Momentum Acceptance Research Articles

Design of the High Rigidity Spectrometer at FRIB

A High Rigidity Spectrometer (HRS) has been designed for experiments at the Facility for Rare-Isotope Beams (FRIB) at Michigan State University (MSU). The HRS will allow experiments to be performed with the most exotic neutron-rich isotopes at high beam energies (≳100MeV/u). The HRS consists of an analysis beamline called the High-Transmission Beamline (HTBL) and the spectrometer proper called the Spectrometer Section. The maximum magnetic rigidity of the HRS is 8Tm, which corresponds to the rigidities at which rare-isotope beams are optimally produced at FRIB. The resolving power, angular acceptance, and momentum acceptance are set to match the anticipated scientific program. An ion-optical design developed for the HRS is described in detail, along with the specifications of the associated magnet and detector systems.

Superconducting Curved Canted–Cosine–Theta (CCT) for the HIE-ISOLDE Recoil Separator Ring at CERN

The ISOLDE facility at CERN delivers the largest range of low-energy radioactive beams, exploited by several detector systems to investigate nuclear properties from the stable isotopes to the very exotic systems close to the neutron or proton drip lines. These studies can largely benefit from the use of a high-resolution fragment separator. To achieve this goal, an innovative spectrometer based on a compact superconducting (SC) ring, the Isolde Superconducting Recoil Separator (ISRS), is being studied. The ring will operate as an isochronous non-scaling fixed-field alternating-gradient (FFAG) system based on Canted-Cosine-Theta (CCT) magnets. These multifunction magnets have two alternating-gradient quadrupoles nested inside an outer dipole. According to preliminary beam dynamics studies, the dipole will need to generate a maximum field of 2.2 T. A maximum quadrupole gradient of approximately 14 T/m will guarantee orbit stability for heavy ions with a maximum kinetic energy of 10 MeV/u. Fine tuning of the CCT magnets and the FFAG optics will provide very large solid angles > 100 msr and momentum acceptances Δp/p > 20%. In this paper we present, the magnet designs and their optimisation. A cost-effective active stray field superconducting coil shield design has been introduced to be able to remove approximate 4000 kg of iron yoke and the complexity of building a tightly curved yoke.

Coil Error Analysis of a Curved Canted-Cosine-Theta Magnet Applied to a Superconducting Gantry

A lightweight superconducting (SC) gantry with large momentum acceptance is under research at Huazhong University of Science and Technology (HUST). The curved alternating gradient Canted-Cosine-Theta (AG-CCT) magnets are the essential components of this SC gantry. This study presents the findings on coil error analysis of the AG-CCT magnets. Based on multi-line model using Biot-Savart law, a coil model built with coil winding error is developed, and it is adopted to evaluate the influence on the proton beam. The tolerance of coil winding is determined by the study on different error amplitude in the beam envelope. Additionally, the compensation method is also discussed.

Feasibility Study of GaToroid Gantries for Carbon Ions

The use of carbon ions in particle therapy can enhance the treatment quality, introducing higher biological effectiveness compared to photons and protons. Rotating gantries are nowadays used to deliver particle beams from different directions to obtain precise conformal dose mapping at the tumor location. The mechanical stability requirements during the rotation usually require heavy structures. Superconducting magnets can be used to reduce the size and weight of the machine, but complex cryogenics systems are needed to maintain superconductivity during the gantry rotation. The seek for novel gantry configurations for carbon ions is one of the greatest challenges that need to be tackled to widen the accessibility of hadron therapy to a larger number of patients. The concept of GaToroid, a steady-state toroidal gantry implemented with superconducting magnets, can be used to deliver the beam from different directions without the rotation of neither the structure nor the patient. In this work, we present the magnetic design of two GaToroid solutions for Carbon ions, conceived to operate with Nb-Ti cables in the range of 6-7 Tesla. The first solution was designed with 20 pairs of coils, to maximize the flexibility of the treatment, and with an internal diameter of 3.5 meters, to allow a complete couch rotation on the plane. The second option, based on a more conservative design with an internal diameter of 2.3 meters and eight couples of coils, aims to be a compromise between the complexity and cost of the machine, and the flexibility of the treatments. For both configurations, the coil geometry and current distribution were optimized to maximize the carbon ion momentum acceptance for complete coverage of the treatment range without variation of the toroidal magnetic field. The studies here presented can be considered as the first milestone toward the design of toroidal gantries for heavy ions.

