Frank Tecker
This paper gives an introduction of longitudinal beam dynamics for circular accelerators. After briefly discussing some types of circular accelerators, it focuses on particle motion in synchrotrons. It summarizes the equations of motion, discusses phase-space matching during beam transfer, and introduces the Hamiltonian of longitudinal motion.
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Transverse breathing mode oscillations in a particle beam can couple energy into longitudinal oscillations in a bunch of finite length and cause significant losses. We develop a model that illustrates this effect and explore the dependence on mismatch size, space-charge tune depression, longitudinal focusing strength, bunch length, and RF bucket length.
A high peak current, flat longitudinal phase space electron beam is desirable for efficient x-ray free electron laser (FEL) radiation in next generation light sources. To attain such a beam requires the extensive design of the linear accelerator (linac) including both linear and nonlinear effects. In this paper, we propose a lumped longitudinal beam dynamics model for fast optimization of the electron beam longitudinal phase space through the accelerator. This model is much faster than available tracking programs and also shows good agreement with the fully three-dimensional element-by-element…
We present measurement and analyses of longitudinal timing jitter of Beijing Electron Positron Collider (BEPCII) linear accelerator electron gun. We simulated longitudinal jitter effect of the gun using PARMELA about beam performance including beam profile, average energy, energy spread, longitudinal phase of reference particle and XY emittance. The maximum percentage difference of the beam parameters are calculated to be; 100%, 13.27%, 42.24%, 7.79% and 65.01%, 86.81%, respectively due to which the bunching efficiency is reduced to 54%. The simulation results are in agreement with test and ar…
In this paper, we get the 1D approximate analytical solution of the plasma electrostatic wake driven by the laser, and get the oscillating frequency of the wake modified by the nonlinear high order terms, and find that the frequency depends on the oscillating amplitudes of the wake and the laser which is the general nonlinear phenomenon. Finally we analyze the longitudinal beam dynamics in this electrostatic wake, and find that the high order terms don't change the topology of the longitudinal phase space.
A new algorithm for calculating the spin tune and the n-axis for circular accelerators is presented. The method resembles the one employed in the existing program code SODOM in that one-turn numerical spin maps at equally spaced orbit angle variables are used but it is more efficient than the latter. Furthermore, it is applicable at large openning angles of the n-axis, whereas the existing SODOM only converges for small angles.
Recent progress in particle accelerator tracking has shown that the field representation is one of the major limits of the prediction accuracy especially for machines, whose aperture is fully filled by the beam and thus higher the artefacts created by higher order modes have to be thoroughly understood. The standard tool for field presentation today are cylindrical circular multipoles due to their straight forward correspondence to the Cartesian coordinates. In this paper we extend the standard approach to other coordinate systems, show how these can be measured next to their realisation in me…
An asynchronous accelerator is described, in which the principle of its operation permits the active longitudinal bunch compression of accelerated proton beams, to overcome the space charge limitation effects of intense bunches. It is shown that accelerated bunches from an RFQ linac can be adapted for Asynchronac injection for a multiple of choices in the acceleration frequencies of the RFQ and the Asynchronac. The offered new type of accelerator system is especially suitable to accelerate proton beams for up to 100MeV energy and hundreds of mA average current.
The resonant laser cooling of circular accelerator beams of relativistic charged particle is studied. It is shown that in the approximation of the given external electromagnetic wave amplitude (small gain free electron laser) the emittance of a beam of charged particles decreases. In the field of particle energy about 100 in the mass energy units the beam energy losses are negligible. The discovered effect can be used for cooling of charged particle beams in various accelerators. The significant cooling rates are possible to achieve by placing of the cooling device in the appropriate points of…
By considering delta function sextupole, octupole, and decapole perturbations and using difference action-angle variable equations, we find some useful analytical formulae for the estimation of the dynamic apertures of circular accelerators due to single sextupole, single octupole, single decapole (single 2$m$ pole in general). Their combined effects are derived based on the Chirikov criterion of the onset of stochastic motions. Comparisons with numerical simulations are made, and the agreement is quite satisfactory. These formulae have been applied to determine the beam-beam limited dynamic a…
Many applications of high brightness, highly relativistic electron beams carry strict requirements on longitudinal phase space quality. To meet these requirements, accelerator systems typically utilize dispersive elements to manipulate the correlated energy spread acquired during acceleration or via collective effects. The many free variables in these systems make finding an optimal configuration difficult. We present here an analytical method for tracking a desired final longitudinal phase space backwards through an accelerator section composed of an acceleration or drift section followed by …
Recent experiments [1] have explored the use of a free-electron laser (FEL) as a buncher for a microwave two-beam accelerator, and the subsequent driving of a standing-wave rf output cavity. Here we present a deeper analysis of the longitudinal dynamics of the electron bunches as they are transported from the end of the FEL and through the output cavity. In particular, we examine the effect of the transport region and cavity aperture to filter the bunched portion of the beam. [1] T. Lefevre, et. al., Phys. Rev. Lett. 84 (2000), 1188.
