-magnitude level, while the RHIC target-holder fin results require the additional RF/end-heating mechanism. For EIC proton flattop operation, carbon-strip polarimetry may remain viable only with reduced dwell time, sufficient detector acceptance, and suppression of RF-induced end heating. For cooled-emittance 3 He, the calculated sublimation-loss scale is far beyond a straightforward RHIC-like carbon-strip extrapolation. Conventional carbon strips are therefore unlikely to remain viable for the most demanding EIC light-ion cases without major changes in target motion, target technology, or diagnostic concept.

43 PARTICLE ACCELERATORS↗

Advancing Superconducting Magnet Diagnostics for Future Colliders

Future colliders will operate at increasingly high magnetic fields pushing limits of electromagnetic and mechanical stress on the conductor [1]. Understanding factors affecting superconducting (SC) magnet performance in challenging conditions of high mechanical stress and cryogenic temperatures is only possible with the use of advanced magnet diagnostics. Diagnostics provide a unique observation window into mechanical and electromagnetic processes associated with magnet operation, and give essential feedback to magnet design, simulations and material research activities. Development of novel diagnostic capabilities is therefore an integral part of next-generation magnet development. In this paper, we summarize diagnostics development needs from a prospective of the US Magnet Development Program (MDP), and define main research directions that could shape this field in the near future.

43 PARTICLE ACCELERATORS↗

Novel Chalcopyrites for Advanced Photoelectrochemical Water Splitting

With the support of DoE’s EERE office, our team has established a unique tool-chest of capabilities, including theoretical modeling (Lawrence Livermore National Laboratory: LLNL), state-of-the-art synthesis (Hawaii Natural Energy Institute: HNEI, Stanford, and the National Renewable Energy Laboratory: NREL) and advanced materials and interfaces characterization (University of Nevada, Las Vegas: UNLV, and Lawrence Berkeley National Laboratory: LBNL), to accelerate the development of high efficiency and durable chalcopyrite materials for advanced photoelectrochemical (PEC) water splitting. Using this synergistic approach, we have successfully created new wide bandgap chalcopyrite photocathodes generating over 10 mA/cm 2 , developed innovative strategies to protect them from corrosion, and engineered novel integration methods to circumvent thin film materials mechanical, chemical and thermal incompatibility. In Task 1 “Modeling and synthesis of chalcopyrite photocathodes”, we expanded our library of wide bandgap chalcopyrites for PEC water splitting. With support from LLNL’s “Computational Materials Diagnostics and Optimization of PEC Devices”, LBNL’s “photophysical” and NREL’s “I-III-VI Compound Semiconductors for Water-Splitting” nodes, we investigated two new chalcopyrite candidates for PEC water splitting: Cu(In,Al)Se 2 and Cu(In,B)Se 2 . We also further developed ordered vacancy compounds, such as CuGa 3 Se 5 , with unprecedented durability during PEC waters splitting in acidic solutions. In Task 2 “Interfaces engineering for enhanced efficiency and durability”, we addressed both the non-ideal band-edge positions of chalcopyrites with respect to water redox potentials, as well as their chemical instability under PEC water splitting, with a buried-junctions approach. With help from NREL’s “High-Throughput Experimental Thin Film Combinatorial Capabilities” and “Corrosion Analysis of Materials” nodes, we engineered environmentally friendly n-type buffers, including Mn x Zn 1-x O, to adjust the chalcopyrite band-edge positions and achieved photovoltages as high as 925 mV. Also, we integrated non-precious catalytic-protecting layers, such as WO 3 , to enhance the water splitting long-term stability of chalcopyrite absorbers. Finally, in Task 3 “Hybrid photoelectrode device integration”, we proposed an innovative method to bond wide bandgap photocathodes onto narrow bandgap PV drivers at room temperature using conductive polymers. Our semi-monolithic approach addressed fundamental processing incompatibility issues, as both the photocathode and the PV driver are processed separately. Proof-of-concept whole-chalcopyrite tandems were obtained by consecutive exfoliation and transfer of fully integrated 1.85 eV CuGa 3 Se 5 and 1.13 eV CuInGaSe 2 stacks from their Mo/SLG substrates onto a new single FTO host substrate.

