SEARCH · Engineering Papers

Results for “beam model”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 811 records · Page 45

All sources NASA NTRS DOE OSTI

DOE OSTI2025

Results of a Geant4 benchmarking study for bio‐medical applications, performed with the G4‐Med system

Geant4, a Monte Carlo Simulation Toolkit extensively used in bio-medical physics, is in continuous evolution to include newest research findings to improve its accuracy and to respond to the evolving needs of a very diverse user community. In 2014, the G4-Med benchmarking system was born from the effort of the Geant4 Medical Simulation Benchmarking Group, to benchmark and monitor the evolution of Geant4 for medical physics applications. The G4-Med system was first described in our Medical Physics Special Report published in 2021. Results of the tests were reported for Geant4 10.5. Purpose In this work, we describe the evolution of the G4-Med benchmarking system. Methods The G4-Med benchmarking suite currently includes 23 tests, which benchmark Geant4 from the calculation of basic physical quantities to the simulation of more clinically relevant set-ups. New tests concern the benchmarking of Geant4-DNA physics and chemistry components for regression testing purposes, dosimetry for brachytherapy with a 125 I source, dosimetry for external x-ray and electron FLASH radiotherapy, experimental microdosimetry for proton therapy, and in vivo PET for carbon and oxygen beams. Regression testing has been performed between Geant4 10.5 and 11.1. Finally, a simple Geant4 simulation has been developed and used to compare Geant4 EM physics constructors and physics lists in terms of execution times. Results In summary, our EM tests show that the parameters of the multiple scattering in the Geant4 EM constructor G4EmStandardPhysics_option3 in Geant4 11.1, while improving the modeling of the electron backscattering in high atomic number targets, are not adequate for dosimetry for clinical x-ray and electron beams. Therefore, these parameters have been reverted back to those of Geant4 10.5 in Geant4 11.2.1. The x-ray radiotherapy test shows significant differences in the modeling of the bremsstrahlung process, especially between G4EmPenelopePhysics and the other constructors under study (G4EmLivermorePhysics, G4EmStandardPhysics_option3, and G4EmStandardPhysics_option4). These differences will be studied in an in-depth investigation within our Group. Improvement in Geant4 11.1 has been observed for the modeling of the proton and carbon ion Bragg peak with energies of clinical interest, thanks to the adoption of ICRU90 to calculate the low energy proton stopping powers in water and of the Linhard–Sorensen ion model, available in Geant4 since version 11.0. Nuclear fragmentation tests of interest for carbon ion therapy show differences between Geant4 10.5 and 11.1 in terms of fragment yields. In particular, a higher production of boron fragments is observed with Geant4 11.1, leading to a better agreement with reference data for this fragment. Conclusions Based on the overall results of our tests, we recommend to use G4EmStandardPhysics_option4 as EM constructor and QGSP_BIC_HP with G4EmStandardPhysics_option4, for hadrontherapy applications. The Geant4-DNA physics lists report differences in modeling electron interactions in water, however, the tests have a pure regression testing purpose so no recommendation can be formulated.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2024

Unraveling the Highly Plastic Behavior of ALD-Aluminum Oxide Encapsulations by Small-Scale Tensile Testing

We present a study directly measuring the electron-beam-induced plasticity of amorphous Al 2 O 3 coatings. Core–shell nanostructures are employed as small-scale model systems for two-dimensional coatings made by atomic layer deposition (ALD). Copper nanowires (NWs) are used as substrates for ALD deposition, representing a model system for interconnects commonly found in integrated circuits. Experiments are performed in situ in a transmission electron microscope (TEM) and further analyzed with electron energy loss spectroscopy (EELS). Our in situ TEM tensile experiments reveal the highly plastic behavior of the ALD shell, which withstands a maximum strain of 188%. Comparable samples under beam-off conditions show a brittle fracture, which underlines the effect of electron irradiation. The electron-beam-activated bond switching within the amorphous network enables compensation of the applied tensile strain, leading to viscous flow. By incorporating an intermediate nanocrystalline layer within the Al 2 O 3 shell, the plasticity is suppressed and brittle fracture occurs. This work directly demonstrates the tuning of mechanical properties in amorphous ALD structures through electron irradiation.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Shrinkage-induced deformations and creep of structural concrete: 1-year measurements and numerical prediction

