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Transformation of Spinors in Accelerators and Beam Transfer Lines

The stable spin direction and the spin tune are two important concepts used when polarized beams are transferred along beam lines or circulating in an accelerator. One of the methods to calculate the stable spin direction and the spin tune of the reference particle of a polarized beam bunch is by integrating simultaneously the Lorentz Force $\vec{F}$ = q($\vec{E}$ +$\vec{v}$ x $\vec{B}$) and the BMT equation of the reference particle as it is transported by the magnets of a beam line or accelerator. A modified version of the Raytrace code was used to integrate the Lorentz equation and the BMT equation. Using the spin motion which is governed by the BMT equation one can compute both, the stable spin direction of the reference particle at any point along the reference orbit of an accelerator or a beam line, and the spin tune of the closed orbit in an accelerator. The simultaneous integration of the Lorentz force and of the BMT equation is the most accurate method to calculate the trajectory and the spin motion of a charged particle moving in an electromagnetic field, however this method requires the accurate description of the electromagnetic fields of the elements in which the charged particles are moving. An alternative method of calculating the stable spin direction and the spin tune of spin ½ charged particles along the reference trajectory of a beam line or an accelerator is the transformation of the spinor which is the wavefunction of spin ½ particles. This method requires the knowledge of the stable spin direction of each element of the beam line or the accelerator. This technical note describes the “spinor-method” to calculate the stable-spin- direction and the spin-tune of a spin ½ particle moving along the reference trajectory of a beam line or an accelerator.

43 PARTICLE ACCELERATORS↗

Beam loss mechanisms in the PIP-II linac and beam transfer line at Fermilab

Beam loss in high-intensity H- linacs, such as the PIP-II linac at Fermilab, is a critical challenge that requires comprehensive study and understanding to ensure efficient and safe operation. This study explores the various beam loss mechanisms encountered in the PIP-II linac and its beam transfer line, drawing parallels from other high-intensity H- linacs. Key loss mechanisms include residual gas stripping, where H- ions interact with residual gas molecules leading to electron detachment; field stripping, caused by the interaction of H- ions with magnetic fields; and intra-beam stripping, resulting from interactions within the beam itself. Beam halo formation, particularly due to Twiss function mismatch, is another significant source of beam loss, which can be exacerbated by Landau damping mechanisms. Adhering to the 1 W/m loss criterion is essential to maintain hands-on maintenance capability and ensure the longevity of the accelerator components. By understanding these mechanisms and implementing targeted mitigation strategies, the PIP-II linac can achieve its design goals while maintaining safe and efficient operations.

43 PARTICLE ACCELERATORS↗

The KATRIN superconducting magnets: Overview and first performance results

The KATRIN experiment aims for the determination of the effective electron anti-neutrino mass from the tritium beta-decay with an unprecedented sub-eV sensitivity. The strong magnetic fields, designed for up to 6 T, adiabatically guide β-electrons from the source to the detector within a magnetic flux of 191 Tcm 2 . A chain of ten single solenoid magnets and two larger superconducting magnet systems have been designed, constructed, and installed in the 70-m-long KATRIN beam line. The beam diameter for the magnetic flux varies from 0.064 m to 9 m, depending on the magnetic flux density along the beam line. Two transport and tritium pumping sections are assembled with chicane beam tubes to avoid direct "line-of-sight" molecular beaming effect of gaseous tritium molecules into the next beam sections. The sophisticated beam alignment has been successfully cross-checked by electron sources. In addition, magnet safety systems were developed to protect the complex magnet systems against coil quenches or other system failures. The main functionality of the magnet safety systems has been successfully tested with the two large magnet systems. The complete chain of the magnets was operated for several weeks at 70% of the design fields for the first test measurements with radioactive krypton gas. The stability of the magnetic fields of the source magnets has been shown to be better than 0.01% per month at 70% of the design fields. This paper gives an overview of the KATRIN superconducting magnets and reports on the first performance results of the magnets.

