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Modeling of a Four-Stage Linear Ionization Cooling Channel for a Muon Collider in g4Beamline

A previous study of an eight-stage rectilinear ionization cooling channel in the ICOOL software demonstrated a five-order-of-magnitude reduction in a muon beam’s 6D emittance. In this study, we look to compare the ways ICOOL and Muons, Inc.’s g4Beamline software model ionization cooling by comparing their modeling of the first four stages of this optimized cooling channel constructed in ICOOL. We begin by identifying the parameters used to construct the optimized ionization cooling channel in ICOOL. We then reconstruct this beam in g4Beamline with identical parameter specifications and simulate the cooling of an identical input beam. Finally, we compare the two simulations based on their beam transmission, longitudinal emittance, and transverse emittance along the channel length. Through this process, we demonstrate that G4Beamline accurately reproduces transverse cooling results but predicts systematically different longitudinal emittance evolution while maintaining similar overall cooling performance, reproducing a 97.9% reduction in 6D emittance over four stages.

Keeler, Dominic [Purdue U., West Lafayette] (ORCID↗

Modeling of a Four-Stage Linear Ionization Cooling Channel for a Muon Collider in G4Beamline

A previous study of an eight-stage rectilinear ionization cooling channel in the ICOOL software demonstrated a five-order-of-magnitude reduction in a muon beam’s 6D emittance. In this study, we look to compare the ways ICOOL and Muons, Inc.’s g4Beamline software model ionization cooling by comparing their modeling of the first four stages to this optimized cooling channel constructed in ICOOL. We begin by identifying the parameters used to construct the optimized ionization cooling channel in ICOOL. We then reconstruct this beam in g4Beamline with identical parameter specifications and simulate the cooling of an identical input beam. Finally, we compare the two simulations based on their beam transmission, longitudinal emittance, and transverse emittance along the channel length. Through this process, we demonstrate that G4Beamline accurately reproduces transverse cooling results but predicts systematically different longitudinal emittance evolution while maintaining similar overall cooling performance, reproducing a 97.9% reduction in 6D emittance over four stages.

Keeler, Dominic [Purdue U., West Lafayette] (ORCID↗

Advanced Simulation Tools for Muon-Based Accelerators

The project developed new software tools incorporating the most accurate theoretical calculations and experimental data available for crucial and not-yet-considered physics processes specific to muon accelerators. These new tools were applied to modeling muon ionization cooling channels for a muon collider or a neutrino factory, the facilities that have the potential to discover and explore new exciting fundamental physics but require the development of demanding technologies and innovative concepts. G4beamline, COSY Infinity, and WARP computer codes are particularly well-suited for addressing muon accelerator modeling problems. G4beamline was chosen for its flexibility and modularity, and for being one of the de facto standard codes used by the muon accelerator community. COSY was selected for speed, ability to take into account high-order nonlinear effects essential for the large beams under consideration, and availability of built-in optimization tools. WARP was chosen for its space charge calculation capabilities, speed and flexibility of implementing new lattice elements such as RF cavities. This final technical report summarizes the efforts on implementing advanced new tools in these computer codes addressing the shortcomings in modeling muon physics processes and using these tools to model muon ionization cooling channels.

43 PARTICLE ACCELERATORS↗

Characterization of muon and electron beams in the Paul Scherrer Institute PiM1 channel for the MUSE experiment

The MUon Scattering Experiment, MUSE, at the Paul Scherrer Institute, Switzerland, investigates the proton charge radius puzzle, lepton universality, and two-photon exchange, via simultaneous measurements of elastic muon-proton and electron-proton scattering. The experiment uses the PiM1 secondary beam channel, which was designed for high precision pion scattering measurements. We review the properties of the beam line established for pions. We discuss the production processes that generate the electron and muon beams, and the simulations of these processes. Simulations of the π/μ/e beams through the channel using TURTLE and G4beamline are compared. The G4beamline simulation is then compared to several experimental measurements of the channel, including the momentum dispersion at the intermediate focal plane and target, the shape of the beam spot at the target, and timing measurements that allow the beam momenta to be determined. Finally, we conclude that the PiM1 channel can be used for high precision π, μ, and e scattering.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Mu2e - Research & Development

