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In this paper, we will give a brief review of some important beam physics in circular and linear electron–positron collider designs, covering beam–beam tune limits, longitudinal and transverse single bunch collective effects, electron cloud and space charge effects, dynamic aperture estimations, etc. The main feature of this review is that the corresponding beam physics treatments are coming from author's previous research works which are scattered in different scientific publications both for circular and linear colliders. With the progresses of future linear colliders, such as ILC, and future circular electron–positron colliders, such as CEPC, it is high time to review the key beam physics issues in the optimization designs of these two kinds of machines.

In order to avoid the pretzel orbit, CEPC is proposed to use partial double ring scheme in CDR. In this paper, a general method of how to make an consistent machine parameter design of CEPC with crab-waist by using analytical expression of maximum beam–beam tune shift and beamstrahlung beam lifetime started from given IP vertical beta, beam power and other technical limitations were developed. FFS with crab sextupoles will be developed and the arc lattice will be redesigned to acheive the lower emittance for crab-waist scheme.

In this paper, a consistent calculation method for the CEPC parameter choice with a crab waist scheme is reported. A crosscheck of luminosity with beam–beam simulations has been done. With this new scheme, a higher Higgs luminosity (+170%) can be reached while keeping Pre-CDR beam power or the beam power (19 MW) can be reduced while keeping the same Pre-CDR luminosity. CEPC is compatible with W and Z experiment. The luminosity for Z is at the level of $10^{35}{\mathrm{\text{cm}}}^{-2}{\mathrm{\text{s}}}^{-1}$. Requirement for energy acceptance of Higgs has been reduced to 1.5% by enlarging the ring to 100 km. The arc optics and the Final Focus System (FFS) with crab sextupoles have been designed, and also some primary Dynamic Aperture (DA) results were introduced.

A future Circular Electron Positron Collider (CEPC) has been proposed by China with the main goal of studying the Higgs boson. Its baseline design, chosen on the basis of its performance, is a double ring scheme; an alternative design is a partial double ring scheme which reduces the budget while maintaining an adequate performance. This paper will present the collider ring lattice design for the double ring scheme. The CEPC will also work as a W and a Z factory. For the W and Z modes, except in the RF region, compatible lattices were obtained by scaling down the magnet strength with energy.

With the discovery of the Higgs boson at around 125 GeV, a circular Higgs factory design with high luminosity $(L\sim 10^{34}{\mathrm{\text{cm}}}^{-2}{\mathrm{\text{s}}}^{-1})$ is becoming more popular in the accelerator world. The CEPC project in China is one of them. Machine Detector Interface (MDI) is the key research area in electron–positron colliders, especially in CEPC; it is one of the criteria to measure the accelerator and detector design performance. Because of the limited space available in the designed tunnel, many equipment including magnets, beam diagnostic instruments, masks, vacuum pumps, and components of the detector must coexist in a very small region. In this paper, some important MDI issues will be reported for the Interaction Region (IR) design, e.g. the final doublet quadrupoles physics design parameters, beam-stay-clear region and beam pipe, synchrotron radiation power and critical energy are also calculated.

The Circular Electron–Positron Collider (CEPC) is a 100-km ring $e^{+}{e}^{-}$ collider for a Higgs factory. The injector of CEPC is composed of Linac and Booster. The Linac is a normal conducting S-band Linac with a frequency of 2860 MHz; it provides electron and positron beams at an energy of up to 10 GeV with 100 Hz repetition frequency of 100 Hz. The Linac design and dynamic simulation results are discussed in detail in this paper, including electron bunching system, positron source, electron bypass transport line, damping ring and main Linacs.

CEPC is a 100-km double-ring circular electron–positron collider operating at 90–240 GeV center-of-mass energy of Z-pole, WW-pair production threshold and Higgs resonance. The conceptual design report (CDR) of CEPC has been published as an important step to move the project forward. The superconducting RF (SRF) system is one of the most important and challenging accelerator systems due to the wide range of beam energy and current. In this paper, the layout, parameters and configuration of the superconducting RF system for the CEPC collider ring will be introduced. Issues of beam cavity interactions including transient beam loading and coupled-bunch instabilities of accelerating mode are discussed.

The interaction region is designed to provide strong focusing at the interaction point. A local correction scheme is adopted to get a large momentum acceptance. The interaction region consists of several modular sections. This paper presents the optics design of each section and its optimization. As an example, the optics design for the CEPC single-ring scheme is presented.

The energy sawtooth will be significant in the future circular Higgs factory with beam energy as high as 120 GeV. For the partial double ring scheme, unlike the double ring scheme, the effects of energy sawtooth cannot be corrected by tapering the magnet strength with beam energy along the beamline. In this paper, the energy sawtooth effects in the partial double ring scheme and its mitigation methods are presented. As an example, the study of the energy sawtooth effects of the CEPC advanced partial double ring scheme is presented.

With the discovery of the Higgs boson at around 125 GeV, a circular Higgs factory design with high luminosity $(L\sim 10^{34}{\mathrm{\text{cm}}}^{-2}{\mathrm{\text{s}}}^{-1})$ is becoming more popular in the accelerator world. The Circular Electron and Positron Collider (CEPC) project in China is one of them. Machine Detector Interface (MDI) is the key research area in electron–positron colliders, especially in CEPC. Since the $e^{+}{e}^{-}$ beams collide at the Interaction Point (IP) with a horizontal angle of 33 mrad, the horizontal trajectory will couple to the vertical. Due to the solenoid and anti-solenoid combined field strength quite high, the maximum could be up to 4.2 T, the transverse magnetic field component is also quite high. Thus synchrotron radiation (SR) from vertical trajectory in combined field should be taken into account. And also synchrotron radiation is an important influential factor in the collimator design of CEPC MDI. These two effects are analyzed in this paper.