08 HYDROGEN↗

Few-femtosecond resolved imaging of laser-driven nanoplasma expansion

Abstract The free expansion of a planar plasma surface is a fundamental non-equilibrium process relevant for various fields but as-yet experimentally still difficult to capture. The significance of the associated spatiotemporal plasma motion ranges from astrophysics and controlled fusion to laser machining, surface high-harmonic generation, plasma mirrors, and laser-driven particle acceleration. Here, we show that x-ray coherent diffractive imaging can surpass existing approaches and enables the quantitative real-time analysis of the sudden free expansion of laser-heated nanoplasmas. For laser-ionized SiO 2 nanospheres, we resolve the formation of the emerging nearly self-similar plasma profile evolution and expose the so far inaccessible shell-wise expansion dynamics including the associated startup delay and rarefaction front velocity. Our results establish time-resolved diffractive imaging as an accurate quantitative diagnostic platform for tracing and characterizing plasma expansion and indicate the possibility to resolve various laser-driven processes including shock formation and wave-breaking phenomena with unprecedented resolution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Data-Enabled Fusion Technology (Final Scientific/Technical Report)

Advancing Scientific Understanding in Fusion Energy and Machine Learning This research represented a significant step forward in machine learning (ML) applications for fusion energy experiments. The project integrated advanced data-driven modeling, optimization techniques, and artificial intelligence to enhance the predictive capabilities and operational efficiency of plasma-based fusion systems. Specifically, tasks focused on ML-enhanced diagnostics, operator guidance tools, and predictive modeling helped improve the ability to interpret complex fusion experiments. Key areas of advancement included: 1) data-driven plasma control, i.e., using ML algorithms to optimize experimental conditions and classify plasma behaviors based on historical data; 2) spectroscopy and diagnostics, i.e., applying AI models to extract previously inaccessible insights from experimental spectroscopy data; and 3) configuration mapping and operator guidance, i.e., developing a predictive framework to assist scientists in identifying the most effective experimental parameters, reducing reliance on manual adjustments. By refining these ML-driven techniques, the project contributed to the broader scientific community’s understanding of plasma dynamics and fusion energy viability. Technical Effectiveness and Economic Feasibility The methods investigated demonstrated high technical effectiveness, as reflected in milestones assessing the predictive accuracy, performance, and optimization of fusion configurations. The development of an Operator Guidance Tool (OGT), for example, led to more precise control of plasma conditions by learning from experimental data and offering real-time adjustments. From an economic standpoint, DeFT provided: 1) the ability to reduce trial-and-error experimentation, which lowered operational costs; 2) improved data interpretation methods, which enabled more efficient resource allocation in large-scale fusion research projects; and 3) the automation of key diagnostic tasks, which reduced manual labor and human error, increasing overall efficiency. 13 The final assessments of predictive models and optimization strategies demonstrated that these approaches were scalable and could be implemented across multiple fusion energy research programs. Public Benefit and Societal Impact This project contributed directly to the broader goal of achieving sustainable and commercially viable fusion energy, which had profound implications for clean energy production and climate change mitigation. The integration of AI-driven solutions into fusion research: 1) sped up scientific discovery, accelerating progress towards achieving energy breakthroughs; 2) reduced the cost of experimentation, making fusion research more accessible; and 3) provided a framework for future AI applications in high-energy physics, benefiting adjacent fields like space exploration, material science, and renewable energy. Additionally, by fostering collaborations between AI researchers and plasma physicists, this project promoted interdisciplinary innovation that could lead to broader applications beyond fusion research.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Characterization of Losses in Superconducting Radio-Frequency Cavities by Combined Temperature and Magnetic Field Mapping

