EM and Thermo-Mechanical Analysis and Design of a Compact-RFQ

EM and Thermo-Mechanical Analysis and Design of a Compact-RFQ J. Portilla1, J. Feuchtwanger1,2, I. Arredondo1, E. Asua1, V. Etxebarria1, N. Vallis1, R. Enparantza3, I. Ariz3, I. Muñoz3, U. Etxebeste4, I. Hernández4 1 IZPILab-Beam Laboratory, Faculty of Science and Technology, University of the Basque Country - UPV/EHU, Leioa, Spain 2 IKERBASQUE, Basque Foundation for Science, Bilbao, Spain 3 TEKNIKER, Basque Research and Technology Alliance (BRTA), Eibar, Spain 4 Egile S.L., Mendaro, Spain Abstract — The design and optimization of a Radio-Frequency Quadrupole (RFQ) for focusing, bunching and accelerating charged particles needs to simultaneously deal with electromagnetic, thermal and mechanical issues to achieve a fully operational structure. Four resonant cavities along the RFQ together with the ending cut backs have to provide a quadrupolar mode at the desired frequency and to produce a flat transversal electrical field amplitude across the overall length of the structure. The operation of an RFQ needs the injection of a very high RF signal power, so a high quality factor Q and appropriate handling of thermal losses is mandatory. A water-cooling circuit is commonly employed inserted in between the resonant lobes, close to the vane tips. On the other hand, RF and vacuum ports have to introduce minimal perturbations in the structure and, finally, a number of RF signal pick-ups and tuners are added to test and adjust the RFQ performance. The complexity of such structure together with the mechanical feasibility with required accuracy and tunability options is even more challenging when dealing with compact RFQ designs. The paper describes the EM and thermomechanical design and optimization of a compact RFQ intended for proton acceleration. The main aspects in this work are linked to the RFQ compactness and with the novel RF signal injection design. Index Terms — Radio Frequency Quadrupole, quadrupolar mode, particle acceleration, particle focusing, particle bunching. I. INTRODUCTION The Radio Frequency Quadrupole (RFQ) is the preferred structure employed in the low energy section of many particle accelerators after the ion source. Kapchinski and Tepliakov proposed the principles of the RFQ in 1969 [1]. A first operational RFQ was constructed at LANL in 1980 [2]. The transversal section of an RFQ for proton acceleration consists of four identical resonant lobes coupled into the center of the structure through the lobe endings in the form of four vane tips. A high-voltage is applied between the vanes by exciting a quadrupolar mode in such a way that an extremely effective electrostatic lens effect is produced over the particle beam travelling along the axis of the RFQ. The modulation of the vane electrodes’ shapes along the structure allows to achieve particle acceleration together with the focusing and bunching effect by means of a single RF quadrupolar field at the resonant frequency. A continuous, alternating quadrupole channel is formed in along the RFQ axis with periodic length. The unitary length depends on the wavelength and the increasing energy of the particles along the RFQ. The RFQ operates under vacuum condition to avoid collisions between air molecules and the particle beam. The EM design goal is to provide the desired RF field structure at the working frequency, which consists of a TE210 mode. The beam dynamics of the RFQ design follows its own process to determine the vane longitudinal geometry. The goals of the EM design are to build this mode inside the structure with minimal losses and by keeping away in frequency other undesired modes that can appear close to the desired one due to the complex geometry of the RFQ. The EM design has also to consider the signal injection, tuning elements, and the effect of other elements such as vacuum ports, signal pick-ups, etc. Typical Q factors achieved are in the order of several thousands but the operation of an RFQ needs a high amount of RF power, so thermal issues have to be managed in order to avoid undesired effects. Thermal simulations are needed to optimize the RFQ both from the EM and the mechanical points of view. Water channels are commonly implemented through the vanes along the structure to dissipate thermal power in the vane tips, whose shape is critical to the RFQ operation. Typical proton RFQs uses a frequency in the range from 300 to 400 MHz such as, for instance, the 324 MHz FETS RFQ at RAL [3] or the 352,2 MHz LINAC4 RFQ developed at CERN as a part of the LHC injector [4]. The use of higher frequencies allows to reduce the RFQ size at the expense of acceleration efficiency. In 2016, CERN