Current efforts are being conducted at Fermi National Laboratory to study potential violations in accepted theory that would otherwise suggest a restructuring of our fundamental understanding of the universe. Mu2e is one of these frontier projects that studies Charged Lepton Flavor Violation (CLFV) which if observed, would suggest physics beyond the Standard Model. Therefore, this note encompasses several projects that contribute to the fruition of Mu2e investigations. Due to the broad range of disciplinary inconsistencies that each project requires, all the work is being presented as a means of justifying contribution to Mu2e. The projects are comprised of a simulation exploring the extinction level of proton pulses after Recycler ring re-bunching by using G4beamline to simulate an 8GeV proton beam interaction with a titanium target, three Cherenkov radiation-based detectors and 2/3-fold and 3/3-fold coincidence rate analysis. Additionally, supplemental work for the implementation of a Micro Telecommunications Computing Architecture (TCA) crate to establish a peak finding algorithm to ensure that the out-of-time beam is less than 10$^{−10}$ fractional level along with single-layer inefficiency analysis on scintillation counters for the Cosmic-Ray Veto (CRV) analysis to ensure the overall inefficiency is 10$^{−4}$. Preliminary results have been achieved for the G4beamline simulation 2/3-fold and 3/3-fold coincidences which are in the order of 10$^{−9}$ and 10$^{−10}$, respectively. Only preliminary results of a triangular counter and four rectangular di-counters for the CRV have been realized. The microTCA crate development is still ongoing.

43 PARTICLE ACCELERATORS↗

Three Approaches for Complete Measurement of the Transverse Beam Optics Along the Fermilab Muon Campus Extraction Line

Traditionally, the process of measuring the optical parameters of a beamline has employed the use of one of two standard methods, namely the three-screen method or a quadrupole magnet scan. Both require either an area of zero dispersion to perform the measurements or knowledge of the dispersion function and momentum spread beforehand in order to provide accurate results. There is however a third method that can be used to measure the standard optical parameters, the beam parameters, the dispersion function, and the momentum spread simultaneously. This method, aptly named the six-screen method, is an extension of the more standard three-screen method. Utilizing the simulation environment of G4beamline, we simulated the 8 GeV proton beam in the M4 beamline and measured the optical and beam parameters using the two standard approaches. Those results were then used as a reference to check the viability of employing the less standard six-screen method in the M4 line. If shown to be a viable option, the six-screen method could be used to retrieve the dispersion function and momentum spread of the beam without needing to change the energy of the beam.

43 PARTICLE ACCELERATORS↗

Final cooling with thick wedges for a muon collider

In the final cooling stages for a muon collider, the transverse emittances are reduced while the longitudinal emittance is allowed to increase. In previous studies, Final 4-D cooling used absorbers within very high field solenoids to cool low-momentum muons. Simulations of the systems did not reach the desired cooling design goals. In this study, we develop and optimize a different conceptual design for the final 4D cooling channel, which is based on using dense wedge absorbers. We used G4Beamline to simulate the channel and Python to generate and analyze particle distributions. We optimized the design parameters of the cooling channel and produced conceptual designs (corresponding to possible starting points for the input beam) which achieve transverse cooling in both x and y by a factor of ~3.5. These channels achieve a lower transverse and longitudinal emittance than the best design previously published.

43 PARTICLE ACCELERATORS↗

Extinction Monitoring of Pulsed Proton Beams Using FPGA-Based Peak Detection

The Mu2e experiment at Fermilab imposes stringent requirements on the elimination of out-of-time beam in its pulsed proton beam - a requirement known as "extinction". We present a method to measure the out-of-time particle rates to calculate the level of extinction in the inter-pulse gaps. The proposed method utilizes an array of quartz Cherenkov radiators and photomultiplier tubes to detect particles scattered from a vacuum chamber in the M4 transfer beamline at Fermilab.The measurement will employ a new μTCA-based FPGA system for data acquisition and signal processing, utilizing real-time peak detection algorithms to count scattered beam particles. By integrating data over many transfers, the time profile of the out-of-time beam will be resolved to fractional levels relative to that of the in-time beam. These results are compared with G4beamline simulations to validate models of beam transport, dynamics, and extinction, providing critical input for optimizing beam delivery to Mu2e.