Superconducting radio-frequency (SRF) cavities are one of the fundamental building blocks of modern particle accelerators. To achieve the highest quality factors (10 10 -10 11 ), SRF cavities are operated at liquid helium temperatures. Magnetic flux trapped on the surface of SRF cavities during cool-down below the critical temperature is one of the leading sources of residual RF losses. Instruments capable of detecting the distribution of trapped flux on the cavity surface are in high demand in order to better understand its relation to the cavity material, surface treatments and environmental conditions. We have designed, developed, and commissioned two novel diagnostic tools to measure the distribution of trapped flux at the surface of SRF cavities. One is a magnetic field scanning system (MFSS) which uses cryogenic Hall probes and anisotropic magnetoresistance sensors that fit the contour of a 1.3 GHz cavity. The second setup is a stationary, combined magnetic and temperature mapping system which uses AMR sensors and carbon resistor temperature sensors, covering the surface of a 3 GHz SRF cavity. The MFSS system revealed a non-uniform distribution of trapped flux on the cavities' surface, dependent on the magnitude of the applied magnetic field during field-cooling below the critical temperature. The MFSS shows that magnetic field scanning as a function of the RF field indicates redistribution of trapped flux at some locations. About ~ 33% of hot-spots observed by temperature mapping during high power RF tests overlapped with the high B-field spots. Almost all high B-field spots observed after field-cool were found to be overlapped on grain boundaries. A clear correlation between the hot- spot formed after quench and local trapped flux was found, providing insight on the RF dissipation of trap vortices. The combined B&T map system showed that the T-map system is capable of detecting hot-spots and quench location on the surface of the 3 GHz SRF cavity. Different distribution of trapped flux was measured after different cool-down and residual B-field, but, no variation in magnetic field distribution was observed during quench, possibly due to magnetic sensors being far from the quench location.

Parajuli, Ishwari↗

Plasma-based particle sources

High-brightness particle beams generated by advanced accelerator concepts have the potential to become an essential part of future accelerator technology. In particular, high-gradient accelerators can generate and rapidly accelerate particle beams to relativistic energies. The rapid acceleration and strong confining fields can minimize irreversible detrimental effects to the beam brightness that occur at low beam energies, such as emittance growth or pulse elongation caused by space charge forces. Due to the high accelerating gradients, these novel accelerators are also significantly more compact than conventional technology. Advanced accelerators can be extremely variable and are capable of generating particle beams with vastly different properties using the same driver and setup with only modest changes to the interaction parameters. So far, efforts have mainly been focused on the generation of electron beams, but there are concepts to extend the sources to generate spin-polarized electron beams or positron beams. The beam parameters of these particle sources are largely determined by the injection and subsequent acceleration processes. Although, over the last decade there has been significant progress, the sources are still lacking a sufficiently high 6-dimensional (D) phase-space density that includes small transverse emittance, small energy spread and high charge, and operation at high repetition rate. This is required for future particle colliders with a sufficiently high luminosity or for more near-term applications, such as enabling the operation of free-electron lasers (FELs) in the X-ray regime. Major research and development efforts are required to address these limitations in order to realize these approaches for a front-end injector for a future collider or next-generation light sources. In particular, this includes methods to control and manipulate the phase-space and spin degrees-of-freedom of ultrashort plasma-based electron bunches with high accuracy, and methods that increase efficiency and repetition rate. These efforts also include the development of high-resolution diagnostics, such as full 6D phase-space measurements, beam polarimetry and high-fidelity simulation tools. A further increase in beam luminosity can be achieve through emittance damping. Emittance cooling via the emission of synchrotron radiation using current technology requires kilometer-scale damping rings. For future colliders, the damping rings might be replaced by a substantially more compact plasma-based approach. Here, plasma wigglers with significantly stronger magnetic fields are used instead of permanent-magnet based wigglers to achieve similar damping performance but over a two orders of magnitude reduced length.