built the first compact proton RFQ at 750 MHz [5]. In the paper, we will describe the EM and thermo-mechanical design of a compact RFQ for proton acceleration. Our design uses a novel RF power injection approach for producing the quadrupole mode operation and it can also serve to mitigate undesired dipole modes. The geometry has also been optimized to achieve high Q with tunability, and keeping in mind thermo2022 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO) 978-1-6654-8633-0/22/$31.00 ©2022 IEEE 2022 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO) | 978-1-6654-8633-0/22/$31.00 ©2022 IEEE | DOI: 10.1109/NEMO51452.2022.10038525 Authorized licensed use limited to: Universidad Pais Vasco. Downloaded on November 12,2025 at 12:47:50 UTC from IEEE Xplore. Restrictions apply. mechanical issues. An important effort has also been oriented towards reducing mechanical fabrication costs. II. EM DESIGN AND SIMULATIONS The RFQ design process has to fulfil some specific requirements from the EM point of view. It has to be excited in a TE210-like quadrupolar mode at the desired frequency, maximizing the Q factor and keeping away in frequency undesired modes, such as it is the case of dipolar modes such as TE110. It is imperative to build a parameterized model in order to simplify EM optimization. The model has to consider the geometry aspects and parameters trying to keep with signal injection, vacuum ports, tunability, thermal issues and to simplify the fabrication process. The common way to couple the RF power in proton RFQs has been the use of loop-couplers inserted into the mid-section of the RFQ lobes. This technique has demonstrated to be reliable and effective but introduces a significant perturbation into the lobe that can be more noticeable when dealing with compact structures. We propose a RF injection scheme using direct connection of the inner coaxial conductor into the RFQ vane body in such a way that the lobe geometry is not perturbed at all and the transversal electrical fields are directly exited through the vanes. By using a mating of such couplers connected to opposed vanes at a given transversal plane of the RFQ it is also possible to excite quadrupolar mode avoiding the excitation of dipolar modes. As a previous stage to this work, a section of an RFQ was designed and manufactured to serve as a cold model (a realistic model but intended to be tested under small-signal conditions) to demonstrate mechanical feasibility and to compare the simulation results with real achieved performance. The lessons learned from the manufacturing process and tests of the RFQ model, including main mechanical and RF characteristics, tuning capabilities and EM fields along the structure, determined through bead-pull perturbation measurements, have been very helpful to define the RFQ parametric model employed in this work. The first step is to design the transversal geometry to fix the quadrupolar mode at the desired frequency with high Q. The final geometry of the lobe sections depends on a tradeoff between resonant frequency at the desired quadrupolar mode, Q factor, and thermo-mechanical issues. At this first design stage, the RFQ is ended at its input and output with metallic walls that null the electrical field at those points. The vane tips distance depends on the beam dynamics. For reference, in this design these tips distance is about a couple of mm. The voltage across the tips is essential for focusing the beam. Beam bunching and acceleration are obtained thanks to the longitudinal modulation of the vane tips. Magnetic field near the axis should be minimized to avoid beam defocusing. The final goal is to obtain a flat electrical field amplitude along the structure. This is undertaken in a second design step by the modification of cut backs sections at the input and output. In Fig. 1, the proposed transversal section and the quadrupolar electrical fields can be observed. Corresponding magnetic fields are shown in Fig. 2. The electrical field amplitude over the RFQ length is shown in Fig. 3, determined at a given short off-axis distance. Note that the electrical field nulls into the axis for the quadrupolar mode. RF coupling, vacuum ports, tuners and pick-ups are added and optimized in a later design stage. The main novelty in our design is linked to the RF injection strategy, avoiding loop couplers inserted in the middle of the resonant lobe sections, thanks to the direct excitation of electric fields into the RFQ vanes. The use of two opposite RF ports in phase allows to excite the quadrupolar mode and to reduce the possibility of dipolar undesired modes. Details of a couple of RF coaxial input ports and two vacuum