Highlights: • Extensive experimental study on drying shrinkage, creep and microcracking of concrete • All specimens prepared from a single batch of ordinary-strength structural concrete • 1st year of measurements of (not only) non-uniformly drying beams with span up to 3-m • The database is downloadable from free-to-use research data repository • Modified MPS model for concrete creep used in blind prediction of all experiments The material models for creep and shrinkage operating on the material point level in FEM are usually intended for challenging complex applications and structures, where the average cross-sectional approach does not suffice. The identification of the growing number of material parameters induced by increasing model capabilities relies on very specific and narrow-oriented yet interconnected experiments which are scarce. The presented comprehensive experiments aim to provide a clearer image of the complicated interaction among the basic phenomena: drying, shrinkage, creep, and microcracking. The cornerstone of this ongoing research is a unique set of 30 partially-sealed unreinforced concrete beams with span 1.75–3.0 m subjected to drying. To minimize material variation, all specimens in this study were cast from a single batch of ordinary strength structural concrete with slag-blended binder. The resulting experimental database will be suitable both for validation and development of the constitutive models.

36 MATERIALS SCIENCE↗

DOE OSTI2023

An Extensible High Energy Density Modeling Tool for Extreme Regimes

The overreaching goal of the project is to develop a simulation capability to model an entire High Energy Density (HED) target heated by an X-ray Free Electron Laser (XFEL) beam including the surrounding material with a focus on target material associated with subsequent shots. Our primary objective is to study target fratricide problems, where radiation/debris from the current shot degrade the target for subsequent shots. This work will have a large impact on research being conducted at HED facilities where the quality of data is directly related to the effective repetition rate of the driver, which is often limited by target fratricide problems. This project focuses on a stream of closely spaced droplet targets that are appropriate for new very high repetition rate sources such as the ~1 MHz LCLS-II upgraded XFEL. The capability of the PISALE (Pacific Island Structured-AMR with ALE) code is extended to model this class of problems. We summarize the capability and improvements made to the HED branch of the PISALE code. We discuss our simulations of target fratricide for small (5 micron) hydrogen droplets heated by an XFEL beam at SLAC. We also compare simulations of the initial dynamics of larger (50 micron) water droplets, heated by the same XFEL beam, with experimental data. We briefly discuss training, dissemination, and related activities associated with this project.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Neutrino beam bunch structure reconstruction with precision timing in the ICARUS liquid argon time projection chamber

The ICARUS detector has been operating smoothly since 2021 as the far detector in the Short Baseline Neutrino (SBN) program at Fermilab, collecting neutrino interactions from both the Booster Neutrino Beam (BNB) and off-axis from the Neutrinos at the Main Injector (NuMI) beam. Analysis of neutrino interactions in ICARUS requires mitigation of substantial cosmogenic backgrounds. This is achieved by using an external Cosmic Ray Tagger (CRT) and a Photomultiplier Tube (PMT) system embedded in the liquid argon. The intrinsic neutrino beam bunch structure, inherited time structure from the Radio Frequency (RF) system used to accelerate the protons, can be resolved at the ICARUS detector using precise timing information. Located at shallow depth, ICARUS is exposed to a high flux of cosmic rays that can be mistaken for neutrino interactions. To mitigate this background, the CRT and a 3-meter-thick concrete overburden were installed. To better model backgrounds, ICARUS makes use of an overlay technique where simulated neutrino events are superimposed on detector beam-off data. PMTs installed within a Time Projection Chamber detect argon scintillation light emitted by high energy charged particles passing through the chamber and provide the event timing of neutrino interactions. The nanosecond-level beam bunch structure is reconstructed with the PMT system and can be used to further understand backgrounds and enhance neutrino physics capabilities. In this thesis, I will discuss background mitigation techniques using precision timing and present a novel technique to select neutrino events from our unbiased data stream using the beam bunch structure.

