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Physical review accelerators and beams 24(4), 040101 (2021). doi:10.1103/PhysRevAccelBeams.24.040101, Published by American Physical Society, College Park, MD

High-frequency linear accelerators are very suitable for carbon ion therapy, thanks to the reduced operational costs and the high beam quality with respect to synchrotrons, which are presently the only available technology for this application. In the framework of the development of a new linac for carbon ion therapy, this article describes the design of a compact 750 MHz Radio Frequency Quadrupole (RFQ) with trapezoidal vanes. A new semi-analytic approach to design the trapezoidal-vane RFQ is introduced together with the relevant beam dynamics properties. The RFQ is split into two decoupled rf cavities, both of which make use of a novel dipole detuning technique by means of length adjustment. The splitting is described both from the rf and the beam dynamics point of view. The paper concludes with the rf design of the full structure, including maximum surface field and thermal studies., Comment: Revised version published in Physical Review Accelerators and Beams on 31 December 2020

Equipartitioning is an efficient beam-dynamics design scheme also for radio frequency quadrupole (RFQ). To realize an equipartitioned RFQ, it is essential to reproduce the nonuniform intervane voltage profile required from the beam dynamics. We developed a cavity design and tuning method to this end. The dimensions of a voltage-ramped four-vane cavity were determined by a three-dimensional rf simulation. To produce the desired vane voltage profile, the longitudinal variation of the cross-sectional shape was adjusted using the least-squares method based on the simulated responses of the vane-base width to the quadrupole-mode field. In the low-level tuning, slug-tuner positions were determined based also on the least-squares solutions obtained from the simulated tuner responses to the field profile. Finally, the deviation of the quadrupole-mode field was within 1.5% from the design profile, and the mixed dipole modes were 1% of the quadrupole-mode field after only two iterations of tuner adjustment; they are sufficiently smaller than the requirement of 2%.

Efficient tuning of complex accelerator chains requires automated procedures, themselves reliant upon beam physical models. The Isotope Separator and ACcelerator (ISAC) facility at TRIUMF requires frequent changes of beam species (isotope), mass to charge ratio and beam energy tailored to experiment requirements, which demands rapid beam tuning. In addition, emergent effects such as long term changes of energy or energy spread require beam optimization that must be based on a complete model of the accelerator. Using an envelope code to build an end-to-end simulation of the accelerator facility for operational purposes reduces computing times by 3 or 4 orders of magnitude, when compared to particle tracking codes, so that the requisite simulations may be carried out in real time, by polling control system data. Herein described is the second order Hamiltonian for an radio frequency quadrupole (RFQ), presented within the framework of the envelope code transoptr. To benchmark the transoptr model, envelope simulations of the TRIUMF-ISAC RFQ have been performed and compared with the multiparticle code parmteq.

The proton-induced x-ray emission (PIXE) is the most commonly used ion beam analysis technique. It allows for nondestructive quantitative elemental characterization and is used in a variety of fields, particularly for the diagnosis of cultural heritage artwork. To provide mobile access to PIXE, a compact transportable radio frequency quadrupole (RFQ) linac has been designed and is being built at CERN. The PIXE RFQ has a length of only one meter and accelerates a proton beam to an energy of 2 MeV. This paper covers various rf design studies for the RFQ operating at 750 MHz. We show simulation results regarding cavity, equipment, and coupler geometry. Thermomechanical and beam dynamics studies are presented as well. The paper concludes with a conceptual study on dipole mode detuning by means of length adjustment.

This paper describes the physical design, rf measurement, and tuning result of a 325 MHz four-vane radio frequency quadrupole (RFQ) with a ramped inter-vane voltage. The 3-meter-long RFQ will accelerate the negative hydrogen ion beam from 50 keV to 3 MeV with a peak current of 5 mA, a pulse width of $10--40\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$, and a maximum repetition rate of 0.5 Hz. During tuning we reveal that the coupling loop of the coaxial coupler adopted for this RFQ enhances the interference between the dipole field distribution and the coupling coefficient. Therefore, an iteration method is adopted to simultaneously achieve the desired field distribution and coupling coefficient. After tuning, the relative error between the measured field distribution and the designed curve for the operating quadrupole mode is within $\ifmmode\pm\else\textpm\fi{}2.7%$, and the dipole components are about $\ifmmode\pm\else\textpm\fi{}1.9%$ of the quadrupole mode. The measured coupling coefficient of the rf power coupler equals 1.03, with the desired value of 1.04.

