The evolution of two colliding beams in a linear accelerator can be described by two coupled Vlasov equations. In PEP-NOTE-325 by S. Kheifets and A. W. Chao the case without external focusing was considered. In this paper we derive the equilibrium distribution and the tune shift in the presence of external focusing. Motion is considered only in the vertical direction and the beams are presumed to be one-dimensional.
This note outline the formulae of luminosity and beam-beam tune shifts applicable to flat-beam asymmetric colliders. The formulae are tested with the machine parameters of SuperKEKB.
The possibility of using in an electron-ion collider the so-called quasi-ordered ion beam deep cooled by electron cooling is considered. The properties of the ordered and quasi-ordered beams are described. The advantages of using the quasi-ordered beam are discussed
C. B. Schroeder, E. Esarey, C. Benedetti, and W. P. Leemans {Phys. Rev. ST Accel. Beams 13, 101301 (2010) and 15, 051301 (2012)} have proposed a set of parameters for a TeV-scale collider based on plasma wake field accelerator principles. In particular, it is suggested that the luminosities greater than 10^34 cm-2s-1 are attainable for an electron-positron collider. In this comment we dispute this set of parameters on the basis of first principles. The interactions of accelerating beam with plasma impose fundamental limitations on beam properties and, thus, on attainable luminosity values.
There were four presentations given during the session 'Beam-beam experience in hadron colliders', reporting the beam-beam observations in SPS [1], Tevatron [2], RHIC [3] and HERA [4]. Presentations were followed by discussions. Below we summarize the major observations, findings and results.
A formula for the collider luminosity is derived for a head-on collision of two beams with different parameters. Three particular cases are presented: the collision of two identical axially symmetric bunches, the collision of a bunch with a coasting beam, and the collision of two coasting beams. The colliding beams have coinciding longitudinal axes. The formula is valid for colliding both counter propagating and co-propagating ("merging") beams.
We perform a beam-beam parameter study for a TeV-scale PWFA (particle-driven plasma wakefield acceleration) $\mathrm{e}^+$$\mathrm{e}^-$ linear collider using GUINEA-PIG simulations. The study shows that the total luminosity follows the $1/\sqrt{σ_z}$-scaling predicted by beamstrahlung theory, where $σ_z$ is the rms beam length, which is advantageous for PWFA, as short beam lengths are preferred. We also derive a parameter set for a 3 TeV PWFA linear collider with main beam parameters optimised for luminosity and luminosity spread introduced by beamstrahlung. Lastly, the study also compare the…
A possible alternative way of producing muons (or other unstable particles) for colliders is proposed. It consists in colliding beams in a "chasing beam" configuration, i.e. collisions of two beams having the same direction but with different energies. This would produce muons with a good collimation, having already a high energy from the beginning, and then a longer life.
During the proton-anti proton collider run several experiments were carried out in order to understand the effect of the beam-beam interaction on backgrounds and lifetimes. In this talk a selection of these experiments will be presented. From these experiments, the importance of relative beam sizes and tune ripple could be demonstrated.
In ring-ring colliders, the collision frequency determines the bunch structures, e.g. the time between the bunches in both rings should be identical. Because of relatively low relativistic speed of the hadron beam in sub-TeV hadron-hadron- and electron-ions-colliders, scanning the hadron beam's energy would require either a change in the circumference of one of the rings, or a switching of the bunch (harmonic) number in a ring. The later would cause so-called 'gear-changing', i.e. the change of the colliding bunches turn by turn. In this article, we study the difficulties in beam dynamics in t…
Our beam-beam parameter study using beam-beam simulations and PWFA (particle-driven plasma acceleration) beam parameters indicates that at 3 TeV, for examined electron beam lengths ${2~μ\mathrm{m}\leqσ_z\leq 10~μ\mathrm{m}}$, the total luminosity, as well as the sharpness of the luminosity spectrum for a $γγ$ collider are independent of the beam length of the electron beams used to scatter the photons, given that the hourglass effect is avoided. The total luminosity can consequently be maximised by minimising the horizontal and vertical beta functions $β_{x,y}^*$ at the interaction point. Furt…
A semi-analytical model has been developed to study a combined effect of Beamstrahlung due to beam-beam interaction and beam coupling impedance in the future lepton colliders CEPC and FCCee. This model allows evaluating an impact of the coupling impedance on the bunch length and energy spread in collision. The model is benchmarked against numerical simulations. Analytical estimates for the supercolliders are presented.