Magnetic Alignment and Mechanical Analysis of Superconducting Bending Section for Proton Therapy

The last bending section of a proton therapy beam line may be mounted on a rotating gantry to target the cancerous cells of patients from all possible angles. To gain such capability, it is sensible to use superconducting magnets because of their high energy density providing a large reduction in weight. In the following work, a configuration of combined function magnets for rotating gantries is presented. It includes two conventional electromagnets and three superconducting magnets using Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn conduction-cooled at around 4.2 K. For such assembly, an alignment procedure is proposed to ensure that a large beam momentum acceptance can be achieved. Besides this proposal, additional 3D mechanical Finite Element analyses were conducted to check that the structural support of the most critical superconducting magnets made of Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn wires and their coil thermal shields could handle their weight as well as the momentum due to the rotation.

Design and Optimization of Combined-Function Quadrupole-Sextupole Magnets

A lightweight superconducting (SC) gantry with large momentum acceptance is under development at Huazhong University of Science and Technology (HUST). Three types of combined-function quadrupole-sextupole (QS) magnets are used to suppress the chromatic dispersion for the large momentum acceptance. This paper introduces the design and optimization of the QS magnets with adjustable sextupole to quadrupole (S/Q) field ratio. The pole shaping method and asymmetric excitation method are discussed in detail for the design. Considering the magnetic field quality deterioration caused by the asymmetry of the pole face, the contour of the pole face and the pole end chamfer are optimized to minimize the harmonics field. After several iterations, the maximum harmonics of the QS2 magnet can be limited within 1E-03. In addition, we investigate the magnetic center shift, when the S/Q ratio changes.

Mechanical and Thermal Analysis of an HTS Superconducting Magnet for an Achromatic Gantry for Proton Therapy

The mechanical and thermal analysis of the superconducting magnets, forming an innovative fixed-field bending section for use in a proton therapy gantry, is presented here. The design concept has a large momentum acceptance, covering the full proton energy range of 70 to 220 MeV with fixed field in the superconducting magnets, and uses a simple magnet geometry based on double-pancake high temperature superconductor coils. The main planned steps for the assembly and fabrication of the magnets are discussed. The mechanical analyses of the magnet, with emphasis on the stress state of the conductor during the powering of the magnet, is here described. The thermal analysis investigating the adequacy of the copper structure surrounding the conductor to extract the heat deposited in the conductor during powering is also discussed in detail.

On the Ambiguity of the Definition of Shear and Spin-Hall Contributions to the Λ Polarization in Heavy-Ion Collisions

Recently proposed thermal-shear and spin-Hall contributions to the particle polarization in heavy-ion collisions are discussed. Alternative definitions of the thermal-shear contribution, i.e., those of Becattini–Buzzegoli–Palermo on the one hand and Liu–Yin on the other, are very similar in the midrapidity region while quite different at forward-backward rapidities, which are measured in fixed-target experiments. It is shown that the thermal-shear contribution to the global polarization with momentum averaging extended to all momenta is very different within these alternative definitions. The spin-Hall contribution to the global polarization, defined similarly to the Liu–Yin shear one, is identically zero, if averaging runs over all momenta. Only application of restrictive momentum acceptance and the boost (to Λ rest frame) correction result in nonzero global spin-Hall polarization. If the spin-Hall contribution were defined similarly to Becattini–Buzzegoli–Palermo shear one, the global spin-Hall polarization would be nonzero even without any acceptance and the boost correction.