We revise a previous version of this paper proposing a method to transfer emittances from the transverse planes to the longitudinal. It turned out the system showed non-Hamiltonian behavior because the longitudinal component of the transverse electric field at ends of the transverse resonator were not included in the model. Including those fields the 6D emittance is conserved. We review the mechanism behind the emittance conservation. It is still possible to produce an emittance transfer with the RF quadrupole field setting the tunes on synchro-betatron resonance for a short period of time the…
In the usual parameter regime of accelerator physics, particle ensembles can be treated as classical. If we approach a regime where $ε_xε_yε_s \approx N_{particles}λ_{Compton}^3\$, however, the granular structure of quantum-mechanical phase space becomes a concern. In particular, we have to consider the Pauli exclusion principle, which will limit the minimum achievable emittance for a beam of fermions. We calculate these lowest emittances for the cases of bunched and coasting beams at zero temperature and their first-order change rate at finite temperature.
Coherent transverse oscillations of a bunch in a ring accelerator are considered. Three different models of the bunch are used: a hollow bunch in a square potential well, a square bunch in a parabolic potential well, and a parabolic bunch in a parabolic well. The bunch space-charge field, wakefield, and chromaticity are taken into account in all the cases. The bunch eigenmodes and various instabilities are studied. The results are compared and analyzed to establish the range of applicability of the models. Role of the Landau damping due to dependence of the SC field on the longitudinal coordin…
The leading Lie generators, including the chromatic effects, due to hard-edge fringe field of single multipole and solenoid are derived from the vector potentials within a Hamiltonian system. These nonlinear generators are applied to the interaction region of PEP-II to analyze the linear errors due to the feed-down from the off-centered quadrupoles and solenoid. The nonlinear effects of tune shifts at large amplitude, the synchro-betatron sidebands near half integer and their impacts on the dynamic aperture are studied in the paper.
Circular particle accelerators at the energy frontier are based on superconducting magnets that are extremely sensitive to beam losses as these might induce quenches, i.e.\ transitions to the normal-conducting state. Furthermore, the energy stored in the circulating beam is so large that hardware integrity is put in serious danger, and machine protection becomes essential for reaching the nominal accelerator performance. In this challenging context, the beam halo becomes a potential source of performance limitations and its dynamics needs to be understood in detail to assess whether it could b…
Electron cloud interaction with high energy positive beam are believed responsible for various undesirable effects such as vacuum degradation, collective beam instability and even beam loss in high power proton circular accelerator. An important uncertainty in predicting electron cloud instability lies in the detail processes on the generation and accumulation of the electron cloud. The simulation on the build-up of electron cloud is necessary to further studies on beam instability caused by electron cloud. China Spallation Neutron Source (CSNS) is the largest scientific project in building, w…
The efficiency of the beam extraction and collimation systems in circular accelerators with the use of the channeling effect in a bent crystal is determined. The dependences of the extraction efficiency on the geometrical parameters of the crystal (its length, thickness, and bending angle), the azimuthal location of the system components, and the offset of the septum or scraper are presented. The influence of crystal imperfections (amorphous layers, misorientation, and torsion) on the efficiency of the systems is considered, and their tolerances are proposed. It is shown that an extraction eff…
Exploring the Potential of Resonance Islands and Bent Crystals for a Novel Slow Extraction from Circular Hadron Accelerators
本研究探讨结合共振岛与弯曲晶体技术，设计圆形强子加速器新型慢引出方法的潜力，该方法有望大幅降低强流束应用中引出装置的束流损失。
This paper is a summary report of the ICFA Beam Dynamics Workshop 'Accelerators for a Higgs Factory: Linear vs. Circular' (HF2012). It discusses four types of accelerators as possible candidates for a Higgs factory: linear e+e- colliders, circular e+e- colliders, muon collider and photon colliders. The comparison includes: physics reach, performance (energy and luminosity), upgrade potential, technology maturity and readiness, and technical challenges requiring further R&D.