47 OTHER INSTRUMENTATION↗

Design and Simulation of the nuSTORM Pion Beamline

The nuSTORM (neutrinos from STORed Muons) proposal presents a detailed design for a neutrino facility based on a muon storage ring, with muon decay in the production straight section of the ring providing well defined neutrino beams. The facility includes a primary high-energy proton beam line, a target station with pion production and collection, and a pion beamline for pion transportation and injection into a muon decay ring. The nuSTORM design uses “stochastic injection”, in which pions are directed by a chicane, referred to as the Orbit Combination Section (OCS), into the production straight section of the storage ring. Pions that decay within that straight section provide muons within the circulating acceptance of the ring. Furthermore, the design enables injection without kickers or a separate pion decay transport line. The beam line that the pions traverse before being extracted from the decay ring is referred to as the pion beamline. Our paper describes the design and simulation of the pion beamline, and includes full beam dynamics simulations of the system.

43 PARTICLE ACCELERATORS↗

Investigation of Beam Emittance and Beam Transport Line Optics on Polarization

Effects of beam emittance, energy spread, optical parameters and magnet misalignment on beam polarization through particle transport systems are investigated. Particular emphasis will be placed on the beam lines being used at Fermilab for the development of the muon beam for the Muon g-2 experiment, including comparisons with the natural polarization resulting from pion decay, and comments on the development of systematic correlations among phase space variables.

43 PARTICLE ACCELERATORS↗

Lattice Design of the Beam Transfer Line (BTL) from PIP-II LINAC to the Booster at Fermilab

PIP-II beam transfer line (BTL) to transport the beam from PIP-II Linac to the Booster ring at Fermilab. The latest design eliminates rolling the dipoles in the beam line to cross over the Tevatron tunnel. Also re-designed is the lattice in the region of the Booster Injection to meet the request of the civil construction needs and accommodate the constrains of the Booster injection request. A beam line to the beam absorber (BAL) is designed based on the request from the results of Mars simulations and ANASYS calculation of the absorber. Simulations with dipole and quadrupole field errors for the Beam Transport Line (BTL) to the Booster, which provides the specifications for all the magnets and Power supplies, will be presented too.

43 PARTICLE ACCELERATORS↗

A transverse emittance and acceptance measurement system in a low-energy beam transport line

A transverse beam emittance and acceptance measurement system has been developed to visualize the relationship between the injected beam emittance and the acceptance of a cyclotron. The system is composed of a steering magnet, two pairs of slits to limit the horizontal and vertical phase-space, a beam intensity detector just behind the slits for the emittance measurement, and a beam intensity detector in the cyclotron for the acceptance measurement. The emittance is obtained by scanning the slits and measuring the beam intensity distribution. The acceptance is obtained by measuring the distribution of relative beam transmission by injecting small emittance beams at various positions in a transverse phase-space using the slits. In the acceptance measurement, the beam from an ion source is deflected to the defined region by the slits using the steering magnet so that measurable acceptance area covers a region outside the injection beam emittance. Measurement tests were carried out under the condition of accelerating a beam of {sup 16}O{sup 6+} from 50.2 keV to 160 MeV. The emittance of the injected beam and the acceptance for accelerating and transporting the beam to the entrance of the extraction deflector were successfully measured. The relationship between the emittance and acceptance is visualized by displaying the results in the same phase-plane.

43 PARTICLE ACCELERATORS↗

An Improved Beam Position Monitor for Scorpius and the DARHT Multi-Pulse Test Line

Beam position monitors (BPMs) provide time-resolved measurements of the current and centroid position of high-current electron beams in linear induction accelerators (LIAs). A frequently used BPM detector is the B-dot loop, which generates a signal from the EMF generated by the time varying magnetic flux through the loop. We have developed a second generation BPM that avoids previously observed diffusion effects in earlier stainless steel through the use of exceptionally high conductivity copper alloy for its construction.