Requirements and R&D for detectors at the future Electron–Ion Collider

The Electron–Ion Collider’s (EIC’s) ability to collide high-energy electron beams with high-energy ion beams will provide access to those regions in the nucleon and nuclei where their structure is dominated by gluons. Moreover, polarized beams in the EIC will give unique access to the spatial and spin structure of gluons and sea-quarks in the proton and light nuclei.The EIC will be an unprecedented collider with luminosities 2–3 orders of magnitude higher than previous e + p colliders over a very wide range of center-of-mass energies, from 20 to 140 GeV, while accommodating highly polarized electron and nucleon beams. Equally demanding are the requirements for the detector(s) that will be needed to carry out the physics program: hermetic coverage in tracking, calorimetry and particle ID within a wide pseudorapidity range, substantial angular and momentum acceptance in the hadron-going direction, as well as high quality hadronic calorimetry among others.This paper gives a brief overview of the detector requirements, current general-purpose detector concepts, and the ongoing EIC detector R&D efforts.

Beam properties within the momentum acceptance of a clinical gantry beamline for proton therapy.

Energy changes in pencil beam scanning proton therapy can be a limiting factor in delivery time, hence, limiting patient throughput and the effectiveness of motion mitigation techniques requiring fast irradiation. In this study, we investigate the feasibility of performing fast and continuous energy modulation within the momentum acceptance of a clinical beamline for proton therapy. The alternative use of a local beam degrader at the gantry coupling point has been compared with a more common upstream regulation. Focusing on clinically relevant parameters, a complete beam properties characterization has been carried out. In particular, the acquired empirical data allowed to model and parametrize the errors in range and beam current to deliver clinical treatment plans. For both options, the local and upstream degrader, depth-dose curves measured in water for off-momentum beams were only marginally distorted (γ(1%, 1mm)>90%) and the errors in the spot position were within the clinical tolerance, even though increasing at the boundaries of the investigated scan range. The impact on the beam size was limited for the upstream degrader, while dedicated strategies could be required to tackle the beam broadening through the local degrader. Range correction models were investigated for the upstream regulation. The impaired beam transport required a dedicated strategy for fine range control and compensation of beam intensity losses. Our current parameterization based on empirical data allowed energy modulation within acceptance with range errors (median 0.05mm) and transmission (median -14%) compatible with clinical operation and remarkably low average 27ms dead time for small energy changes. The technique, tested for the delivery of a skull glioma treatment, resulted in high gamma pass rates at 1%, 1mm compared to conventional deliveries in experimental measurements with about 45% reduction of the energy switching time when regulation could be performed within acceptance. Fast energy modulation within beamline acceptance has potential for clinical applications and, when realized with an upstream degrader, does not require modification in the beamline hardware, therefore, being potentially applicable in any running facility. Centers with slow energy switching time can particularly profit from such a technique for reducing dead time during treatment delivery.

Proton number cumulants and correlation functions in Au-Au collisions at sNN=7.7 –200 GeV from hydrodynamics

We present a dynamical description of (anti)proton number fluctuations cumulants and correlation functions in central Au-Au collisions at $\sqrt{s_{\rm NN}} = 7.7-200$ GeV by utilizing viscous hydrodynamics simulations. The cumulants of proton and baryon number are calculated in a given momentum acceptance analytically, via an appropriately extended Cooper-Frye procedure describing particlization of an interacting hadron resonance gas. The effects of global baryon number conservation are taken into account using a generalized subensemble acceptance method. The experimental data of the STAR collaboration are consistent at $\sqrt{s_{\rm NN}} \gtrsim 20$ GeV with simultaneous effects of global baryon number conservation and repulsive interactions in baryon sector, the latter being in line with the behavior of baryon number susceptibilities observed in lattice QCD. The data at lower collision energies show possible indications for sizable attractive interactions among baryons. The data also indicate sizable negative two-particle correlations between antiprotons that are not satisfactorily described by baryon conservation and excluded volume effects. We also discuss differences between cumulants and correlation functions (factorial cumulants) of (anti)proton number distribution, proton versus baryon number fluctuations, and effects of hadronic afterburner.