Plasma accelerators driven by intense laser or particle beams provide gigavolt-per-meter accelerating fields, promising to drastically shrink particle accelerators for high-energy physics and photon science. Applications such as linear colliders and free-electron lasers (FELs) require high energy and energy efficiency, but also high stability and beam quality. The latter includes low energy spread, which can be achieved by precise beam loading of the plasma wakefield using longitudinally shaped bunches, resulting in efficient and uniform acceleration. However, the plasma wavelength, which sets…
We give an overview of our current/future analytical and numerical work on the spin polarization in high-energy electron storage rings. Our goal is to study the possibility of polarization for the CEPC and FCC-ee. Our work is based on the so-called Bloch equation for the polarization density introduced by Derbenev and Kondratenko in 1975. We also give an outline of the standard approach, the latter being based on the Derbenev-Kondratenko formulas.
We consider acceleration of protons in a cavity with such dimensions as length l = 10 m, width b = 20 m, height a = 1.01 m, located between two bending (180)degree magnets with isochronous magnetic field. The cavity is loaded with rows of drift plates (tubes), being excited by a wave of E110 type at the frequency fo = 148.5 MHz, excitation power P1 = 5.65 MW. Additionally, the cavity is fed with the power P2 = 8 MW, transmitted into a beam of protons with such parameters as the final energy 0.8 GeV, pulse beam current I = 10 mA, pulse width 25 microseconds, repetition rate 10 Hz. We discuss th…
Electron cloud effects have become one of the main performance limitations for circular particle accelerators operating with positively-charged beams. Among other machines worldwide, the CERN Super Proton Synchrotron (SPS), as well as the Large Hadron Collider (LHC) are affected by these phenomena. Intense efforts have been devoted in recent years to improve the understanding of electron cloud (EC) generation with the aim of finding efficient mitigation measures. In a different domain of accelerator physics, non-linear resonances in the transverse phase space have been proposed as novel means …
Energy-frontier accelerators provide powerful tools performing high precision measurements confirming the fundamental of the physics and broadening new research horizons. Such machines are either driven by circular or linear accelerators. The circular machines, having the center-mass (CM) energy values reaching 200 GeV (for leptons) and above, experience beam energy loss and quality dilution, for example, due to synchrotron radiation, limiting the overall CM energy achievable and requiring a constant energy top-up to compensate the loss and the beam quality dilution. Linear colliders overcome …
Many advanced techniques have been developed, tested and implemented in the last decades in almost all circular accelerators across the world to measure the linear optics. However, the greater availability and accuracy of beam diagnostics and the ever better correction of linear magnetic lattice imperfections (beta beating at 1% level and coupling at 0.1%) are reaching what seems to be the intrinsic accuracy and precision of different measurement techniques. This paper aims to highlight and quantify, when possible, the limitations of one standard method, the harmonic analysis of turn-by-turn b…
It is reported that [Z. Huang et al., Phys. Rev. Lett. 109, 204801 (2012)], high-gain free-electron laser (FEL) can be generated by transverse-dispersed electron beams from laser-plasma accelerators (LPAs) using transverse-gradient undulator (TGU) assuming an ideal constant dispersion function without focusing optics. The constant dispersion function keeps electrons beyond the resonant energy bandwidth still being on resonant with the FEL radiation. Instead, in this paper, the case with focusing optics in an LPA-driven FEL using TGU is numerically studied, in which the dispersion function shou…
The transverse instability of a bunch in a circular accelerator is elaborated in this paper. A new tree-modes model is proposed and developed to describe the most unstable modes of the bunch. This simple and flexible model includes chromaticity and space charge, and can be used with any bunch and wake forms. The dispersion equation for the bunch eigentunes is obtained in form of a third-order algebraic equation. The known head-tail and TMCI modes appear as the limiting cases which are distinctly bounded at zero chromaticity only. It is shown that the instability parameters depend only slightly…
Controlling non-linear effects in the transverse dynamics of charged particle beams in circular accelerators opens new possibilities for controlling some of the beam properties. Beam splitting by crossing a stable 1D non-linear resonance is part of the routine operation of the CERN Proton Synchrotron. The beam undergoes trapping and transport inside stable islands created in the horizontal plane to allow multi-turn extraction towards the Super Proton Synchrotron, where the beam is used for fixed-target experiments. This process acts only on the horizontal beam emittance, inducing a reduction o…