Heggestuen, Anna [Colorado State U.] (ORCID:000000↗

DOE OSTI2025

Compare low-gain 1D and 3D models toward a storage ring-based X-ray free-electron-laser oscillator

Fourth-generation diffraction-limited synchrotron light sources (DL-SLS) present a compelling platform for advanced light source applications due to their ultra-low emittance (around tens of picometers), sub-micrometer beam stability, and high repetition rates (greater than 1 MHz). Despite these advantages, fundamental limitations, such as long bunch durations (tens of picoseconds), large relative energy spread (~10⁻³), and low peak current (<300 A), have hindered their effectiveness in free-electron laser (FEL) applications. Using a low-gain three-dimensional (3D) model based on NSLS-II upgrade lattice parameters, we demonstrate that a 6% single-pass gain is achievable with an optimized transverse gradient undulator (TGU). Concurrently, recent advances in X-ray optics—specifically, a four-mirror bow-tie resonator utilizing diamond mirrors and beryllium compound refractive lenses (CRLs)—enable total round-trip losses below 4% and an output coupling efficiency near 1%, rendering a Storage Ring based X-ray FEL oscillator (XFELO) a realistic possibility. In the 3D framework, the TGU effectively mitigates the detrimental effects of large energy spread by spatially dispersing the beam, leading to enhanced gain relative to conventional one-dimensional (1D) models. We establish both analytical and numerical connections between the 1D and 3D descriptions, leveraging GENESIS simulations to map equivalent gain conditions. While 1D resonance is defined in the energy domain, the 3D TGU system shifts the resonance dependence to transverse gradient and dispersion parameters. Once optimized, this framework allows predictive modeling using 1D formulas, which can then be validated through full 3D simulations.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Beyond the Standard Model physics prospects at the Deep Underground Neutrino Experiment

The Deep Underground Neutrino Experiment (DUNE) is an international project for neutrino physics and proton-decay searches, currently in the design and planning stages. Once built, DUNE will consist of two detectors exposed to the world's most intense neutrino beam. The near detector at Fermilab will record neutrino interactions near the beginning of the beam line. The other, much larger, detector, comprising four 10-kton liquid argon time projection chambers (LArTPCs), will be installed at a depth of 1.5 km at the Sanford Underground Research Facility in South Dakota, about 1,300 km away from the neutrino source. The unique combination of the high-intensity neutrino beam, DUNE's high-resolution near detector system, and massive LArTPC far detector enables a variety of probes of Beyond-the-Standard-Model (BSM) physics, from the discovery of new particles (sterile neutrinos or dark matter), to precision tests of beyond the three-flavor mixing paradigm, non-standard neutrino interactions (NSIs), heavy neutral leptons, and the detailed study of rare processes (e.g., neutrino trident production). This article reviews these physics topics and discusses the prospects for their discovery at the DUNE experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Probing Axion-Like-Particles at the CERN Gamma Factory

We report the aim of the proposed CERN Gamma Factory is to produce ≈10 17 photons per second with energies up to 400 MeV. The photon beam intensity is expected to be a factor of $\mathcal{O}$(10 7 ) larger than that of the presently available photon beams in the MeV energy range. In this work, its potential to probe physics beyond the Standard Model is explored. In particular, searches for axion like particles (ALPs) with dominant couplings to photons are discussed and various production scenarios - fixed target, photon-photon collision, and conversion by a magnetic field - and detection schemes considered - via decay to photons or back-conversion. It is found that the Gamma Factory in a fixed target mode can probe ALPs with mass m a ≲ $\mathcal{O}$(100 MeV) and decay constants larger than 10 7 GeV, improving by an order of magnitude the discovery potential of previous beam dump experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Combining diagnostics, modeling, and control systems for automated alignment of the TES beamline

X-ray beamlines are essential components of all synchrotron light sources. Practical operations involve frequent variation in beamline component positions and orientation, particularly when photon beam parameters shift due to experimental needs, or due to variations in the incoming photon beam. The alignment process can be time consuming and takes away from valuable beam time for experimental data collection. We describe progress in the automation of certain alignment tasks on the tender-energy X-ray spectroscopy (TES) beamline at the National Synchrotron Light Source II (NSLS-II). The beamline is controlled using the BlueSky software in which high level experimental plans guide the beamline components during an experiment. Numerous software packages exist for beamline modeling, and they may be tied to the beamline control system using a package we are continuing to develop called Sirepo-Bluesky. The photon beam distribution may be measured with fluorescent screens, and a relation between beam and machine state can be found by varying the mirror and aperture settings over a multi-dimensional range. We describe the results of such parameter varying measurements and how we are combining Sirepo-Bluesky with machine learning methods and reduced models to automate mirror alignment on the TES beamline.

