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There has been a renewed interest in applying multiobjective (MO) optimization methods to a number of problems in the physical sciences, including to rf structure design. The results of these optimizations generate large datasets, which makes visualizing the data and selecting individual solutions difficult. Using the generated results, Pareto fronts can be found giving the trade-off between different objectives, allowing one to utilize this key information in design decisions. Although various visualization techniques exist, it can be difficult to know which technique is appropriate and how to apply them successfully to the problem at hand. First, we present the setup and execution of MO optimizations of one standing wave and one traveling wave accelerating cavity, including constraint handling and an algorithm comparison. In order to understand the generated Pareto frontiers, we discuss several visualization techniques, applying them to the problem, and give the benefits and drawbacks of each. We found that the best techniques involve clustering the resulting data first to narrow down the possible choices and then using multidimensional visualization methods such as parallel coordinate plots and decision maps to view the clustered results and select individual solutions. Finally, we give some examples of the application of these methods and the cavities selected based on arbitrary design requirements.

Recirculating energy recovery linacs are a promising technology for delivering high power particle beams (∼GW) while only requiring low power (∼kW) rf sources. This is achieved by decelerating the used bunches and using the energy they deposit in the accelerating structures to accelerate new bunches. We present studies of the impact of the bunch packet filling pattern on the performance of the accelerating rf system. We perform rf beam loading simulations under various noise levels and beam loading phases with different injection schemes. We also present a mathematical description of the rf system during the beam loading, which can identify optimal beam filling patterns under different conditions. The results of these studies have major implications for design constraints for future energy recovery linacs, by providing a quantitative metric for different machine designs and topologies.

Beam breakup instability is a potential issue for all particle accelerators and is often the limiting factor for the maximum beam current that can be achieved. This is particularly relevant for energy recovery linacs (ERLs)with multiple passes where a relatively small amount of charge can result in a large beam current. Recent studies have shown that the choice of filling pattern and recirculation scheme for a multipass energy recovery linac can drastically affect the interactions between the beam and rf system. In this paper, we further explore this topic to study how filling patterns affect the beam breakup instability and how this can allow us to optimize the design in order to minimize this effect. We present a theoretical model of the beam-rf interaction as well as numerical modeling and show that the threshold current can vary by a factor of 5, and potentially, even more, depending on the machine design parameters. Therefore a judicious choice of filling pattern can greatly increase the onset of beam breakup, expanding the utility of future ERLs.

Radio-frequency cavities used in modern particle accelerators operate inTMm10-like modes composed of a single, dominant multipole of orderm;m=0modes are used for the longitudinal acceleration of a particle beam andm≠0modes for controlling transverse beam dynamics. The practical design of the latter, however, can be complex and require extensive analysis through the iteration of both approximate mathematical models and computationally expensive simulations to optimize the performance of the structure. In this paper we present a new, systematic method for designing azimuthally modulated rf cavities that support modes composed of any number and magnitude of user-specified transverse multipoles, either with or without a longitudinally accelerating component. Two case studies are presented of rf cavity designs that support modes composed of a longitudinally accelerating field in addition to a single transverse multipole, and designs that support modes composed of two transverse multipoles. We discuss generalizing the discoveries and conclusions from the two case studies to designing cavities that support modes composed of any number of multipoles. The theoretical work is verified with analysis of 3D simulations and experimental measurements are presented of a cavity operating in a 3 GHz mode that simultaneously longitudinally accelerates and transversely focuses a beam.

The CompactLight design for a next-generation x-ray free-electron laser utilizes a C-band injector. This requires that the harmonic system used to linearize the beam’s phase space must operate at X-band rf or higher. We investigate the optimum frequency for the harmonic system in the range of frequencies from 12 to 48 GHz. We describe the reasoning behind selecting 36 GHz (Ka-band) as our working harmonic frequency. The full linearizer system design including the power source, pulse compressor, and linearizing structure, along with options, is considered and presented. These designs are compared in terms of rf and beam dynamics performance. Two potential MW-level rf sources are discussed; a multibeam klystron and a gyro-klystron, while a klystron-based upconverter with an X-band driver is briefly discussed as an alternative path if even higher peak powers are needed. To further increase peak power, novel options for pulse compressors at Ka-band are discussed. Traveling and standing wave solutions for the structure are presented.

A high-resolution, intratrain position feedback system has been developed to achieve and maintain collisions at the proposed future electron-positron International Linear Collider (ILC). A prototype has been commissioned and tested with a beam in the extraction line of the Accelerator Test Facility at the High Energy Accelerator Research Organization in Japan. It consists of a stripline beam position monitor (BPM) with analogue signal-processing electronics, a custom digital board to perform the feedback calculation, and a stripline kicker driven by a high-current amplifier. The closed-loop feedback latency is 148 ns. For a three-bunch train with 154 ns bunch spacing, the feedback system has been used to stabilize the third bunch to 450 nm. The kicker response is linear, and the feedback performance is maintained, over a correction range of over±60μm. The propagation of the correction has been confirmed by using an independent stripline BPM located downstream of the feedback system. The system has been demonstrated to meet the BPM resolution, beam kick, and latency requirements for the ILC.