Trapezoidal modulation of quadrupole electrodes offers additional benefits to the concept of a radio-frequency quadrupole (RFQ). Because of the significant increase of the effective shunt impedance, RFQs with trapezoidal modulation have a reduced interelectrode voltage or resonator length as compared to conventional RFQs with sinusoidal modulation. This feature is especially valuable for RFQs operating in cw mode, since it reduces the required rf power. We develop a detailed procedure for the design of RFQ electrodes with trapezoidal modulation. With our design procedure and by properly choosing the trapezoidal cell parameters, we can easily control the peak surface fields in the RFQ to the same level as for sinusoidal cell modulation. The procedure is applied to the design of the electrodes for the ReA3 RFQ at Michigan State University.

A deuteron radio-frequency quadrupole (RFQ) is being built by the RFQ group at Peking University. It is a very compact high-current RFQ, operating at 162.5 MHz in continuous-wave mode. By optimizing the beam dynamics design, our simulations reached 98% transmission efficiency for acceleration of the 50-mA deuteron beam from 50 keV to 1 MeV, with an intervane voltage of 60 kV and a length of 1.809 m. This RFQ adopts a window-type structure, with low power consumption and sufficient mode separation, with no stabilizing rods required. Its magnetic coupling windows have been optimized by both electromagnetic simulation and the construction of an equivalent circuit model. The empirical equation based on the circuit model provides a new way to evaluate the effect of the window size on the frequency. In addition, an aluminum model of the full-length RFQ has been built and tested, and the results show good agreement with the simulations. During the tuning process, the magnetic coupling effect between quadrants was found to be unique to the window-type RFQ. We also propose a method to estimate the effects of different degrees of electric field unflatness on the beam transmission. For the cooling system design, the results of thermostructural analysis, verified by comparing results from ansys and cst, show that the special cooling channels provide a high cooling efficiency around the magnetic coupling windows. The maximal deformation of the structure was approximately 75 μm. The beam-loading effect caused by a high current, and the coupler design, are also discussed.

The SHIRaC prototype is a recently developed radio-frequency quadrupole (RFQ) beam cooler with an improved optics design to deliver the required beam quality to a high resolution separator (HRS). For an isobaric separation of isotopes, the HRS demands beams with emittance not exceeding $3\ensuremath{\pi}\text{ }\text{ }\mathrm{mm}\text{ }\mathrm{mrad}$ and longitudinal energy spread $\ensuremath{\sim}1\text{ }\text{ }\mathrm{eV}$. Simulation studies showed a significant contribution of the buffer gas diffusion, space charge effect and mainly the rf fringe field to degrade the achieved beam quality at the RFQ exit. A miniature rf quadrupole ($\ensuremath{\mu}\mathrm{RFQ}$) has been implemented at that exit to remove the degrading effects and provide beams with 1 eV of energy spread and around $1.75\ensuremath{\pi}\text{ }\text{ }\mathrm{mm}\text{ }\mathrm{mrad}$ of emittance for 4 Pa gas pressure. This solution enables also to transmit more than 60% of the incoming ions for currents up to $1\text{ }\text{ }\ensuremath{\mu}\mathrm{A}$. Detailed studies of this development are presented and discussed in this paper. Transport of beams from SHIRaC towards the HRS has been done with an electrostatic quadrupole triplet. Simulations and first experimental tests showed that more than 95% of ions can reach the HRS. Because SPIRAL-2 beams are of high current and very radioactive, the buffer gas will be highly contaminated. Safe maintenance of the SHIRaC beam line needs exceptional treatment of radioactive contaminants. For that, special vinyl sleep should be mounted on elements to be maintained. A detailed maintenance process will be presented.