43 PARTICLE ACCELERATORS↗

Experimental depth dose curves of a 67.5 MeV proton beam for benchmarking and validation of Monte Carlo simulation

Purpose: To measure depth dose curves for a 67.5 ± 0.1 MeV proton beam for benchmarking and validation of Monte Carlo simulation. Methods: Depth dose curves were measured in 2 beam lines. Protons in the raw beam line traversed a Ta scattering foil, 0.1016 or 0.381 mm thick, a secondary emission monitor comprised of thin Al foils, and a thin Kapton exit window. The beam energy and peak width and the composition and density of material traversed by the beam were known with sufficient accuracy to permit benchmark quality measurements. Diodes for charged particle dosimetry from two different manufacturers were used to scan the depth dose curves with 0.003 mm depth reproducibility in a water tank placed 300 mm from the exit window. Depth in water was determined with an uncertainty of 0.15 mm, including the uncertainty in the water equivalent depth of the sensitive volume of the detector. Parallel-plate chambers were used to verify the accuracy of the shape of the Bragg peak and the peak-to-plateau ratio measured with the diodes. The uncertainty in the measured peak-to-plateau ratio was 4%. Depth dose curves were also measured with a diode for a Bragg curve and treatment beam spread out Bragg peak (SOBP) on the beam line used for eye treatment. The measurements were compared to Monte Carlo simulation done with GEANT4 using TOPAS. Results: The 80% dose at the distal side of the Bragg peak for the thinner foil was at 37.47 ± 0.11 mm (average of measurement with diodes from two different manufacturers), compared to the simulated value of 37.20 mm. The 80% dose for the thicker foil was at 35.08 ± 0.15 mm, compared to the simulated value of 34.90 mm. The measured peak-to-plateau ratio was within one standard deviation experimental uncertainty of the simulated result for the thinnest foil and two standard deviations for the thickest foil. It was necessary to include the collimation in the simulation, which had a more pronounced effect on the peak-to-plateau ratio for the thicker foil. The treatment beam, being unfocussed, had a broader Bragg peak than the raw beam. A 1.3 ± 0.1 MeV FWHM peak width in the energy distribution was used in the simulation to match the Bragg peak width. An additional 1.3–2.24 mm of water in the water column was required over the nominal values to match the measured depth penetration. Conclusions: The proton Bragg curve measured for the 0.1016 mm thick Ta foil provided the most accurate benchmark, having a low contribution of proton scatter from upstream of the water tank. The accuracy was 0.15% in measured beam energy and 0.3% in measured depth penetration at the Bragg peak. The depth of the distal edge of the Bragg peak in the simulation fell short of measurement, suggesting that the mean ionization potential of water is 2–5 eV higher than the 78 eV used in the stopping power calculation for the simulation. The eye treatment beam line depth dose curves provide validation of Monte Carlo simulation of a Bragg curve and SOBP with 4%/2 mm accuracy.

60 APPLIED LIFE SCIENCES↗

Design and simulation of the nuSTORM facility

This thesis provides a full design and simulation of the nuSTORM beam line facility including the pion beam line , the pion and muon orbit combination section, and the muon decay ring. The study also includes the development of numerical optimization methods and their application to the design. At nuSTORM, one proton batch from the Main Injector (MI) is extracted and transported to the target station to bombard a solid target. A magnetic horn is used as the collection device for the secondary particles such as pions and kaons. A pion beam line is designed to transport the secondary particles downstream to the muon decay ring. In order to avoid the use of a fast kicker with a large aperture for the injection, an Orbit Combination Section (OCS) was designed to combine the reference pion orbit with the circulating muon orbit. This ful lls the stochastic injection scheme proposed in the 1980s. It is shown through the simulation that the pion beam line is able to deliver 0.011 muons per proton on target within the acceptance of the ring. In order to improve the circulating muon ux, an optimization of the magnetic collection horn was studied. A Multi-Objective Genetic Algorithm (MOGA), that was modi ed to integrate Message Passing Interface (MPI) in the process, is applied to the optimization. The number of muons within the ring acceptance from the pion decay is estimated by the pions after the collection horn. This new method was proposed to lower the requirement on the computing resources for the optimization. The study gives a new and better target and horn con guration after a full investigation of the system. The nuSTORM ring is examined with two optics designs. With di erent features, the two designs are optimized via correcting the nonlinearities with sextupolar eld distribution in the ring. A modi ed MPI-based Simulated Annealing (SA) algorithm was applied to obtain the optimal ring acceptance. The comparison with the GA shows good agreements on the achieved optimal ring acceptance. The pion and muon beams at nuSTORM were simulated and yield avor-pure and precisely measurable neutrino beams, which can be used to provide a de nite statement about the existence of a sterile neutrino.