43 PARTICLE ACCELERATORS↗

New high-throughput endstation to accelerate the experimental optimization pipeline for synchrotron X-ray footprinting

Synchrotron X-ray footprinting (XF) is a growing structural biology technique that leverages radiation-induced chemical modifications via X-ray radiolysis of water to produce hydroxyl radicals that probe changes in macromolecular structure and dynamics in solution states of interest. The X-ray Footprinting of Biological Materials (XFP) beamline at the National Synchrotron Light Source II provides the structural biology community with access to instrumentation and expert support in the XF method, and is also a platform for development of new technological capabilities in this field. Hee, the design and implementation of a new high-throughput endstation device based around use of a 96-well PCR plate form factor and supporting diagnostic instrumentation for synchrotron XF is described. This development enables a pipeline for rapid comprehensive screening of the influence of sample chemistry on hydroxyl radical dose using a convenient fluorescent assay, illustrated here with a study of 26 organic compounds. The new high-throughput endstation device and sample evaluation pipeline now available at the XFP beamline provide the worldwide structural biology community with a robust resource for carrying out well optimized synchrotron XF studies of challenging biological systems with complex sample compositions.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Formulation, Implementation and Validation of a 1D Boundary Layer Inflow Scheme for the QUIC Modeling System

Recent studies have highlighted the importance of accurate meteorological conditions for urban transport and dispersion calculations. In this work, we present a novel scheme to compute the meteorological input in the Quick Urban & Industrial Complex () diagnostic urban wind solver to improve the characterization of upstream wind veer and shear in the Atmospheric Boundary Layer (ABL). The new formulation is based on a coupled set of Ordinary Differential Equations (ODEs) derived from the Reynolds Averaged Navier–Stokes (RANS) equations, and is fast to compute. Building upon recent progress in modeling the idealized ABL, we include effects from surface roughness, turbulent stress, Coriolis force, buoyancy and baroclinicity. We verify the performance of the new scheme with canonical Large Eddy Simulation (LES) tests with the GPU-accelerated FastEddy"Equation missing" solver in neutral, stable, unstable and baroclinic conditions with different surface roughness. Furthermore, we evaluate QUIC calculations with and without the new inflow scheme with real data from the Urban Threat Dispersion (UTD) field experiment, which includes Lidar-based wind measurements as well as concentration observations from multiple outdoor releases of a non-reactive tracer in downtown New York City. Compared to previous inflow capabilities that were limited to a constant wind direction with height, we show that the new scheme can model wind veer in the ABL and enhance the prediction of the surface cross-isobaric angle, improving evaluation statistics of simulated concentrations paired in time and space with UTD measurements.

54 ENVIRONMENTAL SCIENCES↗

Image plate multi-scan response to fusion protons in the range of 1–14 MeV

Image plates (IPs) are a quickly recoverable and reusable radiation detector often used to measure proton and x-ray fluence in laser-driven experiments. Recently, IPs have been used in a proton radiography detector stack on the OMEGA laser, a diagnostic historically implemented with CR-39, or radiochromic film. The IPs used in this and other diagnostics detect charged particles, neutrons, and x-rays indiscriminately. IPs detect radiation using a photo-stimulated luminescence (PSL) material, often phosphor, in which electrons are excited to metastable states by ionizing radiation. Protons at MeV energies deposit energy deeper into the IP compared with x rays below ∼20 keV due to the Bragg peak present for protons. This property is exploited to discriminate between radiation types. Doses of mono-energetic protons between 1.7 and 14 MeV are applied to IPs using the MIT linear electrostatic ion accelerator. This paper presents the results from consecutive scans of IPs irradiated with different proton energies. The PSL ratios between subsequent scans are shown to depend on proton energy, with higher energy protons having lower PSL ratios for each scan. This finding is separate from the known energy dependence in the absolute sensitivity of IPs. The results can be compared to complimentary work on x rays, showing a difference between protons and x rays, forging a path to discriminate between proton and x-ray fluence in mixed radiation environments.

Instruments & Instrumentation↗

Characterizing extreme laser intensities by ponderomotive acceleration of protons from rarified gas

Abstract A new method to diagnose extreme laser intensities through measurement of angular and spectral distributions of protons directly accelerated by the laser focused into a rarefied gas is proposed. We simulated a laser pulse focused by an off-axis parabolic mirror by Stratton–Chu integrals, that enables description of laser pulse with different spatial-temporal profiles focusing in a focal spot down to the diffraction limit, that makes our theoretical predictions be a basis for experimental realization. The relationship between characteristics of the proton distributions and parameters of the laser pulse have been analyzed. The analytical and numerical results obtained justify the new method of laser diagnostics. The proposed scheme should be valuable for the commissioning of new extreme intensity laser facilities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Microscopy X-ray imaging enriched with small angle X-ray scattering for few nanometer resolution reveals shock waves and compression in intense short pulse laser irradiation of solids