A high-resolution, low-latency beam position monitor (BPM) system has been developed for use in particle accelerators and beam lines that operate with trains of particle bunches with bunch separations as low as several tens of nanoseconds, such as future linear electron-positron colliders and free-electron lasers. The system was tested with electron beams in the extraction line of the Accelerator Test Facility at the High Energy Accelerator Research Organization (KEK) in Japan. It consists of three stripline BPMs instrumented with analogue signal-processing electronics and a custom digitizer for logging the data. The design of the analogue processor units is presented in detail, along with measurements of the system performance. The processor latency is 15.6±0.1ns . A single-pass beam position resolution of 291±10nm has been achieved, using a beam with a bunch charge of approximately 1 nC.

Studies of the crab cavities at KEKB revealed that the rf phase could shift by up to 50° within∼50μs during a quench; while the cavity voltage is still at approximately 75% of its nominal amplitude. If such a failure were to occur on the HL-LHC crab cavities, it is likely that the machine would sustain substantial damage to the beam line and surrounding infrastructure due to uncontrolled beam loss before the machine protection system could dump the beam. We have developed a low-level rf system model, including detuning mechanisms and beam loading, and use this to simulate the behavior of a crab cavity during a quench, modeling the low-level rf system, detuning mechanisms and beam loading. We supplement this with measurement data of the actual rf response of the proof of principle double-quarter wave crab cravity during a quench. Extrapolating these measurements to the HL-LHC, we show that Lorentz force detuning is the dominant effect leading to phase shifts in the crab cavity during quenches; rather than pressure detuning which is expected to be dominant for the KEKB crab cavities. The total frequency shift for the HL-LHC crab cavities during quenches is expected to be about 460 Hz, leading to a phase shift of no more than 3°. The results of the quench model are read into a particle tracking simulation, SixTrack, and used to determine the effect of quenches on the HL-LHC beam. The quench model has been benchmarked against the KEKB experimental measurements. In this paper we present the results of the simulations on a crab cavity failure for HL-LHC as well as for the SPS and show that beam loss is negligible when using a realistic low-level rf response.

A 4-rod deflecting structure is proposed as a possible crab cavity design for the LHC high luminosity upgrade. Crab cavities are required for the LHC luminosity upgrade to provide a greater bunch overlap in the presence of a crossing angle, but must fit in the existing limited space. The structure has two parallel sections consisting of two longitudinally opposing quarter-wave rods, where each rod has the opposite charge from each of its nearest neighbors. The structure is transversely compact because the frequency is dependent on the rod lengths rather than the cavity radius. Simulations were undertaken to investigate the effect of rod shape on surface fields, higher order multipole terms and induced wakefields in order to obtain the optimal rod shape. The simulation results presented show that the addition of focus electrodes or by shaping the rods the sextupole contribution of the cavity voltage can be negated; the sextupole contribution is 321.57mTm/m2 , Epeak=27.7MV/m , and Bpeak=63.9mT at the design voltage of 3 MV. The damping requirements for the LHC are critical and suitable couplers to damp all modes but the operating mode are presented. The results of various testing cycles of the first SRF 4 rod prototype cavity are presented and show that the cavity has reached the required transverse voltage of 3 MV.

High-energy particle accelerators have been crucial in providing a deeper understanding of fundamental particles and the forces that govern their interactions. To increase the energy of the particles or to reduce the size of the accelerator, new acceleration schemes need to be developed. Plasma wakefield acceleration 1 – 5 , in which the electrons in a plasma are excited, leading to strong electric fields (so called ‘wakefields’), is one such promising acceleration technique. Experiments have shown that an intense laser pulse 6 – 9 or electron bunch 10 , 11 traversing a plasma can drive electric fields of tens of gigavolts per metre and above—well beyond those achieved in conventional radio-frequency accelerators (about 0.1 gigavolt per metre). However, the low stored energy of laser pulses and electron bunches means that multiple acceleration stages are needed to reach very high particle energies 5 , 12 . The use of proton bunches is compelling because they have the potential to drive wakefields and to accelerate electrons to high energy in a single acceleration stage 13 . Long, thin proton bunches can be used because they undergo a process called self-modulation 14 – 16 , a particle–plasma interaction that splits the bunch longitudinally into a series of high-density microbunches, which then act resonantly to create large wakefields. The Advanced Wakefield (AWAKE) experiment at CERN 17 – 19 uses high-intensity proton bunches—in which each proton has an energy of 400 gigaelectronvolts, resulting in a total bunch energy of 19 kilojoules—to drive a wakefield in a ten-metre-long plasma. Electron bunches are then injected into this wakefield. Here we present measurements of electrons accelerated up to two gigaelectronvolts at the AWAKE experiment, in a demonstration of proton-driven plasma wakefield acceleration. Measurements were conducted under various plasma conditions and the acceleration was found to be consistent and reliable. The potential for this scheme to produce very high-energy electron bunches in a single accelerating stage 20 means that our results are an important step towards the development of future high-energy particle accelerators 21 , 22 . Electron acceleration to very high energies is achieved in a single step by injecting electrons into a ‘wake’ of charge created in a 10-metre-long plasma by speeding long proton bunches.