Achieving a realistic design for a superconducting gantry with large momentum acceptance for proton therapy

Purpose:A systematic design procedure for a superconducting gantry is presented. To increase the momentum acceptance of the gantry beamline, alternating-gradient combined-function magnets were used to suppress dispersion. Methods:The main difficulties and challenges occurring in the design procedure, such as the difference between low- and high-order optics and the difference in beam behavior between simplified optics models and realistic magnetic fields, were analyzed. On the basic of these analyses, a step-by-step iterative design approach was proposed. In these steps, a genetic algorithm (GA) was used for multi-objective optimization, and graphics processing unit (GPU) acceleration was adopted for realistic model simulation. Results:The results of the design demonstrated that momentum acceptance of −7%∼5% was achieved for particle tracking in realistic magnetic fields. Conclusions:Using a GA, multi-objective optics fitting up to the fifth order became feasible. The optimization procedure was also more intelligent compared with the traditional one, which depends on experience and manual intervention. The use of GPU acceleration in magnetic field calculation and particle tracking dramatically reduced the overall optimization time. Finally, design optimization for a large momentum acceptance gantry beamline with realistic magnetic fields was achieved.

Longitudinal Beam Dynamics and Coherent Synchrotron Radiation at cSTART

The compact STorage ring for Accelerator Research and Technology (cSTART) project aims to store electron bunches of LWFA-like beams in a very large momentum acceptance storage ring. The project will be realized at the Karlsruhe Institute of Technology (KIT, Germany). Initially, the Ferninfrarot Linac- Und Test-Experiment (FLUTE), a source of ultra-short bunches, will serve as an injector for cSTART to benchmark and emulate laser-wakefield accelerator-like beams. In a second stage a laser-plasma accelerator will be used as an injector, which is being developed as part of the ATHENA project in collaboration with DESY and Helmholtz Institute Jena (HIJ). With an energy of 50 MeV and damping times of several seconds, the electron beam does not reach equilibrium emittance. Furthermore, the critical frequency of synchrotron radiation is 50 THz and in the same order as the bunch spectrum, which implies that the entire bunch radiates coherently. We perform longitudinal particle tracking simulations to investigate the evolution of the bunch length and spectrum as well as the emitted coherent synchrotron radiation. Finally, different options for the RF system are discussed.

Design study of APS-U-type hybrid-MBA lattice for mid-energy DLSR

In recent years, a new generation of storage ring-based light sources, known as diffraction-limited storage rings (DLSRs), whose emittance approaches the diffraction limit for the range of X-ray wavelengths of interest to the scientific community, has garnered significant attention worldwide. Researchers have begun to design and build DLSRs. Among various DLSR proposals, the hybrid multibend achromat (H-MBA) lattice enables sextupole strengths to be maintained at a reasonable level when minimizing the emittance; hence, it has been adopted in many DLSR designs. Based on the H-7BA lattice, the design of the Advanced Photon Source Upgrade Project (APS-U) can effectively reduce emittance by replacing six quadrupoles with anti-bends. Herein, we discuss the feasibility of designing an APS-U-type H-MBA lattice for the Southern Advanced Photon Source, a mid-energy DLSR light source with ultralow emittance that has been proposed to be built adjacent to the China Spallation Neutron Source. Both linear and nonlinear dynamics are optimized to obtain a detailed design of this type of lattice. The emittance is minimized, while a sufficiently large dynamic aperture (DA) and momentum acceptance (MA) are maintained. A design comprising 36 APS-U type H-7BAs, with an energy of 3 GeV and a circumference of 972 m, is achieved. The horizontal natural emittance is 20 pm·rad, with a horizontal DA of 5.8 mm, a vertical DA of 4.5 mm, and an MA of 4%, as well as a long longitudinal damping time of 120 ms. Subsequently, a few modifications are performed based on the APS-U-type lattice to reduce the maximum value of damping time from 120 to 44 ms while maintaining other performance parameters at the same level.