Several proposals exist for future circular electron-positron colliders designed for precise measurements of the Higgs boson characteristics and electroweak processes. At very high energies, synchrotron radiation of the particles in a strong electromagnetic field of the oncoming bunch (beamstrahlung) becomes extremely important, because of degradation of the beam lifetime and luminosity. We present theoretical calculations of beamstrahlung (including the beam lifetime reduction and the energy spread increase) which are benchmarked against quasi strong-strong computer simulation. Calculation re…
A Super Proton-Proton Collider (SPPC) that aims to explore new physics beyond the standard model will be built in China. Here we focus on the impact of beam-beam interactions in the SPPC. Simulations show that with the current optics and nominal tunes, the dynamic aperture (DA) with all the beam-beam interactions is less than 6σ, the dominant cause being the long-range interactions. First, we show the results of a tune scan done to maximize the DA. Next, we discuss the compensation of the long-range interactions by increasing the crossing angle and also by using current carrying wires.
Physically speaking, the delta function like beam-beam nonlinear forces at interaction points (IPs) act as a sum of delta function nonlinear multipoles. By applying the general theory established in ref. 1, in this paper we investigate analytically the beam-beam interaction limited dynamic apertures and the corresponding beam lifetimes for both the round and the flat beams. Relations between the beam-beam limited beam lifetimes and the beam-beam tune shifts are established, which show clearly why experimentally one has always a maximum beam-beam tune shift, ξ_{y, max}, around 0.045 for e-^+e$^…
Although we believe most of the results presented here are correct, they are correct only in the limit of negligible beam disruption, which is not the ILC case. Also, the paper needs a convincing treatment of beam pipe shielding effects, though we believe that these effects will be proven to be small eventually.
Different limitations on luminosity of linac-ring type colliders coming from beam dynamics issues are considered for the examples of the $ep$ options of the THERA and LinacXLHC proposals. It is shown that $L=1.3\times 10^{31}$ for THERA and $L=2.7\times 10^{32}$ for LinacXLHC can be achieved for round beams case. Corresponding sets of parameters are given with the explanations.
Renewed interest in circular e+e- colliders has spurred designs of single beam-pipe machines, like the CEPC in China, and double beam pipe ones, such as the FCC-ee effort at CERN. Single beam-pipe designs profit from lower costs but are limited by the number of bunches that can be accommodated in the machine. We analyse these performance limitations and propose a solution that can accommodate O(1000) bunches while keeping more than 90% of the ring with a single beam pipe.
Intrabeam scattering studies with large-emittance-ratio ion beams in the Relativistic Heavy Ion Collider, and implications for the Electron-Ion Collider
Long-range beam-beam effects are a potential limit to the LHC performance with the nominal design parameters, and certain upgrade scenarios under discussion. To mitigate long-range effects, current carrying wires parallel to the beam were proposed and space is reserved in the LHC for such wires. Two current carrying wires were installed in RHIC to study the effect of strong long-range beam-beam effects in a collider, as well as test the compensation of a single long-range interaction. The experimental data were used to benchmark simulations. We summarize this work.
The design luminosity for the future linear colliders is very demanding and challenging. Beam-based feedback systems will be required to achieve the necessary beam-beam stability and steer the two beams into collision. In particular we have studied the luminosity performance improvement by intra-train beam-based feedback systems for position and angle corrections at the interaction point. We have set up a simulation model which introduces different machine imperfections and can be applied to both the International Linear Collider (ILC) and the Compact Linear Collider (CLIC).