New crystal technique - array of bent strips and a fan-type reflector, based on thin straight plates - have been used for research of extraction and collimation a circulating beam in the U-70 accelerator at the energy 50 GeV and 1.3 GeV. It is shown, that new devices can effectively steer a beam in a wide energy range. For protons with energy 50 GeV efficiency of extraction and collimation about 90 % has been achieved which is record for this method. Reduction of particle losses in 2-3 times was observed also in accelerator at application of different crystals in comparison with the usual one-…
Crossing the transition energy is always a delicate process, representing a potential source of strong perturbations of the dynamics of charged particle beams in a hadron circular accelerator. Since the first generation of multi-GeV rings, intense studies have been devoted to understanding the possible harmful mechanisms involved in transition crossing and to devise mitigation measures. Nowadays, several circular particle accelerators are successfully operating across transition and this process is well mastered. In a completely different context, stable resonances of the traverse phase space …
We study the energetics of wake excitation during the laser-plasma interaction in application to laser wakefield accelerators. We find that both the wake amplitude and the accelerating efficiency (transformer ratio) can be maximized by properly shaping the longitudinal profile of the driving laser pulse. The corresponding family of laser pulse shapes is derived in the nonlinear regime of laser-plasma interaction. Such shapes provide theoretical upper limit on the magnitude of the wakefield and efficiency by allowing for uniform photon deceleration inside the laser pulse. We also construct real…
This chapter gives an overview of the longitudinal dynamics of the particles in an accelerator and, closely related to that, the issue of synchronization between the particles and the accelerating field. Beginning with the trivial case of electrostatic accelerators, the synchronization condition is explained for a number of driven accelerators like Alvarez linacs, cyclotrons and finally synchrotrons and storage rings, where it plays a crucial role. In the case of the latter, the principle of phase focusing is motivated qualitatively as well as on a mathematically more correct level and the pro…
This paper introduces the protection of circular particle accelerators from accidental beam losses. Already the energy stored in the beams for accelerators such as the TEVATRON at Fermilab and Super Proton Synchrotron (SPS) at CERN could cause serious damage in case of uncontrolled beam loss. With the CERN Large Hadron Collider (LHC), the energy stored in particle beams has reached a value two orders of magnitude above previous accelerators and poses new threats with respect to hazards from the energy stored in the particle beams. A single accident damaging vital parts of the accelerator could…
What prevents us from building super-high intensity accelerators? The answer is case-specific, but it often points to one of the following phenomena: machine resonances, various tune shifts (and spreads), and instabilities. These three phenomena are interdependent in all present machines. In this paper we propose a path toward alleviating these phenomena by making accelerators nonlinear. This idea is not new: Orlov (1963) and McMillan (1967) have proposed initial ideas on nonlinear focusing systems for accelerators. However, practical implementations of such ideas proved elusive, until recentl…
Electron nonlinear dynamics in a compact accelerator based on the circular rotating TM110 mode
研究了不均匀静磁场中旋转TM110模式微波场的电子自共振加速，通过建立微分方程并设计磁场分布，成功将30 keV电子加速至200 keV，为医疗和安检X射线源的射频加速器设计提供了理论依据。
Here we calculate the effects of astrophysical gravitational waves (GWs) on the travel times of proton bunch test masses in circular particle accelerators. We show that a high-precision proton bunch time-tagging detector could turn a circular particle accelerator facility into a GW observatory sensitive to millihertz (mHz) GWs. We comment on sources of noise and the technological feasibility of ultrafast single photon detectors by conducting a case study of the Large Hadron Collider (LHC) at CERN.
Phase space matching between two plasma-accelerator (PA) stages and between a PA and a traditional accelerator component is a critical issue for emittance preservation of beams accelerated by PAs. The drastic differences of the transverse focusing strengths as the beam propagates between different stages and components may lead to a catastrophic emittance growth in the presence of both finite energy spread and lack of proper matching. We propose using the linear focusing forces from nonlinear wakes in longitudinally tailored plasma density profiles to provide exact phase space matching to prop…
A diffusion model of the time evolution of loss rates caused by a step in collimator position is presented. It builds upon the model of Seidel (1994) and its assumptions: (1) constant diffusion rate within the range of the step and (2) linear halo tails. These hypotheses allow one to obtain analytical expressions for the solutions of the diffusion equation and for the corresponding loss rates vs. time. The present model addresses some of the limitiations of the previous model and expands it in the following ways: (a) losses before, during, and after the step are predicted; (b) different steady…
The course gives a summary of longitudinal beam dynamics for both linear and circular accelerators. After discussing different types of acceleration methods and synchronism conditions, it focuses on the particle motion in synchrotrons.