Simulation of the transit-time optical stochastic cooling process in the Cornell Electron Storage Ring

In preparation for a demonstration of optical stochastic cooling in the Cornell Electron Storage Ring (CESR) we have developed a particle tracking simulation to study the relevant beam dynamics. Optical radiation emitted in the pickup undulator gives a momentum kick to that same particle in the kicker undulator. The optics of the electron bypass from pickup to kicker couples betatron amplitude and momentum offset to path length so that the momentum kick reduces emittance and momentum spread. Nearby electrons contribute an incoherent noise. Layout of the bypass line is presented that accommodates optics with a range of transverse and longitudinal cooling parameters. The simulation is used to determine cooling rates and their dependence on bunch and lattice parameters for bypass optics with distinct emittance and momentum acceptance.

Energy spread estimation of radioactive oxygen ion beams using optical imaging

Radioactive ion (RI) beams combined with in-beam positron emission tomography enable accurate in situ beam range verification in heavy ion therapy. However, the energy spread of the radioactive beams generated as secondary beams is wider than that of conventional stable heavy ion beams which causes Bragg peak region and distal falloff region broadening. Therefore, the energy spread of the RI beams should be measured carefully for their quality control. Here, we proposed an optical imaging technique for the energy spread estimation of radioactive oxygen ion beams. A polymethyl methacrylate phantom (10.0 × 10.0 × 9.9 cm3) was irradiated with an 15O beam (mean energy = 247.7 MeV u−1, standard deviation = 6.8 MeV u−1) in the Heavy Ion Medical Accelerator in Chiba. Three different momentum acceptances of 1%, 2% and 4% were used to get energy spreads of 1.9 MeV u−1, 3.4 MeV u−1 and 5.5 MeV u−1, respectively. The in-beam luminescence light and offline beam Cerenkov light images were acquired with an optical system consisting of a lens and a cooled charge-coupled device camera. To estimate the energy spread of the 15O ion beams, we proposed three optical parameters: (1) distal-50% falloff length of the prompt luminescence signals; (2) full-width at half maximum of the Cerenkov light signals in the beam direction; and (3) positional difference between the peaks of the Cerenkov light and the luminescence signals. These parameters estimated the energy spread with the respective mean squared errors of 2.52 × 10−3 MeV u−1, 5.91 × 10−3 MeV u−1, and 0.182 MeV u−1. The distal-50% falloff length of the luminescence signals provided the lowest mean squared error among the optical parameters. From the findings, we concluded optical imaging using luminescence and Cerenkov light signals offers an accurate energy spread estimation of 15O ion beams. In the future, the proposed optical parameters will be used for energy spread estimation of other RI beams as well as stable ion beams.

The potential of Gantry beamline large momentum acceptance for real time tumour tracking in pencil beam scanning proton therapy

Tumour tracking is an advanced radiotherapy technique for precise treatment of tumours subject to organ motion. In this work, we addressed crucial aspects of dose delivery for its realisation in pencil beam scanning proton therapy, exploring the momentum acceptance and global achromaticity of a Gantry beamline to perform continuous energy regulation with a standard upstream degrader. This novel approach is validated on simulation data from three geometric phantoms of increasing complexity and one liver cancer patient using 4D dose calculations. Results from a standard high-to-low beamline ramping scheme were compared to alternative energy meandering schemes including combinations with rescanning. Target coverage and dose conformity were generally well recovered with tumour tracking even though for particularly small targets, large variations are reported for the different approaches. Meandering in energy while rescanning has a positive impact on target homogeneity and similarly, hot spots outside the targets are mitigated with a relatively fast convergence rate for most tracking scenarios, halving the volume of hot spots after as little as 3 rescans. This work investigates the yet unexplored potential of having a large momentum acceptance in medical beam line, and provides an alternative to take tumour tracking with particle therapy closer to clinical translation.