Understanding how laser pulses compress solids into high-energy-density states requires diagnostics that simultaneously resolve macroscopic geometry and nanometer-scale structure. Here we present a combined X-ray imaging (XRM) and small-angle X-ray scattering (SAXS) approach that bridges this diagnostic gap. Using the Matter in Extreme Conditions end station at LCLS, we irradiated 25 μm copper wires with 45 fs, 0.9 J, 800 nm pulses at 3.5 × 10 19 W/cm 2 while probing with 8.2 keV XFEL pulses. XRM visualizes the evolution of ablation, compression, and inward-propagating fronts with ∼ 200 nm resolution, while SAXS quantifies their nanometer-scale sharpness via the time-resolved evolution of scattering streaks. The joint analysis reveals that an initially smooth compression steepens into a nanometer-sharp shock front after t sh ≈ (18 ± 3) ps, consistent with an analytical steepening model and hydrodynamic simulations. The front reaches a velocity of c sh ≈ 25 k m / s and a lateral width of several tens of microns, demonstrating direct observation of shock formation and decay at solid density for the first time with few-nanometer precision. This integrated XRM–SAXS method establishes a quantitative, multi-scale diagnostic of laser-driven shocks in dense plasmas relevant to inertial confinement fusion, warm dense matter, and planetary physics.

Kluge, Thomas [Helmholtz-Zentrum Dresden-Rossendor↗

Interplay between beam-driven chirping modes and plasma confinement transitions in spherical tokamak ST40

Experiments on the high field spherical tokamak ST40 have led to the recent observation of interplay between beam-driven modes of sweeping frequency (chirping modes) and transitions to the enhanced global confinement regime (H-mode) and back to the low confinement regime (L-mode). The H-modes of plasma confinement are identified from decreased intensity of D α signal and from clear distinctions in the edge gradients of the visible plasma boundary (observed as a sharp plasma edge in camera images). The beam-driven chirping modes, identified as ideal magnetohydrodynamics beta-induced Alfvén acoustic eigenmodes modes, are observed in Mirnov coil signals, interferometry, and soft x-ray diagnostics. A moderate amplitude ‘primer’ chirping mode usually precedes an H–L transition. This is followed by a ‘dominant’ chirping mode with higher amplitude during the L-mode. The L–H transition back to the improved confinement occurs on a longer time scale of tens of ms, consistent with the slowing down time scale of fast beam ions. A dramatic decrease in toroidal plasma rotation is systematically observed associated with chirping modes sweeping down to zero frequency. Resonance maps built for the beam-driven chirping modes with the ASCOT (accelerated simulation of charged particle orbits in torodoial devices) code show that the resonant beam ions have orbits near the trapped-passing boundary. The ASCOT modelling assesses how losses of the resonant fast ions caused by the chirping modes with high enough amplitude modify the torque, potentially affecting the plasma rotation.

magnetic confinement fusion↗

Accelerating the rate of discovery: toward high-repetition-rate HED science

As high-intensity short-pulse lasers that can operate at high-repetition-rate (HRR) (>10 H z ) come online around the world, the high energy density (HED) science they enable will experience a radical paradigm shift. The >10 3 increase in shot rate over today's shot-per-hour drivers translates into dramatically faster data acquisition, more experiments, and the ability to exploit machine learning, and thus the potential to significantly accelerate the advancement of HED science. A wide range of HED experiments, from opacity investigations to secondary source generation to plasma nuclear physics, will benefit from the increased statistics, precision, and exploration of phase space. Besides increasing the rate at which scientific experiments can be performed, HRR also allows for the rapid delivery of optimal experiments supported by simulations and modeling augmented by close coupling to empirical data. To fully realize such an HRR framework, numerous subsystems must be developed and brought together, including feedback laser control loops, high-throughput targetry and diagnostics, cognitive simulation, enhanced HED codes, and advanced data analytics. This paper describes the vision for an integrated HRR laser experimental HED system and outlines some of the major considerations and challenges for realizing it.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Measurement of Beam Energy in the Fermilab's Linac taken at the transfer Line