Various beam-based methods are widely used for machine study and accurate tuning. Beam closed orbit (CO) responses are routinely used worldwide for magnetic elements alignment and lattice correction. The paper presents the beam-based field mapping technique, applied for measurement of pulsed septum magnet stray field at VEPP-2000 electron-positron collider. Relatively slow pulse of weak leakage field disturbs the CO allowing detecting field longitudinal integral. While scanning with transverse coordinate in wide range one can measure the field map of the localized perturbation at machine in si…
The use of resonant depolarization has been suggested for precise beam energy measurements (better than 100 keV) in the $e^{+}e^{-}$ Future Circular Collider (FCC-$e^{+}e^{-}$) for Z and WW physics at 45 and 80 GeV beam energy respectively. Longitudinal beam polarization would benefit the Z peak physics program; however it is not essential and therefore it will be not investigated here. In this paper the possibility of self-polarized leptons is considered. Preliminary results of simulations in presence of quadrupole misalignments and beam position monitors (BPMs) errors for a simplified FCC-$e…
The baseline configuration of the International Linear Collider requires 2 beam dumps per interaction region, each rated to 18MW of beam power, together with additional beam dumps for tuning purposes and machine protection. The baseline design uses high pressure moving water dumps, first developed for the SLC and used in the TESLA design, although a gas based dump is also being considered. In this paper we discuss the progress made by the international community on both physics and engineering studies for the beam dumps.
Northern Illinois University（北伊利诺伊大学）；Arizona State University（亚利桑那州立大学）；Thomas Jefferson National Accelerator facility（托马斯·杰斐逊国家加速器设施）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）
This paper presents a review of the recent Machine Learning activities carried out on beam measurements performed at the CERN Large Hadron Collider. This paper has been accepted for publication in IEEE Instrumentation and Measurement Magazine and in the published version no abstract is provided.
Effects of electromagnetic interactions of colliding bunches in the Tevatron had a variety of manifestations in beam dynamics presenting vast opportunities for development of simulation models and tools. In this paper the computer code for simulation of weak-strong beam-beam effects in hadron colliders is described. We report the collider operational experience relevant to beam-beam interactions, explain major effects limiting the collider performance and compare results of observations and measurements with simulations.
We examine through numerical calculation the collision of counter-propagating trains of optically spaced electron/positron microbunches in a 1 TeV collider scenario for a dielectric laser accelerator (DLA). A time-dependent envelope equation is derived for arbitrary number of bunches in the classical limit, with inclusion of the radiation reaction force (RRF). Example parameters are examined based on a constrained luminosity relation that takes into account the bunch charge for optimal efficiency, material damage limits, and power constraints. We find that for initially identical counter-propa…
We recently developed an analytic theory of cumulative multibunch beam breakup that includes a linear variation of transverse focusing across the bunch train. The focusing variation saturates the exponential growth of the beam breakup and establishes an algebraic decay of the transverse bunch displacement versus bunch number. In this paper we illustrate how the focusing variation works to suppress multibunch beam breakup, as well as how the mechanism scales with accelerator and beam parameters.
We study a method of laser-Compton cooling of electron beams for future linear colliders. Using a Monte Carlo code, we evaluate the effects of the laser-electron interaction for transverse cooling. The optics with and without chromatic correction for the cooling are examined. The laser-Compton cooling for JLC/NLC at $E_0=2$ GeV is considered.
We develop theoretical expressions for the luminosity and beam-beam tune shifts in the presence of both a crossing angle and hourglass effects for the present and next generation of symmetric e$^+$-e$^-$ colliders. The theory is applied to the design of the Fermilab site filler Higgs factory and to the FCC-ee collider.