The new design for a spatially periodical rf quadrupole focusing linac is proposed. It consists of accelerating gaps formed between conventional cylindrical drift tubes, between drift tubes and rf quadrupoles with nonzero axial potential, and inside these rf quadrupoles, formed in the same way as in a conventional radio-frequency quadrupole (RFQ) linac with modulated electrodes. Such a combination provides both higher energy gain rate than conventional RFQ and stability of transverse motion for ion beams. The structure can be designed using various combinations of quadrupoles and drift tubes. Some options are considered in the paper using the smooth approximation method and computer simulation of beam dynamics. Transverse stability of particles has been studied. The proposed structure can provide suppression of rf defocusing effects on transverse beam dynamics. Some limitations of the spatially periodic rf quadrupole structure are mentioned.

The 10 MeV accelerator-driven subcritical system (ADS) Injector I test stand at Institute of High Energy Physics (IHEP) is a testing facility dedicated to demonstrate one of the two injector design schemes [Injector Scheme-I, which works at 325 MHz], for the ADS project in China. The injector is composed of two parts, the linac part and the beam dump line. The former is designed on the basis of 325 MHz four-vane type copper structure radio frequency quadrupole and superconducting (SC) spoke cavities with beta = 0.12. The latter is designed to transport the beamcoming out of the SC section of the linac to the beam dump, where the beam transverse profile is fairly enlarged and unformed to simplify the beam target design. The SC section consists of two cryomodules with 14 beta = 0.12 Spoke cavities, 14 solenoid and 14 BPMs in total. The first challenge in the physics design comes from the necessary space required for the cryomodule separation where the periodical lattice is destroyed at a relatively lower energy of similar to 5 MeV. Another challenge is the beam dump line design, as it will be the first beam dump line being built by using a step field magnet for the transverse beam expansion and uniformity in the world. This paper gives an overview of the physics design study together with the design principles and machine construction considerations. The results of an optimized design, fabrication status and end to end simulations including machine errors are presented.

We have developed a new design for a 176 MHz cw radio-frequency quadrupole (RFQ) for the SARAF upgrade project. At this frequency, the proposed design is a conventional four-vane structure. The main design goals are to provide the highest possible shunt impedance while limiting the required rf power to about 120 kW for reliable cw operation, and the length to about 4 meters. If built as designed, the proposed RFQ will be the first four-vane cw RFQ built as a single cavity (no resonant coupling required) that does not require π -mode stabilizing loops or dipole rods. For this, we rely on very detailed 3D simulations of all aspects of the structure and the level of machining precision achieved on the recently developed ATLAS upgrade RFQ. A full 3D model of the structure including vane modulation was developed. The design was optimized using electromagnetic and multiphysics simulations. Following the choice of the vane type and geometry, the vane undercuts were optimized to produce a flat field along the structure. The final design has good mode separation and should not need dipole rods if built as designed, but their effect was studied in the case of manufacturing errors. The tuners were also designed and optimized to tune the main mode without affecting the field flatness. Following the electromagnetic (EM) design optimization, a multiphysics engineering analysis of the structure was performed. The multiphysics analysis is a coupled electromagnetic, thermal and mechanical analysis. The cooling channels, including their paths and sizes, were optimized based on the limiting temperature and deformation requirements. The frequency sensitivity to the RFQ body and vane cooling water temperatures was carefully studied in order to use it for frequency fine-tuning. Finally, an inductive rf power coupler design based on the ATLAS RFQ coupler was developed and simulated. The EM design optimization was performed using cst Microwave Studio and the results were verified using both hfss and ansys . The engineering analysis was performed using hfss and ansys and most of the results were verified using the newly developed cst Multiphysics package.

After 30 years of operation, the Cockcroft-Walton based injector at the Fermi National Accelerator Laboratory has been replaced by a new beam line including a dimpled magnetron 35 keV source in combination with a 750 keV four-rod radio frequency quadrupole (RFQ). The new injector is followed by the existing drift tube linac. Prior to installation, a test beam line was built which included the magnetron source and the four-rod RFQ with a number of beam measurement instrumentation. The first beam test with the RFQ showed an output energy deviation greater than 2.5%. Other problems also showed up which led to investigations of the output energy, power consumption and transmission properties using rf simulations which were complemented with additional beam measurements. The sources of this deviation and the mechanical modifications of the RFQ to solve this matter will be presented in this paper. Meanwhile, the nominal output energy of 750 keV has been confirmed and the new injector with the four-rod RFQ is in full operation.