36 MATERIALS SCIENCE↗

DOE OSTI2026

First Search for Dark Sector e+e- Explanations of the MiniBooNE Anomaly at MicroBooNE

The MiniBooNE anomaly has puzzled the neutrino physics community for over two decades. MicroBooNE has previously searched for anomalous electron and photon excesses as potential explanations but the mystery persists. In this poster, we present the first direct test of dark sector models in which dark neutrinos scatter, then decay into e+e− pairs and missing energy, mimicking the MiniBooNE signal. These models have recently emerged as compelling candidates that evade existing constraints. Using 6.87×1020 protons-on-target in the Booster Neutrino Beam, we select forward-going, coherently produced e+e− events in the MicroBooNE detector. We observe 95 events against a constrained background prediction of 69.7±17.3. We set the world's first direct limits on this class of dark sector models, excluding at 95% CL the majority of parameter space viable as a solution to the MiniBooNE anomaly.

Basque, Vincent Marc [Edinburgh U.] (ORCID:0000000↗

DOE OSTI2021

Transverse mode analysis for free-space laser beams using Bayesian analysis

Reliable and rapid assessment of the transverse mode quality of a free-space laser beam has a wide range of applications in laser development, research, and utilization. It has become even more important with recent advances in developing orbital angular momentum photon beams across a broad spectral region. In this work, a general modal analysis method for a free-space multimode laser beam has been developed based on Bayesian analysis. After transforming mode decomposition into a linear system problem, a Gaussian probabilistic model is used to find a closed-form solution. The method is found to be robust with the presence of Gaussian noise. Prior knowledge about the mode content can be incorporated into the method to improve the solution for situations when coherent disturbances or contamination are present in the laser beam. This method can be used to analyze the mode content for laser beams in different bases, such as Hermite–Gaussian (HG) modes and Laguerre–Gaussian (LG) modes. Three applications of this method are presented: a detailed modal analysis of the beam image from the incoherent intensity addition of HG modes and two examples of mode decomposition using the complex wavefront from the coherent superposition of HG and LG modes. The feasibility of this method is demonstrated using various simulation results. Based on digital images of a laser beam recorded without complex wavelength-limiting optics, in principle, this method can be used in a wide wavelength range from infrared to ultraviolet, and possibly x ray.

Liu, Peifan (ORCID:0000000273816153)↗

DOE OSTI2021

A Joint Measurement of $\nu_{\mu}$-Disappearance and $\nu_{e}$e-Appearance in the NuMI beam using the NOvA Experiment

The discovery of neutrino oscillations provides the first indication of a lepton flavor violating (LFV) process, one that isn't predicted by the Standard Model. As such, NOvA is part of a rich experimental program to constrain unknown parameters in the neutrino oscillation model, described for three neutrino flavors using the PMNS unitary matrix. It is a long baseline experiment utilizing two detectors, a Near Detector at Fermilab and a Far Detector in Ash River, Minnesota for a total baseline of 810 km. It receives a predominantly ${\nu_\mu}/\overline{\bar\nu_\mu}$ beam peaking at 1:8 GeV from the NuMI beam facility at Fermilab. There are four oscillation channels used in the analysis, ${\nu_\mu} \to {\nu_\mu}$, ${\nu_\mu} \to {\nu_e}$, ${\overline{\nu}_\mu} \to {\overline{\nu}_\mu}$ and ${\overline{\nu}_\mu} \to {\overline{\nu}_e }$. With a total exposure of 13:6_10$^{20}$ and 12:5_10$^{20}$ protons on target for the neutrino and anti-neutrino beam modes respectively, 82 candidates are seen in the ${\nu_\mu} \to {\nu_e}$ channel for a total predicted backgroundof 26:8 events. Similarly, 33 candidates are seen in the corresponding anti-neutrino channel for a total predicted background of 14:0 events. In the ${\nu_\mu} \to {\nu_\mu}$ $(\overline{\nu}_\mu \to \overline{\nu}_\mu}$ channel, 211 (105) candidates are seen with an expectation of 1156.1 (488.1) events at no oscillations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