Hensley, Ryan [UC, Davis]↗

R&D toward design for a pion-production target for Mu2e-II

The Mu2e experiment at Fermilab will search for evidence of charged lepton flavor violation by observing the conversion of a negative muon into an electron in the Coulomb field of a nucleus without emission of neutrinos and will probe effective new-physics mass scales in the 103-104 TeV range. One of the main parts of the Mu2e experimental setup is its target station in which negative pions are generated in interactions of the 8 GeV primary proton beam with a tungsten target, which will be capable of producing $2\times10^{17}$ negative muons per year. Mu2e can be extended by a next generation experiment, Mu2e-II, with a sensitivity improved by another factor of 10 or more as enabled by the PIP-II accelerator upgrade project. PIP-II is a 250-meter-long linac capable of accelerating a 2 mA proton beam to a kinetic energy of 800 MeV corresponding to 1.6 MW of power. To achieve another factor of ten improvement in sensitivity, Mu2e-II will require about 100 kW of proton beam on target, and the added power requires a new target design. We will present our progress in RD of a target station conceptual design for Mu2e-II, using the MARS15 and G4beamline Monte-Carlo codes toward a selection between granular, conveyor, and rotating cylindrical target options.

Lynch, Kevin Richard↗

Negative Muon Count for the FNAL Muon g-2 Experiment

The primary goal of the FNAL Muon g-2 Experiment, located in Batavia, IL, USA, is to measure the anomalous magnetic dipole moment, a μ = (g-2)/2, of a muon to a precision of 0.14 ppm. Initial results from the experiment confirm a discrepancy between the experimental value of the muon anomaly compared with the theoretical value first discovered by the Brookhaven Muon g-2 Experiment in 2001. This discrepancy hints at new physics. However, running the experiment with negative muons is essential in order to verify the experimental value of the muon anomaly. As neither experiments nor simulation studies pertaining to the muon anomaly have been performed with negative muons, the goal of this work is to estimate the rates of negative muons arriving at the FNAL Muon g-2 experiment so that scientists can estimate the time required to run the experiment with negative muons. In order to do this, we performed several simulations of the Muon Campus, which delivers muons to the FNAL Muon g-2 Experiment, using the G4Beamline v. 3.06 at the National Energy Research Computing Center. We performed separate simulations for different sections of the muon campus, and simulations were repeated twice, once for negative muons and once for positive muons. An initial 10 9 protons were shot on target for both the negative and positive muon simulations. We found that the rate of negative muons arriving at the experiment was 0.549 times the rate of positive muons arriving at the experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Secondary Pion Production using the LINAC Beam on Graphite and Tungsten Targets

The Fermilab 400-MeV Linac primary proton beam can produce precision, single-species secondary beams using a production target in the MeV Test Area experimental hall; specifically, pions from 4 up to 120 MeV kinetic energy. (These low energy pions rapidly decay into a muon beam in a secondary collection and transport beamline.) Although graphite is a standard production target material given its ultra-high temperature tolerance and low impact on the post-target primary beam, secondary pion/muon total production cross sections increase approximately as Z1/3 for positive muons and N2/3 for negative muons. Higher mass targets such as tungsten can potentially increase low-energy m+ and m- rates by factors of 3 and 8, respectively. Initial production studies have confirmed higher muon yield from heavy targets (tungsten vs carbon), but also, surprisingly, show significant differences in pion production between modern hadronic models (GENIEhad) and between GEANT and MCNP, state of the art production modeling codes. This project will further investigate the production discrepancies between these two target materials and between different physics models with high-statistics runs using the GEANT-based code, G4Beamline to better quantify the results and compare with production data which will be obtained using the MTA secondary beamline.

Ahmed, Shiza↗

Final Cooling with Thick Wedges for a Muon Collider

A muon collider is a particle accelerator that collides muons rather than protons or electrons. An important component of such a collider is cooling, in which the emittance of the muon beam is reduced to make it suitable for use in a collider. In the last stage of this process, called final 4D cooling, emittance in the transverse axes is reduced while emittance in the longitudinal axis is allowed to grow. In previous studies, Final 4-D cooling used absorbers within very high field solenoids to cool low-momentum muons. Simulations of the systems did not reach the desired cooling design goals. In this study, we develop and optimize a different conceptual design for the final 4D cooling channel, which is based on single thick wedges. We used G4Beamline to simulate the channel and Python to generate and analyze particle distributions. We characterized the effects of various parameters on the performance of this system, including the initial emittances and Twiss parameters, the length and angle of the wedges, the length of the drift channel, and the length, frequency, gradient, and phase of the RF cavities. We optimized the design parameters of the cooling channel and produced two conceptual designs (corresponding to two possible starting points for the input beam) which achieve transverse cooling in both x and y by a factor of ≈ 3.5. These channels achieve a lower transverse and longitudinal emittance than the best design previously published.