The field flatness of any radio frequency quadrupole (RFQ) is an important parameter that needs to be carefully tuned because it can affect beam transmission efficiency. In four-rod RFQs, the heights of a set of tuning plates determine the quality of the field flatness. The goals of this paper are (a) to show that by using a lumped circuit model of a four-rod RFQ, the field flatness profile for any tuning plate height distribution can be quickly calculated, (b) to derive a perturbative solution of the model so that insights into the physics of the tuning process and its effects can be understood, and (c) to compare the predicted field profiles to measurements.

We have developed a new full 3D approach for the electromagnetic and beam dynamics design and simulation of a radio-frequency quadrupole (RFQ). A detailed full 3D model including vane modulation was simulated, which was made possible by the ever advancing computing capabilities. The electromagnetic (EM) design approach was first validated using experimental measurements on an existing prototype RFQ and more recently on the actual full size RFQ. Two design options have been studied, the original with standard sinusoidal modulation over the full length of the RFQ; in the second design, a trapezoidal modulation was used in the accelerating section of the RFQ to achieve a higher energy gain for the same power and length. A detailed comparison of both options is presented supporting our decision to select the trapezoidal design. The trapezoidal modulation increased the shunt impedance of the RFQ by 34%, the output energy by 15% with a similar increase in the peak surface electric field, but practically no change in the dynamics of the accelerated beam. The beam dynamics simulations were performed using three different field methods. The first uses the standard eight-term potential to derive the fields, the second uses 3D fields from individual cell-by-cell models, and the third uses the 3D fields for the whole RFQ as a single cavity. A detailed comparison of the results from TRACK shows a very good agreement, validating the 3D fields approach used for the beam dynamics studies. The EM simulations were mainly performed using the CST Microwave-Studio with the final results verified using other software. Detailed segment-by-segment and full RFQ frequency calculations were performed and compared to the measured data. The maximum frequency deviation is about 100 kHz. The frequencies of higher-order modes have also been calculated and finally the modulation and tuners effects on both the frequency and field flatness have been studied. We believe that with this new full 3D approach, the enhanced computing capabilities and the calculation precision the electromagnetic design software offer, we may be able to skip the prototyping phase and build the final product at once, although we recognize that prototyping is still needed to establish and validate the fabrication procedure.

Design and some performance results of the pulsed digital low level radio frequency (LLRF) for the radio frequency quadrupole (RFQ) systems of Rutherford Appleton Laboratory-front end test stand and the future European Spallation Source Bilbao linac are presented. For rf field regulation, the design is based on direct rf-to-baseband conversion using an analog in-phase quadrature (IQ) demodulator, high-speed sampling of the I/Q components, baseband signal processing in a field-programmable gate array (FPGA), conversion to analog, and IQ modulation. This concept leads to a simple and versatile LLRF system which can be used for a large variety of rf frequencies and virtually any LLRF application including cw, ramping, and pulsed. In order to improve the accuracy of the probe voltage measurement, errors associated with the use of analog IQ demodulators have been identified and corrected by FPGA algorithms and proper setting of the feedback loop parameters. Furthermore, a baseband-equivalent model for the rf plant is developed in MATLAB-Simulink to study the RFQ transient response under beam loading in the presence of phase and delay errors. The effect of the unwanted resonant modes on the feedback loop stability and the LLRF considerations to avoid such instabilities are discussed and compared to some other machines such as the ILC and the European free electron laser. The practical results obtained from tests with a mock-up cavity and an RFQ cold model verify that amplitude and phase stabilities down to a fraction of one percent and one degree and phase margins larger than ±50° can be achieved with this method preserving the linearity and bandwidth of the feedback loops. © 2011 American Physical Society.