Self-focusing of cosh-Gaussian laser beam and its effect on the excitation of ion-acoustic wave and stimulated Brillouin backscattering in collisionless plasma

An analytical and numerical study has been carried out for self-focusing of an intense cosh-Gaussian laser beam in collisionless plasma and its impact on the excitation of ion-acoustic wave and stimulated Brillouin backscattering process. The analytical model has been developed under Wentzel–Kramers–Brillouin and paraxial ray approximations. The nonlinearities of ponderomotive force on electron and the relativistic oscillation of the electron mass have been used in this study. The nonlinear differential equations have been set up for the beam width parameters of the main beam, ion-acoustic wave, backscattered wave and back reflectivity of stimulated Brillouin scattering (SBS). These equations have been solved numerically for different values of decentred parameter (b), relative plasma density (ω{sub p0}/ω{sub 0}) and incident laser intensity (a). The results have been compared with only relativistic nonlinearity and Gaussian profile of laser beam. The focusing of laser beam, ion-acoustic wave and scattered wave are found to be strong under relativistic-ponderomotive regime compared to only relativistic regime. Further, it is observed that focusing/intensity of main laser beam, ion acoustic wave and SBS back reflectivity increases with increasing the values of b and ω{sub p0}/ω{sub 0}. Itis also found that back reflectivity of SBS process gets suppressed with the increase in the value of a. This study may be useful in laser induced fusion scheme where back scattering of SBS plays very important role.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Understanding neutrinos with accelerator beams and liquid argon time-projection chambers: ICARUS and DUNE

A global program of experiments has worked towards characterizing neutrino oscillation over the past few decades. However, important parameters remain to be measured, and mysteries remain to be elucidated. Current and upcoming experiments are targeting the open questions and probing the consistency of the neutrino oscillation paradigm. Likewise, the liquid argon (LAr) time-projection chamber (TPC) has emerged as a sensitive particle detection technology for neutrino experiments. A current generation of LAr TPC detectors are being used to study neutrinos while also gaining important experience in operating and analyzing with this technology. SBND, MicroBooNE, and ICARUS have collected or are collecting data from beams at Fermilab (near Chicago) to explore the possibility of a sterile neutrino and/or other beyond Standard Model (BSM) physics. SBND and ICARUS will be used to conduct a two-detector analysis as part of the Short Baseline Neutrino (SBN) Program. Additionally, these detectors are enabling important neutrino interaction studies necessary to prepare for the next generation of oscillation experiments. One such oscillation experiment that will come online over the next years is the Deep Underground Neutrino Experiment (DUNE), which will install multiple 10 kiloton LAr TPCs underground in South Dakota (south of Saskatchewan) to conduct oscillation measurements with neutrinos originating in a beamline at Fermilab. A detector complex will be installed at Fermilab as well, to study the beam before the expected flavour oscillations. This “near detector” will also employ a LAr TPC, with a segmented and pixel-based design, as well as other technologies to constrain uncertainties in the oscillation measurement by characterizing the beam and neutrino interactions. This talk will discuss the ICARUS and DUNE experiments, the LAr TPC detector technology, and the efforts to realize and leverage these experiments to better understand the properties of neutrinos.

Howard, Bruce L. [Fermilab]↗

DOE OSTI2024

Deep Multitask Learning Models for Radiation Estimation at High Energy Accelerator Facility

Controlling the dose of radiation exposure in potential radioactive facilities is critical for ensuring the safety of staff and the public. Here, in this paper, we developed machine learning models to estimate radiation exposure efficiently at the Thomas Jefferson National Accelerator Facility (JLab), aiming to enhance safety in both accelerator facilities and public areas. Multiple sensors were deployed around the three experimental halls at JLab. Data on single-beam currents, energy levels, and radiation values at the sensor locations were collected during accelerator operation. We proposed a multi-task learning model for radiation estimation, utilizing either one-dimensional convolutional neural networks (1-D CNNs) or long short-term memory networks (LSTMs) as the backbone. The proposed model was trained to simultaneously estimate radiation levels at the sensor locations. Experimental results demonstrated that the proposed model with LSTM backbone achieved the best estimation performance, with an average R 2 score of 0.7557 for estimation within the same year and 0.7157 for estimation across different years. These results significantly surpassed those of competing models.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