43 PARTICLE ACCELERATORS↗

Mu2e - Extinction Monitor Research & Development

Current efforts are being conducted at Fermi National Laboratory to study potential violations in accepted theory that would otherwise suggest a restructuring of our fundamental understanding of the universe. Mu2e is one of these frontier projects that studies charged lepton flavor violation (CLFV) which if observed, would suggest physics beyond the Standard Model. Therefore, this note encompasses several projects that contribute to the fruition of Mu2e investigations. Due to the broad range of disciplinary inconsistencies that each project requires, all the work is being presented as a means of justifying contribution to Mu2e. The projects are comprised of a G4Beamline simulation analyzing 8GeV proton beam interaction with a titanium window of Recycler ring extinction rates using three Cherenkov radiation-based detectors and supplemental work for the implementation of a micro–Telecommunications Computing Architecture (MicroTCA) crate to establish a peak finding algorithm to ensure that the out-of-time beam is less than 10^-10 fractional level along with inefficiency analysis on scintillation counters for the Cosmic-Ray Veto (CRV) analysis. Preliminary results have been achieved for extinction rate simulation by achieving coincidence rates for 2/3-fold and 3/3-fold on the detectors in the order of 10^-9 and 10^-10, respectively. Only preliminary results of a triangular counter and four rectangular di-counters for the CRV have been realized but other non-experimental contributions were made to the development of the MicroTCA crate.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Passive Absorbers for Maximizing the Performance of the Mu2e-II Experiment

The Fermilab’s Mu2e experiment is designed to search for Charged Lepton Flavour Violation in direct, neutrinoless conversion of a muon into an electron in the presence of a nuclear electromagnetic field. The quantity, which is observed is the ratio between the rate of the above BSM (Beyond Standard Model) conversion reaction and the rate of muon capture on the nucleus. The measurement precision is expected to reach up to 10 -17 [1]. Mu2e-II is the name for the second phase of the experiment, which is planned to run with the lower energy, higher intensity primary proton beam provided by the PIP-II [2] accelerator, currently under construction. Ionization cooling with a wedge absorber is introduced into Mu2e-II setup to potentially increase the number of low momentum muons reaching the target. A study is made into the position and size of the wedge inside the beamline using G4Beamline simulation framework. Results show an increase up to 12% for muons with momentum P below 30 MeV/c and 7% for muons with P <40 MeV/c when the beam is measured right after the wedge. Further studies are necessary to investigate how this gain can be delivered to the stopping target.

43 PARTICLE ACCELERATORS↗

Reconstruction of Six-Dimensional Phase Space

A phase space is a mathematical representation of all possible physical states of a system. Particle beams at Fermilab exist within a six-dimensional (6D) phase space defined by three positional components, (x, y, z) and three momentum components, (px, py, pz). To reconstruct this space implies taking measurement data from detectors and mapping out particle behavior using computational methods. The beam detectors, however, are only able to detect spatial distribution among the events of the beam, therefore being limited to positional data. Also, due to the vast number of events in a particle beam, it is extremely difficult to analyze and differentiate every single one’s behavior. However, with Machine Learning (ML), which can distinguish between patterns and map out particle behavior more efficiently. We first used the particle beam software, G4beamline, to simulate a 10,000-event muon beam, adjusting parameters such as initial momentum magnitude (p¬0) and virtual detector position. Using ten virtual detectors, we analyzed p0 values such that minimum 9,990 events were analyzed by every detector. We then input the data from these beam simulations to a C++ program, that randomly selects 100 events, and creates a 2D histogram based on spatial distribution, detector position, and event intensity. This process is repeated 100 times to create 100 histograms per p0 value. These images were then input to a modified ResNet18 Convolutional Neural Network (CNN) for training, and to predict p0 from some unseen set of histograms. The model was accurate when trained on momentum increments of 5 MeV/c and provided with denser training samples around highly variable test values. These results displayed machine learning being able to accurately predict p0 from being trained on different particle behaviors.

Shirlee, Jermain [Fermilab]↗