ports which have been inserted in a given transversal plane of the RFQ can be observed in Fig. 1 and Fig. 2. Fig. 1. Quadrupolar electric fields in a transversal cut of the RFQ. Fig. 2. Quadrupolar magnetic fields in a transversal cut of the RFQ. Fig. 3. Amplitude of electric field along the RFQ. 2022 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO) Authorized licensed use limited to: Universidad Pais Vasco. Downloaded on November 12,2025 at 12:47:50 UTC from IEEE Xplore. Restrictions apply. Fig. 4 shows a picture of the global RFQ geometry including four RF injection and vacuum ports. The magnetic field streamlines across the structure can be also observed. The final RFQ will include eight tuners and four pick-ups inside each lobe. A change in the tuners penetration depth of 1 mm produces a frequency shift in the order of 1MHz. This may be essential to adjust the RFQ due to mechanical and thermal deviations and will also be helpful in obtaining a flat electrical field. The final detailed analysis and optimization of the RFQ is made by using a simplified model only including one lobe and magnetic boundary conditions, thanks to the symmetry of the structure and the quadrupolar nature of the operating EM mode. Fig. 4. Quadrupolar mode magnetic streamlines across the RFQ. III. THERMO-MECHANICAL SIMULATIONS Power deposition into the metallic walls produces losses and thermal expansion of the material that it is particularly critical to the vane tips. The RFQ under design will use four RF couplers for injecting a peak power up to 80kW each. Although the RFQ will be operated at a few percent duty cycle, this means that power on the order of kWs could be deposited in each lobe, producing deformation and mechanical stress at some critical points. Thermo-mechanical simulations are key for determining the temperature distribution and mechanical stress. Water-cooling channels are inserted into each vane along the RFQ, close to the vane tips, to reduce mechanical-thermal issues. The geometry of the vanes, lobes and cut ends has to be optimized to reduce the impact of such problems, with mechanical feasibility in mind. Simulations show that temperature could reach up to hundreds of ºC in the absence of cooling. Thanks to cooling channels, temperatures can typically be controlled under 40ºC. Figure 5 shows an example of temperature distribution, over one lobe taking advantage of the RFQ symmetry. On the other hand, purely mechanical simulations are also carried out to consider mechanical load and stress produced to the RFQ structure due to the different auxiliary components such as vacuum pumps, RF couplers, etc. VI. CONCLUSION The EM design and thermo-mechanical analysis of a compact RFQ intended for proton acceleration have been reported in the paper. One key aspect in this work is the RFQ compact size, which significantly impacts the thermal and mechanical issues. On the other hand, a novel approach has been adopted concerning the RF signal excitation of the quadrupolar mode making use of a direct connection of the inner conductor of the RF coaxial port to the RFQ vanes. This solution avoids the insertion of loop-couplers in the RFQ lobes. The electrical fields are directly exited into the vanes and, moreover, the use of in-phase coupling in opposite vanes allows to set the quadrupolar mode and to prevent undesired dipolar modes. Fig. 5. Example of temperature distribution in one-lobe RFQ section. ACKNOWLEDGEMENT The authors wish to acknowledge the funding received from the Basque Government through the Elkartek program, which make possible a multidisciplinary team involving people from university, a technological research center and of a highprecision mechanical company. Authors also acknowledge A. Letchford, from STFC RAL, for demonstrating a kind interest in this work and for his high Q comments. REFERENCES [1] I.M. Kapchinskii, V.A. Teplyakov, “A Linear Ion Accelerator With Spatially Uniform Hard Focusing”, Prib. Tekh. Eksp. 1970 (1970) 2, pp. 19-22. [2] J. T. Ahearne., “RFQ is Alive and Well”, Atom, Los Alamos Scientific Laboratory, Vol. 17, nº 4, 1980, pp. 2-8. [3] A. Letchford et al., “Status of the RAL front end test stand”, Proc. IPAC’15, Richmond, VA, USA, paper THPF105, pp. 3959-3960. [4] M. Vretenar et al., “The LINAC4 project at CERN”, IPAC11, San Sebastian, Spain, 2011, pp. 900-902. [5] A. Lombardi et al., “Beam Dynamics In a High Frequency RFQ”, IPAC2015 Proceedings, Richmond, VA, USA, 2015, pp. 24082412. 2022 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO) Authorized licensed use limited to: Universidad Pais Vasco. Downloaded on November 12,2025 at 12:47:50 UTC from IEEE Xplore. Restrictions apply.