Linac is the first machine in the Accelerator chain at Fermilab where 𝐻− particles are accelerated from 35 keV to 400 MeV and travel to the Booster where they are stripped. of the extra electrons to become protons. The Booster requires stable beam energy at injection. The Linac extraction energy tuning has been performed using two Beam Velocity Monitors (a.k.a Griffin detectors) to maintain stable relative energy between the Booster and the Linac. Our goal is to control the Linac energy parameters using Machine Learning techniques to increase reliability and quality of beam delivered from Linac. The first step is to understand the data from the Linac extraction diagnostics; and develop reliable, accurate methods for energy measurement and control before implementing machine learning. There were two methods of energy measurement implemented, and the results of these are compared. The first method was time of flight measurements using the Phase probes inside B eam Position Monitors (BPM) that provide the beam’s phase of arrival data. The second method used the relation between beam position data from the BPMs and dispersion values from the 400MeV MAD-X model to calculate momentum variation. The results of these two energy measurement methods compare well as the Linac energy is varied.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Magnetic Field Measurements of First Pre-series Full -Length 4.2 m Quadrupole MQXFA03 Using PCB Rotating Coils for the Hi Hi-Lumi LHC Project

The U.S. Hi-Lumi LHC Accelerator Upgrade Project (AUP) and CERN have joined efforts to develop high field quad-rupoles for the Hi-Lumi LHC upgrade. The US national laborato-ries in the AUP project will deliver 10 magnets and each cryostat has two 4.2 m high gradient quadrupoles in it. These magnets are made of Nb3Sn conductors, with large aperture (150 mm) and in-tegrated gradient of 556.9 T. This paper reports on magnetic measurements performed during the vertical test at Brookhaven National Laboratory (BNL) in 2019-2020. A warm measurement Z-Scan (+/- 15 A) with 42 Z-positions before cool-down was per-formed at BNL. The results were directly compared to field data measured at LBNL during magnet assembly. Measured harmonics and magnetic center offsets (ΔX and ΔY) have provided timely and informative diagnostics on the magnet structure’s shape at both warm and cold temperatures. A new centering fixture was de-signed and added to better center the warm bore tube which con-tains the rotating coil probe. After the quench training to 16.47 kA was achieved, a complete set of cold measurements (Z-Scan at 16.47 kA and I-Scan from 960 A to 16.47 kA and back to 960 A) was made. Periodic axial variation of allowed and nonallowed harmonics was observed which is related to the coil radial and/or mid-plane variations along the magnet axis. Overall, the average harmonics in the straight section are within the required field boundaries.

43 PARTICLE ACCELERATORS↗

DARHT Axis 1 Bremsstrahlung Dose Measurements

he Dual-Axis Radiographic Hydrodynamic Test (DARHT) facility provides flash radiography ca pabilities using two electron Linear Induction Accelerators (LIA’s). Axis-1 of DARHT produces, nominally, a 20-MeV, 1.5-kA, 80-ns-Full Width at Half Max (FWHM) electron beam. The elec tron beam is focused on to a tantalum target to produce a Bremsstrahlung x-ray dose for flash radiography of dynamic systems. This paper will describe and compare a variety of techniques for determining the x-ray dose for two different beam currents produced by a 55mm and 70mm diameter cathode. The data was taken in November of 2022 on DARHT Axis 1. The experimen tal measurement techniques include a platinum calorimeter, a diamond radiation detector (DRD), and a Compton diode (CD). Gafchromic EBT3 self-developing dosimetry film was also used, but no useful results were obtained. Beam charge and energy were recorded and dose was calculated with this information using xtr with Dosecalcx, and simple dose charge-energy scaling. In this pa per, we will discuss the target geometry and experimental layout, the methods of measuring dose, dose diagnostics and measurement of beam charge and energy, and the comparisons of data and calculations.

43 PARTICLE ACCELERATORS↗