The development of compact accelerator facilities providing high-brightness beams is one of the most challenging tasks in field of next-generation compact and cost affordable particle accelerators, to be used in many fields for industrial, medical and research applications. The ability to shape the beam longitudinal phase-space, in particular, plays a key role to achieve high-peak brightness. Here we present a new approach that allows to tune the longitudinal phase-space of a high-brightness beam by means of a plasma wakefields. The electron beam passing through the plasma drives large wakefie…
Space Charge in Circular Machines
本研究聚焦环形加速器中的空间电荷效应，阐述了空间电荷力的来源与构成，分析其在高流强低能加速器中引发的能散、自由振荡频率偏移及不稳定性等束流动力学影响，并将系统探究该效应的基本特性。
Laser-plasma accelerators can produce high quality electron beams, up to giga-electronvolts in energy, from a centimeter scale device. The properties of the electron beams and the accelerator stability are largely determined by the injection stage of electrons into the accelerator. The simplest mechanism of injection is self-injection, in which the wakefield is strong enough to trap cold plasma electrons into the laser wake. The main drawback of this method is its lack of shot-to-shot stability. Here we present experimental and numerical results that demonstrate the existence of two different …
The nuclear physics experiments at the Thomas Jefferson National Accelerator Facility often require longitudinally polarized electrons to be simultaneously delivered to three experimental halls. The degree of longitudinal polarization to each hall varies as function of the accelerator settings, making it challenging in certain situations to deliver a high degree of longitudinal polarization to all the halls simultaneously. Normally, the degree of longitudinal polarization the halls receive is optimized by changing the initial spin direction at the beginning of the machine with a Wien filter. H…
Determining a model for the time scaling of the dynamic aperture of a circular accelerator is a topic of strong interest and intense research efforts in accelerator physics. The motivation arises in the possibility of finding a method to reliably extrapolate the results of numerical simulations well beyond what is currently possible in terms of CPU time. In earlier work, a proposal for a model based on Nekhoroshev theorem and Kolmogorov--Arnold--Moser theory was made. This model has been studied in detail and proved successful in describing the evolution of the dynamic aperture in numerical si…
Longitudinal space charge (LSC) effects are generally considered harmful in free-electron lasers as they can seed unfavorable energy modulations that can result in density modulations with associated emittance dilution. It was pointed out, however, that such "micro-bunching instabilities" could be potentially useful to support the generation of broadband coherent radiation. Therefore there has been an increasing interest in devising accelerator beam lines capable of controlling LSC induced density modulations. In the present paper we augment these previous investigations by combining a grid-le…
Beam lifetime in storage rings and colliders is affected by, among other effects, lattice nonlinearities. Their control are of great benefit to the dynamic aperture of an accelerator, whose enlargement leads in general to more efficient injection and longer lifetime. This article describes a procedure to evaluate and correct unwanted nonlinearities by using turn-by-turn beam position monitor data, which is an evolution of previous works on the resonance driving terms (RDTs). Effective sextupole magnetic errors and tilts at the ESRF electron storage ring are evaluated and corrected (when possib…
Longitudinal tapering in meter-scale gas jets for increased efficiency of laser plasma accelerators
本文研究通过纵向调节气体射流喉部宽度和角度实现米级等离子体密度渐变，模拟与实验表明该方法可将激光等离子体加速器电子束能量从约9 GeV提升至12 GeV以上，并显著增加加速电荷。
Generation of circular field harmonics in quasi-polygonal magnet apertures using superconducting canted-cosine-theta coils
本文提出准多边形孔径超导磁体解析设计框架，利用共形映射建立与圆形孔径设计的联系，并将电流分布应用于CCT线圈，实现单一或混合圆形场谐波生成，拓展了CCT技术对复杂几何的适用性。
Longitudinal Compression of Macro Relativistic Electron Beam
本研究提出一种利用均匀磁场中电子螺旋运动实现相对论电子束纵向束团串压缩的新方法，经模拟验证其可比同尺寸装置实现更大尺度压缩，为低成本紧凑式高功率束流生成提供新路径。
Analytic formulas for the rapid evaluation of the orbit response matrix and chromatic functions from lattice parameters in circular accelerators
本文针对圆形加速器推导了基于格点参数评估轨道响应矩阵和色散函数的解析公式，通过扩展李代数与共振驱动项至偏离动量状态，大幅提升了数据分析速度，并在不同格点配置下验证了公式的鲁棒性。