97 MATHEMATICS AND COMPUTING↗

SU-E-T-130: Are Proton Gantries Needed? An Analysis of 4332 Patient Proton Gantry Treatment Plans From the Past 10 Years

Purpose: To ascertain the necessity of a proton gantry, as compared to the feasibility of using a horizontal fixed proton beam-line for treatment with advanced technology. Methods: To calculate the percentage of patients that can be treated with a horizontal fixed beam-line instead of a gantry, we analyze the distributions of beam orientations of our proton gantry patients treated over the past 10 years. We identify three horizontal fixed beam geometries (FIXED, BEND and MOVE) with the patient in lying and/or sitting positions. The FIXED geometry includes only table/chair rotations and translations. In BEND, the beam can be bent up/down for up to 20 degrees. MOVE allows for patient head/body angle adjustment. Based on the analysis, we select eight patients whose plan involves beams which are still challenging to achieve with a horizontal fixed beam. These beams are removed in the pencil beam scanning (PBS) plan optimized for the fixed beam-line (PBS-fix). We generate non-coplanar PBS-gantry plans for comparison, and perform a robustness analysis. Results: The percentage of patients with head-and-neck/brain tumors that can be treated with horizontal fixed beam is 44% in FIXED, 70% in 20-degrees BEND, and 100% in 90-degrees MOVE. For torso regions, 99% of the patients can be treated in 20-degree BEND. The target coverage is more homogeneous with PBS-fix plans compared to the clinical scattering treatment plans. The PBS-fix plans reduce the mean dose to organs-at-risk by a factor of 1.1–28.5. PBS-gantry plans are as good as PBS-fix plans, sometimes marginally better. Conclusion: The majority of the beam orientations can be realized with a horizontal fixed beam-line. Challenging non-coplanar beams can be eliminated with PBS delivery. Clinical implementation of the proposed fixed beam-line requires use of robotic patient positioning, further developments in immobilization, and image guidance. However, our results suggest that fixed beam-lines can be as effective as gantries.

60 APPLIED LIFE SCIENCES↗

Phase Trombone Design in the Beam Transfer line for the Project PIP-II at Fermilab

PIP-II beam transfer line (BTL) to transport the beam from PIP-II Linac to the Booster ring at Fermilab. One crucial aspect of the BTL design involved the implementation of collimators. These collimators play a vital role in removing large amplitude particles from the beamline that might otherwise miss the horizontal and vertical edge of the foil at the point of the Booster injection. To ensure the effectiveness of these collimators, simulation was conducted to determine their optical placement within the BTL. The simulation revealed that the precise control of accumulated phase advances between the collimators and the foil was crucial. To achieve this control, a phase trombone is needed within the BTL. The phase trombone serves as an adjustment mechanism, allowing for the fine-tuning of the phase advance between the collimators and the foil, thus optimizing the performance of the collimation process. This paper discusses and presents the details of the design and implementation of the phase trombone within the PIP-II BTL.

43 PARTICLE ACCELERATORS↗

Effect of subdominant species on the evolution of intense primary beam in a low energy beam transport line

The dynamics of space-charge-dominated multispecies beam with different distributions has been studied in a solenoid based low energy beam transport line using a particle-in-cell simulation method. Results are presented in wide parameter regimes covering emittance dominated as well as space charge dominated multispecies beams consisting of p, H{sub 2}{sup +}, and H{sub 3}{sup +} beams. Simulation shows the formation of hollow distribution of H{sub 2}{sup +} and H{sub 3}{sup +} beams around the desired proton beam and separation is more distinct as the fraction of proton is increased. The hollow formation is almost independent of combination of H{sub 2}{sup +} and H{sub 3}{sup +} beams, once the fraction of proton beam is fixed. The emittance growth of proton is found to increase sharply in the space-charge-dominated regime and is more in the cases where proton fraction is low.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

TH-A-19A-10: Fast Four Dimensional Monte Carlo Dose Computations for Proton Therapy of Lung Cancer