Influence of momentum acceptance on range monitoring of 11C and 15O ion beams using in-beam PET

In heavy-ion therapy, the stopping position of primary ions in tumours needs to be monitored for effective treatment and to prevent overdose exposure to normal tissues. Positron-emitting ion beams, such as 11C and 15O, have been suggested for range verification in heavy-ion therapy using in-beam positron emission tomography (PET) imaging, which offers the capability of visualizing the ion stopping position with a high signal-to-noise ratio. We have previously demonstrated the feasibility of in-beam PET imaging for the range verification of 11C and 15O ion beams and observed a slight shift between the beam stopping position and the dose peak position in simulations, depending on the initial beam energy spread. In this study, we focused on the experimental confirmation of the shift between the Bragg peak position and the position of the maximum detected positron-emitting fragments via a PET system for positron-emitting ion beams of 11C (210 MeV u−1) and 15O (312 MeV u−1) with momentum acceptances of 5% and 0.5%. For this purpose, we measured the depth doses and performed in-beam PET imaging using a polymethyl methacrylate (PMMA) phantom for both beams with different momentum acceptances. The shifts between the Bragg peak position and the PET peak position in an irradiated PMMA phantom for the 15O ion beams were 1.8 mm and 0.3 mm for momentum acceptances of 5% and 0.5%, respectively. The shifts between the positions of two peaks for the 11C ion beam were 2.1 mm and 0.1 mm for momentum acceptances of 5% and 0.5%, respectively. We observed larger shifts between the Bragg peak and the PET peak positions for a momentum acceptance of 5% for both beams, which is consistent with the simulation results reported in our previous study. The biological doses were also estimated from the calculated relative biological effectiveness (RBE) values using a modified microdosimetric kinetic model (mMKM) and Monte Carlo simulation. Beams with a momentum acceptance of 5% should be used with caution for therapeutic applications to avoid extra dose to normal tissues beyond the tumour when the dose distal fall-off is located beyond the treatment volume.

Baseline study for net-proton number fluctuations at top energies available at the BNL Relativistic Heavy Ion Collider and at the CERN Large Hadron Collider with the Angantyr model

The multiplicity percentile dependence of cumulants, of net-proton number distributions in Au$-$Au collisions at $\sqrt{s_{NN}} = $ 200 GeV and Pb$-$Pb collisions at $\sqrt{s_{NN}} = $ 2.76 TeV has been investigated using the Angantyr model (the heavy-ion extension of the \textsc{Pythia 8} model). The effects of finite transverse momentum ($p_{\mathrm T}$) and pseudorapidity ($\eta$) acceptance on the net-proton cumulants have also been studied. Furthermore, the effects of the hydrodynamic expansion and feed down from weak decays were explored. It was found that radial flow has substantial impact on the cumulants and their ratios, while weak decays have a finite but relatively smaller effect. The obtained values of cumulants and their ratios with the Angantyr model, where the formation of thermalized medium is not assumed can serve as a baseline for future measurements.

Design and optimization of beam optics for a superconducting gantry applied to proton therapy

PurposeProton therapy (PT) is a precise and effective radiotherapy method for tumors. To reduce the weight and footprint of normal conducting gantries applied to PT, a lightweight superconducting (SC) gantry with large momentum acceptance is studied at Huazhong University of Science and Technology. MethodsTo limit the frequency of field changing in SC magnets, a local-achromaticity beamline is designed with large momentum acceptance. Based on the analysis of high order aberrations, the lattice of the gantry beamline is composed of two symmetric bending sections to limit high-order aberrations, and sextupole fields are superimposed to further eliminate dispersion up to second order. ResultsWe presented a second order beam optics design of a SC gantry. The optics fitting is completed with COSY Infinity and the result of particle tracking shows a momentum acceptance of ±8%. Alternating gradient canted-cosine-theta (CCT) magnets are applied to implement combined functions of beam bending and focusing. Some methods are proposed to minimize the field distortion in curved CCT magnets. ConclusionsThe beam optics with high order considerations of a lightweight SC gantry with large momentum acceptance is presented.