At the Large Hadron Collider (LHC), the interplay between a series of effects, including intrabeam scattering (IBS), synchrotron radiation, longitudinal beam manipulations, two beam effects (beam-beam, e-cloud) and machine non-linearities, can change the population of the core and tails and lead to non-Gaussian beam distributions, at different periods during the beam cycle. By employing generalised distribution functions, it can be demonstrated that the modified non-Gaussian beam profiles have an impact in the beam emittance evolution by itself and thereby to the collider luminosity. This pape…
CLIC is a linear $e^+e^-$ ($γγ$) collider project which uses a drive beam to accelerate the main beam. The drive beam provides RF power for each corresponding unit of the main linac through energy extracting RF structures. CLIC has a wide range of center-of-mass energy options from 150 GeV to 3 TeV. The present paper contains optimization of Free Electron Laser (FEL) using one bunch of CLIC drive beam in order to provide polarized light amplification using appropriate wiggler and luminosity spectrum of $γγ$ collider for $E_{cm}$=0.5 TeV. Then amplified laser can be converted to a polarized hig…
The ILC beam dumps are a key part of the accelerator design. At Snowmass 2005, the current status of the beam dump designs were reviewed, and the options for the overall dump layout considered. This paper describes the available dump options for the baseline and the alternatives and considers issues for the dumps that require resolution.
This document presents in detail the derivation of the formulas that describe the resonance driving terms and the tune spread with amplitude generated by the beam-beam long range interactions and the DC wire compensators in cyclical machines. This analysis make use of the weak-strong approximation.
At the Linear Collider mismatches between the two beams will result in an intense beamstrahlung. We have studied how this beamstrahlung would evolve as a function of the offset between the two beams and we suggest ways of monitoring it.
The Supper Proton-Proton Collider is a next-generation hadron collider that is now being designed. A baseline design aims for a peak luminosity of about 1*10^35 cm^-2 s^-1. The focus of this article is the effect of beam-beam interactions which are expected to strongly influence stability in the beams. We start with a discussion of a scheme to generate the crossing angles at the interaction points while also correcting the dispersion thus created. The optics constraints on the achievable \b{eta}* were studied. Weak-strong simulations were performed to study single particle dynamics via tune fo…
The CLIC study of a high-energy (0.5 - 5 TeV), high-luminosity (1034 - 1035 cm-2 sec-1) e+e- linear collider is presented. Beam acceleration using high frequency (30 GHz) normal-conducting structures operating at high accelerating fields (150 MV/m) significantly reduces the length and, in consequence, the cost of the linac. Using parameters derived from general scaling laws for linear colliders, the beam stability is shown to be similar to lower frequency designs in spite of the strong wake-field dependency on frequency. A new cost-effective and efficient drive beam generation scheme for RF po…
This archive summarizes a working paper and conference proceedings related to laser wire scanner development for the Future Linear Collider (FLC) in the years 2001 to 2006. In particular the design, setup and data taking for the laser wire experiments at PETRA II and CT2 are described. The material is focused on the activities undertaken by Royal Holloway University of London (RHUL).
We present a concept for control of the ion polarization, called a transparent spin method. The spin transparency is achieved by designing such a synchrotron structure that the net spin rotation angle in one particle turn is zero. The polarization direction of any ions including deuterons can be efficiently controlled using weak quasi-static fields. These fields allow for dynamic adjustment of the polarization direction during an experiment. The main features of the Transparent Spin method are illustrated in a figure-8 collider. The results are relevant to the Electron-Ion Collider considered …
In this paper, we present the effects of linear transverse-longitudinal coupling on beam size at Interaction Point (IP) of a collider with local crab crossing scheme, when time dependent transverse deflection (crab kicks) and dispersive orbit intertwine near IP. The analytic propagation formula and the closed orbit form of the crab dispersion and momentum dispersion are derived. The non-zero momentum dispersion at crab cavities and the non-ideal phase from crab cavities to IP are detailed with the derived propagation formula to predict the beam size distortion at IP with or without the beam-be…
We review the different performance limitations of circular colliders, namely the limitations of energy reach, maximum attainable luminosity and beam lifetime. This paper considers only head-on collisions. We consider the range of beam energies from 45GeV to 250 GeV and collider circumferences from 20 to 100kms.