The MicroBooNE Single-Photon Low-Energy Excess Search (Public Note 1087)

MicroBooNE is a short baseline neutrino experiment at Fermilab designed to address the low energy excess observed by the MiniBooNE experiment. This note describes and presents preliminary results for the MicroBooNE analysis developed to address this excess as a single photon plus one or zero protons in the final state. The analysis assumes neutrino neutral current Δ resonance production followed by Δ radiative decay on argon (NC Δ → Nγ ) as the "signal model"; event reconstruction and selection have been developed and optimized in order to maximize efficiency and reduce cosmogenic and other beam-related backgrounds to the NC Δ → Nγ signal. We present the analysis methodology and validation checks performed on limited-statistics open data sets, corresponding to 5 x10 19 protons on target (POT), following a blind analysis, as well as the projected sensitivities for testing the Standard Model (SM) predicted rate for the NC Δ → Nγ process and for testing the interpretation of the previously observed MiniBooNE low energy excess as NC Δ → Nγ events, using the full anticipated MicroBooNE data set of 12.25 x 10 20 POT.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Beam Dynamics of the Muon $g\textrm{-}2$ Experiment

The Muon $g\textrm{-}2$ Experiment (E989) at Fermilab aims to measure the muon anomalous magnetic moment $a_{\mu}$ with unprecedented precision, potentially uncovering physics beyond the Standard Model of particle physics. The result based on Runs 1-3, released in 2023, achieved a precision of 0.20 ppm. The experiment circulates muons in a storage ring, measuring $a_{\mu}$ from decay positron time and energy measurements collected with calorimeters. To achieve the required accuracy, it is crucial to measure and control the magnetic field in the ring with high precision. Beam dynamics corrections are necessary for muons not orbiting exactly in the midplane, for their oscillations, and for electric field effects. Highly accurate beam dynamics simulations are instrumental for quantifying and validating the beam dynamics corrections, ultimately improving the precision of the $a_{\mu}$ measurement and facilitating the achievement of the ambitious $70\:\mathrm{ppb}$ systematic uncertainty goal. The measured field data was incorporated into models for simulations using three codes: \texttt{gm2ringsim} (an internal Geant4-based code), \textit{COSY INFINITY}, and \textit{BMAD}. The advantages of \texttt{gm2ringsim} include using CAD-based geometry and modelling the detector effects. \textit{COSY INFINITY} is a highly accurate and efficient code that uses high-order differential-algebraic transfer maps, precise fringe field calculations, and advanced symplectification methods. Symplectification is important for maintaining the physical correctness of the muon beam behaviour with high precision over the storage time, ensuring conservation of phase space volume and preventing artificial damping or excitation of particle motion. The experiment completed its final Run 6 in July 2023, collecting 21 times more data than the previous BNL experiment. Analyses of data from Runs 4-6 are ongoing, with results planned for release in 2025, potentially resolving the current tension between experiment and theory.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

A Two-Dimensional Non-Linear Magnetic Equivalent Circuit Model to Facilitate the Preliminary Design of a Normal Conducting Quadrupole

Normal conducting quadrupoles have been used to focus charged particle beams in synchrotrons, beam transfer lines, medical linacs, etc. for a long time. Optimization techniques based on analytical expressions combined with the use of a numerical field analysis tool exist in the literature for the design of an optimal pole tip shape. However, the initial shape and dimensions of the remaining yoke (including the pole itself and yoke base that act as the return path) are usually less well defined. This article discusses a design methodology for a normal conducting quadrupole based on a two-dimensional magnetic equivalent circuit. Here, this approach considers the geometry of the entire magnet and the non-linear behavior of the yoke material, thereby eliminating the initial iterations. The design outcome of this exercise serves as a competent starting point and can then be used to refine the pole tip, pole taper, yoke size, and add other geometrical features to achieve the required field quality, gradient, coil considerations, etc. by employing a finite element analysis tool. An example design study to demonstrate the proposed methodology is presented.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