Purpose: To develop and validate a fast and accurate four dimensional (4D) Monte Carlo (MC) dose computation system for proton therapy of lung cancer and other thoracic and abdominal malignancies in which the delivered dose distributions can be affected by respiratory motion of the patient. Methods: A 4D computer tomography (CT) scan for a lung cancer patient treated with protons in our clinic was used to create a time dependent patient model using our in-house, MCNPX-based Monte Carlo system (“MC{sup 2}”). The beam line configurations for two passively scattered proton beams used in the actual treatment were extracted from the clinical treatment plan and a set of input files was created automatically using MC{sup 2}. A full MC simulation of the beam line was computed using MCNPX and a set of phase space files for each beam was collected at the distal surface of the range compensator. The particles from these phase space files were transported through the 10 voxelized patient models corresponding to the 10 phases of the breathing cycle in the 4DCT, using MCNPX and an accelerated (fast) MC code called “FDC”, developed by us and which is based on the track repeating algorithm. The accuracy of the fast algorithm was assessed by comparing the two time dependent dose distributions. Results: The error of less than 1% in 100% of the voxels in all phases of the breathing cycle was achieved using this method with a speedup of more than 1000 times. Conclusion: The proposed method, which uses full MC to simulate the beam line and the accelerated MC code FDC for the time consuming particle transport inside the complex, time dependent, geometry of the patient shows excellent accuracy together with an extraordinary speed.

60 APPLIED LIFE SCIENCES↗

High intensity proton injector for facility of antiproton and ion research

The high current ion source with the low energy beam transport (LEBT) will serve as injector into the proton LINAC to provide primary proton beam for the production of antiprotons. The pulsed ion source developed and built in CEA/Saclay operates with a frequency of 2.45 GHz based on ECR plasma production with two coils with 87.5 mT magnetic field necessary for the electron cyclotron resonance. The compact LEBT consists of two solenoids with a maximum magnetic field of 500 mT including two integrated magnetic steerers to adjust the horizontal and vertical beam positions. The total length of the compact LEBT is 2.3 m and was made as short as possible to reduced emittance growth along the beam line. To measure ion beam intensity behind the pentode extraction system, between solenoids and at the end of the beam line, two current transformers and a Faraday cup are installed. To get information about the beam quality and position, the diagnostic chamber with different equipment will be installed between the two solenoids. This article reports the current status of the proton injector for the facility of antiproton and ion research.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Space-charge compensation measurements in electron cyclotron resonance ion source low energy beam transport lines with a retarding field analyzer

In this paper we describe the first systematic measurement of beam neutralization (space charge compensation) in the ECR low energy transport line with a retarding field analyzer, which can be used to measure the potential of the beam. Expected trends for the space charge compensation levels such as increase with residual gas pressure, beam current, and beam density could be observed. However, the overall levels of neutralization are consistently low (<60%). The results and the processes involved for neutralizing ion beams are discussed for conditions typical for ECR injector beam lines. The results are compared to a simple theoretical beam plasma model as well as simulations.

43 PARTICLE ACCELERATORS↗

A RHIC-style IPM in the Brookhaven AGS

Beam profiles in the two storage rings of the Relativistic Heavy-Ion Collider (RHIC) at Brookhaven National Lab (BNL) are measured with ionization profile monitors (IPMs). Each ring has a vertical and horizontal detector. An IPM measures the distribution of electrons produced in the beam line by beam ionization of background gas. These detectors have been developed at BNL in a program that began in 1996. The current detectors are a design that was based on a prototype built in 2007 and used in RHIC from 2007 to 2012. During the 2012 shutdown we refurbished this prototype and installed it into the Alternating-Gradient Synchrotron (AGS). This paper describes the new AGS IPM and shows data from the detector commissioning.

43 PARTICLE ACCELERATORS↗

The FFAG return loop for the CBETA Energy Recovery Linac

The CBETA energy recovery linac uses a single xed eld alternating gradient (FFAG) beam line to return the beam for electron beams with four energies, ranging from 42 MeV to 150 MeV. To keep the beam line compact, the ends of the return line have a small radius of curvature, but the central part of the return line is straight. These are connected by transition lines that adiabatically change from one to the other. We rst describe the design or the arc cell. We then describe how a straight cell is created to be a good match to this arc cell. We then describe the design of the transition line between them. The design process makes use of eld maps for the desired magnets. Because we switch magnet types as we move from the arc, through the transition, and into the straight, there are discrete jumps in the elds that degrade the adiabaticity of the transition, and we describe corrections to manage that.

43 PARTICLE ACCELERATORS↗