In the tracking of the future circular Higgs factories, significant reduction of dynamic aperture due to the synchrotron radiation has been observed. This paper will analyze the synchrotron radiation effects including the closed orbit and optics distortion, radiation damping and quantum excitation for the lattice of CEPC.

The CEPC booster needs to provide electron and positron beams to the collider at different energy with required injection speed. A 10 GeV linac is adopted as the injector for CDR. Then the beam energy is accelerated to specific energy according to three modes of operation of the CEPC collider ring ($H$, $W$ and $Z$). The geometry of the booster is designed carefully in order to share the same tunnel with the collider. The design status of the booster with the CDR lattice including parameters, optics and dynamic aperture is discussed in this paper.

Since the first idea of a collider was patented by Rolf Wideröe (1902–1996) in 1943 and the first $e^{+}{e}^{-}$ circular collider, AdA, was successfully principle-proved in LAL, Orsay, France in 1963, different kinds of colliders have been built in the past and planned for the future. In this paper, we will make a rather complete and brief review of the history of different colliders and give a perspective for the future.

In this paper, we give preliminary designs of beam polarization manipulations by inserting three different types of insertions in the Circular Electron–Positron Collider (CEPC) at center-of-mass energies of 91 GeV ($Z$-pole). With the wigglers in the collider ring, we can obtain 5% transverse polarization in 1.1 h for the precise energy measurement. To overcome depolarization effects as the beam energy rises from 10 GeV to 45.5 GeV in the booster ring, Siberian snakes based on helical magnets are adopted. Finally, for longitudinally polarized beam collisions, a schematic design of spin rotators based on solenoids in the collider ring is studied.

Radio frequency (RF) parameters design is an important part in RF system design. In this paper we will introduce a general method of choosing appropriate RF parameters for a circular $e^{+}{e}^{-}$ collider. The RF parameters are determined with several analytical formulas. With this method, the RF parameters of the Circular Electron–Positron Collider (CEPC) for Conceptual Design Report (CDR) are verified. A new set of RF parameters for the CEPC with 1-cell LG Nb cavities is also designed. Besides, the RF parameters of the CEPC Advanced Partial Double Ring (APDR) and the CEPC Damping Ring (DR) are designed for the first time, and a preliminary study of the beam loading effects of APDR and DR is also carried out.

A damping ring system which includes a small 1.1 GeV ring and two transport lines is introduced in CEPC linac in order to reduce the transverse emittance of positron beam at the end of linac and hence reduce the beam loss in the booster. This paper introduces the parameter choice and optics study of damping ring. The corresponding instability effect and IBS effect are also checked to make sure the design current and design emittance can be realized. Except for damping ring, two transport lines are needed to match the parameters between linac and damping ring. Both designs for energy compressor and bunch compressor including beam simulations are discussed in this paper.

With the discovery of the Higgs boson at around 125 GeV, a circular Higgs factory design with high luminosity ($L\sim 10^{34} {\mathrm{\text{cm}}}^{-2} {\text{s}}^{-1}$) is becoming more popular in the accelerator world. The CEPC project in China is one of them. Machine Detector Interface (MDI) is the key research area in electron–positron colliders, especially in CEPC, since the synchrotron radiation (SR) photons can contribute to the heat load of the beam pipe and radiation dose may damage the components. And the heat load can cause the temperature rise in some part, and if the temperature rise is too high, the beryllium pipe in the interaction region will melt and the superconducting magnet may quench. Thus, the heat load distribution from synchrotron radiation and beam loss in the interaction region are analyzed carefully and results are given in this paper.

The CEPC includes a main ring and an injector. The injector consists of a booster and a linac. In order to meet the requirements of the booster, the baseline design of the linac is a 10 GeV electron and positron linac. Two alternative linac designs have also been introduced in this paper. For the linac baseline design, one-bunch-per-pulse is adopted. A 1.1 GeV damping ring is used to reduce the transverse emittance of positron beam. The main RF system of the linac adopts normal conducting S-band structure. Some key technologies of linac are development. The S-band structure and pulse compressor have been researched and studied. In the damping ring, two cavities used to provide 2 MV voltage. The preliminary cavity design has finished.

The Circular Electron Positron Collider (CEPC) is a proposed Higgs factory with center-of-mass energy of 240GeV to measure the properties of Higgs boson and test the standard model accurately. Synchrotron radiation (SR) generated from the final doublet (FD) magnets in the interaction region of CEPC double ring scheme is one of the typical issues. SR photons can contribute to the heat load of the beam pipe and cause photon background to the experiments. Furthermore, the radiation dose can damage detector components. In this paper, SR generated from FD magnets is analyzed when beam is with tails and offset. SR from the dipole leakage field of the FD superconducting magnets is also analyzed and the physics limit is given to protect the detector.

The Circular Electron Positron Collider (CEPC) is a proposed Higgs factory with center-of-mass energy of 240GeV to measure the properties of Higgs boson and test the standard model accurately. Beam loss background in detectors is an important topic at CEPC. During manufacture and installation, magnets are not perfect and with many kinds of errors. Beam–beam interaction in high-energy electron positron collider is the action of external field force, which changes the momentum of each beam bunch. Thus, beam loss background can be affected by the magnet errors and beam–beam effect. In this paper, the beam loss background with magnet errors and beam–beam effect is simulated in CEPC.