Electron accelerators with higher and higher longitudinal field gradients are desirable, as they allow for the production of high energy beams by means of compact and cheap setups. The new laser-plasma acceleration technique appears to constitute the more promising breakthrough in this direction, delivering unprecedent field gradients up to TV/m. In this article we give a quantitative description of the impact of longitudinal wake fields on the electron beam. Our paper is based on the solution of Maxwell's equations for the longitudinal field. Our conclusions are valid when the acceleration di…
Betatron oscillation is a commonly known phenomenon in laser or beam driven plasma wakefield accelerators. In the conventional model, the plasma wake provides a linear focusing force to a relativistic electron, and the electron oscillates in one transverse direction with the betatron frequency proportional to $1/\sqrtγ$, where $γ$ is the Lorentz factor of the electron. In this work, we extend this model to three-dimensional by considering the oscillation in two transverse and one longitudinal directions. The long-term equations, with motion in the betatron time scale averaged out, are obtained…
In this work we analyze the longitudinal instabilities of propagating acceleration structures that are driven by a relativistically intense laser at the moving plasma critical layer [1]. These instabilities affect the energy-spectra of the accelerated ion-beams in propagating critical layer acceleration schemes [2][3]. Specifically, using analytical theory and PIC simulations we look into three fundamental physical processes and their interplay that are crucial to the understanding of energy spectral control by making the laser-plasma ion accelerators stable. The interacting processes are (i) …
Beam halo is one of the crucial issues limiting the machine performance and causing radioactivation in high-intensity accelerators. A clear picture of beam-halo formation is of great importance for successful suppression of the undesired beam loss. We present numerical and experimental studies of transverse and longitudinal halos in the KEK Accelerator Test Facility. The fair accordance between predictions and observations in various conditions indicates that the Touschek scattering is the dominant mechanism forming the horizontal and momentum halos.
The generation of very high quality electron bunches (high brightness and low energy spread) from a plasma-based accelerator in the three-dimensional blowout regime using self-injection in tailored plasma density profiles is analyzed theoretically and with particle-in-cell simulations. The underlying physical mechanism that leads to the generation of high quality electrons is uncovered by tracking the trajectories of the electrons as they cross the sheath and are trapped by the wake. Details on how the intensity of the driver and the density scale-length of the plasma control the ultimate beam…
As the second stage of the CEPC-SPPC project, SPPC (Super Proton-Proton Collider) aims at exploring new physics beyond the Standard Model. The key design goal for the SPPC accelerator complex is to reach 75 TeV in center of mass energy with a circumference of 100 km for the collider and an injector chain of four accelerators in cascade to support the collider. As an important part of the SPPC conceptual study, the longitudinal beam dynamics was studied systematically, which includes the dynamics in the collider and its complex injector chain. First, the bunch filling scheme of the SPPC complex…
Radio Frequency Quadrupole (RFQ) accelerators often need to face the challenges of space charge effects from high beam currents. This study investigated how to reach RFQ beam dynamics designs with not only high beam transmission and short structure length but also high beam quality simultaneously. To avoid beam instabilities induced by emittance transfer, a so-called el/et (ratio of the longitudinal and transverse emittances) = 1.0 design guideline is being proposed. The application of this design guideline integrated with the BABBLE/NFSP design method for a high current, high frequency, high …
We discuss the goals, the designs, the state of technical readiness, and the critical R&D needs of the accelerators that are currently under discussion as Higgs and electroweak factories. We also address the respective staging options enabling future energy-frontier colliders. The accelerators covered are based on many different techniques and approaches. They include several circular colliders, various linear colliders, colliders based on energy recovery linacs (ERLs), ERL-ring combinations, as well as gamma-gamma colliders. The linear colliders proposed consist of options for the Internation…
Generalized threshold of longitudinal multi-bunch instability in synchrotrons
针对纵向耦合束团不稳定性与单束团朗道阻尼损失，提出数值求解稳定性问题的新方法并推导解析阈值，发现LLD会降低CBI阈值，解释了CERN SPS观测结果并适用于未来加速器设计。
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