The beam aperture of a particle accelerator defines the clearance available for the circulating beams and is a parameter of paramount importance for the accelerator performance. At the CERN Large Hadron Collider (LHC), the knowledge and control of the available aperture is crucial because the nominal proton beams carry an energy of 362 MJ stored in a superconducting environment. Even a tiny fraction of beam losses could quench the superconducting magnets or cause severe material damage. Furthermore, in a circular collider, the performance in terms of peak luminosity depends to a large extent o…
Since the beginning of the Large Hadron Collider (LHC) commissioning, spectral components at harmonics of the mains frequency (50 Hz) have been observed in the transverse beam spectrum. This paper presents an overview of the most important observations, collected during the latest physics operation of the LHC in 2018, which clearly indicates that the harmonics are the result of a real beam excitation rather than an instrumental feature. Based on these findings, potential sources of the perturbation are discussed and a correlation with power supply ripple originating from the magnets' power sup…
We present a new conceptual and optical design for the Next Linear Collider post-linac collimation system. Energy collimation and passive protection against off-energy beams are achieved in a system with large horizontal dispersion and vertical betatron functions. Betatron collimation is performed in a relatively low-beta (FODO-like) lattice in which only thin spoilers intercept particles near the beam core, while thick absorbers maintain a large stay-clear from the beam. Two possible schemes for the spoilers are considered: one in which the spoilers are capable of tolerating a certain number …
Particle acceleration in plasma creates a possibility of exceptionally high accelerating gradients and appears as a very attractive option for future linear electron-positron and/or photon-photon colliders. These high accelerating gradients were already demonstrated in a number of experiments. However, a linear collider requires exceptionally high beam brightness which still needs to be demonstrated. In this article we discuss major phenomena which limit the beam brightness of accelerated beam and, consequently, the collider luminosity.
RF cavity design and beam loading effects in the rectilinear cooling channel for a muon collider
European Organization for Nuclear Research (CERN)（欧洲核子研究中心）；Northern Illinois University（北伊利诺伊大学）；Argonne National Laboratory（阿贡国家实验室）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
The current designs of future electron-positron linear colliders incorporate large and complex damping rings to produce asymmetric beams for beamstrahlung suppression. Here we present the design of an electron injector capable of delivering flat electron beams with phase-space partition comparable to the electron-beam parameters produced downstream of the damping ring in the proposed international linear collider (ILC) design. Our design does not employ a damping ring but is instead based on cross-plane phase-space-manipulation techniques. The performance of the proposed configuration, its sen…
Comments on the paper "Eliminating beam-induced depolarizing effects in the hydrogen jet target for high-precision proton beam polarimetry at the Electron-Ion Collider"
A system for bunch-by-bunch detection of transverse proton and antiproton coherent oscillations in the Tevatron is described. It is based on the signal from a single beam-position monitor located in a region of the ring with large amplitude functions. The signal is digitized over a large number of turns and Fourier-analyzed offline with a dedicated algorithm. To enhance the signal, band-limited noise is applied to the beam for about 1 s. This excitation does not adversely affect the circulating beams even at high luminosities. The device has a response time of a few seconds, a frequency resolu…
We present results from luminosity, energy and polarization studies at a future Linear Collider. We compare e+e- and e-e- modes of operation and consider both NLC and TESLA beam parameter specifications at a center-of-mass energy of 500 GeV. Realistic colliding beam distributions are used, which include dynamic effects of the beam transport from the Damping Rings to the Interaction Point. Beam-beam deflections scans and their impact for beam-based feedbacks are considered. A transverse kink instability is studied, including its impact on determining the luminosity-weighted center-of-mass energ…