The Spallation Neutron Source (SNS) radio-frequency quadrupole (RFQ) had resonance control instabilities at duty factors higher than approximately 4%. Systematic investigations have been carried out to understand the cause of the instability and to ensure the operational stability of the RFQ. The most critical source of the instability is revealed to be an interaction between hydrogen released by beam bombardments and the RFQ rf field resulting in a discharge, which consumes additional rf power and could cause the RFQ to operate in an unstable region. This paper reports improvement of the SNS RFQ operational stability based on the findings during the SNS operation.

Nonscaling fixed field alternating gradient (FFAG) rings for cancer hadron therapy offer reduced physical aperture and large dynamic aperture as compared to scaling FFAGs. The variation of tune with energy implies the crossing of resonances during acceleration. Our design avoids intrinsic resonances, although imperfection resonances must be crossed. We consider a system of three nonscaling FFAG rings for cancer therapy with 250 MeV protons and $400\text{ }\mathrm{MeV}/u$ carbon ions. Hadrons are accelerated in a common radio frequency quadrupole and linear accelerator, and injected into the FFAG rings at $v/c=0.1294$. ${\mathrm{H}}^{+}/{\mathrm{C}}^{6+}$ ions are accelerated in the two smaller/larger rings to 31 and $250\text{ }\text{ }\mathrm{MeV}/68.8$ and $400\text{ }\mathrm{MeV}/u$ kinetic energy, respectively. The lattices consist of doublet cells with a straight section for rf cavities. The gantry with triplet cells accepts the whole required momentum range at fixed field. This unique design uses either high-temperature superconductors or superconducting magnets reducing gantry magnet size and weight. Elements with a variable field at the beginning and at the end set the extracted beam at the correct position for a range of energies.

The design and operation support of hadron (proton and heavy-ion) linear accelerators require substantial use of beam dynamics simulation tools. The beam dynamics code TRACK has been originally developed at Argonne National Laboratory (ANL) to fulfill the special requirements of the rare isotope accelerator (RIA) accelerator systems. From the beginning, the code has been developed to make it useful in the three stages of a linear accelerator project, namely, the design, commissioning, and operation of the machine. To realize this concept, the code has unique features such as end-to-end simulations from the ion source to the final beam destination and automatic procedures for tuning of a multiple charge state heavy-ion beam. The TRACK code has become a general beam dynamics code for hadron linacs and has found wide applications worldwide. Until recently, the code has remained serial except for a simple parallelization used for the simulation of multiple seeds to study the machine errors. To speed up computation, the TRACK Poisson solver has been parallelized. This paper discusses different parallel models for solving the Poisson equation with the primary goal to extend the scalability of the code onto 1024 and more processors of the new generation of supercomputers known as BlueGene (BG/L). Domain decomposition techniques have been adapted and incorporated into the parallel version of the TRACK code. To demonstrate the new capabilities of the parallelized TRACK code, the dynamics of a 45 mA proton beam represented by 10^{8} particles has been simulated through the 325 MHz radio frequency quadrupole and initial accelerator section of the proposed FNAL proton driver. The results show the benefits and advantages of large-scale parallel computing in beam dynamics simulations.

A hybrid single cavity (HSC) linac, combined with radio frequency quadrupole and drift tube structure in a single interdigital-H cavity, operates with high rf power as a prototype injector for cancer therapy synchrotron. The HSC adopts a direct plasma injection scheme (DPIS) with a laser ion source. The input beam current of the HSC is designed to be 20 mA ${\mathrm{C}}^{6+}$ ions. According to simulations, the HSC can accelerate a 6-mA ${\mathrm{C}}^{6+}$ beam which meets the requirement of the particle number for cancer therapy ($1{0}^{8\ensuremath{\sim}9}\text{ }\text{ions}/\text{pulse}$). The HSC injector with DPIS makes the existing multiturn injection system and stripping system unnecessary; what is more, it can also bring down the size of the beam pipe in existing synchrotron magnets, which can reduce the whole cost of the synchrotron. Details of the field measurements of the HSC linac and results of the high power test are reported in this paper.